A function does not have any x-intercepts. What
might be true about its domain and range?

Answer:

Step-by-step explanation:

f(x) = -1 is actually the same as y = -1.  Find y = -1 on the y axis and then draw a horizontal line through this point.  The resulting graph is that called for here.

Answer:

She could wear 7 different outfits

"no terms independent of x" basically means there is no constant term, or the coefficient of x ⁰ is zero.

Recall the binomial theorem:

[tex]\displaystyle (a+b)^n=\sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]

So we have

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 \binom 6k \left(\frac2x\right)^{6-k}(-3x)^k[/tex]

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}[/tex]

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}+a\sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-4}[/tex]

The first sum contributes a x ⁰ term for 2k - 6 = 0, or k = 3, while the second sum contributes a x ⁰ term for 2k - 4 = 0, or k = 2. The coefficient of the sum of these terms must be zero:

[tex]2^{6-3}(-3)^3\dbinom 63 + a\times2^{6-2}(-3)^2\dbinom 62 = 0[/tex]

which reduces to

2160a - 4320 = 0

2160a = 4320

a = 2

Answer:

1/8

Step-by-step explanation:

We want to find the slope of any line that is perpendicular to the line passing through the points M(-1, 5) and N(0, -3).

Recall that the slopes of perpendicular lines are negative reciprocals of each other. In other words, the slope of any line perpendicular to line MN must be the negative reciprocal of the slope of line MN.

Find the slope of MN using the slope formula:

[tex]\displaystyle m_{MN} = \frac{\Delta y}{\Delta x} = \frac{(-3)-(5)}{(0)-(-1)} = \frac{-8}{1}=-8[/tex]

So, the slope of line MN is -8.

The slope of any line perpendicular to MN must be its negative reciprocal. The negative reciprocal of -8 is 1/8.

Therefore, the slope of any line perpendicular to the line passing through the points M(-1, 5) and N(0, -3) is 1/8.

Answer:

65.03 meters

Step-by-step explanation:

The line of best fit, for the distance of the winning throw, in x years after 1980 is:

[tex]y = 0.34x + 44.63[/tex]

Using the line of best fit, estimate what the distance of the gold medal winning discus throw was in 1980.

1980 - 1920 = 60, so this is y(60).

[tex]y(60) = 0.34(60) + 44.63 = 65.03[/tex]

So the answer is 65.03 meters.

Answer:

3 bookcases

Step-by-step explanation:

Answer:

width = 17 m ; length = 31 m

Step-by-step explanation:

w = width

l = length

perimeter of a rectangle = (length + width) * 2

l = 14 + w

(14 + w + w) * 2 = 96

(14 + 2w) * 2 = 96

28 + 4w = 96

4w = 68

w = 17 m

l = 14 + 17 = 31 m

Answer:

y = 9x-10

Step-by-step explanation:

Slope-Intercept form is y = mx + b where m is the slope and b is the y intercept.

plug in what we are given

8 = 9(2) + b

solve for the y intercept (b)

8=18+b

8-18 = b

-10 = b

plug the slope (m) and y intercept (b) into our formula

y = 9x - 10

Answer:

Graph the same exact curve, but move every y value up 6.

Step-by-step explanation:

A transformation to the y-values is outside of the argument of the function. i.e., outside of the parentheses.

Answer:

None of the given system of linear inequalities

Step-by-step explanation:

Given

[tex](x,y) =(3,-2)[/tex]

Required

The line inequalities with the above solution

The first set of linear inequalities, we have:

[tex]y < -3[/tex]

[tex]y \ge \frac{2}{3}x - 4[/tex]

[tex]y < -3[/tex] implies that the values of y is -4,-5.....

While [tex](x,y) =(3,-2)[/tex] implies that y = -2

Hence, the first set is wrong

The second set of linear inequalities, we have:

[tex]y > - 2[/tex]

[tex]y \ge \frac{2}{3}x - 4[/tex]

[tex]y > - 2[/tex] implies that the values of y is -1,0.....

While [tex](x,y) =(3,-2)[/tex] implies that y = -2

Hence, the second set is wrong

The system of linear inequalities having the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.

A system of linear inequalities is known to be a composition of  linear inequalities that can be found in the same variables.

The graph that is showing  y > -3; y ≥ 2/3x - 4

-2 > -3  is true

y ≥ 2/3x - 4

-2 ≥ -2  is true

Therefore,  y > -3; y ≥ 2/3x - 4 has the point (3, -2) in its solution set.

Learn more about  linear inequalities from

https://brainly.com/question/12649320

Answer:

3.75 miles per hour

Step-by-step explanation:

(5/8)/(1/6)=3.75 mph, or you could do 5/8 x 6, since 1/6 x 6 equals one hour

Answer:

3 3/4 miles per hour

Step-by-step explanation:

Take the miles and divide by the hours

5/8 ÷ 1/6

Copy dot flip

5/8 * 6/1

Rewriting

5/1 * 6/8

5/1 * 3/4

15/4

3 3/4

Answer:

D. 9n = 27

Step-by-step explanation:

If we need one adult for every 9 students, we can represent that as 9n:

if n is the number of adults.

Because we have 27 students, the equation 9n = 27 works.

A better way of formatting the equation is:

n = 27/9

Because it directly shows what the number of adults is, but with some reformatting, it is clearly the same equation.

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Starting from right to left...

9 is in the ones place

8 is in the tenths place

4 is in the hundreds place

7 is in the thousands place.

I hope this helps!

Answer:

I think 55%

Step-by-step explanation:

Answer:

Step-by-step explanation:

price on monday go to: 100% + 20% = 120% = 1,2 x first price

price on tuesday go to: 125% of 120% = 1,25 x 1,2 = 1,5 x first price

Increases = 50%

on Wednesday, sammy must decrease 50% (of price after second increases) to return to original price

For example for understanding:

If original price is $100

firs increase: new price: $100 + $20 = $120

second increase: new new price: $120 + $30 = $150

final price - original price = $150 - $100 = $50

And  icreases/original = $50/$100 =0,5 = 50%

For return to orignial price, sammy must have to reduce 50% the price of avocados in wednesday

Answer:

After 7 years, the value would be $9,046.

After 13 years, the value would be $3,660

Step-by-step explanation:

Answer:

m<DCA=45°

Step-by-step explanation:

m<DCA=m<ACB-m<DCB

m<DCA=180°-135°

m<DCA=45°

Answer: [tex]6.12\ \text{years}[/tex]

Step-by-step explanation:

Given

Rate of interest is [tex]r=3\%[/tex] compounded quarterly

So, annually it is [tex]r=12\%[/tex]

Suppose [tex]P[/tex] is the Principal and A is the amount after certain time period.

Amount in Compound interest is given by

[tex]\Rightarrow A=P[1+r\%]^t[/tex]

for given conditions

[tex]\Rightarrow 2P=P[1+0.12]^t\\\Rightarrow 2=(1.12)^t\\\\\Rightarrow t=\dfrac{\ln (2)}{\ln (1.12)}\\\\\Rightarrow t=6.116\approx 6.12\ \text{years}[/tex]

It take [tex]6.12\ \text{years}[/tex] to double the invested amount.

Answer: width = 4 and length = 10

Step-by-step explanation:

Width = w and length = w + 6

2(w) + 2 (w + 6) = 28

2w + 2w + 12 = 28

4w = 28 - 12

W = 16/4

W = 4 (width)

Length = w + 6

4 + 6 = 10

Answer:

m = -6

Step-by-step explanation:

The slope of a line is calculated as the change in y divided by the change in x.

Teachers use the phrase "rise over run". In this case the rise is negative as the line moves from a higher y value to a lower y value as x increases.

(y-final - y-initial)/(x-final - x-initial)

You are given two points on the line and just plug them in.

(1-7)/(7-6) = -6/1 = -6

Answer:

yefeihuerijohiftv3ugrhoerfujfy

Step-by-step explanation:

Answer:

$150

Step-by-step explanation:

discount=60%

let the price=x

(100-60)% of x=$60

40% of x=60

x=60×(100/40)=150

Answer:

(1)

[tex]E(x) = 0.72[/tex]

[tex]Var(x) = 1.1616[/tex]

[tex]\sigma = 1.078[/tex]

(2)

[tex]E(x) = 12[/tex]

[tex]Var(x) = 1.3[/tex]

[tex]\sigma = 1.14[/tex]

Step-by-step explanation:

Solving (1):

[tex]\begin{array}{ccccccc}{Days} & {0} & {1} & {2} & {3} & {4}& {5} \ \\ {Probability} & {0.60} & {0.20} & {0.12} & {0.04} & {0.04} & {0.00} \ \end{array}[/tex]

(a): Mean

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 0 * 0.60 + 1 * 0.20 + 2 * 0.12 + 3 * 0.04 + 4 * 0.04 + 5 * 0.00[/tex]

[tex]E(x) = 0.72[/tex]

Solving (b): The variance

This is calculated as:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Where:

[tex]E(x) = 0.72[/tex]

and [tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 0^2 * 0.60 + 1^2 * 0.20 + 2^2 * 0.12 + 3^2 * 0.04 + 4^2 * 0.04 + 5^2 * 0.00[/tex]

[tex]E(x^2) = 1.68[/tex]

So, we have:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = 1.68 - 0.72^2[/tex]

[tex]Var(x) = 1.1616[/tex]

Solving (c): The standard deviation.

This is calculated as:

[tex]\sigma = \sqrt{Var(x)}[/tex]

[tex]\sigma = \sqrt{1.1616}[/tex]

[tex]\sigma = 1.078[/tex]

Solving (2):

[tex]\begin{array}{ccccccc}{x} & {10} & {11} & {12} & {13} & {14}& { } \ \\ {P(x)} & {0.1} & {0.25} & {0.3} & {0.25} & {0.1} & { } \ \end{array}[/tex]

(a): Mean

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 10 * 0.10 + 11 * 0.25 + 12 * 0.3 + 13 * 0.25 + 14 * 0.1[/tex]

[tex]E(x) = 12[/tex]

Solving (b): The variance

This is calculated as:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Where:

[tex]E(x) = 12[/tex]

and [tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 10^2 * 0.10 + 11^2 * 0.25 + 12^2 * 0.3 + 13^2 * 0.25 + 14^2 * 0.1[/tex]

[tex]E(x^2) = 145.3[/tex]

So, we have:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = 145.3 - 12^2[/tex]

[tex]Var(x) = 1.3[/tex]

Solving (c): The standard deviation.

This is calculated as:

[tex]\sigma = \sqrt{Var(x)}[/tex]

[tex]\sigma = \sqrt{1.3}[/tex]

[tex]\sigma = 1.14[/tex]

Answer:

(0.123 ; 0.277)

Step-by-step explanation:

Given :

Sample size, n = 180

x = 36

Proportion, p = x / n = 36/180 = 0.2

Confidence interval for sample proportion :

Confidence interval :

p ± Zcritical * √p(1 - p) / n

Zcritical at 99% = 2.576

0.2 ± 2.576 * √0.2(1 - 0.2) / 180

0.2 ± 2.576 * 0.0298142

0.2 ± 0.0768013792

(0.123 ; 0.277)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

Answer:

0.84

Step-by-step explanation:

4x2+13a+10=7

13a=7-10-8

13a=-11

a=-11:13

a=0.84

Answer:

Harry collected 180 stamps

Harry's sister collected 60 stamps

Step-by-step explanation:

Let X be the number of stamps that Harry's sister colleted.

The number of stamps Harry colleted is 3 time as many as his sister's

⇒ 3*X + X = 240

⇒ X = 60

⇒ 240 - 60= 180

Answer:

180 for harry and 60 for his sister

Step-by-step explanation:

Answer:

undefined

0

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

m = (-7 -5)/(-6 - -6)

   = (-7-5)/(-6+6)

   -12 /0

undefined

m = (y2-y1)/(x2-x1)

m = (-3 - -3)/(7 - -8)

    = (-3+3)/(7+8)

    = 0/15

   = 0

Slope Formula: (y2 - y1) / (x2 - x1)

#1.

Point 1 = (-6,5)

Point 2 = (-6,-7)

Slope = (-7 - 5) / (-6 - -6) = -12 / 0 = undefined

#2.

Point 1 = (-8,-3)

Point 2 = (7,-3)

Slope = (-3 - - 3) / (7 - - 8) = 0 / 15 = 0 slope

Hope this helps!

[tex]\boxed{ \sf{Answer}} [/tex]

[tex]\sf \: g(x) = {x}^{2} - 4 \\ \\ \sf \: x = 5 \\ \\ \sf \: g(5) = {5}^{2} - 4 \\ \sf \: g(5) = 25 - 4 \\ \sf \: g(5) =\underline 2\underline1[/tex]

Answer ↦21 [Option C]

[tex]\tt \: g(x) = {x}^{2} - 4[/tex]

Substitute the value of x as 5 (given) in the above equation. The equation changes too..

[tex]\tt \: g(5) = {5}^{2} - 4[/tex]

Now you can easily solve the equation.

[tex]\tt \: g(5) = {5}^{2} - 4 \\\tt g(5) =( 5 \times 5) - 4 \\ \tt \: g(5) = 25 - 4 \\ \tt \: g(5) = 21[/tex]

Answer - [tex]\boxed{\sf{21}}[/tex]