Answer:
a. Growth
b. 1.3
c. 30%
d. 1
Explanation:
The exponential equation given can be written in the form
[tex]y=1.3^x=1(1.3)^x[/tex]From this form, we see that
a. the function represents a growth since 1.3 > 1
b. the growth factor is 1.3
c. The rate of growth is (1.3 - 1) * 100% = 30%
d. the initial value is 1.
Hence, the answers
a. Growth
b. 1.3
c. 30%
d. 1
2) Tell whether each relationship is a direct variation. If it is a direct variation, find the constant of variation. (Remember, the constant of variation is the k.) Explain.
2a) it is not a direct variation
2b) it is a direct variation; k = -4
Explanantion:For the relationship to be a direct variation, it must follow the formula:
y = kx
where k = constant of variation
k = y/x
The value of k must be constant for all
for 2a:
when y = 0, x = -3
k = 0/-3 = 0
when y = 3, x = 1
k = 3/1 = 3
when y = 6, x = 3
k = 6/3 = 2
From the above, the value of k is not constant. hence, it is not a direct variation
for 2b:
when y = -10, x = 2.5
k = -10/2.5 = -4
when y = -20, x = 5
k = -20/5 = -4
when y = -30, x = 7.5
k = -30/7.5 = -4
From the above, the value of k is constant. Hence, it is a direct variation
The constant of variation, k = -4
Find the volume of a cone with a base radius
Solution
Step 1:
Write the formula for the volume of a cone.
[tex]\begin{gathered} Volume\text{ of a cone = }\frac{1}{3}\pi r^2h \\ \text{r = radius} \\ \text{h = height} \end{gathered}[/tex]Step 2:
Given data
r = 6 in
h = 8 in
Step 3
Substitute in the formula to find the volume.
[tex]\begin{gathered} Volume\text{ of a cone = }\frac{1}{3}\pi r^2h \\ \text{= }\frac{1}{3}\times\pi\times6^2\times8 \\ =\text{ }\frac{1}{3}\times\pi\times36\times8 \\ =\text{ }\frac{288\pi}{3} \\ =\text{ 96}\pi\text{ in}^3 \end{gathered}[/tex]Final answer
[tex]Volume\text{ of the cone = 96}\pi\text{ in}^3[/tex]A line passes through (1, -1) and (3, 5).What is the equation of the line in slope-intercept form?
Step 1 : Let's find the points given in the cartesian plane and let's draw the line.
Step 2: Let's calculate m (slope), as follows:
m = (Y - Y1)/((X -X1)
Replacing with the values we already know, we have:
m = (5 - (-1)/ 3 - 1
m = 6 /2 = 3
Step 3: Now, we can write the equation, as follows:
y - y1 = m (x -x1)
y - (-1) = 3 (x - 1)
y + 1 = 3x - 3
y = 3x -4
This is the equation that solves the question: y = 3x - 4
e and all other answers should be rounded to X = 28 X
Since we're in a right triangle, we'll have that:
[tex]\cos 26=\frac{x}{28}[/tex]Solving for x :
[tex]\cos 26=\frac{x}{28}\rightarrow28\cos 26=x\rightarrow x=25.17[/tex]Therefore, x = 25.17
coordinate of the vertices after a rotation 270 grades counterclockwise around the origin d (2 2) F (3 4)E(9 2)
If the point (x, y) is rotated 270 degrees counterclockwise around the origin
Then its image is (y, -x)
We change the sign of the x-coordinate and switch the two coordinates
Since point D = (2, 2), then
Its image is D' = (2, -2)
Since point E = (9, 2), then
Its image E' = (2, -9)
Since point F = (3, 4), then
Its image F' = (4, -3)
Rich works 140 hours in a month. if his schedule stays the same ,how many hours he work in 3/4 of a month
Let's identify first what informations were given in the scenario:
What is Given: Rich works: 140 hours in a month.
What is being asked: How many hours he work in 3/4 of a month?
To be able to determine how many hours did Rich works in 3/4 of a month, we generate this equation:
[tex]Rich^{\prime}s\text{ work hours in 3/4 month = (Work hours in a month)(3/4)}[/tex][tex]\text{ = (140)(3/4) = }\frac{140\text{ x 3}}{4}[/tex][tex]\text{ = }\frac{420}{4}[/tex][tex]\text{Rich's work hours in 3/4 month = 105 hours}[/tex]Therefore, Rich works 105 hours in 3/4 of a month.
The graph shows the number of centimeters a particular plant grows over time. What is the slope of the line? Reasoning What does the slope mean?
We have the following:
The slope is about 1
The slope is the increment per unit, in this case it would be the increment in cm per week.
[tex]undefined[/tex]create 3 equivalent fractions for the fraction 2/7 . Explain how all of those are equivalent
create 3 equivalent fractions for the fraction 2/7 . Explain how all of those are equivalent
we have the fraction
2/7
Remember that equivalent fractions are fractions that the quotient is the same
If you multiply a number by 1 or 1/1 the result is the same number
Example
if you have 2/7 and you multiply by (3/3)
(2/7)*(3/3)
remember that 3/3=1
so
(2/7)*(3/3)=6/21
2/7 and 6/21 are equivalent fractions
because
2/7=0.2857
6/21=0.2857
second equivalent fraction
2/7 multiply by 5/5
(2/7)(5/5)=10/35
2/7 and 10/35 are equivalent
because
2/7=0.2857
10/35=0.2857
third equivalent fraction
2/7 multiply by 4/4
(2/7)(4/4)=8/28
2/7 and 8/28 are equivalent
because
2/7=8/28
multiply in cross
2*28=7*8
56=56 ----> is true
that means
fractions are equivalent
Remember
If you multiply the numerator and denominator of a fraction, by the same number, you obtain a equivalent fraction
The length of a rectangle is 5 yd more than twice the width x. The area is 462 yd".
The given problem is about rectangle areas.
The area of a rectangle is defined as
[tex]A=w\cdot l[/tex]Where w is width and l is the length.
In this case, we know that the length is 5 yards more than twice the width, where the last one is expressed as x.
[tex]l=2x+5,w=x[/tex]We also know by given that
[tex]A=462yd^2[/tex]Using all the given information, we have
[tex]462=x(2x+5)[/tex]Where we solve for x, first, we apply the distributive property.
[tex]462=2x^2+5x[/tex]Now, we move all terms to one side only
[tex]2x^2+5x-462=0[/tex]Using a calculator, we have
[tex]x_1=14,x_2=-\frac{33}{2}[/tex]Where 14 represents the width because distances cannot be expressed by negative numbers.
[tex]l=2(14)+5=28+5=33[/tex]Therefore, the width of the rectangle is 14 yards, and its length is 33 yards.1. A ball is thrown with an initial velocity of 86 feetper second 4 feet from the ground. The functionn(t) = -16t2 + 86t + 4 represents the height, h, of theball t seconds after it was thrown. After how manyseconds will the ball hit the ground?A. 4.7 secondsB. 4.9 secondsC. 5.2 secondsD. 5.4 secondsА A
D. 5.4 seconds
1) Since the course of that ball is described by the function h(t) = -16t² +86t +4.
So we can sketch out:
When the ball hits the ground, we'll have to find out the 2nd root of that function since when t=0, h =4. So let's find out the roots:
[tex]\begin{gathered} h(t)\text{ =-16t²+86t+4} \\ \Delta=(86)^2-4(-16)(4) \\ \Delta=7396+256 \\ x=\frac{-86\pm\sqrt[]{7652}}{2(-16)} \\ x_1=5.42 \\ x_2=-0.046 \end{gathered}[/tex]3) Since just the positive answer is interesting, then we can state that the answer is D (rounded off to the nearest tenth
how did the temperature change? First, it went up by 25% then went down by 40%
Answer:
24.6%
Step-by-step explanation:
24.6 is the answer
Answer:
The temperature decreased by 25%.
Step-by-step explanation:
Which expression best completes the following definition of a complexnumber?where a and bare real numbers and iThe set of all numbers in the formequals -1.
we are given that a and b are real numbers . and that i is a square root of -1
so we expect a and be to be real numbers , this can be expressed as
a + b (i)
so option B is correct .
Net Worth Statement Assets House (current value) Checking account Automobile Investments Total Assets Value $85,000 $2,500 $18,500 $7,000 $113,000 Llabilities Mortgage Credit card debt Total Liabilities $62,000 $9,500 $71,500 Based on the information in the statement, what is Phillip's net worth? A $184,500B $41,500 C $71,500D $41,500
Value of total assests is ;
$85,000 +$2,500 +$18,500 +$7000=$113,000
Value of total liabilities = $62,000 + $9,500 = $71,000
Net worth = $ 113,000-$71,500 =$41,500
use the Pythagorean theorem to find the length of the hypotenuse in the Triangle
Answer:
10 units
Explanation:
The Pythagorean theorem says that the hypotenuse c of a triangle is equal to:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where a and b are the length of the other sides of the triangle.
So, replacing a by 6 and b by 8, we get that the hypothenuse is equal to:
[tex]\begin{gathered} c=\sqrt[]{6^2+8^2} \\ c=\sqrt[]{36+64} \\ c=\sqrt[]{100} \\ c=10 \end{gathered}[/tex]Therefore, the length of the hypothenuse is 10 units
Hello! I’m struggling badly! I need to find the x, y and z
Let O be the point where the height about point C intercepts the segment AB:
Assume that CO is perpendicular to AB, C is a right angle, the length CO is equal to 4 and the length CB is equal to 5.
Since COB is a right angle, its sides must satisfy the Pythagorean Theorem:
[tex]y^2+4^2=5^2[/tex]Solve for y:
[tex]\Rightarrow y=\sqrt[]{5^2-4^2}=\sqrt[]{25-16}=\sqrt[]{9}=3[/tex]Notice that COB, AOC and ACB are similar triangles because they are all right angles and they have the same acute angles.
Then, the quotients between corresponding parts of the triangles are the same.
The legs of AOC are x and 4, and the corresponding legs of COB are 4 and 3. Then:
[tex]\begin{gathered} \frac{x}{4}=\frac{4}{3} \\ \Rightarrow x=\frac{4}{3}\times4=\frac{16}{3} \end{gathered}[/tex]Notice that z must be equal to the sum of x and y. Then:
[tex]z=x+y=\frac{16}{3}+3=\frac{16}{3}+\frac{9}{3}=\frac{25}{3}[/tex]Therefore, the values of x, y and z are:
[tex]\begin{gathered} x=\frac{16}{3} \\ y=3 \\ z=\frac{25}{3} \end{gathered}[/tex]Warning:
We have found this solution ignoring that the length AC was set to be equal to 15. That cannot be true, since the construction of the triangle ACB and the point O already tells us the values of x, y and z if CB=5 and CO=4. Using this construction, it is possible to deduce that the length AC must be 20/3.
The roots of x2 - 4x = 5, in ascending order, are ? and ?
For finding the roots of the function, we have to writte the equation in this form:
[tex]ax^2+bx+c=0[/tex]So in our problem will be:
[tex]x^2+(-4)x-5=0[/tex]Now we can use the cuadratic equation that is:
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]and in our problem will be:
[tex]\begin{gathered} \frac{4\pm\sqrt[]{16^{}-4(1)(-5)}}{2(1)} \\ \frac{4\pm\sqrt[]{16^{}+20}}{2} \\ \frac{4\pm\sqrt[]{36}}{2} \\ \frac{4\pm6}{2} \end{gathered}[/tex]Now we can find our two solutions or roots, one with the + and the other with the -
1)
[tex]\begin{gathered} x=\frac{4+6}{2} \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]2)
[tex]\begin{gathered} x=\frac{4-6}{2} \\ x=\frac{-2}{2} \\ x=-1 \end{gathered}[/tex]so the roots are going to be: -1, 5
Your baseball team is holding a silent auction as a fundraiser dinner to pay for the team uniforms. The list shows all the expenses for the silent actions A tablet costs $320Orioles tickets that cost $150A gift card that costs $30The cost of the food is $400The meme era of the baseball team will be selling tickets to the silent auction. A ticket to the silent auction includes chances to win prizes and dinner. The ticket cost is set so 50 tickets will pay for the cost of the prizes and food.Build a function that can be used to find the total profit f(x), the baseball team earns by selling x tickets
The first step to determine the function is to find the total cost of the auction. This is done by adding all the prizes and the cost of the food.
[tex]\begin{gathered} \text{ cost}=320+150+30+400 \\ \text{ cost}=900 \end{gathered}[/tex]The total cost of the auction is $900. Since the cost of 50 tickets should be able to cover the cost, we need to divide the total cost by the number of tickets to determine the cost of each ticket.
[tex]\begin{gathered} x=\frac{900}{50} \\ x=18 \end{gathered}[/tex]Each ticket must be sold as $18. The whole function is:
[tex]f(x)=18\cdot x-900[/tex]12. Zea has a credit limit of $2,000 on her credit card. Each month, she charges
about $200 and makes a payment of $125.
a. Estimate the number of months that Zea can continue this pattern until
she reaches her credit limit.
9001
b. Consider that part of the $125 Zea pays each month will be for finance
charges. How will the number of months from part a be affected by these
charges?
Answer:
Step-by-step explanation:
1. It will take Zea 27 months to reach her credit card limit.
2. The number of months will be less than 27.
The length of cell A is 3x10-5 m. The length of cell B is 0.000001 m.What is the ratio of cell A's length to cell B's length? Use pencil and paper. Is it easier to find the ratiowhen the numbers are expressed in scientific notation or in standard form? Explain your reasoning.The ratio of cell A's length to cell B's length is(Type the ratio as a simplified fraction.)
we have the following:
[tex]\begin{gathered} r=\frac{L_A}{L_B} \\ r=\frac{3\cdot10^{-5}}{0.000001}=\frac{3\cdot10^{-5}}{1\cdot10^{-6}} \\ r=30 \end{gathered}[/tex]the rario is 30
can you please help me this is my last one!
281 is the same (equal) as the total (sum) of f and 270
281 = f +270
Right angle ABC is taken by dilation with center P and scale factor 1/2 to angle A’B’C’. What is the measure of angle A’B’C’
The measure of angle A'B'C' will be 90 degree.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Right angle ABC is taken by dilation with center P and scale factor 1/2 to angle A’B’C’.
Now,
Since, We know that;
When a figure is dilated by a scale factor then the shape of the figure is not change.
Thus, The measure of ABC is same as the measure of A'B'C'.
Here, The measure of angle ABC = 90 degree
Hence, The measure of angle A'B'C' = 90 degree.
Therefore, The measure of angle A'B'C' will be 90 degree.
Learn more about the dilation visit:
https://brainly.com/question/10855880
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How many period s of the function are there between
The period of a tangent function y = atan(bx) is the distance between any two consecutive vertical asymptotes. And it is given by:
[tex]period=\frac{\pi}{|b|}[/tex]So, given the function y = tan x, we have that b = 1, therefore the period is:
[tex]\text{period}=\frac{\pi}{|1|}=\pi[/tex]Next, between the given points:
[tex]\begin{gathered} -\frac{5\pi}{2}=-2.5\pi \\ and \\ \frac{7\pi}{2}=3.5\pi \end{gathered}[/tex]There are:
[tex]3.5\pi-(-2.5\pi)=6\pi[/tex]Since the period is π, so:
[tex]\frac{6\pi}{\pi}=6[/tex]Answer: 6
Determine if the following statements are true or false. False [481] = |-481 -21 = -21 976976 1-94 = 94
I understand that you typed by error a square bracket instead of an absolute value vertical bar, right?
|481| = 481 this is a TRUE statement
|-21| = - 21 This is a FALSE statement since |-21| = 21
|976| = - |976| This is a FALSE statement, since |976| = |976| and not equal to the negative of it.
Is the last expression
|-94| = 94?
If such is the case, the statement is TRUE, since the absolute value of a number is ALWAYS the positive of that number.
|-94| = 94 TRUE statement.
The number of kilograms of water in a human body varies directly as the mass of the body. A 66 kg person contains 44 kg of water. How many kilograms of water are in a 144 kg person?
Given:
A 66 kg person contains 44 kg of water.
To find:
The number of kilograms in a 144kg person.
Explanation:
According to the problem, 66 kg person contains 44 kg of water.
For 1 kg person contains,
[tex]\begin{gathered} 1kg\text{ of person}=\frac{44}{66}kg\text{ of water} \\ =\frac{2}{3}kg\text{ of water} \end{gathered}[/tex]Then, for 144kg of a person contains,
[tex]\begin{gathered} 144kg\text{ of a person}=144\times\frac{2}{3}kg\text{ of water} \\ =96kg\text{ of water} \end{gathered}[/tex]Therefore, 144kg per person contains 96 kg of water.
Final answer:
144kg per person contains 96 kg of water.
Write the equation of an absolute value function that has been stretched by a factor of 2, reflected across x axis, and shifted 6 units to the right
The absolute value function is the function;
[tex]y=|x|[/tex]STEP 1: To stretch this function vertically by a factor of 2 would mean multiplying the function by 2, we have as a result;
[tex]y=2|x|[/tex]STEP 2: To reflect the function over the x-axis, this means that the entire function is multiplied by a negative sign, we have as a result;
[tex]y=-2|x|[/tex]STEP 3: To shift a function horizontally by 6 units to the right means subtracting 6 from every x- value. we have as a final result;
[tex]y=-2|x-6|[/tex]Therefore, the equation of an absolute value function that has been stretched by a factor of 2, reflected across x-axis, and shifted 6 units to the right is;
[tex]y=-2|x-6|[/tex]Hello! I'm a little stumped on this one I think it should be scatter plot
We have a data set that includes the test scores of a class.
We can represent this data, as it is univariate, with a box-and-whisker plot. This will let us graph the distribution of the scores.
A circle graph is only applicable if we group the data in classes. The same for the histogram.
They are not suitable for individual data points that are not grouped.
A scatter plot is also not suitable, as it needs ordered pairs. It will show the relation between two variables, and in this case we have only one variable in the data set.
Answer: box-and-whisker plot.
about 120 out of every 320 people are left-handed. if 3,360 students attended Davis High School, about how many are left handed
Using the rule of 3
120 - 320
x - 3360
120*3,360 = 320x
403,200 = 320x
403,200/320 = x
x = 1,260
About 1,260 students are left handed.
The students in a first-grade class were all asked to time how long (in seconds) they could hold their breath. The resultswere tallied and are presented in the following histogram.How many of those students held their breath greater than 12.5 and less than 15.5 seconds?
ANSWER:
13 students
STEP-BY-STEP EXPLANATION:
To find the answer we must add the number of students between the values 12.5 and 15.5, just like this:
[tex]\begin{gathered} 12.5-13.5=2\text{ students} \\ 13.5-14.5=5\text{ students} \\ 15.5-15.5=6\text{ students} \\ \text{Total}=\text{ }12.5-15.5=2+5+6=\text{ 13 students} \end{gathered}[/tex]
If AC=20, AE = 25, and AB= 5, what is the length of AD?
Answer:
it is 5 because if ab=5 and ac=20
If ZY = 26, what is the length of the diameter of circle X?
Given ZY = 26
To find the length of the diameter of circle X.
From the figure shown, it can be observed that ZY is the radius of circle Y.
If ZY is the radius of circle Y, the diameter of circle Y is ZX, which is twice the radius of circle Y.
[tex]\begin{gathered} ZX=2\times ZY \\ ZY=26 \\ ZX=2\times26 \\ ZX=52 \end{gathered}[/tex]ZX is the radius of the circle X.
If ZX is the radius of circle X, the diameter of circle X would be twice the radius of circle X.
[tex]\begin{gathered} D_{\text{circel X}}=2\times ZX \\ ZX=52 \\ D_{\text{circle X}}=2\times52 \\ D_{\text{circle X}}=104 \end{gathered}[/tex]Hence, the length of the diameter of circle X is 104 units