which set of side lengths can be used to form a right triangle?

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:

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:

the answer is 9

Step-by-step explanation:

the answer is 9

Answer:

B)

Step-by-step explanation:

Answer:

Mass Media

Step-by-step explanation:

Answer: Got an (A) on my test, it is (Mass media)

Step-by-step explanation: OOOOFFF is my word

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]

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:

x=-5

Step-by-step explanation:

-4x-10=10

-4x=10+10

-4x=20

x=20/-4

x=-5

Answer:

3/5

Step-by-step explanation:

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

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:

[tex]y=1500\cdot(0.902)^T[/tex]

Step-by-step explanation:

Let T be the number of years since the start of the study and y be the area that the forest covers in [tex]\text{km}^2[/tex].

We have been given that at the beginning of an environmental study a forest cover an area of 1500 [tex]\text{km}^2[/tex]. Since then this area has decreased by 9.8% each year.

We know that an exponential function is in form [tex]y=a\cdot(1-r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Decay rate in decimal form,

x = Time.

Let us convert 9.8% into decimal as:

[tex]9.8\%=\frac{9.8}{100}=0.098[/tex]

We have been given that initial value (a) is [tex]1500[/tex].

Upon substituting our given values, we will get:

[tex]y=1500\cdot(1-0.098)^T[/tex]

[tex]y=1500\cdot(0.902)^T[/tex]

Therefore, our required exponential function would be [tex]y=1500\cdot(0.902)^T[/tex].

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:

..

Option A

Volume of bed is [tex]2\frac{2}{3}[/tex] cubic inches

Solution:

Given are the dimensions of bed

To find: volume of bed

Since bed is generally of cuboid shape, we can use the volume of cuboid formula

volume of cuboid is given as:

[tex]\text{ volume of cuboid } = l \times w \times h[/tex]

Where, "l" is the length and "w" is the width and "h" is the height of cuboid

From attached figure in question

[tex]l = 2\frac{2}{3} inches = \frac{3 \times 2 + 2}{3} = \frac{8}{3} inches[/tex]

[tex]w = 3 inches[/tex]

[tex]h = \frac{1}{3} inches[/tex]

Substituting the values in formula,

[tex]v = \frac{8}{3} \times 3 \times \frac{1}{3}\\\\v = \frac{8}{3} = 2\frac{2}{3}[/tex]

Therefore volume of bed is [tex]2\frac{2}{3}[/tex] cubic inches

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:

0.0007

Step-by-step explanation:

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.

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:

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:

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

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:

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:

Neither

Step-by-step explanation:

Can be determined because there is enough information (Length, width, and height).

Not congruent because from the picture itself, the figures are in different sizes.

Not similar because:

The height ratio is not the same as the ratios of other dimensions.

1 : 4 is not similar to 6 : 12 and 4 : 8

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:

y-8=-3/2(x+8)

Step-by-step explanation:

y-y1=m(x-x1)

y-8=-3/2(x-(-8))

y-8=-3/2(x+8)

Final answer:

The equation of the line in the point-slope form that passes through (-8, 8) with a slope of -3/2 is y - 8 = (-3/2)(x + 8).

Explanation:

To write an equation in point-slope form for a line that passes through a given point with a known slope, we use the formula y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.

For the line that passes through the point (-8, 8) with a slope of -3/2, we substitute these values into the point-slope form equation:

y - 8 = (-3/2)(x + 8)

This equation represents the specific line asked in the problem.

The race-car will have to go for 730 miles

Step-by-step explanation:

The given is:

We need to find how far it will have to go

∵ The car will move around the park

- That means it moves the distance equal the perimeter of the park

∵ The dimensions of the park are 4.6 mile long and 2.7 miles wide

∵ The perimeter of the park = 2(length + width)

∴ The perimeter of the park = 2(4.6 + 2.7)

∴ The perimeter of the park = 2(7.3)

∴ The perimeter of the park = 14.6 miles

∵ The car will move around the park 50 times

∵ The distance of one round is 14.6 miles

∴ The distance for 50 rounds = 14.6 × 50

∴ The distance for 50 rounds = 730 miles

The race-car will have to go for 730 miles

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The shortest possible height of tower is 24 cm.

Tim used 4 blue blocks and his brother used 3 green blocks.

Step-by-step explanation:

Given,

Height of blue block = 6 cm

Height of green block = 8 cm

We will take least common multiple to find the shortest possible height.

6 = 2*3

8 = 2*2*2

LCM = 2*2*2*3 = 24 cm

The shortest possible height of tower is 24 cm.

Number of blue blocks used = [tex]\frac{24}{6} = 4[/tex]

Number of green blocks used = [tex]\frac{24}{8} = 3[/tex]

Tim used 4 blue blocks and his brother used 3 green blocks.

Keywords: LCM, multiplication

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answer: 3a^4 is the correct answer

Answer:3a^4

Step-by-step explanation:

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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