Answer:
B. 32
Step-by-step explanation:
5+3=8
8×4=32
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Solve the following quadratic equation.
(x - 16)^2 = 256
A. x = -32 and x = 0
B. x = 30 and x = -4
C. x = -30 and x = 4
D. x = 32 and x = 0
The answer is D. x = 32 and x = 0
============================================================
Explanation:
Think of x-16 as y. In other words, let y = x-16
We have (x-16)^2 = 256 become y^2 = 256.
Solve for y to get y = 16 or y = -16. You apply the square root to both sides. Don't forget about the plus/minus. This is because (-16)^2 = (-16)*(-16) = 256. We square the negative as well.
--------
If y = 16, then y = x-16 solves for x to get
y = x-16
16 = x-16
x-16 = 16
x = 16+16
x = 32 is one solution
---------
Plug in y = -16 and isolate x
y = x-16
x-16 = y
x-16 = -16
x = -16+16
x = 0 is the other solution
----------
We can check each answer by plugging them back into the original equation
Let's try x = 0
(x-16)^2 = 256
(0-16)^2 = 256
(-16)^2 = 256
256 = 256 ... works
Now try x = 32
(x-16)^2 = 256
(32-16)^2 = 256
(16)^2 = 256
256 = 256 ... also works; both answers have been confirmed
What is the domain of f(x) = 3x – 2? {x | x > 0} {x | x < 0} {x | x = 0} {x | x is a real number}
Answer:
Option (4). {x | x is a real number}
Step-by-step explanation:
Domain of any function is defined by the x values (Input values) and range by the y-values (Output values).
Given function is f(x) = 3x - 2
When we graph this function, we get a straight line.
That means the given function is defined for all real numbers.
Therefore, domain of this function will be all real numbers.
Domain: {x | x is a real number}
Option (4) will be the answer.
Answer:
D) {x | x is a real number}
Suppose figure A underwent a dilation to produce figure B. Are figure A and figure B similar?
Answer:
Figure A and B are still congruent to each other. the only change is the size of the shape.
Step-by-step explanation:
Yes, figure A and figure B similar because even though their side lengths are different, their internal angles are the same.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Suppose figure A underwent a dilation to produce figure B.
Now, A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
if Dilation factor N then image Size is multiplied by N
if Scale factor < 1 then image get reduced
if scale factor > 1 then image get enlarged
scale factor = 1 lead to Same size image
Hence, Figure A and figure B similar because even though their side lengths are different, their internal angles are the same.
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4 (9x+6) = 36x - 7 what does x =
-1/3 multiplied by 1/4
Answer:
[tex] - \frac{1}{12} \\ [/tex]
Step-by-step explanation:
[tex] - \frac{1}{3} \times \frac{1}{4} \\ \\ = - \frac{1}{12} [/tex]
The slope of the rafter is 15 m.Half the run of the rafter measure 12m.find the height of the ridge from the base
Answer:
[tex]9\; \rm m[/tex].
Step-by-step explanation:
Assume that the run of this rafter is level. Then the height of the ridge (the line with a question mark next to it in the diagram) should be perpendicular to the line marked with [tex]\rm 12\; m[/tex]. The three labelled lines in this diagram will form a right triangle.
The line marked as [tex]15\; \rm m[/tex] will be the hypotenuse of this right triangle.The line marked as [tex]12\; \rm m[/tex] will be one of the triangle's legs.The line representing the height of the ridge (the one with the question mark) will be the other leg of this right triangle.Hence, the height of this ridge can be found with the Pythagorean Theorem. By the Pythagorean Theorem:
[tex](\text{First Leg})^2 + (\text{Second Leg})^2 = (\text{Hypotenuse})^2[/tex].
In this particular right triangle:
[tex](\text{Height})^2 + (12\; \rm m)^2 = (15\; \rm m)^2[/tex].
[tex](\text{Height})^2 = (15\; \rm m)^2 - (12\; \rm m)^2[/tex].
Therefore, the height of this ridge would be [tex]\sqrt{81}\; \rm m = 9\; \rm m[/tex]. (Note the unit.)
what are the domain and range of the function on the graph
Please help there’s a picture to explain more
110
70
X=?
Answer:
Step-by-step explanation:
110 = 70 + X [ extarior angle property]
or, 110 - 70 = X
or , 40 = X
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A farmer harvested 21 1/4 fewer bushels of sweet corn this year than the previous year. If the farmer's sweet corn crop is planted across 3 acres, what is the average loss per acre?
Answer: 85/12 fewer bushels per acre
Step-by-step explanation:
Hi, to answer this question we have to write an expression with the information given and solve it:
We simply have to divide the total loss (21 1/4) by the number of acres (3):
Mathematically speaking:
21 1/4 ÷3 = (21(4) +1)/4 ÷3 = 85/4 ÷ 3= 85/12 fewer bushels per acre
Feel free to ask for more if needed or if you did not understand something
The average loss per acre is [tex]7\frac{1}{12}[/tex]
The average loss per acre = difference in bushels harvested last year and this year ÷ total number of acres
[tex]21\frac{1}{4}[/tex] ÷ 3
In order to solve this question, the mixed number has to be changed to an improper fraction.
Steps to take :
1. Multiply the whole number by the denominator ( 4 x 21 = 84)
2. Add the numerator to the answer gotten in the previous step (84 + 1 = 85)
3. divide the number gotten in the previous step by the denominator (85/4)
[tex]\frac{85}{4}[/tex] ÷ 3
= [tex]\frac{85}{4}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{85}{12}[/tex] = [tex]7\frac{1}{12}[/tex]
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What is the theme of a story? 100 PTS!
Answer:
The theme in a story is its underlying message, or 'big idea".
Answer: its underlying message, or 'big idea. ' In other words, what critical belief about life is the author trying to convey in the writing.
Step-by-step explanation: what the author is trying to tell you.
Find m∠HIJ if m∠HIQ=25x+1 and m∠QIJ= 100 ∘ and m∠HIJ=127x−1, What is HIJ?
8. Solve for a:
p+q=2ab
[tex]\text{Solve for a:}\\\\p+q=2ab\\\\\text{Since we want to solve for a, it needs to be by itself}\\\\\text{To do this, we have to divide both sides by 2b}\\\\\frac{p+q}{2b}=a\\\\\text{Now since A it's by itself, that'll be your answer}\\\\\boxed{\frac{p+q}{2b}=a}[/tex]
If a and b must be positive integers, what is the largest integer n such that 13a + 18b = n has no solutions?
Answer:
Any integer that is not integer multiple of 234 is not a solution.
Step-by-step explanation:
We are required to find the largest integer n such that 13a + 18b = n has no solution, where a and b are integers.
13a + 18b = n
For a = 1, b = 0
n = 13
For a = 0, b = 1
n = 18
So, for the solution sets (1, 0), (0, 1), n will always have a solutions.
Consider n = 13 × 18 = 234
This means that any integer that is not integer multiple of 234 is not a solution.
Teena's calculator is broken and does not have key 9 that works! With this broken calculator she found out the value of (-35) x 99. Explain your reasoning carefully and clearly
Answer:
(-35) * (100 - 1)
Step-by-step explanation:
She was able to find the value of (-35) * 99 without using the missing 9 button on her calculator.
The easiest way to do this is to replace 99 with another set of numbers that has the same value as 99.
(100 - 1) has the same value as 99. So, Teena can replace 99 with (100 - 1):
(-35) * (100 - 1)
It will yield the desired result.
there are 48 cards in a pack and each card is either red or black.the ratio of the number of red cards to the number of black cards is 1:1.
8 red cards are removed from the pack
find the ratio of the number of red cards now in the pack to the number of black cards now in the pack
Answer:
2:3
Step-by-step explanation:
We know that there are 24 red and black cards in the 48 pack because their ratio is 1:1. When 8 red cards are removed we have 16 red and 24 black cards. The ratio of this is 16:24 which simplifies to 2:3.
The ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1
Calculation of ratioThe total amount of cards (red or black) in the pack is = 48
The ratio of the number of red cards to the number of black cards is = 1:1
The number of cards removed from the pack = 8
Therefore the total number of cards( red or black = 48 -8
= 40 cards
But to calculate the number of red card
= 1+1 = 2
40/2 = 20 red cards
The number of black cards
1+1 = 2
40/2 = 20 black cards
The ratio of red is to black cards = 20:20 or 20/20 = 1:1 or 1/1
Therefore the ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1
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Simplify the expression.
4(-8x + 5) - (-33x - 26) =
Answer: x=-46
Step-by-step explanation:
Assuming the expression equals 0 (I'm not sure since you didn't explicitly state that, but I inferred for the sake of answering the question):
4(-8x+5)-(-33x-26)=0
-32x+20+33x+26=0
1x+46=0
x=-46
Hope that helps!
Answer:
x+46
Step-by-step explanation:
I used distribution for the first half of the equation, and got -32x+20. I used the negative on the second and mad it positive: 33x+26. I combine like terms, adding 33 to -32, got 1, then added 20 and 26. My answer was as listed above.
Hope this helped!
A professor must randomly select 4 students to participate in a mock debate.
There are 20 students in his class. In how many different ways can these
students be selected, if the order of selection does not matter?
Answer:
Step-by-step explanation:
We can use combinations
20 choose 4:
20!/(16!*4!)
= (20*19*18*17)/4!
= 4845
rational numbers are always sometimes never natural numbers
Answer:
Rational numbers are sometimes natural numbers
Step-by-step explanation:
8 is a Rational number and is natural too
1/2 is a Rational number and but is not natural
Find the diameter of a cone that has a volume of 56.52 cubic inches and a height of 6 inches. Use 3.14 for pi
Answer:
d=6
Step-by-step explanation:
Answer: diameter is 6
Step-by-step explanation:
Whenever there are _____________ in a set of data, the mean is not a good way to describe the data.
A. quartiles
B. modes
C. medians
D. outliers
Answer:
The answer is D because outliers are data far away from the main data set.
Answer:
d
Step-by-step explanation:
What is the leading coefficient of 5-6x^4+8x^2-2x^3
Answer:
-6
Step-by-step explanation:
Rewrite the equation with the number that has the highest exponent in the front.
-6x^4 -2x^3 + 8x +5
The leading coefficient is the number beside the x value
In this case it is -6
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How do I find value of X
Answer:
147°
Step-by-step explanation:
106°+139°+126°+141°+112°+129°+x =900°
753°+x = 900°
x = 900°-753°
x= 147° (sum of the interior angles of a heptagon=900°)
The perimeter of an equilateral triangle is 120mm.
State the length of one of its sides.
Answer:
[tex]40 \:mm[/tex]
Step-by-step explanation:
An equilateral triangle has 3 equal sides.
[tex]\frac{120}{3} =40[/tex]
Answer:
40mm
Step-by-step explanation:
Perimeter of an equilateral=3a
120=3a
a=120/3
a=40mm
Find the areas of the sectors formed by ∠DFE. Round your answers to the nearest hundredth.
Answer:
Area of the sector in red = 177.87 cm²
Area of the sector in blue = 437. cm²
Step-by-step explanation:
Area of the sector = [tex]\frac{\theta}{360}(\pi )(r)^2[/tex]
Area of the sector shaded in blue = [tex]\frac{256}{360}(\pi )(14)^2[/tex]
= 437.87 cm²
Central angle formed by sector shaded in red = 360 - 256 = 104°
Area of the sector shaded in red = [tex]\frac{104}{360}(\pi )(14)^2[/tex]
= 177.884
≈ 177.88 cm²
Therefore, area of the sector shaded in red = 177.87 cm² and area of the sector in blue = 437.88 cm²
Jade has $451.89 in her checking account. After 3 checks, each for the same amount, are deducted from her account, she has $358.92 left in her account.
Assume she makes no other withdrawals or deposits. Which equations represent c, the amount of one check, in dollars? Select three options.
451.89 minus c = 358.92
451.89 minus 3 c = 358.92
358.92 + 3 c = 451.89
358.92 + c + c + c = 451.89
c = 3 (451.89 minus 358.92)
for ed, it should be:
B
C
D
if not, then idk what happened
The equations that represents the amount of one check are:
451.89 minus 3 c = 358.92
358.92 + 3 c = 451.89
358.92 + c + c + c = 451.89
What equation represent the amount of one check?The equation that represents the amount of one check is:
Total amount in the account - total value of 3 checks = amount left
Total amount in the account - amount left = total value of 3 checks
Value of one check = (total amount in the account - amount left) / 3
$451.89 - 3c = $358.93
$451.89 - $358.93 = 3c
($451.89 - $358.93) / 3
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Please answer correctly!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
see below
Step-by-step explanation:
g(x) = sqrt(x+3)
g(-6) = sqrt(-6+3) = sqrt(-3) not a real number not in domain
g(-3) = sqrt(-3+3) = sqrt(0) 0 in domain
g(3) = sqrt(3+3) = sqrt(6) in domain
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Find the arc length of the partial circle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answer:
4π
Step-by-step explanation:
find the circumference first
2π r
2π 8=16π
then find the arc length
16π * 1/4
4π
Tarek reaches into a can that contains 30 25-fils coins, 25 10-fils coins, 40
5-fils coins and 15 1-fils coins. What is the probability that the first coin
he picks is a 25-fils coin or a 1-fils coin?
Answer:
9/22
Step-by-step explanation:
They are 30 25-fils coins, 25 10-fils coins, 40 5-fils coins and 15 1-fils coins.
The total number of fils coins = 30 + 25 + 40 + 15 = 110 coins
The probability of picking n-fils coin = number of n fils coin / total number of fils coins.
Therefore:
The probability of picking 25-fils coin = number of 25 fils coin / total number of fils coins = 30/110 = 3/11
The probability of picking 10-fils coin = number of 10 fils coin / total number of fils coins = 25/110 = 5/22
The probability of picking 5-fils coin = number of 5 fils coin / total number of fils coins = 40/110 = 4/11
The probability of picking 1-fils coin = number of 1 fils coin / total number of fils coins = 15/110 = 3/22
The probability that the first coin he picks is a 25-fils coin or a 1-fils coin = The probability of picking 25-fils coin + The probability of picking 1-fils coin = 3/11 + 3/22 = 9/22
sue's tyre pressure gauge shows a reading which is 8% higher than the actual pressure.
What is the actual pressure when sue's gauge shows 39.42?
Answer:
36.5 is the answer
Hope this helps!
Step-by-step explanation:
Let the actual pressure be x
The actual pressure is 100% of x
The pressure is showing 8% more
So the pressure showing now is the actual pressure + the extra pressure
= 100%+8% = 108%
= 108/100
So the equation is:
108/100 x = 39.42
108x = 39.42*100
108x = 3942
x= 3942/108
= 36.5
Therefore the actual pressure is 36.5
what is the probability that the next person you meet was not born in February? No leap years.
Answer:
A
Step-by-step explanation:
Since there are 28 days in a regular February and 365 days in a total year, the probability that a random person is born in February is 28/365. This means that the probability that they were NOT born in February is 337/365, or answer choice A. Hope this helps!
Answer:
a.
Step-by-step explanation:
A non leap year has 365 days. February of a non leap year has 28 days.
365 - 28 = 337
There are 337 days in a non leap year that are not in February.
p(not February) = 337/365