Solve the equation.
8 – 2x = -8х + 14
A) x= -1
B) x= -3/5
C) x= 3/5
D) x= 1

Answer: 20

Step-by-step explanation:

Given: Point [tex]\text{G}[/tex] is on line segment [tex]\text{FH}[/tex]. Given [tex]\text{FH}[/tex] is [tex]4\text{x}+8[/tex] , [tex]\text{FG}[/tex]. is [tex]\text{x}[/tex], and [tex]\text{GH}[/tex] is [tex]5\text{x}[/tex].

To Find: the numerical length for [tex]\text{GH}[/tex].

Solution:

Point [tex]\text{G}[/tex] is on the line segment [tex]\text{FH}[/tex]

therefore,

[tex]\text{FH}=\text{FG}+\text{GH}[/tex]

putting the values

[tex]4\text{x}+8=\text{x}+5\text{x}[/tex]

[tex]4\text{x}+8=6\text{x}[/tex]

[tex]8=2\text{x}[/tex]

[tex]\text{x}=4[/tex]

Now,

[tex]\text{GH}=5\text{x}[/tex]

[tex]\text{GH}=5\times4[/tex]

[tex]\text{GH}=20[/tex]

Hence numerical length of line segment [tex]\text{GH}[/tex] is [tex]20[/tex]

The numerical length of GH is 20

If Point G is on the line segment FH, this means that:

Given the following parameters:

FH=4x+8

FG=x

GH=5x

Substitute the given values into the formula as shown:

x + 5x = 4x + 8

6x = 4x + 8

6x - 4x = 8

2x = 8

Divide both sides by 2

2x/2 = 8/2

x = 4

Get the length of GH

GH = 5x

GH = 5(4)

GH = 20

Hence the numerical length of GH is 20

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Answer:

15

Step-by-step explanation:

Substitute x = - 5 into f(x)

f(- 5) = 5(- 5) + 40 = - 25 + 40 = 15

The best name for the part of the figure identified by the arrow is line of symmetry.

The best name for the part of the figure identified by the arrow is line of symmetry. It refers to a line that divides a figure into two equal halves, which are mirror images of each other.

The line of symmetry can be identified by the arrow in the figure where the reflection occurs.

For example, in the letter 'A', the line through the middle vertically is the line of symmetry, as both sides of the letter are identical when folded along that line.

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Answer:

(8,-10)

Step-by-step explanation:

step 1

Find the slope of line KL

K(-6,8),L(6,0)

m=(0-8)/(6+6)

m=-8/12=-2/3

step 2

Find the slope of the line that is parallel to KL

we know that

If two lines are parallel , then their slopes are the same

therefore

The slope of the parallel line to KL is m=-2/3

step 3

Find the equation of the line parallel to KL that pass through the point M

M(-4,-2)

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

substitute

y+2=-(2/3)(x+4)

step 4

Verify the points

we know that

If the point lie on the line, then the point must satisfy the equation of the line

case a) (-10,0)

substitute the value of x and the value of y in the equation and then compare the result

-10+2=-(2/3)(0+4)

-8=-8/3 -----> is not true

therefore

The point is not on the line

case b) (-6,2)

substitute the value of x and the value of y in the equation and then compare the result

2+2=-(2/3)(-6+4)

4=4/3 -----> is not true

therefore

The point is not on the line

case c) (0,-6)

substitute the value of x and the value of y in the equation and then compare the result

-6+2=-(2/3)(0+4)

-4=-8/3 -----> is not true

therefore

The point is not on the line

case d) (8,-10)

substitute the value of x and the value of y in the equation and then compare the result

-10+2=-(2/3)(8+4)

-8=-8 -----> is true

therefore

The point is on the line

Answer:

[tex]\large\boxed{B)\ \dfrac{3V}{3.14r^2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{3}\cdot3.14\cdot r^2h=V\\\\\dfrac{3.14}{3}r^2h=V\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{3.14}{3\!\!\!\!\diagup_1}r^2h=3V\\\\3.14r^2h=3V\qquad\text{divide both sides by}\ 3.14r^2\\\\h=\dfrac{3V}{3.14r^2}[/tex]

[tex]\bf \begin{cases} f(x)=3x^2\\ g(x)=4x^3+1 \end{cases}\qquad (f\cdot g)(x)\implies f(x)\cdot g(x)\implies [3x^2]\cdot [4x^3+1] \\\\\\ 12x^2x^3+3x^2\implies 12x^{2+3}3x^2\implies \stackrel{\textit{5th degree}}{12x^{\stackrel{\downarrow }{5}}+3x^2}[/tex]

Answer:

The vertical distance from the ground to the bird's eyes is 47.67 m

Step-by-step explanation:

* Lets explain the situation of the problem

- There is a bird on the top of  a tree

- The bird looks down on a field mouse at an angle of depression of 50°

- The field mouse is 40 meters from the base of the tree

* Consider that the vertical distance from the ground to the bird's eyes,

 the distance from the field mouse to the base of the tree distance

 from the bird eyes to the field mouse formed a right triangle

- The hypotenuse is the distance from the bird eyes to the field mouse

- The horizontal side is the distance from the field mouse to the base

 of the tree

- The angle between the hypotenuse and the horizontal side is the

 angle of depression which = 50°

- The opposite side to the angle of measure 50° is the vertical distance

 from the ground to the bird's eyes

* Lets use trigonometry functions to find the vertical distance

∵ The length of the adjacent side to the angle of measure 50° is 40 m

∵ The length of the opposite side to the angle of measure 50° is h m

∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф

∵ Ф = 50°

∴ tan 50° = h/40 ⇒ by using cross multiplication

∴ 40 tan 50° = h

∴ h = 47.67 m

* The vertical distance from the ground to the bird's eyes is 47.67 m

Answer:

The y-intercept is the point (0,5)

Step-by-step explanation:

step 1

Find the slope of the line perpendicular to the line y=(3/4)x+3

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

we have

m1=3/4 -----> the slope of the line y=(3/4)x+3

Find m2

substitute

(3/4)*m2=-1

m2=-4/3

step 2

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=-4/3

(x1,y1)=(3,1)

substitute

y-1=-(4/3)(x-3) ----> equation of the line into point slope form

step 3

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation of the line and solve for y

y-1=-(4/3)(0-3)

y-1=4

y=4+1=5

The y-intercept is the point (0,5)

Final answer:

The y-intercept of the line perpendicular to y = 3/4x+3 that includes the point (3, 1) is 5.

Explanation:

To find the y-intercept of the line perpendicular to the line y = 3/4x+3 that includes the point (3, 1), we first need to determine the slope of the perpendicular line. Since the given line has a slope of 3/4, the slope of the perpendicular line will be the negative reciprocal, which is -4/3. We then use the point-slope form of a line equation, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.

Substituting the point (3, 1) and the slope -4/3 into the equation gives us y - 1 = -4/3(x - 3). Simplifying, we get y = -4/3x + 5. The y-intercept of this line is the y-value when x is zero, which in this case is 5.

Answer:

Q1. The solution for the quadratic equation on a graph is same as the value of x-intercept(zeros)

Q2. discriminant(b^2-4ac) when y=ax^2 + bx + c

there are 3 situations:

1. discriminant > 0 → 2 real solutions(2 x-intercepts/zeros)

2. discriminant = 0 → 1 real solution(1 x-intercept/zero)

3. discriminant < 0 → 0 real solution(0 x-intercept/zero) → also 2 imaginary solution

Hope it helped!

Step-by-step explanation:

Answer:

1) You find the solution by identifying the x-intercepts.

2) Possible real solutions:

- One real solution.

- Two distinct real solutions.

Step-by-step explanation:

1) The graph of a quadratic equation is a parabola.

By definition, the x-intercepts (Where [tex]y=0[/tex]) are the solutions of the quadratic equation .

2) Given a quadratic equation [tex]ax^2+bx+c=0[/tex], you can know the number of real solutions by using this formula to find the Discriminant :

[tex]D=b^2-4ac[/tex]

If  [tex]D=0[/tex], then there is one real solution with multiplicity two.

If  [tex]D>0[/tex], then there are two distinct real solutions.

On a graph:

-If the graph has two x-intercepts, then the quadratic equation has two real solutions.

 -If the graph has one x-intercept , then the quadratic equation has one real solution.

The correct option is:

C. [tex]2(y+1)+y=7[/tex]

To find which of the given options are not the result of a substitution in the given system, we need to isolate the variable in function of the other variable, and then substitute it.

So, substituting and discarding, we have:

- First equation:

[tex]2x+y=7[/tex]

Isolating "y", we have:

[tex]y=7-2x[/tex]

Then, substituting it into the second equation, we have:

[tex]y-x=1[/tex]

[tex]7-2x-x=1[/tex]

We have that it's a result of a substitutiong in the following system (option A)

- Second equation:

[tex]y-x=1[/tex]

Isolating "y", we have:

[tex]y=x+1[/tex]

Then, substituting it into the first equation, we have:

[tex]2x+y=7[/tex]

[tex]2x+(x+1)=7[/tex

[tex]2x+x+=7[/tex

We have that it's a result of a substitution in the following system (option B)

Hence, we have that the option C is not a result of a substitution in the given system of equations since there is not a possible value of the variable "x" that is equal "y+1".

So, the correct option is:

C. [tex]2(y+1)+y=7[/tex]

Have a nice day!

Answer:

C. 2(y + 1) + y = 7​

Step-by-step explanation:

Answer:5x2+12x-14

Step-by-step explanation:

(5x2+11x-9)-(2x-3x+5)

5x2+11x-9-2x+3x-5

5x2+12x-14

[tex](5x^2 + 11x - 9) - (2x - 3x + 5)=5x^2+11x-9-2x+3x-5=5x^2+12x-14[/tex]

-------------------------------------------------

[tex](5x^2 + 11x - 9) - (2x^2 - 3x + 5)=5x^2+11x-9-2x^2+3x-5=3x^2+14x-14[/tex]

Answer:

1/(x+3)+7/(x+2)

Step-by-step explanation:

I'm assuming the full numerator is (8x+23)... and by making that assumption I'm assumed the fraction was (8x+23)/[(x+3)(x+2)].

(8x+23)/[(x+3)(x+2)]=A/(x+3)+B/(x+2)

8x+23=A(x+2)+B(x+3)                   I multiply both sides by (x+3)(x+2)

Set x to -2 that gives -16+23=B          so this means B=7

Set x to -3 instead that gives -24+23=A(-1)   so this means A=1

So (8x+23)/[(x+3)(x+2)]=1/(x+3)+7/(x+2)

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} B=\stackrel{183\times 183}{33489}\\ h=110 \end{cases}\implies V=\cfrac{1}{3}(33489)(110)\implies V=1227930[/tex]

Answer:

V =1127930 m^3

Step-by-step explanation:

The volume is

V = 1/3 B h

where B is the area of the base

B = area of the square

B = 183*183 since it is a square

B = 33489

V = 1/3 *(33489) * 110

V =1127930 m^3

Word Problem #1:

You are in a submarine at a depth of some unknown value x. The submarine rises 15 feet. After this point, you are able to record the depth to be 18 feet below sea level.

x = original depth

15 = height you rise up

-18 = final depth

x+15 = final depth

x+15 = -18 is the equation we solve to find the value of x

=========================================================

Word Problem #2:

You are in debt to your friend. Debt is represented by negative numbers. For example, writing -2 means you are 2 dollars in debt. If you start off being x dollars in debt, but pay off $15, then you will have a balance of x+15 dollars. If this new final balance is -18, then we can say x+15 = -18

So in short: you go from x dollars in debt to 18 dollars in debt after paying off $15 to your friend.

Answer:

1/32768

Step-by-step explanation:

First, solve the parenthesis:

2^3 = 2 * 2 * 2 = (2 * 2) * 2 = (4) * 2 = 8

Next, solve the outer power. Note that it has a negative sign, which means that after you solve for the power sign, you have to put the number under 1.

(8)^-5 = 1/(8 * 8 * 8 * 8 * 8) = 1/32768

1/32768 is your answer.

~

Answer:

A) 1/2^15

Step-by-step explanation:

edge2021

Answer:

90 recipes

Step-by-step explanation:

we know that

Fiona posted a total 216 recipes in 36 weeks

using proportion

Find out  how many recipes did she upload in 15 weeks'

Let

x -----> the number of recipes

[tex]\frac{216}{36}\frac{recipes}{weeks}=\frac{x}{15}\frac{recipes}{weeks} \\\\x=216*15/36\\\\x= 90\ recipes[/tex]

Answer:

x=8 ?

Step-by-step explanation:

Step-by-step explanation:

[tex]1 \div 2 \times base \times height = area[/tex]

[tex]1 \div 2 \times x \times 42.2 = \ 369.25 \[/tex]

[tex]x = 369.25 \div 21.1[/tex]

[tex] = 17.5[/tex]

Answer:

Base = 17.5 inches.

Step-by-step explanation:

Given  : A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches.

To find : What is the length of the base of the triangle.

Solution : We have given

Area of triangle = 369.25 square inches.

Height =  42.2 inches.

Area of triangle = [tex]\frac{1}{2}*base*height[/tex].

Plugging the values.

369.25 =  [tex]\frac{1}{2}*base*42.2[/tex].

On multiplying both sides by 2

369.25 * 2 = base * 42.2

738.5 = base * 42.2

On dividing both sides by 42.2

Base = 17.5 inches.

Therefore, Base = 17.5 inches.

The correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).

To use the distributive property, we need to distribute the first factor,

(2x^2 +4−7), over the two factors in the second set of parentheses, (x) and  (x−2).

This means we multiply each term in the first factor by each term in the second set of parentheses, and then add the products together.

Here is the correct distribution:

(2x^2+4-7)(x) + (2x^2+4-7)(x-2)

= (2x^3+4x-7x) + (2x^3-4x+14x-14)

= 4x^3-3x+7 + 10x-14

= 4x^3+7x-7

Therefore, the correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).

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Answer:

2nd choice B.

Step-by-step explanation:

You can use the options A-D to help you eliminate pretty quickly without actually graphing

So first chose says you have the graph on the left when x<1 But you should see our visual actually says we want to include what happens at 1 (the filled dot) so this isn't the answer

Second choice Possible

Third choice... I'm just going to look at one of the parts... x^2+4 for x<=1 says we should have part of a parabola to the left of x=1 (inclusive) but there is not parabola in our visual

Fourth choice: same reason as third choice

Answer is the 2nd

Answer:

[tex]{\boxed{\text{A. }\math{k = -7}}[/tex]

Step-by-step explanation:

The general rule for vertical translation of a function ƒ(x) ⟶ ƒ(x) + k .

A positive value of k means that the graph is shifted up by k units.

The graph of ƒ(x) was shifted from (0, 1) to (0, -6).

[tex]\text{The graph was shifted down by seven units, so }{\boxed{\mathbf{k = -7}}[/tex]

The value of k is -7.

Vertical translation refers to the up or down movement of the graph of a function.

Here, the shape of the function remains the same.

It is also known as the movement/shifting of the graph along the y-axis.

In vertical translation, each point on the graph moves k units vertically and the graph is said to translated k units vertically.

The general rule for vertical translation of a function,

f(x)= g(x) + k .

here, the graph is shifted up by k units.

As, seen from the graph of g(x) is shifted from point (0, 1) to (0, -6).

Hence, the graph is shifted by -7 units.

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Answer:

Step-by-step explanation:

Slope = y/x

y1-y2/x1-x2=slope of 2 points

8-3/-6-2 = 5/-8 which equals -5/8 or -.625.

The slope of line for the points is -5/8.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

given:

We have the Points (–6, 8), (2, 3).

So, the slope is

m = (3- 8)/ (2- (-6))

m = -5 / (2+6)

m = -5 / 8

Thus, the Slope is -5/8.

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Answer:

3^2=x+1 is the equivalent

Step-by-step explanation:

3^2=(x+1)  is equivalent to log_3(x+1)=2

where x+1 is positive

The problem is solved by calculating that there are 24 nickels and 12 dimes to make a total of $2.40, given that there are twice as many nickels as dimes.

The subject of this question is Mathematics, specifically dealing with simple money-based equations. In the problem you're presented with, you've been asked to figure out the number of nickels and dimes that make up $2.40, given that there are twice as many nickels as there are dimes.

First, we can start by understanding the value of each coin. A nickel is worth $0.05, and a dime is worth $0.10. With the condition expressed in the problem, let's express the number of dimes as x, thus the number of nickels would then be 2x.

Because of their respective values, the total value of the dimes would be 0.10x and the total value of the nickels would be 0.05 × 2x or 0.10x. Adding both together, we'd have 0.10x + 0.10x = 0.20x, which we know equals $2.40 from the problem. Solving the equation 0.20x = 2.40 gives us x = 12. That's your number of dimes. The nickels would be 2 × 12 = 24. So, the answer to your problem would be 24 nickels and 12 dimes.

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Answer:

[5, 0]

Step-by-step explanation:

x-intercept is where 0 = y. Just simply plug in 0 for y, then your x is given to you in your face.

Answer:

Step-by-step explanation:

First, factor the denominator: (x-5)(x+4)

Since the denominator already has the two values, you only need to multiply it by (x+3), which means you need to multiply the numerator by (x+3):

(x-1)(x+3)/(x-5)(x+4)(x+3)

(x-1)(x+3) then simplifies to [tex]x^2+2x-3[/tex]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{5}{2}[/tex] and (a, b) = (- 6, 2), so

y - 2 = - [tex]\frac{5}{2}[/tex] (x - (- 6)), that is

y - 2 = - [tex]\frac{5}{2}[/tex] (x + 6) ← in point- slope form

An equation in point slope form for this line y - 2 = -5/2  (x + 6) .

The point slope form of a straight line in geometry is used to represent the equation of a straight line using its slope 'm' and a point(x, y) that lies on the given line.

equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Now,  m = - 5/2

and (a, b) = (- 6, 2)

So, the equation of line be

y-2=  -5/2 (x+6)

Hence,

y - 2 = -5/2  (x + 6) in point- slope form.

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Answer:

Variability is when there is no consistency.

Step-by-step explanation:

Variation in data can be due to various factors. Variability can also be called the spread of data.

Standard deviation is a measure of variability as standard deviation measures the spread of data.

!!

Answer:

[tex]\large\boxed{V=\dfrac{32}{3}\pi\ cm^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{We have}\ D=4\ cm\to R=\dfrac{4}{2}\ cm=2\ cm\\\\\text{Substitute:}\\\\V=\dfrac{4}{3}\pi(2)^3=\dfrac{4}{3}\pi(8)=\dfrac{32}{3}\pi\ cm^3[/tex]

Answer:

C. 40°

Step-by-step explanation:

From the diagram, in triangle XYZ, XY=XZ=6 units. This means triangle XYZ is isosceles triangle with base YZ.

In isoscels triangle angles adjacent to the base are congruent, so

∠ZYX=∠YZX=70°

The sum of all interior angles in triangle is always 180°, so

∠ZYX+∠YZX+∠ZXY=180°

∠ZXY=180°-70°-70°

∠ZXY=40°

∠ZXY is ∠X, so ∠X=40°