Graph the solutions of the inequality

Answer:

1b  2d   3c   4d    5a  

Step-by-step explanation:

There exists exactly one parallel line that can be drawn through a given point not on the original line. This line will have the same slope but a different y-intercept as the original line.

The answer to your question, 'Through a given point not on a line, there exists exactly one ___ to the given line' is Parallel Line.

In geometry, a line is said to be parallel to another if they are at the same plane and they never intersect, no matter how far they are extended. This principle also applies to lines on the graph of a linear equation such as y = a + bx which represents a straight line.

For example, assume we have a line graph that uses x and y as its axes where y = 3x + 9. Now let's say there's a point on the graph that is not on this line. You can draw exactly one line through this point that would be parallel to the original line of y = 3x + 9. This line would have the same slope as the first line, but a different y-intercept, and thus, would never intersect the original line.

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Answer:

45

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

The slope of line that contain the points ( - 0.5 , 4 ) and has y- intercept of - 5 is -18

Step-by-step explanation:

Given as :

The points that satisfy the line is ( - 0.5 , 4 )

The y - intercept = - 5

The equation of line is

y = m x + c

Where m is the slope of line

∵ For y- intercept , c = - 5

Now, points on the line is ( - 0.5 , 4 ) and y  intercept c = - 5 is

y = m x + c

or,  4 = m × ( - 0. 5 ) + ( - 5 )

Or, 4 = - 0. 5 m - 5

or, 4 + 5 = - 0.5 m

Or, 9 = - 0. 5 m

∴ m = [tex]\frac{-9}{0.5}[/tex]

So, Slope = m = - 18

Hence the slope of line that contain the points ( - 0.5 , 4 ) and has y- intercept of - 5 is -18   Answer

Final answer:

The slope of a line that contains the point (-0.5, 4) and has a y-intercept of -5 is -18. This is calculated using the slope formula, resulting in a negative slope.

Explanation:

To find the slope of a line with a given point and a y-intercept, we can use the slope formula slope = (y2 - y1) / (x2 - x1), where (x1, y1) is the given point and (x2, y2) is the y-intercept point. Since the y-intercept is at a point where x = 0, the second point is (0, -5).

The given point is (-0.5, 4), so after substituting into the slope formula we get: slope = (-5 - 4) / (0 - (-0.5)) = (-9) / (0.5) = -18. The slope of the line is -18, indicating a negative slope meaning the line will move downwards on the graph as the x-value increases.

The width of rectangle is 9 units.

Step-by-step explanation:

Given,

Width of rectangle = w

Length of rectangle = l = w - 6

Area of rectangle = A = 27 units

[tex]Area\ of\ rectangle=\l*w\\27=(w-6)(w)\\27=w^2-6w\\0=w^2-6w-27\\w^2-6w-27=0\\w^2+3w-9w-27=0\\w(w+3)-9(w+3)=0\\(w+3)(w-9)=0\\[/tex]

Either,

w+3=0     =>w= -3

Or,

w-9=0      =>w=9

As width cannot be negative, therefore,

Width = 9 units

The width of rectangle is 9 units.

Keywords: rectangle, area

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Answer:

177.87

Explanation:

162.75 * 100  = 177.87

     91.5

177.87 * 0.915 = 162.75

Answer:

177.87 is the correct answer. Really hope that this helped :)

Step-by-step explanation:

Step-by-step explanation:

radius =diameter÷2

r=5.7÷2=2.85

let pi=x (since there is no symbol for pi on the phone )

Circumference =2xr

Circumference =2x×2.85=5.7x (5.7pi)

The  circumference of the circle whose diameter is 5.7 cm is 5.7π cm.

The circumference is the distance around the boundary of a closed curve or geometric figure.

In the context of a circle, the circumference is the length of the boundary that encloses the circular shape.

It is calculated using the formula:

Circumference = 2 π r = 2d

Given: diameter of the circle is 5.7 cm

Substitute d= 5.7 cm into the formula:

C = π * 5.7 cm

Thus, the circumference is 5.7π cm.

Learn more about circumference of circle here:

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The total amount petra has to pay after 1 year is $ 209

The equation used is: Total amount to pay back = Amount Borrowed + Amount of Interest

Given that,

Petra borrowed $ 200 for 1 year with simple interest rate 4.5 %

We are asked to find the amount that petra has to pay back after 1 year

Total to Pay Back = Amount Borrowed + Amount of Interest

Let us first calculate the amount of interest Petra has to pay for 1 year

Given that simple interest rate = 4.5%

The simple interest is given as:

[tex]\text { simple interest }=\frac{\text { principal } \times \text {rate} \text { of interest } \times \text { number of years }}{100}[/tex]

[tex]\text { simple interest }=\frac{200 \times 4.5 \times 1}{100}=2 \times 4.5=9[/tex]

Thus the amount of interest = $ 9

Total to Pay Back = Amount Borrowed + Amount of Interest

Total to Pay Back = 200 + 9 = 209

Thus the total amount petra has to pay after 1 year is $ 209

Answer:

Step-by-step explanation:

25.

Combine like terms.

4t+7=-33

subtract 7 from both sides

4t=-40

divide both sides by 4

t=-10

26.

Subtract 2a from both sides

5=7a-16

add 16 to both sides

21=7a

divideby 7 on both sides

a = 3

I'd suggest getting the app photomath or using cymath to help you with these problems. they give you the answer and how to get it step by step

Answer:

Which is equal to 0.0865 hectometers?

86.5 millimeters

865 millimeters

8,650 millimeters

86,500 millimeters

Step-by-step explanation:

Answer: 8% of 525 is 42

Step-by-step explanation:

Answer:

Step-by-step explanation:

a good way to find 8% is find 1% and multiply it by 8 (5.25 * 8 = 42)

another way would be to simply multiply 525 by 0.08 (525 * 0.08 = 42)

either way, the answer is 42

Answer:

105

Step-by-step explanation:

Theorem:

If parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Lines AB and CD are parallel, and angles 3 and 6 are same-side interior angles, so by the theorem above, angles 3 and 6 are supplementary. That means that the sum of their measures is 180 deg.

m<3 + m<6 = 180

m<3 + 75 = 180

Subtract 75 from both sides.

m<3 = 105

Answer: 105 degrees

Answer:

yes

Step-by-step explanation:

Note that a [tex]\frac{-}{-}[/tex] results in a +, thus

[tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]

Ắner:-2:-1=2

-5:-1=5

-2/-5=2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The system of linear equations have:

one solution, infinitely many solutions or no solution.

One solution if the lines intersect.

Infinitely many solutions if the lines are the same (overlap)

There is no solution if the lines are parallel (they do not have a common point).

In the graph, two lines intersect. Therefore, the system of equations has one solution (0, 3).

Answer:

A=32

Step-by-step explanation:

Step-by-step explanation:

[tex]\dfrac{-3}{(x+2)(x-5)}\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=\dfrac{-3}{(x)(x)+(x)(-5)+(2)(x)+(2)(-5)}\\\\=\dfrac{-3}{x^2-5x+2x-10}\qquad\text{combine like terms}\\\\=\dfrac{-3}{x^2-3x-10}[/tex]

[tex]\dfrac{64x-8x^2}{10x-80}=\dfrac{-8x(x-8)}{10(x-8)}\qquad\text{cancel}\ (x-18)\\\\=\dfrac{-8x}{10}=-\dfrac{8x:2}{10:2}=-\dfrac{4}{5}x[/tex]

Step-by-step explanation:

Given that [tex]F(x)=x^{2}[/tex] and [tex]G(x)=\frac{2}{3}x^{2}[/tex]

[tex]F(x)[/tex] is always positive because [tex]x^{2}[/tex] is always positive.

[tex]G(x)[/tex] is always positive because [tex]\frac{2}{3}x^{2}[/tex] is always positive.

So,both are always positive.

So,there is no flipping over x-axis.

In [tex]F(x)[/tex],the height of a point at [tex]x_{0}[/tex] is [tex]x_{0}^{2}[/tex]

In [tex]G(x)[/tex],the height of a point at [tex]x_{0}[/tex] is [tex]\frac{2}{3}x_{0}^{2}[/tex]

So,height of any point has less height in [tex]G(x)[/tex] than [tex]F(x)[/tex]

So,the graph of [tex]G(x)[/tex] is the graph of [tex]F(x)[/tex] compressed vertically.

Answer:

C.

Step-by-step explanation:

Answer: not a right triangle

Step-by-step explanation:

if it is a right triangle the pyth. theorem must stand

12^2+12^2 does not equal 15^2

so it is not a right triangle

Answer:

150

Step-by-step explanation:

60 x 1/4 = 150

Answer:

15

Step-by-step explanation:

" 60 times one fourth" can be written as 60/4, which in turn is 15.

Answer:

63 Inches.

Step-by-step explanation:

2 yards - 9 inches is equal to 1.75 yards and when converted to inches, equals 63 inches.

Answer:

63 inches

Step-by-step explanation:

2 yards - 9 inches = 1.75 yards and when converted is 63 inches

Answer:

AAS

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x - y = 5         subtract 2x from both sides

2x - 2x - y = -2x + 5

-y = -2x + 5          change the signs

y = 2x - 5

Answer:

300

Step-by-step explanation:

Let x be the initial number. Initially, this number was 100%.

After an increase of 40%, it became 420 and 100% + 40% = 140% in percent.

So,

x - 100%

420 - 140%

Write a proportion:

[tex]\dfrac{x}{420}=\dfrac{100\%}{140\%}[/tex]

Cross multiply:

[tex]140\cdot x=420\cdot 100\\ \\140x=42,000\\ \\14x=4,200\\ \\x=\dfrac{4,200}{14}=\dfrac{600}{2}=300[/tex]

Answer:

Just going to create this answer so the other person can get brainliest.

Step-by-step explanation:

:) :D <3

Answer:

1. x=160 (here given as ques no. 5)

2. x=81 (here given as ques no.5)

4.  No (here given as ques no. 8)

Step-by-step explanation:

1. Given ∠STR=∠SRT=20°

   we know ∠STR+∠STU=180

                 x+20=180

                  x=160

2.  By external angle property

         x+24=105

           x=81

3. By Angle Sum Property

∠ 1=∠2=∠3=∠4=90

and

∠5=∠6=∠7=∠8=90

Hence all angles are equal to 90

and we know only parallel lines have

∠4=∠5

∠3=∠6

hence line 'r' and line 't' are parallel.

4. For being parallel side pieces must not form a triangle(i.e. sum two interior angle must be equal to 180)

But here sum of interior angle 174

Hence a triangle is possible.

So , lines are not possible .

Final answer:

The two numbers are 40 and 13.

Explanation:

We are given that the sum of two numbers is 53, and their difference is 27. Let's denote the two unknown numbers as x and y, where x is the larger number.

The system of equations based on the given information is:

By adding the two equations, the y's cancel out:

Now, we can find the value of y by substituting x into the first equation:

The two numbers are 40 and 13.

Answer:

n and (n - 1) are consecutive integers.

Step-by-step explanation:

We are given 'n', a positive integer.

This 'n' can either be odd or even.

Case I:

When 'n' is odd

The n - 1 is even.

Note that the product of odd and even is always even. That is the product of n and (n - 1) is even.

Case II:

when 'n' is even

Then n - 1 is odd.

Again, using the similar logic we can say that the product of n and n - 1 should be even because here, 'n - 1' is even and 'n' is odd.

Answer:

2 baskets

Step-by-step explanation:

so basically find LCM(least common multiple) of 88, 60 and 54. prime factor 88 to get 2^3, and 11, 60 for 2^2, 3, 5 and 54 for 3^3, 2. we then find the numbers that are in all of them which is only two, once

Equation of line passing through (2, -2) and parallel to 2x+3y = -8 is [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]

Need to write equation of line parallel to 2x+3y=-8 and passes through the point (2, -2)

Generic slope intercept form of a line is given by y = mx + c

where "m" = slope of the line and "c" is the y - intercept

Let’s first find slope intercept form of 2x+3y=-8 to get slope of line

[tex]\begin{array}{l}{2 x+3 y=-8} \\\\ {=>y=\frac{-2 x-8}{3}} \\\\ {\Rightarrow y=-\frac{2}{3} x-\frac{8}{3}}\end{array}[/tex]

On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c,

[tex]\text {for line } 2 x+3 y=-8, \text { slope } m=-\frac{2}{3}[/tex]

We know that slopes of parallel lines are always equal

So the slope of line passing through (2, -2) is also [tex]m=-\frac{2}{3}[/tex]

Equation of line passing through [tex](x_1 , y_1)[/tex] and having slope of m is given by

[tex]\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)[/tex]

[tex]\text { In our case } x_{1}=2 \text { and } y_{1}=-2[/tex]

Substituting the values in equation of line we get

[tex](y-(-2))=-\frac{2}{3}(x-2)[/tex]

[tex]\begin{array}{l}{\Rightarrow y+2=\frac{-2 x+4}{3}} \\\\ {=>3(y+2)=-2 x+4} \\\\ {=>3 y+6=-2 x+4} \\\\ {3 y=-2 x-2}\end{array}[/tex]

[tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]

Hence equation of line passing through (2 , -2) and parallel to 2x + 3y = -8 is given as [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]

Answer:

NO

 To purchase 10 used video games and 3 new video games you need $166.With $150 is not enough

Step-by-step explanation:

7(10) + 32(3)    =

70+96= 166

You can purchase 12 used and 2 new And you will have $2 left

7(12) +2(32) = 148

84+62=148

You cannot purchase 10 used video games and 3 new video games because their total cost of $166 exceeds your budget of $150.

Given inequality: 7x + 32y = 150

Substitute x = 10 and y = 3 into the inequality:

=7(10) + 32(3)

=70 + 96 = 166

Compare with the budget:

166 > 150

Hence, 7(10) + 32(3) = 166

Thus, 66 > 150