Solve x2 – 8x + 15 < 0.

Select the critical points for the inequality shown.

Answer:

Slope = 6

Step-by-step explanation:

Use the slope formula:

[tex]m=\frac{y_1-y_2}{x_1-x_2}\\m=\frac{-4-8}{3-5}\\m=\frac{-12}{-2}\\m=6[/tex]

Answer:

6

Step-by-step explanation:

(3,-4) and (5,8)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(8 - (-4)) / (5 - 3)

Simplify the parentheses.

= (8 + 4) / (5 - 3)

= (12) / (2)

Simplify the fraction.

12/2

= 6

This is your slope.

Hope this helps!

Answer:

The choose (D)

[tex] {g }^{ \frac{5}{6} } [/tex]

The expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex] is [tex]g^{\frac{5}{6} }[/tex].

The number of times a number has been multiplied by itself is referred to as an exponent. It could be an integer, a fraction, a negative integer, or a decimal. Powers or indices are other names for exponents. For instance, 6⁵ indicates that we are multiplying 6 by five. It is 6 × 6 × 6 × 6 × 6 in its expanded form.

The expression is [tex]\sqrt[6]({g}^{5})[/tex].

[tex]\sqrt[6]{g}[/tex] can be written as [tex]g^{\frac{1}{6} }[/tex].

Then the given expression can be written as [tex]g^{\frac{5}{6} }[/tex].

Therefore, the expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex], g > 0 is [tex]g^{\frac{5}{6} }[/tex]. So, option D is correct.

Learn more about exponents here -

https://brainly.com/question/27850853

#SPJ2

Answer:

You could change 1 4/5 to 1 8/10 to make it easier to plot.

Answer:

Well the volume is 1570.8 cubed. but i don't know what it would be in your range of answers.

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

mLA : mLB : mLC = 1:2:1 => 1+2+1=4 (equivalent with 180°)

so, mL2 = mLC = 1/4 ×180° = 45°

Answer:

200 m

-15 m

215 m

Step-by-step explanation:

Given :

Top of hill = 200 m above sea level ; height of hill top is positive 200m = 200 m

Bottom of lagoon = 15m *below sea level ; bottom of lagoon = - 15m

We have related the height of the two points with respect to sea level ; points above sea level are represented as positive ; points below are represented as negative.

Difference between the two heights :

Hill top - bottom of lagoon :

200 m - (-15) m

200 m + 15 m

215 m

Difference between the heights is 215 m

Answer:

The total bill is $6900 because 69 is a man which hair is multi colour

Answer:

it might be 3 but I'm not sure

Answer:

C

Step-by-step explanation:

Let us first write an equation. Using the SOHCAHTOA rule, we should know that the tangent of an angle equals it's [tex]\frac{opposite}{adjacent}[/tex]. The opposite of our given 20° angle is 9, and the adjacent side is x.

[tex]tan(20[/tex]°[tex])=\frac{9}{x}[/tex]

[tex]0.364=\frac{9}{x} \\x=\frac{9}{0.364}\\x=24.7[/tex]

C

I hope this helps! Let me know if you have any questions :)

Answer:

I guess it's False...Hope it helps you.

Answer:

true

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

Answer:4000000

Step-by-step explanation:783

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

Explanation:

The y is a placeholder for a number. In this case, we'll replace it with 4.

So [tex]5y^2 - 10[/tex] becomes [tex]5(4)^2-10[/tex]

Use the order of operations PEMDAS to simplify

[tex]5(4)^2-10\\\\5(16)-10\\\\80-10\\\\70\\\\[/tex]

Therefore, [tex]5y^2-10\\\\[/tex] evaluates to 70 when y = 4.

Put another way, the equation [tex]5y^2-10 = 70\\\\[/tex] has one solution that is y = 4.

The table shows ordered pairs of the function y=8-2 x . What is the value of y when x=8 ?

The given value of x is 8.

we have to find the value of 'y' , so,

▶️ y = 8-2 x

▶️ y = 8-2 × 8

▶️ y = 8-16

▶️ y = -8

The value of y is -8.

[tex] \\ \\ [/tex]

Answers:

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

Explanation:

Let A = 50 degrees and C = 30 degrees. The side opposite angle uppercase C is lowercase c = 8. Convention usually has uppercase letters as the angles, while the lowercase letters are side lengths. A goes opposite 'a', B goes opposite b, and C goes opposite c.

Let's use the given angles to find the missing angle B

A+B+C = 180

50+B+30 = 180

B+80 = 180

B = 180-80

B = 100

Now we can apply the law of sines to find side b

b/sin(B) = c/sin(C)

b/sin(100) = 8/sin(30)

b = sin(100)*8/sin(30)

b = 15.7569240481953

b = 15.8

Make sure your calculator is in degree mode.

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

We'll do the same thing to find side 'a'

a/sin(A) = c/sin(C)

a/sin(50) = 8/sin(30)

a = sin(50)*8/sin(30)

a = 12.2567110899037

a = 12.3

Both values for 'a' and b are approximate (even before rounding).

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

Extra info (optional)

Answer:

B=100

b=15.7

a=12.25

Step-by-step explanation:

first find the missing angle:

B=180-50-30

B=100

then use the law of sines:

[tex] \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) ) } = \frac{c}{ \sin(c) } [/tex]

then

[tex] \frac{a}{ \sin(50) } = \frac{8}{ \sin(30) } \\ \\ a = 12.25[/tex]

use the same way to find the other side

[tex] \frac{b}{ \sin(100) } = \frac{8}{ \sin(30) } \\ b = 15.7[/tex]

Answer:

Step-by-step explanation:

1

Answer:

(2,6) and (-1,3)

Step-by-step explanation:

Hi there!

We're given the system of equations:

y=x+4

y=x²+2

and we need to solve the system

You may first notice that both equations are equal to y, so we can set them to equal each other via a property known as transitivity (if a=b and b=c, then a=c)

x²+2=x+4

subtract x from both sides

x²-x+2=4

subtract 4 from both sides

x²-x-2=0

we can factor the polynomial

the numbers that add up to -1 and multiply to get -2 are -2 and 1

(x-2)(x+1)=0

solve

x=2, x=-1

both values of x work- so we'll have 2 solutions in this case

now we need to solve for y; we can do this by substituting the value of x into one of the equations to solve for y

let's use y=x+4

so if we'll use x=2,

y=2+4

y=6

one solution will be (2,6)

and if we use x=-1

y=-1+4

y=3

and the other will be (-1,3)

Hope this helps! :)

Answer:

x=2 and y=1

Step-by-step explanation:

Add the two equations to remove "y" and solve for x:

4x+8y=16

6x-8y=4

________

10x=20

x=2

Plug x=2 into one of the original equations to get the value of "y":

4x+8y=16

4(2)+8y=16

8+8y=16

8y=8

y=1

Therefore, x=2 and y=1

Answer:

Z = -1.65

Step-by-step explanation:

Z-score:

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.

What is the critical value for the 5% significance level?

One-tailed statistic, so Z with a p-value of 0.05.

Looking at the z-table, this is Z = -1.65, so this is the critical value for the 5% significance leve.

Answer:

El a+b tiene 1 terminó porque para separar un término el factor es el +Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Angles in a triangle add up to equal 180

Hence, 10x - 1 + 78 + 53 = 180

( Note that we just created an equation that we can use to solve for x )

We now solve for x using the equation we created

10x - 1 + 78 + 53 = 180

Combine like terms

10x + 130 = 180

Subtract 130 from both sides

10x = 50

Divide both sides by 10

x = 5

Answer:

it seems like you already have this answered?

Answer:

data set 3 would have the least mean absolute deviation among the three sets since there is less spread of the data and the data values in set-3 lie close to the mean.

Step-by-step explanation:

The mean absolute deviation is a  measure of spread of the data.

If the data values in the given data set are widely spread then we obtain a higher mean absolute deviation.

if the data values of a given data set are close to each other i.e there is a less spread of the data and hence the mean absolute deviation will be low as the data values will lie close to the mean.

We are given three data set as:

set- 1             42, 48, 50, 88, 49

set- 2             63, 29, 35, 28, 30

set- 3                2, 5, 3, 8

Hence, we could observe that the data values in set 1 and set 2 are widely spread.

In set-1 the data value 88 is  much higher value as compared to other data values.

Similarly in set-2 the data value 63 is again a much higher value as compared to other data values.

Whereas in set-3 the data values are all closely related and there is not much spread in the data.

Answer:

4p

Step-by-step explanation:

The period is basically the difference in x from one "peak" to the other "peak".

The peaks are the highest points of a sinosodial function, and the figure them out, use the formula:

[tex]|peak_1-peak_2|=period[/tex]

We know the first peak is at about x=0[tex]\pi[/tex]

We know the second peak is at about x=4[tex]\pi[/tex]

So plugging this in:

[tex]|0-4\pi |=4\pi[/tex]

So the period is [tex]4\pi[/tex]

I am assuming "p" stands for [tex]\pi[/tex], so the answer should be 4p.

There are other ways to find the period, for instance if you are given a sinusodial function in writing instead of a graph.

Here is an example:

5sin(5x+2)+3

If we want to find period, we need to find what we call "b"

b is the number in front of x, which we can identify as bx, which in this case is 5x above.

Now what do we do with this "b"?

This is the value we need to find our period.

If you know b, you can use this formula to find the period:

[tex]\frac{2\pi }{b}=p[/tex]

And when we plug in b:

[tex]\frac{2\pi }{5}[/tex]

=

1.257, which would be your period.

THis can also be reworked so that you can find b:

If the formula for period is [tex]\frac{2\pi }{b}=p[/tex], then the opposite formula would be [tex]\frac{2\pi }{ p}=b[/tex]

And when you plug the period you have in:

[tex]\frac{2\pi }{1.257}[/tex]

=

5

Anyway, your answer is 4p.

Hope this helps!

Answer:

below

Step-by-step explanation:

Clare's mistake was the writing of 4000 in standard form

he wrote 4 ×10²

instead of 4 ×10³

Answer:

Step 1

Step-by-step explanation:

I believe Claire's mistake is when she tries to simplify 4000

She says that 4000 = 4 × 10²

4000 is actually equal to 4 ×10³

Answer:

The volume of the cone is increasing at a rate of 1926 cubic inches per second.

Step-by-step explanation:

Volume of a right circular cone:

The volume of a right circular cone, with radius r and height h, is given by the following formula:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Implicit derivation:

To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So

[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]

Radius is 107 in. and the height is 151 in.

This means that [tex]r = 107, h = 151[/tex]

The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.

This means that [tex]\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6[/tex]

At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.

This is [tex]\frac{dV}{dt}[/tex]. So

[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]

[tex]\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))[/tex]

[tex]\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}[/tex]

[tex]\frac{dV}{dt} = 1926[/tex]

Positive, so increasing.

The volume of the cone is increasing at a rate of 1926 cubic inches per second.

Answer:

5 overtime hours

Step-by-step explanation:

Given that :

Pay per hour = 240

Overtime pay = 1 1/2 * pay per hour = 1 1/2 * 240 = 360 per hour

Amount earned for the week = 11400

Let overtime hours = x

Total hours worked = 40 + x

Earning for the week based on hours worked :

240(40) + 360x = 11400

9600 + 360x = 11400

360x = 1800

x = 1800 / 360

x = 5 hours

Answer:

a) 0.00136008

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of any other customer. Thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

9.8% of his customers buy a magazine

This means that [tex]p = 0.098[/tex]

What is the probability that exactly 5 out of the first 10 customers buy a magazine?

This is [tex]P(X = 5)[/tex] when [tex]n = 10[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{10,5}.(0.098)^{5}.(0.902)^{5} = 0.00136008[/tex]

Thus, the correct answer is given by option A.

Answer:

False

Step-by-step explanation: