Which expression is equivalent to x² - 4x - 45?
А
(x - 9)(x - 5)
B
(x + 9)(x+5)
(20 +9)(x - 5)
D
(x - 9)(x+5)
Answers
Answer:
D. (x - 9)(x+5)
Step-by-step explanation:
[tex]x^{2} - 4x - 45[/tex] is your expression, so you have to factor it out. Since from the options available it's clear that the factors of -45 you use are some form of 9 and 5, we can use the process of elimination to figure out which are the correct ones.
First, through FOIL u know that in any factored form the last two terms in each bracket multiply together to make the last term in the expanded form.
So first, look at A. the last two terms are -9 and -5, which = 45 when multiplied together. 45 does not = -45, so it can't be A.
B has 9 and 5. When they're multiplied, they = 45, which does not = -45, so its not B
It can't be C either, because the first term of the first bracket in C is 20, and when multiplied with x it doesn't produce x^2.
Therefore it has to be D. u can check this by multiplying -9 and 5, which = -45, the final term in the expanded form. Also, -9 + 5 = -4, which is the middle term of the expanded form.
The equivalent expression to x² - 4x - 45 is (x - 9)(x + 5), which corresponds to option A.
To factor the quadratic expression x² - 4x - 45, we need to find two binomials that, when multiplied, give us the original expression.
We look for two numbers whose product is -45 (the coefficient of the constant term) and whose sum is -4 (the coefficient of the linear term, -4x). After some exploration, we find that the numbers -9 and 5 satisfy these conditions.
Thus, we can express x² - 4x - 45 as (x - 9)(x + 5). This is because when we multiply the two binomials (x - 9) and (x + 5) using the distributive property, we obtain the original quadratic expression.
This factored form, (x - 9)(x + 5), represents the equivalent expression to x² - 4x - 45.
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Related Questions
Pls help i need this quickly ill give brainliest
factor the following completely: x^3*y^2-x^2*y^3
Answers
Answer:
Step-by-step explanation:
x³y² = x * x * x * y * y
x²y³ = x * x * y *y * y
GCF = x * x * y * y = x²y²
x³y² - x²y³ = x²y² ( x - y)
At Pete's pizza, the cost of a 1 topping pizza is $17.35 and the cost of a 3 topping pizza is $21.05.
Assuming the cost of a pizza follows a linear model, write an equation that represents C, the cost of any pizza with t,toppings.
Answers
Answer:
3
Step-by-step explanation:
17.35 * 3
could you help me with the 2 questions plz
Answers
Answer:
2. 64
3. 2
Step-by-step explanation:
On a Saturday, Saul can cut 4 lawns in 6 hours. If Mitch can mow lawns at the same rate, how long will it take him to mow 9 lawns?
12 hours
12 3/4 hours
6 hours
13 1/2 hours
Answers
Answer:
13 1/2 is your answer.
Step-by-step explanation:
With the same ratio the time taken Mitch to mow 9 lawns will be 13 + 1/2 thus option (D) is correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
Saul can cut 4 lawns in 6 hours.
The ratio of hours to lawns will be as,
6/4
Suppose the time taken to mow 9 lawns to Mitch is x hours.
The ratio of hours to lawns will be as
x/9
Since the rate is the same thus ratio must be the same.
x/9 = 6/4
x = 6/4 x 9
x = 13.5 = 13 + 1/2
Hence"With the same ratio, the time taken Mitch to mow 9 lawns will be 13 + 1/2".
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How to find the slope and y intercept from two coordinate pairs
Answers
m = (y2-y1)/(x2-x1)
and then find the y intercept by (0,b)
then plug m and b into
y=mx+b
Answer:
Slope: y2-y1/x2-x1
Step-by-step explanation:
You find slope from two coordinate pairs by using the slope formula(y2-y1/x2-x1) or rise over run from a graph.
To find y-intercept, x needs to be 0 on a graph.
Hope this helps!
Suppose () = 46%; ( and ) = 10%; and ( or ) = 62% Find (Not ). Can this really be a probability? If not, explain why not.
Answers
Answer:
[tex]P(E) = 26 \%[/tex]
Step-by-step explanation:
Given
[tex]P(F) = 46\%[/tex]
[tex]P(E\ and\ F) = 10\%[/tex]
[tex]P(E\ or\ F) = 62\%[/tex]
Required
Find P(E)
In probability:
[tex]P(E\ and\ F) = P(E) + P(F) - p(E\ or\ F)[/tex]
Substitute the right values
[tex]10\% = P(E) + 46\% - 62\%[/tex]
[tex]10\% = P(E) -16 \%[/tex]
Collect Like Terms
[tex]P(E) = 10\% +16 \%[/tex]
[tex]P(E) = 26 \%[/tex]
It is a probability because all probabilities are within the range 0 to 100%
Solve the simulataneous equations. 5x-4y=19 x+2y=8
Answers
Answer:
(5, 1.5 )
Step-by-step explanation:
Given the 2 equations
5x - 4y = 19 → (1)
x + 2y = 8 → (2)
Multiplying (2) by 2 and adding to (1) will eliminate the y- term
2x + 4y = 16 → (3)
Add (1) and (3) term by term to eliminate y
7x + 0 = 35
7x = 35 ( divide both sides by 7 )
x = 5
Substitute x = 5 into either of the 2 equations and solve for y
Substituting into (2)
5 + 2y = 8 ( subtract 5 from both sides )
2y = 3 ( divide both sides by 2 )
y = 1.5
solution is (5, 1.5 )
Which of the following is a solution of x2 + 4x + 6? (1 point)
Answers
Answer:
I LOVE ALGEBRA anyways
othe ans is in the picture and the steps how got the ans
(hope it helps can i plz have brainlist it will make my day :D hehe)
Step-by-step explanation:
Please tell me the answers i am confused and need help
Answers
Answer:
Simplified= 7x+6 When x=3 the expression=27
Step-by-step explanation:
HELP I WILL GIVE BRAINLIEST
Solve for x.
7x + 14 – 2x = −x + 12 – x − 19
A. x = −3
B. x = −1
C. x = 1
D. x = 3
Answers
Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
X COULD BE 2 OR 7
Step-by-step explanation:
Answer:
A. x= -3
Step-by-step explanation:
firstly collect all the terms . then move the term so it'd look like 5x+14 = -2x - 7 then calculate it then it would look like this : 5x+2x = -7 -14 after you move the terms you again calculate it and then the finish product would look like this : 7x = -21 so after you get that you divide by both sides and the answer is -3 . (im sorry if that don't make sense) but the answer is A.
A cylindrical can of tennis balls holds a stack of three tennis balls so that they touch the can at the top,bottom,and sides. The radius of each tennis ball is 1.25 inches. Find the volume inside the can that is not taken up by three tennis balls.round to the nearest tenths.
Answers
Answer:
3.7555555536321
Step-by-step explanation:
Kira ,Charlie , and Miguel have a total of $105 in their wallets . Kira has $9 less than Miguel. Charlie has 4 times what Miguel has . How much does each have ?
Answers
Let the money with Miguel be x.
Then :
Money with Kira = x - 9
Money with Charlie = 4x
Total money in their wallet = $105
This can be written in an equation as :
[tex] = \tt \: x + x - 9 + 4x = 105[/tex]
[tex] = \tt2x + 4x - 9 = 105[/tex]
[tex] = \tt 6x - 9 = 105[/tex]
[tex] = \tt6x = 105 + 9[/tex]
[tex] = \tt6x = 114[/tex]
[tex] = \tt x = \frac{114}{6} [/tex]
[tex] = \tt x = 19[/tex]
Which means :
Money with Miguel = $19
Money with Kira :
= 19 - 9
Thus, Kira has $10 in her wallet.
Money with Charlie :
= 4 × 19
= 76
Thus, Charlie has $76 in his wallet.
Therefore, Money with Kira = $10Money with Charlie = $76Money with Miguel = $19Answer:
Let the money with Miguel be x.
Then :
Money with Kira = x - 9
Money with Charlie = 4x
Total money in their wallet = $105
This can be written in an equation as :
= \tt \: x + x - 9 + 4x = 105=x+x−9+4x=105
= \tt2x + 4x - 9 = 105=2x+4x−9=105
= \tt 6x - 9 = 105=6x−9=105
= \tt6x = 105 + 9=6x=105+9
= \tt6x = 114=6x=114
= \tt x = \frac{114}{6}=x=
6
114
= \tt x = 19=x=19
Which means :
Money with Miguel = $19
Money with Kira :
= 19 - 9
Thus, Kira has $10 in her wallet.
Money with Charlie :
= 4 × 19
= 76
Thus, Charlie has $76 in his wallet.
Therefore,
Money with Kira = $10
Money with Charlie = $76
Money with Miguel = $19
Which expression represents "the product of a and b decreased by 9"?
Answers
Answer:
ab-9
Step-by-step explanation:
the product of a and b: a*b
decreased by 9: -9
Answer:
The person above be is correct
Step-by-step explanation:
I figured I would let everyone know so they can trust it anyway have a good day☺️
what are the coefficients in the expression 4x+y+6z+12
Answers
Answer:
4, 1, 6
Step-by-step explanation:
The coefficient of x is 4
The coefficient of y is 1
The coefficient of z is 6
The coefficient of a variable is the number that appears before it.
Graph the points:
(-1, -2); (0 -1), (1, 0)
• What is the fourth point?
HELP PLZZ I'm abouta fail this grade and I cant
Answers
Answer:
(2,1)
Step-by-step explanation:
bro if im wrong blame me-- but yeah
What is the Y intercept of y=3-4x?
Answers
Answer:
13
Step-by-step explanation:
I need help with this can you help me
Answers
Answer: 2.5 in, 7.5 in, and 5 in.
Step-by-step explanation:
you would divide each side by 2
5 inches to 2.5
15 inches to 7.5
and 10 inches to 5
Suppose that the height H of a Ferris wheel can be modeled by the function n H(t)= -16cos(t/45)+24, where t is the time in seconds. What is the maximum height of a cabin? Use 3.14 for π
Answers
Answer:
40 feet.
Step-by-step explanation:
The height of the Ferris Wheel is modeled by:
[tex]\displaystyle H(t)=-16\cos\Big(\frac{t}{45}\Big)+24[/tex]
Where H(t) is the height (in feet (assuming)) and t is the time in seconds.
Remember that the value of cosine, regardless of the input, will always be between -1 and 1. That is:
[tex]-1\leq \cos(t)\leq 1[/tex]
So, we can use the two maximums. Testing -1 and 1, we get:
[tex]H(t)=-16(1)+24=8[/tex]
And:
[tex]H(t)=-16(-1)+24=40[/tex]
Therefore, the maximum height of a cabin of the Ferris Wheel will be 40 feet in the air.
Notes:
And the minimum height will be 8 feet.
We are not asked to find t. To do so, however, set H(t) = 40 and find the general solution for t.
The senior class at Clearville ISD is having a fundraiser to raise money for their prom. They are seling coupon books in the local community. The number currently sold by each of the students was used to create the box plot shown below. HHH 8 10 12 14 16 18 20 22 24 26 28 30 32 If one of the students calculated the mean of the data to be 14.5, would this be an appropriate mean? OA. Yes, the mean is appropriate. OB. There is not enough information to determine if the mean is appropriate. O C. No, the mean should be lower. OD. No, the mean should be higher. Reset Submit
Answers
Answer:
The answer is D
Step-by-step explanation:
If you add them all, and divide them it wouldn’t get 14.5
Answer:
No, the mean should be higher.
Step-by-step explanation:
Have a good day :)
2. In the middle school band, there is 1 oboe for every 7 clarinets. Write three equivalent ratios to compare the oboes to the clarinets
Answers
1/7, 2/14, 3/21
I took the test
The three equivalent ratios to compare the oboes to the clarinets are,
⇒ 2 : 14
⇒ 3 : 21
⇒ 4 : 28
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
We have to given that;
In the middle school band, there is 1 oboe for every 7 clarinets.
Here, The ratio of the oboes to the clarinets is,
⇒ 1 : 7
Hence, Three three equivalent ratios to compare the oboes to the clarinets are,
⇒ 1 : 7
⇒ 1 / 7
⇒ 1×2 / 7×2
⇒ 2 / 14
And, 1 : 7
⇒ 1×3 / 7×3
⇒ 3 / 21
And, 1 : 7
⇒ 1×4 / 7×4
⇒ 4 / 28
The three equivalent ratios to compare the oboes to the clarinets are,
⇒ 2 : 14
⇒ 3 : 21
⇒ 4 : 28
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Can someone please Classify the angles ? I don’t need a conclusion ....
Answers
Answer:
Right triangle
Step-by-step explanation:
A right triangle is a triangle in which one angle is a right angle.
-2y+6=-12
What does y equal?
Answers
Answer:
y = 9
Step-by-step explanation:
-2y+6=-12
subtract 6 on both sides: -2y=-18
divide both sides by -2: y=9
Answer:
[tex]y = 9[/tex]
Step-by-step explanation:
1) Subtract 6 from both sides.
[tex] - 2y = - 12 - 6[/tex]
2) Simplify -12-6 to -18.
[tex] - 2y = - 18[/tex]
3) Divide both sides by -2.
[tex]y = \frac{ - 18}{ - 2} [/tex]
4) Two negative makes a positive.
[tex]y = \frac{18}{2} [/tex]
5) Simplify 18/2 to 9.
[tex]y = 9[/tex]
So, Yherefor, the answer is, y = 9.
Drag and drop each equation to match the type of solution.
Answers
Answer:
B, A, C
Step-by-step explanation:
3x-2y=12 and 3x+5y=33
Answers
Answer:
x=6, y=3. (6, 3).
Step-by-step explanation:
3x-2y=12
3x+5y=33
--------------
-3x+2y=-12
3x+5y=33
-------------------
7y=21
y=21/7=3
3x-2(3)=12
3x-6=12
3x=12+6
3x=18
x=18/3=6
please help me on this will give you brainliest!!
Answers
Answer:
9+(c*2)
im pretty sure this is correct, sorry for misreading it at first <3
Use the midpoint formula to estimate the sales of Cars, Inc. in 2009, given the sales in 2008 and 2010. Assume that the sales of Cars, Inc. sales always follow a linear pattern. (Round to nearest whole number) Year Sales (in millions) 2008 240 2010 280 millions Enter the answer
Answers
Answer:
The estimated sales were $260 million
Step-by-step explanation:
Assume the endpoints of a segment are (x1,y1) and (x2,y2).
The midpoint (xm,ym) is calculated as follows:
[tex]\displaystyle x_m=\frac{x_1+x_2}{2}[/tex]
[tex]\displaystyle y_m=\frac{y_1+y_2}{2}[/tex]
The sales ov Cars, Inc. were (2008,240 million) and (2010,280 million). We need to use the midpoint to estimate the sales in 2009:
[tex]\displaystyle x_m=\frac{2008+2010}{2}=2009[/tex]
[tex]\displaystyle y_m=\frac{240+280}{2}=260[/tex]
The estimated sales were $260 million
What is the value of the missing angle ?
Answers
Answer:
30
Step-by-step explanation:
? = 180 - 150 = 30
Answer:
30°
Step-by-step explanation:
The line is 180 degrees so all you have to do is subtract 150° from 180°
You should end up with 30°
Whenever you see a straight line (IT HAS TO BE STRAIGHT), it is equal to 180°.
HELP MEEEEEEEEEEE plz :D
Answers
B = -60
C = -45
D = -15
E = 15
F = 30
Find the area, to the nearest hundredth, of the figure
Answers
Answer:
Step-by-step explanation:
hypotenuse = √(14.4² + 6²) = √243.36 = 15.6 mi
area of triangle = 0.5×6×14.4 = 43.2 mi²
radius of semicircle = 15.6/2 = 7.8
area of semicircle = πr² = 60.84π mi²
total area = 43.2 + 60.84π ≅ 234.33 mi²
VW = WX = YW = ZX = VX = view image attached thank youuu!
Answers
Answer:
assuming this is a rectangle:
VW=31
WX=19
YW=36.36
ZX=18.18
VX=36.36
Step-by-step explanation:
VW=VX
VW=31
WX=VX
WX=19
YW^2=19^2+31^2
YW^2=361+961
YW^2=1322
YW=36.36
ZX=1/2VX
ZX=18.18
VX=YW
VX=36.36
The measures of the rectangle are
a) The measure of VW = 31
b) The measure of WX = 19
c) The measure of YW = 36.36
d) The measure of ZX = 18.18
e) The measure of VZ = 18.18
What is the diagonal of a rectangle?The diagonal of a rectangle is calculated by the formula
From the Pythagoras Theorem , The hypotenuse² = base² + height² , and
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
Given data ,
Let the rectangle be represented as VWXY
Now , the diagonals of the rectangle are VX and WY
Substituting the values in the equation , we get
The measure of VY = 19
The measure of XY = 31
Now , for a rectangle the opposite sides are congruent
So , the measure of VY = measure of WX
And , the measure of XY = measure of VW
On simplifying the equation , we get
The measure of WX = 19
The measure of VW = 31
And , the diagonal of the rectangle = √ ( Length )² + ( Width )²
Substituting the values in the equation , we get
The diagonal of the rectangle YW = √ ( 31 )² + ( 19 )²
The diagonal of the rectangle YW = √ ( 961 + 361 )
The diagonal of the rectangle YW = 36.359 ≈ 36.36
And , the measure of VX = measure of YW = 36.36
Now , the measure of ZX = measure of VZ = measure of VX / 2
So , the measure of ZX and VZ = 36.36 / 2 = 18.18
Hence , the diagonal of the rectangles is 36.36
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