Find g(x), where g(x) is the translation 1 unit left of f(x)=9x–8.

Answer:

x = 19/2 or 9.5

Step-by-step explanation:

a) Distribute.

(4)(x) + (4)(−5) = 18

4x + −20 = 18

4x − 20 = 18

b) Add 20 to both sides.

4x − 20 + 20 = 18 + 20

4x = 38

c) Divide both sides by 4.

4x/4 = 38/4

x = 19/2 or 9.5

Answer:

9.5 or 19/2

Step-by-step explanation:

4 ( x - 5 ) = 18

Step 1 : Divide 4 on both sides.

x - 5 = 18/4

x - 5 = 4.5

Step 2 : Add 5 on both sides.

x = 4.5 + 5

x = 9.5

Value of x in fraction = 95/10 = 19/2

Value of x in decimal = 9.5

Answer:

(15-3x³) is the answer.

Step-by-step explanation:

2*15-2*3x³

which is 30-6x³.

10 + 10i

Apply Multiplicative Distribution Law: 12i - 9 x i^2 - 2i - i^2

Rewrite by definition: i^2 = -1:12i - 9 x (-1) -2i - (-1)

Remove the parentheses: 12i + 9 - 2i + 1

Combine like terms: 10 + 10i

Answer 10 + 10i

Answer:

10 + 10i

Step-by-step explanation:

Given expression:

[tex]3i(4 - 3i) - i (2 + i)[/tex]

Expand:

[tex]\implies 12i-9i^2-2i-i^2[/tex]

[tex]\implies 12i-2i-9i^2-i^2[/tex]

[tex]\implies 10i-10i^2[/tex]

Apply the imaginary number rule  i² = -1 :

[tex]\implies 10i-10(-1)[/tex]

Simplify:

[tex]\implies 10i+10[/tex]

Rewrite in standard complex form  a + bi:

[tex]\implies 10+10i[/tex]

Answer:

Read the given problem, look at the given figure of intersecting lines, and identify the angle given and the unknown angles.

Step-by-step explanation:

Answer: 65°

Step-by-step explanation:

You can determine the total degree within a shape by using the formula 180°(n-2), where n is the number of sides of the shape. Thus, the total degree within the parallelogram is 360°.

Angles sum up to the total degree, meaning we need to add up all the angles we see and set them equal to the total degree. We have two (2x-15) and two x's.  

2(2x-15) + 2x = 360

Distribute the 2 to (2x-15), you will get 4x - 30.

4x - 30 + 2x = 360

Add like terms, 4x + 2x to get 6x.

6x - 30 = 360

Add both sides by 30 to isolate the 6x, because we are trying to determine the value of x, we need to isolate the term.

6x = 390

Divide both sides by 6, and you are left with the value of x being 65°

Answer:

The two numbers are [tex]3[/tex] and [tex]-16[/tex].

Step-by-step explanation:

Two numbers that, when multiplied, result in a product of [tex]-48[/tex]:

[tex]x \cdot y = -48[/tex]

Same two numbers when added get a sum of [tex]-13[/tex]:

[tex]x + y = -13[/tex]

Solve for x in the summation identity:

[tex]y = -13 - x[/tex]

Plug the value back into the product identity and solve for [tex]x[/tex]:

[tex]x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0[/tex]

The roots we found for [tex]x[/tex] were:

[tex]x = 3\\x = -16[/tex]

Our two numbers are [tex]3[/tex] and [tex]-16[/tex]. We can test this:

[tex]3 + (-16) = -13\\3 * -16 = -48[/tex]

The equation of line passes through the point (1, -5) will be;

⇒ y = - 3x - 14

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (1, -5).

And, The slope of the line is,

⇒ m = - 3

Now,

Since, The equation of line passes through the point (1, -5).

And, Slope of the line is,

⇒ m = - 3

Thus, The equation of line with slope - 3 is,

⇒ y - 1 = - 3 (x - (-5))

⇒ y - 1 = - 3 (x + 5)

⇒ y - 1 = - 3x - 15

⇒ y = - 3x + 1 - 15

⇒ y = - 3x - 14

Therefore, The equation of line passes through the point (1, - 5) will be;

⇒ y = - 3x - 14

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Answer: Your answer is $7.30

Step-by-step explanation:

Finding the amount for a tip is simple!

all that's required is multiplying the bill (36.50) by the amount you want to tip (.20, because 20% is equal to .20)

36.50×.2= $7.30

The population in 208 years based on the information is 10193600.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Since the city doubles its size every 52 years. The number of times that it'll double in 208 years will be:

= 208 / 52

= 4 times

The population in 208 years will be:

= 637100 × 2⁴

= 637100 × 16

= 10193600

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Answer:

C

Step-by-step explanation:

C has a directly proportional relationship. 27 glasses are in 9 cases, and 81 glasses are in 27 cases. Directly proportional since 9×3=27 (cases) and 27×3=81 (glasses)

Second table represents an exponential function of the form y = b when 0

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered. In addition to many other applications, exponential functions are used to estimate populations, carbon date artefacts, assist coroners in determining the time of death, compute investments, and many more. Three of the most popular applications—population expansion, exponential decay, and compound interest—will be covered in this session.

Given,

Second table represents an exponential function of the form y = b when 0

Function: y = bˣ

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x is the independent variable and H(x) is the dependent variable

A dependent variable is a variable whose value depends upon independent variables.

An independent variable is a variable that does not depend on any other variable for its value.

For example, in an expression, y = 3x + 2, x is an independent and y is a dependent variable because y depends on x for its value

Given: H(x) = 3+0.5x

Therefore, x is the independent variable and H(x) is the dependent variable because it is a function of x

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The ratio Illustrated shows that the number of vanilla marshmallow is 121.

A ratio shows how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. It should be noted tjat.A/B will be the formula if one is comparing one data point (A) to another data point (B).

Let the vanilla marshmallow be represented be x.

Since the ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11, the vanilla will be:

= 11 / (5 + 11) × 176

= 11/16 × 176

= 11 × 11

= 121

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Complete question

The ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11. There are 176 chocolate marshmallows in the bag, how many marshmallows are vanilla?

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

As given in the question,

Given equation is :

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x

Simplify the original equation to get the equivalent equation

Least common multiple is 2 and 2x is equal to 2x

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:

( x + 1) / 2x = (x² -7x +10)/4x

Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

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The percentage of women that answered that they don't even like soccer is 85%

From the information, in the a survey of 500 women, 75 answered that they like soccer. Those that don't like soccer will be the difference between the values. This will be:

= 500 - 75

= 425

Therefore, the percentage of women that answered that they don't even like soccer will be:

= Those that don't like soccer / Total number × 100

= 425/500 × 100

= 85%

The percentage is 85%.

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Complete question

In a survey of 500 women, 75 answered that they like soccer. What percentage of women answered that they don't even like soccer?

As per the given equation in form of inequality 4x - 2y > 12 gives  the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.

As given in the question,

Given equation in inequality form is :

4x - 2y > 12

Simplify the given equation in intercept form we get,

2y < 4x -12

⇒ y < 2x -6

If we write this inequality in equation form we have,

y = 2x -6

slope of the line is 2

x -intercept is x = 3

y - intercept is y = -6

And in inequality form x > 3 and y < -6.

Therefore, for the given equation in form of inequality 4x - 2y > 12 gives  the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.

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Answer:

y=1/3x+6

Step-by-step explanation:

Use the formula "Y=mx+b"

Answer:

y= -1/3x - 6

Step-by-step explanation:

x+3y = -18

3y = -x -18

y= -1/3x - 6

Considering the triangle with exterior angles and interior angles as described. The statements that are true include

The problem is solved considering this 3 theorems about triangles

exterior angles theorem: m∠2 + m∠3 = m∠6

If a triangle side is created, the outside angle that results is equal to the sum of the two opposite internal angles.

Linear pair theorem: m∠5 + m∠6 =180°

Linear pairs are particular instances of supplementary angles that only involve two neighboring angles.

Sum of angles in a triangle is equal to 180 degrees:

m∠2 + m∠3 + m∠5 = 180°

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For the given triangle, the value of x would be 12.

What is the geometric mean theorem of a triangle?

According to the geometric mean theorem, the length of an altitude drawn from a triangle's right angle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

For the given triangle, we can apply the geometric mean theorem,

                      By the geometric mean theorem, we can write

                                      6² = 3 * x

                                      36 =  3 * x

                                  ⇒ x = 36/3

                                  ⇒ x = 12.

Hence, for the given triangle, the value of x would be 12.

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Answer:

-24

Step-by-step explanation:

b²-2ac

⇒Plug in the values given in places and simplify.

[tex]=(-4)^{2} -2(-4)(-5)\\=16-2(20)\\=16-40\\=-24[/tex]

-24 is the answer after substitution of the known values.

Answer:i had forgot

Step-by-step explanation:

Answer:4

Step-by-step explanation:

u add den subtract den divide then there

The solution for x in the expression given as 15 + ax/5 =  10 is x = -25/a

From the question, the algebraic expression is given as

15 + ax/5 =  10

There is a constant to add to or subtract from the expression

So, the we subtract 15 from both sides

- 15 + 15 + ax/5 =  10 - 15

Evaluate

ax/5 = -5

Multiply both sides of the equation by 5

This gives

5 * ax/5 = -5 * 5

Evaluate the products

So, we have the following equation

ax = -25

Multiply both sides of the equation by 1/a

This gives

1/a * ax = -25 * 1/a

Evaluate the products in the above expression

x = -25/a

Hence, the solution is x = -25/a

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Answer: $372

Step-by-step explanation:

330 + (1.5% of 330) = 334.95

334.95 + (1.5% of 334.95) = 339.97425

339.97425 + (1.5% of 339.97425) = 345.073864

345.073864 + (1.5% of 345.073864) = 350.249972

350.249972 + (1.5% of 350.249972) = 355.503772

355.503772 + (1.5% of 355.503772) = 360.836392

360.836392 + (1.5% of 360.836392) = 366.248398

366.248398 + (1.5% of 366.248398) = 371.742124

Please thank and rate :)

For the given triangle JKL, the value of x is 10. An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint.

Given information:

In  ∠J K L,JL is extended through point L to point M.

[tex]$&m \angle J K L=(2 x+14)^{\circ} \\[/tex]

[tex]$&m \angle L J K=(3 x+15)^{\circ} \\[/tex]

[tex]$&m \angle K L M=(7 x+9)^{\circ}[/tex]

See the attached figure.

At point L, the measure of angle JLK will be as,

[tex]$&m \angle J L K=180-m \angle K L M=180-7 x-9 \\[/tex]

[tex]$&=(171-7 x)^{\circ}[/tex]

Now, in triangle JKL, use the angle sum property to find the value of x as,

[tex]$$m \angle J K L+m \angle L J K+m \angle J L K=180[/tex]

[tex]$$$(2 x+14)^{\circ}+(3 x+15)^{\circ}+(171-7 x)^{\circ}=180$[/tex]

-2 x+200=180

2 x=20

x=10

Therefore, the value of x for the given triangle JKL is 10.

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The value of sec θ is -5/3 ,and  the value of cot θ is 3/4 in the unit circle.

Given:

The point -3/5 , -4/5 in the third quadrant corresponds to angle θ on the unit circle.

here x = -3/5 and y = -4/5

radius r = [tex]\sqrt{(-3/5)^{2}+(-4/5)^{2} }[/tex]

= [tex]\sqrt{9/25 + 16/25}[/tex]

r = 1.(which is hypotenuse in unit circle).

sec θ = hypotenuse / adjacent

= 1/-3/5

sec θ = -5/3

cot θ = adjacent / opposite

= -3/5 / -4/5

= 3*5/5*4

= 15/20

cot θ= 3/4

Therefore the value of sec θ is -5/3 ,and  the value of cot θ is 3/4.

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Answer: No

Step-by-step explanation: to find out how much more money Eugene will be making we need to isolate the increased value provided by the raise and then add it to his already existing earnings. We do this by multiplying $2700 by 3.5%.

We would write this as 2700 x .035

This is because 100% can be converted to 1, for example if Eugene got a 100% raise we would multiply 2700 by 1 (which changes nothing) then add 2700 and 2700 together.

Since Eugene is only getting a 3.5% raise we would write it as .035 instead of 1

Now that we have our equation we first need to simplify. In this case it means we remove the two zero's from 2700 to make it 27. To make sure the answer does not get messed up will make the other side of the equation larger by moving everything two decimal points (one for each removed zero) like this.

27 x 3.5

This is much easier to work with but I will still show the steps I am using to prevent confusion.

27 x .5 = 13.5

27 x 3 = 20 x 3 + 7 x 3

20 x 3 = 60

7 x 3 =21

60+21 =81

81+13.5=94.5

Since 2700 + 94.5 = 2794.5 Eugene will not make more than $2800 dollars a month after his raise.

Hi, your answer will be 2.6 tons. Hope it helps.

Answer:

2.6 tons can be lifted by a rope with a diameter of 2 inches.

Step-by-step explanation:

2 = √39 / π

hope this helps you

Answer:

LCM of 90 and 225 = 450

I'm not too sure I understand

2 x 3 x 3 x 5 = 90, and 3 x 3 x 5 x 5 = 225

90: 90, 180, 270, 360, 450

225: 225, 450

LCM = 450

The domain of the graph is (d) all set of real values

The graph represents the given parameter

This graph represents a function

Say the graph represents the function f(x)

The x values represent the domain

i.e domain = Set of all x values

On the graph, we can see that the graph extends across the x-axis till infinity on both sides

This means that

Domain = All set of real values

Hence, the domain of the relation is (d) all set of real values

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