Answer:
y = 2x + 4
slope: 2
y-intercept: (0,4)
Step-by-step explanation:
to find the slope and y-intercept of the two points, we can use the following formula:
y2 - y1/ x2 - x1 = slope
to solve, we plug in the values into the equation
we will treat (0,4) as x1, y1 and (7,18) as x2, y2
y2 - y1 = 18 - 4 = 14
x2 - x1 = 7 - 0 = 7
14/7 is the slope, but we can simplify as 14/7 is equal to 2
so the slope is 2 (can also be said as 2/1)
we can now put the following slope into slope-intercept form (y=mx+b)
y = 2x + b < b is the slope, we so we need to solve for b
looking at our points (0,4) and (7,18), we see that we have the y-intercept, as the y-intercept has the x-coordinate 0, and any y-coordinate. the y-intercept is (0,4)
but if we dont have the y-intercept that easily, we can plug in any coordinate that we are given into the equation and solve for b. for this example, ill use (0,4) to plug into the equation
4 = 2(0) + b
4 = b
the y-intercept is 4
the final equation would be the following:
y = 2x + 4
The equation of the line that passes through two points (0, 4) and (7, 18) is y = 2x + 4.
To determine the equation of the line using the given information, we first need to find the slope and y-intercept. The slope of a line can be calculated using the formula:
slope (m) = (change in y-coordinates) / (change in x-coordinates)
Using the points (0, 4) and (7, 18), we can calculate the slope:
slope (m) = (18 - 4) / (7 - 0) = 14 / 7 = 2
So, the slope of the line is 2.
Next, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can substitute one of the points into the equation and solve for b.
Using the point (0, 4):
4 = 2(0) + b
b = 4
Therefore, the y-intercept (b) is 4.
Finally, we can write the equation of the line:
y = 2x + 4
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Which statement about the diagram are correct check all that apply
where is the picture for the problem?
Answer: here’s the possibile picture and answer
Step-by-step explanation:
(C & D)
how to find slope??................................
y2-y1/x2-x1
Y(subscript 2) - Y(subscript 1) / X(subscript 2) - X(subscript 1)
The formula for slope is the difference in y-values divided by the difference in x-values. the slope of a line is its steepness or its rate of change. There are 4 types of slopes positive, negative, zero, and undefined.
Use a calculator to find the value of each expression. Round your answer to the nearest hundredth.
11. Arcsin(1/5)
12. Arcsin(-0.34)
13. Arcsin(0.6)
Answer:
Arcsin(1/5) = 0.20
Arcsin(-0.34) = -0.35
Arcsin(0.6) = 0.64
Step-by-step explanation:
Using a calculator we can find the value of each expression:
Arcsin(1/5) = 0.20135792079, rounding to the nearest hundredth we have that: Arcsin(1/5) = 0.20.
Arcsin(-0.34) = -0.346916897527, rounding to the nearest hundredth we have that: Arcsin(-0.34) = -0.35
Arcsin(0.6) = 0.643501108793, rounding to the nearest hundredth we have that: Arcsin(0.6) = 0.64
We found the arc-sin (or inverse sine) of three different values using a calculator, rounding to the nearest hundredth decimal place: Arcsin(1/5) is approximately 0.20, Arcsin(-0.34) is -0.34, and Arcsin(0.6) is about 0.64.
Explanation:The student asked to find the arc-sine (inverse sine) of three values and round the answers to the nearest hundredth. You use your calculator to find these values:
Arcsin(1/5): When you input this into your calculator, you'll get a value of approximately 0.201. So, arc-sin of 1/5 is about 0.20,Arcsin(-0.34): Inputting this into your calculator gives an approximate value of -0.344. So, arc-sin of -0.34 is around -0.34,Arcsin(0.6): Inputting this into your calculator gives about 0.643. So, arc-sin of 0.6 is approximately 0.64.Note: Arcsine is a trigonometric function which checks the angle whose sine is a given number.
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Which graph best represents the function f(x) = 3(1.5)x?
graph of increasing exponential function going through point 0, 2
graph of increasing exponential function going through point 0, 3
graph of increasing exponential function going through point 0, 1
graph of increasing exponential function going through point 0, 4
Answer:
B). graph of increasing exponential function going through point (0, 3)
Step-by-step explanation:
Given function is [tex]f\left(x\right)=3\left(1.5\right)^x[/tex]
Now we need to find about which of the given choices best describes the given function. Where given choices are:
A). graph of increasing exponential function going through point 0, 2
B). graph of increasing exponential function going through point 0, 3
C). graph of increasing exponential function going through point 0, 1
D). graph of increasing exponential function going through point 0, 4
plug x=0 into given function
[tex]f\left(x\right)=3\left(1.5\right)^x[/tex]
[tex]f\left(0\right)=3\left(1.5\right)^0=3(1)=3[/tex]
Hence graph passes through point (0,3).
growth factor 1.5 is greater than 1 so that means it is increasing function.
Hence correct choice is:
B). graph of increasing exponential function going through point (0, 3)
Emilee signed a finance agreement for her purchase what is the total amount she will pay back under this agreement
To calculate the total amount Emilee will pay back under a finance agreement, one needs to know the specifics of the loan. Joanna's example, with a known interest rate and term, shows how to use the present value of an annuity formula to find out the maximum loan and total amount paid over time.
Explanation:The question pertains to calculating the total amount that Emilee will pay back under a finance agreement for her purchase. To determine this amount, one must know the principal amount of the loan, the interest rate, and the term of the loan.
For instance, if Joanna can afford to pay $12,000 a year for a house loan at an annual interest rate of 4.2% for 30 years, one can use the formula for the present value of an annuity to calculate the maximum loan she can afford. The formula is PV = PMT [1 - (1 + i)^(-n)] / i, where PV is the present value (the maximum loan), PMT is the annual payment ($12,000), i is the interest rate per period (4.2% annually), and n is the number of periods (30 years).
By applying this formula, Joanna can afford a maximum loan of approximately $202,556.98. Over 30 years, she will end up paying $12,000 times 30, which equals $360,000 in total. Similarly, to determine the total amount Emilee will repay, the same types of calculations would apply based on the terms of her finance agreement.
Answer: $1308
Step-by-step explanation: APEX
12 monthly payments of $109 = $1308
look at picture and plzz help
Answer:
a= 3 b=6 c= 5
Step-by-step explanation:
For this case we have the following expression:
[tex]3 ^ {\frac {6} {5}}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [c] {a ^ b} = a ^ {\frac {b} {c}}[/tex]
Then according to the given expression we have the following:
[tex]a = 3\\b = 6\\c = 5[/tex]
Answer:
[tex]a = 3\\b = 6\\c = 5[/tex]
If the first of three consecutive integers is subtracted from 138, the result is the sum of the second and third. What are the integers?
Answer:
45, 46, 47Step-by-step explanation:
n, n + 1, n + 2 - three consecutive integers
The equation:
138 - n = (n + 1) + (n + 2)
138 - n = n + 1 + n + 2 combile like terms
138 - n = 2n + 3 subtract 138 from both sides
-n = 2n - 135 subtract 2n from both sides
-3n = -135 divide both sides by (-3)
n = 45
n + 1 = 46
n + 2 = 47
The three consecutive integers in question are 45, 46, and 47. This was solved by setting up and solving a simple algebraic equation.
Explanation:Solution:Let the three consecutive integers be x, x+1, and x+2. According to the problem, the sum of the second and third integers is equal to 138 minus the first one. This can be written mathematically as:
x + (x + 1) + (x + 2) = 138
Solving this equation gives:
3x + 3 = 138
3x = 135
x = 45
Hence, the three consecutive integers are 45, 46, 47.
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Waves with an amplitude of 2ft pass a doc every 30 seconds. Write an equation for a cosine model the height of a water particle above and below the mean water line
[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{C}{B}\\ ~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}[/tex]
[tex]\bf \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)[/tex]
with that template in mind, let's see.
[tex]\bf \stackrel{A = 2}{g(x) = 2cos(Bx+C)}\qquad \begin{cases} \stackrel{\textit{period of 30 seconds}}{\cfrac{2\pi }{B}=30}\\\\ \cfrac{2\pi }{30}=B\\\\ \cfrac{\pi }{15}=B \end{cases}\implies g(x)=2cos\left( \frac{\pi }{15}x+C \right)[/tex]
now, since the period is 30, and cos(x) starts off at 1, recall cos(0) = 1, so then le'ts move the starting point over by simply doing a horizontal shift to the right by a quarter of the period, 30/4 = 15/2 units, that way the initial "hump" starts off at 0.
[tex]\bf \stackrel{\textit{horizontal shift of }\frac{15}{2}}{\cfrac{15}{2}=\cfrac{C}{B}}\implies \cfrac{15}{2}=\cfrac{C}{~~\frac{\pi }{15}~~}\implies \cfrac{15}{2}=\cfrac{15C}{\pi }\implies 15\pi =30C \\\\\\ \cfrac{15\pi }{30}=C\implies \cfrac{\pi }{2}=C~\hfill \stackrel{\textit{horizontally to the right}}{-\cfrac{\pi }{2}=C} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=2cos\left(\frac{\pi }{15}x-\frac{\pi }{2} \right)~\hfill[/tex]
Check the picture below.
what is the average rate of change for this quadratic function for the interval from x= -4 to x= -2
Answer:
B. 6.
Step-by-step explanation:
We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].
We will use formula [tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(-2)-f(-4)}{-2--4}[/tex]
[tex]\text{Average rate of change}=\frac{6--6}{-2+4}[/tex]
[tex]\text{Average rate of change}=\frac{6+6}{2}[/tex]
[tex]\text{Average rate of change}=\frac{12}{2}[/tex]
[tex]\text{Average rate of change}=6[/tex]
Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.
Answer:
6
Step-by-step explanation:
just took on A P E X
5x - 2y = 3
-5x + 4y = 9
Solve the system of equations.
A) x = 6, y = 3
B) x = 6, y = 13
1
2
C) x = 3, y = 6
D) x = 1, y = 0
Answer: Your answer is c
Step-by-step explanation: The first thing you can do is add the two equations together to cancel out x
5x-2y=3
-5x+4y=9
added them together will get us 2y=12, from here divide 2 and get y=6
Plug 6 into the first equation and solve for x.
5x-2(6)=3
5x-12=3, add 13 to the other side
5x=15, divide 5 and get the answer
x=3
what is the midpoint of the segment shown below? (-3,4) (-6,-1)
Answer:
-9/2 , 3/2
Step-by-step explanation:
The coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).
What are the coordinates of the midpoint of the line segment AB?Suppose we've two endpoints of a line segment as A(p,q), and B(m,n), then let the midpoint be M(x,y) on that line segment. Then, its coordinates are x =(p+m)/2 and y = (q+n)/2.
Given the endpoints of the line segment are A(-3,4) and B(-6,-1), then the coordinates of the midpoint will be,
x = (-3-6)/2 = -9/2 = -4.5
y = (4-1)/2 = 3/2 = 1.5
Hence, the coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).
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Four thousand students at a school were asked to name their favorite pizza topping. The results were 800 Pepperoni, 1,000 Sausage, 1,200 Mushrooms, 560 Peppers, 240 Onions, and 200 Other. Your friend expresses these results in this circle graph. Your friend made a mistake, however. What is wrong with his graph?
Answer:
The pepperoni and peppers are mixed up
Step-by-step explanation:
Answer:
The mistake my friend made was that pepperoni and peppers are mixed up, pepperoni is suppose to be 20% while peppers is supposed to be 14%
Step-by-step explanation:
Given that 4000 students
Pepperoni = 800
Sausage = 1,000
Mushrooms = 1,200
Peppers = 560
Onions = 240
Other = 200
To find the degree of each on the circle graph, we have:
Pepperoni = 800/4,000 * 100 = 20%
Sausage = 1,000/4,000 * 100 = 25%
Mushrooms = 1,200/4,000 * 100 = 30%
Peppers = 560/4,000 * 100 = 14%
Onions = 240/4,000 * 100 = 6%
Other = 200/4,000 * 100 = 5%
The mistake my friend made is that pepperoni and peppers are mixed up, pepperoni is suppose to be 20% while peppers is supposed to be 14%
What is the slope of the line that is represented by the equation y−15=−6(x+7)?
Enter your answer as a number, like this: 42
Or, if your answer is a fraction, such as 314, enter it like this: 3/14
Answer:
slope = - 6
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 15 = - 6(x + 7) ← is in point- slope form
with slope m = - 6
The slope of the line that is represented by the equation y-15=-6(x+7) is -6.
The given equation is y-15=-6(x+7).
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The standard form of the slope intercept form is y=mx+c.
Where, m=slope and c=y-intercept
Here, y-15=-6(x+7) can be written as y-15=-6x-42
⇒ y=-6x-42+15
⇒ y=-6x-27
So, slope of an equation is -6.
Therefore, the slope of the line that is represented by the equation y-15=-6(x+7) is -6.
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Elaina is planning to save enough money to buy laptop computer. She needs $600. She already has $200 in her bank account. She is planning to deposit $40 each week into her bank account. Write an equation to represent Elaina’s plan to save for a laptop computer based on X weeks.
Answer: 200+40x=600
Step-by-step explanation:
200+40x=600
600-200=400
40x=400
40/40= 1 or x
400/ 40=10
x=10
plzzz help me with this question look at picture
ANSWER
B. 81
EXPLANATION
The given expression is:
[tex] {3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } [/tex]
Recall that:
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
We simplify the expression using the properties of exponents to obtain:
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11}{5} - - \frac{9}{5} } [/tex]
We simplify the exponents to get;
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11 + 9}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{20}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{4} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = 81[/tex]
The correct answer is B. 81
Y+2=-3(x-4)
Find the missing value in the solution to the equation. ( , -2)
Answer:
(4,-2)
Step-by-step explanation:
plug in and simplify;
y+2=-3(x-4)
-2+2=-3(x-4)
0=-3x+12
3x=12
x=4
The missing value in the solution of the equation is ( 4 , -2)
What is an Equation ?An equation is a mathematical statement that consists of two algebraic expression equated by an equal sign.
The given equation is
y +2 = -3 (x-4)
The value of x at y = -2 ,
Substituting the value of y in the equation
-2 + 2 = -3 ( x -4)
0 = -3x +12
-12 = -3x
x = 4
The value of x is 4
Therefore the missing value in the solution of the equation is ( 4 , -2)
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Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 1.75 minutes?
Answer:
Step-by-step explanation:
12 seconds for 28 claps
1 second for (28/12) claps
? claps for 1.75 mins?
1.75 minutes = 105 seconds (1.75×60 = 105)
105 seconds for (28/12)×105 claps
= 245 claps
Answer:
Your friends can clap their hands 245 times in 1.75 minutes.
Step-by-step explanation:
First of all, you should know how many seconds represents 1.75 minutes, because the amount of applause your friends can make is in that measure of time. In order to make this conversion, a simple rule of three is made, knowing that 1 minutes is 60 seconds:
If 1 minute is 60 seconds, how many seconds are 1.75 minutes?
[tex]\frac{1.75minutes*60seconds}{1minute} =105 seconds[/tex]
Knowing that your friend can clap his hands 28 times in 12 seconds and knowing that 1.75 minutes is 105 seconds, you can perform a rule of three again:
If they can clap their hands 28 times in 12 seconds, how many applause can they make in 105 seconds?
[tex]\frac{105seconds*28applause}{12} =245 applause[/tex]
Then your friends can clap their hands 245 times in 105 seconds, which is 1.75 minutes.
Express the polynomial as a product of linear factors. 3x^3+12x^2+3x-18
Answer:
f(x) = 3(x + 2)(x - 1)(x + 3)
Step-by-step explanation:
A logical first step would be to factor 3 out of all four terms:
f(x) = 3x^3+12x^2+3x-18 = 3(x^3 + 4x^2 + x - 6)
Roots of this x^3 + 4x^2 + x - 6 could be factors of 6: {±1, ±2, ±3, ±6}.
I would use synthetic division here to determine which, if any, of these possibilities are actually roots of x^3 + 4x^2 + x - 6. Let's try x = 1 and see whether the remainder of this synth. div. is 0, which would indicate that 1 is indeed a root of x^3 + 4x^2 + x - 6:
1 / 1 4 1 -6
1 5 6
------------------------
1 5 6 0
Yes, 1 is a root of x^3 + 4x^2 + x - 6, and so (x - 1) is a factor of x^3 + 4x^2 + x - 6.
Look at the coefficients of the quotient, which are 1, 5 and 6.
This represents the quadratic 1x² + 5x + 6, whose factors are (x + 2) and
(x + 3).
Thus, the given polynomial in factored form is:
f(x) = 3x^3+12x^2+3x-18 = 3(x + 2)(x - 1)(x + 3)
Answer:
3(x + 2)(x - 1)(x + 3)
Step-by-step explanation:
apex
four friends were born on consecutive years the sum of their ages is 62 what is the youngest friend
Answer:
The age of youngest friend = 14 years
Step-by-step explanation:
It is given that, four friends were born on consecutive years the sum of their ages is 62
Let 'x' be the age of youngest friend
age of other friends are (x + 1), (x + 2) and (x + 3)
To find the age of youngest friend
From the given information we can write,
x + (x + 1) + (x + 2) + (x + 3) = 62
4x + 6 = 62
4x = 62 - 6 = 56
x = 56/4 = 14
Therefore age of youngest friend = 14
A map is drawn using the scale 2 cm:100 mi. On the map, Town B is 3.5 centimeters from Town A, and Town C is 2 centimeters past Town B. How many miles apart are Town A and Town C?
A.) 275 miles
B.) 200 miles
C.) 550 miles
D.) 1,100 miles
Answer:
275 miles
Step-by-step explanation:
3.5 cm = 175 and 2 more centimeters past that is 100 so 175 +100=275
so your answer is a 275 miles
Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6in. The height of the prism is 10in
ANSWER
[tex]211.2 {in}^{2} [/tex]
EXPLANATION
The surface area of a triangular prism is
equal to the area of two triangular faces
plus the area of the three rectangular faces.
The area of the equilateral triangle is calculated using the formula:
[tex] = 2 \times \frac{ \sqrt{3} }{4} {s}^{2} + 3 \times \: bh[/tex]
where s=6 is the length of one side.
and b=6 is the breadth of the rectangle and h=10 is the height of the rectangle.
Surface area
[tex]= 2 \times \frac{ \sqrt{3} }{4} \times {6}^{2} + 3 \times \: 6 \times 10[/tex]
[tex]= 18\sqrt{3} + 180[/tex]
=211.2square inches.
Simplify (7x2 - 2x + 9) + (3x2 + 15x - 4)
Answer: 10x+13x+5
Step-by-step explanation:
Answer:
Step-by-step explanation:
7x^2 + 3x^2 = 10x^2
-2x + 15x = 13x
9 - 4 = 5
Put these together. Don't do any more than putting them together in a string.
Answer: 10x^2 + 13x + 5
Is there an outlier in the data set? Explain your reasoning.
Answer:
no
Step-by-step explanation:
there is not one point that is very distant from all of the other ones
no there is not an outlier :)
A iron worker will cut 2.4 meters of a iron rod into 4 smaller rods. The smaller rods will all be the same length. What should the length of the 4 smaller rods be?
Answer:
.6 meters
Step-by-step explanation:
We need to take the total length and divide it by 4, since that is the number of rods we want and they are all the same length
2.4/4 =.6 meters
Each rod will be .6 meters long
find the sum of the geometric series 6Σ3i i=2
[tex]
\sum_{3}^{6}2=\sum_{0}^{3}2=2+2+2=\boxed{6}
[/tex]
Or did you mean:
[tex]
6\times\sum{3i}=6\times\sum{6}=6\times6=\boxed{36}[/tex]
two business partners, Ellen and Bob, invested money in their business at a ratio of 3 to 7. Bob invested the greater amount. the total amount invested was 200 dollars. how much did each partner invest?
Answer:
Ellen invested $60 and Bob invested $140
Step-by-step explanation:
let the two amounts invested by 3x and 7x
(notice 3x : 7x = 3 : 7 )
then 3x + 7x = 200
10x = 200
x = 20
then 3x = 3(20) = 60
and 7x = 7(20) = 140
60+140=200
Ellen invested $60, and Bob invested $140 in their business.
The student's question involves determining how much each business partner invested in their business based on a given ratio and total investment amount. Ellen and Bob invested money at a ratio of 3 to 7 with a total of $200 invested. To solve this, we need to find out what each 'part' of the ratio is worth in dollars.
Let's consider the total number of parts in the ratio, which is 3 (for Ellen) + 7 (for Bob) = 10 parts in total. Since the total amount invested is $200, each part of the ratio is worth $200 divided by 10, which is $20. Therefore:
Ellen invested 3 parts: 3 parts * $20 per part = $60.Bob invested 7 parts: 7 parts * $20 per part = $140.Hence, Ellen invested $60, and Bob invested $140 in their business.
in need help ASAP!! 25 points!
Kami and her mother offer tours of a nearby canyon. They charge a $50 base rate plus $10 per person for a 2.5 hour tour. Which equation represents A, the amount they make to tour p people thorough the canyon?
A. 2.5p+50=10A
B. 10p+50=A
C. 2.5p=50=A
D. 10/p+50=A
Answer:
b
Step-by-step explanation:
becuase 10p which it states in the equation the 10 dollars per person and plus 50 base and 2.5 is not in the equation
Drag each tile to the correct box.
Find the y-intercept of each exponential function and order the functions from least to greatest y-intercept.
Answer:
1) g(x) ----> y-intercept -3
2) h(x) ----> y-intercept -1
3) f(x) ----> y-intercept 2
Step-by-step explanation:
we know that
The y-intercept or initial value, is the value of y when the value of x is equal to zero
Calculate the y-intercept of each exponential function
case 1) A function g, has a growth factor of 2 and a value of 1, and passes through the point (1,-2)
The exponential function is equal to
[tex]g(x)=1(2)^{x}+c[/tex]
Find the value of c
For x=1, g(x)=-2
substitute
[tex]-2=(2)^{1}+c[/tex]
[tex]-2=2+c[/tex]
[tex]c=-4[/tex]
so
[tex]g(x)=(2)^{x}-4[/tex]
Find the y-intercept
For x=0
[tex]g(0)=(2)^{0}-4[/tex]
[tex]g(0)=-3[/tex]
case 2) Observing the table
For x=0
f(0)=2
therefore
The y-intercept of f(x) is 2
case 3) Observing the graph
For x=0
h(0)=-1
therefore
The y-intercept of h(x) is -1
Order the functions from least to greatest y-intercept
1) g(x) ----> y-intercept -3
2) h(x) ----> y-intercept -1
3) f(x) ----> y-intercept 2
Final answer:
To find the y-intercept of an exponential function, evaluate it at x = 0. The constant term in the function represents the y-intercept. Order the functions by comparing these constant terms from least to greatest.
Explanation:
To find the y-intercept of an exponential function, we need to evaluate the function when x is equal to zero. The exponential function is usually given in the form f(x) =[tex]ab^x[/tex], where a is the y-intercept. This is because any number (except zero) raised to the power of zero is 1, so[tex]b^0[/tex] will always be 1, leaving us with f(0) = a.
After finding the y-intercept for each function, order them from least to greatest to complete the task. For example, if we have functions such as f(x) = [tex]2(3)^x, g(x) = 5(2)^x[/tex], and h(x) = [tex]-1(4)^x,[/tex] their y-intercepts would be 2, 5, and -1 respectively. Ordered from least to greatest, the functions by their y-intercepts would be h(x), f(x), g(x).
Simplify the expression. Write your answer as a power.
2¹⁹×2⁵÷2¹²×2³
Answer:
32768^1
Step-by-step explanation:
Solved the equation and added the first power.
Sydney needs 70cm of fringe for each scarf she make how many scarves can she make if she has 6 meters if Fringe
Answer:
Sydney can she make 8 scarves
Step-by-step explanation:
Remember that
1 m=100 cm
so
6 m=6*100=600 cm
using proportion
70/1=600/x
x=600/70
x=8.6 scarves
therefore
Round down
Sydney can she make 8 scarves