Graph the linear equation. Find the three points that solve the equation then plot on the graph. -y=-x+1

Answer:

[tex]\large\boxed{\dfrac{7x^2}{6x-10}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7x^2}{2x+6}\div\dfrac{3x-5}{x+3}=\dfrac{7x^2}{2(x+3)}\cdot\dfrac{x+3}{3x-5}\\\\\text{cancel}\ (x+3)\\\\=\dfrac{7x^2}{2}\cdot\dfrac{1}{3x-5}=\dfrac{(7x^2)(1)}{(2)(3x-5)}\\\\\text{use the distributive property}\ a(b-c)=ab-ac\\\\=\dfrac{7x^2}{6x-10}[/tex]

Answer:

C. Black grapes cost more per pound than green grapes.

Step-by-step explanation:

Verify each statement

A. Three pounds of green grapes cost $6.00

The statement is False

Because

For x=3 pounds

y=1.5x

y=1.5(3)=$4.5

B. Black grapes cost less per pound than green grapes

The statement is False

Because

For x=1 pound

The green grapes cost ----> y=1.5(1)=$1.5

Observing the graph

For x=1 pound

The black grapes cost $2

C. Black grapes cost more per pound than green grapes.

The statement is True

D. Two pounds of black grapes cost $3.00.

The statement is False

Because

Observing the graph

Two pounds of black grapes cost $4

An equation is formed of two equal expressions. The third statement is true.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.) The cost of a pound of green grapes is,

Y = 1.5X = 1.5×3 = 4.5

Hence, the first statement is false.

B.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the second statement is false.

C.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the third statement is true.

D.) As per the graph, the cost of 2 pounds of grapes is $4. Thus, the fourth statement is wrong.

Hence, the third statement is true.

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Answer:

9

Step-by-step explanation:

What you're going to do is

-take the area and divide it by the amount of sides (a square has 4)

36/4=9

Answer: The mean

Step-by-step explanation: a) The mean:

To find the mean, we just simply need to add the hours spent by the students playing games and divide by the number of hours.

Mean =  = 2.85

b) The median:

We will arrange the number of hours for in ascending order and the middle value will be the median.

Median = 3

c) The mode:

Mode is the number which occurs most frequently. So in this case Mode = 2, 3.

d)Percentage of the students play video games for more than 4 hours in a month  =  = 45%

Answer:

a and f

Step-by-step explanation:

Vertical angles are directly opposite each other, created by two lines intersecting.

∠A and ∠F are congruent to each other because they are vertically opposite angles. Then the correct option is D.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

∠A and ∠F, ∠B and ∠E, ∠C and ∠H, and ∠D and ∠G are congruent to each other because they are vertically opposite angles.

Then the correct option is D.

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Check the picture below.

The answer is a=8 btw

Answer:

Angle addition postulate and 2x=56

Step-by-step explanation:

The value of x is 28 degree.

Linear pair of angles are formed when two lines intersect each other at a single point.

Given:

m∠ELG = 124

as, m∠ELG and m∠ELD are in linear pair.

So, 124 + 2x =180

2x =56

x -28

Hence, the value of x is 28 degree

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Answer:

The area of triangle ABC is [tex]25\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of triangle ABC is equal to the area of triangle ABO minus the area of triangle ACO

see the attached figure to better understand the problem

step 1

Find the area of triangle ABO

The area is equal to

[tex]A=\frac{1}{2}(AO)(BO)[/tex]

substitute values

[tex]A=\frac{1}{2}(10)(5+2)=35\ cm^{2}[/tex]

step 2

Find the area of triangle ACO

The area is equal to

[tex]A=\frac{1}{2}(AO)(CO)[/tex]

substitute values

[tex]A=\frac{1}{2}(10)(2)=10\ cm^{2}[/tex]

step 3

Find the area of triangle ABC

[tex]35\ cm^{2}-10\ cm^{2}=25\ cm^{2}[/tex]

Answer:

False

Step-by-step explanation:

12 × 15 = 180

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 180

Answer:

180.

Step-by-step explanation:

Something wrong there. Mine says 180.

12 * 15 = 12*10 + 12*5

= 120 + 60

= 180.

Answer:

Downwards.

Step-by-step explanation:

The coefficient of x^2 is negative (-3) so it opens downwards. All values of x will be 0 or negative.

I do not see an illustration.

Answer: 6 units

Step-by-step explanation:

Area = 1/2 (base1 + base2) X height <-------- Formula for a trapezoid

24 = 1/2 (2 + 6) X h <----- We know that the area of the trapezoid is 24 units

squared and that both of the bases are 2 units and 6 units.

24 = 1/2 (8) X h <------- Add 6 + 2

24 = 4 X h <-----  Half of 8 is 4

h = 6 <------  6 X 4 = 24 , therefore the height is 6 units.

Hope this helps!

ANSWER

The coordinates of the image are (2,2)

EXPLANATION

The mapping for a reflection across the line y=k is :

[tex](x,y)\to (x,2k-y)[/tex]

We want to find the image of the point (2,-4) after a reflection in the line y=-1.

In this case k=-1.

[tex](2, - 4)\to (2,2( - 1)- - 4)[/tex]

This simplifies to,

[tex](2, - 4)\to (2, - 2 + 4)[/tex]

[tex](2, - 4)\to (2, 2)[/tex]

Hence the image is (2,2)

Answer:

  650 kg/m³

Step-by-step explanation:

The density is the ratio of mass to volume. The volume is the product of the dimensions of the prism.

  density = (146.25 kg)/((1.5 m)(0.75 m)(0.2 m)) = 146.25/0.225 kg/m³

  = 650 kg/m³

Answer:

  650 kg/m³

Step-by-step explanation:

Answer:

The measure of angle LMW is [tex]m\angle LMW=67\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc MW

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK][/tex]

substitute the given values

[tex]65\°=\frac{1}{2}[arc\ MW+68\°][/tex]

[tex]130\°=[arc\ MW+68\°][/tex]

[tex]arc\ MW=130\°-68\°=62\°[/tex]

step 2

Find the measure of arc LK

we know that

[tex]arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°[/tex] -----> by complete circle

substitute the given values

[tex]164\°+62\°+68\°+arc\ LK=360\°[/tex]

[tex]294\°+arc\ LK=360\°[/tex]

[tex]arc\ LK=360\°-294\°=66\°[/tex]

step 3

Find the measure of angle LMW

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK][/tex]

substitute the given values

[tex]m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°[/tex]

Applying the inscribed angle theorem, the measure of angle LMW is found as: 67°.

According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that is intercepted.

Given:

Find m(MK):

m(MK) = 2(m∠MLK) (inscribed angle theorem)

Substitute

m(MK) = 2(65°)

m(MK) = 130°

Find m(LK):

m(LK) = 360° - m(LM) - m(MK) (full circle)

Substitute

m(LK) = 360° - 164° - 130°

m(LK) = 66°

Therefore:

m∠LMW = 1/2[m(LK) + m(WK) (inscribed angle theorem)

Substitute

m∠LMW = 1/2[66° + 68°]

m∠LMW = 1/2[134°]

m∠LMW = 67°

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]g(x)=2^{x-1}+3[/tex]

This is a exponential function

The domain is the interval ----> (-∞,∞)

All real numbers

The range is the interval ----> (3,∞)

All real numbers greater than 3

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

For x=0

[tex]g(0)=2^{0-1}+3[/tex]

[tex]g(0)=2^{-1}+3[/tex]

[tex]g(0)=\frac{1}{2} +3[/tex]

[tex]g(0)=3.5[/tex]

The y-intercept is the point (0,3.5)

using a graphing tool

The graph in the attached figure

Answer:

The first answer

Step-by-step explanation:

I took the test

Answer:

a) 235.62in³

b) 904.78in³

Step-by-step explanation:

a) The formula to find the volume of a cylinder is:

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

We are given that r = 5 and h = 3, so we can just plug in and solve:

[tex]V = \pi(5)^2(3) = 235.62in^3[/tex]

b) The formula to find the volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

We are given that the diameter is 12in, which means that the radius (r) must be 6in (half the diameter). Now, we can plug in and solve:

[tex]V = \frac{4}{3}\pi (6)^3 = 904.78in^3[/tex]

ANSWER

D. 135 m^2

EXPLANATION

The area of a kite is half the product of the diagonals.

The first diagonal is

9m+6m=15m

Note that the vertical diagonal is the axis of symmetry of the kite.

This diagonal bisect the kite

Therefore the second diagonal is

2(9m)=18m

The area of the kite

[tex] = \frac{1}{2} \times 18 \times 15[/tex]

[tex] = 9 \times 15[/tex]

[tex] = 135 {m}^{2} [/tex]

Answer:

[tex]A_{T}=135 m^{2[/tex]

Step-by-step explanation:

Hello

To solve this problem we can divide the kite into simpler geometric figures to find its area, we have four triangles

the area of a triangle =(b*h)/2

b is the base and his the heigth

Step 1

triangle 1 (LEFT UP)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{1} =40.5\ m^{2}[/tex]

Step 2

triangle 2 (RIGHT UP)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{2} =40.5\ m^{2}[/tex]

Step 3

triangle 3 (LEFT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{3} =27\ m^{2}[/tex]

Step 4

triangle 4 (RIGHT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{4} =27\ m^{2}[/tex]

Step 5

Total Area

the total area is

[tex]A_{T}=A_{1}+A_{2}+A_{3}+A_{4}   \\A_{T}=(40.5+40.5+27+27)m^{2} \\A_{T}=135 m^{2}[/tex]

Have a great day

Answer:

A

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent in the terms of the polynomial. The leading coefficient is the coefficient of the term with the largest exponent.

Given

f(x) = 2x³ + 2x² - [tex]\frac{1}{x}[/tex]

The term - [tex]\frac{1}{x}[/tex] means that f(x) is not a polynomial

Since terms with division by a variable are not allowed.

The answers are:

First box: 7 times the cube of the sum of x and 8

Second box: 8 added to the cube of 7x.

Third box: 8 added to 7 and x cubed.

Fourth box: the cube of the sum of 7x and 8.

We are given the expression and we need to macth to the correct verbal description, so we have:

First box:

[tex]7(x+8)x^{3}[/tex]

It's 7 times the cube of the sum of x and 8

Second box:

[tex](7x)^{3}+8[/tex]

We have that "7x" is cubed and then, added to 8, so,  it's 8 added to the cube of 7x.

Third box:

[tex]7x^{3}+8[/tex]

We have "7" times "x" cubed and added to 8, so it's 8 added to 7 and x cubed.

Fourth box:

[tex](7x+8)x^{3}[/tex]

We have "7x" added to 8, and the expression is cubed, so, it's the cube of the sum of 7x and 8.

Have a nice day!

Answer: -30

I really hope this helped you

To solve 3 3/5 x (-8 1/3), we convert the mixed numbers into improper fractions, multiply them, and simplify to get the answer -30.

The student is asking to perform multiplication between a mixed number and a mixed number with a negative sign. To compute 3 3/5 x (-8 1/3), we first convert the mixed numbers into improper fractions. The number 3 3/5 can be converted to 18/5 (since 3*5 + 3 = 18) and -8 1/3 can be converted to -25/3 (since -8*3 + 1 = -25). Multiplying these two improper fractions gives us (18/5) * (-25/3). To multiply fractions, we multiply the numerators together and the denominators together, giving us -450/15. Simplifying this fraction, we get the final answer, which is -30.

so the bike costs $129, but she already has $24 saved, then she'll be saving $3 per week so let's take a peek at a table of those savings

week 1..................... total amount......... 24 + 3(1)

week 2..................... total amount......... 24 + 3(2)

week 3..................... total amount......... 24 + 3(3)

week 4..................... total amount......... 24 + 3(4)

week 5..................... total amount......... 24 + 3(5)

week w..................... total amount......... 24 + 3(w)

[tex]\bf \stackrel{\textit{total savings}}{s(x)}=\stackrel{\textit{initial amount}}{24}+\stackrel{\textit{weekly savings}}{3w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{cost of the bike}}{129}=24+3w\implies 105=3w\implies \cfrac{105}{3}=w\implies 35=w[/tex]

Answer:

24 + 3x = 129

35 weeks

Step-by-step explanation:

She already has 24 dollars saved, but will save 3 dollars every week. Use x to represent the number of weeks. In total she will save 129.

Solve for x using the equation:

24-24 + 3x = 129-24

3x = 105

3x/3 = 105/3

x= 35

0=1/2(2x²+13x+20)

0=x²+6,5x+10

[tex]x = \frac{ - 6.5 + \sqrt{2.25} }{2} \\ x = - 2.5 \\ x = - 4[/tex]

Answer:

x = - 2.5, x = - 4

Step-by-step explanation:

To find the zeros, set y = 0, that is

[tex]\frac{1}{2}[/tex](2x + 5)(x + 4) = 0

Equate each of the factors to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - 2.5

x + 4 = 0 ⇒ x = - 4

Answer:

4

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards

From the given diagram this is represented by angle 4

Answer:

5

Step-by-step explanation:

total sum of the 6 numbers

= 4 ×6

= 24

sum of numbers without the two 2s

= 24 - 2(2)

= 20

average of other 4 numbers

= 20 ÷ 4

= 5

The average of the other four numbers is 5.

How to find the average?

The average of six numbers is 4. If the of two of those numbers is 2.

The total sum of the 6 numbers

= 4 ×6

= 24

The sum of numbers without the two 2s

= 24 - 2(2)

= 20

The average of other 4 numbers

= 20 ÷ 4

= 5

Hence, The average of the other four numbers is 5.

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Answer:

The numbers are 44 and 46

Step-by-step explanation:

Let

x, x+2 ----> the two consecutive positive even integers

we know that

[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]

Solve the quadratic equation using a graphing calculator

The solution is x=44

see the attached figure

x+2=44+2=46

therefore

The numbers are 44 and 46

Answer: -8n^4 + 3n^2

(The ^ is the exponent)

Answer:

-23

Step-by-step explanation:

Each term is 6 less than the past term. Hopw this helps!

There is no "standard" way to solve an exercise like this: you just have to eyeball the sequence and try to find/guess the pattern.

The most common (and easy!) examples are arithmetic or geometric sequence, where the difference or ratio between two consecutive terms is constant.

This is one of those cases: this is an arithmetic sequence, because you obtain every next term by subtracting 6 from the previous one:

[tex]a_1 = 7\\a_2 = a_1-6 = 7-6 = 1\\a_3 = a_2-6 = 1-6 = -5\\a_4 = a_3-6 = -5-6 = -11\\a_5 = a_4-6 = -11-6 = -17[/tex]

So, we can deduce

[tex]a_6 = a_5-6 = -17-6 = -23[/tex]

Answer: X = 8 And Y = 5 "First Choice Letter A"

Step-by-step explanation: x + y = 13......x = 13 - y

2x - 3y = 1

2(13 - y) - 3y = 1

26 - 2y - 3y = 1

-2y - 3y = 1 - 26

-5y = -25

y = -25/-5

y = 5

x + y = 13

x + 5 = 13

x = 13 - 5

x = 8

so, x = 8 and y = 5

Answer:

Degree: 5

Y-intercept: 12

Step-by-step explanation:

The given expression is

[tex]f(x)=-(x+1)^2(2x-3)(x+2)^2[/tex]

Since the factors are multiplying, we can analyse the degree of each factor and add them to find the degree of the polynomial.

The degree of the factor [tex]-(x+1)^2[/tex] is 2.

The degree of [tex](2x-3)[/tex] is 1

The degree of [tex](x+2)^2[/tex] is 2

Therefore the degree of the polynomial is 2+1+2=5

To find the y-intercept, we put x=0.

[tex]f(0)=-(0+1)^2(2(0)-3)(0+2)^2[/tex]

[tex]f(0)=-(-3)(4)=12[/tex]

The y-intercept is 12