What is the distance on a number line between 17 and −9.

Answer:

Step-by-step explanation:

We know:

If a ≤ b ≤ c are the sides of a triangle, then a + b > c.

We have a = x, b = 2x and c = 15 cm.

Therefore x ≤ 15 and 2x ≤ 15 ⇒ x ≤ 7.5

Therefore we have the inequality:

x + 2x > 15

3x > 15          divide both sides by 3

x > 5 and x ≤ 7.5

Finally x = 6

Answer:

4 ft

Step-by-step explanation:

12 ft - 8 ft = 4ft

Best regards

Answer:

The answer should be A) be square root of 11 is 3.3

Step-by-step explanation:

Answer:

1. Volume of cube-shaped box = 91.125 cubic inches

2. Volume of shipping box = 729 cubic inches

3. 8 boxes of office supplies can be packed into the larger box for shipping.

Step-by-step explanation:

1.

The first question asks for the volume of a cube. The formula is  V = s^3, where, s is the side length and V is the volume. Thus plugging in, we get:

[tex]V=s^3\\V=(4\frac{1}{2})^3\\V=(4.5)^3\\V=91.125[/tex]

Volume of cube-shaped box = 91.125 cubic inches

2.

The second question asks for the volume of the shipping box. Since 3 measurements are given, the shipping box is a rectangular prism. The volume of a rectangular prism is  V = l * w * h, where

V is the volume

l is the length

w is the width, and

h is the height

Plugging in all the info we know (multiplying the 3 numbers - dimensions), we can get the volume of the shipping box. So:

[tex]V=lwh\\V=(18)(9)(4\frac{1}{2})\\V=(18)(9)(4.5)\\V=729[/tex]

Volume of shipping box = 729 cubic inches

3.

Since the volume of a single box of office supplies (cub-shape) is 91.125 cu. in., and the volume of larger shipping box is 729, we can divide 729 by 91.125 to find how many of them would fit the large box.

[tex]\frac{729}{91.125}=8[/tex]

Hence, 8 boxes of office supplies can be packed into the larger box for shipping.

Answer:

8

Step-by-step explanation:

4 1/2=9/2*9/2=81/4*9/2=729/8

9/1*9/2*18/1=1,458/2

1,458/2*8/729=11,664/1,458

=8

So eight boxs of office supplies can be packed.

Answer: B

Step-by-step explanation:

If she bought 9 packs of pens at 2.50$ each then she spent 22.50$ on pens. If you add up the packs and multiply by the price you get your answer. 2.50 * (2+3+4) = 22.50$

Answer:

Volume of cube= a^3

=(2/√3)^3

=8/3√3 cubic units. (~1.5396 cubic units)

Step-by-step explanation:

Such a cube has diagonal lengths (DF, AG, EC & HB)=diameter of sphere=2 units.

Let the sides of the cube (FG, GC, CB, BF, etc.) be 'a'.

Hence facial diagonal of the cube (FC, BG, FH, etc.) will be √2a (Pythagoras' Theorem).

Applying Pythagoras' theorem for △DFC:

FC²+DC²=FD²

⇒(√2a)²+a²=2²

⇒3a²=4

⇒a=2/√3 units

Answer:

a. 267 hrs b.

Step-by-step explanation:

a.)4 secs divided by 5 gals is .8 secs per gal, multiply by 20,000 gals, is 16,000 secs, divide that by 60 secs in an hour and you get 266.666 hrs

b.)42 hrs with both hoses

.8 secs per gal and 7.2 secs per gal = 8 secs per gal

20,000 = 8 gals per hour = 2500 secs  divided by 60 secs per hour = 41.66

Answer:

The radius of the cone is [tex]5\ ft[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

In this problem we have

[tex]V=50\pi\ ft^{3}[/tex]

[tex]h=6\ ft[/tex]

substitute in the formula and solve for r

[tex]50\pi=\frac{1}{3}\pi r^{2}(6)[/tex]

Simplify

[tex]25=r^{2}[/tex]

square root both sides

[tex]r=5\ ft[/tex]

Answer:

5ft

Step-by-step explanation:

I did the test

The correct option is c.

The area of the figure is [tex]\( 320 \)[/tex] square millimeters.

To find the area of the given figure, which is composed of a triangle and a rectangle, follow these steps:

1. Calculate the area of the rectangle: The area of a rectangle is found by multiplying the length by the width. From the figure, we see that the length is 20 mm and the width is 15 mm. So, the area [tex]\( A_{\text{rectangle}} \)[/tex] is:

[tex]\[ A_{\text{rectangle}} = \text{length} \times \text{width} = 20 \, \text{mm} \times 15 \, \text{mm} \][/tex]

2. Calculate the area of the triangle: The area of a triangle is found by using the formula [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \)[/tex]. The base of the triangle is 20 mm (same as the length of the rectangle) and the height, which is the perpendicular distance from the base to the opposite vertex, is 2 mm. So, the area [tex]\( A_{\text{triangle}} \)[/tex] is:

[tex]\[ A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \, \text{mm} \times 2 \, \text{mm} \][/tex]

3. Add the areas of the rectangle and triangle to find the total area: The total area [tex]\( A_{\text{total}} \)[/tex] is the sum of [tex]\( A_{\text{rectangle}} \)[/tex] and [tex]\( A_{\text{triangle}} \)[/tex].

 [tex]\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} \][/tex]

Now let's calculate the areas with the given dimensions.

The area of the rectangle is [tex]\( 300 \)[/tex] square millimeters, and the area of the triangle is [tex]\( 20 \)[/tex] square millimeters. Adding these together gives us the total area of the figure:

[tex]\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 300 \, \text{mm}^2 + 20 \, \text{mm}^2 = 320 \, \text{mm}^2 \][/tex]

Therefore, the answer is [tex]\( 320 \)[/tex] square millimeters.

The options are give here:

A. 175 square millimeters.

B. 200 square millimeters.

C. 320 square millimeters.

D. 350 square millimeters.

Answer:

The absolute number of a number a is written as

|a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation

|x|=a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

|x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

or

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality

|x|<2

Represents the distance between x and 0 that is less than 2

picture42

Whereas the inequality

|x|>2

Represents the distance between x and 0 that is greater than 2

picture43

You can write an absolute value inequality as a compound inequality.

$$\left | x \right |<2\: or

−2<x<2

This holds true for all absolute value inequalities.

|ax+b|<c,wherec>0

=−c<ax+b<c

|ax+b|>c,wherec>0

=ax+b<−corax+b>c

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

Sorry If its not what your looking for but i tried

Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems.

Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems. Here's how you can do it:

Representing Constraints with "less than" or "greater than" inequalities:

Suppose you have a variable "x" and a fixed value "a." If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than some constant "k," you can write it as:

| x - a | < k

For example, if you want to constrain "x" to be within 3 units from 5, you write:

| x - 5 | < 3

Representing Constraints with "less than or equal to" or "greater than or equal to" inequalities:

If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than or equal to some constant "k," you can write it as:

| x - a | ≤ k

For example, if you want to constrain "x" to be within 2 units from 8, you write:

| x - 8 | ≤ 2

Using absolute value equations allows you to handle situations where the variable needs to be close to a certain value or within a specific range, regardless of whether it is greater or smaller than that value. This flexibility is particularly useful in various mathematical and optimization problems, including linear programming and constrained optimization.

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Answer:

[tex]\large{\boxed{\text{the multiplication property of equality}}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x}{5}+5=20\qquad\text{subtract 5 from both sides}\\\boxed{\text{the subtraction property of equality}}\\\\\dfrac{3x}{5}+5-5=20-5\\\\\dfrac{3x}{5}=15\qquad\text{multiply both sides by}\ \dfrac{5}{3}\\\boxed{\text{the multiplication property of equality}}\\\\\dfrac{3\!\!\!\!\diagup^1}{5\!\!\!\!\diagup_1}\cdot\dfrac{5\!\!\!\!\diagup^1x}{3\!\!\!\!\diagup_1}=\dfrac{5}{3\!\!\!\!\diagup_1}\cdot15\!\!\!\!\!\diagup^5\\\\x=(5)(5)\\\\x=25[/tex]

Answer: C

Step-by-step explanation:

Answer:

X is equal to 0.18

Step-by-step explanation:

X is that number

then

2X equal to 0.36

X equal to 0.36 divided 2

X is equal to 0.18

Best regards

Answer:

1. A(3/2,6)

B(15,33)

2.A(2/9,1/3)

B(2/3,-1/3)

Step-by-step explanation:

1) y−2x=3; A(...; 6), B(15; ...)

We know y =6

Substitute this into the equation

6 -2x =3

Subtract 6 from each side

6-6 -2x=3-6

-2x = -3

Divide by -2

x = -3/-2

x = 3/2

A(3/2,6)

We know x = 15

y - 2(15) =3

y - 30 = 3

Add 30 to each side

y-30+30 = 3+30

y = 33

B(15,33)

2) 4.5x+3y=2; A(...; 1/3 ), B( 2/3 ; ...)

We know y = 1/3

4.5x + 3(1/3) = 2

4.5x +1 =2

Subtract 1 from each side

4.5x +1-1=2-1

4.5x = 1

Divide each side by 4.5

x = 1/4.5

x = 10/45

x =2/9

A(2/9,1/3)

Let x =2/3

4.5(2/3) +3y =2

3 +3y =2

Subtract 3 from each side

3-3+3y = 2-3

3y = -1

Divide by 3

y = -1/3

B(2/3,-1/3)

Answer:

1. A(3/2;6) B(15;33)

slope=2

2. A(2/9;1/3) B(2/3;-1/3)

slope=-1.5

Step-by-step explanation:

Hope this helps,

Have a great day

Answer:

See attached picture.

y-intercept at (0,5) and asymptote at y = 4.

Step-by-step explanation:

This graph has a base 3/4 that is less than 1. This means it will start high and end low.

It has also been shifted up 4 units by adding 4. This means the asymptote moves to from y = 0 to y =4. The y-intercept of the parent function will also move from (0,1) to (0,5).

it is a function because each input (x) has a unique output (y) that is not repeated

In order for a relationship between numbers x and y to be considered a function from x to y, you need to have one unique y for every x. This doesn’t mean that each y needs exactly one x; for instance, the function y = x² is a function from x to y and has two y values associated with most x values (x = 2 and x = -2, for instance, both give you y = 4).

Essentially, if we give a function some x value, we want to know exactly what y value we’re getting out of it.

The pictured table gives you two possible values for x = 2; given a 2 as input, we have no idea whether to go to 1 or 7 for our output, so it would not be a function from x to y.

(Interestingly, a function from y to x would satisfy that “one output per input” requirement, so if you wanted to impress your teacher, you could answer “yes, but only from y to x, NOT x to y”)

Answer:

correct option is F

Step-by-step explanation:

Suppose there is a book the cost of which is $100

You got  successive discounts of 15% off and then 25% off

So after getting 15% discount cost of book=$85

again on $85 there is a discount of 25%

it means

25% discount on $85=[tex]\frac{25\times 85}{100} \\[/tex]

=$21.25

It means after successive discounts of 15% off and then 25% off cost of book=[tex]85-21.25[/tex]

after successive discounts of 15% off and then 25% off cost of book=$63.75

On the other hand if you got 40% discount on the same book which costs $100

then after discount of 40% its cost will be=$60

It means,Taking successive discounts of 15% off and then 25% off is not same as taking a one time discount of 40%.

Therefore correct option is F

Answer:

false

Step-by-step explanation:

got it right on edg

Answer:

OPTION B:  [tex]2(3x+5)[/tex]

Step-by-step explanation:

To solve the exercise you can simplify the expression given in the problem, as following:

- Add the like terms:

[tex]3x+3x+5+5\\6x+10[/tex]

- Find the greatest common factor (GCF) of 6 and 10:

[tex]6=2*3\\10=2*5\\\\GCF=2[/tex]

- Factor ir out.

Then, you obtain the following equivalent expression:

[tex]2(3x+5)[/tex]

Answer:

6x + 10

Step-by-step explanation:

Combine like terms:

3x + 3x = 6x, and

5+5 = 10

and so the final sum is 6x + 10

Answer:

Step-by-step explanation:

What you are trying to do is a nice way to solve this problem. Without knowing any physics, you are using what math you know to get the answer. You are actually very close to being correct, and you are right. You do have to divide by 60.

Here's why and it is the one bit of physics you have to know.

The speed is km/hour. That word hour is the culprit. Your time is in minutes and you have to get it into hours. In physics, the units have to be consistent.

So ...

b1 = 19 minutes which is 19 min [1 hour / 60 minutes] = 19/60 = 0.31667 hour

b2 = 26 minutes which is 26 min [ 1 hour/60 minutes] =  26/60 = 0.4333 hour

h = 40 km/hour

Area = (0.31667 hour + 0.4333 hour)*40 km/hour /2

Area = 0.75 hour * 40 km/hr //2

Area = 15 km

Answer:

C. 27 40 cubic yard

Step-by-step explanation:

The base area is 9 10 square yard and a height of 3 4 yard.

Volume of the prism will be given by the formula;

= Base area × height

=  9 10 square yard × 3 4 yard

= 27 40 cubic yard

is their operations that you didnt list

Answer: The answer is, 20x7y9z8.

Step-by-step explanation:

Answer:

angle = 35 degrees

Step-by-step explanation:

The rocket traveled

5 miles in the       x direction

3.5 miles in the    y direction

The rocket was launched with a slope of

m =y/x = 3.5 miles / 5 miles   = 0.7

The slope is equal to the tangent of the angle of elevation

tan (angle) = m

angle  =  tan^-1 (0.7)

angle = 34.99 ≈ 35 degrees

To determine the angle of elevation, we use the tangent function: the angle θ is the arctan of the altitude over the horizontal distance, which is approximately 35 degrees.

The angle of elevation that the rocket was launched at can be determined using trigonometric functions. Specifically, we can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side (altitude in this case) over the adjacent side (horizontal distance).

The formula is:

tan(\(\theta\)) = \(\frac{{opposite}}{{adjacent}}\).

So, the angle \(\theta\) is:

\(\theta = tan^{-1}\left(\frac{{3.5 \text{{ miles}}}}{{5 \text{{ miles}}}}\right)\).

Using a calculator, we find that:

\(\theta\approx 35.0^\circ).

The rocket was thus launched at an angle of approximately 35 degrees.

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Answer:

Step-by-step explanation:

The perimeter of the given figure is equal to the circumference of whole circle.

The formula of a circumference of a circle:

[tex]C=\pi d[/tex]

d - diameter

We have d = 70 cm. Substitute:

[tex]C=70\pi\ cm[/tex]

The area of given figure is equal to the area of rectangle 70cm × 35cm.

(look at the picture).

The area of a rectangle:

[tex]A=(70)(35)=2,450\ cm^2[/tex]

Answer:

y = (-1/8)x + 10.5

Step-by-step explanation:

The given equation is y = 8x -1.  The slope is 8.

Any line perpendicular to the given equation/line has a slope which is the negative reciprocal of 8:  That would be -1/8.

We'll use the point-slope formula of a straight line to come up with a formula for this specific problem:   y - k = m(x - h), where (h, k) is the point in question and m is the slope.

Here we have y - 10 = (-1/8)(x - 4).  This is complete in itself,  But you could also present it in more compact form, as follows:

Add 10 to both sides.  We get y = (-1/8)(x - 4) + 10.

Perform the indicated mult.:  y = (-1/8)x + 1/2 + 10, or

                                                y = (-1/8)x + 10.5

Square, Rectangle and Rhombus

Answer:

C

Step-by-step explanation:

1/2 is positive unlike the other two so it is obviously last.

Now it's between -3/4 and -2/3

-3/4 = -0.75

-2/3 = -0.67

Since -0.75 < -0.67, -3/4 is first and -2/3 is second.

Answer:

Your answer would be C.

Step-by-step explanation:

Answer:

Part a) The weight of the original statue is [tex]9,483\ pounds[/tex]

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is [tex]8.4^{3}[/tex]

Part b)  [tex]221,184\ pounds[/tex]

Step-by-step explanation:

Part a)

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its volumes or weights is equal to the scale factor elevated to the cube

step 1

Find the scale factor

remember that

[tex]1\ ft=12\ in[/tex]

The original statue is 7 ft tall

Convert to inches

[tex]7\ ft=7*12=84\ in[/tex]

Divide the height of the original statue by the height of the model to find the scale factor

[tex]\frac{84}{10}=8.4[/tex]

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=8.4[/tex]

[tex]y=16\ lb[/tex]

substitute

[tex]8.4^{3}=\frac{x}{16}[/tex]

[tex]x=16(8.4^{3})=9,483\ pounds[/tex]

The weight of the original statue is [tex]9,483\ pounds[/tex]

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is [tex]8.4^{3}[/tex]

Part b) If the original statue were 20 ft tall, how much would it weight?

step 1

Find the scale factor

remember that

[tex]1\ ft=12\ in[/tex]

The original statue is 20 ft tall

Convert to inches

[tex]20\ ft=20*12=240\ in[/tex]

Divide the height of the original statue by the height of the model to find the scale factor

[tex]\frac{240}{10}=24[/tex]

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=24[/tex]

[tex]y=16\ lb[/tex]

substitute

[tex]24^{3}=\frac{x}{16}[/tex]

[tex]x=16(24^{3})=221,184\ pounds[/tex]

(2b^3 -7b^2) + (3b^2 + 3b^3) =

2b^3 + 3b^3 -7b^2 + 3b^2=

5b^3 -4b^2

Answer:

3x + 20 = 152

x= 44

Step-by-step explanation:

Answer:

The one that stands out as incorrect is B

Step-by-Step Explanation:

I'll assume that by 12, you meant 1/2 because if the scale factor is 12, then none of the choices are correct. B is the only one that stands out because while in the x, 10 does turn into 5 after being multiplied by 1/2, the 2 in the y remained the same instead of being turned into 1.

Answer:

This figure is dilated by a factor of 12, with the origin as center.  

Which statement is NOT correct?

A)R(2, 8) → R'(1, 4)

B)Q(10, 2) → Q'(5, 2)

C)P(2, -4) → P'(1, -2)

 D)S(-10, 2) → S'(-5, 1)

​

Step-by-step explanation:

As you can see in A,C and D, the x-coordinate and the y-coordinate is divided by 2.

E.g.  2 / 2 =1     8/2=4    so ⇒R'(1, 4)  

but in B, the first x-coordinate is divided by 2 but the y-coordinate is divided by 1.

Answer:

x = 5

Step-by-step explanation:

As you know 32 = 2^5

so

2^x = 32

2^x = 2^5

Since both have same base 2

x = 5

32=2^x

Prime factors of 32

32 = 2 * 16

16 = 2 * 8

8 = 2 * 4

4 = 2 * 2

32 = 2*2*2*2*2

32 = 2^5

x=5

Hope this helps :)