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Jessica wants to add a border around the edge of the solar panels to help protect them from weather events.
Write the standard form expression that represents the amount of border material Jessica will need.
Enter the correct answer in the box.
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The error of Fatima is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).

An exponent in any expression is the letter or number on the right of a base in an expression.

In the evaluated expression shown, the base that the exponent "-2" applies to is "m", and does not include 4. If we substitute the value of m = -2, into the evaluated expression, the base that the exponent "-2" applies to is "-2" and does not include "4".

Therefore, Fatima's mistake is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).

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The maximum height of the rocket is 78.4m

Given the function that represents the height of a function expressed as:

h(t) = -4.9t² +9.8t + 73.5.

The rocket will reach its maximum height at the point where h'(t) = 0

h'(t) = -9.8t +9.8

Equate to zero

0 = -9.8t + 9.8

9.8t = 9.8

t = 1

Substitute

h(1) = -4.9(1)²+9.8(1) + 73.5

h(1) = 4.9 + 73.5

h(1) = 78.4m

Hence the maximum height of the rocket is 78.4m

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Answer:

52.9%

Step-by-step explanation:

There are 17 shapes total. Nine of those shapes are triangles. Therefore the probability of choosing a triangle is 9/17.

To find that as a percentage type 9 divided by 17 into the calculator. The answer to that is 0.5294117647058824. To turn a decimal into a percentage move the decimal point two places over making the percentage: 52.94117647058824%.

Since the yellow text states to round the answer to the nearest hundredth of the percent the answer is 52.9%.

52.94%

Step-by-step explanation:

there are 17 objects and you divide the 9 triangles by 17 and get .529411765. Which is 52.94 percent.

Answer:

6/17

Step-by-step explanation:

Robyn paid $45,

Rachel paid $65

Rocky paid $60.

Total amount paid = $45 + $65 + $60 = $170

Fraction paid by Rocky will be:

= 60/170

= 6/17

$194.97 is the cost of the credit loan.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

The total cost of the dishwasher with sales tax can be found by multiplying the price by 1.04:

$1249.99 × 1.04 = $1299.99

The cost of credit is the total amount paid through the installment loan minus the cost of the dishwasher:

12 × $124.58 = $1494.96

$1494.96 - $1299.99 = $194.97

Therefore, the cost of credit for this loan is $194.97.

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Triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.

Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Also, corresponding angles are congruent.

Triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.

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Answer:

down below

Step-by-step explanation:

Hope this helps =)

The truth of the given function that we have here is  The function increases at a constant multiplicative rate.

The table is given as

x            0   1    2      3

f(x)         2   3   4.5   6.75

We have x ranging from 0 to 3 while y ranges from 2 to 6.75.

The observations that we can make about the y values is that they produce the next value at the same rate of multiplication.

This is shown here

2 x 1.5 = 3

3 x 1.5 = 4.5

4.5 x 1.5 = 6.75

Hence we can conclude that it increases at a constant multiplicative rate of 1.5.

A table representing the function f(x) = 2(three-halves) Superscript x is shown below. A 2-column table has 4 rows. The first column is labeled x with entries (0, 1, 2, 3). The second column is labeled f (x) with entries 2, 3, 4.5, 6.75. What is true of the given function? The function increases at a constant additive rate. The function increases at a constant multiplicative rate. The function has an initial value of 0. As each x value increases by 1, the y values increase by 1.

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The length of DC based on the information given about the triangle is 19.37.

Based on the given information, it should be noted that:

AB² = AD² + BD²

25² = AD² + 5²

625 = AD² + 25

AD² = 625 - 25

AD² = 600

AD = √600

AD = 24.5

DC² = AD² + - AB² (Pythagoras theorem)

DC² = 24.5² + 15²

DC² = 375.25

DC = 19.37

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Answer: [tex]\frac{1}{3}[/tex] or about 33%

Step-by-step explanation:

       We will divide the wanted outcomes by the possible outcomes.        

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{Number of numbers greater than 4}}{\text{number of numbers 1 through 6}} =\frac{2}{6}=\frac{1}{3}\;\; \text{or about 33\%}[/tex]

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Answer: 1/3

Step-by-step explanation:

There are only 2 numbers greater than 4. 5 and 6.

2/6= 1/3 chance

Answer:

Step-by-step explanation:

     Switching the order of the terms comes out as an equivalent expression.

Whatever A is, if we multiply it by 8 and add 2, it will be equivalent to the sum of the same number times multiplied by 8 and 2.

I hope that helps!

Answer:

2(a +4)

Step-by-step explanation:

Distributive property:  a*b + a * c = a*(b+c)

Factorize 2 & 8  and find GCF of 2 & 8

2 = 2

8 = 2* 2*2

GCF = 2

2a + 8 =  2a + 2*4

           = 2(a + 4)

Answer:

60inches

Step-by-step explanation:

this because If you multiply 4 by 10 equals 40 add 40 to 20 equals 60

Answer:

70

Step-by-step explanation:

Frogs are at the pond = 12.

Given,

There are some frogs and some lily pads at a pond. If lily pads with frogs on them have two frogs each, then there are 3 lily pads with no frogs on them. If each lily pad has exactly one frog on it, then there are 3 frogs with no lily pad.

= 2( n-3) = n+3

= 2n -6 = n+3

=> n = 9

9 pads, 12 frogs.

Hence, Frogs are at the pond = 12.

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The difference between the number of hotdogs and hamburgers is 60

The ratio is given as:

Hotdog : Hamburger = 3 : 6

When the total hamburger is 120.

We have:

Hotdog : 120  =3 : 6

Multiply 3 : 6 by 20

Hotdog : 120  =3 * 20 : 6 * 20

Evaluate

Hotdog : 120  = 60 : 120

By comparison, we have

Hotdog = 60

So, the difference is

Difference = 120 - 60

Evaluate

Difference = 60

Hence, the difference is 60

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The graph of the inequality can be seen in the image below.

Here we have:

-3 < y - 7x < 15

Isolating y, we get:

-3 + 7x < y < 15 + 7x

So we need to graph two linear inequalities:

y > -3 + 7x

y < 15 + 7x

So we need to graph two parallel lines (with dashed lines, the lines aren't solutions) and shade the region above the first line and below the second line.

The graph is below:

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The representation of the equation as a standard quadratic equation is given by:

x² + 16x + 71 = 0.

The standard representation of a quadratic equation is given by:

ax² + bx + c = 0.

In this problem, the equation is:

-7 = (x + 8)²

Then:

x² + 16x + 64 = -7.

x² + 16x + 71 = 0.

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By the Congruent Supplements Theorem, we can conclude that,

∠FBC ≅ ∠DBG.

What is Congruent Supplements Theorem?

The Congruent Supplements Theorem states that two angles are said to be congruent if they are supplements of the same angle or even congruent angles.

If there are 4 lines such that, right angles are created when a horizontal line with the points F, B, and G crosses a vertical line with the points A, B, and E at point B. Between angles F and B and A and G, a third diagonal line with the points D, B, and C is intersecting the other two lines at point B. At points A, C, and G, there is a fourth line that joins three other lines.

Drawing Conclusion

In case the angle FBC and angle CBG are supplementary angles, angle DBG and angle DBF are another pair of supplementary angles, and angle CBG is-congruent-to angle DBF, we can apply congruent supplement theorem and draw the following inference,

∠FBC ≅ ∠DBG

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Answer: tis B :D

Step-by-step explanation:

Answer:

Caleb’s error was :

instead of selecting the least exponent ,Caleb took the highest exponent.

Step-by-step explanation:

3x² = 3 • x • x

(in this factorization the exponent of 3 is 1 and the exponent of x is 2)

9x = 3 • 3 • x

(in this factorization the exponent of 3 is 2 and the exponent of x is 1)

• The common factors of 3x² and 9x are 3 and x

In order to determine the GCF ,we have to Compare the exponents of the  common factors then take the numbers which have the least exponent value.

• in the factorization of 3x² the exponent of 3 is 1

and in the factorization of 9x the exponent of 3 is 2

The least exponent is 1 Then we take it.

• in the factorization of 3x² the exponent of x is 2

and in the factorization of 9x the exponent of x is 1

The least exponent is 1 Then we take it.

Conclusion:

GCF(3x² , 9x) = 3¹ × x¹ = 3x

Answer:  £5.36

Step-by-step explanation: You can find this by dividing £64.32 by 12

Answer:

jsjsjd b ebejisnskskhdbd zkzkz z.

Answer:

5

Step-by-step explanation:

10+5=15

20-15=5 . that is the solution

Answer:

(i) Total cost of the flat is Rs. 540000.

(ii) Expenditure incurred on labour is Rs. 150000

Step-by-step explanation:

According to the question, cement cost is Rs. 112500, which represents 75° in the pie chart.

(i) The total cost of the flat is represented by the total 360° in the pie chart.

∴ Using unitary method

75° represents Rs. 112500

⇒ 360° represents = [tex]\frac{112500}{75}[/tex]  ×  360

                                = Rs. 540000

∴  Total cost of flat = Rs. 540000

(ii) Similarly, to calculate the cost of labour, represented by 100° in the pie chart, we can use the unitary method:

75° represents Rs. 112500

⇒ 100° represents =  [tex]\frac{112500}{75}[/tex]  ×  100

                               = Rs. 150000

∴ Cost of labour = Rs. 150000

Using proportions, the total acceleration you would have applied to the car would be of -33 m/s².

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For one crash, the acceleration is of -3 m/s². Hence, for 11 crashes, the total acceleration would be of:

a = -3 x 11 = -33 m/s².

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The expression 21x⁴ + 56x³ + 49x² represents the area of the entire rectangle.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The area of the rectangle = length x width

= (3x² + 8x + 7)(7x²)

[tex]\rm =7x^2\cdot \:3x^2+7x^2\cdot \:8x+7x^2\cdot \:7[/tex]

= 21x⁴ + 56x³ + 49x²

Thus, the expression 21x⁴ + 56x³ + 49x² represents the area of the entire rectangle.

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Answer:

areas of AXYZ=10 square units1

Answer:

10 units squared

Step-by-step explanation:

Area of a triangle = 1/2 × base × height

Use the distance between two points formula to find the measure of the height and base of ΔXYZ.

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]

Height of Triangle

Define the points:

Substitute the points into the distance formula to find the height of the triangle:

[tex]\begin{aligned}\implies \sf height & =\sqrt{(4-2)^2+(5-1)^2}\\& = \sqrt{2^2+4^2}\\& = \sqrt{20}\end{aligned}[/tex]

Base of Triangle

Define the points:

Substitute the points into the distance formula to find the height of the triangle:

[tex]\begin{aligned}\implies \sf base & =\sqrt{(4-0)^2+(0-2)^2}\\& = \sqrt{4^2+(-2)^2}\\& = \sqrt{20}\end{aligned}[/tex]

Area of Triangle

[tex]\begin{aligned}\implies \sf Area & = \dfrac{1}{2} \times \sf base \times height\\& = \dfrac{1}{2}\sqrt{20}\sqrt{20}\\& = \dfrac{1}{2}(20)\\& = 10 \sf \:\:units^2 \end{aligned}[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[ a ] $ 20 for 8 lb

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]❖ \: \sf \:unit \: \: rate = simplest \: \: ratio \: in \: which \: it\: exists[/tex]

[tex] \qquad◈ \: \: \sf \: \cfrac{5}{2} \: \: \$ \:per \: \: lb[/tex]

Now, check out the options -

[ a ]

[tex] \qquad◈ \: \: \sf \: \cfrac{20}{8} [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: \cfrac{5}{2} \: \: \$ \:per \: \: lb[/tex]

Same as the given one.

[ b ]

[tex] \qquad◈ \: \: \sf \: \cfrac{16}{6} [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: \cfrac{8}{3} \: \: \$ \:per \: \: lb[/tex]

Not the same.

[ c ]

[tex] \qquad◈ \: \: \sf \: \cfrac{24}{8} [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: 3 \: \: \$ \:per \: \: lb[/tex]

Not the same.

[ d ]

[tex] \qquad◈ \: \: \sf \: \dfrac{12}{4} \: \: [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: 3 \: \: \$ \:per \: \: lb[/tex]

Not the same.

[tex] \qquad \large \sf {Conclusion} : [/tex]

The Correct answer is [ a ] $ 20 for 8 lb

Answer:

one possible solution is 5/6

Step-by-step explanation:

Solving for x

0 < 3x - 2 < 1

Add 2 to each side

0+2 < 3x - 2+2 < 1+2

2 < 3x<3

Divide each side by 3

2/3 < 3x/3 < 3/3

2/3 < x < 1

X must be between 2/3 and 1

Getting a common denominator

4/6 < x < 6/6

So x can be 5/6