Answers
Answer:
1)D 2)C 3)A 4)B 5) A
Step-by-step explanation:
1) The area rectangle is 36x^2 -1
We know ,
A= l*b
=36x^2 -1
=(6x)^2 -1
=(6x+1) (6x-2)
This the value of l,b respectively.
So, Perimeter of rectangle is 2(l+b)
P=2(6x+1) + 2(6x-1)
=24x
2)The area of square is 4(x+5)^2
We know,
A=l^2
=4(x+5)^2
=4(x^2 + 10x + 25)
=(2x+10)^2
This is the value of l=2x+10.
So, Perimeter of square is 4l
P=4(2x+10)
=8x+40
3)The fully factorized form is
= -2x^2 + 10x +12
= -2x^2 + 12x -2x +12
= -2x(x-6) -2(x-6)
= -2(x-6) (x+1)
4)The fully factorized form is
=x^4 -81
=(x^2)^2 -9^2
=(x^2 + 9) (x^2 - 9)
=(x^2 + 9) (x^2 - 3^2)
=(x^2 + 9) (x + 3) (x - 3)
5)The fully factorized form is
= 5x^4 - 320
= 5(x^4 - 64)
= 5((x^2)^2 - 8^2)
= 5(x^2 + 8) (x^2-8)
Related Questions
What is 30% of 80? show two strategies for solving this problem
by both directly multiplying 0.3(80) AND setting up equivalent ratios and solving with cross products
30/100= x/80. You
must show all of your work!
Answers
Answer:
24
Step-by-step explanation:
30/100=x/80
cross multiply:
100x=2400
divide by 100:
x=24
Not quite sure how you want me to explain the other way step by step... Hope this helps!
80*.3=24
An investment counselor calls with a hot stock tip. He believes that if the economy remain strong the investment rules will result In a profit of $30,000. If the economy grows at a moderate pace the investment will result in a profit of $10,000 however if the economy goes into recession the investment will result in a loss of $30,000. You contact and economics who believes there is a 20% probability the economy will remain strong a 70% probability the economy will grow at a moderate pace in a 10% probability the economy will slip into recession. What is the expected profit from this investment?
Answers
Answer: $10,000
Step-by-step explanation:
Given the following :
Profit if economy remains strong = $30,000
Profit if economy grows at moderate pace = $10, 000
Loss if economy goes into recession = $30,000
Probability that economy will remain strong = 20% = 0.2
probability the economy will grow at a moderate pace = 70% = 0.7
probability the economy will slip into recession = 10% = 0.1
Expected value = sum of (x * p(x))
Here expected value equals;
Strong economy profit = $30,000 * 0.2 = $6000
Moderate economy profit = $10,000 * 0.7 = $7000
Loss on Recession = $30,000 * 0.1 = $3000
Expected profit = $(6000 + 7000 - 3000)
Expected profit = $10,000
PLEASE HELP THIS SOUL Jeremy is close to breaking his high school record for field-goal points in a basketball game. He needs 17 points to tie the record and 18 points to break the record. A field goal can be worth either 2 or 3 points. Which inequality shows that he failed to tie or break the record?
Answers
Answer:
2x + 3y < 17
Step-by-step explanation:
Let x be 2-pointers and y be 3-pointers. You're trying to prove that he failed to both tie OR break the record, so he has to have under 17 points total. Knowing our x and y values, just plug it into an inequality equation, and you have your answer.
Please answer this in two minutes
Answers
Answer:
X = 59°Step-by-step explanation:
To find Angle X we use sine
sin∅ = opposite/ hypotenuse
From the question
WY is the opposite
WX is the hypotenuse
So we have
sin X = WY/ WX
sin X = 6/7
X = sin-¹ 6/7
X = 58.99
X = 59° to the nearest tenth
Hope this helps you
Answer:
x=arcsine (6/7) = 58.98 degrees
Step-by-step explanation:
Performing a trigonometrical function. We can find the value of the angle:
1) sin x =6/7
x=arcsine (6/7)
x= 58.98º
which real life object is an example of a parabolic arc? a. objects being thrown straight into the air b. floating clouds c. the way light is focused in a flashlight d. the way a processor works in a computer e. the angle of the roof on a house f. how light is bent in eye glasses g. the heat of pavement in the summer
Answers
Answer:
A, E, F, G
Step-by-step explanation:
The picture below represents a parabolic arc.
An example can be an object being thrown up in the air then then coming back down.
How does the graph of g(x) =
X+4
-6 compare to the graph of the parent function )-te
g(x) is shifted 4 units right and 6 units up from f(x).
O g(x) is shifted 4 units right and 6 units down from f(x).
O g(x) is shifted 4 units left and 6 units up from f(x).
O g(x) is shifted 4 units left and 6 units down from f(x).
Answers
Answer:
O g(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
O g(x) is shifted 4 units left and 6 units down from f(x).
The graph of g(x) is shifted 4 units to the left and 6 units down from f(x).
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given functions are,
g(x) = 1/(x + 4) - 6
f(x) = 1/x
Here when a function f(x) changes to f(x + k) when it is translated k units left.
Here 1/x changes to 1/(x + 4).
So g(x) is shifted 4 units left.
Similarly a function f(x) changes to f(x) - k, if it is translated k units down.
So g(x) also shifted 6 units down.
Hence the correct option is D.
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For the following system, use the second equation to make a substitution for y in the first equation. 3x + y = 1 y + 4 = 5x What is the resulting equation? 1. 3x + 5x - 4 = 1 2. 3x + 4 - 5x = 1 3. 3x + 5x + 4 = 1
Answers
Answer:
The answer is A.
Step-by-step explanation:
So we have the two equations:
[tex]3x+y=1\\y+4=5x[/tex]
To make a substitution of the second equation into the first equation, we need to isolate the y variable in the second equation. Thus:
[tex]y+4=5x\\y=5x-4[/tex]
Now, we can substitute this into the first equation. Therefore:
[tex]3x+y=1\\3x+(5x-4)=1\\3x+5x-4=1[/tex]
Which of the following options could represent a possible set of interior angles of a triangle? 100°, 130°, and 130° 30°, 70°, and 80° 25°, 3°, and 35° 45°, 105°, and 120°
Answers
Answer:
2) 30, 70, 80
Step-by-step explanation:
Well there has to be 3 angles that all add up to 180°.
1)
100+130+130
=360
2)
30+70+80
= 180
3)
25+3+35
=63
4)
45 + 105 + 120
=150
150+120
270
four pencils and a ruler cost $1. six pencils and three rulers cost $2.10. find the cost of three pencils and thirteen rulers.
Answers
Answer:
$ 5.65
Step-by-step explanation:
let the cost of a pencil and a ruler be $p and $r respectively.
4p +r= 1 -----(1)
6p +3r= 2.10
divide by 3 throughout:
2p +r= 0.70 -----(2)
Q: 3p +13r= ?
(1) -(2):
(4p +r) -(2p +r)= 1 -0.70
4p +r -2p -r= 0.30 (expand)
2p= 0.30 (simplify)
p= 0.30 ÷2 (÷2 on both sides)
p= 0.15
subst. into (1):
4(0.15) +r= 1
r +0.60= 1
r= 1 -0.60
r= 0.40
cost of three pencils and thirteen rulers
= 3p + 13r
= 3(0.15) + 13(0.40)
= 0.45 + 5.20
= $5.65
find the value of the letter in each of the following and give reasons for the steps involved 1 2 A+6 A B=A 0 9
Answers
Question:
Find the value of the letter in each of the following and give reasons for the steps involved:
1 2 A
+ 6 A B =
A 0 9
Answer:
128 + 681 = 809
Step-by-step explanation:
Here, let's use the general form of numbers where any letter must represent one value and each digit must be represented by just one letter.
Take the following:
A = 8
B = 1
Thus, A +B = 8 + 1 = 9
Also add:
8 + 2 = 10
In general form, tens digit is zero and the 1 is carried over.
I.e, A = 1 + 6 + 1 = 8
We can now see that,
A = 8
B = 1
Therefore,
1 2 A
+ 6 A B =
A 0 9
Will be written as:
128 + 681 = 809
What is the relationship between the sine and cosine of complementary angles? a They are the same. b They are reciprocals. c There is no relationship d They equal 0.
Answers
Answer:
A. They are the same.
Step-by-step explanation:
The sine of any acute angle is equal to its cosine.
evaluate 2/5g + 3h - 6 when g = 10 and z = 6
Answers
Answer:
16
Step-by-step explanation:
Well first we need to plug in 10 for g and 6 for h.
2/5(10) + 3(6) - 6
4 + 18 - 6
22 - 6
16
Thus,
the answer is 16.
Hipe this helps :)
Answer:
16
Step-by-step explanation:
We are given the expression:
2/5g+ 3h - 6
We know that g=10 and h=6. Therefore, we can substitute 10 and 6 into the expression and solve according to PEMDAS( Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
2/5(10)+3(6)-6
First, multiply 2/5 and 10
4+ 3(6)-6
Next, multiply 3 and 6
4+18-6
Next, add 4 and 18
22-6
Finally, subtract 6 from 22
16
2/5g + 3h - 6 when g=10 and h= 6 is 16.
Please answer this in two minutes
Answers
Answer:
[tex] csc (R) = \frac{13}{12} [/tex]
Step-by-step explanation:
Formula for any given angle (Ѳ) is given as csc Ѳ = length of hypotenuse side//length of opposite side. It is the inverse of sin Ѳ.
In the right triangle given above, the opposite length = 24, while the length of the hypotenuse = 26
Thus,
[tex] csc (R) = \frac{hypotenuse}{opposite} [/tex]
[tex] csc (R) = \frac{26}{24} [/tex]
[tex] csc (R) = \frac{26}{24} [/tex]
[tex] csc (R) = \frac{13}{12} [/tex]
Which ordered pair is in the solution set of the system of linear inequalities?
y > Three-halvesx – 1
y < Three-halvesx – 1
On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (0, negative 1) and (2, 2). Everything to the right of the line is shaded. The second line has a positive slope and goes through (0, negative 1) and (2, 2). Everything to the left of the line is shaded.
(–5, 2)
(2, 2)
(5, 2)
no solution
Answers
Answer: No solution
Step-by-step explanation: If you are doing the Unit Test on edge2020 then D No solution is the answer.
Answer:
the answer is no "solution"
Unit Test on Edge 2023
Which is a true statement about an isosceles right triangle? A: Each leg is √3 times as long as the hypotenuse. B: The hypotenuse is √3 times as long as either leg. C: The hypotenuse is √2 times as long as either leg. D: Each leg is √2 times as long as the hypotenuse.
Answers
Answer:
C. The hypotenuse is [tex]\sqrt{2}[/tex] times as long as either leg.
Step-by-step explanation:
The hypotenuse is square root 2 times as long as the sides is a true statement.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We have to find the true statement about an isosceles right triangle.
Let us use pythagoras theorem to find this
h²=a²+b²
In this case since its an isosceles right triangle, a and b most be the same.
Let's say that the measure of the sides that are equal is x and the hypotenuse is h.
Pythagoras tells us the following:
h²=x²+x²
h²=2x²
Take square root on both sides
h=√2x
Hence, the hypotenuse is square root 2 times as long as the sides
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ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
The logarithmic parent function is the only one with negative numbers in the range
Step-by-step explanation:
Hello,
These functions have been very well known, I remind you their graphs below
The logarithmic parent function is the only one with negative numbers in the range
range for square root is [tex]\mathbb{R^{+}}[/tex]
range for logarithmic is [tex]\mathbb{R}[/tex]
range for exponential is [tex]\mathbb{R^{+}}[/tex]
THAT S TRUE
The square root and logarithmic parent functions have the same domain
domain for square root is [tex]\mathbb{R^{+}}[/tex]
domain for logarithmic is [tex]\mathbb{R}[/tex]
THAT S WRONG
The square root parent function domain is the most restricted
domain for square root is [tex]\mathbb{R^{+}}[/tex]
domain for exponential is [tex]\mathbb{R^{+}}[/tex]
THAT S WRONG
All three parent functions have the same domain
domain for square root is [tex]\mathbb{R^{+}}[/tex]
domain for exponential is [tex]\mathbb{R^{+}}[/tex]
domain for logarithmic is [tex]\mathbb{R}[/tex]
THAT S WRONG
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each figure with the number of edges it has.
Answers
Answer:
Rectangular pyramid 8 edges
Rectangular prism 12 edges
Triangular Prism 9 edges
Triangular Pyramid 6 edges
Step-by-step explanation: Faces connected at edges
Rectangular pyramid 1 Base and 4 slanted triangular sides
Rectangular prism 2 top and bottom bases and 4 sides
Triangular Prism 2 top and bottom triangular bases 3 rectangular sides
Triangular Pyramid 1 triangular base, 3 slanted triangular sides
The matching is as follow:
Rectangular pyramid: 8 edges
Rectangular prism: 12 edges
Triangular Prism: 9 edges
Triangular Pyramid: 6 edges
What is Pyramid and Prism?A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.
Rectangular pyramid have one Base and 4 slanted triangular sides
Rectangular prism have 2 top and bottom bases and 4 sides
Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.
Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.
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Find the distance between the pair of points:
(-6, -2) and (0, -1).
Distance = ✓
Answers
Answer:
The answer is
√37 unitsStep-by-step explanation:
The distance between two points is found by using the formula
[tex] \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } [/tex]
Where (x1 , y1) and ( x2 , y2) are the points
The distance between (-6, -2) and (0, -1) is
[tex] \sqrt{ {( - 6 - 0)}^{2} + {( - 2 + 1)}^{2} } \\ \\ = \sqrt{ {( - 6})^{2} + {( - 1)}^{2} } \\ \\ = \sqrt{36 + 1} \\ \\ = \sqrt{37} \: units[/tex]
Hope this helps you
Answer: √37 units
hope that helped!
Lyla i am not cheating Guys please helps.
Answers
Answer:
C. 6√5
Step-by-step explanation:
√20 +√80= √4*5 + √16*5 = 2√5 + 4√5 = 6√5
Triangle ABC has vertices at A(2,5), B(4,11) and C(-1,6). Determine the angles in this triangle.
I need this solved using vectors please
Answers
Answer:
The angles are
∠A = 90°, ∠B = 26.56°, ∠C = 63.43°
Step-by-step explanation:
We have that the angles of a vector are given as follows;
[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]
Whereby the vertices are represented as
A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),
AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) , BA = (-2, -6, 0)
BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)
AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)
θ₁ = AB·AC
a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0
Therefore, θ₁ = 90°
BA·BC = (-2)×(-5) + (-6)×(-5) = 40
[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72
cos(θ₂) = 40/44.72 = 0.894
cos⁻¹(0.894) =θ₂= 26.56°
CA·CB = 5×3 + 5×(-1) = 10
[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36
10/22.36 = 0.447
cos(θ₃) = 0.447
θ₃ = cos⁻¹(0.447) = 63.43°.
Determine the equation for the total cost of snow tubing, the rest of the chart:
8 . 20
10 . 25
PLEASE HELP ASAP!!! *grade 9 work* best answer gets brainliest :)
Answers
Step-by-step explanation:
Notice how you get the same value each time when you divide the cost by the number of downhill rides
5/2 = 2.5 10/4 = 2.5 15/6 = 2.5Moreover when the downhill rides grow by 2 the total cost grows by 5
so we can state :
n+2 ⇒c+50+2 ⇒ 0+5 0+6 ⇒0+ (3*3)To complet the chart we can use the proportionaliyu relation:
2⇒520⇒ Cc = [tex]\frac{20*5}{2}[/tex]= 50so 20 goes with 50
same method:
2⇒525⇒ C C = [tex]\frac{25*5}{2}[/tex] =62.5so 25 goes with 62.5
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 61 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 61 and 94?
Answers
Answer:
P(61≤ X≤94) = 49.85%
Step-by-step explanation:
From the given information:
The mean of the bell shaped fluorescent light bulb μ = 61
The standard deviation σ = 11
The objective of this question is to determine the approximate percentage of light bulb replacement requests numbering between 61 and 94 i.e P(61≤ X≤94)
Using the empirical (68-95-99.7)rule ;
At 68% , the data lies between μ - σ and μ + σ
i.e
61 - 11 and 61 + 11
50 and 72
At 95%, the data lies between μ - 2σ and μ + 2σ
i.e
61 - 2(11) and 61 + 2(11)
61 - 22 and 61 +22
39 and 83
At 99.7%, the data lies between μ - 3σ and μ + 3σ
i.e
61 - 3(11) and 61 + 3(11)
61 - 33 and 61 + 33
28 and 94
the probability equivalent to 94 is when P(28≤ X≤94) =99.7%
This implies that ,
P(28≤ X≤94) + P(61≤ X≤94) = 99.7%
P(28≤ X≤94) = P(61≤ X≤94) = 99.7 %
This is so because the distribution is symmetric about the mean
P(61≤ X≤94) = 99.7 %/2
P(61≤ X≤94) = 49.85%
PLEASE HELP. YOU NEED TO FIND SLOPE. THANK YOU!
Answers
Answer:
5
Step-by-step explanation:
Due to the direction the line is facing it can be concluded that its slope is positive.
You need two definite points on the line to find the slope.
(x¹,y¹) ( x²,y²)
Points (5,20) (0, -5)
Slope = (y² - y¹) ÷ (x² - x¹)
= (-5 - 20) ÷ (0 -5)
= (-25) ÷ (-5)
= 5
Have a great day!
Convert 2.41 cm2 into mm2 *the 2 means squared
Answers
Answer:
241 mm^2.
Step-by-step explanation:
There are 10 mm in a cm so there are 10*10 = 100 mm^2 in a cm^2.
So the answer is 2.41 * 100 = 241 mm^2.
Answer:
241mm²
Step-by-step explanation:
If 10mm = 1cm,
then 100mm² = 1cm²
2.41 × 100 = 241mm²
Prove that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures.
Answers
Answer:
The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB
Here is what is given: Rectangle ABCD
Here is what you need to prove: segment AC ≅ segment BD
Since ABCD is a rectangle, it is also a parallelogram.
Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.
Please help! "Create a real-life scenario involving an angle of elevation or depression. Draw an appropriate diagram and explain how to solve your example."
Answers
Answer:
Height of the kite = 86.60 meter (Approx)
Step-by-step explanation:
The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.
Given:
Length of thread = 100 meter
Angle of elevation = 60°
Find:
Height of the kite.
Computation:
Using trigonometry application:
Height of the kite / Length of thread = Sin 60°
Height of the kite / 100 = √3 / 2
Height of the kite = [√3 / 2]100
Height of the kite = 50√3
Height of the kite = 86.60 meter (Approx)
Pls help asap. I will give Brainliest. Show ur work. 2 attachments. (; For the fractions, subtract, and make sure the answer is simplified plz. (: Number 16 for the fractions says: 9 - 2 2/3. PLZ HELP ASAP!!!! U SHALL NAME THEE BRAINLIEST!!!! (:
Answers
Answer:
1) 3x + 44
2) 2y - 8
3) x - 6
15) 5 7/8
16) 6 1/3
17) 3 7/9
Step-by-step explanation:
1) 49 + 4 - 5 - 4 + 3x = 3x + 44
2) -y - 5 + y + 2(y) - 3 = 2y - 8
3) 4x - 3 - 3(x + 1) = 4x - 3 - 3x - 3 = x - 6
15) 7 1/4 - 1 3/8 = 7 2/8 - 1 3/8 = 6 10/8 - 1 3/8 = 5 7/8
16) 9 - 2 2/3 = 8 3/3 - 2 2/3 = 6 1/3
17) 10 1/3 - 6 5/9 = 10 3/9 - 6 5/9 = 9 12/9 - 6 5/9 = 3 7/9
WILL MARK BRAINLIEST!!! PLZ HELP!!!
Answers
Answer:
x = -5.
Step-by-step explanation:
The solutions of the equation is when the two functions intersect. That is at (-5, 5.5), so where x = -5.
Hope this helps!
Answer:
x = -5
Step-by-step explanation:
f(x) = g(x) has more than one solution, because they intersect at two points.
The question asks for one solution of f(x) = g(x).
One point where they intersect is at (-5, 5.5), as shown in the graph.
(x , y)
x = -5, y = 5.5
The martins' swimming pool is a square and is in the center of a square plot that is 35 meters on a side. They have 1,081 square meters of lawn. How long is a side of the pool?
Answers
Answer:
The length of a side of the pool is 12 m²
Step-by-step explanation:
Let the area of the square plot be A. Since it is a square plot of 35 m side, its area is A = 35² = 1225 m².
Let A' be the area of the lawn. Since the area of the lawn is 1081 m², A' = 1081 m².
Now the area of the pool is the difference in area between the area of the square plot and the area of the lawn. So, let A'' be the area of the square swimming pool.
So, A'' = A - A'
A'' = 1225 m² - 1081 m²
A'' = 144 m².
Since the swimming pool is a square, the length of its side, L is thus
L = √A''
L = √144 m²
L = 12 m
So, the length of a side of the pool is 12 m.
12 of 18
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Properties of Operations: Tutorial
Activity
Question 1
Gretchen and her friend Hayley bought three bags of apples and three bunches of bananas from the fruit vendor. Gretchen and Hayley want to
find the total number of pieces of fruit that they bought. Gretchen thinks she should multiply 3 by the number of apples in each bag, X, and add it
to 3 times the number of bananas in each bunch, y, to find the total number of pieces of fruit. Hayley thinks Gretchen should add the number of
apples in each bag, x, to the number of bananas in each bunch, y, and then multiply that sum by 3.
Part A
Write an expression based on Gretchen's method to find the total number of pieces of fruit.
PEE
B
U X X
Font Sizes
AA-
Which property can you apply to Hayley’s expression to show that it is equivalent to Gretchen’s expression
Answers
Answer:
3x+3y and distributive property
Step-by-step explanation:
It is given that
Gretchen buys three bags of apples = 3X
Hayley buys three bunches of bananas = 3Y
As it is also mentioned that it first it is multiplied and then it is added
So, the expression for determining the total number of fruit pieces is
3X + 3Y
And, this expression denotes the distributive property in which we multiplied the each variable and then added it