Answer:
The solutions to the equation are -3,-2,2
Step-by-step explanation:
x^3+3x^2=4x+12
Subtract 4x +12 from each side
x^3+3x^2-4x-12=4x+12-4x-12
x^3+3x^2-4x-12=0
I will use factoring by grouping
x^3+3x^2 -4x-12=0
I will factor out x^2 from the first group and -4 from the second group
x^2 (x+3) -4(x+3) =0
Now we can factor out (x+3)
(x+3) (x^2-4) =0
We can use the zero product principle since the right hand side is equal to 0
x+3 =0 x^2-4 =0
x+3-3=0-3 x^2 -4+4=0+4
x=-3 x^2=4
Take the square root of each side
sqrt(x^2) = sqrt(4)
x=±2
The solutions to the equation are -3,-2,2
(EASY) WILL MARK BRAINEST! Question: Write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph
(-9,-2) y=-4x+1
Answer:
y = -4x - 38
Step-by-step explanation:
Parallel lines are parallel because they never intersect. As such, they have the same slope. The slope of the line y = -4x + 1 is -4. Substitute m = -4 and the point (-9,-2) into the point slope form of a line.
[tex]y -y_1 = m(x-x_1)\\y --2 = -4(x --9)\\y + 2 = -4(x+9)\\[/tex]
Apply the distributive property to find the slope intercept form.
y + 2 = -4(x+9)
y + 2 = -4x - 36
y = -4x - 38
find the product: (2/3)(5/3)(21)
Answer:
Here is the following answers I got.
Step-by-step explanation:
(70/3)
23.3333
23 1/3
Would you use more centimeters or meters to measure the length of a car? Explain.
Answer:
Meters
Step-by-step explanation:
Because centimeters are to small to be a reasonable measurement for a car so you would have to use meters
Louis spins the spinner twice. Which probability are correct? Check all that apply
Answer:
Step-by-step explanation:
Only first one
P(both green) : [tex]\frac{1}{16}[/tex], P(both blue) : [tex]\frac{1}{4}[/tex], P(first orange and then blue) : [tex]\frac{1}{8}[/tex]
These probabilities are correct.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
According to the question
Louis spins the spinner twice.
Total number of favorable outcomes = {OB, OO, OB,OG, BB, BO, BB, BG, GG, GB, GO, GB, BB, BO, BB, BG} = 16
P(both green) :
Number of favorable outcomes = 1
P(both green) = [tex]\frac{1}{16}[/tex]
It is applicable.
P(both blue) :
Number of favorable outcomes = 4
P(both blue) = [tex]\frac{4}{16}[/tex] = [tex]\frac{1}{4}[/tex]
It is applicable.
P(first green and then blue) :
Number of favorable outcomes = 1
P(first green and then blue) = [tex]\frac{1}{16}[/tex]
P(first orange and then blue) :
Number of favorable outcomes = 2
P(first orange and then blue) = [tex]\frac{2}{16}=\frac{1}{8}[/tex]
It is applicable.
P(first orange and then green) :
Number of favorable outcomes = 1
P(first orange and then green) = [tex]\frac{1}{16}[/tex]
Hence,
P(both green) : [tex]\frac{1}{16}[/tex], P(both blue) : [tex]\frac{1}{4}[/tex], P(first orange and then blue) : [tex]\frac{1}{8}[/tex]
These probabilities are correct.
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Answer dis in a big hurry and will give brainliest!!!
Round 281 to the nearest whole number
Answer:um i belevie it is 300
Step-by-step explanation:
hope this helps
Answer:
281 is already a whole number
Step-by-step explanation:
There is no decimal point
Hope your day is great!
m∠A=(x+45)°,
mKE =(x+20)°,
mEW=(3x)° ,
Find: mKW.
Answer:
The measure of the arc KW is [tex]160\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<A=\frac{1}{2}(arc\ KE+arc\ EW)[/tex]
substitute the values and solve for x
[tex](x+45)\°=\frac{1}{2}(x+20+3x)\°[/tex]
[tex](2x+90)\°=(4x+20)\°[/tex]
[tex]4x-2x=90\°-20\°[/tex]
[tex]2x=70\°[/tex]
[tex]x=70\°/2=35\°[/tex]
Find the measure of the arc KW
[tex]arc\ KW=(arc\ KE+arc\ EW)=(4x+20)\°[/tex]
substitute the value of x
[tex]arc\ KW=4(35\°)+20\°=160\°[/tex]
Plz help me with it
Answer: a. 1
Step-by-step explanation:
[tex]\sqrt{2x+7}+1=\sqrt{2x+14}\\\\(\sqrt{2x+7}+1)^2=(\sqrt{2x+14})^2\\\\2x+7+2\sqrt{2x+7}+1=2x+14\\\\2x+8+2\sqrt{2x+7}=2x+14\\\\2\sqrt{2x+7}=6\\\\\sqrt{2x+7}=3\\\\(\sqrt{2x+7})^2=(3)^2\\\\2x+7=9\\\\2x=2\\\\x=1\\\\\\Check:\\\sqrt{2(1)+7}+1=\sqrt{2(1)+14}\\\\\sqrt9+1=\sqrt16\\\\3+1=4\ \checkmark[/tex]
Which expression does the fraction 3/8 represent?
1.8/3 2.3-8 3. 3/8 4. 3*8
Answer:
Im gonna guess and say it is answer 3.
Step-by-step explanation:
A line segment with endpoints (5,8) and (-6,8) is rotated around the origin 270 clockwise how long will the new segment be?
A rotation doesn't change the length of anything.
The length of the rotated line segment would be the same as the original line segment.
Because both Y values are the same, you just need to calculate the length of the X values.
5 to 0 = 5
0 to -6 = 6
Total length = 5 +6 = 11 units long.
2. The two figures are similar.
a) Write the similarity statement.
b) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
c) What is the scale factor? Explain.
Answer:
Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure.(the scale factor is greater than 1)
Part c) The scale factor is [tex]3[/tex]
Step-by-step explanation:
Part a) Write the similarity statement
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
substitute the values
[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45'}[/tex]
[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3'}[/tex] ----> is true
therefore
the figures are similar
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure. (the scale factor is greater than 1)
Part c) we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z------> the scale factor
x-----> corresponding side of the image
y------> corresponding side of the original figure
so
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=A'B'=27\ units[/tex]
[tex]y=AB=9\ units[/tex]
substitute
[tex]z=\frac{27}{9}=3[/tex]
The scale factor is greater than 1
therefore
Is an enlargement
Answer:(A) ab/a’b’=bc/b’c’=ac/a’c’ (B) Figure a’b’c’ is an enlargement because it increase it’s sides larger than 1. (C) So we have to divide to get the scale factor for both of these figures 18/6=3 then you found the scale factor 3.
Step-by-step explanation:
What is the answer????
ANSWER
f(x) is an odd function.
EXPLANATION
The given function is symmetric with respect to the origin.
Hence it is an odd function.
We can also see from the graph that,
[tex]f(1) = 2[/tex]
and
[tex]f( - 1) = - 2[/tex]
This implies that,
[tex]f( - 1) = - f(1)[/tex]
Since
[tex]f( - x) = - f(x)[/tex]
the function is odd.
The correct answer is A.
What is the product?
Answer:
So option B is the correct answer .
Step-by-step explanation:
Since it is the multiplication of 1 X 3 matrix to 3 X 3 order matrix,
so the resultant product should be 1 X 3 because when we multiply two matrices it is the condition that if A is of order p X q and B is of order q X r,
the product matrix (suppose C ) will be of order p X r.
so the product will be
= [-1*3+2*2+4*0 -1*6+2*4+4*6 -1*1+2*0+4*2]
= [ 1 26 7] .
The area of a circular trampoline is 112.07 square feet. What is the radius
Answer: The correct answer is B. 5.97 feet
Step-by-step explanation:
Formula⇒A=π r2
* Hopefully the work helps:) Mark me the brainliest;)!!!
Answer:
5.97 feet
Step-by-step explanation:
Set up your equation as 112.07 = Pi*r^2
To simplify, divide 112.07 by Pi or an approximation of it and then find the square root of your answer.
112.07 = Pi*r^2
112.07/Pi = r^2
(112.07/Pi)^0.5=r
rewrite lnx=4 as an exponential equation
rewrite as a logarithmic equation: e^8=y
[tex]\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ln(x)=4\implies log_e(x)=4\implies e^4=x \\\\\\ e^8=y\implies log_e(y)=8\implies ln(y)=8[/tex]
Mary has rehearsed her ballet solo for five and a half hours. A week from now, she wants to have rehearsed at least a total of nineteen and a half hours. If she rehearses for the same amount of time each day for the next 7 days, at least how many hours must she rehearse per day?
Answer:
2 hours per day
Step-by-step explanation:
19.5 - 5.5 = 14
14 / 7 = 2 hours per day
Mary needs to rehearse 2 hours per day for the next 7 days to meet her total rehearsal goal.
To calculate the total rehearsal time for Mary:
She has rehearsed for 5.5 hours.
She wants to rehearse a total of 19.5 hours.
Therefore, 19.5 - 5.5 = 14 hours
She needs to rehearse an additional 14 hours in the upcoming week.
To find out how many hours Mary must rehearse per day in the next 7 days:
14 / 7 = 2 hours/day
What is the approximate circumference of a circle with the diameter of 6
Circumference= [tex]2\pi r[/tex]
If the diameter is 6 the radius will be 3
[tex]2\pi (3)[/tex]
Circumference= 18.85
Hey there!
The formula for circumference is πd, where d is diameter.
We are given that the diameter is 6, so the circumference is 6π.
However, we are asked for the approximate circumference, not the exact.
So, let's use 3.14 as π and simplify.
6 x 3.14 = 18.84
The approximate circumference of a circle with the diameter of 6 is 18.84.
Hope this helps!
Brainliest + Points! Please help ^_^
Laura could sell her car for $18,000, and she owes $5,500 on it. Which statement best describes how this situation affects her net worth?
A.
Laura has an $18,000 asset and a $5,500 liability.
B.
Laura has a $15,500 asset and an $18,000 liability.
C.
Laura's car is considered a liability only because she still owes money on it.
D.
Laura's car is considered an asset only because it is worth more than she owes.
Laura has a $5,500 liability because that's what she owes and she is liable for it. She hasn't paid for it fully so the car has not become an asset. The answer is C.
Hope this helps
Answer:
I think th answer is A
Explanation:
Asset is a valuable or useful thing. The car is worth 18,000 so it is the asset. Liability is being responsible for things like debt, or something you own by law. She is responsible for the $5,500 she owes, so that is the liability. Hope this helps!
Carly draws quadrilateral JKLM with vertices J(-3,3), K(3,3), L(2,-1),and M(-2, -1). What is the best way to classify the quadrilateral?
Answer:
Trapezoid
Step-by-step explanation:
The points are shown in the attached graph.
You can clearly see from the picture that it is a "Trapezoid".
Trapezoid is basically a quadrilateral (4 sided-figure) that has 1/2 pair of parallel sides.
On the other hand, a parallelogram has 2 pair of parallel sides.
Thus, a parallelogram is a special type of trapezoid where there are 2 pair of parallel sides. But trapezoid need not be a parallelogram.
The picture shows 1 pair of parallel sides, hence it is a trapezoid.
help please asap thanks
Answer:B
Step-by-step explanation:Probably not A
B,C,D are probably the ones
but i think its b
All rectangles are parallelorams.Are all parallelograms rectangles? Explain
Answer:
See explanation
Step-by-step explanation:
Definitions of parallelogram and rectangle:
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
A rectangle is a parallelogram with four right angles.
This gives us that each rectangle is a parallelogram.
But an arbitrary parallelogram can have angles that are not necessarily right (for example, 60°, 120°, 60°, 120°). Thus, there are a lot of parallelograms that are not rectangles.
Three years ago, Sherman was twice as old as Clive. If Clive’s present age is c, which expression represents Sherman’s present age in terms of Clive’s age?
A.
2c − 3
B.
2c + 6
C.
2(c − 3)
D.
2c + 3
Erik is 4.23 feet tall. Stacy is 4.3 feet tall. Who is taller? Explain. Plssss answerrr
Answer:
Stacy
Step-by-step explanation:
4.23 < 4.3
Stacy is 0.07 feet taller than Erik, as of the given conditions.
Given that,
Erik is 4.23 feet tall. Stacy is 4.3 feet tall.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Heights
Stacy = 4.3 feet
Erik = 4.23 feet
Difference = 4.3 - 4.23 = 0.07 feet
Thus, Stacy is 0.07 feet taller than Erik, as of the given conditions.
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A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere.
ANSWER
[tex]V_{cone}=\frac{1}{3} \pi t^2k[/tex]
EXPLANATION
The volume of a cylinder is given by
[tex]V_{cylinder}=\pi r^2h[/tex]
The radius of the given cylinder is r=t.
The height of the cylinder is h=k.
The volume of the given cylinder is
[tex]V_{cylinder}=\pi t^2k[/tex]
The volume of a cone with the same base radius and height is
[tex]V_{cone}= \frac{1}{3} \pi t^2k[/tex]
Answer:
The correct answer is Option 2
1/3 πt²k
Step-by-step explanation:
points to remember
Volume of cone = 1/3 πr²h
Where r - Radius of cone and
h - Height of cone
To find the volume of given cone
Here radius of cone r = t and
Height of cone h = k
Therefore we can write,
volume of cone = 1/3 πr²h = 1/3 πt²k
Therefore the correct answer is option 2
If 3x-6=21, what is the value of x-2?
A. 3
B. 5
c. 7
D. 11
Answer:
[tex]\large\boxed{c.\ 7}[/tex]
Step-by-step explanation:
[tex]3x-6=21\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}-\dfrac{6}{3}=\dfrac{21}{3}\\\\x-2=7[/tex]
can someone help me?
The correct answer is B.
Hope this helps.
Answer:
San Fransisco
Step-by-step explanation:
If Geneva is 12°C colder than her hometown, this means that her hometown is 12°C warmer than -3°C.
Since warmer means a higher number, we find 12 + -3, which is 9°C.
The town that is 9°C is San Fransisco.
-2x+15y=-24
2x+9y=24
Answer:
x = 12 and y = 0
Step-by-step explanation:
Use elimination by adding the equations together.
-2x + 15y =-24
2x + 9y = 24
---------------
24y = 0
y=0
Then substitute y = 0 into one equation to find x.
-2x + 15(0) = -24
-2x + 0 = -24
-2x = -24
x = 12
Answer: x = 12 y = 0
Step-by-step explanation:
If 6 pencils cost $3.60 what is the unit price of the pencils
The unit price of one pencil is $0.60.
Explanation:The cost of one pencil (the unit price) can be found by dividing the total cost by the number of pencils. In this case, we have $3.60 divided by 6. This gives us a unit price of $0.60 per pencil.
Step by step solution
Identify the total cost, which is $3.60, and the total number of pencils, which is 6. Divide the total cost by the total number of pencils: $3.60 ÷ 6 = $0.60. Therefore, the unit price for these pencils is $0.60 each.Learn more about Unit Price here:
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I don’t get how the answer is one..
not sure how to factor/reduce what I was able to reduce to equal 1
Did I do something wrong
Answer:
see explanation
Step-by-step explanation:
Factorise the numerators on both fractions
a² + 10a + 25 = (a + 5)(a + 5) ← perfect square
a² - 25 = (a - 5 )(a + 5) ← difference of squares
To divide, leave the first fraction, change division to multiplication and turn the second fraction upside down.
Hence
= [tex]\frac{(a+5)(a+5)}{a+5}[/tex] × [tex]\frac{a-5}{(a-5)(a+5)}[/tex]
Cancel both the (a + 5) factors on the numerator/ denominators and the (a - 5) factor on the numerator/denominator, leaving
= 1 ← as required
Someone help me please
Answer:
Look at the picture
Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\\text{Therefore}\\\\f(x)=b^x\to y=b^x\\\\\text{find}\ f^{-1}(x).\ \text{Exchange}\ x\ \text{and}\ y\ \text{and solve for}\ y:\\\\b^y=x\qquad\text{logarithm iwth base b of both sides}\\\\\log_bb^y=\log_b(x)\qquad\text{use}\ \log_ab^m=m\log_ab\\\\y\log_bb=\log_b(x)\qquad\text{use}\ \log_aa=1\\\\y=\log_b(x)\\\\f^{-1}(x)=\log_b(x)\to g(x)=f^{-1}(x)\\\\\text{Then:}\ f(a)=b\to g(b)=a[/tex]