Help! ASAP! #4 and #3 12 points!

Applying properties of exponents, the equivalent expression is given as follows:

[tex](5^{-2})^{5} \times 5^4 = 5^{-6}[/tex]

The expression is given as follows:

[tex](5^{-2})^{5} \times 5^4[/tex]

First the power of power rule is applied, which states that if we have a base elevated to multiple powers, the base is kept while the powers are multiplied, hence:

[tex](5^{-2})^{5} = 5^{-10}[/tex]

(as -2 x 5 = -10)

Then the expression is written as follows:

[tex](5^{-2})^{5} \times 5^4 = 5^{-10} \times 5^4[/tex]

Now we have the multiplication of two terms with the same base and different exponents, meaning that we keep the base and add the exponents.

Hence the equivalent expression is given as follows:

[tex]5^{-10} \times 5^4 = 5^{-6}[/tex]

(as -10 + 4 = -6).

The problem is given by the image at the end of the answer.

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1) Yes, all multiples of 3 also multiples of 6.

2) Yes, If 9 is a factor of a number, 3 is a factor of the same number.

3)  Yes, If 8 is a factor of a number, then 4 is a factor of the same number.

4) No, If 4 is a factor of a number, then 8 is not a factor of the same number.

5) Yes, all multiples of 4 are also multiples of 2.

6) No, not all multiples of 2 are multiples of 4.

7) Yes, If both 2 and 5 are factors of a number, is 10 a factor of the same number

1) Every multiple of 3 is a multiple of 6, and as such all multiples of 6 are also multiples of 3 because 3 is a factor of 6.

2) 3 is a factor of 9 because it is divisible by 9. Thus, every number that has 9 as a factor also has 3 as a factor.

3) 4 is a factor of 8 because it is divisible by 8. Thus, every number that has 8 as a factor also has 4as a factor.

4) Similar to answer 3 above, but this is not true because 8 is not a factor of 4.

5) 2 is a factor of 4 and this means that 2 is divisible by 4. Thus, all multiples of 4 must be divisible by 2 and as such all multiples of 4 are also multiples of 2.

6) Not all multiples of 2 are multiples of 4 because 4 is not a multiple of 2.

6) Yes if both 2 and 5 are factors of a number, then 10 is also a factor because 10 is divisible by 2 and 5.

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The area of the polygon is 341.1

We need to find first the base of the triangle

using Pythagorean theorem, a^2+b^2 = c^2

we have the base of 4.18

since the polygon is symmetric and regular, we have 16 same triangles within the polygon

using the area of the triangle multiply by 16 we can get 341.1

The equation for the perpendicular bisector of the given line segment is y = 2x + 2.

Here, we are given a line segment with end points (3,−7) and (−9,−1)

Thus, the slope of the line can be calculated as-

(y1 - y2)/ (x2 - x1)

= (-1 + 7)/ (-9 - 3)

= 6/ -12

= -1/2

Now, since we the slope of 2 lines that are perpendicular to each other is negative of the reciprocal, thus-

slope of the perpendicular bisector = 2

Now, the midpoint of the given line segment will be-

{(x1 + x2)/2, (y1 + y2)/2}

= {(3-9)/2, (-7-1)/2}

= {-6/2, -8/2}

= (-3, -4)

Now, we can use the point slope form to find the equation of the perpendicular bisector-

(y- y1) = m(x - x1) where m is the slope and (x1, y1) is a point on the line.

⇒ (y+4) = 2(x+3)

y + 4 = 2x + 6

y = 2x + 2

Thus, the equation for the perpendicular bisector of the given line segment is y = 2x + 2.

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Answer:

x = 2

Explanation:

The given expression is

7x - 4 - 3x = -3x + 10

First, we need to add the like terms on the left side

(7x - 3x) - 4 = -3x + 10

4x - 4 = -3x + 10

Add 4 to both sides

4x - 4 + 4 = -3x + 10 + 4

4x = -3x + 14

Add 3x to both sides

4x + 3x = -3x + 14 + 3x

7x = 14

Finally, divide by 7

7x/7 = 14/7

x = 2

Therefore, the answer is x = 2

Answer:

2.2815

Step-by-step explanation:

4563/2000 X 2 and 563/2000

The value of A = 625 ft.

What is substitution?

Substitution is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Given,

A = [tex]s^{2}[/tex]

when s = 25, A = 25(25)

A= 625 ft.

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Answer:

f(-4) = -6

Step-by-step explanation:

- From the step wise function given, -4 is in range of the first function;

[tex]{ \tt{f(x) = - {(x + 1)}^{2} + 3 }} \\ \\ { \tt{f( - 4) = - \{( - 4) + 1) {}^{2} + 3}} \\ \\ { \tt{f( - 4) = - ( - 3) { }^{2} + 3}} \\ \\ { \tt{f( - 4) = - 9 + 3}} \\ \\ { \tt{f( - 4) = - 6}}[/tex]

Answer:

f(- 4) = - 6

Step-by-step explanation:

f(- 4) with x = - 4 is in the interval - 4 ≤ x < - 1 , then f(x) = - (x + 1)² + 3

thus

f(- 4) = - (- 4 + 1)² + 3

        = - (- 3)² + 3

         = - 9 + 3

        = - 6

then f(- 4) = - 6

Answer: 3 / 8 of the puppies have red collars

Answer:

20°

Step-by-step explanation:

Exterior angle property: The exterior angle of a triangle equals the sum of opposite interior angles.

  ∠XYZ  = ∠YWX + ∠WXY

10x - 5   = 3x + 17 + 3x + 2

 10x - 5  = 3x + 3x + 17 + 2

  10x - 5 = 6x + 19

        10x = 6x + 19 + 5

        10x = 6x + 24

10x - 6x  = 24

        4x  = 24

         x   = 24÷ 4

           [tex]\sf \boxed{x = 6}[/tex]

∠WXY =  3x + 2

           = 3*6 + 2

          = 18 + 2

          = 20°

Answer:

1. False. The only term is the number of miles traveled or z

2. True 1.50 is being multiplied so it is a coefficient of z

3. False. there is no division being done.

Answer:

Step-by-step explanation:

Try to solve with a different mindset and or perspective.

Answer: Part A: 460 x 0.10

              Part B: 460/10

              Part C: 460/10 = 46

Step-by-step explanation: If the price of 10 textbooks is $460, then 1 textbook is $46.

Managers should utilize Graph 3 to stress that the defect rate has remained largely stable over the course of the year.

In graph 1, the timeline is typically placed on the horizontal axis for simplicity, and the amount to be measured is typically placed on the y-axis. The time is on the vertical axis (x-axis) in graph 1, making it a poor choice for the management. The vertical axis of time is used again in graph 2 in the same way. So using graph 2 is not a good idea.

The number of flaws in Graph 3 may be best highlighted by placing time on the horizontal axis and the quantity to be displayed on the vertical axis. Second, because the vertical axis range is less, it is simpler to see the data set on the graph rather clearly. The optimum choice is therefore graph 3.

Graph 4's vertical axis range is fairly large, which causes the dispersion or display of the data to be quite compressed and difficult to visualize. Graph 4's vertical and horizontal axes are situated correctly.

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Answer:

0.375 kilometers, or 3/8 of a kilometer.

Step-by-step explanation:

Answer: 0.375 or 3/8 of a kilometer

Step-by-step explanation:

divide the numbers

9 / 24

0.375 or 3/8 of a kilometer

Answer:

Equation of parallel line:
[tex]y = -5x + 6[/tex]

Equation of perpendicular line:
[tex]y = \dfrac{1}{5}x - \dfrac{22}{5}[/tex]

Step-by-step explanation:

Parallel lines have same slope

Slope of y = -5x + 9 is -5

Parallel line will also have slope -5

Equation is y = -5x + b where b is the y intercept to be determined

Since line passes through (2, -4) these values of x and y must satisfy the equation for the parallel line

Plugging in we get
-4  = -5(2) + b

-4 = -10 + b

b = 10 - 4 = 6

Equation of parallel line is y = -5x + 6

Perpendicular lines have slope = negative of reciprocal of each other

Original line has slope -5

Perpendicular line will have slope -(-1/5) = 1/5

Equation of perpendicular line is
y = -1/5 x + b

Plugging in (2, -4)

=>   -4 = 1/5(2) + b

=>    -4 = 2/5 + b

==> -4 - 2/5 = b

b = -22/5

Equation of perpendicular line is
y = (-1/5)x - 22/5

The number of different selections that a customer can make is of 210.

To calculate the number of different selections that the customer can make, we need to verify if the order of the selections matters or not, then:

In the context of this problem, the order does not matter, hence the combination formula is used.

The number of combinations, from a set of n elements, of x elements, is given according to the following rule:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, the number of selections is of 4 samples from a set of 10 samples, hence it is calculated as follows:

[tex]C_{10,4} = \frac{10!}{4!6!} = 210[/tex]

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One of the possible solution is x = 0 and y = 12.

The amount of money earned by washing cars is 7 dollars per hour.

The amount of money earned by landscaping is 10 dollars per hour.

The maximum number of working hours is 12.

The minimum amount of money to be earned is 90 dollars.

The number of hours of washing cars is represented by "x".

The number of hours of landscaping is represented by "y".

The inequalities formed are given below :

x + y ≤ 12

7x + 10y ≥ 90

The solution is the area which is common to both the inequalities and in the first quadrant. The graph is attached below.

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The 20 in. by 20 in. cardboard used make the box by cutting out squares of length x from the corners gives;

The dimensions that will yield maximum volume are;

Length =

The dimensions of the cut square that gives the maximum volume is approximately 3.3 feet, while the dimensions of the box are;

Length; 13.3 feet

Width; 13.3 feet

Height; 3 feet

The maximum volume of the box is approximately 592.6 ft³

The maximum value of a function is the peak or highest point on the graph of the function.

The volume, V, of a box of Length, L, Width, W and Height, H, is given by the formula;

V = L×W×H

The length, width, and height of the box obtained by cutting a square of side length, x from the corners are;

Height of the box formed = x

Length of the cardboard box = 20 - 2•x

Width of the cardboard box = 20 - 2•x

The volume of the box is therefore;

V(x) = (20 - 2•x)•(20 - 2•x)•x = 4•x³ - 80•x² + 400•x

At the maximum point, we have;

V'(x) = (3×4)•x² - (2×80)•x + 400 = 0

V'(x) = 12•x² - 160•x + 400 = 0

Which gives;

3•x² - 40•x + 100 = 0

(3•x - 10)•(x - 10) = 0

Therefore;

[tex] \displaystyle{x = \frac{10}{3} }[/tex] and x = 10

When x = 10, we have;

V(10) = 4×10³ - 80×10² + 400×10 = 0

When x = 10/3, we have;

V(10) = 4×(10/3)³ - 80×(10/3)² + 400×(10/3) ≈ 592.6

Therefore, the dimensions of the box that gives the maximum volume is [tex] \displaystyle{x = \frac{10}{3} \approx 3.3}

The dimensions that yield maximum volume are therefore;

The maximum of the box is 592.6 ft³

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There is no real solution for the equation X√x + 7x + 10.

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind. For instance, factorizing the number 15 as 3 5

Solve  X√x + 7x + 10 for x.

Subtract 7x from both sides

X√x + 7x + 10 - 7x = -7x

X√x + 10 =  -7x

Subtract 10  from both sides

X√x + 10 - 10 =  -7x - 10

X√x = -7x - 10

Divide both sides by √x

X√x / √x  = (-7x - 10) / √x

x =  (-7x - 10) / √x  

The defined range

(0 , ∝)

Hence, The equation Xx + 7x + 10 has no actual solution.

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Answer:B 66.72

Step-by-step explanation:

complementary means if two angles are added up they will equal 90. we and eliminate d cause 23.28+23.28=46.56 so d is wrong now let's try c 46.56+23.28=69.84 so c is wrong cause it doesn't equal 90 now let's try a 156.72+23.28=180 its wrong since we are using complementary angles instead of supplementary angles Supplementary are angle two angles that add up to 180. so that just leaves b cause 23.28+66.72=90. i hope this helps and i made sure to explain it as best as i can have a great day

The solution is Option B.

The measure of the complementary angles are 66.72° and 23.28°

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.

Let the first angle and second angle be a and b respectively such that

a + b = 90°

Given data ,

Let the first angle be represented as A

Now , the value of A is = 23.28°

Let the second angle be represented as B

Now , the value of B is = B

The angles A and B are complementary ,

So , A + B = 90°   be equation (1)

Substituting the values in the equation , we get

23.28° + B = 90°

On simplifying the equation , we get

Subtracting 23.28° on both sides of the equation , we get

B = 90° - 23.28°

B = 66.72°

Therefore , the value of B is 66.72°

Hence , the measure of the angle is 66.72°

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The area of the clock  = 315.41 inch[tex]squre[/tex]

The clock's face has been provided to us, and it is =  63 inch

Explanation?

The clock's face has been provided to us, and it is =  63 inch

So the circumference of the clock is also that amount.

given that the clock has a circular shape.

[tex]2\pi (r)= 63inch[/tex]

So

We will use this information to compute the radius[tex](r)[/tex] (of the circular clock.

Then

[tex]2\pi (R) = 63 inch =63/2\pi =10.2 inch[/tex]

The area of the circle equation will now be changed to include this value of (r) in order to obtain the area of the clock.

Now  

[tex]\pi ( r)^{2} = \pi (10.02)^{2} = 315.41 in^{2}[/tex]

The area of the clock's face is therefore = [tex]315.41in^{2}[/tex]

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Answer:

F

Step-by-step explanation:

The shape ABCD is reflected over the given line. If you were to fold the shape over to overlap the new figure FGHI, point A would correspond with point F

Answer:  F.

Step-by-step explanation:

because that's the answer.

Using BODMAS, the resultant answer of the given expression is 81.4.

Given, problem is (5.44×10−4)+(3.6×10−5):

First, solve inside the brackets, and will start with multiplication.

We get,

now, solving the values inside the brackets, we get

Now, we will open the brackets and apply addition, we get

Hence, the value is given by 81.4.

Therefore, using BODMAS, the resultant answer of the given expression is 81.4.

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6.72 liters per 100km

35 miles per gallon is 6.7204 liters per 100 kilometers

Here given ,

1 mile = 1.609km

1 gallon = 4.546 liters

We have to find 35 MPG to L/100km,

35 miles per gallon = 6.7204 liters per 100km

6.7204 to 3 significant figures = 6.72 liters per 100km

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Answer:

20m

11m

20m2

5m

11m

8x8

11x2

Given:

Principal amount = P (o

Interest = 0.6% = 0.006 (divide by 100 since it's in percentage)

The algebraic expression is:

P + 0.006P = 1.006P

ANSWER:

P + 0.006P = 1.006P

For the given data set the frequency of the number in the range of 16 – 20 will be 6.

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell by the total frequency.

It is given that frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.

Calculate the frequency of each class by counting the tally marks. The proportion of data items in a data class is its relative frequency.

The table shows the value and the frequency of all the numbers. It is obtained that the values occur in the range of 16 and 20 is 6.

Thus, for the given data set the frequency of the number in the range of 16 – 20 will be 6.

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The corresponding equation is 4q + 3p = 22.

What is the slope of a line ?

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.

Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.

Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.

m = (y2 - y1)/(x2 - x1)

34 = (q - 1/2)/-8 - p

-24 - 3p = 4q - 2

4q + 3p = 22

The corresponding equation is 4q + 3p = 22.

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