Consider the linear equation y = 5x – 4.
1. Provide 3 ordered pairs that are solutions to this linear
equation.
2. Test the point (-5, -29) to see if it is a solution to the
linear equation.
Be sure to show all work.

Answer:

One solution

Step-by-step explanation:

Discriminant

[tex]\textsf{Discriminant}:b^2-4ac}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{If}\quad b^2-4ac=0 \implies \textsf{one solution}[/tex]

[tex]\textsf{If}\quad b^2-4ac > 0 \implies \textsf{two solutions}[/tex]

[tex]\textsf{If}\quad b^2-4ac < 0 \implies \textsf{no solutions}[/tex]

Given equation:

[tex]-8x^2-8x-2=0[/tex]

Swap sides:

[tex]\implies 8x^2+8x+2=0[/tex]

Using discriminant:

[tex]\implies b^2-4ac=8^2-4(8)(2)=0[/tex]

Therefore, there is one solution

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

Proof

[tex]8x^2+8x+2=0[/tex]

Divide both sides by 2:

[tex]\implies 4x^2+4x+1=0[/tex]

Separate the middle term:

[tex]\implies 4x^2+2x+2x+1=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 2x(2x+1)+1(2x+1)=0[/tex]

Factor out the common term [tex](2x+1)[/tex]:

[tex]\implies (2x+1)(2x+1)=0[/tex]

Therefore:

[tex]\implies 2x+1=0[/tex]

[tex]\implies x=-\dfrac12[/tex]

Thus proving there is one solution.

Here

Discriminate

Roots are equal hence one solution

Answer:

-12

Step-by-step explanation:

1. Create an Equation

-3-9

2. Solve

-3-9 <=== subtract -3 and -9 together to get your answer

-12

3. Check

-12+3 <=== create this equation or this one ===> -12+9 to check if we calculated correctly

-12+3= -9 -12+9= -3

this shows the answer is corrrect

Answer:

six hundred and sixty-two by twenty-six

Step-by-step explanation:

Answer:

333 remainder 6

Step-by-step explanation:

       333   R 6

26/8664

  - 78

     086

     - 78

        084

          -78

              6

I struggled to show the work formatted how I would normally write this problem out, so I'll also talk through how I got the answer.

The first step in long division by hand is to take the number that is furthest to the left and seeing how many times your divisor (26) will go into it.

In this case the digit in the thoudands place (our furthest left) is 8.  Obivously 26 does not fit into 8. So our answer will have a 0 in the thousands place and we move one place to the right.  

We now have 86.  26 fits into 86 three times and leaves a difference of 8 remaining in the hundreds place, and we move the right again to the tens place.

We again have 86. 26 again fits in three time and leaves a difference of 8. As we move to the right to the ones place we are left with 84.  

26 fits into 84 three times, but we have a difference of 6 this time.

We cannot continue as 26 will never fit into our remainder of 6.

We had a 0 in the thousands place, a 3 in the hundreds place, a 3 in the tens place and a 3 in the ones palce with 6 left over.

So the final answer is 333 remainder 6

Answer:

m = ± [tex]\sqrt{n}[/tex]

Step-by-step explanation:

m² = n ( take square root of both sides )

m = ± [tex]\sqrt{n}[/tex]

Answer:

5. During the day, the temperature on the surface of Mars rises at a rate of 9 degrees C every hour

a. In 2 hours: 18 a. in 3 hours: 27    in n hours: 9n

b. y=9n

c. 108

d. -540

6. Kaite saves 5 dollars every week, so far she has saved a total of $63

a. y=5x+63

b. 25

hope it helps

Answer:

153.722 fl oz

Answer:

According to my calculation it came like this.Hope the picture will help you.

Answer:

Subtract 3 from both sides.

Step-by-step explanation:

x + 3 = 5

x = 5 - 3

x = 2

I know I`m late sorry, still wanted to answer

. _ .

Answer:

First option

Step-by-step explanation:

Given the following question:

[tex]x+3=5[/tex]

To find the answer we need to subtract three on both sides, since we are given a positive three ( + 3) instead of a negative three (- 3) If the equation was " x - 3 = 5 " we would then add three on both sides but in this case we have a positive three.

[tex]x+3=5[/tex]
[tex]3-3=0[/tex]
[tex]5-3=2[/tex]
[tex]x=2[/tex]

Which means your answer is the first option or "subtract 3 from both sides."

Hope this helps.

Answer:

sqrt(2593)

Step-by-step explanation:

17^2+48^2 = 2593^2

Answer:

7 (1-6)

Step-by-step explanation:

you find the greatest common factor of 7 and 42.

7

7x1

42

1x42

2x21

3x14

6x7

Answer:

666.888.000.333

Step-by-step explanation:

yeah I said what I said

bye

Based on the amount that Felix deposited in the account and the 5% compounded annual interest, the interest Felix will earn in 2 years is $10.25

First, find the amount the $100 would have accrued to in 2 years:

= Amount deposited x (1 + rate) ^ number of years

Solving gives:

= 100 x (1 + 5%)²

= $110.25

The interest earned is:

= Amount in 2 years - Amount deposited

= 110.25 - 100

= $10.25

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Answer:10.25

Step-by-step explanation:

Step-by-step explanation:

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables and c is the constant term. The other different forms to find and represent the equation of a line are slope-intercept form, point-slope form, two-point form, intercept form, and normal form.

Answer:

6144

Step-by-step explanation:

The answer is 6144 because if you do 256×24 you will get 6144

Answer:

bh/2

Meaning :

base times height, halfed

Answer:

Step-by-step explanation:

A = hb/2 or 1/2×hb

Where h is the vertical height and b is the base length.

Answer: 28

Step-by-step explanation: 80 x 0.35 = 28

when we multilpy we get 80×0.35 = 28

Answer:

D. Multiply by 3

Step-by-step explanation:

Given:

To find:

Notice that if you keep multiplying by 3:

Then you will get exact sequence as given, so next 3 missing terms have to be:

Hence, the pattern for this sequence is to multiply by 3.

Note

Answer:

I think it is (n - 5) x 4 - 7, but I am not sure.

Answer:

x=4

Step-by-step explanation:

3x+8 = 20

subtract 8 both sides

3x=12

divide 3 both sides

x=4

Without going too much into the proofs angle ACD is congruent to angle DBA.

If ACD is ~= DBA then

ACD = 54 degrees

Explanation:

The figure is a reflection. While orientation isnt preserved in reflections side lengths and angle measures are.

This means that both triangles have the same side length measures and have the same angle measures.

You are given the angle measures of one of the triangles. We also know both triangles are congruent since they both fit perfectly inscribed in the circle.

With this in mind you can prove that all the angles of each triangle are congruent.

Thus

ACD = 54 degrees

Answer:

43.98229 ft

Step-by-step explanation:

The diameter is 14ft, meaning the radius, which is half of it, is 7ft. Plug 7 into the r. C= 2pi(7) which 14pi. Now you multiply 14 by 3.14, which is the value of pi, and round it to whatever you need to give you your value.

The value of circumference of this circle is,

⇒ circumference = 14π ft

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Diameter = 14 ft

Hence, We get;

Radius = 7 ft

Thus, The value of circumference of this circle is,

⇒ circumference = 2πr

⇒ circumference = 2 × π × 7

⇒ circumference = 14π ft

Thus, The value of circumference of this circle is,

⇒ circumference = 14π ft

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Answer:

65.2%

Step-by-step explanation:

~Hope this helps~

Step-by-step explanation:

[tex] \frac{2 {x}^{2} - 50}{ {x}^{2} + 7x + 10 } [/tex]

[tex] \frac{2( {x}^{2} - 25) }{(x + 5)(x + 2} [/tex]

[tex] \frac{2(x + 5)(x - 5)}{(x + 5)(x + 2)} [/tex]

[tex] \frac{2(x - 5)}{x + 2} [/tex]

#a

H(0)

It refers to y value on graph when x is 0

So here it refers to y intercept

Hence

#b

Observe the graph

y intercept is not 0 so it's not true

#3

Domain is set of x values in graph

#4

Range is set of y values on graph

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 12.75}}{\left( \cfrac{6}{100} \right)12.75}\implies 0.765~~\approx 0.77~~\textit{about 77 cents}[/tex]

The graph is not symmetric, and it has no vertical or horizontal asymptotes.

Coordinate geometry is a branch of mathematics that combines algebraic and geometric concepts to study the properties of geometric figures using a coordinate system. It involves representing geometric figures such as points, lines, curves, and shapes in a plane or space using numerical values called coordinates.

The graph of the function [tex]f(x)=-3(x+1)^2 (x-3) (x-5)^3[/tex] is a cubic polynomial function with several important characteristics:

Degree: The degree of the function is 7, which means that the graph has 7 x-intercepts.

Symmetry: The function is not symmetric with respect to the y-axis or the origin.

End Behavior: As x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches negative infinity.

Zeros: The function has x-intercepts at x = -1, x = 3, and x = 5. The intercept at x = -1 has a multiplicity of 2, while the intercepts at x = 3 and x = 5 have a multiplicity of 3. This means that the graph touches the x-axis at x = -1 and bounces off at x = 3 and x = 5.

Turning Points: The function has two turning points, one at x = -1 and one at x = 3. The turning point at x = -1 is a local maximum, while the turning point at x = 3 is a local minimum.

Behavior near Zeros: Near each of the x-intercepts, the function changes direction. At x = -1, the function changes from decreasing to increasing. At x = 3 and x = 5, the function changes from increasing to decreasing.

Vertical Asymptotes: The function has no vertical asymptotes.

Horizontal Asymptotes: The function has no horizontal asymptotes.

Intercepts: The y-intercept of the function is at y = 0.

Overall, the graph of the function [tex]f(x)=-3(x+1)^2 (x-3) (x-5)^3[/tex] is a complicated cubic polynomial with multiple x-intercepts, turning points, and changing directions near the intercepts.

Therefore, the graph is not symmetric, and it has no vertical or horizontal asymptotes.

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Answer:

Step-by-step explanation:

Sin (90 + Ф ) =Cos Ф

135° = 90 + 45

Sin 135° = Sin (90 + 45)

             = Cos 45°

             [tex]= \dfrac{1}{\sqrt{2}}[/tex]

Answer:

Step-by-step explanation:

Answer:

cosA = [tex]\frac{9}{41}[/tex]

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{9}{41}[/tex]