A prism with a rectangular base.
Complete the statements about the figure shown.
The figure is a ___ prism.
A lateral face of a solid is any face that is not a base. The prism has ___ lateral faces.

Answer:

hope this help

Step-by-step explanation:

10x + 4 = 10x + 16 -12 = 10x + 4

infinite solution of x ( for x is real number)

Answer:

The answers are;

a. None

b. None

c. Infinite

d. None

e. None

Step-by-step explanation:

The number of non congruent triangles that can be drawn depends on the uniqueness of the triangle

The parameters of a unique triangle are;

Knowing the Side Side Side (SSS)

Knowing the Side Angle Side (SAS)

Knowing the Angle Side Angle (ASA)

Knowing the Angle Angle Side (AAS)

However, knowing only the Side Side Angle it is possible to draw two non-congruent triangles

Therefore, considering each of the triangles gives;

a. Sides 7 inches, 8 in., and 16 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided properties

b. Similarly, the given triangle parameters are 4 in., 4 in., and 6 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided information

c. The parameters of the triangle given here are angles 30°, 60°, and 90° which is of the form Angle Angle Angle, or AAA for which the sides can be scaled to form an infinite number of non-congruent triangles

d. The parameters given are three angles measuring 120° which does not form a triangle as the sum of triangles in a triangle = 180°

Hence the number of non-congruent triangles that can be drawn in this case = 0

e. The parameters given are two angles measuring 45° and one side length of 10 in., hence the parameter is of the forms AAS or ASA hence the triangle is unique and it is not possible to draw two non-congruent triangle with the provided properties.

Original formula:

P/2-5 when p=14

You just need to plug in 14 in place of where the variable p is at. This is called substitution.

14/2-5

By the rules of PEMDAS, we will execute 14/2 first. (7)

7-5

2 is your final answer.

Answer:

15 years old

Step-by-step explanation:

The equation would be

8x + 2x + x = 53

3x = 45

x = 15

Answer:

BOC= 110 degrees

Step-by-step explanation:

you can refer the above explanation

Answer: Conditional frequencies enables users to get more specific information when analyzing a dataset.

Step-by-step explanation: Frequency refers to the count of occurrence of a particular variable.

Relative frequency is obtained by taking the ratio of the counts a particular variable and the total counts and of all available variables in the experiment or data.

Conditional Frequency allows us to input additional constraints to our frequency counts, especially in a two-way table. Enabling us to get more specific information by using conditional statements.

Answer:

length of the zip line = 121. 63 ft

Step-by-step explanation:

The length of the zip line AB forms a triangle  ABC. To find the length AB we need to know the length of 2 sides of the triangle an angle.

Triangle ADC

We need to find the hypotenuse side AC using the SOHCAHTOA principle.

Therefore,

sin 41° = opposite/hypotenuse

opposite = 65 ft

sin 41° = 65/AC

cross multiply

0.65605902899 AC = 65

divide both sides by 0.65605902899

AC = 65/0.65605902899

AC = 99.0764506359  ft

AC ≈ 99.08 ft

Triangle BCE

We are looking for side BC. The triangle BCE is also a right angle triangle so we use the same methodology like the triangle ADC.

sin 62° = opposite/hypotenuse

opposite = 85 ft

sin 62° = 85/BC

cross multiply

BC sin 62° = 85

BC = 85/sin 62°

BC = 85/0.88294759285

BC = 96.2684543086

BC ≈ 96.27 ft

The angle ACB can be gotten when you subtract 62° and 41° from 180 (angle on a straight line).

Therefore,

∠ACB = 180° - 62° - 41°

∠ACB  = 77°

Now let us use the cosine law to find the zip line AB.

c² = a² + b² - 2ab cos C

a = 96.27 ft

b = 99.08 ft

c² = 96.27² + 99.08² - 2 × 96.27 × 99.08 cos 77°

c² = 9267.9129 + 9816.8464 - 19076.8632 cos 77°  

c² = 19084.7593 - 19076.8632 × 0.22495105434

c²  = 19084.7593 - 4291.36049041

c² = 14793.398810

square root both sides

c = √14793.398810

c = 121.628116856

c ≈ 121. 63 ft

length of the zip line = 121. 63 ft

Answer:

x>-1.25

Step-by-step explanation:

3(5x-10)<30x

15x-20<30x

-20<15x

-20/15<x

-1.25<x

x>-1.25

Step-by-step explanation:

Step 1:  Distribute

[tex]3(5x - 10) < 30x[/tex]

[tex](3 * 5x) + (3 * -10) < 30x[/tex]

[tex]15x - 30 < 30x[/tex]

Step 2:  Subtract 15x from both sides

[tex]15x - 15x - 30 < 30x - 15x[/tex]

[tex]-30 < 15x[/tex]

Step 3:  Divide both sides by 15

[tex]-30 / 15 < 15x / 15[/tex]

[tex]-2 < x[/tex]

Answer:  [tex]x > -2[/tex]

Answer:

y-1 = -(x-2)

Step-by-step explanation:

First find the slope

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

   = (5-1)/(-2 -2)

    = 4/-4

   = -1

We are using point slope form using the point (2,1)

y-y1 = m(x-x-1)

y-1 = -1(x-2)

y-1 = -(x-2)

Step-by-step explanation:

a.)

= 15a - 13a

= a(15 - 13)

= a(2)

= 2a

b.)

= -6x - 18y

= -(x + 3y)

c.)

= 36abc + 54ad

= 6a(6bc + 9d)

Answer:

[tex]a \: ) \: \: 15a - 13a \\ = a(15 - 13) \\ = a(2) \\ = 2a[/tex]

[tex]b) \: \: - 6x - 18y \\ = - 6(x + 3y)[/tex]

[tex]c) \: \: 36abc + 54ad \\ = 9a(4bc + 6d)[/tex]

Answer:

d: 1/2

Step-by-step explanation:

Answer:D. 1/2 c

Step-by-step explanation:A recipe is 100% and 3/4 is 75%. 75% of 2/3 is 1/2.

Answer:

The statement "500 divided by 50 is 10" is a true statement

Step-by-step explanation:

In mathematics, we have a term that we refer to as Place Value.

Place Value in mathematics can be defined as the value that a digit has based on its position or place in a number.

Examples of place value is:

Thousands represented by Th

Hundreds represented by H

Tens represented by T

Units represented by U

In the above question,

500 ÷ 50 gives us 10.

This is true because, 500 as a number, the Digit 5 has a place value of hundreds

50 as a number , the digit 5 has a place values of Tens.

10 as a number, the digit 1 has a place value of Tens.

In mathematics, the multiplication of 2 numbers in a place value of Tens always gives us a place value of hundreds.

For example, 10 × 50 = 500

Likewise, when we divide, a number with a place value of hundreds by a number with a place value of tens, we have a number with a place value of tens.

For example: 500 ÷ 50 = 10.

Therefore, the statement "500 divided by 50 is 10" is a true statement

Answer:

C=62 maybe

Step-by-step explanation:

3x=x+20

-x    -x

2x=20

divide by 2

x=10

2*10=20+38=58

10+20=30

3*10=30

30+30=60+58=118

180-118=62

Answer:

846.3

Step-by-step explanation:

76.7+769.6=846.3

Answer:

3/8

Step-by-step explanation:

The spinner A has 4 possible values:

1, 2, 3, 4

The spinner B has 4 possible values:

2, 3, 4, 5

The possible pairs we can have are:

(1,2), (1,3), (1,4), (1,5),

(2,2), (2,3), (2,4), (2,5),

(3,2), (3,3), (3,4), (3,5),

(4,2), (4,3), (4,4), (4,5).

The sum of these pair of values are:

3, 4, 5, 6,

4, 5, 6, 7,

5, 6, 7, 8,

6, 7, 8, 9.

So we have 6 values that are 5 or less, in a total of 16 values, so the probability of the sum being 5 or less is P = 6/16 = 3/8

Answer:

1). [tex]f^{-1}(x)[/tex] = (200 - [tex]\frac{x}{0.85}[/tex])

2). Inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.

Step-by-step explanation:

Function representing the maximum heart rate is,

f(x) = 0.85(220 - x)

Here x = age of the client

Equation form of the function will be,

y = 0.85(220 - x)

To get the inverse of the given function, replace 'x' by 'y' and 'y' by 'x' and solve for y.

x = 0.85(220 - y)

220 - y = [tex]\frac{x}{0.85}[/tex]

y = 220 - [tex]\frac{x}{0.85}[/tex]

Now convert this equation into a function.

[tex]f^{-1}(x)[/tex] = (200 - [tex]\frac{x}{0.85}[/tex])

Here inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.

Answer:

a^2 +a -6

Step-by-step explanation:

(a + 3)(a - 2)

FOIL

first: a*a = a^2

outer: -2*a = -2a

inner: 3*a =3a

Last : -2*3 = -6

Add them together

a^2 -2a+3a -6

Combine like terms

a^2 +a -6

Answer:

a² + a - 6

Step-by-step explanation:

(a + 3)(a - 2) = a² - 2a + 3a - 6 = a² + a - 6

Answer:

x = -0.4

Step-by-step explanation:

First subtract the 0.4 from both sides. Then divide both sides by -9 to solve for x.

Answer:

-0.4

Step-by-step explanation:

Subtract 0.4 from both sides.

-9x + 0.4 = 4

       -0.4    -0.4

-9x = 3.6

Divide both sides by -9.

-9x/-9 = 3.6/-9

Simplify

x = -0.4

I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!

Answer:

The answer is [tex]s = - \frac{3}{2}[/tex] .

Step-by-step explanation:

Solve the equation:

[tex]0.5s + 1 = 7 + 4.5s[/tex]

-Subtract [tex]4.5s[/tex] from [tex]0.5s[/tex] :

[tex]0.5s + 1 -4.5s = 7 + 4.5s -4.5s[/tex]

[tex]-4s + 1 = 7[/tex]

-Subtract both sides by [tex]1[/tex] :

[tex]-4s + 1 - 1 = 7 -1[/tex]

[tex]-4s = 6[/tex]

-Divide both sides by [tex]-4[/tex] :

[tex]\frac{-4s}{-4} = \frac{6}{-4}[/tex]

[tex]s = -\frac{3}{2}[/tex]

So, therefore, the final answer is [tex]s = -\frac{3}{2}[/tex] .

Answer:

[tex]9\pi[/tex], which is approximately [tex]28.26[/tex].

Step-by-step explanation:

Consider two sectors in the same circle. The area of the two sectors is proportional to their central angles. In other words, if the central angle is [tex]\theta_1[/tex] for the first sector in this circle, and [tex]\theta_2[/tex] for the second, then:

[tex]\displaystyle \frac{\text{Area of Sector 1}}{\text{Area of Sector 2}} = \frac{\theta_1}{\theta_2}[/tex].

In this question, think about the whole circle as a sector. The central angle of this "sector" would be [tex]360^\circ[/tex] (a full circle.) Compare the area of this circle to that of the [tex]60^\circ[/tex]-sector in this circle:

[tex]\displaystyle \frac{\text{Area of Circle}}{\text{Area of $60^\circ$-Sector}} = \frac{360^\circ}{60^\circ} = 6[/tex].

In other words, the area of this circle is six times that of the [tex]60^\circ[/tex]-sector in it.

The area of that [tex]60^\circ[/tex]-sector is [tex]\displaystyle \frac{3}{2}\pi[/tex]. Therefore, the area of this full circle will be [tex]\displaystyle 6 \times \frac{3}{2}\pi = 9\pi \approx 28.26[/tex].

Answer:

(x + 1)² + (y + 3)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² + 2x + 6y - 6 = 0

Collect the x and y terms together and add 6 to both sides

x² + 2x + y² + 6y = 6

To complete the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(1)x + 1 + y² + 2(3)y + 9 = 6 + 1 + 9

(x + 1)² + (y + 3)² = 16

with centre = (- 1, - 3) and r = [tex]\sqrt{16}[/tex] = 4

Answer:

You Do y= mx+b

Step-by-step explanation:

Answer:

y-intercept is 2 because line passes through (0,2) and the slope is 3.

The equation of this line is y=3x+2.

Answer:

x = 5

Step-by-step explanation:

Steps to solve:

(x - 5)(x - 5) = 0

~Set both factors to equal 0

x - 5 = 0

x - 5 = 0

~Solve for x

x - 5 = 0

x - 5 + 5 = 0 + 5

x = 5

We only solved for one factor since they are both the same and the x value for both are also the same.

Best of Luck!

Answer:

30 cm.

Step-by-step explanation:

Answer:

30 cm

Step-by-step explanation:

Perimeter is the outside measurement/ outline, add 10+10+5+5 which is all the sides together and you get your answer for perimeter

Answer:

We just have to solve each power.

[tex]8^{2} = 8 \times 8 = 64\\10^{-2} =\frac{1}{10^{2} } =\frac{1}{100}=0.01 \\(-4)^{4}=(-4) \times (-4) \times (-4) \times (-4)=256 \\(-6)^{4}=(-6) \times (-6) \times (-6) \times (-6)=1,296[/tex]

Remember, to solve a power, we just need to multiply its base as many times indicates its exponent.

It's important to know that the negative exponent indicates a position, that's why in the second exercise we needed to change the position of the power to continue.

Answer:

Irrational numbers

Step-by-step explanation:

To find out which subsets of real numbers [tex]\sqrt{42}[/tex] is in, we can look at what it does not fall into.

Natural numbers- These include 1, 2, 3..., which means that [tex]\sqrt{42}[/tex] cannot be a part of it

Whole numbers - These include 0, 1, 2 ..., which means that [tex]\sqrt{42}[/tex] cannot be a part of it

Integers- These include -2, -1, 0, 1, 2..., which means that [tex]\sqrt{42}[/tex] cannot be a part of it.

Rational - These include all the previous as well as anything that can be written as a fraction, which means that [tex]\sqrt{42}[/tex] cannot be a part of it

Irrational numbers - This includes anything that continues on endlessly, which this does when converted to a decimal, which means that this is the subset of real numbers that [tex]\sqrt{42}[/tex] belongs.

Answer:

Step-by-step explanation

The two other forms are written form and expanded from. That first blank is for written from and the answer is four and eight-hundred twenty-sixth thousandths. For the other ones i think for the first blank it is 4 then 8 then 20 and then 6.

Answer:

6:5

Step-by-step explanation

boys : girls

= 18 : 15

Now time to simplify:

18/3: 15/3

= 6:5

Answer: 0.44mm

Step-by-step explanation:

In this problem we are asked for the height of a single playing chip. We know the volume of a cylinder is 25120 mm^3.

V=πr²h

25120=πr²h

The problem also gives the diameter of the case: 40mm.

To find radius, you divide the diameter in half.

d=2r

40=2r

r=20

With the radius, we can add that to the volume equation.

25120=[tex]\pi[/tex](20)^2h

25120=400πh

All we have left is to find the height.

h=25120/(400π)

h≈20mm

Now that we know the height, we can find the height of a single chip. The problem states about 50 chips can fit in a case. To find the height of a single chip, you would divide 20 by 50.

20mm/50 chips=0.4mm/chip.