Answer:
(x + 6)(x - 2)
Step-by-step explanation:
To factor the quadratic
Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term ( + 4)
The factors are + 6 and - 2 since
+ 6 × - 2 = - 12 and + 6 - 2 = + 4, hence
x² + 4x - 12 = (x + 6)(x - 2)
If a = 22 ft, b = 10 ft, and c = 14 ft, what is the surface area of the geometric shape formed by this net?
A: 470 sq ft.
B: 580 sq ft.
C: 588 sq ft.
D: 668 sq ft.
Answer:
answer is 580 sq. ft.
Step-by-step explanation:
Find the value of x. 12.5, -10, -7.5, x; The mean is 11.5
11.55
sto you multiply sothat you can get the anster
need help with this
Answer:
x y
15 -1
12 0
9 1
6 2
3 3
0 4
Step-by-step explanation:
This is a function table. For a linear function, find the average rate of change between the listed points called slope. Then use the slope to fill in other inputs and outputs for the function.
[tex]m = \frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-12} =\frac{4}{-12} =- \frac{1}{3}[/tex]
This means for every 3 units made in the input, the function moves down 1 output.
x y
15 -1
12 0
9 1
6 2
3 3
0 4
30 points! I will give brainliest.
Consider the expression 6r – r + 8(15 – r) + 23 – 6 .
Part A Is –3r + 137 equivalent to the given expression? Write your answer in the space provided .
6r -4 +8(15-r) + 23
expand brackets
6r -4 +120 -8r + 23
collect like terms
120 + 23 - 4 = 139
6r - 8r = -2r
139 - 2r
139 - 2r = -3r + 137
-137 from both sides
-2r = -3r -2
add 3r
R = -2
sub in both equations and see if you get the same value
-3r + 137
-3 (-2) + 137
6 +137 = 143
139 - 2r
139 - 2(-2)
139 + 4
143
yes they are equal
Final answer:
After simplifying the given expression by combining like terms and using the distributive property, we find that the simplified form is indeed -3r + 137, which means it is equivalent to the original expression.
Explanation:
To determine if the expression -3r + 137 is equivalent to the given expression 6r – r + 8(15 – r) + 23 – 6, we need to simplify the given expression.
Let's simplify the given expression step-by-step:
Combine like terms: 6r - r = 5r.Distribute the 8 within the parentheses: 8(15) - 8(r) = 120 - 8r.Combine the constants: 23 - 6 = 17.Add the constant from step 3 to the constant from step 2: 120 + 17 = 137.Combine the results from steps 1 and 2: 5r - 8r = -3r.Add the results from steps 4 and 5 to get the simplified expression: -3r + 137.Therefore, the simplified form of the given expression is indeed -3r + 137, which means it is equivalent to the given expression.
A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft. Which expression represents the possible values of n, in feet? Express your answer in simplest terms. x – 1 < n < 3x + 5 n = 3x + 5 n = x – 1 3x + 5 < n < x – 1
Answer:
[tex]x-1<n<3x+5.[/tex]
Step-by-step explanation:
If a, b and c are the lengths of the triangle's sides, then
[tex]a+b>c,\\ \\a+c>b,\\ \\b+c>a.[/tex]
Since
[tex]a=2x+2,\\ \\b=x+3,\\ \\z=n,[/tex]
then
[tex]2x+2+x+3>n\Rightarrow n<3x+5,\\ \\2x+2+n>x+3\Rightarrow n>1-x,\\ \\x+3+n>2x+2\Rightarrow n>x-1.[/tex]
Thus,
[tex]x-1<n<3x+5.[/tex]
Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is A, 3x + 5 > n > x - 1.
What is triangle inequality theorem?Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b) > c
(b+c) > a
(c+a) > b
Given the three sides of the triangle 2x + 2 ft, x + 3 ft, and n ft. Now using the triangle inequality theorem we can write,
2x + 2 + x + 3 > n → 3x + 5 > n
2x + 2 + n > x + 3 → n > -x + 1
x + 3 + n > 2x + 2 → n > x - 1
Since x can not be a negative term therefore, we can write,
3x + 5 > n > x - 1
Hence, the correct option is A, 3x + 5 > n > x - 1.
Learn more about Triangle Inequality Theorem:
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On her way to visit her parents, Jennifer drives 265 miles in 5 hours. What is her average rate of speed in miles per hour?
Answer:
53 miles per hour
Answer:
53 miles
Step-by-step explanation:
Total Distance: 265
Then, take that number and divide by 5. 265/5
= 53
Question 1 options:
x2 +x − 4 = 0
You will solve this using the Quadratic Formula.
First, what are the values of a, b, and c?
a =
Answer:
x = 1.56 or x = -2.56
Step-by-step explanation:
From the equation;
x2 +x − 4 = 0
a = 1 , b = 1, and c = -4
x = (-b ± √(b² -4ac))/2a
= (-1 ± √(1²- 4×1×-4))/2
= ( -1 ± √(17)/2
= (-1 ± 4.12)/2
= (-1 + 4.12)/2 or (-1 - 4.12)/2
x = 1.56 or x = -2.56
Help with this problem on setting it up please! Thank you!
Answer:
The number of cones sold was 88
Step-by-step explanation:
Let
x------> the number of cones sold
y----> the number of sundaes sold
we know that
[tex]1.10x+2.35y=294.20[/tex] ----> equation A
[tex]x+y=172[/tex] ----> equation B
using a graphing tool
we know that
The solution of the system of equations is the intersection point both graphs
The intersection point is (88,84)
see the attached figure
therefore
The number of cones sold was 88
The number of sundaes sold was 84
What is the volume of the prism
The volume of a rectangular prism or cube is: Length × Width × Height
In this case,
- the length of the prism is 2 feet
- the width of the prism is 1.5 feet
- the height of the prism is 1.5 feet
Multiply the above to find the volume: 2 × 1.5 × 1.5 = 4.5 ft³
Keep in mind that volume is represented in cubic units!
[tex]\text{Hey there!}[/tex]
[tex]\text{Formula: v = lwh}[/tex]
[tex]\text{l = length}\\\text{w = width}\\\text{h = height}[/tex]
[tex]\text{L = 2}[/tex]
[tex]\text{W = 1}\frac{1}{2}\text{ also known as 1.5}[/tex]
[tex]\text{H = 1}\frac{1}{2}\text{ also known as 1.5}[/tex]
[tex]\text{1}\frac{1}{2}\times1\frac{1}{2}\text{ = }\frac{3}{2}\times\frac{3}{2}=2\frac{1}{4}[/tex]
[tex]4\frac{1}{2}\times2=4\frac{1}{2}[/tex]
[tex]\boxed{\boxed{\bf{Answer: Fraction\rightarrow4\frac{1}{2}ft^2\ \& Decimal: 4.5ft^2}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Simplify 3 sqrt 2 × 3 sqrt 3
Answer:
[tex]9\sqrt{6}[/tex]
Step-by-step explanation:
Multiply the numbers outside of the radicand, which is 3 x 3 = 9.
Then multiply the numbers inside of the radicand, which is 2 x 3 = 6.
Therefore the answer is [tex]9\sqrt{6}[/tex].
Edit:
Is this what the problem looks like?
[tex]3\sqrt{2}[/tex] x [tex]3\sqrt{3}[/tex]
(p+q)*(p-q) can you show the process
Answer:
p²-q²
Step-by-step explanation:
(p+q)×(p-q)
=p×(p-q)+q×(p-q)
=p×p-p×q+p×q-q×q
=p²-p×q+p×q-q²
=p²-q²
Sean uses the point (10, 8) to represent the location of his house and uses the point (1, 3) to represent the
location of the gym. Each unit on the graph represents 1 mi. How far is the gym from Sean’s house? Round to
the nearest tenth. Show your work.
Answer:
[tex]10.3\ mi[/tex]
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(10,8)\\B(1,3)[/tex]
substitute the values
[tex]d=\sqrt{(3-8)^{2}+(1-10)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(-9)^{2}}[/tex]
[tex]d=\sqrt{25+81}[/tex]
[tex]d=\sqrt{106}[/tex]
[tex]d=10.3\ mi[/tex]
Travis are 2/3 of a small pizza Kai are 11/15 of a small pizza who ate more?
Answer:
11/15
Step-by-step explanation:
If you convert them to a decimal 11/15 would be more
what is the mode for the data set 49,47,46,40,48,41,44,49,45,42,43
Mode: the number that occurs the most in a set of data.
Although it's optional, I always like to order the numbers from least to greatest so it makes it easier to see what number repeats more than anything else.
Least to greatest - 40,41,42,43,44,45,46,47,48,49,49
The mode for this set of data is 49. The mode is 49 because 49 is the only number that occurs more than once. No other numbers in this set of data appear twice except 41.
rewrite the function f(x)=x^2-6x-60 by completing the square
To rewrite f(x) = x^2 - 6x - 60 by completing the square, you add and subtract (6/2)^2 within the equation and refactor to get f(x) = (x - 3)^2 - 69, with the vertex at (3, -69).
To rewrite the function f(x) = x^2 - 6x - 60 by completing the square, follow these steps:
Write the equation in the form x^2 - bx = c.Find (b/2)^2, which is the number to be added to both sides to complete the square. For our equation, (6/2)^2 = 9.Add and subtract this number inside the equation. So you have: f(x) = x^2 - 6x + 9 - 9 - 60.Rewrite the quadratic part as a binomial square: f(x) = (x - 3)^2 - 69.The function is now in the completed square form. The vertex of this parabola is at (3, -69).
There are 29 pencils in a basket. 7 of these pencils are green. The rest of them are yellow.
(A) what is the ratio of yellow pencinls to green pencils?
(b) what is the ratio of all pencils in the basket to yellow pencils
[tex]\huge\boxed{22:7}\ \huge\boxed{29:22}[/tex]
First, we need to find the number of yellow pencils in the basket. We'll represent the number of green pencils with [tex]g[/tex] and the number of yellow pencils with [tex]y[/tex].
[tex]\begin{aligned}7+y&=29&&\smash{\Big|}&&\text{Start with what we already know.}\\y&=22&&\smash{\Big|}&&\text{Subtract 7 from both sides.}\end{aligned}[/tex]
Our first ratio is [tex]y:g[/tex], or [tex]\boxed{22:7}[/tex].
The second ratio is [tex](g+y):y[/tex]:
[tex]\begin{aligned}(g+y)&:y\\(7+22)&:22\\29&:22\end{aligned}[/tex]
Consider the expression below. Place the steps required to determine the sum of the two expressions in the correct order. 3x+6/x^2-x-6 + 2x/x^2+x-12
Answer:
1) Factor the denominator and the numerator of each fraction.
2) Simplify.
3) Find the Least common denominator (LCD).
4) Rewrite the LCD. Divide it by the denominator of the first fraction and multiply the result of the division by its numerator (The LCD is the same denominator of the second fraction, so its numerator stays the same).
5) Apply Distributive property on the numerator and on the denominator.
6) Add like terms.
Step-by-step explanation:
The steps required to determine the sum of the two expressions are:
1) Factor the denominator and the numerator of each fraction:
[tex]\frac{3x+6}{x^2-x-6}+\frac{2x}{x^2+x-12}=\frac{3(x+2)}{(x-3)(x+2)}+\frac{2x}{(x-3)(x+4)}[/tex]
2) Simplify (Remember that [tex]\frac{(x+2)}{(x+2)}=1[/tex]):
[tex]\frac{3}{(x-3)}+\frac{2x}{(x-3)(x+4)}[/tex]
3) Find the Least common denominator (LCD). In this case this is:
[tex]LCD=(x-3)(x+4)[/tex]
4) Rewrite the LCD. Divide it by the denominator of the first fraction and multiply the result of the division by its numerator. As the LCD is the same denominator of the second fraction, its numerator stays the same:
[tex]=\frac{3(x+4)+2x}{(x-3)(x+4)}[/tex]
5) Apply Distributive property on the numerator and on the denominator:
[tex]=\frac{3x+12+2x}{x^2+x-12}[/tex]
6) Add like terms:
[tex]=\frac{5x+12}{x^2+x-12}[/tex]
Answer:
x-5 edg
Step-by-step explanation:
how many solutions can be found for the equation 4X equals 4X
ZERO
ONE
TWO
INFINITELY MANY
Answer: Simplifying
4x = 4x
Add '-4x' to each side of the equation.
4x + -4x = 4x + -4x
Combine like terms: 4x + -4x = 0
0 = 4x + -4x
Combine like terms: 4x + -4x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Can someone please tell me if my answers are correct??
Answer:
I think they are all correct but 2 and 4 might be wrong. (I don't see the shapes very well.)
I can't see that well but on #2, can't you half it? If you can, it has 1 line of Symmetry. If you can't, it has no lines of symmetry
On #4, you might be able to half it from the lower left corner and the upper right corner. If it works, there is 1 line of symmetry, if it doesn't it has none
determine the domain and range of the function f(×)=
[tex]2 \sqrt[3]{108} 2x[/tex]
Answer:
Simplifies to:
748.245949x
Find a mixture that will make the same shade of green but a larger amount
Answer:
It would be blue and yellow
Step-by-step explanation:
Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3). A) y = − 1/5 x + 16/5 B) y = −5x − 5/16 C) y = 5x + 10 D) y = 1/5 x − 2
Answer:
A
Step-by-step explanation:
Parallel lines have the same slope. Find the slope by converting the equation x + 5y = 10 into y = mx+b form. It becomes y = -1/5x + 2. The slope is -1/5.
Substitute -1/5 and the point (1,3) into the point slope form.
[tex]y - y_1 = m(x-x_1)\\y - 3 = -\frac{1}{5}(x - 1)\\y - 3 = -\frac{1}{5}x + \frac{1}{5}\\y = -\frac{1}{5}x + \frac{16}{5}[/tex]
Answer:
It's aaaaaaaaaaaaaaaaaaaaaaa!!!
Step-by-step explanation:
choose the system of inequalities that best matches the graph below.
a) y<2x+2, y<x
b) y<2x, y<_x
c) y<_x-2, y>-x
D) y<2x+2, y> -x
Answer:
D) [tex]y\:<\:2x+2[/tex], [tex]y\:>\:-x[/tex]
Step-by-step explanation:
The blue boundary line has a y-intercept of 2 and a slope of 2.
It has equation : [tex]y=2x+2[/tex]
Since the boundary line is not solid and the lower half plane of this line is shaded, its inequality is
[tex]y\:<\:2x+2[/tex]
The blue boundary line passes through the origin and has slope [tex]-1[/tex].
Its equation is [tex]y=-x.[/tex]
Since the boundary line is not solid and the right half-plane is shaded, its inequality is [tex]y\:>\:-x[/tex]
The correct choice is D.
The correct choice is D: y < 2x + 2, y > -x.
The blue boundary line is represented by the equation y = 2x + 2.
Since the lower half-plane is shaded, the inequality is y < 2x + 2.
The blue boundary line also passes through the origin and has a slope of -1, which gives it the equation y = -x.
Since the right half-plane is shaded, the inequality is y > -x.
So, the correct choice is D: y < 2x + 2, y > -x.
for such more question on boundary line
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a fair die is cast four times. Calculate the probability of obtaining exactly two 6's
Answer:
25/216 or 0.1157
Step-by-step explanation:
The probability of getting a 6 is 1/6.
The probability of not getting a 6 is 5/6
We roll a die 4 times and want 2 sixes, and 2 not sixes.
We want a combination of 2 sixes from 4 rolls, so we can use the binomial formula to solve this...
(4C2)(1/6)²(5/6)² = 6(1/36)(25/36) = (1/6)(25/36) = 25/216 = 0.1157
The long hand way of solving this is to list the 6 ways we can roll our desired result along with their probabilities...
We could get
6, 6, not 6, not 6 (1/6)(1/6)(5/6)(5/6) = 25/1296
6, not 6, 6, not 6 (1/6)(5/6)(1/6)(5/6) = 25/1296
6, not 6, not 6, 6 (1/6)(5/6)(5/6)(1/6) = 25/1296
not 6, not 6, 6, 6 (5/6)(5/6)(1/6)(1/6) = 25/1296
not 6, 6, not 6, 6 (5/6)(1/6)(5/6)(1/6) = 25/1296
not 6, 6, 6 not 6 (5/6)(1/6)(1/6)(5/6) = 25/1296
There are 6 different way this can happen, each having a probability of 25/196. We add up the probabilities, getting 150/1296, which reduces to
25/216
Answer:
11.6%
Step-by-step explanation:
[tex]\frac{4!}{2!\left(4-2\right)!}\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)^2 = 0.116 = 11.6[/tex]
can u help me with unit rates
Answer:
sure
Step-by-step explanation:
unit rates are similar to rates.
rates are : 20/2
and unit rates are very similar: 10/1
unit rates are never 5/4, 6/10, 9/2, or 3/2 because unit rates are always loney and single having the denominator one
ex: 2/1, 4/2, 6/2, 8/2, 10/2
2/1 in the sequence is the only unit rate. and remember there can not be more than one unit rate in a sequence.
plz give me a brainliestttttt
Answer:
Unit Rates are any numbers over one.
For example:
A car is driving 60 miles per hour. So that is a unit rate because it is expressed over one.60/1
Step-by-step explanation:
Which value is equivalent to x-7/7-x
Answer:
[tex]\large\boxed{\dfrac{7-x}{x-7}=-1}[/tex]
Step-by-step explanation:
[tex]\dfrac{7-x}{x-7}=\dfrac{-(x-7)}{x-7}\\\\\text{cancel}\ (x-t)\\\\\dfrac{7-x}{x-7}=\dfrac{-1}{1}\\\\\dfrac{7-x}{x-7}=-1[/tex]
Answer:
-1
Step-By Step:
The Answer on Ed
Could someone please help me
Answer:
c
Step-by-step explanation:
I think its c but I could be wrong
In a classroom,
3
-
10
of the students are wearing blue shirts , and
3
-
5
are wearing white shirts. There are 30 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts?
Answer:
i did this question b4 but completely forgot the answer ://
Step-by-step explanation:
If two sides of one triangle are proportional to two sides of another and included angles are equal, then the triangles are similar. True False
Answer:
True
Step-by-step explanation:
It was correct on my quiz
Help! Please! Brainliest answer offered!!
your answer is 1 :) hope this helps
Answer:
It's B) 1
Step-by-step explanation:
(3)(2x)+(3)(−1)=( 1 2 )(4x)+( 1 2 )(−2)+2(Distribute)
6x−3=2x+1
6x−3−2x=2x+1−2x
4x−3=1
4x−3+3=1+3
4x/4 = 4/4
x = 1
i know confusing