Answer:
5 = a
Step-by-step explanation:
Use the model y - k = a(x - h)^2, where (h, k) represents the vertex. Here we have:
y + 2 = a(x - 3)^2
Now substitute 4 for x and 3 for y:
3 + 2 = a(4 - 1)^2, or 5 = a
For her birthday, Monica can invite 6 of her 15 student friends to join her at a theme park. If she chooses to invite friends at random, what is the probability that friends Tessa, Guido, Brendan, Faith, Charlotte and Rhianna are chosen? 1 out of 3,603,600 10 out of 27,358 1 out of 5,005 1 out of 720
Answer:
(C)1 out of 5,005
Step-by-step explanation:
There are a total of 15 student friends.
Monica wants to invite 6 of her friends.
The number of ways this can be done is:
[tex]^{15}C_6=\dfrac{15!}{(15-6)!6!} \\=\dfrac{15!}{9!6!}\\\\=5005[/tex]
Therefore, the probability that friends Tessa, Guido, Brendan, Faith, Charlotte and Rhianna are chosen
[tex]=\dfrac{1}{5005}[/tex]
A plant will become invasive when the number of plants reaches 10,000. There are 500 plants, and the annual growth rate is 7%. How many years will it take for the plant to become invasive?
Answer:
It will take 44.3 years to reach 10,000 plants.
Step-by-step explanation:
the function describing the growth is
f(t) = 500*(1.07^t) = 10000
Take log on both sides
t*log(1.07) = log(10000/500)
t = log(20)/log(1.07) = 44.277 years
The number years it take for the plant to become invasive are 44.3 years.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
Given that,
Use Amount= Initial value(1+r/100)ⁿ, where n is number of years
Now, 10000=500(1+7/100)ⁿ
20=(1+0.07)ⁿ
20=(1.07)ⁿ
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
n=ln(20)/ln(1.07)
Decimal Form:
n=44.3 years
Therefore, the number years it take for the plant to become invasive are 44.3 years.
Learn more about the exponential function here:
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Flashback! Do you remember what these numbers tell you? The 10 means it will pay only $10,000 maximum for injury to any one person in an accident. The 20 means it will pay a minimum of $20,000 total to people injured in one accident. The 20 means it will pay a maximum of $20,000 total to people injured in one accident. The 5 means that it will pay a maximum of $5,000 in property damage for one accident. The 5 means that it will pay a minimum of $5000 in property damage for one accident. PLEASE HURRY
Answer:
10 -- $10k to any one person20 -- $20k to all persons, total5 -- $5k for property damageall are maximum values
Step-by-step explanation:
Insurance contracts specify maximum payments, not minimum payments. The numbers mean ...
The 10 means it will pay only $10,000 maximum for injury to any one person in an accident.
The 20 means it will pay a maximum of $20,000 total to people injured in one accident.
The 5 means that it will pay a maximum of $5,000 in property damage for one accident.
27. Theodore had 24 baseball cards. He sells 1/4 of his cards
to Tom, 13 of his cards to Larry. How many baseball cards
does Theodore have left?
(A) 14
(B) 15
(C) 12
(D) 10
Pls help xDDDDD thx!
Answer:
-25
Step-by-step explanation:
Based on the function F(x) = x^4 - 3x^3+ x^2 +2 and the graph of G(X) below,
which of the following statements is true?
Answer:
Option A
Step-by-step explanation:
According to the graph it never crosses the x axis meaning that it has 0 roots beecasue roots is another word for x-values.
(9,-4); slope =2/3 write the equation of the line
The lengths of a rectangular garden, the inner rectangle, is 9ft more than its width. For the garden. Let x = width, x + 9 = length. It is surrounded by a brick walkway 4ft wide. Suppose the total area of the walkway is 400ft^2.
a. Write a polynomial to represent the length of PQ
b. What are the dimensions of the garden?
Answer:
[tex]PQ = x + 13[/tex]
The dimension of the garden is 52.5ft by 43.5ft
Step-by-step explanation:
Given
The shape above
Required
Determine PQ
Determine dimension of the garden
Calculating Length PQ
Represent the length of the inner rectangle as L
Represent the width of the inner rectangle as W
[tex]W = x[/tex]
[tex]L = x + 9[/tex]
The distance between the inner rectangle and the outer triangle is 4ft
This implies that;
[tex]PQ = L + 4[/tex]
Substitute [tex]x + 9[/tex] for [tex]L[/tex]
[tex]PQ = x + 9 + 4[/tex]
[tex]PQ = x + 13[/tex]
Also;
[tex]QR = W + 4[/tex]
Substitute [tex]x[/tex] for [tex]W[/tex]
[tex]QR = x + 4[/tex]
Calculating The Dimension of The Garden
First, we need to determine the Area of the inner rectangle
[tex]Area_1 = L * W[/tex]
Recall that [tex]W = x[/tex] and [tex]L = x + 9[/tex]
So;
[tex]Area_1 = x * (x + 9)[/tex]
For the bigger rectangle
[tex]Area_2 = PQ * QR[/tex]
Recall that [tex]PQ = x + 13[/tex] and [tex]QR = x + 4[/tex]
So;
[tex]Area_2 = (x + 13)(x + 4)[/tex]
Given that the Area of the walkway is [tex]400ft^2[/tex]
This implies that
[tex]Area_2 = Area_1 + 400[/tex]
Substitute [tex]Area_1 = x * (x + 9)[/tex] and [tex]Area_2 = (x + 13)(x + 4)[/tex]
[tex](x + 13)(x + 4) = x * (x + 9) + 400[/tex]
Open All Brackets
[tex]x^2 + 13x + 4x + 52 = x^2 + 9x + 400[/tex]
[tex]x^2 + 17x + 52 = x^2 + 9x + 400[/tex]
Collect Like Terms
[tex]x^2 - x^2 + 17x - 9x = 400- 52[/tex]
[tex]8x = 348[/tex]
Divide both sides by 8
[tex]\frac{8x}{8} = \frac{348}{8}[/tex]
[tex]x = \frac{348}{8}[/tex]
[tex]x =43.5[/tex]
Since the dimensions of the garden is [tex]W = x[/tex] and [tex]L = x + 9[/tex]
Substitute 43.5 for x in both cases
[tex]L = 43.5 + 9 = 52.5[/tex]
[tex]W = 43.5[/tex]
Hence, the dimension of the garden is 52.5ft by 43.5ft
(SAT Prep) Find the value of x.
Answer:
24 degrees
Step-by-step explanation:
94+41 = 135 degrees
180 - 135 = 45 degrees
111 + 45 = 156 degrees
180 - 156 = x = 24 degrees
Hope I could help :)
Answer:
24
Step-by-step explanation:
Write an algebraic equation to match each graph. (These graphs are not drawn to scale!)
Answer:
y=|x+1|
Step-by-step explanation:
The y value appears to be 1 more than the x value, so we need to add one to the x to make them even. (x+1)
But the y value doesn’t go below zero, so we need to add the absolute value brackets |x+1|
So y=|x+1|
The graph represents the equation : g(x) = |x + 1|
We have a graph given to us.
We have to write the algebraic expression depicting this graph.
What is Modulus of the function y = f(x) = x ?The modulus of the function y = f(x) = x is given by -
y = |x| = [tex]\left \{ {{x\;\;for\;x > 0} \atop {-x\;\;for\;x < 0}} \right.[/tex]
Using the above property, we can find out the number of solutions of any modulus equation.
The algebraic equation for the graph can be written as -
g(x) = [tex]\left \{ {{x+1;\;for\;x \geq 0} \atop {-x-1\;for\;x < 0}} \right.[/tex]
In the form of modulus function, we can write the above equation as -
g(x) = |x + 1|
Hence, the graph represents the equation : g(x) = |x + 1|
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A train traveling at 100 km an hour takes 3 seconds to enter a tunnel and an additional thirty seconds to pass completely through it. Find the length, in kilometers, of the train. Express your answer as a common fraction
Find the correct algebraic representation of the rotation shown below.
a. (y, -x)
b. (-x, -y)
c. (-y, x)
d. (y, x)
Answer:
-y, x
Step-by-step explanation:
x values go from negative to positive and the y values remain negative
What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x? Discriminant = b2 – 4ac
Answer:
The answer is 16.
Step-by-step explanation:
First, you have to make the equation into 0 by moving all the terms to one side :
[tex] - 3 = - {x}^{2} + 2x[/tex]
[tex] {x}^{2} - 2x - 3 = 0[/tex]
Next, you have to apply Discriminant Law, D = b² - 4ac :
[tex]D = {b}^{2} - 4ac[/tex]
[tex]let \: a = 1 \: , \: b = - 2 \: , \: c = - 3[/tex]
[tex]D = {( - 2)}^{2} - 4(1)( - 3)[/tex]
[tex]D = 4 + 12[/tex]
[tex]D = 16[/tex]
Inspired by election season, Evan decided to run for class president. He earned 80% of the votes in his class. If he earned 24 votes, how many students were in his class? ( with a explanation on how you got the answer)
Answer:
30 students (30 total voters)
Step-by-step explanation:
Let s represent the number of students in the class. Evan earned 80% of these votes, which came to 24 votes. Symbolically, we have:
24 votes
0.80s = 24 votes. Therefore, s = total number of voters = ---------------- = 30 voters 0.8
The total number of students (voters) in his class was 30.
Answer:
It is 30.
Step-by-step explanation:
-2<3 multiple each side by -5 what is the resulting inequality
Answer:
[tex]\boxed{10>-15}[/tex]
Step-by-step explanation:
[tex]-2<3[/tex]
Multiply each side by -5.
[tex]-2 \times -5 <3 \times -5[/tex]
Switch signs when multiplying or dividing by a negative integer.
[tex]10>-15[/tex]
Answer:
10 > -15
Step-by-step explanation:
-2 < 3
We want to multiply each side by -5 and we want to see what happens:
-2 * -5 < 3 * -5
= 10 < -15
This is a wrong inequality as 10 is ahead of -15 on the number line.
Mrs. Lobo earns a salary of $50,000 per year plus a 4% commission on her sales. The average price of a share
she sells is $50.
Write an inequality to describe about how many shares Mrs. Lobo must sell to make an annual income of at
least $70,000
Select one:
O a. 50,000 + 2x > 70,000
O b. 50,000 + 2x < 70,000
O c. 50,000 -- 2x > 70,000
d. 50,000 + 2 > 70,000
Answer:
a) 50,000 + 2x > 70,000
Step-by-step explanation:
Mrs. Lobo has an annual salary of $50000 per year plus 4% commission on her sales.
If she makes $y commission from sales, Mrs Lobo total income per year is:
$50000 + $y.
She makes 4% commission on her sales of share with the average price of a share = $50
Average commission from sales = 4% × $50 = 0.04 × 50 = $2
If she sales x shares in a year, her commission would be $2x for the year. Therefore her total income for that year would be:
50000 + 2x
The amount of shares Mrs Lobbo must sell to make an annual income of at
least $70,000 is given by the inequality:
50,000 + 2x > 70,000
Please help me on this answer, I am very confused and don't know the correct steps to take. Solve
Answer:
102
Step-by-step explanation:
Since 2 + 8 = 10, then the cube root of 5x+2 = 8
Since 8×8×8=512, then 5x+2=512
5x=510, so x=102
Answer:
C) 102
Step-by-step explanation:
Hello !
2 + ∛(5x + 2) = 10
∛(5x + 2) = 10 - 2
∛(5x + 2) = 8
(∛(5x + 2))³ = 8³
5x + 2 = 512
5x = 512 - 2
5x = 510
x = 510 : 5
x = 102
Good luck !
Graph a line with this information: a slope of -5 and y intercept of 4.
Answer:
See below.
Step-by-step explanation:
The y intercept is 4 so you can mark a point on the line at (0, 4).This is a point on the y-axis 4 units up from the origin (origin is where the axis cross).
The slope is negative so the line will rise to the left.
Mark a point which is 1 unit horizontally to the left of point (0, 4) and 5 units vertically upwards.
Then draw the line to pass through this point and the point (0, 4)
The equation of the line is y = -5x + 4.
Jerry solved the system of equations. x minus 3 y = 1. 7 x + 2 y = 7. As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement? The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution. The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7. The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2. The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.
Answer:
The reason Max will give is:
The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
x - 3y=1
7x+2y=7
Jerry's way of solving the equation
2y=7-7x
Divide both sides by 2
2y/2=7-7x/2
y=7-7x/2
Substitute y=7-7x/2 into (2)
7x+2y=7
7x+2(7-7x/2)=7
This is a complex way of solving the equation
Max's proposed efficient way
x - 3y=1 (1)
7x+2y=7 (2)
From (1)
x=1+3y
The reason Max will give is:
The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Substitute x=1+3y into (2)
7x+2y=7
7(1+3y)=7
7+21y=7
Divide through by 7
1+y=7
y=7-1
y=6
Is the efficient way that Max proposed
Answer:
A
Step-by-step explanation:
Brainliest?
FIRST RIGHT ANSWER GETS BRAINLLEST If you spin the spinner below 20 times, which of the following outcomes are reasonable? Select all that apply. A) Lands on blue 18 times B) Lands on red 6 times C) Lands on yellow 4 times D) Lands on blue 4 times
Answer:
B) Lands on red 6 times
C) Lands on yellow 4 times
Step-by-step explanation:
The rest are way too much/too little for their predicted probability.
Answer:
B C
Step-by-step explanation:
If u spin the spinner below 20 times it will land on red around 4 times.
6 is only 2 greater than 4 so it works.
Same thing with yellow.
If your good in math pls help me I’m not that great and I’m ineed of help !
Answer:
The base is 2
Step-by-step explanation:
Exponents or powers are on top of the base.
[tex]2^x[/tex]
x is the exponent and the base is 2.
Find all exact values of
If there are multiple solutions, list the solutions in numerical order separated by commas. If there is no solution, use Ø.
Provide your answer below:
Answer:
General solution
θ =[tex]\frac{2n\pi }{3} +\frac{\pi }{2}[/tex]
Put n=1
θ = 210°
put n =2
θ = 330°
put n=3
θ = 270°
Step-by-step explanation:
Explanation:-
Given equation
sin 2θ cosθ + cos 2θ sinθ = -1
we know that
Sin (A+B) = sin A cos B +Cos A sin B
sin( 2θ+θ) = sin (180+90)
= [tex]Sin(\pi +\frac{\pi }{2})[/tex]
sin 3θ = sin (3π/2)
General solution of sinθ = sinα
θ = 2 n π ±α
3θ = 2 n π ±3π/2
θ =[tex]\frac{2n\pi }{3} +\frac{3\pi }{6}[/tex]
θ =[tex]\frac{2n\pi }{3} +\frac{\pi }{2}[/tex]
Put n=1
θ=[tex]\frac{2\pi }{3} +\frac{\pi }{2}=\frac{4\pi +3\pi }{6} =\frac{7\pi }{6}[/tex] = 210°
put n =2
θ=[tex]\frac{4\pi }{3} +\frac{\pi }{2}=\frac{8\pi +3\pi }{6} =\frac{11\pi }{6}[/tex] = 330°
Put n=3
θ=[tex]\frac{2 (3)\pi }{3} +\frac{\pi }{2}=2\pi +\frac{\pi }{2} = \frac{3\pi }{2}[/tex] = 270°
15 POINTS!!!!! How is a linear function affected when a constant is multiplied by y?
Answer:
a constant multiplied by y can affect the linear, because it determines a dependent variables.
Step-by-step explanation:
a linear relationship is a statistical term used to described a straight line relationship between two variables.
what is 3^3/2 equal to?
Answer:
D. 2^3/2
Explanation:
3 3/2
= ²√3³
= ²√27
Hope this helped! :D
Answer:
The answer is D
Step-by-step explanation:
hope this helps ^_^
Please help me with this question! I will give the brainliest to the one with the right answer!!!
Answer:
x =4
Step-by-step explanation:
hope this is the correct answer
Answer: B
Step-by-step explanation: B: 5^2-3^2 = 25-9 = 16. the square root of 16 is 4, so x=4
Find the odds in favor of rolling two different numbers when rolling a pair of dice.
Answer:
5/6Step-by-step explanation:
The total number of outcomes is 6 x 6 (because a dice has 6 sides) or 36. On the dice, there are 6 sets of matching numbers:
1,1
2,2
3,3
4,4
5,5
6,6
The probability of this is 6/36 or 1/6. The probability of not matching is 30/36 or 5/6.
I'm always happy to help :)The probability of rolling a pair of different numbers when two dices are rolled is 5/6.
What is probability?The probability is the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
How to calculate probability?Total number of combinations when two dices are rolled=[tex]6^{2}[/tex]=36.
Combinations having same pair of numbers=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6).
Number of combinations having same pair of numbers=6.
Number of combinations having different pairs of numbers=36-6=30.
Probability of having different pair of numbers=Number of combinations having different pair of numbers/Total combinations
Probability=30/36
=5/6
Hence the probability of rolling a pair of different numbers when two dices are rolled is 5/6.
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Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3+3y2+ay−3y2−ay−27. What is the value of a in the polynomial? 3 9 18 27
Answer:
a = 9
Step-by-step explanation:
In the product (y−3)(y2+3y+9), we can get the first degree term of y in two ways,
y*(9), or -3*(3y)...............value in parentheses are from the second factor
therefore a = 9
Answer:
a = 9
Step-by-step explanation:
Let's work on the product to answer the question:
[tex](y-3)\,(y^2+3y+9)= y^3+3y^2+9y-3y^2-9y-27[/tex]
therefore the value of the requested "a" is 9
Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin.
==================================================
Explanation:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2 means we multiply each coordinate of each point by the value 2
A = (0,0) becomes A' = (0,0). No change happens. This point is fixed
B = (2,-4) becomes B' = (4,-8). This point does move
C = (-4,-4) becomes C' = (-8,-8). This moves as well
So all you need to do from here is draw triangle A'B'C'.
-----------------
Side note: the lengths of triangle A'B'C' are twice as long as their counterparts on triangle ABC. Consequently, this means the perimeter of A'B'C' is twice as long as the perimeter of ABC. Also, triangle A'B'C's area is four times larger than the area of triangle ABC.
Triangle with the three corner points at
A' = (0,0). B' = (4,-8). C' = (-8,-8). what is Dilation?Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the objects. The result of this transformation is an image with the same shape as the original.
Given:
Let's label the corner points of the triangle A,B,C starting at the origin and moving clockwise
A = (0,0)
B = (2,-4)
C = (-4,-4)
Dilating with a scale factor 2
A = (0,0) --> A' = (0,0).
B = (2,-4) --> B' = (4,-8).
C = (-4,-4) --> C' = (-8,-8).
Learn more about Dilation here:
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Could I please have some help?
Answer:
1,910
Step-by-step explanation:
8 x 6 = 48 x 4 = 192 x 10 = 1,920 now 1,920 minus 10 = 1,910
i guess..but good luck
Answer:
144mi^2
Step-by-step explanation:
The first step would be to find the top and bottom of the shape which are two triangles.
The way you find the area of a triangle is
[tex]A= \frac{L*W}{2}[/tex]
The length is 6 and the width is 8 so you can plug in the numbers
[tex]A=\frac{6*8}{2}[/tex]
Then multiply 6 by 8
[tex]A=\frac{48}{2}[/tex]
And divide by two
[tex]A=24[/tex]
because there are two identical triangles, multiply 24 by 2 to get 48.
The two triangles make 48mi
Now you must find the area of all the rectangles on the sides separately.
The way to find the area of a rectangle is
[tex]A=L*W[/tex]
You must do one at a time, first, I will so the side with a length of 4 and width of 10
[tex]A=4*10[/tex]
Multiply 4 by 10 to get
[tex]A=40[/tex]
One of the rectangles has the area of 40mi
Now you must find the area of the other rectangles with the same formula. I will be doing the one with a length of 4 and a width of 8 next
[tex]A=4*8[/tex]
Multiply 4 by 8 to get
[tex]A=32[/tex]
The area of the second rectangle is 32mi
Finally, you want to find the area of the last rectangle that has a length of 4 and a width of 6. We will be using the same formula again
[tex]A=4*6[/tex]
Multiply 4 by 6 to get
[tex]A=24[/tex]
The area of the last rectangle is 24mi
The last step is to add all the areas together to get the surface area of the figure.
First the two triangles, then the first rectangle, the second, and finally the third.
[tex]SA = 48+40+32+24[/tex] (SA is surface area)
Once you add them all, you get
[tex]SA=144[/tex]
So the Surface area of the whole figure is 144mi^2
Hope this helps!
Feel free to ask any other questions if you have any.
Have a good day! :)
6÷2(1+2) isn't that should be 1 , cause in the calculator it said 9 but the order is the parenthisis/brakets first ?? so it should be like 2 times 3 then 6÷6 which gives 1 .
Answer:
9
Step-by-step explanation:
because it is 6 divided by 2 then (1+2) 3x3
Answer:
yes your are right
Step-by-step explanation:
got it right