The base of a triangular prism is an equilateral triangle with a perimeter of 15in. If the height of the prism is 4in, find the surface area.

Answers

Answer 1

we know that
surface area=2*[area of the base]+perimeter of the base*height
find the area of the base

is an equilateral triangle
b=15/3----> 5 in
applying the law of sines to find the area
Area=(1/2)*b²*sin 60°------> area=(1/2)*5²*sin 60°----> 10.8253 in²

alternative method to find the area of the equilateral triangle
find the h value
applying the Pythagoras theorem
h²=5²-2.5²-----> h=√18.75-----> h=4.33 in
area=b*h/2----> area=5*4.33/2----> 10.8253 in²

surface area=2*[10.8253]+15*4-----> 81.65 in²

the answer is
81.65 in²

Related Questions

hey can you please help me posted picture of question

Answers

Correct answer is option D.

The solution is listed below

[tex]F(x)=4x+7 \\ \\ y=4x+7 \\ \\ y-7=4x \\ \\ \frac{y-7}{4}=x \\ \\ x= \frac{y-7}{4} \\ \\ f-^{1}(y) = \frac{y-7}{4} \\ \\ f-^{1}(x) = \frac{x-7}{4} \\ \\ [/tex]

a number cube is labeled 1 to 6 Find each probability write each answer as a fraction , a decimal, and percent P(2)

Answers

P(1) = 1/6 = 0.166666 = 16.7%
P(2) = 1/6 = 0.166666 = 16.7%
P(3) = 1/6 = 0.166666 = 16.7%
P(4) = 1/6 = 0.166666 = 16.7%
P(5) = the same as the 4 above.
P(6) = the same thing as those numbered P(1) to P(4)

You might wonder how I got the %

any decimal expressed as a percent means multiply the decimal by 100.

0.1666666 * 100 = 16.66666 % which I rounded to 16.7%

Please help!!! I very much need help, thank you!

Answers

The Pythagorean theorem tells you the square of the hypotenuse is equal to the sum of the squares of the sides.
BC² = AB² + AC²
BC² = 4² +4² = 32
BC = √32 = 4√2
BC = 4*1.41 = 5.64

The length of segment BC is 5.64 m.

find the mean, median, and mode of he data set. round to the nearest tenth. 7, 5, 4, 2, 1, 1, 2, 3, 5, 4, 5

Answers

Hello!

First you need to list the numbers from least to greatest

1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 7

To find the mean you add all the numbers up and divide the sum by the amount of numbers added

1 + 1 + 2 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 7 = 39

39 / 10 = 3.9

The mean is 3.9
------------------------------------------------------------------------------------------------------
To find the median you find the number in the middle

The median is 4
------------------------------------------------------------------------------------------------------
The mode is the number that appears the most

The mode is 5

Hope this helps!

Hello!

Mean: 7 + 5 + 4 + 2 + 1 + 1 + 2 + 3 + 5 + 4 + 5 = 39

39 ÷ 11 = 3.5

The mean is 3.5

~~~~~~~~~~~~

Median: 1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 7 - Which number is in the center?

The median is 4

~~~~~~~~~~~~~~~~~

Mode: Which number appears most often?

The mode is 5.

Hope I helped! :3

Fill in the missing statements and reasons in the proof.
Given: PQRS is a parallelogram.
Prove: PR and QS bisect each other at T.

Answers

Answer:

We have to complete the proof.

PQRS is a parallelogram 1. Given

2. [tex]\overline{PQ}\:is\:parallel\:to\:\overline{RS}[/tex] Definition of a parallelogram

m∠1 ≅ m∠3 4. Alternate interior angles are equal or

m∠2 ≅ m∠4 congruent.

[tex]\overline{PQ}\:\cong\:\overline{RS}[/tex] Opposite sides of a parallelogram are congruent

ΔPQT ≅ ΔRST 5. Triangle are congruent by Angle-Side-

Angle congruent rule

[tex]\overline{PT}\:\cong\:\overline{RT}[/tex] 6. Corresponding parts of Congruent triangles

[tex]\overline{QT}\:\cong\:\overline{ST}[/tex]

7. PR and QS bisect each other at T Definition of a bisector

To prove that PR and QS bisect each other at T in a parallelogram PQRS, we can show that PR and QS intersect at T and divide each other into equal segments.

To prove that PR and QS bisect each other at T, we can use the fact that PQRS is a parallelogram.

We can start by showing that PR and QS intersect at a point, say T. Since PQRS is a parallelogram, its opposite sides are congruent. Therefore, PR is congruent to QS.

Next, we can show that PR and QS divide each other into equal segments. We can do this by proving that triangle PTR is congruent to triangle STQ using the side-angle-side (SAS) congruence criteria.

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Consider f and c below. f(x, y) = (3 + 4xy2)i + 4x2yj, c is the arc of the hyperbola y = 1/x from (1, 1) to 3, 1 3 (a) find a function f such that f = ∇f. f(x, y) = (b) use part (a) to evaluate c f · dr along the given curve
c.

Answers

We want to find a scalar function [tex]f(x,y)[/tex] such that [tex]\nabla f(x,y)=\mathbf f(x,y)=\dfrac{\partial f}{\partial x}\,\mathbf i+\dfrac{\partial f}{\partial y}\,\mathbf j[/tex].
So we need to have
[tex]\dfrac{\partial f}{\partial x}=3+4xy^2[/tex]
Integrating both sides with respect to [tex]x[/tex] gives
[tex]f(x,y)=3x+2x^2y^2+g(y)[/tex]
Differentiating with respect to [tex]y[/tex] gives
[tex]\dfrac{\partial f}{\partial y}=4x^2y+\dfrac{\mathrm dg}{\mathrm dy}=4x^2y[/tex][tex]\implies\dfrac{\mathrm dg}{\mathrm dy}=0[/tex][tex]\implies g(y)=C[/tex]
So we find that
[tex]f(x,y)=3x+2x^2y^2+C[/tex]
By the fundamental theorem of calculus, we then know the line integral depends only on the values of [tex]f(x,y)[/tex] at the endpoints of the path. Therefore

[tex]\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(3,\frac13\right)-f(1,1)=11-5=6[/tex]

Final answer:

Find the function f whose gradient is equal to the vector function f, then evaluate the line integral of f along the given hyperbolic arc from (1,1) to (3,1/3). This involves calculus and the concept of vector fields.

Explanation:

This problem involves calculus, specifically the concept of vector fields and line integrals. First, we are asked to find a function f(x, y) such that its gradient is equal to a given vector function f(x, y). To find this scalar function, we need to perform the integral of each component of the vector function f in terms of x and y.

Then we need to evaluate the line integral of the vector function f along a curve c, which is given as an arc of the hyperbola y = 1/x. The definite integral from point (1,1) to point (3,1/3) should be calculated. This integral represents the work done by the field f along the curve c.

Keep in mind that when you perform a line integral, you are adding up the contributions of a field (in this case, the vector field f) along a path (here, the hyperbola). Therefore, the path must be parameterized, and the limits of integration should be the parameter values that correspond to the points (1, 1) and (3, 1/3).

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Hey can you please help me posted picture of question

Answers

Vertically compressed means multiplying the function by a number between -1 and 1

From the given options only option C contains such an expression in which x² is multiplied with a number between -1 and 1.

Thus,

G(x) = 3/4 x²

So, the correct answer is option C

simplify x to the 5/8 over x to the 1/8

Answers

[tex]\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\\\ \textit{}a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}} \\\\ -------------------------------[/tex]

[tex]\bf \cfrac{x^{\frac{5}{8}}}{x^{\frac{1}{8}}}\implies x^{\frac{5}{8}}\cdot x^{-\frac{1}{8}}\implies x^{\frac{5}{8}-\frac{1}{8}}\implies x^{\frac{4}{8}}\implies x^{\frac{1}{2}}\implies \sqrt[2]{x^1}\implies \sqrt{x}[/tex]

Two cars leave at the same time from points A and B, the distance between them is 280 km. If the cars meet each other, they’ll meet in 2 hours. But if they go in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of both of the cars?

Answers

Set up the following equations:

[tex]2x + 2y = 280[/tex]

[tex]14x - 14y = 280[/tex]

x represents car A's speed, and y represents car B's speed.

We'll use elimination to solve this system of equations. Multiply the first equation by 7:

[tex](2x + 2y = 280) * 7 = 14x + 14y = 1960[/tex]

[tex]14x - 14y = 280[/tex]

Combine both equations:

[tex]28x = 2240[/tex]

Divide both sides by 28 to get x by itself:

[tex]x = 80[/tex]

The speed of car A is 80 mph.

Since we now know the value of one of the variables, we can plug it into the first equation:

[tex]2(80) + 2y = 280[/tex]

[tex]160 + 2y = 280[/tex]

Subtract 160 from both sides.

[tex]2y = 120[/tex]

Divide both sides by 2 to get y by itself:

[tex]y = 60[/tex]

The speed of car B is 60 mph.

PLZ HELP ASAP FEATURES OF A CRICLE FROM AN EXPANDED EQUATION

Answers

First we need to convert the given equation to standard form.

[tex] x^{2} + y^{2} -2y-99=0 \\ \\ x^{2} + y^{2}-2(y)(1)=99 \\ \\ x^{2} + y^{2}-2(y)(1)+1=99+1 \\ \\ x^{2} + (y-1)^{2}=100 [/tex]

Comparing this equation to the standard equation of circle, we can write:

The center of the circle is (0, 1) and the radius of the given circle is 10

Hey can you please help me out on my question posted picture

Answers

There are 3 outcomes in each game.

For 1st game, there can be either win (W), lose(L) or Tie (T).
For each of these outcome, there can be 3 possible outcomes in 2nd game i.e. either W, L or T

So, the tree diagram will have 3 branches, each further dividing into 3 more branches(nodes)

Thus option C gives the correct tree diagram.

A lunch in a fancy restaurant is three times as expensive as a lunch in a cafeeria. The lunch in the fancy restaurant costs 36. In five day workweek Mary eats at the fancy restaurant once and in the cafeteria the rest of the days. How much does she spend on lunches in that week

Answers

In this item, we first solve for the cost of eating in a cafeteria. From the given it is stated that the cost of eating in a fancy restaurant is 3 times the cost of eating in cafeteria. Mathematically,

3x = 36

where x is the cost of eating in cafeteria.

The value of x from the equation is 12.

In a five-day workweek, she eats at the fancy restaurant once and four times in cafeteria. To determine the total cost,

T = 4(12) + 36

T = 84

Thus, the answer to this item is 84.

let:

f = fancy restaurant price
c = cafeteria price

f = 3c

f = 36
c = 36/3 = 12

36 + 12*4 = 84

she spends 84 on lunches for a fiveday workweek

what does it mean for an equation to be radical equation

Answers

A radical equation just means that there is a square root symbol over the equation or part of the equation.

A radical equation is just like any other equation, but having some algebraic expression of x's given inside a square-root symbol. It could be as simple as y = [tex]\sqrt{x}[/tex] or it could be any complex algebraic expression inside the radical sign.

The main condition for existence of any radical equation is that we can not have negative values inside square-root i.e. the algebraic expression given inside radical sign must have non-negative values (zero or positive real values).

1/2
of the children within the city limits have a dog,
1/3
have a cat, and
1/6
have a dog and a cat. What fraction of those who have a dog also have a cat?

Answers

It is 1/6 because it says that in the problem that "1/6 people have a dog and a cat" and it is asking "What fraction of those who have a dog also have a cat?" It says the answer in the problem

Answer: The fraction of the children who have a dog also have a cat is [tex]\dfrac{1}{3}.[/tex]

Step-by-step explanation: Given that [tex]\frac{1}{2}[/tex] of the children within the city limits have a dog, [tex]\frac{1}{3}[/tex] have a cat, and [tex]\frac{1}{6}[/tex] have a dog and a cat.

We are to find the fraction of those children who have a dog also have a cat.

Let, S denote the sample space of the given experiment.

Then, n(S) = 1.

Let, event A and event B represents the fractions of children having a dog and a cat respectively.

Then, according to the given information, we have

[tex]n(A)=\dfrac{1}{2},~~~n(B)=\dfrac{1}{3},~~~n(A\cap B)=\dfrac{1}{6}.[/tex]

The fraction of children who have a dog also have a cat is given by the conditional probability of event B given A.

That is, he required probability is

[tex]P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\frac{1}{6}}{\frac{1}{2}}=\dfrac{1}{3}.[/tex]

Thus, the fraction of the children who have a dog also have a cat is [tex]\dfrac{1}{3}.[/tex]

In which type of investment do you lend your money to a government agency or a corporation for a fixed period of time and earn interest?
a) bonds
b) stocks
c) mutual funds

Answers

Answer: a. Bonds

Step-by-step explanation:

Bond is a kind of money investment issued by private corporations or government banks.

Buying a bond is like issuing a loan to the issuer. The issuer will pay back the face value of the issued loan along with interest money. It is issued for a fixed period of time.

Answer:

a) bonds

Step-by-step explanation:

was right

Anisha invested $8,000 in an account that earns 10% interest How much money will she have in 15 years of the interest is compound quarterly

Answers

Answer:

A = $35,198.32

Step-by-step explanation:

Use the formula to calculate compound interest:

A = P(1 + i)ⁿ

"A" for total amount after the time period

"P" for principal, or starting money

"i" for the interest rate in a compounding period

To calculate "i":

i = r / c

"n" for the number of compounding periods

To calculate "n":

n = tc

So, we can combine the formulas into:

[tex]A = P(1+\frac{r}{c})^{tc}[/tex]

"c" is the compounding periods in a year. (quarterly = 4)

We know:

P = 8000

r = 10% / 100 = 0.1

t = 15

c = 4

Substitute the information in the formula.

[tex]A = P(1+\frac{r}{c})^{tc}[/tex]

[tex]A = 8000(1+\frac{0.1}{4})^{15*4}[/tex] Solve "i" and "n"

[tex]A = 8000(1+0.025)^{60}[/tex] Solve inside the brackets

[tex]A = 8000(1.025)^{60}[/tex] Do the exponent before multiplying by 8000

A = 35198.318 Exact answer

A ≈ 35198.32 Round to two decimal places for money

Therefore she will have $35,198.32 after 15 years.

Final answer:

Anisha will have approximately $25,266.57 after 15 years of compound interest at a rate of 10% compounded quarterly on her initial investment of $8,000.

Explanation:

Anisha invested $8,000 in an account that earns 10% interest compounded quarterly. To calculate the amount of money she will have in 15 years, we can use the formula for compound interest:

Amount = Principal * (1 + (Rate / Frequency))^(Frequency * Time)

Amount = $8,000 * (1 + (0.10 / 4))^(4 * 15)

Amount = $8,000 * (1 + 0.025)^60

Amount = $8,000 * (1.025)^60

Using a calculator, we find that the amount of money Anisha will have after 15 years is approximately $25,266.57

what is the first 10000 numbers of pi

Answers

1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959 5082953311 6861727855 8890750983 8175463746 4939319255 0604009277 0167113900 9848824012 8583616035 6370766010 4710181942 9555961989 4676783744 9448255379 7747268471 0404753464 6208046684 2590694912 9331367702 8989152104 7521620569 6602405803 8150193511 2533824300 3558764024 7496473263 9141992726 0426992279 6782354781 6360093417 2164121992 4586315030 2861829745 5570674983 8505494588 5869269956 9092721079 7509302955 3211653449 8720275596 0236480665 4991198818 3479775356 6369807426 5425278625 5181841757 4672890977 7727938000 8164706001 6145249192 1732172147 7235014144 1973568548 1613611573 5255213347 5741849468 4385233239 0739414333 4547762416 8625189835 6948556209 9219222184 2725502542 5688767179 0494601653 4668049886 2723279178 6085784383 8279679766 8145410095 3883786360 9506800642 2512520511 7392984896 0841284886 2694560424 1965285022 2106611863 0674427862 2039194945 0471237137 8696095636 4371917287 4677646575 7396241389 0865832645 9958133904 7802759009 9465764078 9512694683 9835259570 9825822620 5224894077 2671947826 8482601476 9909026401 3639443745 5305068203 4962524517 4939965143 1429809190 6592509372 2169646151 5709858387 4105978859 5977297549 8930161753 9284681382 6868386894 2774155991 8559252459 5395943104 9972524680 8459872736 4469584865 3836736222 6260991246 0805124388 4390451244 1365497627 8079771569 1435997700 1296160894 4169486855 5848406353 4220722258 2848864815 8456028506 0168427394 5226746767 8895252138 5225499546 6672782398 6456596116 3548862305 7745649803 5593634568 1743241125 1507606947 9451096596 0940252288 7971089314 5669136867 2287489405 6010150330 8617928680 9208747609 1782493858 9009714909 6759852613 6554978189 3129784821 6829989487 2265880485 7564014270 4775551323 7964145152 3746234364 5428584447 9526586782 1051141354 7357395231 1342716610 2135969536 2314429524 8493718711 0145765403 5902799344 0374200731 0578539062 1983874478 0847848968 3321445713 8687519435 0643021845 3191048481 0053706146 8067491927 8191197939 9520614196 6342875444 0643745123 7181921799 9839101591 9561814675 1426912397 4894090718 6494231961
5679452080 9514655022 5231603881 9301420937 6213785595 6638937787 0830390697 9207734672 2182562599 6615014215 0306803844 7734549202 6054146659 2520149744 2850732518 6660021324 3408819071 0486331734 6496514539 0579626856 1005508106 6587969981 6357473638 4052571459 1028970641 4011097120 6280439039 7595156771 5770042033 7869936007 2305587631 7635942187 3125147120 5329281918 2618612586 7321579198 4148488291 6447060957 5270695722 0917567116 7229109816 9091528017 3506712748 5832228718 3520935396 5725121083 5791513698 8209144421 0067510334 6711031412 6711136990 8658516398 3150197016 5151168517 1437657618 3515565088 4909989859 9823873455 2833163550 7647918535 8932261854 8963213293 3089857064 2046752590 7091548141 6549859461 6371802709 8199430992 4488957571 2828905923 2332609729 9712084433 5732654893 8239119325 9746366730 5836041428 1388303203 8249037589 8524374417 0291327656 1809377344 4030707469 2112019130 2033038019 7621101100 4492932151 6084244485 9637669838 9522868478 3123552658 2131449576 8572624334 4189303968 6426243410 7732269780 2807318915 4411010446

Answer:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 38095 25720 10654 85863 27886 59361 53381 82796 82303 01952 03530 18529 68995 77362 25994 13891 24972 17752 83479 13151 55748 57242 45415 06959 50829 53311 68617 27855 88907 50983 81754 63746 49393 19255 06040 09277 01671 13900 98488 24012 85836 16035 63707 66010 47101 81942 95559 61989 46767 83744 94482 55379 77472 68471 04047 53464 62080 46684 25906 94912 93313 67702 89891 52104 75216 20569 66024 05803 81501 93511 25338 24300 35587 64024 74964 73263 91419 92726 04269 92279 67823 54781 63600 93417 21641 21992 45863 15030 28618 29745 55706 74983 85054 94588 58692 69956 90927 21079 75093 02955 32116 53449 87202 75596 02364 80665 49911 98818 34797 75356 63698 07426 54252 78625 51818 41757 46728 90977 77279 38000 81647 06001 61452 49192 17321 72147 72350 14144 19735

Step-by-step explanation:

i cant add the rest

A theater received $8,917 in ticket sales for one performance of a play. Tickets for preferred seats cost $45 each and regular seats cost $34 each. All of the theaters 75?preffered seats were sold out that evening. How many tickets were sold?

Answers

Let
P = Number of ticket for preferred seats costing $45 per seat
R = Number of regular seats costing $34 per seat.

Total revenue = P*45 + R*34 =8,917

45P + 34R = 8917

But, number of preferred seats is 75 or P=75 seats
Then,
45*75 +34R = 8917
3375 +34R = 8917
34R = 5542
R = 5542/34 = 163

Total number of seats = P+R = 75+163 = 238 seats. If each seat is sold for one ticket, then 238 tickets wee sold.

Use the information to answer the questions. In triangle ABC, a = 11 in., m

Answers

The rest of the question is as following
m<B=70, and c=9 in. Which information about the triangle is given.
======================================================
Solution:
Given the following:
a = 11 in , ∠B = 70° , c = 9 in
The given information can be used in the cosine law.
Which is ⇒⇒⇒ b² = a² + c² - 2 a c * cos (B)

The correct answer is the third option.

Express the polynomial −4p + 3p + 2p2 in standard form and then classify it.

Answers

Final answer:

The simplified form of the polynomial −4p + 3p + 2p^2 is 2p^2 - p. It is a quadratic polynomial, given that its highest degree of p is 2.

Explanation:

The polynomial −4p + 3p + 2p2 can first be simplified by combining like terms. This results in −p + 2p2. In standard form, always organize the terms in a polynomial so that the powers of x decrease from left to right. Therefore, the standard form of the polynomial is 2p2 - p.

This polynomial can be classified as a quadratic polynomial because the highest power of the variable (p) is 2. A quadratic polynomial is represented by the general form ax2 + bx + c, with 'a' being a non-zero number.

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Select an appropriate type of display for the data gathered for each situation from bar graph, line graph, line plot, histogram, and box plot.

1. The amount of sales a company has over 6 months.

2. The prices of five different brands of tennis shoes at an athletic store.

3. The shape of the distribution of a team's football scores for one season.

Answers

For #1, the best graph would be a line graph because this data is being described over a period of time. Line graphs best represent change over time.

For #2, the best graph would be a bar graph because you will easily be able to see the comparison between the prices in the bars. You will be able to easily see approximate differences and how many times greater or smaller.

For #3, a histogram will best display this data because there will be many scores from a football season to represent, and a histogram organizes a lot of data into intervals while still allowing us to see tendencies in the bars.

A line passes through the ordered pairs (4,1) and (2,8). What is the slope? Please help due today

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 4 &,& 1~) % (c,d) &&(~ 2 &,& 8~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-1}{2-4}\implies \cfrac{7}{-2}\implies -\cfrac{7}{2}[/tex]

A square on the coordinate plane has vertices at (−2, 2), (2, 2), (2, −2), and (−2, −2). A dilation of the square has vertices at (−4, 4), (4, 4), (4, −4), and (−4, −4). Find the scale factor and the perimeter of each square.

Answers

The smaller square has length of 4. So its perimeter is 4*4 = 16
The larger square has length of 8 and its perimeter is 8*4 = 32

The scale factor is 2. Since the larger square is twice the size of the smaller square (Or you can say that the scale factor is 1/2 if you are looking at the perspective of the larger square to the smaller square).

Final answer:

The scale factor between the original and dilated square is 2. The perimeter of the original square is 16 units, and the perimeter of the dilated square is 32 units.

Explanation:

The student asked for the scale factor and the perimeter of each square after a dilation on the coordinate plane. The original square has vertices at (-2, 2), (2, 2), (2, -2), and (-2, -2), and the dilated square has vertices at (-4, 4), (4, 4), (4, -4), and (-4, -4).

To find the scale factor, we can compare the coordinates of the original and dilated squares. The x-coordinates (and y-coordinates) of the dilated square are twice those of the original square, indicating that the scale factor is 2. The side length of the original square is 2 - (-2) = 4 units. Given the scale factor of 2, the side length of the dilated square is 4 units × 2 = 8 units.

To calculate the perimeter of each square, we multiply the side length by 4 (since a square has 4 equal sides). The perimeter of the original square is 4 units × 4 = 16 units, and the perimeter of the dilated square is 8 units × 4 = 32 units.

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -x2 -5. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answers

Part (1):
To get the x-intercepts, we will need to equate the equation to zero and solve for x.
For the parent function, we have:
x² = 0
x = 0
Therefore, the function intersects the x-axis at one point which is the origin.

For the image function we have:
-x² - 5 = 0
x² = -5
x = √-5 which does not exist in real numbers
This means that the image function does not intersect the x-axis at all.

Based on the above, the parent function has one x-intercept while the image one doesn't have any x-intercepts.

Part (2):
I have attached the image containing the two functions , the parent one as well as the image.
As we can note, two changes occurred to the parent function in order to form the image:
1- The parabola was flipped to be pointing downwards instead of pointing upwards
2- The vertex was translated 5 units downwards to be at (0,-5) instead of (0,0)

x^2 only touches the x axis when x=0 and it increases without bound on either side of 0.

-x^2-5 never touches the x axis reaching a maximum at (0,-5) and decreasing without bound on either side of 0

g(x) is f(x) inverted and moved down five units...

On February 1, the electricity meter reading for the Smith residence was 19,423 kilowatt hours. On March 1, the meter read 20,288 kilowatt hours. On April 1, the meter read 21,163 kilowatt hours. a. How many kilowatt hours of electricity did the Smiths use during February? b. How many kilowatt hours did they use during March?

Answers

a. How many kilowatt hours of electricity did the Smiths use during February?

Kilowatt hours of electricity the Smiths used during February:
Meter read on March 1 - meter read on February 1 =
20,288 kilowatt hours - 19,423 kilowatt hours =
865 kilowatt hours
Answer: The Smiths used 865 kilowatt hours of electricity during February

b. How many kilowatt hours did they use during March?

Kilowatt hours of electricity the Smiths used during March:
Meter read on April 1 - meter read on March 1 =
21,163 kilowatt hours - 20,288 kilowatt hours =
875 kilowatt hours
Answer: The Smiths used 875 kilowatt hours of electricity during March

This diagram shows a scale drawing for small amphitheater if the scale factor is 1 cm= 10m, what is the area of the actual amphitheater.

A. =40m2
B.=80m2
C.=4,000m2
D.=8,000m2

Please help I will put who right

Answers

A =(b1+b2)h/2
actual b1 =10cm*10m/1cm =100m
actual b2 = 6cm*10m/1 cm = 60m
height = 5 cm*10m/1cm = 50m

A=(100+60)*50/2 = 160*50/2 =80*50= 4,000 m²

Answer : C.=4,000 m²

Answer:

4,000cm^2

Step-by-step explanation:

hey can you please help me posted picture of question

Answers

The inverse of the inverse function will give us back the original function.

So the inverse of the inverse function x² -2 will be √(x+2), which i s thus our original function.

So, the answer to this question is option A.

A way to validate the answer is take the composition of the original function and its inverse, the will give the result equal to x

find the midpoint of the line segment with the given endpoint (7,4) (9,-1)

Answers

Midpoint = [tex]( \frac{X2-X1}{2} , \frac{Y2-Y1}{2} )[/tex]

So plug into that.

You get (9 - 7)/2 , (- 1 - 4)/2

Which gives you 2/2 , - 5/2

This simplifies to the ordered pair (2, - 5/2)

Answer:

(8, 1.5)

Step-by-step explanation:

The figure consists of a quarter circle and a parallelogram. What is the area of the composite figure? Use 3.14 for pi. Round to the nearest whole number. please answer as soon as poossible
70 in
84 in
154 in
224 in

Answers

The area of a full circle is given by
A = π*r^2
so the area of a 1/4 circle will be 1/4 of that:
A = (π/4)*r^2

The area of a parallelogram is the product of base length and height:
A = bh

Your composite figure will have an area that is the sum of the areas of the parts.
A = (quarter circle area) + (parallelogram area)
A ≈ (3.14/4)*(14 in)^2 +(14 in)*(5 in)
A ≈ 223.86 in^2 ≈ 224 in^2

The most appropriate selection is the last one,
224 in^2

The area of composite figure of both Quarter circle and Parallelogram is 224inches.

What is Quarter circle?

"When a Circle is divided into four equal parts, then each parts of a circle is called Quarter of a Circle".

What is Parallelogram?

A parallelogram is "two dimensional geometrical shape, whose sides are parallel to each other".

According to the question,

Area of circle =πr²

Formula for Area of quarter Circle = (π/4)r²

Formula for Area of parallelogram = base × height = (b×h)

In order to find the area of composite figure

Formula for Area of composite figure = Area of quarter Circle + Area of parallelogram

= (π/4)r² + (b×h)

= (3.14/4)(14)² + (14×5)

= 223.86inches ≈ 224inches

Hence, the area of composite figure of both Quarter circle and Parallelogram is 224 inches.

To learn more about Quarter circle and Parallelogram here

https://brainly.com/question/15249201

#SPJ2

What is the volume of the composite space figure to the nearest whole number?

Answers

check the picture below.

the volume of a rectangular prism is just the product of its 3 dimensions, so the volume of those two there is 4*9*6 and 3*6*5.

so the volume for the composite figure is just the sum of those two products.

Answer:

A u just have to multiply

Step-by-step explanation:

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