Using relations in a right triangle and the Pythagorean Theorem, it is found that the missing side lengths are as follows:
a = 14.4.c = 15.24.What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
tan(A) = b/a.
Hence:
5/12 = 6/a
Applying cross multiplication, the side a is found as follows:
5a = 72
a = 72/5
a = 14.4.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Hence the hypotenuse c is given as follows:
c² = 5² + 14.4²
c = sqrt(5² + 14.4²)
c = 15.24.
What is the missing information?For the triangle, we have that:
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The surface area of a cylinder = 2ny? + 2rh. Use 3.14 for n. What is the
surface area of this cylinder? You may use the calculator tool in the menu.
The surface area of this cylinder is 6.28y? + 2rh square units.
What does a cylinder's smooth surface look like?
A cylinder has a curving surface that unfolds into a rectangle and two flat surfaces that are both circular.
Given:
The surface area of a cylinder = 2ny? + 2rh.
n = 3.14
therefore putting the value of n
we get,
=2 . 3.14 . y? + 2rh
=6.28y? + 2rh
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A clothing store is tracking how much money adults are spending on clothes each month from their only store. Which description represents a population?
adults who buy any clothes
adults who buy their children’s clothes
adults who are not married
adults who are in college
Answer: If I understood correctly, the answer would be A, adults who buy any clothes. I'm not too sure though that would make sense.
I purchased a scooter for $290.00 but was charged an additional 5% for delivery. What was the total, including delivery charges, for the scooter?
Answer: $275.50
Step-by-step explanation:
5% = 0.05
So we take 290.00 time 0.05 and get `14.50. Then we 290.00 - 14.50= 275.50.
So the answer is $275.50
Store A sells 2 bags of chips for $2.50. Store B sells 3 bags of chips for $3.25. Which store offers the better deal?
Answer:
Store B
Step-by-step explanation:
Since the lowest common multiple of 2 and 3 is 6, so let's find the cost of 6 bags of chips from each store.
Store A
cost for 6 bags of chips
= 3(2.5)
= $7.50
Store B
cost for 6 bags of chips
= 2(3.25)
= $6.50
Since store B offers a cheaper price for 6 bags of chips, it offers a better deal.
Alternatively, you could work out the cost of each bag of chips for both stores.
a marathon ran 26.2 miles in 2 hours and 30 minutes. how many miles did he run in one hour?
Answer:
10.48 miles ran in one hour .
B. What is the rate of change of the line that contains the points (2, 4), (6, 6), (12, 9)??
Answer: 1/2
Step-by-step explanation:
The rate of change is the same as the slope.
Taking the points (2, 4) and (6,6), the slope is [tex]\frac{6-4}{6-2}=\frac{1}{2}[/tex]
Can anybody help me? 50 points, studying for math test! Thank you!
For this problem, please write down the first 5 terms for the sequence.
The first five terms of the sequence are 1, 1, 2, 3, 5.
An arithmetic progression is sequence of numbers in which the difference between the consecutive terms is constant.
[tex]a_{1} = 1 = a_{2}[/tex] ( first two terms given)
[tex]a_{n} = a_{n-1} +a_{n-2}[/tex] ( given sequence formula)
[tex]a_{3} = a_{2}+a_{1}[/tex]
= 1+1
= 2 ( third term)
[tex]a_{4} = a_{3}+a_{2}[/tex]
= 2 + 1
= 3 (fourth term)
[tex]a_{5} =a_{4} +a_{3}[/tex]
= 3 + 2
= 5 (fifth term)
Therefore, we conclude that the first 5 terms for the sequence
[tex]a_{n} = a_{n-1} +a_{n-2}[/tex] are 1, 1, 2, 3 and 5.
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Lisa and Joey just became parents to their son, David. They want to start saving for their newborn’s college, so they open a new, empty savings account. They agree that they will put an equal amount of money every month, so that as David gets older and time goes by, the account gets filled with money for David’s future. Describe what is happening to the variables here (hint: time is almost always on the x-axis). Is this a variation equation?
If Lisa and Joey put the same amount of money every month in the savings account for David's future and the situation is plotted in a graph where time is on the x-axis, then there will be straight line with a constant slope.
As per the question statement, Lisa and Joey just became parents to their son, David and they decided to start a savings account for their newborn's future, where they agreed to put an equal amount of money every month.
We are required to determine the condition of the variables if the above-mentioned situation is plotted into graph and the account gets constantly filled with money as David grows older.
To solve this question, first let us consider the time to be plotted on the X-axis (As mentioned in question statement that "Time" is almost always on the x-axis) and the money collected to be plotted on the Y-axis.
Since, an equal amount of money is put into the account every month, therefore, taking 1 month as unit time to plot our graph, the money will grow diagonally in a straight line with a constant slope. Hence, both the variables (abscissa and ordinates) will increase on a constant ratio along the first quadrant.
Slope of a Line: In mathematics, the slope or gradient of a line is a value that describes both the direction and the steepness of the line and is calculated by the change in y coordinate with respect to the change in x coordinate.To learn more about Slope of a Line, click on the link below.
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15 points for correct answer! Can someone help me solve:
1<|x|<2
Thank you!
Answer:
[tex]-2<x<-1, 1<x<2[/tex]
Step-by-step explanation:
[tex]|x|>1 \implies x<-1[/tex] or [tex]x>1[/tex]
[tex]|x|<2 \implies -2<x<2[/tex]
Taking the union of the intervals, [tex]-2<x<-1, 1<x<2[/tex]
companies are often concerned with the notion of worst probable case performance of their portfolios. they wish to know the mean return such that we would expect 99% of samples of 38 stocks to perform better than this mean return. compute this value and report the answer to two decimal places.
Expected Return is usually based on anticipated income and anticipated capital appreciation of the companies performance..
Portfolio is simply defined as a list of securities showing how much is (or will be) invested in each of them.
The expected return on a portfolio is calculated as the weighted average of the expected returns on the securities that the portfolio involves. The weight of each security is the a Portion or a fraction of wealth invested in that security. Expected return on a portfolio of N securities is: rp= sum (Xr).
Expected Return is usually based on anticipated income and anticipated capital appreciation.
The expected return on a portfolio is defined as the expected amount of returns that a portfolio may generate. And it is established on the weighting of assets in a portfolio and their anticipated capital appreciation and must be equal to or greater than the expected return of the worst-performing security in the portfolio.
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4. Brianna deposited $2,000 into a savings account that earns
5% simple interest. How much interest did he earn after three
years?
To on
Answer:
Step-by-step-learn is 4
LeeAnn is taking care of her 3 brothers.
She has four pieces of toast and wants
to divide them equally among her
brothers.
How much toast does each get?
Each gets [tex]\frac{1}{4}[/tex] pieces of toast.
What is fraction?A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
Given Data
LeeAnn is taking care of her 3 brothers. She has four pieces of toast and wants to divide them equally among her brothers.
So,
Total pieces of toast = 4
Each gets = 1
Fraction of toast each gets = [tex]\frac{1}{4}[/tex]
Each gets [tex]\frac{1}{4}[/tex] pieces of toast.
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Triangle ABC and Triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CE?
The proportion that can be used to show that AC and CE has equal slope is: 2 - 0/3 - 0 = 4 - 2/6 - 3.
How to Determine the Slope of a Line?Using any two points on a given line, the formula to find the slope of the line is given as:
Slope (m) = change in y / change in x = rise/run or the line.
Given that triangles ABC and CDE are two similar right triangles, find the slope of AC and CE as explained below:
Point A is at (0, 0)
Point C is at (3, 2)
Point E is at (6, 4)
Slope of AC = change in y / change in x = 2 - 0/3 - 0 = 2/3
Slope of CE = 4 - 2/6 - 3 = 2/3
Thus, the proportion showing that the slope of AC and the slope of CE are the same would be expressed as:
2 - 0/3 - 0 = 4 - 2/6 - 3.
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Which equation represents the written description?
Seven times the difference between 35.8 and a number is equal to 53.4
7(35.8) − m = 53.4
7(35.8 − m) = 53.4
7(m − 35.8) = 53.4
7m − 35.8 = 53.4
Answer:
the answer to the question is 7(35.8-m)53.4)
Answer:
the answer to the question is 7(35.8-m)53.4)
Step-by-step explanation:
1. A rectangular box has dimensions 4 feet by 3 feet by 5 feet. Increasing each
dimension by the same amount yields a new box with twice the volume of
the old box. Determine the new dimensions of the box.
The new dimensions of the box are 5 feet, 4 feet, and 6 feet.
Given:
A rectangular box has dimensions of 4 feet by 3 feet by 5 feet.
So, Length = 4 feet ,width = 3 feet and height = 5 feet.
Volume of rectangular box = length × width × height
= 4 × 3 × 5 = 60 feet³
Now, increasing each dimension by the same amount yields a new box.
Let the increase in dimension be x feet.
The dimensions of the new box are,
Length = (4 + x) feet ,width = (3 + x) feet and height = (5 + x) feet.
Volume of new box = length × width × height
= (4 + x) (3 + x) (5 + x)
It is given that the volume of the new box is twice the volume of the old box, 2 × 60 feet³ = 120 feet³
So, equate the volume to find the value of x.
(4 + x) (3 + x) (5 + x) = 120
(12 + 7x + x²) (5 + x) = 120
60 + 12x + 35x + 7x² + 5x² + x³ = 120
60 + 47x + 12x² + x³ = 120
x³ + 12x² + 47x - 60 = 0
x = 1
Hence each dimension was increased by 1 foot.
The new dimensions of the box are 5 feet, 4 feet, and 6 feet.
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write the equation of the line that passes through the point (-9, 2) and is perpendicular to the line 10x - 5y = 6
The equation of the line that passes through the point (-9, 2) and is perpendicular to the line 10x - 5y = 6 is y = - 1 / 2 x - 5 /2
How to find equation of a line?The equation of a line can be represented in slope intercept form.
Therefore,
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is perpendicular to 10x - 5y = 6.
5y = 10x - 6
y = 2x - 6 / 5
Perpendicular lines follows the rule below:
m₁m₂ = -1
Therefore,
2m₂ = -1
m₂ = -1 / 2
The slope of the line is - 1 / 2. Now, let's find the equation of the line as it passes through (-9, 2)
y = - 1 / 2 x + b
2 = - 1 / 2 (-9) + b
2 = 9 / 2 + b
b = 2 - 9 / 2
b = 4 - 9 / 2
b = - 5 / 2
Therefore, the equation of the line is as follows:
y = - 1 / 2 x - 5 /2
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HELP! PLEASE? The question is in the photo. Work does not need to be shown.
Answer:
about 22 square units
Step-by-step explanation:
Count the number of squares which is completely inside the border. Then count the number of squares which is half or more than half inside the border as 1 square.
The angle of elevation of the top of the building at a distance of 50 Marin it’s foot on a horizontal plane is found to be 60.Find the height of the building
Answer:
If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?
Step-by-step explanation:
equation. h(x) = x - 11
Answer:
6
Step-by-step explanation:
Let the required input be y.
[tex]h(y)=y-11=-5 \\ \\ y=6[/tex]
A ball is released from rest and falls 125 meters in 5 seconds. What was the magnitude of its acceleration?
From the calculations using the data provided, the acceleration of the ball is 10 m/s^2
What is the acceleration?We know that the acceleration is the rate at which there is an increase or a decrease in the velocity of a body. In this case, we are told that A ball is released from rest and falls 125 meters in 5 seconds.
We have the following;
Distance of the object = 125 meters
Time taken = 5 seconds
Given that;
s = ut + 1/2at^2
u = 0 m/s because it was released from rest
s = 1/2at^2
a = 2s/t^2
a = 2(125)/(5)^2
a = 250/25
a = 10 m/s^2
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Determine how many outfit outcomes are possible with the choices of 3 pairs of pants, 4 shirts, and 3 pairs of shoes.
Number of outfit outcomes are possible with the choices of 3 pairs of pants , 4 shirts and 3 pairs of shoes are equal to 36 outfits.
As given in the question,
Number of choices given
Possibilities with the choices
Number of pairs of pants 'n' = 3 pairs
Number of shirts 'p' = 4 shirts
Number of pairs of shoes 'r' = 3 pairs of shoes
Using Fundamental counting of Principle
Total number of outfit outcomes with the given choices
= n × p × r
= 3 × 4 × 3
= 36 outfits.
Therefore, number of outfit outcomes are possible with the choices of 3 pairs of pants , 4 shirts and 3 pairs of shoes are equal to 36 outfits.
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Help me ASAP for 10 points!
The required ratio of actual length of tunnel to that of construction is 64:1.
Ratio and proportionFraction is written as a ratio of two integers. Given the following parameters:
length of construction plan = 21/2 feet long
length of actual tunnel = 53 1/3 yards long
Determine the ratio
Ratio = actual/construction
Ratio = 160ft/2.5ft
Ratio = 64/1
Hence the ratio of the actual to the construction plan is 64:1
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Please help me answer this!
The system of linear inequalities as shown in the given graph is:
y < 1/3x + 2
y ≤ -2x + 2
How to Write a System of Inequalities Represented by a Graph?Depending on the inequality sign, we can express the linear inequality in slope-intercept form as, y = mx + b. The sign "=" would be placed by the appropriate inequality sign, the m represents the slope and b represents the y-intercept of the line.
One of the lines is dashed, and the shaded part is beneath it, therefore, the inequality sign for the dashed line would be "<".
For the solid line, the inequality sign to use would be "≤" because the shaded part is also beneath it.
Both lines intercept the y-axis at y = 2, therefore, the y-intercept (b) for both lines would be: b = 2.
Slope of the dashed line (m) = rise/run = 1/3
Slope of the solid line (m) = rise/run = -2/1 = -2
The inequality for the dashed line would be written by substituting m = 1/3 and b = 2 into y < mx + b:
y < 1/3x + 2
The inequality for the solid line would be written by substituting m = -2 and b = 2 into y ≤ mx + b:
y ≤ -2x + 2
The system would be:
y < 1/3x + 2
y ≤ -2x + 2
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Multiplying Rational Numbers- 1 3/4 (-2 1/7)
The rational numbers - 1 3/4 (-2 1/7) are multiplied to give 105/28
What is a fraction?A fraction can be defined as the part of a whole element.
There are several types of fractions, which includes;
Mixed fractionsSimple fractionsImproper fractionsProper fractionsComplex fractionsWhat are rational numbers?Rational numbers are defined as types of real numbers that are in form of fractions.
For instance: a/b where a is not equal to zero.
Given the rational numbers;
- 1 3/4 (-2 1/7)
To determine the product, take the following steps
Turn into improper fractions
-7/4 × -15/ 7
Now, multiply the numerators and denominators
105/28
Hence, the value is 105/28
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Which of the following functions is graphed below?
Answer:
It is a quadratic funcion with vertex in (4,0)
Step-by-step explanation:
6. Find the amount an account is worth that earns 6% interest compounded twice per year if $4,000
is deposited in the account for ten years.
I need help to find the answer.
EXPLANATION:
Given;
We are given a parallel pair of lines m and n, and a transversal that cuts both lines.
Required;
We are required to find the value of x.
Step-by-step solution;
When a pair of parallel lines are cut by a transversal, the angle formed by the point of intersection of one line and the transversal is equal to that formed by the other line and the transversal when they both lie on the same side of the transversal.
This means on the diagram given;
This means angle 167 on line n is equal to angle 167 on line m. These are called corresponding angles.
The same applies to angle x on the line m and the other angle on line n. They both are also corresponding angles.
Next, take note that angles that lie on either side of a vertex where two lines intersect are called vertically opposite angles (or just opposite angles).
Therefore, angle x = 167 and angle 167 = x.
ANSWER:
[tex]x=167\degree[/tex]For the function f(x) = -3x+8, determine f(-4).
Answer:
[tex]{ \tt{f(x) = - 3x + 8}} \\ \\ { \tt{f( - 4) = - 3( - 4) + 8}} \\ \\ { \tt{f( - 4) = 12 + 8}} \\ \\ { \tt{f( - 4) = 20}}[/tex]
For the function f(x) = -3x + 8, f(-4) is 20.
Given, f(x) = -3x + 8 and f(-4)
Put the value -4, wherever x is present,
f(x) = -3x + 8
f(-4) = (-3 × -4) + 8
f(-4) = 12 + 8
f(-4) = 20
∴ The value of f(-4) is 20 for function f(x) = -3x + 8
This function connects an input to an output. "f(x) = ..." is the classic way to write a function. We will see different ways of thinking about functions, but there are always three main parts: input, relation, and output.
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Given sequence
7,5,2,1
Find the general term of the sequence
Answer:
Step-by-step explanation:
What is the justification for each step in the solution of the equation? (5x−4)/2=2x−1 Select from the drop-down menus to correctly justify each step.
THE OPTIONS TO CHOOSE FROM-
Addition or subtraction property of equality
Multiplication or division property of equality
Distributive property of equality
Combine like terms
The justification for each step in the solution of the equation (5x−4)/2=2x−1 is:
Step 1: (5x-4)/2 = 2x-1 (As Given)
Step 2: ((5x-4)/2) × 2 = 2 × (2x-1)
The Multiplication Property of Equality asserts that when both sides of an equation are multiplied by the same number, the two sides remain equal.
Step 3: (5x-4) = 4x-2
The Distributive Property of Equality asserts that equality holds after distributing by multiplication.
Step 4: 5x - 4 + 4 = 4x - 2 + 4
The Addition Property of Equality states adding the same number on both sides of an equation yields equivalent results.
⇒ 5x = 4x + 2
Step 5: 5x - 4x = 4x + 2 - 4x
The Subtraction Property of Equality states that you can get an equivalent equation by subtracting the same integer from both sides of an equation.
⇒ x = 2
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According to the solving each step in the solution of the equation (5x−4)/2=2x−1 is:
Step 1: (5x-4)/2 = 2x-1
Step 2: ((5x-4)/2) × 2 = 2 × (2x-1)
Step 3: (5x-4) = 4x-2
Step 4: 5x - 4 + 4 = 4x - 2 + 4
Step 5: 5x - 4x = 4x + 2 - 4x
What are the four mathematical equality properties?The four properties of equality—addition, subtraction, multiplication, and division—can be used to solve an equation. To get the value of an equation's unknown variable, we can easily add, subtract, multiply, or divide the two sides of the equation.
According to the given equation:(5x-4)/2 = 2x-1 (As Given)
((5x-4)/2) × 2 = 2 × (2x-1)
According to the Multiplication Property of Equality, an equation's two sides stay equal even after being multiplied by the same number.
Step 3: (5x-4) = 4x-2
According to the distributive property of equality, multiplicative distribution still maintains equality.
Step 4: 5x - 4 + 4 = 4x - 2 + 4
According to the Addition Property of Equality, an equation produces equivalent outcomes when the same integer is added to both sides.
⇒ 5x = 4x + 2
Step 5: 5x - 4x = 4x + 2 - 4x
According to the "Subtraction Property of Equality," subtracting the same number from both sides of an equation will result in an identical equation..
⇒ x = 2
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