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Answer: (x-2)2

Step-by-step explanation:

The required equation is  [tex]y=(x-2)^2[/tex]

The correct answer is an option (C)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

We have been given four equations.

We need to find an equation for which y is always greater than or equal

to -1.

Consider,

A. y = ∣x∣ - 2

We know that the minimum value of ∣x∣ is 0.

So, the minimum value of y becomes -2

Hence, this is not a required equation.

B. [tex]y=x^{2} -2[/tex]

We know that the square of any number is always positive.

The minimum value of [tex]x^{2}[/tex] is 0.

So, the minimum value of y becomes −2

Hence, this is not a required equation.

C. [tex]y=(x-2)^2[/tex]

We know that the square of any number is always positive.

The minimum value of y is zero.

This means, the y value of equation  [tex]y=(x-2)^2[/tex] is always greater than -1.

D. [tex]y=x^3-2[/tex]

We know that [tex]x^3[/tex] can go have negative values. This means it may have value that tends to negative infinity.

This means, the y can be less than -1 and this is not a required equation.

Therefore, the required equation is  [tex]y=(x-2)^2[/tex]

The correct answer is an option (C)

Learn more about the equation here:

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Answer:

∠DAB = 133°

Step-by-step explanation:

Given - Quadrilateral ABCD is a parallelogram. ∠D = 3x + 17, ∠B = 5x - 3

To find - What is the measure of ∠DAB?

Proof -

We know that In a parallelogram, opposite angles are equal.

So, ∠A = ∠C and ∠B = ∠D

Now,

As ∠B = ∠D

⇒3x + 17 = 5x - 3

⇒17 + 3 = 5x - 3x

⇒20 = 2x

⇒x = 10

So,

∠B = 5(10) - 3 = 50 - 3 = 47

⇒∠B = 47°

Also, we know that

∠A + ∠B = 180°

⇒∠A = 180° - ∠B

⇒∠A = 180° - 47° = 133°

⇒∠A = 133°

⇒∠DAB = 133°

Answer:

p(x) = x^2 - 8x + 41

Step-by-step explanation:

If a polynomial with rational coefficients has a complex root, then the roots come in complex conjugate pairs. If the polynomial we need to find has the root 4 - 5i, then it must also have its complex conjugate 4 + 5i as a root.

p(x) = [x - (4 - 5i)][x - (4 + 5i)]

p(x) = [(x - 4) + 5i][(x - 4) - 5i]

Now it's a difference of two squares.

p(x) = (x - 4)^2 - (5i)^2

p(x) = x^2 - 8x + 16 + 25

p(x) = x^2 - 8x + 41

Answer:

[tex]f(x)=2(x-2)(x^2+64)[/tex]

Step-by-step explanation:

A standard polynomial in factored form is given by:

[tex]f(x)=a(x-p)(x-q)...[/tex]

Where p and q are the zeros.

We want to find a third-degree polynomial with zeros x = 2 and x = -8i and equals 320 when x = 4.

First, by the Complex Root Theorem, if x = -8i is a root, then x = 8i must also be a root.

Therefore, we acquire:

[tex]f(x)=a(x-(2))(x-(-8i))(x-(8i))[/tex]

Simplify:

[tex]f(x)=a(x-2)(x+8i)(x-8i)[/tex]

Expand the second and third factors:

[tex]=(x+8i)x+(x+8i)(-8i)\\\\=(x^2+8ix)+(-8ix-64i^2)\\\\=(x^2)+(8ix-8ix)+(-64i^2)\\\\=x^2-64(-1)\\\\ =x^2+64[/tex]

Hence, our function is now:

[tex]f(x)=a(x-2)(x^2+64)[/tex]

It equals 320 when x = 4. Therefore:

[tex]320=a(4-2)(4^2+64)[/tex]

Solve for a. Evaluate:

[tex]320=(2)(80)a[/tex]

So:

[tex]320=160a\Rightarrow a=2[/tex]

Our third-degree polynomial equation is:

[tex]f(x)=2(x-2)(x^2+64)[/tex]

Answer:

f(x)=2(x-2)(x^2+64)

Step-by-step explanation:

Answer:

p = 16.8

[tex] r \geqslant 5.5[/tex]

Step-by-step explanation:

12)

p + 2.1 = 18.9

p = 18.9 - 2.1

p = 16.8

13)

[tex]r \geqslant 5.5[/tex]

Answer:

a. A capital letter that have corresponding angles is the letter 'E'

b. A capital letter that have alternate angles is the letter 'N'

Step-by-step explanation:

The capital letter 'F' is made two horizontal parallel lines that touch a common transversal. Therefore, in the letter F, the two horizontal parallel lines form corresponding angles with the transversal below each parallel line

Similarly, the letter Z form alternate angles below the horizontal parallel lines and the inclined diagonal

a. Another capital letter that have corresponding angles is the letter 'E'

b. Another capital letter that have alternate angles is the letter 'N'

Answer:

A

Step-by-step explanation:

the answer is a

Answer:

missing angle = 30 degrees

Step-by-step explanation:

all triangles have an interior angle or 180 degrees.

to find the missing angle, just take the know angles and add them together:

120 + 30 = 150

then take the sum and subtract it from 180:

180 - 150 = 30

Answer:

Answer:

18+(93-57)

18+(36)

54

Step-by-step explanation:

Multiply before addition.Using bodmas

Answer:

Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Average cumulative debt of recent college graduates is about $22,500, standard deviation of $7,000.

This means that [tex]\mu = 22500, \sigma = 7000[/tex]

Proportion more than 30000.

1 subtracted by the pvalue of Z when X = 30000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30000 - 22500}{7000}[/tex]

[tex]Z = 1.07[/tex]

[tex]Z = 1.07[/tex] has a pvalue of 0.8577

1 - 0.8577 = 0.1423

Approximately how many recent college graduates have accumulated a student loan of more than $30,000?

0.1423 out of 1.8 million.

0.1423*1.8 = 0.25614 million = 256,140

Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.

Answer:

The percentage change from 98 to 80 is -18.37 %

Step-by-step explanation:

((y2 - y1) / y1)*100 = your percentage change

(where y1=start value and y2=end value)

((80 - 98) / 98) * 100 = -18.37 %

Answer:

A) $6.87

B) $3.09

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The cost of 5 notebooks (5x)

Less than (<)

The cost of 3 notebooks (3x)

Plus a 2 dollar pen (2)

All together: 5x < 3x + 2

Matches with the given expression.

Answer:

4

a. 12

b. 8

c. 30

d. 40

Step-by-step explanation:

each exterior = 360/n

30*n=360

divide both side by 30

Answer is 12

The same apply to others to 4d

so first its 4

a. 12

b. 8

c. 30

d. 40

i will try to explain:

each exterior = 360/n

30*n=360

divide both side by 30

Answer is 12

The same apply to others to 4d

Answer:

6

Step-by-step explanation:

70/84 = 5/N

70N = 420

N = 420/70 = 6

23.4 ft2

Step-by-step explanation:

jvuctctctcrxrxrxrxrxr

Answer:

The corner is 90 degrees so I believe you add them so 60+90+30 is 180!!!

Answer:

Binomial probability, with [tex]n = 5, p = 0.352[/tex]

Step-by-step explanation:

For each time Mookie Betts went to bat, there were only two possible outcomes. Either he got a base-hit, or he did not. The probability of getting a hit on each at-bat is independent of any other at-bat. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

His average was 0.352.

This means that [tex]p = 0.352[/tex]

Assume he has five times at bat tonight in the Red Sox-Yankees game.

This means that [tex]n = 5[/tex]

a. This is an example of what type of probability

Binomial probability, with [tex]n = 5, p = 0.352[/tex]

Answer:

43.96

Step-by-step explanation:

Well, the first step is finding out the diameter. And then the basic outline is d x 3.14. So I simply just punched in 14 x 3.14 in my calculator.

Answer:

14π cm

Step-by-step explanation:

Circumference of the circle

= 2πr

= 2π(14/2)

= 14π cm

Answer:

Step-by-step explanation:It isn’t. There are really 4 different versions of the exponential function. Positive (like the growth of money invested at 5%), negative (like the US debt constantly becoming more negative), positive decay (like the half life of a radioactive element), or negative decay ( pay half your loan amount in year 1, 1/4 in year two, 1/8 in year three, you in theory will never pay your loan completely but the debt is growing closer to zero.

Answer:

Step-by-step explanation:

2/5 = 0.4

2/4 = 0.5

0.5 - 0.4 = 0.1

Sally picked 1/10 of a basket more than Maggie picked

Answer:

1 this could change depending on how many berries are in each basket

Step-by-step explanation:

2/5 = 0.4

2/4 = 0.5

Answer:

2

Step-by-step explanation:

the rate of change is Rise/ Run

= Δy / Δx

= (y2 – y1) / (x2 – x1)

= (1 - (-1))/(-1 - (-2))

=2/1

=2

Answer:

[tex]4.3 \pm 2.306\frac{1.5}{\sqrt{9}}[/tex], option c

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 9 - 1 = 8

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.306

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.306\frac{1.5}{\sqrt{9}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Confidence interval:

The confidence interval is the sample mean plus/minus the margin of error. So

[tex]4.3 \pm 2.306\frac{1.5}{\sqrt{9}}[/tex]

The correct answer is given by option c.

Answer:

A.) Population : All employees at a firm

B.) μ = 5.4

C.) Sample : 80 employees at a firm

D.) Sample mean, x bar = 4.5

Step-by-step explanation:

From the question :

E.)

H0: μ ≥ 5.4

H1 : μ < 5.4

F.)

If Pvalue < α ; Reject H0

G.)

Test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(4.5 - 5.4) ÷ (2.7/sqrt(80))

-0.9 ÷ 0.3018691

= - 2.98

H.)

Pvalue fro Zscore calculator, α = 0.10 = 0.002882

I.)

Decision :

0.002882 < 0.10

Since, Pvalue < α ; We reject the Null

J.)

We Can conclude that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced

Answer:

Interest = [tex] \boxed{\$ 789.75} [/tex]

Explanation:

Interest [I] = principle × rate × time [prt]

______________________________

x% = x/100

a b/c = a + (b/c) = (ac + b) / c

______________________

I = prt

I = ($1,950)(4 ½%)(9)

I = ($1,950)(0.045)(9)

I = ($87.75)(9)

I = ($789.75)

I = $789.75

Answer:

6m-2m+12 and 4(m+3)

Step-by-step explanation:

4(m+12)=4m+48❎

3m-m+12=2m+12❎

6m-2m+12=4m+12✅

4(m+3)=4m+12✅