[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (3a)(a^{-3})\implies 3a\cdot \cfrac{1}{a^3}\implies \cfrac{3a}{a^3}\implies \cfrac{3~~\begin{matrix} a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{aa~~\begin{matrix} a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{3}{a^2}[/tex]
amanda is 5.5 ft tall she casts a shadow of 2.75 ft she is standing next to the basketball hoop that is 10 ft high how much of a shadow will it cast
Final answer:
Using similar triangles, the basketball hoop which is 10 ft high will cast a 5 ft long shadow.
Explanation:
To find out how much of a shadow the basketball hoop will cast, we can use the concept of similar triangles. Amanda, who is 5.5 ft tall, casts a shadow that is 2.75 ft long.
The basketball hoop is 10 ft high.
To find the length of the shadow cast by the hoop, we set up a proportion based on the heights and shadow lengths:
Height of Amanda / Shadow of Amanda = Height of Basketball Hoop / Shadow of Basketball Hoo
5.5 ft / 2.75 ft = 10 ft / X ft
Cross-multiply to solve for X (the shadow of the basketball hoop):
5.5 * X = 10 * 2.75
X = (10 * 2.75) / 5.5
X = 27.5 / 5.5
X = 5 ft
So, the basketball hoop will cast a shadow that is 5 ft long.
Can anyone please help me with this questions 2-51 “Plot triangle ABC with vertices A(0,0), B(3,4), and C(3,0) on graph paper. Using the origin as the point of dilation, enlarge it by...
Answer:My guess might not be correct, but here it is anyway: On the online math textbook, there's this thing called Homework help. Click on that where this problem and a graph show up on your screen. Click on the hint box, then you'll see an answer box below that. Add up the three side lengths, and you should have your answer. Then, you'll need to to look up on how to calculate an area and perimeter on a triangle. And that's it! Hope this helped Rosa.
Step-by-step explanation:
21. When Brooke buys lunch at the cafeteria,
money is withdrawn from a lunch account.
The table shows amounts withdrawn in
one week. By how much did the amount in
Brooke's lunch account change by the end
of that week?
25.
Answer:
The amount in Brooke's lunch account change by the end of that week is $-20 or $20 decrease.
Step-by-step explanation:
Consider the provided information.
Each day Brooke buys lunch and withdrawn the same amount i.e $4.
The number of days are 5.
To calculate the change by the end of that week, find the total amount withdrawn in 5 days.
To represent withdrawn use a negative sign.
[tex]5(-4)[/tex]
The product of the numbers will be a negative number as they have opposite sign.
[tex]5(-4)=-20[/tex]
Hence, the amount in Brooke's lunch account change by the end of that week is $-20 or $20 decrease.
The amount in Brooke's lunch account change by $20.
Using the parameters given for our Calculation;
Initial balance = $28Amount spent per day = $4Number of days = 5The total amount spent is ;
5 * $4 = $20The change in the amount spent;
Initial balance - Total amount spentNow we have ;
$28 - $20The change in the lunch account by the end of the week is $20.
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Daryl used a ruler to measure the distance between two cities on a map with a scale of 1 inch to 40 miles. He reported the actual distance between the two cities as 200 miles, with a measurement error of 10 miles. What is the smallest increment on the ruler Daryl used?
A. 0.25 in.
B. 0.5 in.
C. 0.75 in.
D. 1 in.
Hey!
-------------------------------------------------
We Know That:
1 inch = 40 miles
200 / 4 = 5
200mi. = 5 x 40mi. (5 x 1mi on scale)
-------------------------------------------------
Solution:
40 / 4 = 10 (not to scale)
1 / 4 = 0.25 (error to scale)
If the scale is 0.25 then it's half way while rounding.
-------------------------------------------------
Answer:
[tex]\large\boxed{B.~0.5~in.}[/tex]
-------------------------------------------------
Hope This Helped! Good Luck!
Answer: Is not A. Its B.
Step-by-step explanation:
I chose A and it is wrong. I would choose B.
400 * 0.5 = 200
400 * 0.25 = 100
translate “one less than the quotient of a number and -5”
(x/-5)-1
one less = -1
quotient= division
What would "x" be? And how do you get it?
Answer:
x would be a variable. Did the instructions say x = 5 or some other number? If so, you can solve it.
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.y=-2/5x+11/5
Answer:
y-intercept (0,11/5)
x-intercept (11/2,0)
Step-by-step explanation:
The y-intercept is obtained when the x-coordinate equals 0 (x=0)
so the y-intercept is (0,11/5)
The x-intercept is obtained when the y-coordinate equals 0 (y=0)
In this case
0 = -(2/5)x+11/5---->(2/5)x = 11/5 ----> x=(5*11)/(5*2) = 11/2
So the x-intercept is (11/2,0)
A family deposited $8000 into an account six years ago. The account earned
simple interest at a yearly rate. So far the total interest earned is $1200. What is
the rate for the account?
Use I = prt
1200 = 8000r(1)
1200/8000 = r
0.15 = r
15% = r
(20 POINTS IF RIGHT)
Which table of ordered pairs represents a proportional relationship?
Answer:
the 4th one
Step-by-step explanation:
x increase by 3 and y increase by 12.
ANSWER: the answer would be 4
Step-by-step explanation:
it is (-3,12) (-6,24) (-9,36) i know because it is going by fours and you have a number you can multiply it by or divide it by
Binh spent 15 game tokens in an amusement park arcade . She won 11 tokens while she was playing the games. If she had no tokens left when she leaves the arcade, how many did she buy while she was playing games? Explain your answer
Answer:she only buy 4 tokens
Step-by-step explanation:
We know that Binh have 15 tokens, and she won 11 tokens. So, she just need buy 4 tokens.
She buys 4 games tokens during playing games.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
The group's total number of items decreases or becomes lower when we subtract from it.
Number of tokens she won = 11
Number of tokens she spent= 15
Number of tokens she buy = Number of tokens she spent - Number of tokens she won
Number of tokens she buy = 15 - 11 = 4
Hence "She buys 4 games tokens during playing games".
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which ordered pair is the solution to the system of equations?
x+3y=-12
y=1/3x-6
a. (10, -2 2/3)
b. (-5, -2 1/3)
c. (3,-5)
d. (-9,-9)
Answer:
c. (3, -5)
Step-by-step explanation:
{x + 3y = -12
{y = ⅓x - 6
x + 3[⅓x - 6] = -12
x + x - 18 = -12
2x - 18 = -12
+ 18 + 18
____________
2x = 6
__ _
2 2
x = 3 [Plug this back into both equations to get the y-coordinate of -5]; -5 = y
I am joyous to assist you anytime.
19/25 into a decimal
Answer:
0.76
Step-by-step explanation:
19 divided by 25 is 0.76.
You pay $60 for 5 yoga classes. How much is one class?
Answer: 12
Step-by-step explanation:
60 divided by 5 is 12.
Hope this helps!
Answer: $12
Step-by-step explanation:
60/5=12
Write 1,840 in scientific notation!!!!!!!!
Answer:
1.84 x10 to the power of 3
Step-by-step explanation:
there is 3 numbers to the right of the decimal making it to the power of three
keep all important numbers, removing the 0 and keeping everything else
i have done maths to this extent in a few months so i would double check
Answer:
1.84 x10 to the power of 3
Step-by-step explanation:
What’s number 9? I know the answer
Answer:
9?
Step-by-step explanation:
15-6=9 or 6+_=15 so 6+9=15 and your final answer is,9?
Find two consecutive odd integers such that the sum of their squares is 34
Answer:
3 and 5
Step-by-step explanation:
use the guess and check method form the numbers 1, 3, 5 since only the square of these 3 numbers are under 34.
The two sets of consecutive odd integers whose squares sum to 34 are 3 and 5, and -5 and -3.
Explanation:To identify the two consecutive odd integers whose squares sum up to 34, we'll first understand that consecutive odd integers can be represented as x, and x+2 (since every other integer is odd). The squares of these integers should equal 34.
This gives us the equation: x^2 + (x+2)^2 = 34. Simplifying this, we get: x^2 + x^2 + 4x + 4 = 34, 2x^2 + 4x - 30 = 0. This simplifies further to x^2 + 2x - 15 = 0. Factoring this equation gives us (x-3)(x+5) = 0. Therefore, the solutions are x = 3 and x = -5.
Therefore, the two pairs of consecutive odd integers that satisfy the conditions are 3 and 5 or -5 and -3.
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which expression is equivalent to 5x - 30?
A =. 5(x-30)
b =. 5( x-6)
c =. x(5 - 30
Answer: I believe the answer is B
Step-by-step explanation:
Because 5 times x and then 5 times 6
That will give you 5x-30
Jasmine has 3 3 /8 pounds of turkey meat. She is making 1/3 pound turkey burgers. Does Jasmine have enough meat to make 12 turkey burgers? Explain.
Answer: no
Step-by-step explanation:
She needs a little less than 4 pounds to make 12 turkey burgers because 1/3 times 12 is about 3.99 pounds. But she only has 3 3/8 pounds which is about 3.375 pounds.
Jasmine does not have enough meat to make 12 turkey burgers as she has 3.375 pounds of turkey while 4 pounds of turkey is needed.
What is Unitary method?The unitary method involves the process of finding the value of a single unit and based on this value, we can find the value of the required number of units.
Given is a girl named jasmine who has 3 3/8 pounds of turkey meat. She is making 1/3 pound turkey burgers.
Now -
1 burger requires → 1/3 pounds of turkey
12 burgers will require → 12 x 1/3 → 4 pounds of turkey
Turkey available with Jasmine → 3 3/8 pounds → 3.375 pounds of turkey
Hence, Jasmine does not have enough meat to make 12 burgers.
Therefore, Jasmine does not have enough meat to make 12 turkey burgers as she has 3.375 pounds of turkey while 4 pounds of turkey is needed.
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Frostburg truth bus travels on a straight road from Frostburg mall to Sojourner Truth park the mall is 2 miles east and 5 miles north of the city center the park is 5 miles west and 5 miles south of the center how far is it from the mall to the park to the nearest 10th of a mile
Answer:
10 miles long i do believe
The distance from the mall to the park is approximately 12.2 miles to the nearest tenth of a mile.
To find the distance from the mall to the park, we can use the Pythagorean theorem since the path forms a right triangle. The legs of the triangle are the distances from the mall to the city center (2 miles east and 5 miles north) and from the park to the city center (5 miles west and 5 miles south).
Let's denote the distance from the mall to the park as d. Then, we can set up the equation:
[tex]\[ (2 + 5)^2 + (5 + 5)^2 = d^2 \][/tex]
Solving this equation:
[tex]\[ (7)^2 + (10)^2 = d^2 \]\[ 49 + 100 = d^2 \][/tex]
[tex]\[ 149 = d^2 \][/tex]
Now, we take the square root of both sides to find d:
[tex]\[ d = \sqrt{149} \][/tex]
Using a calculator, we find:
[tex]\[ d \approx 12.2 \][/tex]
Need it asap plz :).
Answer:
I have no idea what this is sorry bro
Step-by-step explanation:
Answer:
1.9 x 10^6
Step-by-step explanation:
2094800-158975=1935825
move the decimal over 1.9
count how many times 6
1.9 x 10^6
Which of the binomials below is a factor of this trinomial?
5х2 - 5x - 100
А. х-4
ОВ. x+ 10
ос. x+5
OD. х- 5
Answer: The correct answer is: [D]: " (x - 5) "
__________________________________________________
Step-by-step explanation:
__________________________________________________
First, let's try to "factor out" the given trinomial:
__________________________________________________
" 5x² - 5x - 100 " ;
__________________________________________________
We can "factor out" a "5" ;
since among the three (3) terms in this trinomial,
We have: 5x² , 5x, and 100 ;
Note that not all of these 3 terms have a variable in them;
→ Consider the value; "100" .
Note that the remaining two (2) terms have the same variable, "x" ;
→ 5x² ; and 5x " ;
Note that each of these 2 (two) terms have a coefficient of "5" ;
Note that the other term, "100" ; is divisible "evenly" by "5" ;
→ that is; when the term, "100", is divided by "5" ; the result is an integer; {specially, " 100 ÷ 5 = 20 " .}.
__________________________________________________
So: Let us being by "factoring out" a "5" ;
Given the trinomial: " 5x² - 5x - 100 " ;
→5(x² - 1x - 20) ; or: 5(x² - x - 20) ;
→ At this point, although this trinomial express is not completely
"factored out" ;
__________________________________________________
Let us consider: Do either of these two (2) factors appear among the answer choices given:
1) " 5" ; or: 2) "(x² - x - 20)" ?? No!
__________________________________________________
Let us continue.
We have: 5(x² - x - 20) ;
→ We can write as: " 5 (x² - 1x - 20) " ;
__________________________________________________
Now, let see if we can further "factor out" the:
→ (x² - 1x - 20) ;
Now, note the " -20" ; and the " -1x " ;
→ What two (2) factors of: "-20" ; add up to "-1" ? ;
__________________________________________________
Let us consider the factor of "-20" :
-20, 1 : -20 + 1 = -19 ; -19 =? -1 ? No.
20, -1 : 20 + (-1) = 20 - 1 = 19 ; 19 =? -1 ? No.
10, -2 : 10 + (-2) = 10 - 2 = 8 ; 8 =? -1 ? No.
-10, 2 : -10 + 2 = -8 ; -8 =? -1 ? No.
-4, 5 : - 4 + 5 = 5 + (-4) = 5 - 4 = 1 ; 1 =? -1 ? No.
4, -5 : 4 + (-5) = -5 + 4 = -1 ; -1 =? -1 ? Yes!
__________________________________________________
So, we have +4 and -5 ;
(+4) * (-5) = -20 ;
(+4) + (-5) = -5 + (+4) = -5 + 4 = -1 ;
__________________________________________________
So, we factor out:
→ (x² - 1x - 20) ;
that is: " (x² - x - 20) " ;
into:
__________________________________________________
" (x + 4) (x - 5) " ;
and to factor out: " 5x² - 5x - 100 " ;
we bring down the "5" ; and write as:
→ " 5 (x + 4) (x - 5) " ,
__________________________________________________
So:
We have three (3) factors when the trinomial expression is "factored out":
→ 5 ; (x + 4) ; and: (x - 5) ;
__________________________________________________
→ Among these three factors, the only one that appears as a given answer choice is:
→ " (x - 5) " ;
→ which is our answer:
__________________________________________________
→ Answer choice: [D]: " (x - 5) " .
__________________________________________________
Hope this answer is helpful to you!
Best wishes!
__________________________________________________
A pizza is advertised as containing 250 square inches of a pizza. To the nearest inch , what is the diameter of the pizza?
The diameter of a pizza with an area of 250 square inches is approximately 18 inches when calculated using the area formula for a circle and rounded to the nearest inch.
Explanation:To find the diameter of a pizza given its area, we can use the formula for the area of a circle, A = πr², where A is the area and r is the radius of the circle. Given that the area is 250 square inches, we can solve for the radius and then find the diameter, which is twice the radius.
First, we rearrange the formula to solve for the radius: r = √(A/π). Plugging in the given area, we have r = √(250/π). Using π approximately equal to 3.14159, we find r ≈ √(250/3.14159) ≈ √(79.577) ≈ 8.92 inches. Therefore, the radius of the pizza is approximately 8.92 inches.
To find the diameter, we simply multiply the radius by 2: diameter = 2r ≈ 2(8.92) ≈ 17.84 inches. To the nearest inch, the diameter of the pizza is approximately 18 inches.
Find the missing factor.
6x2 + 13x - 5 = (3x - 1
)
Answer:
(2x+5)
Step-by-step explanation:
(-14i6)(-6i3)(2i8)
What is the domain of the function
f(x)= square root of (1/3)x+2?
Answer:
The domain of f(x) = √[(1/3)x +2] is [-6, ∞).
Step-by-step explanation:
GIven f(x) = √[(1/3)x +2], you have to find the values for which the the expression inseide the square will be possitive (for negative values the function is not defined for Reals.
(1/3)x + 2 = 0 ⇒ (1/3)x = -2 ⇒ x = -2/(1/3) ⇒ x = -6
Finally the domain of f(x) is (-6, ∞).
Answer:
✔️ X [tex]\geq[/tex] -6
9. Is the relationship shown by the data linear? If so, model the
data with an equation.
Answer:
D
Step-by-step explanation:
Its C because as you can tell its not a negative , so D is incorrect the its not a because there is a relationship and c is incorrect because Y is less than X which is 2 more than X and that is how i got D
Select the correct answer. The temperature in Bloomington on Sunday was 32.6°C. On Monday, the temperature changed by -8.25°C. What was the temperature on Monday?
24.35°C is the answer
Final answer:
The temperature on Monday was 24.35°C.
Explanation:
To find the temperature on Monday, we need to subtract the change in temperature from the temperature on Sunday. The temperature on Monday was 32.6°C and the change in temperature was -8.25°C.
Therefore, the temperature on Monday was 32.6°C + (-8.25°C) = 24.35°C.
Some students prepare 3 different snacks. They make 1/8 pound bags of nut mix, 1/4 pound bags of cherries, and 1/6 pound bags of dried fruit. If they buy 3 pounds of nut mix, 5 pounds of cherries, and 4 pounds of dried fruit, how many of each type of snack bag will they be able to make?
Answer:
24 bags, 20 bags and 24 bags
Step-by-step explanation:
Students made a bag of nut mix by using = [tex]\frac{1}{8}[/tex] pound
They bought nut mix = 3 pounds
they will be able to make number of nut mix bags = [tex]\frac{3}{\frac{1}{8} }[/tex]
= [tex]\frac{3\times 8}{1}[/tex]
= 24 bags
Students made a bag of cherries by using = [tex]\frac{1}{4}[/tex] pound
They bought cherries = 5 pounds
they will be able to make number of cherries bags = [tex]\frac{5}{\frac{1}{4} }[/tex]
= [tex]\frac{5\times 4}{1}[/tex]
= 20 bags
Students make a bag of dried fruit by using = [tex]\frac{1}{6}[/tex] pound
They bought dried fruit = 4 pounds
they will be able to make number of dried fruit bags = [tex]\frac{4}{\frac{1}{6} }[/tex]
= [tex]\frac{4\times 6}{1}[/tex]
= 24 bags
Students would be able to make 24 bags of nut mix, 20 bags of cherries and 24 bags of dried fruit.
The students would be able to make 24 sacks of nut mix, 20 sacks of cherries and 24 sacks of dried fruit.
EquationAn equation is an expression that shows the relationship between two or more variables and numbers.
For 3 pounds of nut mix:
Number of snack bag = 3 pounds / (1/8 pound) = 24 sacks
For 5 pounds of cherries:
Number of snack bag = 5 pounds / (1/4 pound) = 20 sacks
For 4 pounds of dried fruit:
Number of snack bag = 4 pounds / (1/6 pound) = 24 sacks
The students would be able to make 24 sacks of nut mix, 20 sacks of cherries and 24 sacks of dried fruit.
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What is the change in temperature from -8°F to 14°F?
22°F
0-22°F
0-6°F
6°F
Answer:
22F
Step-by-step explanation:
Absolute value of -8 is 8. Therefor, that'll put you at 0. Then from 0 you want to get to 14, so you'll take the 14 and add 8 to it which will leave you with 22.
A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. An adult ticket costs as much as the combined cost of a student ticket and a child ticket. you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23.
what are 3 system of equations?
what is the price per ticket for each type of ticket?
Answer:
The price per ticket for adults is $5
The price per ticket for students is $4
The price per ticket for child between the ages of 3 and 8 is $1
Step-by-step explanation:
Let
x -----> the price per ticket for adults
y -----> the price per ticket for students
z -----> the price per ticket for child between the ages of 3 and 8
we know that
The system of equations is
[tex]2x+y+z=15[/tex] ------> equation A
[tex]x=y+z[/tex] ------> equation B
[tex]x+4y+2z=23[/tex] -----> equation C
substitute equation B in equation A and solve for x
[tex]2x+(x)=15[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
Substitute the value of x in equation B and equation C
[tex]5=y+z[/tex] -----> equation B
[tex]5+4y+2z=23[/tex]
[tex]4y+2z=18[/tex] -----> equation C
Solve the system by graphing
Remember that the solution is the intersection point both graphs
Using a graphing tool
The solution is the point (1,4)
so
z=1, y=4
therefore
The price per ticket for adults is $5
The price per ticket for students is $4
The price per ticket for child between the ages of 3 and 8 is $1