Answer:
(
5
x
−
2
)
(
x
+
2
)
is the factorised form of the expression.
Explanation:
5
x
2
+
8
x
−
4
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
5
⋅
(
−
4
)
=
−
20
AND
N
1
+
N
2
=
b
=
8
After trying out a few numbers we get
N
1
=
10
and
N
2
=
−
2
10
⋅
(
−
2
)
=
−
20
, and
10
+
(
−
2
)
=
8
5
x
2
+
8
x
−
4
=
5
x
2
+
10
x
−
2
x
−
4
=
5
x
(
x
+
2
)
−
2
(
x
+
2
)
(
x
+
2
)
is a common factor to each of the terms
=
(
5
x
−
2
)
(
x
+
2
)
(
5
x
−
2
)
(
x
+
2
)
is the factorised form of the expression.
y=x^2-8x+6 complete the square to determine the vertex and maximum or minimum value. Determine the number of x-intercepts.
Answer:
Below in bold.
Step-by-step explanation:
y = x^2-8x+6
y = (x - 4)^2 - 16 + 6
y = (x - 4)^2 - 10
So the vertex is at (4, -10)
The coefficient of x^2 of this function is 1 ( positive) so there will be a minimum value.
Minimum value = -10.
x-intercepts:
(x - 4)^2 - 10 = 0
(x - 4)^2 = 10
x - 4 = +/- √10
x = 4 +/- √10
- therefore there are 2 x-intercepts.
Would you please look at this question?
Answer:
The answer to this question is "x"-meter = 48 = B)
Which ordered pair is in the solution set of
Answer:
D. (-1, 3)
Step-by-step explanation:
Substitute the points for x and y, until you find the one that makes the equation true.
A. (-5, 3)
-3x + 4y < 20 <== substitute
-3(-5) + 4(3) < 20
15 + 12 < 20
27 < 20
This statement is false (27 is greater than 20, not less than)
B. (-3, 5)
-3x + 4y < 20
-3(-3) + 4(5) < 20
9 + 20 < 20
29 < 20
This statement is false (29 is greater than 20, not less than)
C. (1, 7)
-3x + 4y < 20
-3(1) + 4(7) < 20
-3 + 28 < 20
25 < 20
This statement is false (25 is greater than 20, not less than)
D. (-1, 3)
-3x + 4y < 20
-3(-1) + 4(3) < 20
3 + 12 < 20
15 < 20
This statement is true (15 is less than 20)
Therefore, the correct answer is D
Hope this helps!
Answer:
[D] (-1,3)
Step-by-step explanation:
To know which ordered pair is in the solution set of -3x+4y < 20 we first need to identify the x-value in the ordered pair and plug it into the equation. When simplify, on the condition the y-value you get is identical as the y-value in the ordered pair, then that ordered pair is a solution to the equation.
Now let's solve:
To find the solution of the equation is ordered pair substitute the value of x and y co-ordinate to check set of ordered pair is the solution of the given equation.
Given:
-3x + 4y < 20
[A] (-5,3)
-3(-5)+4(3)<20
The left side 27 is not less than the right side 20, which means the statement is false
-3x + 4y < 20
[B] (-3,5)
-3(-3)+4(5)<20
The left side 29 is not less than the right side 20, which means the statement is false
-3x + 4y < 20
[C] (1,7)
-3(1)+4(7)<20
The left side 25 is not less than the right side 20, which means that the given statement is false.
-3x + 4y < 20
[D] (-1,3)
-3(-1)+4(3)<20
The left side 15 is less than the right side 20, which means that the given statement is always true.
Hence, Answer is [D] (-1,3)
[RevyBreeze]
A construction crew is lengthening a road that originally measured 53 miles. The crew is adding one mile to the road each day.
Answer:
Equation: 1=1
Length of the road after 16 days: 16 miles (if not adding to 53. if adding to 53, the answer is 69)
Explanation:
If they add one mile of road every day, its 1(mile) = 1(day.
Since its one mile every day, 16 days is 16 miles. Adding 53 + 16 = 69
Fiona is studying how income taxes impact various families and their finances .she creates a table with various amounts of taxes owed and estimates that this represents 9%of each familys gross income
Income tax is the tax that is imposed by the government on the income that is generated by individuals and businesses.
What is a tax?Your information is incomplete. Therefore, an overview of a tax will be given. It should be noted that a tax is a compulsory levy that is paid by individuals and businesses.
Also, income tax is the tax that is imposed by the government on the income that is generated by individuals and businesses. This is important to generate revenue for the government.
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The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified? y > x2 – 2 y ≥ –x2 + 5
Two rigid transformations must be applied:
Vertical translation 7 units in the +y direction.Reflection around the line y = 5.The solution set can be identified by the fact that domain of quadratic functions is the real domain.
How to use rigid transformations
In the field of the Euclidean geometry rigid transformations are transformations applied on geometric loci such that Euclidean distances within the latter are conserved and herein we must determine what rigid transformations we should apply on f(x) to obtain g(x).
After a careful examination, we conclude that following two rigid transformations must be applied:
Vertical translation 7 units in the +y direction.Reflection around the line y = 5.The solution set represents the set of x-values such that the function exists. As both functions are quadratic equations, then their solutions are described the entire real domain.
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find the measures of the interior angles
Answer:
B is 88 and C is 44
Step-by-step explanation:
I know I am right and I did the math
Fill in the blank to make the fractions equivalent. 10/16 and /8 ?
Answer:
5 or 5/8
Step-by-step explanation:
To go from 10/16 to a bottom number/denominator of 8, you have to divide by 2.
Whatever you do to the top, you also do to the bottom, so you would divide 10, the numberator, by 2 to find the missing value.
10/2 is 5.
There is your answer.
Fran is going to transfer her credit card balance over to a new card. she has an existing balance of $752.69. her current card charges her a transfer fee of 12.5%, added to her balance, for transferring her debt. the new card has an opening fee of $50, which is also added to her balance. she will also have to make an immediate minimum payment, which is 3.35% of her total balance. how much will her balance be after she makes this payment, assuming that she pays the minimum amount? round all dollar values to the nearest cent. a. $866.74 b. $868.40 c. $818.41 d. $926.82 please select the best answer from the choices provided a b c d
The Fran's balance will be $866.73.
She has an existing balance of $752.69
Her current card charges her a transfer fee of 12.5%, added to her balance, for transferring her debt.
What is the meaning of balance?An even distribution of weight enabling someone or something to remain upright and steady.
Which is given by,
[tex]0.125\times 752.69=94.04[/tex]
The total is given by,
[tex]752.69+94.04=846.77[/tex]
The new card has an opening fee of $50, which is also added to her balance.
This becomes now = [tex]846.77+50=896.77[/tex]
She also have to make an immediate minimum payment, which is 3.35% of her total balance.
This amount is = [tex]0.0335\times 896.77=30.04[/tex]
Now balance in her account is = [tex]0.0335 \times 896.77=30.04[/tex]
Therefore, Fran's balance will be $866.73.
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Given A, B and C are sets, consider the following text:
(1) If B ∩ C = ∅ and A ⊂ (B ∪ C) then (A ∪ B) ∩ C = A ∩ B
(2) A ∪ (B ∩ C) ⊂ (A ∪ C) ∩ B
(3) If set A has 9 elements, set B has 7 elements and power set of A - B has 32 elements then power set of B - A has 16 elements.
Which statements are correct?
A. (1) and (2) are correct but (3) is not.
B. (1) and (3) are correct but (2) is not.
C. (2) and (3) are correct but (1) is not.
D. All are correct.
E. All are incorrect.
Let's check one by one
#1
B$\cap$ C=ØAnd
A$\subset$ (B U C)A$\subset$ B U A$\subset$ CTill now it's ok but
(A UB)$\cap$ CA$\cap$ C U B$\cap$CBut as B$\cap$ C has no elements this expression yields A$\cap$ C
Hence
False#2
Solve RHS
(A UC )$\cap$ BA$\cap$ B U B$\cap$ CBut according to first statement second part has no elements so it yields only
A$\cap$ BAnd
It denotes to common elements of A and B not all elements of A
Hence
False#3
[tex]\\ \rm\Rrightarrow P(A-B)=32[/tex]
[tex]\\ \rm\Rrightarrow 2^{|A-B|}=32[/tex]
[tex]\\ \rm\Rrightarrow 2^{|A-B|}=2^5[/tex]
[tex]\\ \rm\Rrightarrow |A-B|=5[/tex]
[tex]\\ \rm\Rrightarrow A-B=\pm 5[/tex]
As elements can't be negative integer it's only 5.
[tex]\\ \rm\Rrightarrow A\cap B=A-(A-B)=9-5=4\star[/tex]
And
[tex]\\ \rm\Rrightarrow P(B-A)=16[/tex]
[tex]\\ \rm\Rrightarrow 2^{|B-A|}=16[/tex]
[tex]\\ \rm\Rrightarrow 2^{|B-A|}=2^4[/tex]
[tex]\\ \rm\Rrightarrow |B-A|=4[/tex]
[tex]\\ \rm\Rrightarrow B-A=\pm 4[/tex]
Again take it positive 4
[tex]\\ \rm\Rrightarrow B\cap A=B-(B-A)=7-4=3[/tex]
As
[tex]\\ \rm\Rrightarrow A\cap B\neq B\cap A[/tex]
This statement is falseConclusion:-All statements are incorrect
Option EArjun rides his bike for 4 kilometers a day for 12 days. How far does Arjun ride his bike in 12 days
Through a regular hexagonal prism whose base edge is 8 cm and whose height is 12 cm, a hole in the shape of a right prism, with its end being a rhombus with diagonals 6 cm and 8 cm is drilled . Find: the total surface area of the remaining solid.
The total surface area of the remaining solid is 48(4+root3) centimeters square.
We have given that,
Through a regular hexagonal prism whose base edge is 8 cm
Whose height is 12 cm, a hole in the shape of a right prism
What is the formula for the total surface area?Total surface area=2(area of the base)+parameter of base×Height
Height=8cm
Parameter of base=12(2)=24
area of the base=6×root3/4×4^2
We use the given value in the formula
=2×6×root3/4×4^2+24×8
=48root3+192
=48(4+root3)cm^2
Therefore the total surface area of the remaining solid is 48(4+root3)cm^2.
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Sonnie deposited $2,500 into an account that earns simple interest. After 5 years, she earned $375 in interest. What was the interest rate of the account?
Answer:
3%
Step-by-step explanation:
The interest on the account is given by the simple interest formula:
I = Prt
where I is the interest, P is the principal invested, r is the annual rate, and t is the number of years
375 = 2500r(5) . . . . . . using the given values in the formula
375/12500 = r = 0.03 . . . . . divide by the coefficient of r
Sonnie's account had a 3% interest rate.
A tour bus in Jaipur serves 400 customers a day. The charge is Rs 50 per person. The owner of the bus service estimates that the company would lose 10 passengers a day for each Rs 5 fare increase.
(i) How much should the fare be in order to maximize the
pls help me wat is 10 × 3 + 4
Answer:
34
Step-by-step explanation:
10 x 3 = 30
30 + 4 = 34
34 is the answer.
Answer:
10×3+4
=30+4
=34
hope this helps you
PLEASE SOLVE!! WILL MARK BRAINLIEST!
Answer:
65
Step-by-step explanation:
Megan is in charge of creating a five-digit code to lock and unlock a secure room. She can use any digit from 0 through 9, and she can use each digit as many times as she wants. She knows she wants to start the code with a 7.
How many possible codes that start with 7 could Megan create?
10,000 codes
70,000 codes
100,000 codes
700,000 codes
Answer:
The Answer Is 10,000 Codes
Proof :
Answer:
10,000
Step-by-step explanation:
Took k-12 quiz
f(x)=x^2. What is g(x)?
A. g(x)=-4x^2
B. g(x)=-x^2-4
C. g(x)=x^2+4
D. g(x)=x^2-4
Answer:
g(x)=(-x²-4)
Step-by-step explanation:
[tex] - {x}^{2} - 4 \: is \: th \: requied \: equation[/tex]
need the answer please help
Answer:
the 2nd option
Step-by-step explanation:
given a quadratic in standard form : y = ax² + bx + c (a ≠ 0 )
• if a > 0 then minimum turning point
• if a < 0 then maximum turning point
the graph here has a minimum turning point , so
the function has a positive leading coefficient.
the function is symmetrical about the y- axis , so is of even degree
the function has 1 turning point at (0, 2 )
the graph does not cross the x- axis so has 0 x- intercepts
If the slope of a line is 2 and the y-intercept is 7, what would the equation be in slope intercept form?
Question 11 options:
y = 7x + 2
y = -2x -7
y = 2x -7
y= 2x + 7
Answer:
y = 2x+7
Step-by-step explanation:
y = mx + c
m = slope
c is the y intercept
so
y = 2x+ 7
HELPPPP 80 POINTS
Solve the right triangle.
Round your answers to the nearest tenth
answer:
A=46°
a=17.983 (tenths- 18, hundredths- 17.98)
b=17.366 (tenths- 17.4, hundredths- 17.37)
explanation:
1. find angle A
it shows that the angle corresponding with the side length of 25 is a right angle, meaning it's 90°. using that information and the angle given to us (44°), we're able to find the missing angle. since all the angles in a triangle always add up to 180°, we can add the two angles together and then subtract that from 180° to find the missing angle.
90°+44°=134°
180°-134°=46°
A=46°
2. find side a
using the law of cosines, we're able to find the length of side a. cosine of an angle equals [tex]\frac{adjacent}{hypotenuse}[/tex]. we'll be using angle B (44°) for our angle. after we plug in the values, we can just solve the equation to find side a.
cosine44°=[tex]\frac{a}{25}[/tex]
(multiply both sides by 25)
25cosine44°=a
a=17.983
3. find side b
finding the length of side b is very similar to how you found side a. you can use the law of cosines again (make sure you use the right side lengths and angles!), but i used the law of sines. the sine of an angle equals [tex]\frac{opposite}{hypotenuse}[/tex]. we're going to be using the same angle for this.
sine44°=[tex]\frac{b}{25}[/tex]
(multiply both sides by 25)
25sine44°=b
b=17.366
--
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A cylinder has a radius of 3 ft and a height of 5 ft. Find the volume
Question :-
A Cylinder has a Radius of 3 Ft and a Height of 5 Ft . Find the Volume .Answer :-
Volume of Cylinder is 141.42 Ft³ .Explanation :-
As per the provided information in the given question, we have been given that the Radius of the Cylinder is 3 Ft . The Height is given as 5 Ft . And, we have been asked to calculate the Volume of Cylinder .
For calculating the Volume , we will use the Formula :-
[tex] \bigstar \: \: \: \boxed{ \sf{ \: Volume \: _{Cylinder} \: = \: \pi {r}^{2}h \: }} [/tex]
Where ,
R denotes to RadiusH denotes to HeightTherefore , by Substituting the given values in the above Formula :-
[tex] \Longrightarrow \: \: \: \sf { Volume \: _{Cylinder} \: = \: \pi {r}^{2}h } [/tex]
[tex] \Longrightarrow \: \: \: \sf { Volume \: _{Cylinder} \: = \: \dfrac {22}{7} \: \times \: ({3})^{2} \: \times \: 5 } \\ [/tex]
[tex] \Longrightarrow \: \: \: \sf { Volume \: _{Cylinder} \: = \: \dfrac {22}{7} \: \times \: 9 \: \times \: 5 } \\ [/tex]
[tex] \Longrightarrow \: \: \: \sf { Volume \: _{Cylinder} \: = \: \dfrac {22\: \times \: 9 \: \times \: 5 }{7}} \\ [/tex]
[tex] \Longrightarrow \: \: \: \sf { Volume \: _{Cylinder} \: = \: \dfrac { \: 990 \: }{7}} \\ [/tex]
[tex] \Longrightarrow \: \: \: \bf { Volume \: _{Cylinder} \: = \: 141.42 } [/tex]
Hence :-
Volume of Cylinder = 141.42 Ft³ .[tex] \underline {\rule {180pt}{4pt}} [/tex]
Answer:
Volume of cylinder is 141.3 ft³ ( Taking value of π as 3.14 )
Step-by-step explanation:
Question : -A cylinder has a radius of 3 ft and a height of 5 ft. Find the volume .
Given : - Radius of cylinder = 3 ftHeight of cylinder = 5 ft To Find : -We have to , volume of Cylinder .
Formula Used : -[tex] \boxed{ \sf{Volume \: of \: Cylinder = \pi r {}^{2} h }}[/tex]
Where ,
π = 3.14r = radius of cylinderh = height of cylinder Solution : -[tex] \longrightarrow \: \pi r {}^{2} h[/tex]
Now , substituting values of radius and height :
[tex]\longrightarrow \: 3.14 \times (3) {}^{2} \times 5[/tex]
Now , calculating :
[tex] \longrightarrow 3.14 \times 9 \times5 [/tex]
Firstly , multiplying 9 and 5 :
[tex]\longrightarrow \: 3.14 \times 45[/tex]
Atlast , multiplying 3.14 and 45 :
[tex] \longrightarrow \: \bold{ 141.3}[/tex]
[tex] \red{ \boxed{ \rm{Therefore , \: volume \: of \: cylinder \: is \: 141.3 \: ft {}^{3} }}}[/tex]
#Keep LearningPlease help i appreciate 1
Answer:
I'm talking about the boxes:
1st-false, there are 7/19, which is not more
2nd-true, there are 12/19 which is the most
3rd-true, 12/20 of the women like dancing
4th-false, 7/20 like dancing
5th-true, 13/20 don't like dancing
In the figure below all lines intersect at point W what is the value of angle VWX?
Answer: 55
Step-by-step explanation:
Angle VWX and the 55 degree angle are vertical angles.
x>-6 on a number line
Step-by-step explanation:
draw a number line and plot on 7 and make an arrow at the other end of the line
UNIT 5: CEREAL BOX PROJECT / PORTFOLIO
HELP
Using the formula for volume and surface area of solids, we have the following:
1. 180 in.³; 258 in.²; $12.9
2. 144 in.³; 184 in.²; $9.2
3. 75 in.³; 228 in.²; $11.4
What is Volume and Surface Area?Volume of a rectangular prism = l × w × h
Surface area of a rectangular prism = 2(wl+hl+hw)
Volume of a square pyramid = 1/3 × a² × h
Surface area of a square pyramid = a² + 2al
Volume of a cylinder = πr²h
Surface area of a cylinder = 2πr( h + r)
1. Volume of the rectangular prism cereal box = 7.5 × 2 × 12 = 180 in.³
Surface area of the rectangular prism cereal box = 2(wl+hl+hw) = 2(2 × 7.5 + 12 × 7.5 + 12 × 2) = 258 in.²
Cost of material for the the rectangular prism cereal box = 258 × 0.05 = $12.9.
2. Volume of the square pyramid cereal box = 1/3 × a² × h = 1/3 × 6² × 12 = 144 in.³
Surface area of the square pyramid cereal box = a² + 2al = 6² + 2(6)(12.3) ≈ 184 in.²
Cost of material for the the square pyramid cereal box = 184 × 0.05 = $9.2.
3. Volume of the cylinder cereal box = πr²h = π(2.5²)(12) = 75 in.³
Surface area of the cylinder cereal box = 2π(2.5)(12 + 2.5) ≈ 228 in.²
Cost of material for the the cylinder cereal box = 228 × 0.05 = $11.4.
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Explain why 5.12 x 4 equals 20.48 with numbers.
Answer: 20.48
Step-by-step explanation: you add 5.12 four time then you get 20.48.
EZ QUESTION - FREE BRAINLIEST: Write the equation of the parabola that has the vertex at point (−2,7) and passes through the point (−1,3).
Answer:
Step One
Use the vertex to determine the basic equation for the parabola.
y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)
What it means is the 2 has to be minus in order that the vertex will shift 2 units in the x direction.
Step Two
Use the point to solve for a.
y = a(x - 2)^2 + 7
When x = - 1
Then y = 3
3 = a(-1 - 2)^2 + 7 combine -1 with - 2
3 = a (-3)^2 + 7
3 = 9a + 7 Subtract 7 from both sides
3 - 7 = 9a
-4 = 9a Divide by 9.
a = -4/9
or
a = - 0.4444
y = -0.4444(x + 2)^2 + 7 <<<<< answer
y = - 4/9 (x + 2)^2 + 7
Note: if you have choices, list them please.
Note: The red graph is y = (x - 2)^2 + 7 ; a = 1
The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444
1 It widens the graph
jcherry99 avatar
It turns the graph upside down. The next one is the tough one.
jcherry99 avatar
It gives the parabola two real roots.
jcherry99 avatar
If you thought of others, so much the better.
Step-by-step explanation:
Answer:
y = - 4x² - 16x - 9
Step-by-step explanation:
the equaion of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (- 2, 7 ) , then
y = a(x + 2)² + 7
to find a substitute (- 1, 3 ) into the equation
3 = a(- 1 + 2)² + 7 ( subtract 7 from both sides )
- 4 = a(1)² = a
then
y = - 4 (x + 2)² + 7 ← in vertex form
= - 4(x² + 4x + 4) + 7
= - 4x² - 16x - 16 + 7
= - 4x² - 16x - 9 ← in standard form
Suppose that a travel bureau claims that the trees in a forest are 84 ft tall on average with a standard deviation of 2 feet. If you took a sample of 64 trees, which of the following mean heights would be outside the 95% confidence interval?
A. 84.6 ft
B. 84.2 ft
C. 84.4 ft
D. 83.6 ft
The value of the mean height for the given data will be 84.6 ft. Option A is correct.
What is the standard deviation?It is a measurement of statistical data dispersion. The degree to which the value varies is known as dispersion.
Given data;
Mean,[tex]\rm\bar x = 84[/tex]
Standard deviation,[tex]\sigma= 2[/tex]
No of sample,n=64
The mean height is foundd as;
[tex]\rightarrow \bar x \pm \frac{\sigma}{\sqrt n} \times Z \\\\ \rightarrow \84 \pm\frac{2}{8} \times 1.96 \\\\ \rightarrow 83.51,84.49[/tex]
84.6>84.49
The value of the mean height for the given data will be 84.6 ft.
Hence option A is correct.
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What is the value of D?
5/6 = 1/3 + D
Answer:
1/3=2/6 d is 2/6
Step-by-step explanation: