An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c. What are the factors of x2 – 144? And
Answers
Answer:
[tex](x -12)(x + 12)[/tex]
Step-by-step explanation:
Given
See attachment for chart
Required
The factors of [tex]x^2 - 144[/tex]
First, express [tex]x^2 - 144[/tex] as [tex]ax^2 + bx + c[/tex]
So, we have:
[tex]x^2 - 144 = x^2 + 0x - 144[/tex]
Compare the above expression to: [tex]ax^2 + bx + c[/tex]
We have:
[tex]ax^2 + bx + c = x^2 + 0x - 144[/tex]
So:
[tex]a =1[/tex]
[tex]b =0[/tex]
[tex]c = -144[/tex]
and
[tex]a * c = d * e[/tex]
Calculate ac
[tex]a* c = 1 * -144[/tex]
[tex]a* c = -144[/tex]
Rewrite as:
[tex]a* c = -12 * 12[/tex]
Recall that:
[tex]a * c = d * e[/tex]
Hence:
[tex]d = -12; e = 12[/tex]
So, on the x chart, we have:
ac
d e
b
This gives:
-144
-12 12
0
The factors are
[tex](x + d)(x + e)[/tex]
[tex](x -12)(x + 12)[/tex]
Answer:
✔ (x – 12)
and
✔ (x + 12)
Step-by-step explanation:
Related Questions
Solve the inequality 2x – 22 < -8.
Answers
2x - 22 < -8
Add 22 to both sides
2x < 14
Divide both sides by 2
X < 7
Answer:
[tex]2x-22<-8[/tex]
Add 22 to both sides
[tex]2x-22+22<-8+22[/tex]
[tex]2x<14[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}<\frac{14}{2}[/tex]
[tex]x<7[/tex]
OAmalOHopeO
There is a proportional relationship between any length measured in centimeters and
the same length measured in millimeters. There are two ways of thinking about this proportional relationship. If you know the length of something in centimeters, you can calculate it’s length in millimeters
Answers
The constant of proportionality is 10.
What is constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality is the fixed or constant pace at which ratios rise and decrease. Two ratios are said to be directly proportional if they share the same constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality. The constant of proportionality is the name given to this consistent pace of growth or decline.
a)
since , 1 cm = 10mm
9cm = 90mm
12.5cm = 125mm
50cm = 500mm
88.49cm = 884.9mm
b)
The constant of proportionality is 10.
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A Triangular Park ABC has sides 120 m, 80m and 50m. a gardener has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of of Rs. 20 per metre leaving a space 3m wide for a gate on one side?
Answers
The perimeter = sum of all sides
= 120 + 80 + 50
= 250
So 250 - 3
247
Left space for gate
Now cost of fencing = Rs 20/per meter
= 247 × 20
= Rs 4,940
Now the area of the triangular park can be found using heron's formula
S = (a+b+c)/2
S = (120+80+50)/2
S = 250/2
S = 125
Now
Herons formula = √s(s-a)(s-b)(s-c)
√125(125-120)(125-80)(120-50)
√125(5)(45)(70)
√5×5×5×5×5×3×3×5×14
After Making pairs
5×5×5×3√14
375√14
Therefore 375√14m is the area of the triangular park
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$\sf\underline\bold{Answer:}$
$\sf\small\underline{\underline{Area\: planted\: by\: the\: gardener : 1452.36m^2}}$$\sf\small\underline{\underline{The\:cost\:of\:fencing\:the\:park:Rs.4940}}$$\space$
$\sf\underline\bold{Step-by-Step:}$
$\space$
$\sf\bold{Given(In \:the\:Q):}$
Sides of the triangular park are 120m,80m and 50m.$\space$
$\sf\bold{To \: find:}$
How much area of the park does she need to plant?The cost of fencing the park ?$\space$
$\sf\small{☆Area\:to\:be\:planted=Area \: of \: ∆ABC}$
$\space$
$\sf\underline\bold{Calculating\:area\:of\:∆ABC:}$
$\space$
Use heron's formula to find the area of the triangle.
$\space$
$\mapsto$ $\sf\small{Heron's\:formula=}$
[tex]\sf\sqrt{s(s-a)(s-b)(s-c)}[/tex]
$\sf{Where\:s=semi\:perimeter}$$\sf{a,b,c\: = side\:of\:the\:∆}$$\sf\small{Here\:a=120,b=80 \:and\: c=50}$$\space$
$\sf\bold{Now,find\:semi\:parameter:-}$
$\sf\small{Perimeter\:of\:the\:∆=120+80+50=250}$
$\sf\small{Semi-Perimeter:}$ $\sf\dfrac{250}{2}$ $\sf\small{=125m}$
$\space$
$\sf\small{Substitute \: the\:values\:in\:heron's\:formula:}$
$\sf{Area\:of\:the\:∆:-}$
$\mapsto$ [tex]\sf\sqrt{125(125-120)(125-80)(125-50)}[/tex]
$\space$
$\mapsto$ $\sf\sqrt{125\times(5)\times(45)\times(75)}$
$\space$
$\mapsto$ $\sf\small\sqrt{2109375}$ $\sf\small{=375}$ $\sf\small\sqrt{15}$
$\space$
$\longmapsto$ $\sf\underline\bold\purple{1452.56m^2}$
______________________________
$\sf\underline\bold{Now,find\:the\:cost\:of\:fencing:}$
$\sf{Cost\:of\:fencing-}$
$\sf{Rate = Rs.20 per \:meter}$ $\sf{Left\:space=3m}$$\space$
$\sf\underline{Hence,the\:gardener\:has\:to\:fence:}$
$\sf{= 250-3=247m.}$$\space$
So,total cost of fencing at the rate of Rs.20 per m:-
$\sf\underline\bold\purple{=247\times20=4940}$___________________________________
4. a) x2 + xy2 + y 4
Answers
Answer:
x2 + xy2 + y 4=（x+y^2)^2-xy^2
Step-by-step explanation:
2 square5 + 5 square5
Answers
Answer:
=2^5+5^5
=32+3125
=3157
A line of best fit predicts that when x equals 28, y will equal 27.255, but y actually equals 26. What is the residual in this case?
A. 0.745
B. -0.745
C. -1.255
D. 1.255
Answers
Answer:
C) -1.255
Step-by-step explanation:
We are tasked to solve for the residual value given that when x equals 29, y will be equals to 27.255. But, when it is tested, y actual value is 26. The formula in solving residual is shown below:
Residual value = Observed value - predicted value
Residual value = 26 - 27.255
Residual values = -1.255
The answer is -1.255 for residual value.
Helpppp pleaseeee !!!!!!
Answers
Answer:
149 inches squared
Step-by-step explanation:
top rectangle: 25 * 7 = 175
second rectangle: 8 * (25 - 17) = 8^2 = 64
triangle in bottom right: 1/2 * (13 - 8) * (15 - 11) = 10
175 + 64 + 10 = 149 sq in
hopefully got this right!
The average of four different positive integers is 9. What is the greatest value for one of the integers?
Answers
From the given information; Let the unknown different positive integers be (a, b, c and d).
An integer is a set of element that are infinite and numeric in nature, these numbers do not contain fractions.
Suppose we make an assumption that (a) should be the greatest value of this integer.
Then, the other three positive integers (b, c and d) can be 1, 2 and 3 respectively in order to make (a) the greatest value of the integer.
Therefore, the average of this integers = 9
Mathematically;
[tex]\mathbf{\dfrac{(a+b+c+d)}{4} =9}[/tex]
[tex]\mathbf{\dfrac{(a+1+2+3)}{4} =9}[/tex]
[tex]\mathbf{\dfrac{(6+a)}{4} =9}[/tex]
By cross multiplying;
6+a = 9 × 4
6+a = 36
a = 36 - 6
a = 30
Therefore, we can conclude that from the average of four positive integers which is equal to 9, the greatest value for one of the selected integers is equal to 30.
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The greatest value for one of the four positive integers is 30.
To find the largest positive integer, you have to minimize the other three positive integers.
The least three different positive integers available = 1, 2, 3let the largest positive integer = ythe sum of the four different positive integers = 1 + 2 + 3 + y = 6 + yFind the average of the four positive integers and equate it to the given value of the average.
[tex]\frac{6 + y}{4} = 9\\\\6+ y = 36\\\\y = 36-6\\\\y = 30[/tex]
Thus, the greatest value for one of the positive integers is 30
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PLEASE HELP!!
Prove the trigonometric identity.
tanx+cotxcscxcosx=sec2x
Drag an expression to each box to correctly complete the proof.
Answers
You're going to have to break all of these identities into sin and cos, and then just resolve them like normal.
The expression [tex]\frac{tan x + cot x}{cosec x* cos x} = sec ^{2} x[/tex] is proved .
What is trigonometric ratio?
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.
formulas for trigonometric ratios is:
sin θ = 1/cosec θ
cos θ = 1/sec θ
tan θ = 1/cot θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
According to the question
[tex]\frac{tan x + cot x}{cosec x* cos x} = sec ^{2} x[/tex]
[tex]\frac{\frac{sin x}{cos x} + \frac{cos x}{sin x}}{\frac{1}{sin x}*cosx } = sec^{2} x[/tex]
[tex]\frac{\frac{sin^{2}x + cos^{2}x }{sinx cosx} }{\frac{cosx}{sinx} } = sec^{2} x[/tex]
[tex]\frac{\frac{1}{sinx cosx} }{\frac{cosx}{sinx} } = sec^{2} x[/tex]
[tex]\frac{\frac{1}{cosx} }{\frac{cosx}{1} } = sec^{2} x[/tex]
[tex]\frac{1}{cos^{2} x} =sec^{2} x[/tex]
[tex]sec^{2} x =sec^{2} x[/tex]
L.H.S = R.H.S
Hence, The expression [tex]\frac{tan x + cot x}{cosec x* cos x} = sec ^{2} x[/tex] is proved .
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3(x-5)=5x-(3-x) solve for x
Answers
Answer:
x = -4
Step-by-step explanation:
[tex]3(x-5)=5x-(3-x)\\\\3x-15=5x-3+x\\\\3x-15=6x-3\\\\-15=3x-3\\\\-12=3x\\\\-4=x[/tex]
Step-by-step explanation:
[tex]3(x - 5) = 5x - (3 - x) \\ 3x - 15 = 5x - 3 + x \\ 3x - 5x - x = - 3 + 15 \\ - 3x = 12 \\ x = \frac{12}{ - 3} \\ x = - 4[/tex]
I hope it helped U
stay safe stay happy
pleaseee help i’m stressing!! i’ll give you those little crown things
Answers
Answer:
4.4 mm
Step-by-step explanation:
help lol i forgot everything of the summer time
fill in the table using this function rule
Answers
Answer:
hope it help you
Step-by-step explanation:
mark me brailiest answer
1. Y=-4(-1)+3
Y=4+3
Y=7
2. Y=-4(0)+3
Y=0+3
Y=3
3. Y=-4(1)+3
Y=-4+3
Y=-1
4. Y=-4(2)+3
Y=-8+3
Y=-5
Hope this helps!! :)
i neeeeeeed help :)))))
Answers
So area of base = 3 x volume / height = 3 x 15pi / 5 = 9pi m^2
The radius of the base will be 3 m but this was not asked for.
What is the y-intercept of the line whose equation is y=−3x ?
Answers
Answer:
y=mx+b
b is the y intercept
b=0, so 0 is the y intercept
Step-by-step explanation:
What is the mathematical expression for seven less then a number
Answers
pleeaseeee help me !!!
Answers
Answer 3. -7.5 is located to the left of 6.5 on a number line oriented from left to right.
Avanced Algebra PLS ANSWER THIS CORRECTLY
Use the function f(x) to answer the questions:
f(x) = 2x^2 − 3x − 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Answers
Answer:
Below
Step-by-step explanation:
Part A: -1 and 2.5
Part B: The vertex is a minimum
Part C: tbh, I'm not quite sure about this part but just use parts A and B to answer :)
(you can also use the website desmos. com/calculator as a graphing calculator)
What is the Compound interest on Rs.1000 at the rate of 20% p.a. semiannually for 1 year and 10 months?
A. Rs. 420.31
B. Rs. 400.29
C. Rs. 419.73
D. Rs. 409.13
Answers
Answer:
420.31
Step-by-step explanation:
A
.Rs.420.31
20ejjdj
Answer:
I think A rs 420.31 is right answet
Solve the following equation for b. Be sure to take into account whether a letter is capitalized or not.
t+1/2b=Y
Answers
Answer:
b = 2(Y - t)Step-by-step explanation:
Given:
t + 1/2b = YIsolate b:
1/2b = Y - tFind b:
b = 2(Y - t)[tex]\\ \sf\longmapsto t+\dfrac{1}{2}b=Y[/tex]
take t right side[tex]\\ \sf\longmapsto \dfrac{1}{2}b=Y-t[/tex]
[tex]\\ \sf\longmapsto \dfrac{b}{2}=Y-t[/tex]
[tex]\\ \sf\longmapsto b=2(Y-t)[/tex]
[tex]\\ \sf\longmapsto b=2Y-2t[/tex]
find the missing side. Round it the nearest tenth.
Answers
Answer: x= 11√3= 19.0525 = 19.1
Step-by-step explanation:
Let the reference angle be 30
so
cos 30 = b/h
√3/2 = x/22
or, 22√3 = 2x
or. x = (22√3)/2
so, x = 11√3
Answer:
x = 19.1 cm
Step-by-step explanation:
→ Find the name of the side you are not given
Opposite
→ Find a formula without opposite in it
Cos = Adjacent ÷ Hypotenuse
→ Rearrange to make adjacent the subject
Adjacent = Cos × Hypotenuse
→ Substitute in the values
Adjacent = Cos ( 30 ) × 22
→ Simplify
Adjacent = 19.1
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
You can visualize data sets using ______________.
A. dot charts
B. dotgrams
C. dot graphs
D. dot plots
Answers
Answer:
Adrenaline: A stress hormone produced within the adrenal gland that quickens the heart beat, strengthens the force of the heart's contraction, and opens up the bronchioles in the lungs, among other effects. The secretion of adrenaline is part of the human 'fight or flight' response to fear, panic, or perceived threat.
Step-by-step explanation:
A bag contains 5 pieces of string. The lengths of the pieces of string are 1 inch, 3 inches, 5 inches, 7 inches, and 9 inches. Suppose you pick three pieces of string from the bag at random and all pieces are equally likely to be chosen. What is the probability you can form a triangle with the three pieces
Answers
Answer:
30%
Step-by-step explanation:
There are 10 possible combinations of sticks that can be drawn from a group of 5 strings
5C3 = (5*4*3)/(3*2) = 10 combinations, which are
1,3,5 ; 1,3,7 ; 1,3,9 ; 1,5,7 ; 1,5,9 ; 1,7,9 ; 3,5,7 ; 3,5,9 ; 3,7,9 ; 5,7,9
to make a triangle, the sum of any two sides must be greater than the third side and if you look at the possible combinations there are only three cases where that is true
so the probability for drawing three sticks that would make a triangle is 3/10 or 30%
Find the equation of the line that is parallel
to the line y = -5x - 9 and passes
through the point (-4,-9) Write the
equation in slope-intercept form.
Answers
A parallel line would contain the same slope and have a different y-intercept.
Using the slope of the original line you would start with:
Y = -5x + b, where b is the new y-intercept.
Using the given point replace x and y and solve for b:
-9 = -5(-4) + b
Simplify:
-9 = 20 + b
Subtract 20 from both sides
-29 = b
Now replace b in the equation to get:
Y = -5x -29
Can anyone help me with this please
Answers
Hi there!
[tex]\large\boxed{\frac{1}{4}, -\frac{3}{2}}[/tex]
13y² + 10y - 3 = 5y²
Begin by moving all terms to one side:
13y² + 10y - 3 - 5y² = 0
Combine like terms:
8y² + 10y - 3 = 0
Factor using the guess-and-check method.
(4y - 1)(2y + 3) = 0
Set each factor equal to 0 to find the solutions:
4y - 1 = 0
4y = 1
y = 1/4
2y + 3 = 0
2y = -3
y = -3/2
2
50
70
85
96
Christina earned 70 on the test. Describe how the scores of Christina's
classmates compared to Christina's score.
A. about 1/4 scored higher, about 3/4 scored lower
B. about 314 scored higher, about 1/2 scored lower
C. about 3/4 scored higher, about 1/4 scored lower
D. about 1/2 scored higher, about 1/2 scored lower
Reset Selection
Answers
Given the five number summary, christina has scored 70 marks which is equal to the median of the test scores, therefore about [tex]\frac{1}{2}[/tex] class scored higher than her and [tex]\frac{1}{2}[/tex] class scored lower than her, making option (d) correct.
The five number summary is the descriptive summary of a data where in you are provided the lowest observation, first quartile, median, third quartile and the maximum observation.
Here, the first quartile is the observation which lies at a point in the ordered data that 25% observations are lesser than it and 75% are greater than it.
the median is the observation which lies at a point in the ordered data that 50% observations are lesser than it and 50% are greater than it.
the third quartile is the observation which lies at a point in the ordered data that 75% observations are lesser than it and 25% are greater than it.
As given in the data,
Christina's marks = 70
median marks = 70
christina's marks = median marks
therefore, by definition of median, about half class scored lower than christina and half more than her.
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The complete question is given below:
Given the five number summary as:
minimum = 2
first quartile = 50
median = 70
third quartile = 85
maximum = 96
Christina earned 70 on the test. Describe how the scores of Christina's
classmates compared to Christina's score.
A. about 1/4 scored higher, about 3/4 scored lower
B. about 314 scored higher, about 1/2 scored lower
C. about 3/4 scored higher, about 1/4 scored lower
D. about 1/2 scored higher, about 1/2 scored lower
Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
Answers
Answer:
the answer is c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
The value of x in the expression 2x/3 - 7 = 5
is
A---8
B---24
C---18
D---36
Answers
Answer:
C. 18Step-by-step explanation:
2x/3 - 7 = 52x/3 = 5 + 72x/3 = 122x = 3*122x = 36x = 36/2x = 18Correct choice is C
[tex]\\ \sf\longmapsto \dfrac{2x}{3}-7=5[/tex]
[tex]\\ \sf\longmapsto \dfrac{2x-21}{3}=5[/tex]
[tex]\\ \sf\longmapsto 2x-21=5(3)[/tex]
[tex]\\ \sf\longmapsto 2x-21=15[/tex]
[tex]\\ \sf\longmapsto 2x=15+21[/tex]
[tex]\\ \sf\longmapsto 2x=36[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{36}{2}[/tex]
[tex]\\ \sf\longmapsto x=18[/tex]
Help me! thank you so much
Answers
Answer:
Step-by-step explanation:
[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]
What is the area of a circle with a diameter of 20 inches if
[tex]\pi[/tex]
=3.1415
Answers
$\sf\underline\bold\blue{Information\:given\:in\:the\:question:}$
π =[tex]\sf{ 3.1415}[/tex]$\sf{Diameter = 20inches}$$\space$
$\sf\underline\bold\blue{What\:we\:have\:to\:find?}$
$\sf{Area\:of\:the\:circle.}$$\space$
$\sf\underline\bold\blue{Answer:}$
$\sf\small{Area\:of\:the\:circle\:is : 314.15}$$\space$
$\sf\underline\bold\blue{Calculations:}$
Here we have the value of the circle's diameter that is 20inches. So, first we have to calculate the radius of the circle using the formula :
$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{Diameter}{2}$
$\space$
$\sf\underline\bold\blue{Calculating\:the\:required\:values:}$
$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{20}{2}$
$\sf{Convert \: to \: the\:lowest\:term(Divide),}$
$\mapsto$ $\sf\underline\bold{Radius=10}$
☆Now we know the value of the radius . So now let's calculate the area of the circle.
$\space$
$\sf\bold{Area\:of\:circle:}$ π$\sf{ r \: ^{2} }$
$\sf\bold{Evaluating \: the\:required\:values:}$
$\sf\bold{Area\:of\:circle=3.1415(10)^2}$
$\space$
$\sf\bold{Area\:of\:the\:circle=3.1415\times10\times10}$
$\sf\bold{Now,}$
$\sf\bold{Area\:of\:the\:circle:3.1415\times100}$
$\space$
$\sf\underline\bold\green{Thus,Area\:of\:the\:circle\: is \: 314.15}$
____________________________
if (-2/15)+(-13/5)=(-13/5)+a/b then a/b is equal to
Answers
The choose C. –2/15
(-2/15) +(-13/5) =(-13/5) +a/b
a/b = (-2/15)+(-13/5) - (-13/5)
a/b = (-2/15) - ( 39/15) +(39/15)
a/b = –2/15
I hope I helped you ^_^
Answer: option 3: a/b = (-2/15)
Step-by-step explanation:
See here when we solve this
(-2/15)+(-13/5) = (-13/5)+a/b
(-2/15) = (-13/5)+a/b-(-3/15)
(-2/15) = a/b
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