What is the area of this triangle in square inches?

Answer:

30, 40, 50

Step-by-step explanation:

30 x 30 + 40 x 40 = 900 + 1600 = 2500

500 x 500 = 2500

sum of two legs² equals hypotenuse²

Answer:

Step-by-step explanation:

30,50,40

Answer:

6x-24

Step-by-step explanation:

6(x-4)=6x-24

Answer:

hi there!

The correct answer is: 6x - 24

Step-by-step explanation:

you distribute 6 into the parenthesis

you first multiply 6 by x  and you get 6x

then you multiply 6 by -4 and you get -24

then you combine both to get 6x-24

Answer:

x=-5

Step-by-step explanation:

-4x-10=10

-4x=10+10

-4x=20

x=20/-4

x=-5

Answer:

I do not think I can answer this without any pictures.

Step-by-step explanation:

Sorry, but could you attach a link or maybe sketch it out?

Answer:

x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given

x² - x - [tex]\frac{3}{4}[/tex] = 0

Multiply through by 4 to clear the fraction

4x² - 4x - 3 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × - 3 = - 12 and sum = - 4

The factors are + 2 and - 6

Use these factors to split the x- term

4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term

(2x + 1)(2x - 3) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

The solutions are x = 3 and x = -7.

To solve the quadratic equation, we first need to bring it to the standard form of ax2 + bx + c = 0. In the example given, we have the equation x2 + 4x - 21 = 0, where a = 1, b = 4, and c = -21. To find the solutions for x, we will use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a).

Substituting the values of a, b, and c into the quadratic formula, we get:

x = (-(4) ± √((4)2 - 4(1)(-21))) / (2(1))

x = (-4 ± √(16 + 84)) / 2

x = (-4 ± √100) / 2

x = (-4 ± 10) / 2

Which gives us two solutions:

x = (6 / 2) = 3

x = (-14 / 2) = -7

Therefore, the solutions to the quadratic equation x2 + 4x - 21 = 0 are x = 3 and x = -7.

Answer: Last option.

Step-by-step explanation:

By definition, a relation is a function if and only if each input value has an unique output value.

For this exercise it is important to remember that the input values are the values of "x" and the ouput values are the values of "y"

Knowing this and given the tables attached which  represent the functions [tex]f(x)[/tex], and [tex]g(x)[/tex],, you can identify that:

1. In the table that represents the function [tex]f(x)[/tex], the input value 1 produces the output value 3.

2. In the table that represents the function [tex]g(x)[/tex], the input value 1 produces the output value 3.

Therefore, based on this, you can determine that the input value that produces the same output value for the two functions is:

[tex]x=1[/tex]

The Answer is:

The histogram on Answer C.

The histogram will reflect the frequency of shirt sizes as shown in the dot plot, with bars representing the number of shirts for each size range; no bar for size 8, bars of height 1, 3, 5, 4, 2, 1, and 1 for sizes 10 through 24 respectively.

The question relates to the representation of data using a histogram based on the information given for a dot plot. A histogram is a type of graph that depicts the distribution of data through contiguous boxes, where the x-axis often represents the data categories (like a number line indicating shirt sizes) and the y-axis shows frequencies or relative frequencies.

To represent the same data as the described dot plot in a histogram, we need to create intervals or bins that will encompass the range of shirt sizes, and each interval will have a frequency corresponding to the number of dots in that size range from the dot plot. We could have intervals such as 8-10, 10-12, 12-14, and so on, with the height of each bar representing the frequency of shirts in each size range.

Histogram bars will correspond to dot plot points as follows: no bar for size 8, a single bar reaching up to 1 for size 10, a bar up to 3 for both sizes 12 and 14, a bar up to 5 for size 16, a bar up to 4 for size 18, bars up to 2 and 1 for sizes 20 and 22 respectively, and a final bar reaching up to 1 for size 24.

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Answer:

3/5

Step-by-step explanation:

4/5 * 3/4 = 12 / 20 = 3 / 5

The ratio 60:5 can be described as follows :

The ratio expression is a way of expressing the division of numerator by a denominator.

Here,

The total number of students is the numerator = 60

The denominator is the number of students per group = 5

Hence, the quotient is the value of the divison obtained which is (60/2) = 12

Therefore, there are 12 groups of 5 students.

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Answer:

40g of chocolate are left.

Step-by-step explanation:

3/5*100=300/5=60

100-60=40

Final answer:

To find the amount of chocolate left, subtract the amount eaten from the original 100g bar.

Explanation:

To find the number of grams of chocolate left, you need to subtract the amount Captain ate from the original 100g bar. Captain ate 3/5 of the bar, so you can calculate the amount eaten by multiplying 3/5 by 100g. This gives you 60g. To find the amount left, you subtract 60g from 100g. The answer is 40g.

Answer:

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\75\%=\dfrac{75}{100}=0.75\\\\50\%=\dfrac{50}{100}=0.5\\\\\dfrac{n}{d}-\text{a fraction}\to(n-\text{numerator},\ \text{denominator})\\\\\text{numerator is decreased by 75}\%\to n-0.75n=0.25n\\\\\text{denominator is decreased by 50}\%\to d-0.5d=0.5d\\\\\text{new fraction}\ \dfrac{0.25n}{0.5d}=\dfrac{0.25\cdot100}{0.5\cdot100}\cdot\dfrac{n}{d}=\dfrac{25}{50}\cdot\dfrac{n}{d}=\dfrac{1}{2}\cdot\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\\\\\dfrac{n}{d}-0.5\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\to\ \text{it's}\ 50\%\ \text{of}\ \dfrac{n}{d}[/tex]

Answer:

  36 objects

Step-by-step explanation:

You want the value of x when t=9, so you're solving ...

  9 = 0.007x^2 +0.003x

  9 = 0.007(x^2 + 3/7x)

From here, we observe that an approximation is probably sufficient.

 9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2

  x ≈ 3/√.007 ≈ 35.9 ≈ 36

We can check:

  .007(36)(36 3/7) = 9.18

  .007(35)(35 3/7) = 8.68

To keep the computer busy for 9 seconds, it needs to sort 36 objects.

Step-by-step explanation:

21 percent of 3,876 is 813.96$, and 17 percent of 4552 is 773.67$. 813.96>773.67

21% of $3,876 is $813.96, while 17% of $4,552 is $773.84. Therefore, 21% of $3,876 inequality sign is greater than 17% of $4,552.

Choosing between 21% of $3,876 or 17% of $4,552 involves calculating each percentage of the given amounts to compare which is greater. To do this:

Calculate 21% of $3,876: 0.21 × 3876 = $813.96.

Calculate 17% of $4,552: 0.17 × 4552 = $773.84.

Comparing these two amounts using an inequality sign, we see that $813.96 is greater than $773.84. So, you would rather have 21% of $3,876 than 17% of $4,552.

The inequality would be written as:

21% of $3,876 > 17% of $4,552

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Answer: When you multiply by 0.1 it is the same as dividing by 10. So it gives you a product that is less than 37.4.

Answer: A: 0.0031

Step-by-step explanation:

Given : In a study of wait times at an amusement park, the most popular roller coaster has a mean wait time of 17.4 minutes with a standard deviation of 5.2 minutes.

i.e. [tex]\mu=17.4[/tex] and [tex]\sigma=5.2[/tex]

We assume that the wait times are normally distributed.

samples size : n= 30

Let x denotes the sample mean wait time.

Then, the probability that the mean wait time is greater than 20 minutes will be :

[tex]P(x>20)=1-P(x\leq20)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{20-17.4}{\dfrac{5.2}{\sqrt{30}}})\\\\=1-P(z\leq2.74)\ \ [\because\ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9969\ \ [\text{ By z table}]\\\\=0.0031[/tex]

Hence, the probability that the mean wait time is greater than 20 minutes.= 0.0031

Thus , the correct answer is A: 0.0031 .

Answer:

Answer: A: 0.0031

Step-by-step explanation:

Answer: -23 feet to sea level

Step-by-step explanation:

start with 0 (sea level)

he dives twenty, -20

he dives ten more, -20 - 10 = -30

he swims up twelve feet; -18

he goes down 5 more; -23 feet

Answer:

20 + 10 = 30

30 - 12 = 18

18 + 5 = 23

His elevation is 23ft below the sea level

Answer:

55%

Step-by-step explanation:

The percent markup is the percent increase from $300 to $465.

Subtract to find the markup: 465 - 300 = 165

Now we find the percent markup.

Divide: 165/300 = 0.55

Multiply: 0.55 * 100 = 55

Answer: 55%

Markup percentage is 55%

Old price of phone = 300

New price of phone = 465

Markup percentage

Markup = [465 - 300] /

Markup = 165 / 300

Markup = 0.55

Markup percentage = 0.55 × 100

Markup percentage = 55%

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Answer:

0.0007

Step-by-step explanation:

Answer:

[tex]2x-3y=19[/tex]

Step-by-step explanation:

we have the ordered pairs

(8, –1) and (2, –5)

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values in the formula

[tex]m=\frac{-5+1}{2-8}[/tex]

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

simplify

[tex]m=\frac{2}{3}[/tex]

The equation of the line in point slope form is

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{2}{3}[/tex]

[tex]point\ (8,-1)[/tex]

substitute

[tex]y+1=\frac{2}{3}(x-8)[/tex]

Convert to standard form

The equation of the line in standard form is equal

[tex]Ax+By=C[/tex]

where

A is a positive integer

B and C are integers

we have

[tex]y+1=\frac{2}{3}(x-8)[/tex]

Multiply by 3 both sides to remove the fraction

[tex]3y+3=2(x-8)[/tex]

apply distributive property right side

[tex]3y+3=2x-16[/tex]

Group the variables in one side and the constants in the other side

[tex]2x-3y=3+16[/tex]

[tex]2x-3y=19[/tex] ---> equation in standard form

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

..

Answer:

[tex]g \leq -24[/tex]  or  [tex]g>6[/tex]

Step-by-step explanation:

Lets solve the first inequality by cross multiplying and doing algebra. THe process is shown below:

[tex]\frac{2g+63}{5} \leq  3\\2g+63 \leq 15\\2g \leq 15-63\\2g \leq -48\\g \leq -24[/tex]

Now, lets solve the next inequality with simple algebra. Process shown below:

[tex]13g-34>44\\13g>44+34\\13g>78\\g>6[/tex]

Hence, we can say:

g is less than or equal to -24  AND  g is greater than 6

Answer:

2

Step-by-step explanation:

You have to find unit rate (I feel like this is wrong, sorry in advance!)

Answer:

she passes 2 per 1 kilometer

Step-by-step explanation:

24 / 2 = 12

12 x 2 = 24

24 / 12 = 2

Answer:

Part a) The equation for the volume of the film canister is

[tex]32\pi=\pi r^{2}(8)[/tex]

Part b) The radius of the film canister is [tex]2\ cm[/tex]

Step-by-step explanation:

The complete question is

A film canister in the shape of a cylinder has a height of  8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

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

where

r is the radius of the circular base

h is the height of the cylinder

we have

[tex]V=32\pi\ cm^3[/tex]

[tex]h=8\ cm[/tex]

substitute

[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

[tex]32\pi=\pi r^{2}(8)[/tex]

[tex]32\pi=8\pi r^{2}[/tex]

Simplify

Divide by 8π both sides

[tex]4=r^{2}[/tex]

square root both sides

[tex]r=2\ cm[/tex]

Answer:

4x-8

Step-by-step explanation:

3/4(4x-8)+1/4(4x-8)

12/4x-24/4+4/4x-8/4

3x-6+x-2

3x+x-6-2

4x-8

Answer:

everything is on the sheet

To simplify the ratio 4:2:2, divide each part by the greatest common factor, which is 2, resulting in a simplest form of 2:1:1.

To express the ratio 4:2:2 in its simplest form, you need to divide each term of the ratio by the greatest common factor of all the terms. In this case, the greatest common factor of 4, 2, and 2 is 2. Therefore, when you divide each part of the ratio by 2, the simplest form of the ratio is 2:1:1.

Here's a step-by-step breakdown:

Identify the greatest common factor (GCF) of the numbers in the ratio. GCF of 4, 2, and 2 is 2.

Divide each term of the ratio by the GCF. So, 4 divided by 2 is 2, and 2 divided by 2 is 1.

Write down the simplified ratio: 2:1:1.

This method is similar to the way coefficients in a balanced chemical equation can be simplified, or how ratios can be used in genetics to represent phenotypic distribution in a dihybrid cross. In health sciences, ratios such as 1:1000 are expressed in simplest form. Similarly, in engineering, gear ratios like 2:1 are given in the simplest way to indicate how many turns of an input gear will result in one turn of an output gear.

The missing choices are:

A. C = 9h + 4

B. C = 4h + 9

C. C = 4(h - 1) + 9

D. C = 13h

C = 4(h - 1) + 9 represents this situation ⇒ answer C

Step-by-step explanation:

The given is:

We need to find which of the following represents this situation

∵ The cost of renting a bicycle is $9 for the first hour

∵ Another $4 for each  additional hour

∵ h represents the number of hours

- Add the cost of the first hour to the cost of the remaining hours

∵ The remaining hours = h - 1

∴ The cost of the remaining hours = 4(h - 1)

∵ C is the cost of renting the bicycle for h hour

- Add 9 to 4(h - 1) to find C

∴ C = 4(h -1) + 9

C = 4(h - 1) + 9 represents this situation

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Answer:

The relationship between the number of scoops and the number of dogs is not proportional

Step-by-step explanation:

Let

x ----> the number of scoops

y ----> the number of dogs

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

First situation

You prepare 8 scoops of dog food for 4 dogs

x=8, y=4

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{4}{8}=0.5[/tex]

Second situation

You prepare 12.5 scoops of dog food for 5 dogs

x=12.5, y=5

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{5}{12.5}=0.4[/tex]

Compare the values of k

[tex]0.5\neq 0.4[/tex]

The values of k are not equal

therefore

The relationship between the number of scoops and the number of dogs is not proportional

Answer:

the answer is 9

Step-by-step explanation:

the answer is 9

Answer:

10, 6 and 11.66

Step-by-step explanation:

10, 6 and the hypothenous is equal to : √(10^2 + 6^2)

= √(100+36)

= √136

= 11.66

Answer:

10,6 and 11.66

Step-by-step explanation:

A right angled triangle has three sides which are the adjacent, the opposite and the hypotenuse.

Looking at the triangle in question, the longest side is the hypotenuse while the other two sides are opposite and adjacent respectively.

Before we can get the hypotenuse, we need to know the value of the other sides first.

Based on the diagram the height of the triangle is (20-10) = 10

The base of the triangle = (7-1) = 6

This are gotten be subtracting the initial point from the final point on which the triangle is standing in space.

Hypotenuse is gotten using the Pythagoras theorem expressed as;

Hypotenuse² = Adjacent² + opposite²

Hypotenuse² = 10²+6²

Hypotenuse² = 100+36

Hypotenuse² = 136

Hypotenuse = √136

Hypotenuse = 11.66

The three sides of the triangles are therefore 10, 6 and 11.66