Answer:
(-6, -36)
Step-by-step explanation:
The vertex [tex](h,k)[/tex] of a function of the form [tex]f(x)=ax^2+bx+c[/tex] is given by the formula:
[tex]h=\frac{-b}{2a}[/tex]
[tex]k=f(h)[/tex] in other words, we find h and then evaluate function at h to find k.
We know from our function that [tex]a=1[/tex], [tex]b=12[/tex].
Replacing values
[tex]h=\frac{-12}{2(1)}[/tex]
[tex]h=-\frac{12}{2}[/tex]
[tex]h=-6[/tex]
Now we can evaluate our function at -6 to find k:
[tex]k=f(h)=f(-6)[/tex]
[tex]k=(-6)^2+12(-6)[/tex]
[tex]k=36-72[/tex]
[tex]k=-36[/tex]
We can conclude that the vertex (h, k) of our function is (-6, -36)
Answer:
(-6,-36)
Step-by-step explanation:
The given function is
[tex]f(x)=x^2+12x[/tex]
We complete the square to write this function in the vertex form.
Add and subtract the square of half the coefficient of x.
[tex]f(x)=x^2+12x+6^2-6^2[/tex]
[tex]f(x)=x^2+12x+36-36[/tex]
The first three terms is now a perfect square trionomial
[tex]f(x)=(x+6)^2-36[/tex]
Or
[tex]f(x)=(x--6)^2-36[/tex]
The function is now in the form:
[tex]f(x)=a(x-h)^2+k[/tex]
where h=-6 and k=-36
The vertex is therefore (h,k)=(-6,-36)
Write the given equation in slope-intercept form, y=mx+b by solving for y. 4x - 2y =10
y = 2x - 5
Here’s a photo of the math
The equation will be y = 2x - 5
Given Equation: 4x - 2y = 10
Step 1: Move 4x to the other side to isolate -2y: -2y = -4x + 10
Step 2: Divide by -2 to solve for y: y = 2x - 5
I need the answers for 1 a-d pleas
We want to find a fraction that is between
[tex]\frac{1}{4}\:and\:\frac{1}{2}[/tex]
There are several ways to go about this.
There are also infinitely many fractions that can be found between the given fractions.
Let us go for the one in the middle of the two fractions.
So we add the two fractions and divide by 2.
a) [tex]\frac{\frac{1}{4} +\frac{1}{2} }{2}[/tex]
Find LCM for the numerator
[tex]\frac{\frac{1+2}{4}}{2}[/tex]
Simplify:
[tex]\frac{\frac{3}{4}}{2}[/tex]
[tex]\frac{\frac{3}{2}}{2}[/tex]
[tex]\frac{3}{8}}[/tex]
b) [tex]\frac{\frac{1}{3} +\frac{3}{4} }{2}=\frac{13}{24}[/tex]
c)[tex]\frac{\frac{1}{2} +\frac{3}{4} }{2}=\frac{5}{8}[/tex]
d)[tex]\frac{\frac{3}{5} +\frac{7}{8} }{2}=\frac{59}{80}[/tex]
Which of the following could represent the scale factor of the larger figure to the smaller figure
Answer:
C. 3:2
D. 21:14
Step-by-step explanation:
The scale factor of the larger figure to the smaller figure is the factor
that gives the dimensions of the smaller figure from the larger figure.
Correct response:
The possible scale factor of the larger to smaller figure is 3:2Method used for the calculationThe possible dimensions given in the question as obtained from a similar question are;
Diameter of a smaller cylinder = 12 m
Diameter of a larger cylinder = 18 m
The scale factor of the larger figure to the small figure is given by ratio
of the diameter diameters is found by dividing the diameter of the larger
figure by the diameter of the smaller figure as follows;
[tex]\mathbf{\dfrac{Larger \ diameter}{Smaller \ diameter} } = \dfrac{18}{12} = \dfrac{3}{2} [/tex]The ratio is 3:2
Therefore;
The possible scale factor of the larger figure to the smaller figure is 3:2Learn more about scale factors here:
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Please Help , Is it ABC or D
Answer:
A
Step-by-step explanation:
To determine the scale factor compare the quotient of the coordinates of the image with the original coordinates
A
[tex]\frac{2}{1}[/tex] = [tex]\frac{4}{2}[/tex] = 2
B
[tex]\frac{4}{2}[/tex] = [tex]\frac{8}{4}[/tex] = 2
C
[tex]\frac{8}{4}[/tex] = [tex]\frac{16}{8}[/tex] = 2
Hence the scale factor is 2
Simplify 12√18-6√20-3√50-8√45
12√18-6√20-3√50-8√45
*Break each radical up into the product of a radical of a perfect square and a second radical*
12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)
*Simplify the radicals*
12(3√2)-6(2√5)-3(5√2)-8(3√5)
*Distribute*
36√2-12√5-15√2-24√5
*Combine like terms*
21√2-36√5
Hope this helps!!
The simplified form of the expression is 21√2-36√5.
Given,
12√18-6√20-3√50-8√45
Here,
12√18-6√20-3√50-8√45
⇒ Break each radical up into the product of a radical of a perfect square and a second radical.
Rewriting the expression,
12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)
⇒ Simplify the radicals
12(3√2)-6(2√5)-3(5√2)-8(3√5)
⇒ Distributive property
36√2-12√5-15√2-24√5
⇒ Combine like terms
21√2-36√5
Thus the simplified expression is 21√2-36√5.
Know more about radicals,
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Which choice correctly describes this event? Every time I flip a coin I will get tails. PLEASE HELP ASAP!!
Answer:
If the coin is fair, then the chances of you getting heads is equal to the chances of getting heads. This means the chances of always getting tails on a fair coin is close to nothing, if not 0.
Step-by-step explanation:
Answer:
The answer is unlikely
Step-by-step explanation:
PLEASE HELP 13 POINTS
Answer: 6/15-5/15=1/5
Answer:
Step-by-step explanation:
To find the common denominator, you must multiply 5 times three to get fifteen. Then you must multiply two times three and then one times three. Your two fractions with the same denominator would be 6/15 minus 5/15 your answer would be 1/15
Colin invests £1200 into his bank account. He receives 3% per year simple interest. How much will Colin have after 4 years? Give your answer to the nearest penny where appropriate.
Colin will have £1344 in his bank account after 4 years. This is calculated using the simple interest formula I = PRT (Interest = Principal x Rate x Time) yielding an interest earned of £144 over four years, which was then added to the initial investment.
Explanation:First, understand that simple interest is calculated as (principal amount × interest rate × time in years). The principal amount here is £1200, the interest rate is 3%, and the time period is 4 years.
Before doing the calculation, convert the 3% interest rate into decimal form by dividing by 100, yielding 0.03.
War is represented by the formula I = PRT, which means Interest = Principal x Rate x Time. So, use these values in the formula: £1200 * 0.03 * 4. This gives you £144, which is the interest earned after 4 years.
To find the total amount in Colin's account after 4 years, you need to add the interest earned to the principal amount. Therefore, £1200 (original amount) + £144 (interest) = £1344.
So, after 4 years, Colin will have £1344 in his bank account.
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Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x. Add: x 5 - 4x 4 + 7x 3 + 8, 9x 3 + 7x 2 - 10, and -2x 5 + 7x 4 - 3x + 8.
Answer:
[tex]-x^5+3x^4+16x^3+7x^2-3x+6[/tex]
Step-by-step explanation:
Given polynomials are:
[tex]x^5-4x^4+7x^3+8[/tex], [tex]9x^3+7x^2-10[/tex] and [tex]-2x^5+7x^4-3x+8[/tex]
Now we need to add the given polynomials, then place the answer in the proper location on the grid. Also we need to write answer in descending powers of x.
So let's add them by combining like terms:
[tex]x^5-4x^4+7x^3+8+9x^3+7x^2-10-2x^5+7x^4-3x+8[/tex]
[tex]-x^5+3x^4+16x^3+7x^2-3x+6[/tex]
Hence final answer in descending order is [tex]-x^5+3x^4+16x^3+7x^2-3x+6[/tex]
Which pair of angles are supplementary?
A) 1 and 4
B) 1 and 5
C) 3 and 5
D) 7 and 2
will mark brainliest if correct and give 50 pts.
Supplementary angles are angles that add up to 180 degrees, aka one straight line. The supplementary angles here are:
1 and 2, 1 and 3, 2 and 4, 3 and 4, 5 and 6, 6 and 8, 7 and 8, and 6 and 7. Well, those are the more obvious ones. 1 and 7 are supplementary because if you envision them next to each other, you’ll see that they create a straight line. So, with that logic, 3 and 5 are supplementary because when you put them together, they create a straight line
Angle ∠5 and angle ∠3 are supplementary angles. Then the correct option is C.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
From the figure, the supplementary are given below.
The angles ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6, ∠7 and ∠8, ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, and ∠6 and ∠8 are supplementary angles.
The sum of angle ∠5 and angle ∠3 is 180 degrees.
Then Angle ∠5 and angle ∠3 are supplementary angles.
Then the correct option is C.
More about the angled link is given below.
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Which expression is equivalent to (x2 – 3x)(4x² + 2x - 9)
Answer:
[tex]\large\boxed{(x^2-3x)(4x^2+2x-9)=4x^4-10x^3-15x^2+27x}[/tex]
Step-by-step explanation:
[tex](x^2-3x)(4x^2+2x-9)\qquad\text{use}\ (a+b)(c+d+e)=ac+ad+ae+bc+bd+be\\\\=(x^2)(4x^2)+(x^2)(2x)+(x^2)(-9)+(-3x)(4x^2)+(-3x)(2x)+(-3x)(-9)\\\\=4x^4+2x^3-9x^2-12x^3-6x^2+27x\qquad\text{combine like terms}\\\\=4x^4+(2x^3-12x^3)+(-9x^2-6x^2)+27x\\\\=4x^4-10x^3-15x^2+27x[/tex]
Heston wagons reported in June that 20 out of 500 wagons failed inspection. In July they reported that 25 out of 625 wagons failed inspection.which proportion can be used to represent the wagon failures?
Answer:
The proportion is [tex]\frac{y}{x} =\frac{1}{25}[/tex]
Step-by-step explanation:
We have to:
In June 20 of 500 wagons failed
On July 25 of 625 wagons failed
If we call x the number of wagons and and the number of wagons that had failures then we have to for June:
[tex]\frac{y}{x} = \frac{20}{500}\\\\\frac{y}{x} = \frac{1}{25}[/tex]
For July we have
[tex]\frac{y}{x} = \frac{25}{625}\\\\\frac{y}{x} = \frac{1}{25}[/tex]
The proportions are the same for both months
[tex]\frac{20}{500} = \frac{25}{625}[/tex]
The proportion is [tex]\frac{y}{x} =\frac{1}{25}[/tex]
This means that of every 25 wagons, one has faults
Answer:
its D
Step-by-step explanation:
hope it helps!
took a test!
Use the counting principle to determine the number of possible outfits that can be created using one item from each category.
7 shirts
6 pairs of pants
6 pairs of socks
4 hats
Answer:
1008
Step-by-step explanation:
To find the total outfits that can be created, we multiply the different number of stuff together. So the answer is 7*6*6*4 = 1008 outfits.
Answer:
I think it would be 1008.
Step-by-step explanation:
Hope this helps!!
help me, I'll give 20 points. Thank you!
Answer:
Step-by-step explanation:
I think it might be the third one
How do you do these type of questions??? Answer????
Let the number of marbles Tim has = X
Then Sue has twice as many, so she has 2X
Jim has 15.
All three of them when added together have 63:
x + 2x + 15 = 63
Combine like terms:
3x +15 = 63
Subtract 15 from both sides:
3x = 48
Divide both sides by 3:
X = 48 /3
x = 16
Tim has 16 marbles.
Arrange the steps to perform this subtraction operation in the correct order.
(1.93x10 to the power of 7) - (9.7x 10 to the power of 6)
Answer with explanation:
W have to find the value of :
[tex][A=1.93 \times 10^7] - [B=9.7 \times 10^6][/tex]
Here exponent of 10 differs in both of these terms. So, to find the difference of A and B, we should make exponent of 10 equal in both the terms.
Exponent of A is Higher,so we will try to make this equal to exponent of 10 in B.
[tex]A=1.93 \times 10^7\\\\A=19.3 \times 10^6\\\\A-B=19.3 \times 10^6-9.7 \times 10^6\\\\=(19.3-9.7) \times 10^6\\\\=9.6\times 10^6[/tex]
Answer:
There you go
Step-by-step explanation:
help me with #3 please please and explain
all you have to do is 524 times 2 and then add m3
there is a formula for the volume of a cylinder. use the given info to plug into formula
Help please answer these questions its comfusing me
Answer:
A pentagonal prism has 7 faces, 10 vertices, and 15 edges.
Step-by-step explanation:
Answer:
7, 15, 10
Step-by-step explanation:
The best thing to do is look a picture of a pentagonal prism first.
A pentagonal prism has two parallel pentagons as the bases and 5 lateral faces. The total number of faces is 7.
Each base has 5 edges. Then there are 5 edges from base to base. The total number of edges is 15.
Each base has 5 vertices. The total number of vertices is 10.
How to get 354 by regrouping
Answer: 627-273
Step-by-step explanation:
Suppose that you ask three friends to go to the mall. Each one has a 0.70 chance of saying yes. What is the probability that all three friends will say they can go to the mall with you? a. 0.027 c. 0.343 b. 0.21 d. 0.657
____________________________________________________
Answer:
Your answer would be 0.343.
____________________________________________________
Step-by-step explanation:
In the probability questions like this one, in order to get the answer,we would use the multiplication rule.
In your questions, we are trying to find the probability of ALL of your friends going to the mall with you.
Lets make it easier for you.
Whenever in probability you can say and, you multiply.
This means that you would try to find if friend 1 and friend 2 and friend 3 will say yes.
That's the same as saying friend 1's probability × friend 2's probability × friend 3's probability
We know that each friend has a 0.70 chance of saying yes.
Using the multiplication rule, we would just multiply 0.7 three times.
[tex]0.7 *0.7*0.7=0.343[/tex]
When you multiply, you should get 0.343.
There is a 0.343 chance of ALL your friends saying yes to go to the mall with you.
0.343 would be your FINAL answer.
____________________________________________________
To solve this problem, you need to consider the probability of each friend agreeing to go to the mall individually, then multiply these probabilities together to find the probability that all three will say yes.
Since each friend has a 0.70 chance of saying yes, we can calculate the combined probability as follows:
For the first friend, the probability is 0.70.
For the second friend, the probability is also 0.70.
For the third friend, the probability remains 0.70.
To find the combined probability that all three friends will say yes, we multiply the individual probabilities together:
\( Probability (All Say Yes) = Probability (Friend1 says Yes) \times Probability (Friend2 says Yes) \times Probability (Friend3 says Yes) \)
\( Probability (All Say Yes) = 0.70 \times 0.70 \times 0.70 \)
When you calculate this, you get:
\( Probability (All Say Yes) = 0.343 \)
So the answer is c. 0.343.
What is the initial value of the function represented by this table?
x y
0 5
1 9
2 13
A) 0
B) 3
C) 4
D) 5
Answer:
Option D. 5
Step-by-step explanation:
we know that
The initial value of the function is the y-intercept, so is the value of the function when the value of x is equal to zero
In this problem observing the table
For x=0
The value of y is equal to y=5
therefore
The initial value is 5
Answer:
It is 5!
Step-by-step explanation:
I just did the test and got it correct.
The total distance around a running track is 1 5/8 miles. Wayne ran 1/4 of the track. What equation can be used to find d, the distance in miles that Wayne ran?
Answer:
1 5/8 * 1/4 = d
Step-by-step explanation:
how do i graph the lines when the equations aren’t in slope intercept form????
Slope-Intercept Form: y=mx+b
Standard Form: ax+by=c
Point- Slope: (y-y1)= m(x-x1)
There are multiple answers to your question-
If you are only missing b(the y-intercept) but are given a set of points, plug the points into x and y and solve for b.If you are only missing the slope(m) but are given a set of points, plug the points into x and y and solve for m.If you are given the standard form/point-slope form, change the equation to slope intercept form. If you are given an complete form(there is an x and y; no missing variables), but are not sure what it is, plug in some numbers in x to find y, then graph.given x-5>-2 choose the solution set
x -5 > -2
Add 5 to both sides:
x > 3
The answer is the 3rd choice.
Answer:
x>3
Step-by-step explanation:
just add 5 to both sides :p
what is the volume of the cone with radius 6 inches and height 10 inches express the answer in terms of pi
Answer:
V = (1/3)(π)(6 in)²(10 in) = 120π in³
Step-by-step explanation:
The volume of a cone of radius r and height h is V = (1/3)πr²h.
Here, that volume is V = (1/3)(π)(6 in)²(10 in) = 120π in³
Answer:
120pi
Step-by-step explanation:
Is .9 greater or less than 95%?
Less than 95%
Why because if you change .9 into a percentage, it turns into 90%
I hope that was correct
[tex]\text{Hey there!}[/tex]
[tex]\text{Is .9 greater or less than 95\%?}[/tex]
[tex]\bf{.9\rightarrow0.9\rightarrow\frac{18}{20}}[/tex]
[tex]\bf{95\%\rightarrow0.95\rightarrow\frac{19}{20}}[/tex]
[tex]\bf{You\ could\ reask\ yourself\ is\frac{18}{20}\ greater\ or\ less\ than\frac{19}{20}}?[/tex]
[tex]\text{Note: Solve the fractions/ decimals/ percentages to where you can}[/tex] [tex]\text{understand it better}[/tex]
[tex]\text{After that you'd find your result to your question}[/tex]
[tex]\boxed{\boxed{\text{Thus your answer will be: .9 is LESS THAN 95\%}}}[/tex] [tex]\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Find the vertical, horizontal, and slant asymptotes, if any, for f(x)=5x^3-51x^2+77x+100/x^2-11x+24
Answer:
Step-by-step explanation:
Given: f(x)=5x^3-51x^2+77x+100/x^2-11x+24
Please use parentheses to eliminate any ambiguity:
f(x) = (5x^3-51x^2+77x+100) / (x^2 - 11x + 24)
or (better yet):
5x^3-51x^2+77x+100
f(x) = ---------------------------------
x^2 - 11x + 24
The vertical asymptotes here are at the zeros of the denominator:
x^2 - 11x + 24 = 0, This quadratic equation has coefficients a = 1, b = -11 and c = 24. Thus, its roots (zeros) are:
-(-11) ± √( 121 - 4(1)(24) )
x = -------------------------------------
2(1)
or:
11 ± √( 25 )
x = --------------------
2
or: x = 8 and x = 3
The vertical asymptotes are x = 8 and x = 3.
If we attempt to divide x^2 - 11x + 24 into 5x^3 - 51x^2 + 77x + 100, we see that the first term of the quotient is 5x. As x increases or decreases without bound, 5x goes to either ∞ or -∞, so we conclude that there is no horiz. asymptote. Continuing this division results in:
5x + 4 + a fraction
This represents the slant asymptote, y = 5x + 4
Answer:
5x+4
Step-by-step explanation:
edge 2020 2021
I think of a number, multiply it by three, and add four. I get twenty two.
Using the statement above, form an equation. Use the letter x for the unknown number.
Answer:
3x+4=22
Step-by-step explanation
So, if you minus 4 from 22 and divided by 3, there will be the answer for x. Which is 6.
The equation that could be formed using the letter x to be represent the unknown number is 3x + 4 = 22
let
x = the unknown number
multiply it by three
= x × 3
= 3x
add four
3x + 4
I get twenty two
3x + 4 = 22
solve for x
3x = 22 - 4
3x = 18
x = 18/3
x = 6
Therefore, the unknown number in the equation 3x + 4 = 22 is 6
check:
3x + 4 = 22
3(6) + 4 = 22
18 + 4 = 22
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Jose traveled 315 miles in 7 hours. Based on this rate, how many miles did Jose travel in one hour?
45 miles in one hour. You take the total of 315 and divide that by the 7 hours and that gives you how much is in the one hours
Answer:
45 MPH
Step-by-step explanation:
To find the unit rate - divide the total miles driven by the total number of hours
315/7 = 45 miles per hour
A recipe for cookies requires 2/3 cup of butter. Anna wants to make 1/4 of the recipe. How many cups of butter should Anna use to make the cookies? You must
Answer:5/12
Step-by-step explanation:2/3-1/4=5/12
For this case we must raise a rule three:
1 recipe ----------------------->[tex]\frac {2} {3}[/tex] butter
[tex]\frac {1} {4}[/tex]recipe -------> x
Where the variable "x" represents the amount of butter that requires a quarter of the cookie recipe.
[tex]x = \frac {\frac {1} {4} * \frac {2} {3}} {1}\\x = \frac {2} {12} = \frac {1} {6}[/tex]
So, Anna requires[tex]\frac {1} {6}[/tex] cup of butter
ANswer:
[tex]\frac {1} {6}[/tex]