Answer:
49
Step-by-step explanation:
Given the monomial y²-14y, in order to make the binomial a perfect square, we need to add a constant to the function using completing the square method.
To get the constant, we will multiply the coefficient of y by 1/2 and then square the resulting value.
- The coefficient of y is -14.
multiplying the coefficient of y by 1/2 will give -14/2 = -7
- squaring -7 will result in (-7)²
= 49
The constant that will be added to the binomial to make it a perfect square trinomial is 49
What objects in your everyday lives are in the shape of a triangular prism?
Answer:
wedge of cheese, slice of watermelon, slice of cake, roof of a house, door-stopper
Step-by-step explanation:
Answer:
wedge of cheese, slice of watermelon, slice of cake, roof of a house, door-stopper
Solve the equation for y: -8x + 4y = 20
21 Points
Answer:
y = 5 + 2x
Step-by-step explanation:
[tex]-8x+4y=20\\ 4y=20+8x\\ y=5+2x[/tex]
Add 8x on both sides
Divide by 4 on both sides
Simplify
Can someone tell me what is 6=2(y+2)
Distribute the 2 through the parentheses
on the right side of the equation.
2(y) is 2y and 2(2) is 4.
So the problem now reads 6 = 2y + 4.
Now we can subtract 4 from both
sides of the equation to get 2 = 2y.
Now divide both sides of the
equation by 2 and 1 = y.
Answer:
the answer is attached to the picture
A table is 3 feet wide. The length of the table can be adjusted as needed. You need at least 24 square feet of space on the table. Write and solve an inequality to represent the minimum length the table should have.
The minimum length of a table that is 3 feet wide to have at least 24 square feet of space is found by solving the inequality 3L ≥ 24, which results in a minimum length of 8 feet.
The question involves finding the minimum length of a table to achieve a certain area, which requires understanding and solving an inequality. Given that the table is 3 feet wide and we need at least 24 square feet of space, we can set up the inequality as follows:
Let L be the length of the table in feet.
The area A of a rectangle is calculated as A = length × width.
Thus, A = L × 3 square feet.
To satisfy the condition of having at least 24 square feet, we have the inequality 3L ≥ 24.
Dividing both sides by 3 to solve for L, we get L ≥ 8.
Therefore, the minimum length the table should have is 8 feet.
can you help please on this question i am stuck
I WILL MARK YOU THE BRAINLIEST OF YOU ANSWER FIRST PLS AND FAST!!
[Deleted Because Incorrect]
Factor the expression using the GCF.
60 – 36 =
Answer
12 (5 - 3)
Step-by-step explanation:
The greatest common factor is the largest number that will divide both numbers evenly. As an example, 6 is a common factor because it divides both 60 and 36. However, it is not the greatest common factor.
If I break 60 into it's prime factors, I would get 2 * 2 * 3 * 5.
If I break 36 into it's prime factors, I would get 2 * 2 * 3 * 3.
The two number have the factors, 2, 2, and 3 in common.
The greatest common factor is then: 2 * 2 * 3, or 12.
The expression can be factored as: 12 ( 5 - 3)
To factor the expression 60 - 36, we need to find the GCF of the numbers. The GCF is 12, so the factored form is 24.
Explanation:To factor the expression using the Greatest Common Factor (GCF) 60 - 36, we need to find the largest number that evenly divides both 60 and 36. The GCF of 60 and 36 is 12.
Therefore, we can rewrite the expression as 12 * (5 - 3). Simplifying further, we get 12 * 2 = 24.
So, the factored form of 60 - 36 is 24.
Learn more about Factoring expressions here:https://brainly.com/question/34538246
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If ∠D is a supplementary angle of ∠E and ∠F is a supplementary angle of ∠E, then which of the following statements is true?
Question 5 options:
A)
∠D ≅ ∠F
B)
∠D + ∠E ≅ ∠F
C)
∠E ≅ ∠F
D)
∠D ≅ ∠E
Answer:
A) ∠D ≅ ∠F
Step-by-step explanation:
Supplementary angles : A pair of angles whose sum is 180° are called supplementary angles
We are given that ∠D is a supplementary angle of ∠E
So,[tex]\angle D+\angle E = 180^{\circ} -----1[/tex]
We are also given that ∠F is a supplementary angle of ∠E
So,[tex]\angle F+\angle E = 180^{\circ} ------2[/tex]
Find the value of ∠E form 1 and 2
From 1 : [tex]\angle E = 180^{\circ}-\angle D[/tex]
From 2 : [tex]\angle E = 180^{\circ}-\angle F[/tex]
So, [tex]180^{\circ}-\angle D=180^{\circ}-\angle F[/tex]
[tex]\angle D=\angle F[/tex]
So, Option A is true
Hence ∠D ≅ ∠F
Answer:
A) ∠D ≅ ∠F
Step-by-step explanation:
71 out of 84 chairs are blue. What percentage of the chairs are blue?
Answer:
84.5 percent
Step-by-step explanation:
(brainliest)Armando found the volume of the figure below by using the steps shown. A rectangular prism with a length of 18 inches, width of 5 inches, and height of 8 inches. A triangular prism with a base of 18 inches and height of 6 inches. The prism has a height of 5 inches. Total Volume = Volume of rectangular prism + volume of triangular prism = 5 (8) (18) + one-half (6) (18) (8) = 720 + 432 = 1,152 cubic inches. What mistake, if any, did Armando make? Armando determined the volume correctly. Armando used the wrong formula for the total volume. Armando used the wrong dimensions for the triangular prism. Armando did not apply the order of operations correctly.
Answer: Armando used the wrong dimensions for the triangular prism.
Step-by-step explanation:
Hi, to answer this question we have to analyze Armando’s work.
Total Volume = Volume of rectangular prism + volume of triangular prism
Total Volume = 5 (8) (18) + one-half (6) (18) (8)
Total Volume= 720 + 432
Total volume = 1,152 cubic inches.
He made a mistake in the second step, where used h=8 for the triangular prism instead of h= 5 . (h=height)
The correct way to solve this is.
Total Volume = 5 (8) (18) + one-half (6) (18) (5)
Total Volume= 720 + 270
Total volume = 990 cubic inches.
Answer:
Armando used the wrong dimensions for the triangular prism.
Step-by-step explanation:
A Ferris wheel has a radius of 20 feet and is rotating at a rate of 4 revolutions per minute. When t = 0 (measured in seconds), a chair at the lowest point on the wheel is 6 feet above the ground. Write a model for the height, h, of the chair as a function of time.
Answer:
the model for the height, h, of the chair at a function of time is [tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]
Step-by-step explanation:
To answer the question, we note that the height of the Ferris will varies proportionately to the angle of rotation, hence we can model the height according to he sine function as follows;
y = a·sin(b·x+c) + d
Where: a = Amplitude = Maximum displacement = r = 20 ft
or [tex]a = \frac{maximum - minimum}{2} = \frac{44 - 4}{2} = 20 \, ft[/tex]
The period, [tex]\frac{2\pi }{b}[/tex] = Time for one complete revolution, for a Ferris wheel making 4 revolutions per minute, we have
Period = 1 minute/4 = 15 seconds
Therefore, [tex]\frac{2\pi }{b}[/tex] = 15 seconds or [tex](b =\frac{2\pi }{15})[/tex]
d = the vertical shift is given by minimum + amplitude or maximum - amplitude = 6 + 20 = 26 ft
c = Phase shift since we want the chair to be at the minimum at t = 0 we put c = π/2
x = Independent variable, which in the case of the question is time, t
Therefore, the model for the height, h, of the chair at a function of time is as follows
[tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]
i.e. y = -20×sin(2π/15 + π/2) + 26.
Final answer:
To model the height of the chair as a function of time on a Ferris wheel, use the equation h(t) = 20 × cos((8π/60)t) + 6, where t is in seconds and h(t) is in feet.
Explanation:
To write a model for the height, h, of the chair as a function of time, t, for a Ferris wheel with a radius of 20 feet and a rotation rate of 4 revolutions per minute, we must consider the motion of the wheel. Since the Ferris wheel completes one rotation in 15 seconds (60 seconds/4 minutes), the chair's height above the ground will depend on the cosine of the angular position of the chair. Including the initial condition of the chair being 6 feet above the ground at its lowest point, the mathematical model will be:
h(t) = 20 × cos(ωt + ϕ) + 6
where angular velocity ω is calculated from the rotation rate (4 revolutions per minute) and phase shift ϕ accounts for the initial position. Since t = 0 corresponds to the lowest point, ϕ is 0 degrees or 0 radians (cos(0) = 1). The angular velocity in radians per second is:
ω = 2π × rotation rate = 2π × 4 / 60 = 8π/60 rad/s
Thus, the final equation for the height of the chair as a function of time is:
h(t) = 20 × cos((8π/60)t) + 6
where t is in seconds and h(t) is in feet.
You deposit $20,000 in an account that pays 7.77% annual interest. Find the balance after 2 years when the interest is compounded monthly.
The balance after 2 years is $.
Answer:
=$23,350.802
Step-by-step explanation:
Compound Interest (A)=P(1+r/n)^nt
Where,
P=principal=$20,000
r=Interest rate=7.77%=7.77/100
=0.0777
n=number of periods=12 month in a year
t=time=2 years
(A)=P(1+r/n)^nt
=$20,000(1+0.0777/12)^12×2
=$20,000(1+0.006475)^24
=$20,000(1.006475)^24
=$20,000(1.1675401)
=$23,350.802
HELP ME ASAP!
What is the volume of the right rectangular prism, in cubic inches?
Area of base = 4 sq.in.
cubic inches
Answer:
V = 48 [tex]inches^{3}[/tex]
Step-by-step explanation:
Volume of a rectangular prism = Area of base * height
Substitute in our values and solve for Volume
V = 4 * 12
V = 48 [tex]inches^{3}[/tex]
Answer:
48 Sq.In
Step-by-step explanation:
Did quiz edge and got righ lol
A student drove 9,500 miles in his car last year. Fixed costs totaled $1,215.
Variable costs totaled $1,985. What is the total annual cost? What was the
cost per mile? (Enter answer: $-----; $-----)
Answer: $7,81; $4.78 per mile
Step-by-step explanation:
To get the cost per mile we have to divide 9,500 by the cost.
(The total cost annual was $3,200)
9,500 divided by $1,215 = $7.81
9,500 divided by $1,985 = $4.78
I hope this helps!
Lexi earns $7 for each pillow she sews. Which table represents this proportional
relationship?
Pillows
5
7
9
Earnings ($)
35
49
63
Pillows
6
8
10
Earnings ($)
42
59
63
O Pillows
4
6
8
Earnings ($)
28
42 54
3
6
Pillows
9
10
Earnings ($)
13
16
Answer:
I got the fourth one
Step-by-step explanation:
if she earns 7 dollars for every sew you multiply each one to get the correct answer and see the sum of the money. because 7 times 35 and 7x7 is 49
Mr.Prieto wants to buy pizza that costs $14 each and 5 sodas for $2 each. He has $94. Write and solve an equation to find out how many pizzas he can buy.
Answer:
Mr. Prieto can buy 6 pizzas
Step-by-step explanation:
Cost of 5 soda's = 5 * 2 = $ 10
Remaining amount with him after buying 5 soda's= 94 - 10 = $ 84
Number of pizza's = Remaining amount/cost of 1 pizza
[tex]=\frac{84}{14}[/tex]
= 6 pizzas
Answer:
he can buy 6 pizzas
Step-by-step explanation:
5 x 2 = 10
94-10 = 84
84 divided by 14 = 6
he can buy 6 pizzas.
will give brainliest if answered correctly!!!
So the right answer is 13.
Look at the attached picture
Hope it will help you
The net of a triangular prism is shown. Which measurement is closest to the total surface area of the triangular prism in square centimeters?
A
6 cm2
B
8 cm2
C
14 cm2
D
20 cm2
Answer:
is the anwser a?
Step-by-step explanation:
The total surface area of the triangular prism will be 14 square centimeter.
Option C is correct.
Total surface area :
From the given diagram of triangular prism,
It is observed that, The total surface area of the triangular prism will be the summation of area of two triangle and area of large rectangle.
Area of one triangle =(1/2)*3*2 = 3 square centimeters
So that, area of both triangle =2 * 3=6 square centimeters
Area of large rectangle=(2.5+3+2.5)*1=8*1=8 square centimeters
total surface area of the triangular prism =8+6=14 square centimeters
Therefore, total surface area of the triangular prism is 14 square centimeters.
Learn more about the surface area here:
https://brainly.com/question/16519513
Which graph represents the solution set to this system of equations? –x + 2y = 6 and 4x + y = 3 On a coordinate plane, a line goes through (negative 1, negative 1) and (0, 3) and another line goes through (1, 4) and (2, 2). On a coordinate plane, a line goes through (negative 4, 0) and (0, 4) and another line goes through (negative 1, 1) and (0, negative 3). On a coordinate plane, a line goes through (0, 3) and (2, 4) and another line goes through (0, 3) and (1, 0). On a coordinate plane, a line goes through (0, 0) and (4, 3) and another line goes through (2, 5) and (4, 4).
Answer:
On a coordinate plane, a line goes through (0, 3) and (2, 4) and another line goes through (0, 3) and (0.75, 0).
This answer almost coincide with option C. I suppose there was a mistype.
Step-by-step explanation:
The system of equations is formed by:
–x + 2y = 6
4x + y = 3
In the picture attached, the solution set is shown.
The first equation goes through (0, 3) and (2, 4), as can be checked by:
–(0) + 2(3) = 6
–(2) + 2(4) = 6
The second goes through (0, 3) and (0.75, 0), as can be checked by:
4(0) + (3) = 3
4(0.75) + (0) = 3
On a coordinate plane, a line goes through (-6, 0) and (0, 3) and another line goes through (0.75, 0) and (0, 3).
Given :
The system of equation -- (-x + 2y = 6) and (4x + y = 3)
The following steps can be used in order to determine the graph represents the solution set to this system of equations:
Step 1 - Write the given system of equations.
-x + 2y = 6 --- (1)
4x + y = 3 --- (2)
Step 2 - The x-intercept of equation (1) is:
-x + 0 = 6
x = -6
Step 3 - The y-intercept of equation (1) is:
0 + 2y = 6
y = 3
Step 4 - The x-intercept of equation (2) is:
4x + 0 = 3
x = 3/4
Step 5 - The y-intercept of equation (2) is:
0 + y = 3
y = 3
On a coordinate plane, a line goes through (-6, 0) and (0, 3) and another line goes through (0.75, 0) and (0, 3).
For more information, refer to the link given below:
https://brainly.com/question/11897796
If a person's eye level is h meters above sea level and he can see d kilometers to the horizon, then d=3.57h. Suppose the person's eye level is 15.21 meters
above sea level. How far can he see to the horizon?
Round your answer to the nearest tenth.
Answer:
54.3m
Step-by-step explanation:
h = distance above sea level
d = distance he can sea above sea level
d = 3.57h
h = 15.21m
d = ?
d = 3.57 × 15.21
d = 54.2997m approximately 54.3m
The person can see up to a distance of 54.3m
Answer:
d = 7.5
Step-by-step explanation:
d = 3.57[tex]\sqrt{h}[/tex]
= 3.57[tex]\sqrt{4.41}[/tex]
= 3.57( 2.1)
= 7.497
d = 7.5!
Which equation represents a circle that contains the point (-5. -3) and has a center at (-2, 1)?
Distance formula: (x2-x1)^2 + (y2-y1)^2
A. (x - 1)2 + (x + 2)2 = 25
B. (x + 2)2 + (-1)2 = 5
C. (x + 2)2 + (x - 1)2 = 25
D. (x - 1)2 + (y + 2)2 = 5
For every $4 Gillian makes, her friend Lucas makes $5.
Lucas makes $54,000 each year. How much does Gillian
make in a year?
Answer:
67500
Step-by-step explanation:
4-----54000
5-----x
4x=54000*5
x=67500
Answer:
43,200
Step-by-step explanation:
4/5=x/54000
What is the diameter of the following?
(x - 9)2 + (– 4)2 = 36
(by the way the 2’s are actually squared but it won’t let me put that on this app:( )
Answer:
12
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 9)² + (y - 4)² = 36 ← is in standard form
with r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6
diameter = 2 × r = 2 × 6 = 12
Which value can be added to the set below without changing its mean?
{4, 10, 14, 18, 22, 22}
O 0
O 15
O 16
O 22
Answer:
15..
Step-by-step explanation:
4, 10, 14, 18, 22, 22
Mean = (4 + 10 + 14 + 18 + 22 + 22)/6
= 90/6
= 15.
Number to be added, 'y'
For the mean to be the same
(90 + y) / 7 = 15
90 + y = 15 × 7
90 + y = 105
y = 105 - 90
= 15
Joanna went to school supply shopping. She spent $31.80 on notebooks and pencils. Notebooks cost $2.05 each and pencils cost $1.50 each. She bought a total of 19 notebooks and pencils. How many of each did she buy?
A.
11 notebooks; 8 pencils
B.
9 notebooks; 10 pencils
C.
6 notebooks; 13 pencils
D.
4 notebooks; 15 pencils
Answer:
C
Step-by-step explanation:
Total number of notebooks and pencils= 19
Assuming that she bought notebooks only,
amount spent
= 19($2.05)
= $38.95
Difference in actual amount spent
= $38.95 -$31.80
= $7.15
This difference in amount is due to the number of wrong assumptions we have made previously, such that we assumed that a certain number of pencils that she bought was notebooks. Thus, let's find the number of wrong assumptions so we can find out how many pencils she bought.
Cost difference of each notebook compared to a pencil
= $2.05 -$1.50
= $0.55
This means that for each wrong assumption, there is an additional $0.55 in the total amount Joanna spent.
Number of sets of extra $0.55
= $7.15 ÷$0.55
= 13
Thus, she bought 13 pencils.
Amount of notebooks bought
= 19 -13
= 6
Let's check our work!
If Joanna bought 13 pencils and 6 notebooks,
total amount spent
= 13($1.50) +6($2.05)
= $19.50 +$12.30
= $31.80
Thus option C is indeed correct as it is given from the question that she spent $31.80.
Answer:
correct answer is c
Step-by-step explanation:
y = 9x - 12. What is the slope of the equation?
Answer:
Step-by-step explanation:
the correct answer is the last option on the bottom
Answer:
Slope: 9 y-intercept (0,-12)
Step-by-step explanation:
y=mx+b
m is always the slope
b is always the y-intercept
y=9x-12
you can see 9 is m and -12 is b
Convert
4pie/3
to degrees.
PLS MARK BRAINLIEST
Joe counts 48 animals with 134 legs among the pigs and chickens on his far. All the pigs have 4 legs and all the chicken have 2 legs.How many pigs and chicken does he have?
Answer:
19 Pigs
29 Chickens
Step-by-step explanation:
19 pigs with 4 legs each =
19 x 4 = 76 legs
+
29 chickens with 2 legs each =
29 x 2 = 58 legs
-----------------------------------------------
48 animals total 134 legs total
Multiply the binomials (3x - 5) and (4x + 6).
A)
12x2 + 38x + 30
B)
12x2 + 38x - 30
C)
12x2 - 2x + 30
D)
12x2 - 2x - 30 PLS ANYONE ANSWER
Answer:
12x² - 2x - 30
Step-by-step explanation:
(3x - 5)(4x + 6)
12x² + 18x - 20x - 30
12x² - 2x - 30
The Multiplication of the binomials (3x - 5) and (4x + 6) will be 12x² - 2x - 30. Then the correct option is D.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The binomails are given below.
(3x - 5) and (4x + 6)
Multiply the binomials (3x - 5) and (4x + 6), then we have
⇒ (3x - 5) · (4x + 6)
⇒ 3x · (4x + 6) - 5 · (4x + 6)
⇒ 12x² + 18x - 20x - 30
⇒ 12x² - 2x - 30
The Multiplication of the binomials (3x - 5) and (4x + 6) will be 12x² - 2x - 30. Then the correct option is D.
More about the polynomial link is given below.
https://brainly.com/question/17822016
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−3−4x≤21 pls help me
Answer:
-7x<21
i think, I'm not fully sure what it's asking.
Step-by-step explanation:
Answer:
x ≥ - 6
Step-by-step explanation:
Given
- 3 - 4x ≤ 21 ( add 3 to both sides )
- 4x ≤ 24
Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity.
x ≥ - 6