4.1.3 How many solutions are there ?
Worksheet

Answer:

[tex]y=4x-7[/tex]

The graph in the attached figure

Step-by-step explanation:

In this problem I will assume the the function is linear

we have the point (2,1)

we know that

y increases by 4  when x increases by 1

Remember that the formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

so

The slope of the linear function is

[tex]m=\frac{4}{1}[/tex]

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y-1=4(x-2)[/tex]

Convert to slope intercept form

Isolate the variable y

[tex]y-1=4x-8\\y=4x-8+1\\y=4x-7[/tex]

see the attached figure to better understand the problem

The question pertains to the characteristics of a linear function whose graph passes through the point (2, 1) with a slope of +4, indicating an increase of 4 in y for every increase of 1 in x. The line's positive slope suggests the graph rises as the x-value increases. The equation of the line is y=4x-7.

The student is asking a question about the characteristics of a linear function based on its graph. Specifically, since the graph passes through the point (2, 1) and the value of y increases by 4 when x increases by 1, we can conclude that the slope of the line is +4. This is because the slope of a line represents the change in y divided by the change in x. Given that the slope is positive, this line will show an upward trend on the graph as the x-value increases, much like other graphs with a positive slope.

To find the equation of the line, we start by using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. We use the point (2, 1) and the slope 4 to solve for b. The process is as follows:
1 = 4(2) + b
1 = 8 + b
b = -7

Therefore, the equation of the function is y = 4x - 7.

Answer:

24x^4+18x^3-15x^2 -42x-24

Step-by-step explanation:

(6x^2-3x-6)(4x^2 +5x+4)=

6x^2*4x^2 +6x^2*5x+6x^2*4

-3x*4x^2 - 3x*5x-3x*4

- 6*4x^2 -6*5x-6*4=

24x^4+30x^3+24x^2-12x^3-15x^2 -12x

-24x^2-30x-24=

24x^4+18x^3-15x^2 -42x-24

Step-by-step explanation:

i hope this helps

Answer:

Look at the rise over run

itd be 10/10 or 1

Answer:

f(0) = 3x

g(-2) = 3x + 6

Step-by-step explanation:

f(x) = 3x

3x = 0

x= 0/3

x = 0

g(x) = 3x+6

3x+6= 0

3x= -6

x= -6/3

x = -2

Answer:

8 to the power of 0

Step-by-step explanation:

[tex]8^{0}[/tex] = 1

[tex]8^{-2}[/tex] = [tex]\frac{1}{64}[/tex]

To compare 8 to the power of 0 and 8 to the power of -2, we focus on understanding negative exponents. The answer is that 8 to the power of 0 is greater than 8 to the power of -2.

To compare 8 to the power of 0 and 8 to the power of -2, we need to understand how negative exponents work. When a power of 10 is transferred from the numerator to the denominator, the sign of the exponent changes. 8 to the power of 0 is 1 and 8 to the power of -2 is 1/64. Therefore, 8 to the power of 0 is greater than 8 to the power of -2.

Answer:

24/35

Step-by-step explanation 3/5 times 8/7 equals 24/35

Answer:

$4

Step-by-step explanation:

10x = 8(x+1)

2x = 8

x = 4

Answer:

40 dollars

Step-by-step explanation:

We can say

x=amount each friend has to pay

Then, the price of the gift would be 10x because there are 10 friends and each pays x dollars. But since two friends dropped out, it will now become 8x. Also,  each of the 8 friends has to pay an extra dollar to go back to the original amount, so 8x+8 is also the price of the gift. We set these two expressions equal to each other (because they both represent the price of the gift) so

10x=8x+8. Using the subtraction property of equality (which says if a=b, then a-c=b-c) we subtract 8x from both sides to get

2x=8. Using the division property of equality (which says if a=b, then a/c=b/c) we divide by 2 on both sides to get x=4. But the question asked how much money they planned to collect, or what was the price of the gift, which is 10x, 10*4=40, 40 dollars.

Answer:

y = 3

x =7

Step-by-step explanation:

to solve this system of equations using substitution method we say, let

5x + 4y = -22 .................... equation 1

2x – 3y = 5...................... equation 2

from equation 2

2x - 3y = 5

2x = 5 + 3y

divide both sides by 2

we have;

2x/2 = (5+3y)/2

x =(5+3y)/2................................ equation 3

put x = (5+3y)/2 in equation 1

5x + 4y = -22 .................... equation 1

5(5+3y)/2 + 4y = -22

(25 + 15y)/2 + 4y = -22

multiply through by 2

25 + 15y + 8y = -44

25 + 23y = -44

collect the like terms

23y = -44 - 25

23y = -69

divide both sides by 23

23y/23 = -69/23

y = 3

put the value of y= 3 into equation 3

x =(5+3y)/2................................ equation 3

x = (5+3(3)]/2

x = 5+9/2

x =14/2

x =7

Answer:

60

Step-by-step explanation:

3:4:6

Add:

3+4+6=13

3:4:6=13

?:?:?=260

Divide:

260/13=20

Multiply 3 and 20:

60

SO there are 60 small uniforms

Answer:

Step-by-step explanation:

C=2πr

18=2×3.14×r

18=6.28r

r=2.88

Arc of a circle

A=®/360°πr

6=®/360°×3.14×r

®=239°

6

Answer:

120

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

5 x 3 = 15

5.5 x 3 = 16.5

Triangle PQR has 3x the amount as ABC on each side, therefore, n = 7.5

Answer:

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

Step-by-step explanation:

Calculate the slope using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1+3}{0+5}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

yup, its positive

two times cancels out, but then the third time made it negative again

Answer:

[tex]x=5\\\\y=2[/tex]

Step-by-step explanation:

Given Equations:

        [tex]-6y= -20 + 2x[/tex]    Equation:1

Solving Equation:1 Adding '[tex]6y[/tex]' to both the sides:

             [tex]2x+6y-20=0[/tex]  

Adding '20' both the sides:

              [tex]2x+6y=20[/tex]   Equation:2

[tex]2x - 4y=0\\[/tex]  Equation:3

Subtracting Equation:3 From Equation:2

          [tex]2x+6y-(2x-4y)=20-0\\\\2x+6y-2x+4y=20\\\\10y=20\\\\y=\frac{20}{10}\\\\ y=2[/tex]

Putting the value of 'y' in equation:3

          [tex]2x - 4y=0\\[/tex]

          [tex]2x-4(2)=0\\\\2x-8=0[/tex]

Adding '8' to both the sides

             [tex]2x=8\\\\x=8/2\\\\x=5[/tex]

SO,  

              [tex]x=5\\\\y=2[/tex]

Answer:

3/180= 60 seconds = 1m/per cut or 60 sec/per cut.

Step-by-step explanation:

This is 3 cuts executed from a board to get 5 parts.

Answer:

he cuts 1.6 section of a board in one minute

Step-by-step explanation:

They're telling you that it takes 3 minutes for the carpenter to cut one board into 5 qual section. Therfore how many sections he's cutting in one minute divide the 5 by three. With that you will have the rate

Answer:

if there is a right angled square shape at the angle

Answer: MARK BRAINLIEST!!!!!!!!!

Because its the only triangle that has a 90 degree angle

Step-by-step explanation:

Answer:

 2X+20 = 400                        

Answer:

That is easy, the answer is B.

Step-by-step explanation:

First you have to graph the points of M and N and then you have to draw a line through the points of M and N and then graph the other points and whichever falls on the M,N line is the answer. So therefor the answer is B, (11,13)

Answer:

B?

Step-by-step explanation:

Answer:

Reflection

Step-by-step explanation:

It is reflecting across the Y axis. It is not a dialation, since it is the same shape, but not a different size. Its not rotation, because it wasnt rotated to get to the new shape. And it is not translation, because it is not exactly the same shape (the shape was mirrored)

Answer:

Step-by-step explanation:

A

Answer:

Answer A

Step-by-step explanation:

Answer:

-1/2, -3/2

Step-by-step explanation:

4b² + 8b + 3 = 0

8² - 4(4)(3) = 16 > 0

Real and distinct solutions

4b² + 6b + 2b + 3 = 0

2b(2b + 3) + 1(2b + 3) = 0

(2b + 3)(2b + 1) = 0

b = -1/2, -3/2

The denominator is equal to the numerator.

Step-by-step explanation:

Answer:

[tex]x = - \: 12.55 \: or \: x = 12.55[/tex]

Step-by-step explanation:

We want to solve for x in

[tex] {x}^{2} + 4.7^{2} = 13.4^{2} [/tex]

We group constants on the right to get:

[tex]{x}^{2} = 13.4^{2} - {4.7}^{2} [/tex]

We apply difference of two squares

[tex]{x}^{2} = (13.4 - {4.7})(13.4 + 4.7)[/tex]

[tex] {x}^{2} = 157.47[/tex]

[tex]x = \pm \sqrt{157.47} [/tex]

[tex]x = \pm \: 12.55[/tex]

Answer:

y < 1.1

Step-by-step explanation:

Step 1:  Subtract 2.1 from both sides

-4.2y + 2.1 - 2.1 > -2.52 - 2.1

-4.2y > -4.62

Step 2:  Divide both sides by -4.2

-4.2y / -4.2 > -4.62 / -4.2

Since you divided by a negative, that flips the sign.

y < 1.1

Answer:  y < 1.1

Answer: Y < 1.1

Step-by-step explanation: I took the quiz, i hope this helps! :)

Answer:z=(pd+59)/(2-p)

Step-by-step explanation:

-p(d+z)=-2z+59

Open bracket

-pd-pz=-2z+59

Collect like terms

2z-pz=pd+59

Factor out z

z(2-p)=pd+59

Divide both sides by (2-p)

z(2-p)/(2-p)=(pd+59)/(2-p)

z=(pd+59)/(2-p)

Answer:

x = (y - 7)/2

Step-by-step explanation:

from the question given  y=2x+7 , so we are to find the value of x now we first make x the subject of the formulae from  y=2x+7

 y=2x+7............. equation 1

y- 7 = 2x

divide both sides by 2

(y-7)/2= 2x/2

x = (y - 7)/2

to check if your answer is correct

put the value of x in to equation 1

y=2x+7............. equation 1

y = 2[ (y-7)/2] + 7

y = y - 7 + 7

y = y.......... proved

Answer:

x = -4 and -2x - 8

Step-by-step explanation:

Step 1:  Distribute

-1/3(6x + 15) - 3

-6/3x - 15/3 - 3

-2x - 5 - 3

-2x - 8

Step 2:  IF NEEDED SOLVE FOR X

-2x - 8 + 8 = 0 + 8

-2x / -2 = 8 / -2

x = -4

Answer:  x = -4 and -2x - 8