The distance that Greg is from home after 12 hours is given as follows:
300 miles.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y = 25x.
Hence the distance after 12 hours is given as follows:
y = 25 x 12
y = 300 miles.
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Select the correct answer. Given the following formula, solve for y. w=x-y/2 -z
Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
Given the following formula,
w=x-y/2 -z
We need to solve for y.
[tex]w = \dfrac{x-y}{2 -z}[/tex]
By cross multiplication
[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]
subtract x both side
2w - wz -x = x - y -x
y = x - 2w + wz
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Simplify the expression.
Show your work.
4 √81m^8n^16
Answer:
hope you can understand
Answer:
3m²n⁴
Step-by-step explanation:
Given :
⇒ [tex]\sqrt[4]{81m^{8}n^{16} }[/tex]
=============================================================
Solving :
⇒ [tex]\sqrt[4]{81}[/tex] × [tex]\sqrt[4]{m^{8} }[/tex] × [tex]\sqrt[4]{n^{16} }[/tex]
⇒ [tex]\sqrt[4]{3^{4} }[/tex] × [tex]\sqrt[4]{(m^{2})^{4} }[/tex] × [tex]\sqrt[4]{(n^{4})^{4} }[/tex]
⇒ 3 × m² × n⁴
⇒ 3m²n⁴
A scale model of a building is 3 inches tall. If the building is 90 feet tall, find the scale of the model.
The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
Scaling of measurementScaling is the way of enlarging or reducing the image of an object.
Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;
Convert both measures to same units
Since 1 feet. = 12 in
90 feet = 90/12 in = 7.5 in
Take the ratio
3 : 7.5 = 30: 75
Reduce to lowest term
30: 75 = 2 : 5
Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
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3 (without using trig table) evaluate
It tan 60 x tan 30 divided by
Tan 60 + tan 30
Answer:
[tex]1.25332[/tex]
Step-by-step explanation:
[tex] tan(30 times tan(60 ) \div \tan(60 \div + 30) [/tex]
Find the lateral area of the prism. 8cm 6cm, I 1 13cm I 10cm Lateral Area = [?]cm² 2008-2012 International Academy of Science, All Rights Reserved. Aid Enter
The lateral area of the prism is 270cm²
What is the lateral area of a prism?
The lateral area of a prism is defined as the sum of the areas of its lateral faces.
How to determine the lateral area of a prismUsing the formula;
Lateral area = (a+ b+ c) h
Where a, b, c, are all the lateral faces and h is the height
Lateral area = (8 + 6 + 13) × 10 = 27 × 10 = 270cm²
Therefore, the lateral area of the prism is 270cm²
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ANSWER QUICK PLSSSS AND MAKE SURE YOUR ANSWER IS CORRECT!!
Which of the following algebraic expressions can be used to express the statement "three less than z squared?" (5 points)
z2 − 3
3 − z2
3 − 2z
2z − 3
what are the soltuions to the quadratic equation below? 12x squared + 4x -5=0
Answer: 0.5 or - 0.834
Step-by-step explanation: Here is the explanation!
Collect info on minimum and maximum temperature if 7 consecutive days in creative manner
calculates the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100
The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
How to calculate arithmetic progression?The first term of an arithmetic progression can be calculated using the following expression:
Sn = n/2 [2a + (n − 1)d]
Where;
a = first termUn = sumn = no of termsd = common ratio100 = 2 [2a + (4 - 1)4]
100 = 4a + 24
4a = 100 - 24
a = 76/4
a = 19
Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
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Find sin A for the triangle below. Give the exact value as an expression and an approximation to the nearest ten-thousandth. Note: The triangle is not drawn to scale.
the exact value of sin A to the nearest ten- thousandth is 0. 6625
Using the pythagorean theorem
a² + b² = c²
The opposite side is unknown, so use the pythagorean theorem to find it
c = hypotenuse = 4
a= opposite site = ?
b= adjacent side = 3
Substitute into the formula
4² = a² + 3²
16 = a² + 9
a² = 16 -9 = 7
Find the square root
a =√7 = 2. 65
To find Sin A, use
Sin A = opposite side ÷ hypotenuse
Sin A = 2. 65 ÷ 4 = 0. 6625
Thus, the value of sin A is 0. 6625
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Help, forgot how to do this, and need to answer asap
Answer:
(a)12
(b)28
(c)1
Step-by-step explanation:
the dots on the plot for a and b and for c It's almost exactly a whole hour decrease of HW a student is likely to do for every extra hour a student watches TV
Expand and simplify: (-7y - 8) (y - 4)
To expand an expression, use FOIL method.
F - FirstMultiply the first term in each expression inside the parentheses.-7y and y are the first terms in each expression.
(-7y)(y) = -7y²
O - Outside Next is to multiply the terms outside. (The first term in the first expression and the last term in the second expression)-7y is the first term in the first expression
-4 is the last term of the second expression
(-7y)(-4) = 28y
I - InsideThe next step is to multiply the terms inside. (The last term in the first expression and the first term in the last expression)-8 is the last term in the first expression
y is the first term in the second expression
(-8)(y) = -8y
L - LastLast step is to multiply the last term in each expression.-8 is the last term of the first expression
-4 is the last term of the second expression
(-8)(-4) = 32
Combine all simplified terms.
-7y² + 28y - 8y + 32-7y + 20y + 32Answer:
-7y + 20y + 32Wxndy~~
Find the surface area of the prism. 8 4 14
Answer:
4 8 1 4 0,683 the (783)-213=509
Please help
Use absolute value to find the distance between 3 and -3 on a number line.
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
Find the surface area of the shape below. Round your answer to two decimal places.
The surface area of the given shape is 285.01 ft²
Surface area of a coneFrom the question, we are to calculate the surface area of the given shape.
The given shape in the diagram is a cone.
The surface area of a cone is given by the formula,
[tex]S = \pi r(r+l)[/tex]
Where S is the surface area
r is the radius
and [tex]l[/tex] is the slant height
First, we will calculate the slant height of the cone
[tex]l^{2}=9^{2} +5.6^{2}[/tex] (Pythagorean theorem)
[tex]l^{2}=81+31.36[/tex]
[tex]l^{2}=112.36[/tex]
[tex]l}=\sqrt{112.36}[/tex]
[tex]l=10.6 \ ft[/tex]
∴ The slant height is 10.6 ft
Now, for the surface area
[tex]S = \pi \times 5.6(5.6+10.6)[/tex]
[tex]S = \pi \times 5.6(16.2)[/tex]
[tex]S = 90.72\pi \ ft^{2}[/tex]
[tex]S = 285.0053 \ ft^{2}[/tex]
S ≅ 285.01 ft²
Hence, the surface area of the given shape is 285.01 ft²
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which expression is equivalent to 15n – 20
2(8n – 6)
6(2n – 9)
5(3n – 4)
5(4n – 3)
A football club is the only one in its region and is therefore able to behave like a monopolist. It sells tickets to Adults (a) and Juniors (j), whose demand curves are given by:
Pa = 200 − Qa
Pj = 160 − Qj
Additionally, the club’s total costs are given by = 20Qi
The club hires an economist to consider its pricing strategy and receives the advice that it should charge different prices to each type of supporter. Find the prices it sets in both markets, the sales (output) in each and its overall level of profit and illustrate profit maximising outputs and prices of each consumer type on a graph (one graph for each type of consumer). Calculate consumer surplus in this case.
Answer:
Adult market
price: 110sales: 9900profit: 8100consumer surplus: 9000Junior market
price: 90sales: 6300profit: 4900consumer surplus: 5600Total profit: 13000
Total consumer surplus: 14600
Step-by-step explanation:
Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.
RevenueEach demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).
R = QP = Q(Pmax -Q)
ProfitThe profit is the difference between revenue and cost.
Profit = R - C = Q(Pmax -Q) -20Q
Profit = Q(Pmax -20 -Q)
Writing the demand equation in terms of P, we find ...
Q = Pmax -P
Substituting this into the Profit equation gives ...
Profit = (Pmax -P)(Pmax -20 -(Pmax -P))
Profit = (Pmax -P)(P -20)
The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:
Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10
PricesIn the adult market, Pmax = 200, so the profit-maximizing ticket price is ...
Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market
In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...
Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market
SalesUsing the revenue equation, we find the sales in each market to be ...
Qa = 200 -Pa = 200 -110 = 90
Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market
Qj = 160 -Pj = 160 -90 = 70
Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market
Overall ProfitThe profit in each market is ...
Adult market profit = 90(110 -20) = 8100
Junior market profit = 70(90 -20) = 4900
The overall profit will be the sum of the profits in each market:
Overall profit = 8100 +4900 = 13000
Consumer surplusThe consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.
CSa = (1/2)(200)Qa = 100(90) = 9000
CSj = (1/2)(160)(Qj) = 80(70) = 5600
The total consumer surplus is ...
CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus
Graph
The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.
The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.
Evaluate the series 12 + 6 + 3 + . .
A) 21
B) 1.5
C) 2
D) 24
All the numbers follow a pattern of division by 2
Therefore the next number is 3/2 which is equal to 1.5
In which triangle is the value of x equal to cos−1(StartFraction 4.3 Over 6.7 EndFraction)?
(Images may not be drawn to scale.)
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle opposite to side with length 4.3 is x.
A right triangle is shown. The length of the hypotenuse is 4.3 and the length of another side is 6.7. The angle between 2 sides is x.
A right triangle is shown. The length of the 2 sides are 6.7 and 4.3. The angle opposite to side with length 4.3 is x.
The correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
The complete figure is attached with the answer below.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
In the given figure of option A, we can see that the hypotenuse is 6.7 and the base is 4.3 and the angle between both the sides is x. Now we will calculate the angle of cosine x.
Cos(x)= Base / Hypotenuse
Cos(x) = ( 4.3 / 6.7 )
(x) = Cos⁻¹ ( 4.3 / 6.7)
Therefore the correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
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Answer:
The answer is A
Step-by-step explanation:
Just took the test
please help! what is the angle of depression from point C to point A
Answer:
The angle shows 90° so that means
90° - 42° = 48°
Therefore the angle of the depression is 48°
The angle of depression from C to point A 48°. The correct option is c. 48°
Angles of depressionFrom the question, we are to determine the angle of depression from C to point A
The angle of depression is the angle formed between the horizontal line and the line of sight when an observer looks downwards at an object
Thus, in the given diagram
The angle of depression is 90° - 42°
Angle of depression = 48°
Hence, the angle of depression from C to point A 48°. The correct option is c. 48°
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Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
108°
Step-by-step explanation:
From the diagram,
Angle X + Angle CXD = 180°
Angle X + 72° = 180°
Angle X = 180° - 72° = 108°
Question 2
Which sign makes the following statement true? 2/5 ___ 6/15
1. =
2. >
3.
Answer:
1 is answer
Step-by-step explanation:
2*3/5*3___6/5
Connor wants to divide 360 jellybeans into equal groups. He wants each group to have more than 5 jellybeans, but less than 100. What are three possible groupings Connor can make?
one group made up of 12 can each have 50 = 600
Answer:
One way is that there can each be 99 for each. 99x3= 297 which, isn't too far from 360. Another way is that they can each have 50. 50x3=150. The last way is to have them each have 30. 30x3=90.
Step-by-step explanation: Hope I helped at least a little bit. Give brainliset to best answer. I don't think my answer was that good. Let me know if it helped at all.
Tess has a garden that is 4 1/2 feet wide and 6 3/4 feet long. How many feet of fencing does she need to put around all sides of her garden?
Answer:
11.25
Step-by-step explanation:
6 3/4 + 4 1/2
What type of function is f(x) = 2x -14?
Exponential
Logarithmic
Polynomial
Rational
The function f(x) = 2x -14 is a polynomial function
How to determine the function type?The equation of the function is given as:
f(x) = 2x -14
A polynomial is represented as:
f(x) =ax^n + bx^(n - 1)....... + c
Where n is at least 1.
The function f(x) = 2x -14 is a polynomial with a degree of 1
Hence, the function f(x) = 2x -14 is a polynomial function
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If 8x + y = -1 is a true equation, what would be the value of y + 8x
Which combined inequality has the same solution set shown in the graph?
Number line ranging from negative sixteen to zero with a line beginning with a close point at negative twelve and continuing to the left without end, and a second line beginning with a closed point at negative five and continuing to the right without end.
a ≤ –12 or a > 5
a ≤ –12 or a > –5
–a ≤ –12 or a > –5
–a ≤ –12 or a < –5
Step-by-step explanation:
there is a problem here. based on your textual description none of the 4 answer possibilities are right.
you said, one line starts with a closed (filled) point at -12 and going to the left (without end). a closed point means the point is included.
so, everything -12 and smaller.
that is a <= -12
the other line starts with a closed (filled) point at -5 and goes to the right without end.
this is a >= -5
so, if your textual description is right, you need an answer option
a <= -12 or a >= -5
FYI
the answer options with -a <= -12 don't make much sense, because that simply means a >= 12. and you don't have any line starting at plus 12 and going to the right.
Need a little help!
Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for .
A sphere has a radius of 12 centimeters.
The volume of the sphere is about
cm³.
What’s the range of this graph?
A) all real numbers
B) all real numbers greater than or equal to 0
C) all real numbers greater than or equal to 1
D) all real numbers greater than or equal to 2
Option d is the correct answer. All real numbers are greater than or equal to 2.
What are domain and range?Domain of a function--The domain of the function is the set or collection of all the x-values for which the function is well defined.
Range of a function--The range of a function is the set of all the values which are attained by a function in its defined domain.
By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2). Hence, the range is: [2,∞).
Thus Option d is the correct answer. All real numbers are greater than or equal to 2.
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Which graph represents y = root(3, x) + 2 ?
Using translation concepts, the graph that represents [tex]y = \sqrt[3]{x} + 2[/tex] is given at the end of the question.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
[tex]y = \sqrt[3]{x} + 2[/tex] is a shift up of 2 units of [tex]y = \sqrt[3]{x}[/tex], hence the graph is given at the end of this question.
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