The x-intercepts of the parabola are (3, 0) and (7,0)
How to determine the x-intercept?The given parameters are:
Vertex (h, k) = (5, -12)
Point (x, y) = (0, 63)
The equation of a parabola is:
y = a(x - h)^2 + k
Substitute (h, k) = (5, -12)
y = a(x - 5)^2 - 12
Substitute (x, y) = (0, 63)
63 = a(0 - 5)^2 - 12
Evaluate
63 = 25a - 12
Add 12 to both sides
25a = 75
Divide by 26
a = 3
Substitute a = 3 in y = a(x - 5)^2 - 12
y = 3(x - 5)^2 - 12
Set y to 0 to determine the x-intercepts
0 = 3(x - 5)^2 - 12
Add 12 to both sides
3(x - 5)^2 = 12
Divide by 3
(x - 5)^2 = 4
Take the square root of both sides
[tex]x - 5 = \pm 2[/tex]
Add 5 to both sides
[tex]x = 5 \pm 2[/tex]
Expand
x = (5 - 2, 5 + 2)
Evaluate
x = (3, 7)
Hence, the x-intercepts of the parabola are (3, 0) and (7,0)
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y=x^2 is y a function of x
Margo borrows $1500, agreeing to pay it back with 3% annual interest after 18 months. How much interest will she pay?
Answer:
67.5
Step-by-step explanation:
I'm assuming this is simple interest.
1500x0.03x1.5=67.5
A horticulture class is filling planters with soil. Each planter is to be filled full.
How many cubic feet of soil will be needed to fill 15 planters measuring 2 feet by
3 feet by 1 foot?
O a.) 55 cu ft
Ob.) 45 cu ft
Oc.) 35 cu ft
O d.) 48 cu ft
Answer:
90 ft³
Step-by-step explanation:
V = LWH
V = (2 ft)(3 ft)(1 ft)
V = 6 ft³
Each planter has a volume of 6 ft³.
total volume = 15 × 6 ft³ = 90 ft³
Megan has 5 yards of cloth to make
napkins. She needs yard for each
napkin. How many napkins can
Megan make with the cloth?
napkins
Answer: 5
5yards = 5napkins
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.[tex]\frac{t^4+t^2+1}{(t^2+4)(t^2+2)^2}[/tex]
The form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
How to decompose the function?The fraction is given as:
[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2}[/tex]
To decompose the above, we make use of the following rule:
[tex]\frac{px^n + qx^m +....+ r}{(x^2 + a)(x^2 + b)^2} = \frac{Ax + B}{(x^2 + a)} + \frac{Cx + D}{(x^2 + b)} + \frac{Ex + F}{(x^2 + b)^2}[/tex]
So, we have:
[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2} = \frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
Hence, the form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]
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Please solve this question
The probability that a randomly selected x-value from the distribution will be in the interval:
P(35 < x < 45) = 0.6827 and,P(30 < x < 40) = 0.47725What is the probability of a normal distribution?The probability of a normal distribution can be determined from the symmetrical curve between 1 to 100%.
From the information given:
Mean = 40Standard deviation = 5To determine the probability that a randomly selected x-value is in the given interval:
P(35<x<45)P(30<x<40)[tex]P(35 < x < 45) = P(\dfrac{35-40}{5} < Z < \dfrac{45-40}{5})[/tex]
[tex]P(35 < x < 45) = P(\dfrac{-5}{5} < Z < \dfrac{5}{5})[/tex]
[tex]P(35 < x < 45) = P(-1 < Z < 1)[/tex]
[tex]\mathbf{P(35 < x < 45) = P[Z\le 1] -P[Z\le -1]}[/tex]
Using normal distribution table:
P(35 < x < 45) = 0.8414 - 0.1587
P(35 < x < 45) = 0.6827
[tex]P(30 < x < 40) = P(\dfrac{30-40}{5} < Z < \dfrac{40-40}{5})[/tex]
[tex]P(30 < x < 40) = P(\dfrac{-10}{5} < Z < \dfrac{0}{5})[/tex]
[tex]P(30 < x < 40) = P(-2 < Z < 0)[/tex]
[tex]\mathbf{P(30 < x < 40) = P[Z\le0]-P[Z\le -2]}[/tex]
Using normal distribution table:
P(30 < x < 40) = 0.5 - 0.02275
P(30 < x < 40) = 0.47725
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Solve 5x-4<2x+5. Enter your answer as an inequality.(Need help ASAP pls!!!)
Answer: x < 3
Step-by-step explanation:
To solve this inequality, we will simplify and isolate the x variable.
Given:
5x - 4 < 2x + 5
Add 4 to both sides:
5x < 2x + 9
Subtract 2x from both sides:
3x< + 9
Divide both sides by 3:
x < 3
Answer:
x < 3
Step-by-step explanation:
Well you want to isolate x so start by subtracting 2x from both equations that way you remove it from the right side and it's only on the left side.
subtract 2x from both equations
[tex]3x-4 < 5[/tex]
add 4 to both equations
[tex]3x < 9[/tex]
divide both sides by 3
[tex]x < 3[/tex]
Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?
The total amount of the drink is 2L. Strawberry concentrate will be X amount, and lemon concentrate will be the other part which is 2 - X.
---Note that we can only use one variable because there is only one equation to be set up here. That's why "the other part" is simply the total amount minus the strawberry amount.
0.4(2) = 0.3(x) + 0.55(2 - x)
---0.4, 0.3 and 0.55 are the decimal equivalents of 40%, 30% and 55%
0.8 = 0.3x + 1.1 - 0.55x
0.8 = -0.25x + 1.1
-0.3 = -0.25x
x = 1.2
Therefore, Chris should use 1.2L of strawberry concentrate and 0.8L of lemon concentrate to get 2L of a 40% concentrate mixture.
Hope this helps!
The common _____ of two rays that make an angle is called the vertex.
your answer goes here
Answer:
endpoint or straight lines
Step-by-step explanation:
same
A living room is 12 feet long and 10 feet wide. If the ceiling is 10 feet high, what is the total surface area of the
four walls?
Answer:
if we plus 12 and 10the answer is 22 feet
x+7/|x+7| for x> -7
absolute value
Answer: 1
Step-by-step explanation:
If [tex]x > -7[/tex], then [tex]x+7 > 0 \implies |x+7|=x+7[/tex]
So, we have the original fraction is equal to
[tex]\frac{x+7}{x+7}=\boxed{1}[/tex]
4. Debbie's nephew comes to live with them over the summer. He eats the same amount as each
of the other three kids. How much does it cost each morning to feed all four kids now?
Show your work.
Note: To feed one kid each morning, it costs $1.12
Each kid eats 1.3 tubs of yogurt and 3.3 ounces of granola each morning.
Answer:
$4.48
Step-by-step explanation:
It takes $1.12 to feed one kid, to find the cost of all four kids we multiply 1.12 by 4
1.12*4 = $4.48
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each equation of the plecewise function represented in the graph to its corresponding plece of the domain.
Matching each equation of the plecewise function represented in the graph will be:
2 < x < 3 = 3 - x0 < x < 2 = 1x = 2 = x3 < x < 5 = 5 - xHow to illustrate the information?It should be noted that a domain simply means the set of inputs that are accepted by the function.
In this case, the equation of the piecewise function represented is given.
The graph is attached.
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let (-5,-7) be a point on the terminal side of theta. find the exact values of cos theta, sec theta, and cot theta
a. The exact value of cosθ = -5/√74
b. The exact value of secθ = -√74/5
c. The exact value of cotθ = 5/7
How to find the trigonometric ratios
Since the terminal side of the θ is the point, (-5, -7), we need to find the length of the terminal side.
So, r = √(x² + y²) where
x = -5 and y = -7So, r = √(x² + y²)
r = √((-5)² + (-7)²)
r = √(25 + 49)
r = √74
The value of the trigonometric ratio cosθ
Since the trigonometric ratio cosθ = x/r
Substituting the values of x and r into the equation, we have
cosθ = x/r
cosθ = -5/√74
So, the exact value of cosθ = -5/√74
The value of the trigonometric ratio secθSince the trigonometric ratio, secθ = r/x
Substituting the values of x and r into the equation, we have
secθ = r/x
secθ = √74/-5
secθ = -√74/5
So, the exact value of secθ = -√74/5
The value of the trigonometric ratio cotθ
Since the trigonometric ratio cotθ = x/y
Substituting the values of x and y into the equation, we have
cotθ = x/y
cotθ = -5/-7
cotθ = 5/7
So, the exact value of cotθ = 5/7
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Which of the following illustrates the truth value of the following conditional?
p: 7 + 1 = 0
q: 2 + 2 = 5
F F → T
T T → T
F T → F
T F → T
The truth table for implication of the equations is F F ⇒ T
What is a truth table?A truth table is a mathematical logic table that shows the truth values of different logic statements combined by a given logic rule.
Analysis:
P: 7 +1 is not equal to 0 making P to be false(F)
q: 2+2 is not equal to 5 making q to be false(F)
so for conditional or implication, F F⇒ T
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Draw a vertical line through a normal distribution for
each of the following z-score locations. Determine
whether the tail is on the right or left side of the line
and find the proportion in the tail.
z= 1.00
z= 0.50
z= -1.25
z= -0.40
The proportion in the tail with regards to the z scores will be:
z = 1.00 = 0.1587z = 0.50 = 0.3085z = -1.25 = 0.1056z = -0.40 = 0.3446How to calculate the values?a. z= 1.00
P(z > 1.00) = 1 - P(Z < 1.00)
= 1 - 0.8413
= 0.1587
The tail will be on the right side.
The proportion of the tail will be 0.1587.
b. z = 0.50
P(z > 0.50) = 1 - P(Z < 0.50)
= 1 - 0.6915
= 0.3085
The tail will be on the right side.
The proportion of the tail will be 0.3085
c. z= -1.25
P(z < -1.25)
= 0.1056
The tail will be on the left side.
The proportion of the tail will be 0.1056.
d. z= -0.40
P(z < -0.40)
= 0.3446
The tail will be on the left side.
The proportion of the tail will be 0.3446.
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What are the slope and the y-intercept of the linear function that is represented by the table? x y Negative three-fourths Negative StartFraction 1 Over 30 EndFraction Negative one-half Negative StartFraction 2 Over 15 EndFraction One-fourth Negative StartFraction 13 Over 30 EndFraction Two-thirds Negative three-fifths a The slope is Negative two-fifths, and the y-intercept is Negative one-third. b The slope is Negative one-third, and the y-intercept is Negative two-fifths. c The slope is One-third, and the y-intercept is Negative two-fifths. d The slope is Two-fifths, and the y-intercept is Negative one-third.
The slope and the y-intercept of the function are: A. Slope = -2/5; y-intercept = -1/3.
How to Find Slope and Y-intercept of a Linear Function?Slope (m) = change in y / change in x.
Using two pairs of points form the table value, (1/4, -13/30) and (2/3, -3/5)"
Slope (m) = (-13/30 - (-3/5))/(1/4 - 2/3)
Slope (m) = (-13/30 + 3/5))/(1/4 - 2/3)
Slope (m) = (1/6)/(-5/12)
Slope (m) = (1/6)(12/-5) = 12/-30
Slope (m) = -2/5
Plug in m = -2/5 and (x, y) = (2/3, -3/5) into y = mx + b to find the y-intercept (b).
-3/5 = -2/5(2/3) + b
-3/5 = -4/15 + b
-3/5 + 4/15 = b
-1/3 = b
b = -1/3
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Answer:
A. Slope = -2/5; y-intercept = -1/3.
Step-by-step explanation:
Hope this helps!!
How is the theoretical probability of an event computed?
The theoretical probability of an event computed as
Theoretical Probability = [tex]\frac{ Number of desired outcomes}{ Number of possible outcomes.}[/tex] This is further explained below.
What is theoretical probability?Generally, The theoretical probability formula is the ratio of the number of successful outcomes to the total number of possible possibilities. We may write this formula out as follows:
In conclusion, the theoretical probability is mathematically given as
Theoretical Probability = [tex]\frac{ Number of desired outcomes}{ Number of possible outcomes.}[/tex]
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Find the compound amount and the interest earned when the given investment has continuous compounding.
$11,000 at 2.3% for 8 years
The compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We know the formula for continuous compounding:
[tex]\rm A = P(e)^{rt}[/tex]
[tex]\rm A = 11000(e)^{0.023\times8}[/tex]
A = $13,222.17
I = A - P = 13,222.17 - 11000
I = $2,222.17
Thus, the compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.
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answer the questions below to find the total surface area of the can
The total surface area of the tomato ketchup given in the diagram can be determined as follows:
The total surface area of a shape is the addition of the areas of its individual surface.
So that the questions can be answered as thus:
A. To find the area of the given circle;
i. Area of a circle = [tex]\pi r^{2}[/tex]
where r is the radius of the circle.
area of the circle = π[tex](2.5)^{2}[/tex]
= 6.25[tex]\pi[/tex]
ii. There are two identical circles in the cylinder.
iii. The total area of all circles = 2(6.25[tex]\pi[/tex])
= 12.5[tex]\pi[/tex] square inches
B. To find the area of the rectangle;
i. one side of the rectangle is 5 inches.
ii. The other side of the rectangle = 2[tex]\pi[/tex]r
= 2(2.5)[tex]\pi[/tex]
= 5[tex]\pi[/tex] inches
iii. The area of the rectangle = l x b
= 5[tex]\pi[/tex] x 5
= 25[tex]\pi[/tex] square inches
C. Total surfce area of the cylinder = 5[tex]\pi[/tex] + 25[tex]\pi[/tex]
= 30[tex]\pi[/tex] square inches
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Answer:
Step-by-step explanation:
First box
6.25
2
12.5
------
Second box
------
5
5
25
------
Last box
------
37.5
A blue line with 5 orange tick marks then one red tick mark then 4 orange tick marks. the number zero is above the red tick mark. calculate the final displacement from 0 if an object first moves 3 cm to the left and then 5 cm to the right. the final displacement is cm to the .
The final displacement is 2cm in the right.
Given that the object begins from 0 and moves 3 cm towards the left side and then, 5 cm towards the right side.
The displacement is known as shortest distance between the initial and final positions.
Let the x-axis be the positive, +ve, and on the right side and negative -ve on the left side.
Thus, displacement would be:
D= 0 -3 +5
D= 2 cm
This implies that the object displaces 2cm towards the right side
Hence, the final displacement when object moves from 0 and 3 cm to the left and then 5 cm to the right is 2cm in the right side.
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Answer:
2cm to the right
Step-by-step explanation:
i got this right hope it helps :)
are the two figures similar? if so give the similarity ratio of the smaller figure to the larger figure. explain why or why not
Answer: no they are not similar
Step-by-step explanation: if you find the ratio of sides 85:17, it is 5
The ratio of sides 30 to 6 is also 5
However, the ratio of sides 54 to 9 is 6 so it is not similar
The ratio has to be the same for all sides to be similar
what is the best estimate of the sum of the fraction? 31/4 +17/3 +8/18
The best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex]
What is a Fraction ?
A fraction is written as p/q , where q [tex]\rm \ne[/tex] 0
It is asked to determine the sum of the fraction
31/4 + 17/3 + 8/18
Taking the LCM of 4 , 3 , 18
LCM of 4 , 3 ,18 is 36
Therefore
[tex]\rm \dfrac{ 31 *9 + 17 *12 + 8 *2}{36 }[/tex]
(279+204+16) /36
499 / 36
[tex]\rm 13 \dfrac {31}{26}[/tex]
Therefore the best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex].
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Help? I tried the first two, can't get them. I don't know how I got the third.
Answer:
See below
Step-by-step explanation:
(6x+14)(x-8) = Expand
6x^2 - 48x + 14x - 112 =
6x^2 - 34x-112 A = 6 B = -34
Answer:
Step-by-step explanation:
[tex]x(6x+14)-8(6x+14)\\6x^2+14x-48x-112\\[/tex]
Rest, you have to substitute the value. Such as A= -112
if f(x)=4x-x^2 find f(x+h)-f(x+h)/2h
Answer:
0
Step-by-step explanation:
same numerator for that it is zero
Answer: A
Step-by-step explanation:
I need help with this one can someone show me step by step
Answer:
A
Step-by-step explanation:
You are given one angle and one side are similar
for Angle-Side-Angle you obviously need one more angle attached to the given side
A angle r = ~ angle c
The price of an item has been reduced by $3.49. The new sale price is $84.42. What was the original price?
$
X
3
Yasmin purchased 6 heads of cabbage that each weighed 2 and StartFraction 3 over 8 EndFraction pounds. How much did the cabbage weigh all together?
The total weight of cabbage is 14 1/4
What is Equation?An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Given:
Yasmin purchased 6 heads of cabbage that each weighed 2 and 3/8 pounds.
So,
2 and 3/8 = 19/8
1 cabbage = 19/8 pounds
6 cabbages = x pounds
1 * x = 6 * 19/8
x = 114/8
x = 14 2/8
x = 14 1/4
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A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles 3:4; but today the greedy hamster placed another 2 pounds of seeds in the bigger pile. He also ate 1/4 pound from the smaller pile and now the quantities of seeds in those piles is in the ratio of 5:16. What was the weight of each pile yesterday
The weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles was 3:4
Let 3x and 4x are the seeds from the smaller and bigger pile.
= 4x + 2 (greedy hamster placed another 2 pounds of seeds in the bigger pile)
= 3x - 1/4 (ate 1/4 pound from the smaller pile)
4x + 2 = 5x
Because the quantities of seeds in those piles is in the ratio of 5:16
After solving:
x = 2
Smaller pile weight = 3x = 3(2) = 6
Bigger pile wieght = 4x = 4(2) = 8
Thus, the weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4
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Solve-2x-8> 3x + 12.
A. x < -4
OB. x>-4
C. x > -3
D. x < -3
Answer:
x < -4
Step-by-step explanation:
add 8 to both sides
Simplify
Subtract 3x from both sides
Simplify, again
Multiply both sides by -1 ( reverse inequality)
Simplify, again
Divide both sides by 5
And vwola x < -4
HOPE THAT HELPS! :)