Answers
The lengths of the sides are:
2x = 12
2x -7 = 5
_____
You can use the Pythagorean theorem to write the relationship between the sides.
(2x)² +(2x -7)² = 13²
4x² +4x² -28x +49 = 169 . . . . . eliminate parentheses
8x² -28x -120 = 0 . . . . . . . . . . . put in standard form
4(2x² -7x -30) = 0 . . . . . . . . . . . factor out 4
(x -6)(2x +5) = 0 . . . . . . . . . . . .. divide by 4 and factor further
x = 6, -5/2 . . . . . . . . . . . . . . . . .. only the positive solution (x=6) is useful
Then 2x = 12; 2x-7 = 5.
Related Questions
From a group of 3 men and 4 women, a delegation of 2 is selected. let x be the random variable that represents the number of women selected. write the probability distribution and find the expected number of women in the delegation?
Answers
x values are 0, 1, 2, 3
The corresponding probabilities are:
P(x=0)= 3C2/7C2=3/21
P(X=1)=3C1*4C1/7C2=12/21
P(X=2)=3C2/7C2=3/21
P(X=3)=3C2/7C2=3/21
Hence the expected value will be:
E(x)=[0*3+1*12+2*3+3*3]/21
E(x)=27/21=1.29
Brad has 3 pairs of pants, 7 tee shirts, and 2 pairs of sneakers. How many different outfit combinations can he wear
Answers
Answer:
42
Step-by-step explanation:
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.
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
Hey can you please help me posted picture of question
Answers
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
Quadrilateral has angles 45 degrees, 150 degrees, 65 degrees, and N degrees
Answers
other angles=260
all interior angles of a quadrilateral add up to 360
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
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]
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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Find the length of JK and the measure of M
Answers
You have two different situations, but both of them are solved the same way.
Step One
Solve for the 2 equal sides.
21x - 9 = 3x + 27 Add 9 to both sides.
21x = 3x + 27 + 9
21x = 3x + 36 Subtract 3x from both sides.
21x - 3x = 36
18x = 36 Divide by 18
x = 36/18
x = 2
That's not quite the answer
Step Two
Find JK
JK = 21x - 9
JK = 21*2 - 9
JK = 42 - 9
JK = 33 <<<<<<< Answer
Step Three
Solve for y
5y + 11 = 12y - 10 Subtract 5y from both sides.
11 = 12y - 5y - 10
11 = 7y - 10 Add 10 to both sides.
11 + 10 = 7y
21 = 7y Divide by 7
21/7 = y
3 = y
Step Four
Solve for M
M = 12y - 10
M = 12*3 - 10
M = 36 - 10
M = 26 <<<<< Answer
M = 74
Hope this Helped!
;D
Brainliest??
A line passes through the ordered pairs (4,1) and (2,8). What is the slope? Please help due today
Answers
Which answer shows a correct order to solve this story problem? Maurine had to pay $2.52 tax on her purchases. She bought 3 books for $12.99 each, 2 pens for $0.69 each, and a magazine for $2.99. How much did Maureen spend? A. Step 1: Add the price of a book and a pen. Step 2: Multiply by 3 and then by 2. Step 3: Add $2.99 to that result. Step 4: Add the tax to the total of the purchases. B. Step 1: Calculate the total price of the 2 pens. Step 2: Add $2.99 to that total. Step 3: Calculate the total price of the 3 books. Step 4: Add the tax to the price of the 3 books C. Step 1: Calculate the total price of the 3 books. Step 2: Calculate the total price of the 2 pens. Step 3: Add $2.99 to the total of the cost of the books and pens. Step 4: Add the tax to the total of the purchases. D. Step 1: Add $2.99 to the amount of the tax. Step 2: Calculate the total price of the 2 pens. Step 3: Calculate the total price of the 3 books. Step 4: Add the prices of the pens to the price of the books.
Answers
C. Step 1: find the price of the books; Step 2: find the price of the pens; Step 3: add the prices of the books, pens, and magazine; Step 4: add the tax.
_____
You can, of course, find and add the constituent prices in any order. Generally, you need to know that subtotal in order to figure the tax, which is then added to that subtotal. If you've ever done any shopping at a store where bills are added manually, or if you pay attention to any cash register receipt, you know this is the process.
hey can you please help me posted picture of question
Answers
C. G(x)=(x-2)^3
The explanation is shown below:
1. You have the the red graph has the equation F(x)=x^3
2. If you shifted two units to the right, you must add -2 to the function x^3, as below:
G(x)=(x-2)^3
3. If you want to verify this is correct, you need to give values to the variable x and plot each point.
4. You will see that the correct answer is the option mentioned above.
hey can you please help me posted picture of question
Answers
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
Question# 12, find the slope
Answers
(0,1) and (-4, -2)
Slope = m = (-2 - 1)/(-4 -0 ) = -3/-4 = 3/4
So the slope of given line is 3/4
Thus the correct answer is option B
m = (y2-y1) / (x2-x1)
We choose the ordered pairs:
(x1, y1) = (0, 1)
(x2, y2) = (4, 4)
Substituting values we have:
m = (4-1) / (4-0)
m = (3) / (4)
m = 3/4
Answer:
The slope for this case is given by:
m = 3/4
option 2
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
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.
find the midpoint of the line segment with the given endpoint (7,4) (9,-1)
Answers
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:
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(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%
hey can you please help me posted picture of question
Answers
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]
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
What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π.
Answers
ω = d/(t*r) = (14.13 ft)/((3 s)*(6 ft))
ω = 0.785 radians/second
There are 180/π degrees per radian, so the angular velocity can also be written as ...
ω = 45 degrees/second
what is the value of x sin x + 11 degrees equals cos 2x + 22 degrees enter your answer in the Box
Answers
(x + 11) + (2x + 22) = 90
Simplifying,
3x + 33 = 90
Further simplification,
3x = 90 - 33 = 57
The value of x from the equation is 19.
Answer: x = 19
Answer:
it is 19
Step-by-step explanation:
I just took this test and got 100 :)
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
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...
Two graphs are shown below:
graph A shows scatter points 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 5graph A shows scatter points 1, 4 and 2, 4 and 3, 4 and 4, 4 and 5, 4
Which scatter plot shows a positive correlation between x and y?
Only graph A
Only graph B
Both graph A and graph B
Neither graph A nor graph B
Answers
The correct answer is graph A
What is the distance d across the lake?
Answers
Answer-
The distance d across the lake is 90ft.
Solution-
In the picture,
ΔABC ≈ ΔCDE
Because,
∠ACB = ∠DCE (∵ vertical opposite angles)∠B = ∠D = 90°∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)So, from similarity properties
[tex]\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}[/tex]
[tex]\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}[/tex]
[tex]\Rightarrow d=\dfrac{120\times 15}{20}=90[/tex]
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
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
Please help!!! I very much need help, thank you!
Answers
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 1/9 as many as 3 divided by 5
Answers
Final answer:
To find 1/9 as many as 3/5, you multiply 3/5 by 1/9 to get 3/45, which simplifies to 1/15.
Explanation:
To solve the student's question, we need to find what is 1/9 as many as 3/5. This involves multiplying the fraction 3/5 by the fraction 1/9. Here is the step-by-step calculation:
Multiply the numerator of the first fraction (3) by the numerator of the second fraction (1) to get the numerator of the answer.Multiply the denominator of the first fraction (5) by the denominator of the second fraction (9) to get the denominator of the answer.Combine these to get the answer in fractional form.The calculation will look like this: (3/5) × (1/9) = 3/45 = 1/15.
Thus, 1/9 as many as 3/5 is 1/15.
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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Hey can you please help me out on my question posted picture
Answers
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.
What is the ratio (fraction) of minivans to all vehicles on the forecourt?
A)1/120
B)1/20
C)1/6
D)1/4
Answers
20/120
1/6
I hope this helps
do u do keystone
? im just wondering i do
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
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]
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
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.
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