The GCF is 4
The polynomial factors to [tex]4(3x^2+x+5)[/tex]
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Further explanation:
Ignore the x terms
We're looking for the GCF of 12, 4 and 20
Factor each to their prime factorization. It might help to do a factor tree, but this is optional.
12 = 2*2*34 = 2*220 = 2*2*5Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.
We can then factor like so
[tex]12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)[/tex]
The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.
The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).
Solve the inequality
2b + 5< 30
Answer:
b < 12.5
Step-by-step explanation:
2b + 5 < 30
1. Subtract 5 from both sides:
2b < 25
2. Divide both sides by 2:
b < 12.5
Final answer: b < 12.5
The value of b is any value that is less (smaller) than 12.5.
Hope this helps!
Calculate the values
Answer:
a=108;b=36;c=72
Step-by-step explanation:
Answer:
a = 108°
b = 36°
c = 72°
Step-by-step explanation:
Note : the sum of the interior angles of a regular pentagon = 540°
Then
The measure of one interior angle of a reg pentagon =540/5 = 108°
Therefore a = 108°
c = 180 - 108 = 72°
SRT is a new isosceles triangle then :
[tex]b=\frac{180-108}{2} = \frac{72}{2} =36[/tex]
does anyone know this answer?
the question says that the samples included 100 people each, so it's just 100 multiplied by the amount of samples:
7×100=700
Answer: It looks like the answer is 50. But i would go over it with a calculator.
Step-by-step explanation:
Martin takes a test that has five multiple choice questions. Each question has three possible
answers. If Martin guesses on each question, in how many different ways can he answer the
questions on the test?
Answer:
about 2/5 of the question probability lol
Which term best describes the trend shown on the scatter plot below?
No trend
Negative Trend
Positive Trend
Answer:
Positive Trend
Step-by-step explanation:
As the y-values tend to increase with increase in x-values, we can consider this scatter plot to have a positive trend.
Suppose a 12 acre plot of land is being divided into 1/4 acre lots for a hosing development. How many lots will there be in the development.
Answer:
48 lots
Step-by-step explanation:
In a sale, the normal price of a bicycle is reduced by 35%.
The sale price of the bicycle is £585
Work out the normal price of the bicycle.
How many balloons are in the air if there are 20 ballons and 5 pop how many are left
Answer:
15 balloons
Step-by-step explanation:
20 - 5 = 15
hope this helps:)
Answer:
15 ballons
Step-by-step explanation:
emergencyyy
Write the given expression in the form f(x)= a(x– h)? +k. Identify the vertex.
f(x) = 2x² - 16x-5
Answer:
vertex = (4, - 37 )
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = 2x² - 16x - 5 ← factor 2 out of the first 2 terms
= 2(x² - 8x) - 5
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² - 8x
f(x) = 2(x² + 2(- 4)x + 16 - 16) - 5
= 2(x - 4)² - 32 - 5
= 2(x - 4)² - 37 ← in vertex form
with vertex = (4, - 37 )
help me find the value of x I will give BRAINLIEST HELP QUICK
Answer:
560
Step-by-step explanation:
If this isn't correct Im sorry I rushed it should be right but if not it should be close.
14. Which of the following is the perimeter of the right triangle shown below?
(1) 63 cm
(2) 64 cm
(3) 70 cm
(4) 74 cm
Answer:
3
Step-by-step explanation:
Using Pythagoras formula
h^2 = (root under) p^2 +b^2
or, h^2= 20^2 + 21^2
or, h^2= 400+441
or, h^2= 841
or, h= (root under) 841
Therefore h= 29
Now,
Perimeter of a triangle= a+b+c
= 20+21+29
=70
y is directly proportional to the square root of x, y is 75 and x is 100. find a formula linking x and y
Answer:
y = 7.5[tex]\sqrt{x}[/tex]
Step-by-step explanation:
given y is directly proportional to [tex]\sqrt{x}[/tex] then the equation relating them is
y = k[tex]\sqrt{x}[/tex] ← k is the constant of proportion
to find k use the condition y = 75 , x = 100 , then
75 = k[tex]\sqrt{100}[/tex] = 10k ( divide both sides by 10 )
7.5 = k
y = 7.5[tex]\sqrt{x}[/tex] ← equation of proportion
Work out
the area of this circle. Take
(Pi) to be
3.142 and give your answer to
2 decimal places.
11.2cm
Four friends are sharing 5 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
Answer:
each friend will get 5/4 or 1.25 cups of lemonade
Step-by-step explanation:
5 divide by 4 since there are 4 friends.
so 5/4 of the lemonade will be shared by each friend.
Step-by-step explanation:
each friend would get 1.25 cups each
Select the dot plot with the least variability.
The dot plot with the least variability will be C.
How does the dot plot work?Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
The dot plot with the least variability will be C.
The graph is given below.
Learn more about dot plots here:
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Need help quick please! Find the surface area. Hint you will need to use Pythagorean theorem
Answer:
80
Step-by-step explanation:
What is the measure of the base of the rectangle if the area
of the triangle is 32 ft2 ?
Answer:
it would be a
Step-by-step explanation:
8x4=32
The base of the given triangle is calculated as: 16 ft
How to find the area of a triangle?The formula that is used to calculate the area of a triangle is expressed as:
Area of triangle= ½ × base × height
We are given that:
Area = 32 ft²
Height = 4 ft
Thus:
32 = ½ × base × 4
32 = 2 * base
base = 32/2
base = 16 ft
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Given 184% what is the equivalent fraction and decimal in simplest form?
Step-by-step explanation:
184% = 46/25 = 1 21/25 as a fraction
Nathaniel bought headphones online for $22. He used a coupon code to get a 40% discount. The website also applied a 10% processing fee to the price after the discount. How much was the discount, in dollars and cents?
Answer:
8.80 if it's the 40°/.
2.20 if it's the 10°/. processing fee
13.20 for how much he paid
a lawn sprinkler waters a lawn in a circle as shown
Part A
I'm assuming you want the area of a circle with radius 17 yards.
We'll use the formula below
A = pi*r^2
A = (22/7)*17^2
A = (22*17^2)/7
A = 6358/7
A = 908 2/7
The sprinkler covers an area of about 908 2/7 square yards.
You'll type 908 in the left-most box
Then for the other two boxes, you'll have 2 up top and 7 down below to represent the fraction 2/7
The number 908 2/7 is a mixed number.
=======================================================
Part B
You mentioned that the radius reduces to 11 yards here. We'll use the same formula as above and pi = 22/7 approximately
A = pi*r^2
A = (22/7)*11^2
A = (22*11^2)/7
A = 2662/7
A = 380 2/7
The sprinklers can water an area of about 380 2/7 square yards.
This value is also a mixed number
380 is the value in the left most box (it's the whole part)
The other two boxes are filled out the same exact way as the previous part above.
What two numbers multiply to -17 but add to -16?
Answer:
-33
Step-by-step explanation:
-17and den u add &16 together soon u have to additional into get -33
the product of the square of a number and the cube of the same number is equal to 243. find the number
Answer:
x=3
Step-by-step explanation:
X^2*x^3 → x^5
x^5 = 243 means x = 3
Answer:
The number is 3.
Step-by-step explanation:
Let "The square of the number" be x^2.
Let "the cube of the same number" be x^3.
"product" means multiplication.
x^2 • x^3 = 243
Multiply. To multiply, add the exponents.
x^5 = 243
Take the 5th root of both sides. You can do this on many scientific calculators with a x^y button. Or raise 243^ (1/5)
1/5 power is the same as 5th root.
You might do it in your head by thinking "what number to the 5th power is 243"
x = 3
Check 3^5 = 243
also
3^2 • 3^3 = 43
9 • 27 = 243
243 = 243 check
Ms. Wimbley surveyed the middle school and found out that 70 students want to go to sky zone for the end of the year field trip. This represents 14% of the middle school. How many students are in the middle school?
Answer:
500
Step-by-step explanation:
If 700 is 14%, then x=100%
We do:
700=14%
x=100%
Then, we cross multiply to get
14x=7000
We divide 14 on each side, and get x=7000/14 which is x=500
So there are 500 total students in the middle school
Hope this helped you! If the answer is wrong, please tell me and I will correct it. Also, I would appriceate if you gave me a Brainliest. It means a lot to me :D
help plsls I’ll brainlist i promise this one’s abit confusing tho.
Answer:
25
Step-by-step explanation:
Please refer to the picture;
Solve for x in the equation 3^2(x+3)÷8(x-4)=64÷2x
Answer:
Hope this helps, it was a hard equation... mark me brainliest
Step-by-step explanation:
9x+27÷8x-24=64÷2x
9x÷8x+3=64÷2x
9x÷8x*2x=61
x^3=244/9
x=
approximately 3.00411
What is the area of the triangle given below?
Answer:
26
Step-by-step explanation:
Solve for the variable:
√5-x= √6-x
Answer:
There are no solutions. this equation seems wrong
Step-by-step explanation:
Let's find 3/4+1/10
First write the addition with a common denominator.
Then add. 3/4+1/10=?/?+?/?=?/?
Answer:
[tex]\frac{34}{40}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}+\frac{1}{10}[/tex]=[tex]\frac{30}{40}+\frac{4}{40}[/tex]=[tex]\frac{34}{40}[/tex]The area of a rectangle is 49d + 91
The length is an integer higher than 1, but is a known number.
Find the width of the rectangle.
Assuming that L and d are known numbers, we can write.
[tex]W = \frac{49d + 91}{L}[/tex]
How to get the width of the rectangle?
Remember that for a rectangle of width W and length L, the area is given by:
A = L*W
In this case, the area is 49d + 91, and the length is a known number, so we know the value of L.
Then we can write:
A = L*W = 49d + 91
To get the value of W, we need to isolate it on one side of the equation.
We can do that by dividing both sides by L.
[tex]W = \frac{49d + 91}{L}[/tex]
We assume that d and L are known, so with the above rational expression, we have W totally determined.
If you want to learn more about rational expressions:
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The catalog is advertising a stack of these cups that is 95 cm tall. Lori says, “That must be a misprint because a stack of that height is not possible.”
Do you agree or disagree with Lori? Explain your reasoning.
Answer:
in particular, the relationship between height of stack and number of cups yields a non-whole number of cups, corresponding to a height of 95 cm. In this context, that is not possible because we do not allow for parts of cups.
Step-by-step explanation:
It is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.
What is Area of Rectangle?The area of Rectangle is length times of width.
Assuming the cups are all the same size and shape, the height of the stack would depend on the number of cups in the stack.
if each cup is 5 cm tall, a stack of 19 cups would be 95 cm tall (19 x 5 = 95).
If the cups are irregularly shaped or have varying sizes, it may be more difficult to stack them in a way that reaches 95 cm in height.
It is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.
It is possible for some stacks of cups to reach this height, but not necessarily all stacks of cups.
Hence, it is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.
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