Step-by-step explanation:
x² - 12x + 32 = 0
the goal is the vertex form : a form like
(x - h)² + k = r²
with (h, k) being the vertex or center and r the radius.
doing all the multiplications we get
x² - 2hx + h² + k - r² = 0
and we compare this with our original equation. we see
x² = x²
-12x = -2hx
-12 = -2h
6 = h
32 = h² + k - r²
32 = 36 + k - r²
-4 = k - r²
possible solution : k = 0 and then r = 2
but also e.h. k = 12, r = 4
so, without the information about e.h. the radius we cannot identify one solution.
so, "A" vertex form (one of many possible ones) is
(x - 6)² = 4
Victoria wants to purchase a skateboard. She has $125 to spend. She
finds one that regularly sells for $140 and is on sale for 15% off. Sales
tax is 7%.
Victoria says that she has enough money to buy the skateboard. Is she
correct?
Answer:
we know that
Victoria has $125 to spend
[purchase price skateboard]=$139.99-0.15*$139.99-----> $139.99-$21
[purchase price skateboard]=$118.99
sales tax is 7%----------> 0.07*$118.99----------> $8.33
sales tax is $8.33
Victoria has to pay [$118.99]+[$8.33]=$127.32
$127.32 > $125
therefore
Victoria has not enough money to buy the skateboard
the answer is
Victoria has not enough money to buy the skateboard
Step-by-step explanation:
HELPPPP HURRY!!!!!!!!!
Describe one way you could graph the equation: y = 4x + 1,?
Answer:
Start at (0,1) and then go up 4 spaces over 1 to the left and repeat going up 4 over 1. To complete the graph by getting it to go behind the y intercept of (0,1) you go from the y intercept down 4 over 1 to the right and repeat going down 4 over 1.
For plotting a line, we need to plot points [tex](0,1)[/tex] and [tex](\frac{-1}{4},0)[/tex] on the cartesian plane and join them to form a line.
What is plotting a line?For plotting a line, we only need two points to graph a line. With that idea, we take advantage of the two “convenient” points which can easily be solved algebraically from the equation of the line; namely, the x-intercept (x,0) and y-intercept (0,y).
[tex]y = 4x + 1\\\\Put\ x = 0 \\y = 1\\we\ get\ (0,1)\ as\ a\ point\ lying\ on\ the\ line. \\\\Put\ y = 0 \\x = \frac{-1}{4} \\we\ get\ (\frac{-1}{4} ,0)\ as\ a\ point\ lying\ on\ the\ line. \\[/tex]
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A survey was given to a random sample of 45 residents of a town to determine
whether they support a new plan to raise taxes in order to increase education
spending. of those surveyed, 9 respondents said they were in favor of the plan. at the
95% confidence level, what is the margin of error for this survey expressed as a
proportion to the nearest thousandth?.
Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.117.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size and the estimate are given as follows:
[tex]n = 45, \pi = \frac{9}{45} = 0.2[/tex]
Hence the margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.2(0.8)}{45}}[/tex]
M = 0.117.
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earth makes one full rotation on its axis in a day how long does it take for it to rotate 150 degrees
Earth rotates one full rotation a day
360° in 3600sSo
It rotates 1° in
3600/360=10sIt rotates 150° in
150(10)1500sWhat is the value of the expression g (g + 1)2 for g = 2 ?
F.
10
G.
12
H.
18
J.
20
K.
36
Answer:
Step-by-step explanation:
2(2 + 1)^2 = 2(3)^2 = 2(9)= 18
A diagonal of a cube measures
150 cm. The diagonal of a face measures 10 cm.
3999
What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
centimeters
Save and Fit
S
Answer: 7cm
Step-by-step explanation:
Use pythagorean theorum:
Variables:
Let the edge = A
Face diagonal (F) = 10cm
Inner diagonal (I) = sqrt(150) cm
A^2 = I^2 - F^2
A^2 = [sqrt(150)]^2 - 10^2
A^2 = 150 - 100
A^2 = 50
A = sqrt(50)
A = 7.0710678 cm
A = 7cm (to the nearest tenth)
so, length of an edge = 7cm
In which number is the value represented by the digit in the hundreds place 10 times
the value represented by the digit in the tens place?
4,771
3,389
3,244
1,437
Answer:
4,771
Step-by-step explanation:
In the number 4771, the hundreds digit (7) is 10 times the tens digit (7).
what is the mean median mode and range of 14, 9, 20, 5, 17, 13
Answer:
no mode, median=8.5 mean 13
Step-by-step explanation:
5, 9, 13, 14, 17, 20
This net will be folded to form a prism.
A net of a rectangular prism. From top to bottom, the rectangles are labeled B, D, E, F. The left side is labeled A and the right side is labeled C.
Which pairs of faces will be opposite one another when the prism is created? Check all that apply.
D and F
A and C
A and B
B and F
B and E
B and C
E and F
A and F
Mark this and return
The opposite faces are D and F, A and C, and B and E. Then the correct options are A, B, and E.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
This net will be folded to form a prism.
A net of a rectangular prism.
From top to bottom, the rectangles are labeled B, D, E, and F.
The left side is labeled A and the right side is labeled C.
Then the pairs of faces will be opposite one another when the prism is created will be
BD, DE, EF, FB, AD, DC, CF, FA, AB, BC, BE, and EA all are the adjacent side faces.
AC, BE, and DF are the opposite faces.
Then the correct options are A, B, and E.
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This is an example of which method/property?
Answer:
distributive
Step-by-step explanation:
(x+y) (z) = xz+ yz is distributive
WILL MARK BRAINIEST
The average of the first three numbers were was six the average of the next 7 numbers was 19 what was the overall average of the 10 numbers
Answer:
3 1 4 7 9 3 8
Step-by-step explanation:
Micah wants to cover the seats with a weatherproofing stain how much stain will he need
Answer:
Enough to cover the seat
Step-by-step explanation: If this is a question dealing with the area of said object (seat) simply make an equation to find the area of your object. So let's say we got a seat that is 4 feet wide and 6 feet tall.
We will multiply 4 feet times 6 feet and that's where we get 24 feet.
So we know how many inches are in a feet right, there are 12 inches per foot. So 12 time 24 is our problem 12 x 24 = 288 inches. So we would need enough stain to cover 288 inches .
I hope this helps, when you ask for an awswer on brainly. I would highly recommend providing as much relevant context as you can. Have a nice day, and don't over think things ;)
A hockey puck strikes a wall at an angle of 30 degrees. the puck then travels away from the wall at the same angle.
Two or more angles whose sum is 180° are called supplementary angles. The measure of the ∠y is 120°.
What are supplementary angles?Two or more angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given the puck strikes the wall at an angle of 30°, it goes away at the same angle of 30°. Therefore, the measure of angle y can be found using the sum of the angle as a supplementary angle. Thus, we can write,
30° + ∠y + 30° = 180°
60° + ∠y = 180°
∠y = 180° - 60° = 120°
Hence, the measure of the ∠y is 120°.
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Hey guys! Sorry to bother but I need help with these. 5th grade math, will give brainliest! (If you see multiple questions by me that look the same, they are all different.)
Answer:
Question 3: 1/15 Question 4: 50
Step-by-step explanation:
Just divide the fractions by the numbers.
A toy store is building a display with two rectangular prisms. The base of each prism is a square with an edge length of 6 inches. One prism is 10 inches tall and the other is twice as tall. The two prisms are stacked on top of each other. What is the total volume of the display?
If the two prisms are stacked on top of each other then the height of the prism is 30 inches. Then the volume of the prism will be 1080 in³.
What is a rectangular prism?A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
A toy store is building a display with two rectangular prisms.
The base of each prism is a square with an edge length of 6 inches.
One prism is 10 inches tall and the other is twice as tall.
The two prisms are stacked on top of each other.
Then the total volume of the display will be
The volume of the prism will be
Volume = Base area × Height
Then the height of the second prism will be
h₂ = 2 × 10 = 20 inches
Then the volume of the prism will be
Volume = 6 × 6 × 10 + 6 × 6 × 20
Volume = 360 + 720
Volume = 1080 cubic inches
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On Amber’s math test, she was asked whether the equation x=1/2y^2 represents a function. She made the following table and graph. Amber concluded that the equation represents a function. Which additional point could be added to the graph to show Amber that the equation does not represent a function?
A. (–2, 2)
B. (0, 0)
C. (8, –4)
D. (8, 8)
Answer:
C
Step-by-step explanation:
I took the test.
The additional point could be added to the graph to show Amber that the equation does not represent a function will be (8, -4). Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The equation is given below.
x = (1/2)y²
For the single value of x, the value of y is not single.
Thus, it is not a function.
The additional point could be added to the graph to show Amber that the equation does not represent a function will be (8, -4).
Then the correct option is C.
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how many quarts are in 2 gallons?
Answer:
8 quarts
Step-by-step explanation:
There are 4 quarts in 1 gallon
So in 2 gallons there would be 4 × 2 = 8 quarts
Its 2 Lquid gallons = 8 Liquid quart
Calculate the distance between the pairs of coordinates, and classify them according to the distance between them.
(3, 4) and (2, 1)
(3, 7) and (5, 2)
(5, -2) and (3, 3)
(-2, 3) and (1, 2)
(-4, -2) and (-3, 1)
(4, -1) and (-1, 1)
Answer:
the first one is 3
second. is -5/2
third is 5/-2
fourth is -1/3
fifth is 3
sixth is 0/-5
Answer:
Square Root of 10: (3, 4) and (2,1)
(-4,-2) and (-3, 1)
(-2, 3) and (1,2)
Square Root of 29:
(3,7) and (5,2)
(5, -2) and (3,3)
(4,-1) and (-1,1)
Step-by-step explanation: Just took the test
An athlete completes one round of a circular track of diameter 200 m in 40 s what will be the distance covered and displacement at the end of 2 min 20s
Answer:
700π m ~ 2199 m
Step-by-step explanation:
diameter = d = 200 m
2 min 20s = 140 s
1 round / 40 s
140 = 40 * 3 + 20
so the athlete will cover 3 round and half
1 round = d * π
covered = c = 3 * 200 * π + 200/2 * π = 700 * π
The two data sets shown below are almost identical. Which of the following
statements are true? (Select TWO)
Data Set 1: 32 41 51 63 66 71
Data Set 2: 32, 41, 51, 3 66, 71
The range of Data Set 2 is smaller than the range of Data Set 1.
The median of Data Set 2 is exactly 30 less than the median of Data Set 1.
The mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.
The standard deviation of Data Set 2 is larger than the standard deviation of Data Set 1.
Based on the calculations, the two (2) statements which are true are:
The mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.Option D.How to calculate the range?Mathematically, range can be calculated by using this formula;
Range = Highest number - Lowest number
Range 1 = 71 - 32
Range 1 = 39.
Range 2 = 71 - 3
Range 2 = 68.
Therefore, the range of Data Set 2 is not smaller than the range of Data Set 1.
How to calculate the mean?Mathematically, the mean for these data sets would be calculated by using this formula:
Mean = [F(x)]/n
For the total number of Data Set 1, we have:
F(x) = 32 + 41 + 51 + 63 + 66 + 71
F(x) = 324.
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean 1 = [324]/6
Mean 1 = 54.
For the total number of Data Set 2, we have:
F(x) = 32 + 41 + 51 + 3 + 66 + 71
F(x) = 324.
Substituting the parameters into the formula, we have:
Mean 2 = [264]/6
Mean 2 = 44.
Difference = Mean 1 - Mean 2
Difference = 54 - 44
Difference = 10.
Therefore, the mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.
For the standard deviation of Data Set 1, we have:
SD₁ = √(1/n × ∑(xi - u₁)²)
SD₁ = √(1/5 × ∑(32 - 54)² + 1/5 × ∑(41 - 54)² + 1/5 × ∑(51 - 54)² + 1/5 × ∑(63 - 54)² + 1/5 × ∑(66 - 54)² + 1/5 × ∑(71 - 54)²)
SD₁ = 15.34.
For the standard deviation of Data Set 2, we have:
SD₂ = √(1/n × ∑(xi - u₂)²)
SD₂ = √(1/5 × ∑(32 - 44)² + 1/5 × ∑(41 - 44)² + 1/5 × ∑(51 - 44)² + 1/5 × ∑(3 - 44)² + 1/5 × ∑(66 - 44)² + 1/5 × ∑(71 - 44)²)
SD₂ = 24.88.
Therefore, the standard deviation of Data Set 2 is larger than the standard deviation of Data Set 1.
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Linet passes through points (2, 2) and (10, 9). Line u is parallel to line t. What is the slope of
line u?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
7/8
Step-by-step explanation:
Understanding the situation
Parallel lines have the same slopes.
If line t is parallel to line u then the slope of line t is the same as the slope of line u.
Finding the slope of line t
Slope formula = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
where the x and y values are derived from points on the line
here, we are given that line to goes through (2,2) and (10,9)
Given that we can assign variables
we have (x1,y1) = (2,2) so x1 = 2 and y1 = 2
we also have (x2,y2) = (10,9) so x2 = 10 and y2 = 9
Now that we have assigned variables we plug them into the formula
Recall formula : [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
==> plug in x1 = 2 , y1 = 2, x2 = 10 and y2 = 9
[tex]slope =\frac{9-2}{10-2}[/tex]
==> simplify top and bottom
[tex]slope =\frac{7}{8}[/tex]
The slope of line t is 7/8
Finding the slope of line u
Because line t and line u are parallel line u also has a slope of 7/8
The area of the triangle is
Answer:
3units squared
Step-by-step explanation:
1/2 the base times the height
1/2 * 2 * 3 = 3
f(x)=(x+3)^2 -8 how many real solutions?
Answer:
2 real solutions
Step-by-step explanation:
[tex]f(x)=(x+3)^2-8\\\\0=(x+3)^2-8\\\\8=(x+3)^2\\\\\pm\sqrt{8}=x+3\\\\x=-3\pm\sqrt{8}[/tex]
Therefore, the function set at [tex]f(x)=0[/tex] has two real solutions (x-intercepts).
You can also check the discriminant of the function by expanding it:
[tex](x+3)^2-8=x^2+6x+9-8=x^2+6x+1\\\\b^2-4ac=6^2-4(1)(1)=36-4=32 > 0[/tex]
Since it's greater than 0, there's two real solutions
can someone please tell me how many cups is 7/2 pints??
Answer:
8
Step-by-step explanation:
Find the distance between (5, 6) and (-9, -2)
Answer:
So we must determine the distance between our two given points and that can be found using the distance formula [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Plugging the values into the equation and solve
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(-9-5)^2+(-2-6)^2}[/tex]
[tex]d=\sqrt{(-14)^2+(-8)^2}[/tex]
[tex]d=\sqrt{196+64}[/tex]
[tex]d=\sqrt{260}[/tex]
[tex]d=16.125\ units[/tex]
Therefore, our final answer is that the distance is 16.125 units
Hope this helps! Let me know if you have any questions
Give the general solution in degrees and radians. 9) 8cosØ = 4
Hi Student!
The first step that we need to take before solving this problem is understand what we need to do and what information we are given to do that. So first they are asking for us to determine the solution (or find theta) in both degrees and radians. The information that is given to us is the equation [tex]8* cos (\theta) = 4[/tex].
After completing the initial step, the next step is to actually start solving the equation for the unknown which in this case is theta or the angle.
Divide both sides by 8
[tex]8* cos (\theta) = 4[/tex][tex]\frac{8* cos (\theta)}{8} = \frac{4}{8}[/tex][tex]cos (\theta) = \frac{1}{2}[/tex][tex]cos (\theta) = 0.5[/tex]Multiply by the inverse of cos
[tex]cos^{-1}(cos (\theta)) = cos^{-1}(0.5)[/tex][tex]\theta = cos^{-1}(0.5)[/tex][tex]\theta = 60[/tex]After solving for the unknown or theta, we were able to determine that the solution for our equation is 60 degrees. Now we can move onto the final step which is to convert our answer to radians to complete the final part of the problem statement.
We can convert from degrees to radians by multiplying by π/180 which would get rid of degrees and give us radians.
Plug in the values
[tex]degrees*\frac{\pi }{180\ degrees}[/tex][tex]60\ degrees*\frac{\pi }{180\ degrees}[/tex]Simplify the expression
[tex]\frac{\pi\ *\ 60\ degrees }{180\ degrees}[/tex][tex]\frac{\pi}{3}[/tex]Therefore, our final answer is that our solution in degrees is 60 degrees and our solution in radians is π/3.
A lock has a three number code made up of 17 numbers if none of the numbers are allowed to repeat how many different ways can you choose three different numbers in order for unit code?
Answer:
680
Step-by-step explanation:
Use the binomial coefficient where you choose [tex]k=3[/tex] numbers out of [tex]n=17[/tex] possible numbers and find the total amount of combinations since order does not matter:
[tex]\displaystyle \binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{17}{3}=\frac{17!}{3!(17-3)!}\\\\\binom{17}{3}=\frac{17!}{3!(14)!}\\\\\binom{17}{3}=\frac{17*16*15}{3*2*1}\\\\\binom{17}{3}=680[/tex]
Thus, you can make 680 three-non-repeating-number codes
-3(7+6t)
Can you tell me the answer
Answer: -21 + -18t
Step-by-step explanation:
-3(7+6t)
-3 x 7= -21
-3 x 6t= 18t
Lottie buys a pack of 50 cans of lemonade.
She pays £17 for the cans.
Lottie sell 32 of the cans for 50p each.
She sells the remaining cans for 20p each.
Work out Lottie's percentage profit.
Give your answer correct to three significant figures.
15.3%
In Order:1) Lotte buys 50 cans for £17.
2) Sells 32 cans for 50 penny each.
3) Sells remaining for 20 penny each.
Solve:Total cost for 32 cans:
price of each can × total cans
50 penny × 32
1600 penny
Remaining Cans : 50 - 32 = 18 cans
Total cost of this 18 cans:
20 penny × 18
360 penny
[tex]\boxed{\bf 100 \ penny \ (p) = 1 \ pound \ ( \sf \£ )}[/tex]
Total Gained : 1600 + 360 = 1960 pence ≈ £19.6
Profit : selling price - cost price : 19.6 - 17 = £2.6
Profit In percentage:
[tex]\sf \dfrac{(selling \ price - cost \ price)\ x \ 100}{cost \ price}[/tex]
[tex]\rightarrow \sf \dfrac{2.6\ x \ 100}{17}[/tex]
[tex]\rightarrow \sf 15.294 \%[/tex]
[tex]\rightarrow \sf 15.3 \% \ \ (rounded \ to \ nearest \ three \ significant \ figure)[/tex]
Lottie's percentage profit based on the provided information is 15.29%
How can the percent be found?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per cent refers to one hundred percent.
The cost will be £17 according to the question
Total amount generated are;
32 cans * £0.50=£16
18 cans * £0.20=£3.60
Then the total will be £16 + £3.60 = £19.60
Profit = amount generated- cost
=£19.60 - £17
= £2.60
The percentage profit:
[tex]= \frac{2.60}{17} * 100 \\\\=[/tex]
15.29%
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can somebody helpp wit these two????
Answer:
i think the answer is c
Step-by-step explanation:
