Does the table represent a function? Why or why not?

X Y
3 1
4 3
5 2
6 5
6 6


A. Yes, because every x-value corresponds to exactly one y-value.
B. Yes, because there are different y values.
C. No, because one x-value corresponds to two different y-values.
D. No, because the y values are positive.

Answer:

Calculate the first differences between the y-values:

[tex]\sf 3 \underset{+1}{\longrightarrow} 4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19[/tex]

As the first differences are not the same, we need to calculate the second differences:

[tex]\sf 1 \underset{+2}{\longrightarrow} 3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7[/tex]

As the second differences are the same, the relationship between the variable is quadratic and will contain an [tex]x^2[/tex]  term.

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To determine the quadratic equation

The coefficient of [tex]x^2[/tex]  is always half of the second difference.

As the second difference is 2, and half of 2 is 1, the coefficient of [tex]x^2[/tex] is 1.

The standard form of a quadratic equation is:  [tex]y=ax^2+bx+c[/tex]

(where a, b and c are constants to be found).

We have already determined that the coefficient of [tex]x^2[/tex] is 1.

Therefore, a = 1

From the given table, when [tex]x=0[/tex], [tex]y=12[/tex].

[tex]\implies a(0)^2+b(0)+c=12[/tex]

[tex]\implies c=12[/tex]

Finally, to find b, substitute the found values of a and c into the equation, then substitute one of the ordered pairs from the given table:

[tex]\begin{aligned}\implies x^2+bx+12 & = y\\ \textsf{at }(1,19) \implies (1)^2+b(1)+12 & = 19\\ 1+b+12 & = 19\\b+13 & =19\\b&=6\end{aligned}[/tex]

Therefore, the quadratic equation for the given ordered pairs is:

[tex]y=x^2+6x+12[/tex]

Answer:

the triangle is not right-angled

Step-by-step explanation:

First of all, we are told that the perimeter of the triangle is 22 and the two sides are given, 8cm and 5cm respectively. This means that the third side is: 22-(8+5) = 9cm

From this as see that 9cm is the highest length we have and if it were a right-angled triangle, this could be the hypotenuse. Now, to be sure of the initial response we use the Pythagoras theorem. We know that the hypotenuse² = adjacent² + opposite²

let's use the measurements we are given in the question

8²+5²=AC²

64+25=89

AC=√89

AC=9.433981132

AC =9.43cm

and when we add 8+5+9.43 to calculate the perimeter we get 22.43 which is not the initial perimeter, this the triangle isn't right-angled

Answer:

Step-by-step explanation:

3x + 2 = (2x + 13)/3

9x + 6 = 2x + 13

9x - 2x = 13 - 6

7x = 7

x = 7 : 7

x = 1

answer is 3/5

since there are 3 red, there is a 3 blocks out of 5 blocks chance that a red block will chosen

Answer for number 1: d and w, or C.

Step-by-step explanation:

because the corner of d and w both are corners of an angle, obtuse. obtuse angles look like this = \_ or _/.  the d and w are in those corners

Answer:

[tex]x = 2, 4[/tex]

Step-by-step explanation:

Given :

[tex]\frac{4-x}{x^{2} -5x+4} + \frac{2}{x-1} =1[/tex]

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

Factorize the denominator of the first term :

⇒ x² - 5x + 4

⇒ x² - x - 4x + 4

⇒ x(x - 1) - 4(x - 1)

⇒ (x - 4)(x - 1)

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

Hence, the equation now is :

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

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

Multiply the second term by (x - 4) in the numerator and denominator :

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

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

Combine the numerator of both terms and bring the denominator to the other side :

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

[tex]4 - x+2x-8 = x^{2} - 5x + 4[/tex]

[tex]x - 4 = x^{2} - 5x + 4[/tex]

[tex]x^{2} -5x-x+4+4=0[/tex]

[tex]x^{2} -6x+8=0[/tex]

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

[tex]x = 2, 4[/tex]

[tex]~~~~~~~~y = (x-4)^2 +6\\\\\implies (x-4)^2 = y-6 \\\\\implies x -4 = \pm\sqrt{y-6}\\\\\implies x = \pm\sqrt{y-6} +4[/tex]

Answer:

3 • 15

Step-by-step explanation:

Add 8 and 7 to factor out the equation, creating an equivalent expression.

Answer:

£74

Step-by-step explanation:

£55.50 = 75%

Find 1% of discounted price by dividing both sides by 75 :

£0.74 = 1%

Using 1%, multiply by 100% to find original price :

£74 = 100%

Check our answer :

£74 × 0.75 (75%) = £55.50 ✅

Hope this helped and brainliest please

Answer:

the original price is 416.25. because you take the 55.50 and times ... percent of discount is 75%, sale price is 55.50

Step-by-step explanation:

[tex]|\Omega|=12\cdot11=132\\|A|=3\cdot4=12\\\\P(A)=\dfrac{12}{132}=\dfrac{1}{11}\approx9.1\%[/tex]

Answer:

A) x = [tex]\frac{11}{5}[/tex]

Step-by-step explanation:

3(4 - 2x) = -x + 1

Distribute on the left:

12 - 6x = -x + 1

    + x     + x

12 - 5x = 1

- 12       - 12

-5x = -11

Divide both sides by -5 to get x on its own:

x = [tex]\frac{-11}{-5}[/tex]

OR

x = [tex]\frac{11}{5}[/tex]

Have a nice day!

The amount of money Clint will plan to spend to replace the floors is $17404.09

The hardwood floor is rectangular.

Therefore,

area of hallway = 18 × 6 = 108 ft²

area of the kitchen = 20 × 30 = 600 ft²

area of the living room = 25 × 45 = 1125 ft²

area of each bedroom = 12 × 16 = 192 ft²

area of master bedroom = 14 × 20 = 280 ft²

Hence,

cost of flooring per square foot is $5.48

total cost for flooring = 108(5.48) + 600(5.48) + 1125(5.48) + 192(5.48) + 192(5.48) + 280(5.48) = $13683.56

Cost of installation is $1.49 per square.

total cost of installation = 108(1.49) + 600(1.49) + 1125(1.49) + 192(1.49) + 192(1.49) + 280(1.49) = $3720.53

Total  amount to replace the floor = 13683.56 + 3720.53 = $17404.09

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Answer:

Yes

Step-by-step explanation:

13 + 5 > 16
16 - 3 < 5
Yes :D

The remainder of (h4 h2 – 2) ÷ (h 3). The remainder is 88.

Given:

(h⁴ + h² – 2) ÷ (h + 3)

Using reminder theorem

First step is to equate:

h + 3 =0

h = - 3

Second step is to determine the remainder

Substitute h = - 3 into (h⁴ + h² – 2)

Hence:

h⁴ + h² – 2 = (-3)⁴ + (-3)² - 2

h⁴ + h² – 2= 81 + 9 - 2

h⁴ + h² – 2=90-2

h⁴ + h² – 2= 88 remainder

Therefore the remainder is 88.

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Answer:

0.41

Step-by-step explanation:

to make a fraction into a decimal you just divide the numerator by the

denominator.

and the numerator is the part of a fraction that is above the line

denominator is at the bottom

so 7 / 17 = 0.41 that means

7/17 in decimal form is 0.41

Hope This Helped

Answer:

7/17 is equal to 41176470588...

Step-by-step explanation:

This is called a never ending decimal. Hope this helps! :)

Answer:

Median 39,000

Step-by-step explanation:

If im lookng at this right the numbers are:

20,000, 25,000, 35,000, 39,000, 41,000, 48,000, 53,000

The middle number is:

20,000, 25,000, 35,000, 39,000, 41,000, 48,000, 53,000

Tell me if im wrong

Answer:

$48

30/10 is equal to 3/1, 16 x 3 equals to 48.

Answer:$48

Step-by-step explanation:

$30/10p = $3 per person

3x6=18

18+30=48

Answer:

c (2,0) and (-2,0) I hope ot helps

Step-by-step explanation:

(2x + 3)(2x + 3)

4x² + 6x + 6x + 9

4x² + 12x + 9

Answer: -1

Step-by-step explanation:

[tex]5^{3b-1}=5^{b-3}\\\\3b-1=b-3\\\\2b-1=-3\\\\2b=-2\\\\b=\boxed{-1}[/tex]

The value of z if x = 36 and y = 6 is 42

Suppose that y varies directly with x and inversely with z, hence the required expression will be:

y = kx/z

If  y = 4 when x = 8 and z = 14 then;

4 = k(8)/14

8k = 56

k = 7

To  find z when x = 36 and y = 6, we  will have:

6 = 7(36)/z
1 = 7(6)/z

z = 42

Hence the value of z if x = 36 and y = 6 is 42

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Answer:

Keep it simple. Answer:

y=kx/z

  k=7

 z=42

Step-by-step explanation:

Answer:

y = 6

Step-by-step explanation:

4y + 2x = 8 → (1)

5y + 2x = 14 → (2)

subtracting (1) from (2) term by term will eliminate x

y + 0 = 6

y = 6

The required sample size is equal to 273.

We have given that,

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

We have to determine the If the candidate only wants an 8% margin of error at a 99% confidence level,

p=0.5 (default since no value is given)

q=1-0.5=0.5

margin of error=5%=0.05

z_c=1.65 at 90% confidence.

The margin of error:

[tex]e= sqrt(p(1-p)/n)*z_c[/tex]

Use the given value in the above formula we get,

0.05=sqrt(0.5*0.5/n)*1.65

n= (0.5*1.65/0.05)^2=272.25

Therefore, The required sample size is equal to 273.

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Answer:

Yes, they are equivalent

Step-by-step explanation:

18 = 3x - 6 + x

+6 +6

24 = 3x + x

24 = 4x

24/4 = 4x/4

6 = x

18 = 4x - 6

+6 +6

24 = 4x

24/4 = 4x/4

6 = x

Both equations are equal to x = 6, therefore they are equivalent

Answer:

Yes

Step-by-step explanation:

18 = 3x - 6 + x

x = 1x

Combine like terms

3x + 1x = 4x

18 = 4x - 6 and 18 = 4x - 6

They are equivalent.

Answer:

the two selected are correct.

Step-by-step explanation:

A relation is a function only if it relates each element in its domain to only one element in the range. When you graph a function, a vertical line will intersect it at only one point. You can determine whether each element of the domain is paired with exactly one element of the range. For example, if given a graph, you could use the vertical line test; if a vertical line intersects the graph more than once, then the relation that the graph represents is not a function. The best way to find out whether an equation represents a function or not is by graphing the equation and then applying the vertical line test. Graph the two-variable equation on graph paper. For a straight line this means graphing two or more points on the line and connecting the dots.

Answer:

14.787ml

for an approximate result, multiply the volume value by 14.787

hope this helps

✎ let's answer it :3

•┈┈┈••✦ answer ✦••┈┈┈•

->(14.787ml )

hope it helps

correct me if I am wrong

Answer:

The complete factored form of the given [tex]f(x)[/tex] is [tex](x+5)(x^2+16)[/tex].

Step-by-step explanation:

Answer:

f(x)=x*3+5x+2+16x+80 y=x*3+5x*2+16x+80 x=y*3+5y*2+16y+80=8 3y+10y+16y+80=x29y+80=x29y=x-80y=1/29x-80/29 f(x)-1=1/29x-80/29