Answer:
Jacks Rate: 3 miles per hour
Jills Rate: 4.5 miles per hour
Time: 40 minutes or 2/3 of an hour
Step-by-step explanation:
Setting up the Algebraic Expressions:This problem in it self isn't necessarily too complex, but a crucial part of it is taking the context given and somehow making that into a algebraic expression which we can then use to solve the equation.
Assigning Unknowns and Variables:So let's first assign two unknowns to the rates at which Jack and Jill walk. Since both of there names start with J, I'll use a subscript to differentiate between the two.
[tex]\text{let }J_a=\text{Jack's walking rate}\\\text{let }J_i = \text{Jill's walking rate}[/tex]
Notice that both have a J, but there is a little letter to the right and below, which is a subscript. This way we can easily tell which person we are referring to while not having to write out their entire name as a variable.
Now let's assign two variables. First let's assign distance: [tex]D=\text{distance from top of hill}[/tex]
and let's also assign time to a variable: [tex]t = \text{time in hours}[/tex]
Deriving Equations:Now let's start making some equations! If jack is two miles away from the top of the hill, in general, the distance from the hill can be calculated using the following equation: [tex]D=2-t*j_a[/tex]
Essentially, Jack starts off with a distance of two miles away, and after one hour, Jack will walk [tex]j_a[/tex] miles, this is his rate, what Jake travels in one hour. After another hour passes, he will do the same thing, but twice. So this is why we're multiplying by time. Since for each hour that passes, he will walk a further: [tex]j_a[/tex] miles, meaning he will be that much closer, so we subtract it from 2, the initial distance.
The same logic can be applied to Jill, except with an initial distance of 3 miles and using the unknown: [tex]j_i[/tex] which is Jill's rate. So we get the following equation: [tex]D=3-t*j_i[/tex]
If we're looking for when they reach the top of the hill, that means that the distance from the hill is zero. So let's set both equations to zero.
[tex]0=3-t*j_i\\0=2-t*j_a[/tex]
From here let's solve for time for both equations. So let's start with the first equation.
[tex]0=3-t*j_i[/tex]
From here let's subtract 3 from both sides to get rid of the 3 on the right side.
[tex]0-3=(3-3)-t*j_i\implies-3=-t*j_i[/tex]
from here let's divide both sides by Jill's rate.
[tex]\frac{-3}{j_i} = \frac{-t*j_i}{j_i} \implies \frac{-3}{j_i}=-t[/tex]
From here let's divide both sides by -1 to get t isolated.
[tex]\frac{\frac{-3}{j_i}}{-1} = \frac{-t}{-1} \implies \frac{3}{j_i}=t[/tex]
We can essentially apply the same steps to the equation we derived from Jack's rate.
[tex]0=2-t*j_a\\\\(0-2)=(2-2)-t*j_a \implies -2 = -t*j_a\\\\ \frac{-2}{j_a} = \frac{-t}{j_a} \implies \frac{-2}{j_a} = -t\\\\\frac{\frac{-2}{j_a}}{-1} = \frac{-t}{-1} \implies \frac{2}{j_a} = t[/tex]
Now we have the equations:
[tex]\frac{2}{j_a} = t\\\\\frac{3}{j_i} = t[/tex]
and this represents the time needed to reach the top of the hill (since we set both equations equal to zero)
Substituting and Solving:From here we need to look once more at the question, specifically where it says: "It takes them the same amount of time to get there". So we set the equations equal to each other.
[tex]\frac{2}{j_a} = \frac{3}{j_i}[/tex]
Now we use our last piece of needed context: "Jill walks 1.5 miles per hour faster than Jack". We can set up one more equation: [tex]J_i = J_a+1.5[/tex].
This is super useful to have, since we can now make a substitution give this equation, converting our two-variable equation into a one-variable equation, allowing us to solve for one numerical value.
We have: [tex]\frac{2}{j_a} = \frac{3}{j_i}[/tex] and we know that: [tex]J_i = J_a+1.5[/tex], so let's simply plug in [tex]J_a+1.5[/tex] for [tex]j_i[/tex].
This gives us the equation:
[tex]\frac{2}{J_a}= \frac{3}{J_a + 1.5}[/tex].
Cross Multiply:
[tex]2(J_a+1.5) = 3(J_a) \implies 2J_a + 3 = 3J_a[/tex].
Subtract [tex]2J_a[/tex]:
[tex]3=J_a[/tex].
We can solve for Jills value, since Jill's value is just 1.5 miles per hour more than this, so [tex]J_i = 3+1.5=4.5[/tex]
Now let's take Jacks value and substitute it into his time equation
[tex]t = \frac{2}{3}[/tex]
we can keep this in hours, or we can convert this into minutes. We can convert this in to minutes by multiplying the amount of minutes in an hour by 2/3, so: [tex]60 * \frac{2}{3} = \frac{120}{3} = 40\text{ minutes}[/tex]
What is the equation of f(x)?
f(x)=8(4)x
f(x)=−8(4)x
f(x)=8
f(x)=−8
Answer:The correct anserw is f(x=-8
Step-by-step explanation:
5. The dimensions of a sandbox can be represented as (x+2) inches and (x+1) inches. The value of the area, in square inches, of the sandbox is equal to the value the perimeter in inches. Write an equation that can be used to find the value of x.
x² - x - 4 = 0 is the equation that can be used to find the value of x.
Given,
The dimensions of a sand box is given as (x + 2) inches and (x + 1) inches.
The value of the area, in square inches, of the sandbox is equal to the value the perimeter in inches.
We have to find an equation that can be used to find the value of x;
Here,
Consider the sand box as a rectangle.
Area of rectangle = length x width
That is,
Area of sand box = (x + 2) (x + 1) = x² + x + 2x + 2 = x² + 3x + 2
Now, Perimeter of rectangle = 2(length + width)
That is,
Perimeter of sand box = 2(x + 2 + x + 1) = 2(2x + 3) = 4x + 6
Now,
Equate both the equations;
x² + 3x + 2 = 4x + 6
x² + 3x + 2 - 4x - 6 = 0
x² - x - 4 = 0
Therefore,
The equation that can be used to find the value of x is x² - x - 4 = 0
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Alliyah’s gift card balance can be represented by the equation y=-5x+50, where y represents the gift card balance after x number of days. Graph this equation.
The graph of the given equation is attached bellow.
What is a graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Here, for instance, we can plot a graph showing the type and quantity of school supplies used by pupils in a class based on the data provided below. Each supply is first counted, and the data is then shown in a table with specific colors in a logical order.
Given equation is y=-5x+50
Where y represents the gift card balance after x number of days.
First find some points on the line.
Putting x = 5 in the given equation:
y = (- 5 × 5) + 50
y = -25+ 50
y = 25
Putting x = 0 in the given equation:
y = (- 5 × 0) + 50
y = -0+ 50
y = 50
Putting x = -1 in the given equation:
y = (- 5 × (-1)) + 50
y = 5+ 50
y = 55
The points on the line are (5, 25), (0,50), and (-1,55).
Plot the points and join them.
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Can you help me with number 4 I can’t solve it I tried many ways. Help me do the full number 4 the x and the and angles please help me! Anyone
Answer:
x = 20 6/7∠3 = 65 3/7∠8 = 65 3/7Step-by-step explanation:
You have transversal n crossing parallel lines l and m, creating angles labeled 1–8. Angles 1, 3, 6, 8 are shown as obtuse, and the others are shown as acute. You want values of x and angles, given certain angle expressions.
4.The acute and obtuse angles are supplementary. Angles 3 and 5 are "consecutive interior angles", so are supplementary.
∠3 +∠5 = 180
(4x -18) +(3x +52) = 180
7x +34 = 180 . . . . . . . . . . collect terms
7x = 146 . . . . . . . . . subtract 34
x = 20 6/7 . . . . divide by 7
The measures of the angles are ...
∠3 = 4x -18 = 4(20 6/7) -18 = 83 3/7 -18 = 65 3/7
∠5 = 3x +52 = 3(20 6/7) +52 = 62 4/7 +52 = 114 4/7
Note that the total of angles 3 and 5 is 180°.
The problem asks for the measure of angle 8. Angle 8 is an alternate interior angle with respect to angle 3, so is congruent.
∠8 = ∠3 = 65 3/7
__
Additional comment
Note that the angle values of question 4 make the angles that appear to be obtuse in the diagram actually have measures less than 90°. The figure is not drawn to scale.
Tyson does 80 sit-ups during his work out. He wants to increase his sit-ups by 25%. Which represents the new amount of sit-ups?
The new amount of sit - ups will be 200.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Tyson does 80 sit-ups during his work out.
And, He wants to increase his sit-ups by 25%.
Now,
Since, Tyson does 80 sit-ups during his work out.
And, He wants to increase his sit-ups by 25%.
Hence, We get;
The new amount of sit-ups = 80 + 25% of 80
= 80 + 25/100 × 80
= 80 + 20
= 100
Thus, The new amount of sit - ups = 200
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Find the value of x
10
4
6
5
The value of x is option (B) 4
Consider the bottom triangle
All the angles of the triangle is equal therefore, the triangle is an equilateral triangle. All the three sides of the equilateral triangle will be equal
One side is given
The length of the side LM = 5 units
The length of the side MK = 5 units
The angle J = Angle MKL
Therefore the triangle MKL is an isosceles triangle
Then, the length of the side MK = The length of the side MJ
Substitute the values in the equation
x + 1 = 5
x = 5 -1
x = 4 units
Therefore, the value of x is 4
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4) A system of equations is shown below. Solve the system of equations using elimination.
(show your work 1 point) (correct answer 1 point)
Equation A: 5x + 9y = 10
Equation B: 4x - 3y = 8
Solving the system of equations 5x + 9y = 104x - 3y = 8 and using elimination, x is 2 and y is 0.
Describe elimination method.The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients. The addition property of equality is used in the elimination technique to solve systems of linear equations. The same value can be added to both sides of an equation. You can therefore add x + y to the left side of the first equation and add 8 to the right side of the equation if your system is x - 6 = 6 and x + y = 8.
Given,
Equation A: 5x + 9y = 10
Equation B: 4x - 3y = 8
Solving the system of equations using elimination,
Multiplying equation B by 3
5x + 9y = 10
12x - 9y = 24
---------------------
17x = 34
x = 2
Equating x = 2 in equation 2
4x - 8 = 3y
4(2) - 8 = 3y
y = 0
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Please help me I don’t understand.
Answer:
A.
Step-by-step explanation:
I'd say A because it's asking for you to explain the answer. the 10 is the tv and it is also an x value the 60 is the y value. Not sure how to explain properly sorry i think this is best i can explain it...
Determine which set of side measurements could be used to form a right triangle.
4, 11, 20
16, 21, 25
5, 13, 25
3, 4, 5
The set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
The side length of the triangle is shown in the option:
As we know,
Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
Using Pythagoras' theorem:
From option(D):
3, 4 and 5
(3)² + (4)² = 5²
9 + 16 = 25 (True)
Thus, the set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.
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Find the circumference of a pizza if the diameter is 10 inches.
0.314 in.
3.14 in.
3.04 in.
31.4 in.
Answer:
31.4 inch
Step-by-step explanation:
So the circumference of a circle is pi times the diameter=10 times 3.14 (pi is around 3.14)=31.4
Classify the following triangle as acute, obtuse, or right.
A. Obtuse
• B. Acute
• C. Right
•. D. None of these
Answer:
A. obtuse
Step-by-step explanation:
process of elimination when looking at examples of different triangles
A line of fit was used to predict the values of ŷ in the table:
x y ŷ
3 12 9.1
7 9 11.9
9 16 13.3
10 14 14
12 5 15.4
15 24 17.5
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is a large number.
No, the equation is not a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.
The line is the best fit because the sum of the residuals is a small number(1.2), so option D is correct.
What is a line of fit?A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.
Calculate the residual as shown below,
[tex]Residual = y - \hat{y}[/tex]
12 - 9.1 = 2.9
9 - 11.9 = -2.9
16 - 13.3 = 2.7
14 - 14 = 0
5 - 15.4 = -10.4
24 - 17.5 = 6.5.
Hence, the sum of the residuals is given as follows:
2.9 - 2.9 + 2.7 + 0 - 10.4 + 6.5 = 1.2
The sum of the residual is a small number, so it is the best fit.
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Find the slope of the line that passes.
(-2, -1) and (-4, -7)
Answer:
m=3
Step-by-step explanation:
Find the equation of a line perpendicular to y = x + 1 that passes through the
point (8,-3).
Oy=x+1
Oy=-x+5
Oy=-x+1
Oy=x+5
The equation of a line perpendicular to y = x + 1 that passes through the
point (8,-3) is y = x+1.
What is line equation?
The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).
[tex]$x$[/tex] - axis interception points of [tex]$x+1: \quad(-1,0)$[/tex]
[tex]$y$[/tex]-axis interception point of [tex]$x+1: \quad(0,1)$[/tex]
X Intercepts: [tex]$(-1,0), \mathrm{Y}$[/tex] Intercepts: [tex]$(0,1)$[/tex]
Slope of [tex]$x+1: \quad m=1$[/tex]
[tex]$x+1$[/tex]
For a line equation for the form of[tex]$y=m x+b$[/tex], the slope is m, m=1
y = x+1
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which expression is equivalent to 2^3/2^7
A. 2^4
B. 1/2^4
C. -2^4
D. - 1/2^4
What happens to y = x when the slope is changed to a number smaller than 1?
Answer:
When the slope of a line is changed to a value that is less than 1, the line becomes less steep. This means that the change in the y-value (the vertical direction) for a given change in the x-value (the horizontal direction) is smaller than it was before. For example, if the original line had a slope of 2 and the new slope is 0.5, the line will be less steep and the change in y for a given change in x will be smaller.
Find the missing side length.
Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer.
Answer:
5 yd
Step-by-step explanation:
Missing side = 11 - 6 = 5 yd
During a sale all items of men clothing were reduced by 20% of marked price if the store made 5% profit on the cost price what % of profit did it make on the marked up price before the sale
Answer: Sales Price = ($17,000 * 20%) + $17,000 = $20,400
The amount of a same le remaining after T days is giving by the equation p(f)=a(1/2) T/h
Answer:
6
Step-by-step explanation:
Question 9 A report states that 56% of homes in Illinois had air conditioning. 4 pts How large a sample is needed to estimate the true proportion of Illinois homes that have air conditioning to within 3% with 99% confidence?
The required sample size to estimate the true proportion of Illinois homes that have air conditioning to within 3% with 99% confidence is of:
1816.
How to obtain the required sample size?The required sample size is obtained using the z-distribution, as we are working with a confidence interval of proportions.
The equation that determines the margin of error of a confidence interval is presented as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The estimate in this problem, along with the desired margin of error, are given as follows:
[tex]\pi = 0.56, M = 0.03[/tex]
Then the needed sample size is calculated as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 2.575\sqrt{\frac{0.56(0.44)}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.575\sqrt{0.56 \times 0.44}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.56 \times 0.44}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.56 \times 0.44}}{0.03}\right)^2[/tex]
n = 1816. (rounded up, as a sample size of 1815 would have a margin of error slightly above 3%).
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I need help with this question pls someone fast I’ll give brainliest and good amount of points
Answer:
a rotation 180°clockwise abt the origin
How do I do this problem
The rule that describes the composition of transformations of triangle ABC to triangle A''B''C'' is given as follows:
R(x-axis) and T(-6,-2)(x,y) -> second option.
What are the transformations?The vertices of the original triangle are given as follows:
A(5,-5), B(1, -2) and C(1,-5).
The triangle A'B'C' was reflected, as the orientation was changed, and the vertices are given as follows:
A'(5,5), B'(1, 2) and C'(1,5).
Hence the rule of the reflection is given as follows:
(x,y) -> (x,-y).
Meaning that it underwent a reflection over the x-axis.
Then triangle A''B''C'' is obtained with a translation of triangle A'B'C', as only the position changed, keeping the orientation equal.
The vertices are given as follows:
A''(-1,3), B'(-5, 0) and C'(-5,3).
Hence the rule is given as follows:
(x,y) -> (x - 6, y - 2).
Which is a translation of 6 units left and 2 units down, meaning that the second option is correct.
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Use the properties of logarithms to write the expression as a single logarithm, if possible.
By logarithm properties, the logarithmic equation 2 · ㏒ₐ (5 · x³) - (1 / 2) · ㏒ₐ (2 · x + 3) is equivalent to ㏒ₐ [(25 · x⁶) / √(2 · x + 3)]. (Correct choice: A)
How to simplify a logarithmic function by propertiesIn this problems we have a logarithmic equation that must be simplified by means of logarithm properties, all of them described below:
Logarithm of a product of two numbers
㏒ₙ (a · b) = ㏒ₙ a + ㏒ₙ b
Logarithm of a division of two numbers
㏒ₙ (a / b) = ㏒ₙ a - ㏒ₙ b
Logarithm of a power of a number
㏒ₙ aˣ = x · ㏒ₙ a
Now we proceed to reduce the logarithmic equation into a single expression:
2 · ㏒ₐ (5 · x³) - (1 / 2) · ㏒ₐ (2 · x + 3)
㏒ₐ (5 · x³)² - ㏒ₐ √(2 · x + 3)
㏒ₐ (25 · x⁶) - ㏒ₐ √(2 · x + 3)
㏒ₐ [(25 · x⁶) / √(2 · x + 3)]
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Ann's Trail Mix Recipe 5 cups oats 3 cups seeds 1 cup nuts 2 cups raisins What is the ratio of seeds to total ingredient
Answer:
3/11
Step-by-step explanation:
To find a ratio of one item to another we divide the quantity of the first item to the second.
We know Ann has 3 cups of seeds, and overall 11 ingredients. So her ratio is 3/11. Or 3 cups of seeds for every 11 ingredients.
Answer:
3 : 11
Step-by-step explanation:
Trail Mix Recipe:
5 cups oats3 cups seeds1 cup nuts2 cups raisinsTotal number of cups of all the ingredients:
⇒ 5 + 3 + 1 + 2 = 11
Therefore, the ratio of seeds to total ingredients is:
seeds : total = 3 : 11Note: The ratio cannot be reduced further since both 3 and 11 are prime numbers.
the rise and run, please help
the slope ( rise over run ) is 1/2
Happy Card Co. designs personalized cards which cost $1.10 per card. The fixed cost to make the cards is $264 per day. If the company charges $5.10 per card, how many cards must be delivered daily to make a profit of $52? Show work below.
Step-by-step explanation:
x = number of cards
the production costs (PC) per day are
PC(x) = 264 + 1.1x
the sales (S) are
S(x) = 5.1x
the profit (P) per day is sales minus costs
P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =
= 5.1x - 264 - 1.1x = 4x - 264
we need to find the value of x, so that P(x) = 52.
52 = 4x - 264
316 = 4x
x = 316/4 = 79
79 cards must be delivered daily to make a profit of $52.
Alpha Industries is considering a project with an initial cost of $8.2 million. The project will produce cash inflows of $1.93 million
per year for 6 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.67 percent and a cost of
equity of 11.31 percent. The debt-equity ratio is .62 and the tax rate is 24 percent. What is the net present value of the project?
O $553,990
O $498.591
O $576,150
O $474,849
O $418.860
The net present value of the project is $347,941.73.
What are the key points for solving this problem?Get the Weighted Average Cost of Capital first (WACC). WACC is the minimal return a project must provide in order to be approved. Thus, it is employed to discount a project's projected cash flows to its present value.
WACC = Ke × E/V + Kd × D/V.
where,
Ke is cost of equity
= 11.31%
E/V is Market Weight of Equity
= (1/1.62 × 100)
= 61.73%
Kd is After tax cost of debt
= 5.67% × ( 1 - 0.21)
= 4.48 %
D/V = Market Weight of Debt
= 0.65/1.65 × 100
= 39.40%
∴ WACC = 11.31% × 0.6773 + 4.48 % × 0.3940
= 9.43 %
Next, calculate the project's net present value using the formula,
i/yr = 9.43 %
$347,941.73.
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Write a summary of what you learned and understand about slope, and slope triangles. Use some of the words below in your summary.
Vertical
Horizontal
m
negative
positive
count
triangle
slope
Line
The answer contains a brief description of the slope and slope triangle.
What is the slope of line?
Determine the slope of the line using the slope formula given two line-side coordinates. The formula m=(y2-y1)/ describes the slope as the proportion of the change in y values to the change in x values (x2-x1). The coordinates of the first point corresponding to x1 and y1. The second points are situated at the coordinates x2, y2, and. It doesn't matter which point you choose to rank as the first and which as the second.
slope triangle:
A slope triangle is a tool that you can use to visually determine a line's slope. Slope here refers to the degree of steepness.
Imagine that you are a pilot and that you have ascended by 1,000 feet in the air vertically. You have advanced (horizontally) 3,000 feet by the time you are 1,000 feet above the ground. You can calculate how steep your rise was using those two measurements. The inclination increases as the plane move ahead a certain distance.
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Select the correct answer. The square of y varies directly as the cube of x. When x = 4, y = 2. Which equation can be used to find other combinations of x and y?
Answer:
y = (2/64)x^3
Step-by-step explanation:
y = (2/64)x^3
Substitute in the given values:
When x = 4, y = (2/64)(4^3)
y = 2
Therefore, the equation is correct. To find other combinations of x and y, simply substitute different values for x in the equation and solve for y.
For example, when x = 3,
y = (2/64)(3^3)
y = (2/64)(27)
y = 1.5
Can anyone help me ??
Answer:
(5,11)
Step-by-step explanation:
try using desmos graphing calculator