What is the equation of the line that passes through the point (5, -20) and has a slope of -6

The graph of the function y = 1/3x - 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

So, the equation is

y = 1/3x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations rules

The graph of the function is added as an attachment

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Answer:

5b* because we have no idea what it could stand for

Answer:

5b

Step-by-step explanation:

However many b's there are that's your number so in this case its 5 and then you just add be to it so 5b

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Work Shown:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.5 - 0.1

P(A or B) = 0.8 - 0.1

P(A or B) = 0.7

Answer:

  4

Step-by-step explanation:

You want the 8th term of the geometric sequence 512, 256, 128, ....

The formula for the n-th term of a geometric sequence is ...

  an = a1×r^(n-1)

where a1 is the first term (512), and r is the common ratio (1/2).

Then the 8th term is ...

  a8 = 512(1/2)^(8-1) = 512/128 = 4

The eighth term of the sequence is 4.

In triangle DEF, the length of segment DF is 15√3. So correct option is C.

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of its sides. There are three primary trigonometric ratios: sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.

Here are the definitions of these trigonometric ratios:

Sine (sin): The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. This can be written as sin(theta) = opposite / hypotenuse.

Cosine (cos): The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse. This can be written as cos(theta) = adjacent / hypotenuse.

Tangent (tan): The tangent of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the adjacent side. This can be written as tan(theta) = opposite / adjacent.

In triangle DEF, we have a right triangle at E, which means that angle DEF is a 90-degree angle. We are also given that angle DFE is 60 degrees, which means that angle EDF is 30 degrees (since the angles in a triangle add up to 180 degrees).

Let DF = x. Then, we can use the trigonometric ratios of the 30-60-90 degree triangle to solve for x

We know that the ratio of the sides in a 30-60-90 degree triangle is x : x√3 : 2x. Therefore, we have:

DE / DF = x√3 / x = √3

Simplifying this, we get:

x = DE / (√3) = 45 / (√3) = 15√3

Therefore, the length of segment DF is 15√3, which is answer choice C.

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Answer:

62

Step-by-step explanation:

180-116 makes us find out that angle C is 64, thus to find out the inner angles you gotta do 64+ (2x+4)+(3x-13)=180

You follow this operation, find out x and perform 3(25)-13, which ends up giving you 62

Answer:

62°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is not sharing a common side

2x + 4 + 3x - 13 = 116° add like terms

5x - 9 = 116°

5x = 125° divide both sides by 5

x = 25 and angle A is 3x - 13 so 3×25 - 13 = 62°

Answer:

20 because 40 is a positive and spent is negative

Step-by-step explanation:

Answer:

122

Step-by-step explanation:

6*20=120 + 2=122

Answer:

2nd statement

Step-by-step explanation:

it is

The expressions that will correctly calculate what percent 19 is of 20 are:

A.19/20 .100

D.19.100/20

The concept that will be used here is percentage. A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

From the options we can see that to find the percentage of 19  of 20, iot can be expressed mathematically as :

(19/20) *100 and this can as well be expressed as (19*100)/20 becausethey will still give use the same value which is 95%

Therefore, option A and D are correct.

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Answer:

In order to find out the equation of liner function first of all u need to find the slope of it (a) then put it in general form of liner functions, afterwards put desire point of x,y table in equation to find the b.

form of liner function : y= ax+b

step 1. finding the slope

\(a = \frac{y1 - y2}{x1 - x2} \)

for example I'll put (-3,4) and (0,2) to this formula,

the slope would be -2/3

step2. finding the b

put a desire point of x,y table for example (3,0)

0 = -2/3 × 3 + b

b would be 2

so the equation is y= -2/3x + 2

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is \((e - 2\sqrt{3} )^2\) = f - 20√3.

Expanding the left side of the equation we have:

\((e - 2\sqrt{3} )^2\) = (e - 2√3)(e - 2√3)

= \(e^2\) - 2e√3 - 2e√3 + 12

= \(e^2\) - 4e√3 + 12

Substituting back in the function

\(e^2\) - 4e√3 + 12 = f - 20√3

\(e^2\) - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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Answer: first, second and fourth are primes, the third is not-prime.

Hope it helps :)

Answer:

A) 12 gallons B) 132 miles C) r is less than 13 gallons

Step-by-step explanation:

A) if you have 17 gallons in a truck and you do 60÷12=5 so 17-5=12

B) Bceause if you do 17·12=204 miles 204-72=132 miles

C) Because r is less than 13 gallons

Answer:

45

Step-by-step explanation:

Answer:

It is 45. 1000 Millileters are in a liter. 750 x 60 = 45000. 45000/1000 = 45.

Step-by-step explanation:

Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

Answer: 2

Step-by-step explanation:

Answer:

I think it's 2kg

Step-by-step explanation:

13/5 ÷ 13/10

Reciprocate

13/5 × 10/13

= 26/13

=2kg

We know what Miguel has 225 baseball cards, and he plans on keeping 75, while giving them the rest of them to his friends. We want to know if he can give an equal number to 6 of his friends.

For this objective, we know what he will have to give to his friends an amount of:

Answer:

the answer is 42 i think

Step-by-step explanation:

Answer:

i think she right (42) but i dont kno wwww

Step-by-step explanation:

Answer:

x²+2x-3=0

According to Vieta's formula:

x²-(Sum of roots)x+(product of roots)=0

Sum of roots=-3+1=-2

Product of roots=-3×1=-3

The equation is x²-(-2)x+(-3)=0

x²+2x-3=0

Using it's concept, the set of ordered pairs that represent a function are:

The set of ordered pairs that do not represent a function are:

A relation represents a function if each input X is mapped to only one output Y.

At (1,9), (-3,-2) (1,-4), input 1 is mapped to outputs 9 and -4, hence it is not a function.

At (0, 3), (0, 7), (4,0), input 0 is mapped to outputs 3 and 7, hence it is not a function.

For the other relations, each input is mapped to only one output, hence they are functions.

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