ANSWER:
6
STEP-BY-STEP EXPLANATION:
We must evaluate the function at those points to know the values of f(x), like this:
[tex]\begin{gathered} f(2)=6\cdot2+6=12+6=18 \\ f(8)=6\cdot8+6=48+6=54 \end{gathered}[/tex]Knowing this, we can calculate the rate of change using the following formula:
[tex]\begin{gathered} r=\frac{f(x_2)-f(x_1)_{}}{x_2-x_1} \\ \text{ replacing} \\ r=\frac{54-18}{8-2}=\frac{36}{6} \\ r=6 \end{gathered}[/tex]The average Rate of Change is 6
lines / and m are parallel. evealute the measure in each figure. solve for the value of X
From figure A, the value of x is similar to 40 degrees. The location of the angle 40 degrees on line l is similar to that of x on line m based on geometry. We call this type of angle corresponding angles
Hence x = 40 degrees (Corresponding angle)
what is the slope-intercept form of the function described by this tableX- 1, 2, 3, 4Y- -2 -6, -10 -14
Let's begin by listing out the information given to us:
[tex](x,y)=(1,-2),(2,-6),(3,-10),(4,-14)[/tex]The slope-intercept form is given by:
[tex]\begin{gathered} y=mx+b \\ where\colon m=slope,b=y-intercept \end{gathered}[/tex]The slope is calculated by picking any two ordered pairs or coordinates and substituted into the slope formula:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(1,-2);(x_2,y_2)=(4,-14) \\ m=\frac{-14-(-2)}{4-1}=\frac{-14+2}{3}=\frac{-12}{3} \\ m=-4 \end{gathered}[/tex]We proceed to use the point-slope equation to derive this function:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=-4 \\ (x_1,y_1)=(1,-2) \\ y-(-2)=-4(x-1) \\ y+2=-4x+4 \\ y=-4x+4-2 \\ y=-4x+2 \\ \\ \therefore y=-4x+2 \end{gathered}[/tex]Which function is best represented by the graph at the right?
Answer:
The function that best represent the given graph is;
[tex]y=\frac{3}{4}x-7[/tex]Explanation:
We want to find the function that best represent the given graph.
Recall that the slope-intercept form of linear equation can be written as;
[tex]y=mx+b[/tex]where;
[tex]\begin{gathered} m=\text{slope} \\ b=\text{intercept on the y-axis} \end{gathered}[/tex]From the given graph, the intercept on the y axis is at;
[tex]\begin{gathered} \text{ point (0,-7)} \\ b=-7 \end{gathered}[/tex]We need to find the slope.
Using two points on the graph;
[tex]\begin{gathered} (0,-7) \\ \text{and} \\ (8,-1) \end{gathered}[/tex]The slope is;
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{substituting the coordinates;} \\ m=\frac{-1-(-7)_{}}{8-0}=\frac{-1+7}{8} \\ m=\frac{6}{8} \\ m=\frac{3}{4} \end{gathered}[/tex]Since we have the slope and the intercept, we can now write the equation of the line;
[tex]\begin{gathered} y=mx+b \\ y=\frac{3}{4}x-7 \end{gathered}[/tex]Therefore, The function that best represent the given graph is;
[tex]y=\frac{3}{4}x-7[/tex]
Jose cooked two batches of cookies yesterday and three more batches of cookies today. Assuming he makes three batches ofcookies each day, write an explicit expression to generate the sequence representing the total number of batches Jose has madeafter each day. I point)Of(n) = 3-2 (1-1)Of(n) = 3+2 (n-1)f(n) = 2-3(n-1)fin) = 2 + 3 (n = 1)
1)
3 cookies per day
Day Cookies
Day 1 2
Day 2 5
Day 3 8
Day 4 11
(...)
2) Let's do an explicit expression, to that Arithmetic Sequence
F(n) = 2 +(n-1)3
Where the first is 2, the common ration is 3.
The volume of a sphere is 1928 m3. What is the surface area of the sphere to the nearest tenth? 2 24.228 m 142.1 m² 1606.9 m² 803.4 m2
Given:
volume = 1928π m^3
And the formula of the volume for the sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]Substitute the value of the volume:
[tex]1928\pi=\frac{4}{3}\pi r^3[/tex]Simplify:
[tex]\begin{gathered} 1928\pi\cdot\frac{3}{4\pi}=\frac{4}{3}\pi r^3\cdot\frac{3}{4\pi} \\ \frac{5784}{4}=r^3 \\ r^3=1446 \end{gathered}[/tex]And solve for r:
[tex]r=\sqrt[3]{1446}=11.31[/tex]Next, the surface area is given by:
[tex]SA=4\pi r^2[/tex]Substitute the values:
[tex]SA=4(3.14)(11.31)^2=1606.9[/tex]Answer: 1606.9 m^2
Translate the following into an inequality:What number plus four is at most 6?k = 4 < 6k + 4 ≤ 6k + 4 > 6k + 4 ≥ 6
1) In this problem, we need to call that number, a variable. Whenever we read or hear "at most" that means "the maximum value is". So we can write out the following expression:
[tex]\begin{gathered} k+4\leq6 \\ k\leq6-4 \\ k\leq2 \end{gathered}[/tex]Note that by solving this inequality we can tell which maximum number k must be.
Thus, the answer is:
[tex]k+4\leqslant6[/tex]Drag the tiles to the boxes to from correct pairs.
If the point (x, y) rotated 90 degrees counter-clockwise, then its image is (-y, x)
If the point (x, y) rotated 180 degrees clockwise or counter-clockwise, then its image is (-x, -y)
It the point (x, ) rotated 90 degrees clockwise or 270 degrees counterclockwise, then its image is (y, -x)
Since point D (2, 2) is roteated 90 degrees counterclockwice, then
D' = (-2, 2)
Since point C (1, 3) is rotated 90 degrees clockwise, then
C'' = (3, -1)
Since point A (-4, 2) is rotated 180 degrees clockwise, then
A''' = 4, -2)
Since the point B (-2, 4) is rotated 270 degrees counterclockwise, then
B'''' = (4, 2)
The coordinates of point D' if polygon ABCD is rotated 90 counterclockwise is (-2, 2)
The coordinates of point C'' if polygon ABCD is rotated 90 degrees clockwise is (3, -1)
The coordinates of point A''' if polygon ABCD is rotated 180 degrees clockwise is (4, -2)
The coordinates of point B'''' if polygon ABCD is rotated 270 degrees counterclockwise is (4, 2)
These figures are similar. The area of one is given. Find the area of the other.3 inarea=24 in6 in[ ? Jin2
ANSWER
[tex]\begin{equation*} 6\text{ }in^2 \end{equation*}[/tex]EXPLANATION
We want to find the area of the other figure.
Since the figures are similar, the areas of the figures are related by the square of the linear scale factor.
To find the linear scale factor, we have to divide a corresponding set of side lengths from the two figures. That is:
[tex]\begin{gathered} \frac{3}{6} \\ \Rightarrow\frac{1}{2} \end{gathered}[/tex]Hence, the areas of the figures have a scale factor of:
[tex]\begin{gathered} (\frac{1}{2})^2 \\ \Rightarrow\frac{1}{4} \end{gathered}[/tex]So, to find the area of the other figure, we have to multiply the area of the figure by 1/4:
[tex]\begin{gathered} 24*\frac{1}{4} \\ \Rightarrow6\text{ }in^2 \end{gathered}[/tex]That is the area of the other figure.
For Problems 7–8, factor the expressions using the GCF. 7. 3x - 24 8. 3x + 15
Explanation
Step 1
7)
[tex]\begin{gathered} 3x-24 \\ \end{gathered}[/tex]
get the factors of each number
[tex]\begin{gathered} 3x=3\cdot x \\ 24=3\cdot2\cdot2\cdot2\cdot=3\cdot8 \end{gathered}[/tex]so, the GCF is 3
[tex]\begin{gathered} 3x-24=3(\frac{3x}{3}-\frac{24}{3}) \\ 3x-24=3(x-8) \end{gathered}[/tex]Step 2
8)
[tex]3x+15[/tex]get the factors of each number
[tex]\begin{gathered} 3x=3\cdot x \\ 15=3\cdot5 \end{gathered}[/tex]so, the GCF is 3
[tex]3x+15\rightarrow3(\frac{3x}{3}+\frac{15}{3})\rightarrow3(x+5)[/tex]I hope this helps you
PLEASE HELP ME NOW I WILL MARK BRAINLIEST!!!!!
a spinner has sections that are number 1 through 7 liam spins the spinner 20 times and records his result in the dot plot.
Use the result to predict the number of times the spinner will land on an odd number in 200 trials.
Step-by-step explanation:
odd numbers : 1, 3, 5, 7
in his 20 attempts he gets 3 + 1 + 2 + 2 = 8 results on odd numbers.
that is a rate of 8/20 = 2/5.
so, we have to assume that the spinner will continue with the same behavior, and we can apply the same rate to 200 spins :
200 × 2/5 = 80
therefore, we predict he will land on an odd number in 80 of 200 trials.
Answer:
The number of times the spinner will land on an odd number in 200 trials is 80 times
The sections on the spinner are given as
Sections = 1 to 7
From these sections, we have
Odd sections = 1, 3, 5 and 7
From the dot plot given, the total frequency of the odd sections is
Frequency of odd sections = 3 + 1 + 2 + 2
Evaluate
Frequency of odd sections = 8
Also, we have
Total frequency = 20
The number of times is then calculated as
Number of times = Frequency of odd sections/Total frequency * 200
So, we have
Number of times = 8/20 * 200
Evaluate
havehaveEvaluateEvaluateNumber of times = 80
Hence, the number of times is 80 times
Clover is planning to take out a home equity loan to pay for the remodeling of her kitchen and bathroom. According to a recent assessment, the market value of her home is $275,000. The remaining principal on her current mortgage is $185,000. If Clover's lender follows the rule of thumb of limiting a mortgage to 80% of the estimated value of the home, what is the highest amount Clover could take out as a home equity loan?
First, let's calculate the limit amount for the mortgage: 80% of the estimated value of the house. Let's use a rule of three:
This way,
[tex]x=\frac{275000\cdot80}{100}\rightarrow x=220000[/tex]Out of those $220,000, Clover currently has $185,000 on her mortgage.
[tex]220000-185000=35000[/tex]Therefore, she could take $35,000 as a home equity loan.
Question 31 The FAA, now figures the average checked bag to weigh 22 pounds. This is up from a previous figure of 10 pounds. Find the amount of increase and the percent of increase, to the nearest whole percent. Amount increase: pounds Percent of increase: %
Amount of increase is 10 pounds
Perecentage of increase is 120%
Here, we want to calculate the amount of increase and the percentage of increase
To get the amount of increase, we simply subtract the old value from the new value
Mathematically, we have that as;
[tex]22-10\text{ = 12 pounds}[/tex]The whole percentage increase can be calculated using the formula below;
[tex]\begin{gathered} \text{percentage increase = }\frac{new\text{ value - old value}}{\text{old value}}\text{ }\times\text{ 100\%} \\ \\ =\text{ }\frac{22-10}{10}\text{ }\times100\text{ = }\frac{12}{10}\times100\text{ = 120\%} \end{gathered}[/tex]Mike invested $37,500 at 4.3% interest, compoundedannually. How much money will he have at the end of6 years?
Amount = P ( 1 + R ) ^n
= 37,500 ( 1 + 4.3% ) ^6
= 37, 500 ( 1. 043 ) ^6
= $ 48, 276. 65
Which of the expressions are equivalent to the one below? Check all that apply. (4•1) - 6
Recall, for multiplication,
a * b = b * a
This means that 4 * 1 = 1 * 4
Since the term outside the parentheses is being subtracted from the product of the terms in the parentheses, the equivalent expression would be
D) (1 * 4) - 6
A store prices tapes by raising the wholesale price 50% and adding 25 cents .What must a tape's wholesale price be if the tape sells for $1.99
Let's call the store value as s and the wholesale price as w. A store prices tapes by raising the wholesale price 50%(0.5 in decimals) and adding 25 cents, writing this as an equation, we have
[tex]s(w)=w+0.5w+0.25[/tex]If we invert the equation we're going to find the the wholesale price as a function of the store price.
[tex]\begin{gathered} s=w+0.5w+0.25 \\ s=1.5w+0.25 \\ s-0.25=1.5w \\ w(s)=\frac{s-0.25}{1.5} \end{gathered}[/tex]Now, to find the wholesale price if the sales price is $1.99, we just need to evaluate s = 1.99 on the function we created.
[tex]w(1.99)=\frac{1.99-0.25}{1.5}=1.16[/tex]The wholesale price is $1.16.
2y ( x-y) +12=5x where x=3
EXPLANATION
Given the expression 2y(x-y) +12=5x , plugging in x=3 into the expression,
2y(3-y) + 12 = 5*3
6y -2y^2 + 12 = 15
Rearranging terms:
[tex]-2y^2+6y+12=15[/tex]Now, we need to apply the quadratic equation:
[tex]\mathrm{For\: a\: quadratic\: equation\: of\: the\: form\: }ax^2+bx+c=0\mathrm{\: the\: solutions\: are\: }[/tex][tex]x_{1,\: 2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex][tex]\mathrm{For\: }\quad a=-2,\: b=6,\: c=-3[/tex][tex]y_{1,2}=\frac{-6\pm\sqrt{6^2-4\left(-2\right)\left(-3\right)}}{2\left(-2\right)}[/tex]Multiplying terms:
[tex]y_{1,2}=\frac{-6\pm\sqrt[]{36-24}}{-4}[/tex]Subtracting numbers:
[tex]y_{1,2}=\frac{-6\pm\sqrt[]{12}}{-4}[/tex]Simplifying:
[tex]\mathrm{The\: solutions\: to\: the\: quadratic\: equation\: are\colon}[/tex][tex]y=\frac{3-\sqrt{3}}{2},\: y=\frac{3+\sqrt{3}}{2}[/tex]Which of the following shows the graphs of the equations?
y = 2x + 6
To find the points
Put x = 0
y = 6
Put y = 0 and solve for x
0 = 2x + 6
2x = -6
x = -3
The points are;
(0, 6) and (-3, 0)
Hence the last option is the graph of the equation
Question:
Which of the following shows the graphs of the equations?
Answer:
Emily and her family are planning to fly to Italy over the summer. If they fly out from LAX, the distance of the trip will be 6,343 miles. If the time to travel 6,343 miles is 9 hours, what is the speed,that the plane traveled at ?
The speed is the ratio between the distance and the time:
[tex]s=\frac{d}{t}[/tex]Data:
d=6343miles
t=9h
[tex]s=\frac{6343\text{miles}}{9h}=704.77\frac{miles}{h}[/tex]Then, the plane traveled at a speed of 704.77 miles per hour.Find a mathematical model for the following statement. "f varies directly as the square of x"
The statement is given
"f varies directly as the square of x"
The mathematical model for the statement is
[tex]f=kx^2[/tex]Here k is the constant of proportionality.
Find the critical value Zalpha /2that corresponds to the given confidence level.
87%
Question content area bottom
Part 1
enter your response here (Round to two decimal places as needed.)
Using the z-distribution, the critical value that corresponds to a confidence level of 87% is:
[tex]z_{\frac{\alpha}{2}} = 1.515[/tex]
Critical value of z-distributionThe critical value is one parameter of confidence intervals, related to the margin of error of the interval, and consequently, the bounds of the interval.
This critical value is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level of the interval. This critical value can be found using either a calculator or the z-score table.
In the context of this problem, the confidence level is of 87%, hence:
[tex]\alpha = 0.87[/tex]
Thus the p-value that we need to find the critical value is:
(1 + 0.87)/2 = 0.935.
Looking at the z-score table, the critical value for the 87% confidence interval is given as follows:
[tex]z_{\frac{\alpha}{2}} = 1.515[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
64mirmiriWhich expression is equivalent to the expression shown? Assume the value of each variable is a positivereal number.OA &OB.O C.C. 332-OD. 32m²O ABOD
...SOLUTON
[tex](\frac{64m^{\frac{1}{2}}r^3}{m^{\frac{5}{2}}r^{\frac{1}{4}}})^{\frac{1}{2}}[/tex][tex][/tex]a famer plants 0.5 of a field with corn . of that corn, 0.3 is sweet corn what part of the Field is sweet corn ?
Let the farm plant be represented with P
corn occupies 0.5 of the field = 0.5 x P => 0.5P
of this 0.5P, 0.3 of this portion is sweet corn
=> 0.3 x 0.5P
= 0.15P
Hence, sweet corn occupies 0.15
or
0.15 % of the field
2/5 (z+ 1) = y for z
The equation given is
[tex]\frac{2}{5}(z+1)=y[/tex]We need to solve for the variable "z".
First, we multiply the term "z + 1" by "2/5" and do a bit algebra to isolate "z".
The steps are shown below:
[tex]\begin{gathered} \frac{2}{5}(z+1)=y \\ \frac{2}{5}(z)+\frac{2}{5}(1)=y \\ \frac{2}{5}z+\frac{2}{5}=y \\ \frac{2}{5}z=y-\frac{2}{5} \\ z=\frac{y-\frac{2}{5}}{\frac{2}{5}} \end{gathered}[/tex]We can simplify this a bit further:
[tex]\begin{gathered} z=\frac{y-\frac{2}{5}}{\frac{2}{5}} \\ z=\frac{y}{\frac{2}{5}}-\frac{\frac{2}{5}}{\frac{2}{5}} \\ z=\frac{5}{2}y-1 \end{gathered}[/tex]Intro to Pythagorean Theorem - Exit Ticket Question 2 2. Evan is using the equation shown to find the missing length of a right triangle. Which triangle would this equation apply to? 10^2 + b^2 = 26^2
Given the equation:
[tex]10^2+b^2=26^2[/tex]The Pythagorean Equation represents that the sum of the square of the legs of a right triangle is equal to the square of its hypotenuse.
[tex]a^2+b^2=c^2[/tex]Where,
a = Adjacent Side (1st Leg)
b = Opposite Side (2nd Leg)
c = Hypotenuse
From the given equation, it is shown that a triangle's Adjacent Side and Hypotenuse is given. Adjacent side at 10 and Hypotenuse at 26.
Therefore, the figure that best fits the equation is the 2nd Triangle, the one at the right side.
12) What is the slope of the line below
solution
For this case we have two points given :
(1,-1) and ( 4,4)
So then we can find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4+1}{4-1}=\frac{5}{3}[/tex]And the slope for this case would be:
m = 5/3
What is the surface area of the cube below?A 150 unitsB. 300 unitsC. 50 unitsO 0.75 units
The formula for the surface area S of a cube can be writte as;
[tex]S=6l^2[/tex]Where;
[tex]l\text{ is the side length of the cube}[/tex]From the attached image, the length of the side of the given cube is 5 units.
[tex]l=\text{ 5 units}[/tex]So, the surface area can be calculated by substituting the value of the length into the formula.
[tex]\begin{gathered} S=6l^{2\text{ }}=6(5)^2 \\ S\text{ = 6}\times25 \\ S=150units^2 \\ \end{gathered}[/tex]Therefore, the surface area of the cube
Suppose that the population of a city was about 370 thousand in 2000 and had been growing by about 8.5% per year.(a) Write an explicit formula for the population of the city t years after 2000 (i.e. t= 0 in 2000), where Pt is measured in thousands of people.Pt = (b) If this trend continues, what will the city's population be in 2016? Round your answer to the nearest whole number. thousand people(c) When does this model predict city's population to exceed 600 thousand? Give your answer as a calendar year (ex: 2000).During the year
The growth is an exponential growth
(a)
[tex]\begin{gathered} \text{ The explicit formula for the population of the city can be represented by } \\ p(t)=p(1+r)^t \\ \text{Where p=initial population} \\ r=\text{growth rate} \\ t=\text{ number of years} \end{gathered}[/tex]For t years after 2000, at 8.5% growth rate per year , we have
[tex]\begin{gathered} p=2000,\text{ r=8.5\%=}\frac{8.5}{100}=0.085\text{ } \\ p(t)=2000(1+0.085)^t \\ p(t)=2000(1.085)^t \end{gathered}[/tex](b) If this trend continues, what will the city's population be in 2016?
from year 2000 to 2016, we have 16 years. Therefore, t=16
put t=16 into p(t) above
we have
[tex]\begin{gathered} p(t)=2000(1.085)^t \\ p(16)=2000(1.085)^{16} \\ p(16)=2000(3.68872) \\ p(16)=7377.44_{} \\ p(16)=7377(\text{ nearest whole number)} \end{gathered}[/tex]The population of the city in 2016 will be 7377 (to nearest whole number)
When does this model predict city's population to exceed 600 thousand?
This can be interpreted as the year when p(t) is greater than 600,000
[tex]\begin{gathered} \text{ that is solve for t when p(t)>600,000} \\ 2000(1.085)^t>600,000 \\ \text{divide both sides by 2000} \\ 1.085^t>300 \\ \text{take logarithm of both sides} \\ \log (1.085)^t>\log 300 \\ t\log 1.085>2.47712 \\ t>\frac{2.47712}{\log 1.085} \\ t>69.916 \\ t>70\text{ (nearest whole number)} \\ \end{gathered}[/tex]This implies that from 70 years from year 2000, the city's population exceed 600 thousand.
In calendar, this will be the year 2070.
Hence, in year 2070 the city's population will exceed 600 thousand.
Solve the formula for y:16x + 4y = 24
ANSWER
y = 6 - 4x
EXPLANATION
We have the formula:
16x + 4y = 24
To solve it for y, we have to make y the subject of the formula by simply isolating it on one side.
That is:
16x + 4y = 24
=> 4y = 24 - 16x
Divide through by 4:
[tex]\begin{gathered} \frac{4}{4}y\text{ = }\frac{24}{4}\text{ - }\frac{16}{4}x \\ \Rightarrow\text{ y = 6 - 4x} \end{gathered}[/tex]We have solved it for y.
Solve x^2+ 14× = 80 by completing the square. If there are multiple answers, list them separated by a comma (e.g.,1,2) Note: If there is no solution, enter Ø.
We have the following:
[tex]x^2+14x=80[/tex]solving:
[tex]\begin{gathered} x^2+14x+7^2=80+7^2 \\ (x+7)^2=129 \\ x+7=\pm\sqrt[]{129} \\ x=\sqrt[]{129}-7 \\ x=-\sqrt[]{129}-7 \end{gathered}[/tex]Which table shows a relationship with a constant rate of change of q? x 2
Test CHOICE A
x 2,4,6,8,10
y 9,9,9,9,9,
rate of change = (9.9) / ( 6-4) = 0/2 = 0
Test CHOICE B
x 2,4,6,8,10
y 11,13,15,17,19
rate of change = (13-11) / (4-2) =