Evaluate.

{3−[−4−(6+2)]}⋅(−5)

A−75

B−57

C−15

D−9

Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.Option C is correct.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Cheryl traveled at a steady pace for 5.5 minutes, then 45 mph for 2.5 minutes after traveling at 65 mph for a minute.

Statement C best describes Cheryl's commute.

Hence option C is correct.

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Answer:

The Father is currently 47 and the Son is 7

Step-by-step explanation:

Let F and S be the present ages of Father and Son, respectively.

We are told that (F-2) = 9(S-2) [2 years ago, father age was nine times the son age]

We also learn that (F+3) = 5(S+3)  [3 years later it will be 5 times only]

Take the first expression and isolate one of the variables (S or F).  I'll isolate F:

(F-2) = 9(S-2)

F = 9S - 16

Now use this in the second expression:

(F+3) = 5(S+3)

((9S-16)+3) = 5(S+3)

9S-13 = 5S+15

4S = 28

S = 7

Since F = 9S-16,

F = 9*(7)-16

F = 47

Father is 47 and Son is 7

CHECK:

Was the father 9 times the age of his son 2 years ago?

Father would have been 45 and son 5.  Yes, 9*5 = 45

In 3 years will he be 5 times older than his son?  Yes, Father would be 50 and son would be 10.  5*(10) = 50

Answer:

89

Step-by-step explanation:

A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x) = (x - 1)(x + 2)(x − 3), therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.

Hence, the zeroes of the functions are -2, 1, and 3.

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Answer:

−1, 2, −3; continues downward to the left and upward to the right

Step-by-step explanation:

Answer:

(n/m) - p

Step-by-step explanation:

Image attached

The required slope of the line given by m = -3/4.

The slope of the given y = -3/4x+2 is m, the line passes from (0, 2) and (4, -1)

A line can be defined by a shortest distance between two points is called as a line.

equation of the given line is |

 y =[tex]\frac{-3}{4}[/tex]x + 2

slope of the given line is given by comparing it to standard equation
y = mx + c
by comparing
m= -3/4
Which required slope of the line.
Since we have two points on line begin or end point (0, 2) and (4, -1) respectively. This satisfies the equation while putting it into the equation.

Thus the required slope of line   y =[tex]\frac{-3}{4}[/tex]x + 2is given by  m= -3/4 , This line passes through points  (0, 2) and (4, -1).

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The volume of the square pyramid is the one-third of the square prism with same height and base area. Then the volume of the pyramid will be 120 cubic cm.

Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

The volume of the square prism will be

V = (L × B × H)

Then the volume of the square pyramid is the one-third of the square prism with same height and base area.

[tex]\rm V_{pyramid} = \dfrac{V_{prism} }{3}[/tex]

A rectangular prism has a square base with a width of 6 and a volume of 360 cm³.

If a square pyramid has a base with the same width and height.

Then the volume of the pyramid will be

V = 360 / 3

V = 120 cubic cm

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Answer:

15 rounded to the nearest whole number is 15 since it’s already a whole number.-

Step-by-step explanation:

Answer:

1728 cm³

Step-by-step explanation:

 Finding the volume of a cube is a simple process that is easy to remember. The formula for finding the volume of a cube is commonly taught as L × W × H (Length × Width × Height). This formula also works with finding the volume of rectangular prisms.

 Since the shape you're finding the volume of is cube, the length is equal to its width as well as its height.

 The first step of this problem is to plug in known values to the formula. Since length L = 12 cm, width W and height H are also equal to 12 cm.

 12 × 12 × 12 is the new expression. The next step is to simplify this expression by multiplying.

 Based on times tables, 12 × 12 = 144. So, the expression can be partially simplified to 144 × 12 for easier multiplication.

 144 × 12 can be split into an addition problem based on the Distributive Property of Multiplication:

144 × (10 + 2)              Expand the expression to remove parentheses.

144 × 10 + 144 × 2       Multiply 144 × 10 and 144 × 2.

1440 + 288                 Add the two addends.

1728                            Remember to add back the units!

1728 cm³

The volume of a cube with side lengths of 12cm is 1728 cm³.

Note:

This step-by-step explanation is for better understanding how to do this mentally or without a calculator. In a calculator, finding the volume of a cube can be found by inputting either of these:

(Side Length) × (Side Length) × (Side Length) =

(Side Length) [(x³) or (³), depending on the model of calculator] =

1) [tex]\overline{RS} \perp \overline{ST}, \overline{RS} \perp \overline{SQ}, \angle STR \cong \angle SQR[/tex] (given)

2) [tex]\overline{RS} \cong \overline{RS}[/tex] (reflexive property)

3) [tex]\angle RST[/tex] and [tex]\angle RSQ[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle RST \cong \triangle RSQ[/tex] (AAS)

The correct simplification of the expression is  4x¹⁴y¹⁷

Given,

The expression is (2x⁷ y)² (y⁵)³

To distribute the exponent, apply the power rule (ab)ⁿ = aⁿbⁿ

Implement the product rule to (2x⁷y)².

Here, we have a = 2x⁷ , b = y and n = 2

=(2x⁷)² y²(y⁵)³

= 2²(x⁷)² y²(y⁵)³

= 4(x⁷)² y²(y⁵)³

Now exponents should be multiplied while using the product rule.

The product rule is (aˣ)ⁿ = aˣⁿ

We apply this to (x⁷)² and (y⁵)³

So the expression becomes,

=4x⁷·² y² (y⁵·³)

= 4x¹⁴ y² y¹⁵

∵ In exponents we have a rule that if bases are same then powers are added i.e, aˣ aⁿ = aˣ⁺ⁿ

∴ 4x¹⁴ y¹⁵ ⁺ ²

= 4x¹⁴ y¹⁷

Hence we get the answer as 4x¹⁴ y¹⁷

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The length and width of the rectangle are: [tex]2x^2y^2 , 3xy^3[/tex]

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The area of a rectangle is represented by the expression [tex]6x^3y^5[/tex].

The area of the rectangle = [tex]2x^2y^2 \times 3xy^3[/tex]

                                          = [tex]6x^3y^5[/tex]

So, the length and width of the rectangle are: [tex]2x^2y^2 , 3xy^3[/tex]

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Answer:

$2

Step by Step:

Four quarters is one dollar

Four quarters is 8 pennies

Multiply 8 by 25 (25 being the value of the quarters)

25 cents is times four is one dollar

.25x4=1, 25x4=100, 100x.25=25

2x4=8 8x25=200

A pound of pennies is worth $12.5.

In mathematics, multiplication is one of the basic operations where one number is multiplied or added repeatedly to itself as times as that of the other number. Multiplication of two numbers a and b is represented as "a × b", read as a multiplied to b or a times b.

For example 2 multiplied to 4 implies that 2 is added to itself like 4 times (2+2+2+2) or 4 is added to itself 2 times (4+4).

We have from the question,

1 quarter = 2 pennies

Also, it is given that,

A pound of quarters = $25

Since 1 quarters = 2 pennies, we have,

A pound of 2 pennies = $25

A pound of 1 penny = 25 / 2

                                 = 12.5

Hence we have a pound of pennies worth $12.5.

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Answer:

No

Step-by-step explanation:

I will not do hard questions

the total area of the figure A = 144.5 cm²

First, the area of a rectangle of length L and width W is:

A = W*L

Here we have:

L = 13cm

W = 9cm

Then the area is:

A = 9cm*13cm = 117 cm²

For a triangle of height H and base B, the area is:

A = B*H/2

Here the base measures 11cm, and the height is:

H = 13cm - 8cm = 5cm

So the area of the triangle is:

A= 5cm*11cm/2 = 27.5cm²

Then the total area of the figure is:

area =  27.5cm² +  117 cm² = 144.5 cm²

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Answer:

38.4 miles per hour

Step-by-step explanation:

30 miles in 45 minutes

18 miles in 30 minutes

Average speed =   total distance / total time

                          =    (30+18) / ( 45 min + 30 min)

                          = 48 miles / ( 1.25 hr ) = 38.4 miles per hour

An equation is formed of two equal expressions. The number of sections that Mario can cut from the rope is 6.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of 8 1/4 - inch sections of rope Mario can cut from the rope be x.

Since the total length of the rope is 7 feet, which is equal to 84 inches(1 foot=12 inches), the instructions are to use 34.5 inches of the rope to tie a tarp on top of the tent. Therefore, the rope for the 8 1/4 inches section is,

Rope left = 84 inches - 34.5 inches

Since the length of a single section is 8 1/4 inches(8.25 inches), therefore the number of sections that can be made from the remaining section is,

The number of sections, n = Rope left/8.25 inches

                                             = (84 -34.5)inches /8.25 inches

                                              = 6

Hence, the number of sections that Mario can cut from the rope is 6.

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Answer:

2y + 3 = 4y + 2; y = 1/2

Step-by-step explanation:

to find this equation we can use the ys and the 1s to create an equation

so

in the left side

there are 2 ys and 3 1s

your equation is

2y + 3

on the other side

it is

4 ys and 2 1s

so

4y + 2 is your equation

then yo uset them equal to each other

2y + 3 = 4y + 2

if you must solve

subtract 2y and 2 from both sides

1 = 2y

then divide both sides by 2

y = 1/2 is your answer

Answer:

The number is 32

Explanation :

Let the 2 number digit be 10x + z

Solution:

X-z=1

(10x+z+8) / (x+z) =8

10x+z+8=8x+8z

2x-7z-(2x-2z)=-8-2

-5=-10

Z = 10/5

Z =2

X=1+2

X=3

10×3+2 = 30 +2 = 32

The answer is 32

Answer:

Step-by-step explanation:

All you have to do is add the four sides together and that should be your answer.

(B.) 4√37 units

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The values that make v >= 1 true are 2, 3, 4, 5....

The inequality is given as:

v >= 1

Rewrite properly as:

v ≥ 1

The above means that the true values of v are values greater than 1.

Hence, the values that make v >= 1 true are 2, 3, 4, 5....

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Answer:

See below

Step-by-step explanation:

The first one IS decay...as 'x' increases the function decreases

the second and third are NOT ...as 'x' increases the value increases

radioactive decay IS decay (obviously)

the one with e^2x   is not ....it grows exponentially as x grows

and finally the last one is decay because as x gets larger the value of y gets smaller

Answer:

[tex]\textsf{A)}\quad y=-\sqrt{x}+2[/tex]

Step-by-step explanation:

Parent function:

[tex]y = \sqrt{x}[/tex]

The properties of the parent function are:

From inspection of the graph, as the x-values increase, the y-values decrease. Therefore there has been a reflection in the x-axis.

The y-intercept is now at (0, 2), therefore the function has been translated 2 units up.

Translations

For a > 0

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

Therefore:

Reflected in the x-axis:  [tex]-f(x)=-\sqrt{x}[/tex]

Then translated 2 units up:  [tex]-f(x)+2=-\sqrt{x}+2[/tex]

So the equation that represents the transformed function is:

[tex]y=-\sqrt{x}+2[/tex]

i. Cube of any odd number is even. False

ii.  A perfect cube does not end with two zeros. True

iii.  If square of a number ends with 5, then its cube ends with 25. False

iv. There is no perfect cube which ends with 8. False

v. The cube of a two digit number may be a three digit number. False

vi.  The cube of a two digit number may have seven or more digits. False

vii. The cube of a single digit number may be a single digit number. True

i.  Cube of any odd number is even. This statement is false because the cube of odd numbers are also odd

ii.  A perfect cube does not end with two zeros. This statement is True because the cube of a two digit number cannot be a 3 digit number and therefore cannot end with two zeros.

iii.  If square of a number ends with 5, then its cube ends with 25. This statement is False

Using the illustration

35^2 = 35 x 35= 1225 , its square ends with 5

35^3= 35 x 35 x 35= 42875 which ends with 75

iv.  There is no perfect cube which ends with 8. This statement is False.

Using the illustration, the cube of 2 is given thus

2 * 2 * 2 = 8

The cube of 2 ends with 8

v. The cube of a two digit number may be a three digit number. This statement is False.

Using the illustration, 10 is a two digit number

10 * 10 * 10 = 1000

The cube of 10 which is a two digit number is not a three digit number and same applies to all two digit numbers

vi  The cube of a two digit number may have seven or more digits. This statement is False because the cube of a two digit number can only be a four digit number.

vii. The cube of a single digit number may be a single digit number. This statement is True because the cube of a single digit number can be a single, two or three digit number.

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Answer: 7/8

What you have to do here is to find the highest number which can be divided by both. Or you have to divide both the numerator and denominator until it can not be divided by any number anymore. You can do this by finding the highest common factor (HCF) of both the number, 35 and 40.

Highest Common Factor: HCF of two or more numbers is the greatest factor that divides the numbers. For example, 2 is the HCF of 4 and 6.

So, the highest number which divides 35 and 40, is 5. Now 35 divided by 5 is 7 and 40 divided by 5 is 8. The final answer is 7/8 and there is no more numbers which can divide both of them by a specific number.

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Answer:

  f(-2) = 0

Step-by-step explanation:

The value of the function for a particular x-value can be read from the graph.

The graph is a map showing the value of f(x) for each value of x for which the function is defined. The x-values are identified by the numbers on the horizontal x-axis. The corresponding function values are found by referencing the vertical y-axis.

To find the function value f(x) for x=-2, we locate the vertical grid line marked with -2 at the x-axis. We then locate the point on the graph of the function where it crosses that vertical grid line. Tracking horizontally from that point to the vertical y-axis, we can read the function value from the vertical scale.

The attachment has a red arrow pointing to the intersection of the graph with the grid line x=-2. That point of intersection lies on the x-axis, where the y-value is 0. That means ...

  f(-2) = 0

__

Additional comment

On this graph, the axis crossing point (x=0, y=0) is not labeled. It is halfway between x=-1 and x=1. Similarly, it is halfway between y=-1 and y=1. Based on this and on experience with similar graphs, you can assume that the axis crossing has coordinates (x, y) = (0, 0).