Consider the function given by f(x)= x² +3. Find its average rate of change from x = -2 to x = 4.
Carefully show the work that leads to your final answer.

Answer:

The system has just one solution, it is (1,4).

Step-by-step explanation:

When we have a system of linear equations, the solution is given by the intersection point of the two lines.

So if we see the graph, the intersect point is at (1,4). Therefore, the system has a unique solution.

I hope it helps you!

Answer:

x = 11

Step-by-step explanation:

sides of triangle measure: 'x', '4x-2' and '4x-2' since isosceles means both legs are equal

perimeter is the sum of all sides, so set up equation:

95 = 4x - 2 + 4x - 2 + x

95 = 8x - 4 + x

95 = 9x - 4

99 = 9x

x = 11

Answer:th hypotenuse and the height can’t possibly be the same size because the Pythagorean theorem is a^2 +b^2=c^2

Step-by-step explanation:

Answer:

hypotenuse is equal to side of this square.

but hypotenuse is never be equal to hieght of the triangle.

Answer:

The initial weight of the bar soap is 123g

Step-by-step explanation:

No options but the question can still be solved.

Given

[tex]y = -5.6x + 123[/tex]

Required

What does the y intercept mean

Start by calculating the y intercept (i.e. when x = 0)

The equation becomes

[tex]y = -5.6*0 + 123[/tex]

[tex]y = 0 + 123[/tex]

[tex]y = 123[/tex]

This means that the initial weight of the bar soap is 123g

Answer:

1 I believe if your asking in in simplified form and if 8/7 and 7/8 are multiplied

Step-by-step explanation:

Answer:

There are infinite solutions because there is always another number between any two numbers.

Step-by-step explanation:

Pick any number (including decimal) add an extra decimal after the smallest one and then you have a number between them. E.g.

1.234 and 2.987

1.2341, 1.2342, 1.2343, ... are all between them

Answer:

D

Step-by-step explanation:

Answer:

9.375 grams

Step-by-step explanation:

30 days = 3(10 days)

m = 75·0.5³ = 9.375 grams

3x+20=100

Now you would need to move the constant to the right side and change within it’s sign

3x=100-20

Now you would subtract the numbers so for 100-20 would give you 80

So now you then do 3x=80

But if you want to divide the equation, divide it by both sides by 3

Which would give you x=80/3, x=26.6 or x=26 2/3

Answer:your answer is D.

Step-by-step explanation:

When dividing fractions you must flip the numerator and denominator so that would leave you with 6/1 divided by 3/4, solve this and then you have an improper fraction so after you multiply by 3 you must divide because of the improper fraction and you will divide by 4.

Answer:

d .the total area multiplied by 3 divided by 4

Step-by-step explanation:

.

the total area multiplied by 3 divided by 4

Answer:

It's D, Sammi's work. Hope it helps! Remember your perfect, your awesome, your worth it, just the way you are, you deserve this world! Have an amazing day!

Step-by-step explanation:

Answer:

The person above me is correct.

Answer:

18, 21

Step-by-step explanation:

By finding the difference between each term, you can find the pattern. 9-6=3, 12-9=3, 15-12=3, so we know that each term is 3 more than the last.

Therefore, by following the pattern of +3, the next term is 15+3=18 and the one after that is 18+3 = 21

Answer:

the next two terms would be 18 and 21

Answer:

The cup would contain 10.16 ounces.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Mean of 10 ounces, standard deviation of 1 ounce:

This means that [tex]\mu = 10, \sigma = 1[/tex]

If we simulated the filling process, and had the random number .564, how many ounces would the cup contain?

This means that we have to find X when Z has a pvalue of 0.564. So X when Z = 0.16. So

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

[tex]0.16 = \frac{X - 10}{1}[/tex]

[tex]X - 10 = 0.16*1[/tex]

[tex]X = 10.16[/tex]

The cup would contain 10.16 ounces.

The difference 0.2−0.05 is equal to 0.15.

To find the difference between 0.2 and 0.05.

The larger number  is 0.2.

The smaller number is 0.05.

When you subtract 0.05 from 0.2, you align the decimal points and subtract each digit accordingly:

[tex]0.2 - 0.05[/tex]

[tex]= 0.15[/tex]

So, the difference between 0.2 and 0.05 is 0.15.

To learn more on Equation:

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Answer:

Pilot error = 347 / 1487 = 0.233 = 23.3%

Other human error = 83 / 1514 = 0.055 = 5.6%

Weather = 596 / 1487 = 0.401 = 40.1%

Mechanical problem = 374 / 1487 = 0.233 = 23.3%

Sabotage = 114 / 1487 = 0.077 = 7.7%

Step-by-step explanation:

Given the data :

Pilot error = 347

Other human error = 83

Weather = 596

Mechanical problem = 374

Sabotage = 114

Cummlative sum = (347 + 83 + 596 + 374 + 114) = 1487

Relative frequency :

Pilot error = 347 / 1487 = 0.233 = 23.3%

Other human error = 83 / 1514 = 0.055 = 5.6%

Weather = 596 / 1487 = 0.401 = 40.1%

Mechanical problem = 374 / 1487 = 0.233 = 23.3%

Sabotage = 114 / 1487 = 0.077 = 7.7%

Based on the relative frequency estimate, Weather is the most serious threat to aviation safety.

Deployment of more weather monitoring technologies

Answer:

14

Step-by-step explanation:

To make 166 a supplementary angle you should add 14 because supplementary angles equal 180.

Answer:

14

Step-by-step explanation:

Supplementary angles add to 180 degrees.

Let x be the unknown supplement

x+166 = 180

x+166-166 = 180-166

x =14

The unknown supplement is 14

Answer:

(5,-6) is a solution

Step-by-step explanation:

Given

[tex]6x + 3y = 12[/tex]

[tex]4x + y = 14[/tex]

Required

Tell whether (5,-6) is a solution

In (5,-6): x = 5 and y = -6.

Substitute these values in the given equations

[tex]6x + 3y = 12[/tex] becomes

[tex]6 * 5 + 3 * -6 = 12[/tex]

[tex]30-18 = 12[/tex]

[tex]12 = 12[/tex]

[tex]4x + y = 14[/tex] becomes

[tex]4 * 5 - 6 = 14[/tex]

[tex]20 - 6 = 14[/tex]

[tex]14 = 14[/tex]

Because both solutions are true, then (5,-6) is a solution

Answer:

[tex]y=\frac{b}{a} x.[/tex]

Step-by-step explanation:

1) if the required straight line is 'l', the given point is A(a;b), then the required equation of line can be written in form:

[tex]\frac{x-a}{x_1-a} =\frac{y-b}{y_1-b},[/tex]

where (x₁;y₁) is other point B, which belongs to the 'l';

2) from the equation it is possible to detect the coordinates of the perpendicular, they are (x₁-a;y₁-b);

3) if the given perpendicular is ax+by=5, then the coordinates of the vector (a;b) are coordinates of the vector, which belongs to the required line 'l', and then: x₁-a=a and y₁-b=b;

4) if to substitute the a=x₁-a and b=y₁-b into the required equation of line 'l', then:

[tex]\frac{x-a}{a} =\frac{y-b}{b};[/tex]

5) finally, the equation is: ay=bx, or y=b/a *x (slope-interception form).

note: the suggested solution is not the only way.

Answer:

h = 452.5 ft

Step-by-step explanation:

Angle of elevation from P to top of the pole = 65°

Horizontal distance between the pole and point P = 21 ft

By Applying tan rule in the given triangle ABP,

tan(∠APB) = [tex]\frac{AB}{PB}[/tex]

tan(65°) = [tex]\frac{h}{21}[/tex]

h = 21[tan(65°)]

h = 452.491

h ≈ 452.5 ft

Therefore, height of the pole is 452.5 ft.

Answer:

I think this is what you meant not sure tho

Step-by-step explanation:

|8| = correct as it is

|-8| = correct as it is

-|8| = |-8|

-|-8| = |8|

Answer:

A

Step-by-step explanation:

Answer:

A cylinder 10 cm high with a circumference of 30 cm would have a greater volume

Step-by-step explanation:

Volume of a Cylinder

Given a cylinder of radius r and height h, the volume is calculated as:

[tex]V=\pi r^2h[/tex]

It's given a rectangular strip of aluminum 30 cm long and 10 cm wide. If we roll it to form a cylinder we can do it in two ways.

Rolling it across its length will make the cylinder have a height of h=10 cm and the circumference of the base equal to 30 cm.

The circumference of a circle of radius r is:

[tex]C=2\pi r[/tex]

Thus the radius is:

[tex]\displaystyle r=\frac{C}{2\pi}[/tex]

[tex]\displaystyle r=\frac{30}{2\pi}=\frac{15}{\pi}[/tex]

Thus the volume of the cylinder is:

[tex]V=\pi ( \frac{15}{\pi})^2*10[/tex]

[tex]V=\pi ( \frac{225}{\pi^2})*10[/tex]

[tex]V= \frac{2250}{\pi}[/tex]

If we rolled the strip across its width, then the height will be h=30 cm and the circumference C=10 cm, thus the radius is:

[tex]\displaystyle r=\frac{10}{2\pi}=\frac{5}{\pi}[/tex]

And the volume is:

[tex]V'=\pi ( \frac{5}{\pi})^2*30[/tex]

[tex]V'=\pi ( \frac{25}{\pi^2})*30[/tex]

[tex]V'= \frac{750}{\pi}[/tex]

Dividing V/V' = 3. The first volume it 3 times as much as the second volume.

A cylinder 10 cm high with a circumference of 30 cm would have a greater volume

Answer: If you divide 202/4=50.5 or 50 1/2

Step-by-step explanation:

Multiply 120 by 18%

Change 18% to a decimal: 0.18

120 x 0.18 = 21.6

Answer: 21.6

Answer:

Amount on 11% note = $106,666.67

Amount on 8% note = $43,333.33

Step-by-step explanation:

Let the amount for the ​short-term note at ​11% interest be x.

Thus, the amount for the ​short-term note at ​8% interest will be (150000 - x)

Now we are told that the total interest paid is $15,200.

Thus;

0.11x + 0.08(150000 - x) = 15200

0.11x + 12000 - 0.08x = 15200

Rearranging gives;

0.03x = 15200 - 12000

0.03x = 3200

x = 3200/0.03

x = $106666.67

Thus, amount for 8% note = $150000 - $106666.67 = $43,333.33

Answer:

7

Step-by-step explanation:

average of 7th grade - average of 8th grade = 7

average of 7th = (52+55+57+57+58+60+60+62+64+65)/10

= 590/10

= 59

average of 4th = 44+48+48+51+52+52+54+54+57+60

= 520/10

= 52

59 - 52 = 7

please give me brainliest if it is helpful for you

Answer: Hoped I help

7 and there is more variability in the height of 7th grade girls

Step-by-step explanation:

4th grade

44+48+48+51+52+52+54+54+57+60

found the median which is 52 and 52 but you add them and divide them by 2 to get the median which is 104/2= 52

7th grade

52+55+57+57+58+60+60+62+64+65

median is 60 + 58=118/2= 59

59-52= 7

and

there is more variabilty in the hieght f 7th grade girls. because 4th grade has a lot of modes already while 7th grade has only like two so 7th grade will have more variability.

Answer:

The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].

Step-by-step explanation:

According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:

[tex]h = h_{o}\cdot r^{n-1}[/tex], [tex]n \in \mathbb{N}[/tex], [tex]0 < r < 1[/tex] (1)

Where:

[tex]h_{o}[/tex] - Height reached by the ball on the first bounce, measured in feet.

[tex]r[/tex] - Decrease rate, no unit.

[tex]n[/tex] - Number of bounces, no unit.

[tex]h[/tex] - Height reached by the ball on the n-th bounce, measured in feet.

The decrease rate is the ratio between heights of two consecutive bounces, that is:

[tex]r = \frac{h_{1}}{h_{o}}[/tex] (2)

Where [tex]h_{1}[/tex] is the height reached by the ball on the second bounce, measured in feet.

If we know that [tex]h_{o} = 6\,ft[/tex] and [tex]h_{1} = 4\,ft[/tex], then the expression for the height of the bouncing ball is:

[tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex]

The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].

Answer:

9 (2/3) ² but insted of 2 its n

Step-by-step explanation:

Answer:

w = 6

Step-by-step explanation:

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]

[tex]\frac{w-[-10]}{10-8}=8\\\\\frac{w+10}{2}=8\\\\w+10= 8*2\\[/tex]

w +10  = 16

        w = 16 - 10

         w = 6

Answer:

21

Step-by-step explanation:

Answer:

1.67

Step-by-step explanation:

25/15 = 1.67

The mean is estimated by dividing the total of the values by the range of values.