Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?
A) 17 miles
B) 32 miles
C) 37 miles
D) 40 miles
Answers
Answer:
D) 40 miles
Step-by-step explanation:
First we must find the distance between the mall and the house. The figure formed is a right triangle. The length of the side from the mall to the house forms the hypotenuse of the triangle. We can use the Pythagorean theorem to find the length:
a² + b² = c²
The two legs of the triangle, a and b, are 15 and 8:
15² + 8² = c²
225 + 64 = c²
289 = c²
Take the square root of each side:
√289 = √(c²)
17 = c
This makes the total distance
15+8+17= 40 miles
Hey! Pretty easy once you get the hang of these problems.
So you start off with the Pythagorean Theorem. Which is : a^2 + b^2 = c^2
Then just fill it in :
15^2 + 8^2 = c^2
225 + 64 = c2
289 = c^2
17 = c
And last :
15 + 8 + 17 = 40 MILES
hoped this helped!! :))
Related Questions
How do you know the sum of a positive and negative integer will be negative?
Answers
[tex]8+(-3)=+5[/tex]
If what you're asking is, under what condition will the sum of a positive and negative be negative, then it's when the absolute value of the negative number is greater than the positive number. For example:
positive number: 8
negative number: -10
[tex]8+(-10)=-2[/tex]
This sum is negative. Note that [tex]\mid{-10}\mid\ \textgreater \ 8[/tex].
What is the positive solution of x2 – 36 = 5x?
Answers
Answer:
The positive solution is x=9
Step-by-step explanation:
Given the equation
[tex]x^2-36=5x[/tex]
we have to find the positive solution of above equation.
[tex]Equation: x^2-5x-36=0[/tex]
By splitting middle-term method
[tex]x^2-5x-36=0[/tex]
[tex]x^2-9x+4x-36=0[/tex]
[tex]x(x-9)+4(x-9)=0[/tex]
[tex](x+4)(x-9)=0[/tex]
[tex]x+4=0, x-9=0[/tex]
The solution is x=-4 and x=9
Hence, the positive solution is x=9
Item 18 A spherical ball with a volume of 972π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?
Answers
Volume of the given box is 5832 in³
Volume of the cube:
Given a spherical ball with a volume of 972π in.³,
Since the volume of a sphere is (4/3)πr³, we can find that the radius of the sphere is 9 inches.
The edge length of the cube (box) is twice the radius (diameter of the sphere), so the edge length of the cube is equal to 18 inches.
The volume of the cube is then (18³) in³
Volume of the cube = 5832 in³
A painter is placing a ladder to reach the third story window, which is 12 feet above the ground and makes an angle of 80 degrees.how far out from the building does the base of the ladder need to be positioned
Answers
tan ∅=opposite side angle ∅/adjacent side angle ∅
adjacent side angle ∅=opposite side angle/tan ∅
in this problem
see the attached figure to better understand the problem
angle ∅=80°
opposite side angle ∅=12 ft (AB)
adjacent side angle ∅=? (AC)
adjacent side angle ∅=12/tan 80°------> 2.12 ft
the answer is
2.12 ft
suppose you deposit 1,000 ina savings account that pays interest at an annual rate of 5%. if no money is added or withdrawn from the account answer the following questions. How much money will be in the account after 3 years? How much will be in the account after 18 years? How many years will it take for the account to contain 1,500? How many years will it take for the account to contain 2,000?
Answers
Time req'd for amount to reach $1500 from $1000:
1500=1000(1+0.05)^t, or 1.5=1.05^t
ln 1.5
ln 1.5 = t ln 1.05, so that t = ------------ = 8.31 years, or 8 yr 3 3/4 months
ln 1.05
Find the equation of the line.
A) y= -3/2 x + 1
B) y= -2/3 x - 1
C) y= 2/3 x + 1
D) y= 3/2 x - 1
Answers
Hope this helps
Answer:
It’s y=2/3x+1 that’s the equation of the line.
Step-by-step explanation:
Solve 6,394 divided by 42 =
Answers
The required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
Given that [tex]6394[/tex] ÷ [tex]42[/tex].
Long division states that [tex]divident= divisor*quotient+remainder[/tex].
Let [tex]a[/tex] and [tex]b[/tex] be any real number. Consider [tex]a[/tex] ÷ [tex]b[/tex] gives
[tex]a=bq+r[/tex], [tex]q[/tex] is quotient [tex]r[/tex] is remainder and its value is [tex]0\leq r < b[/tex].
[tex]\begin{array}{ccccc}42)&006394(152&\\-&42____________&\\&219& \\&\\-&210&\\&0094\\-&0084\\&0010\end{array}\right][/tex]
Hence, the required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
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find the solution of this system of equations
-6x-2y=8
7x-2y=-5
Answers
A person who is 55 feet tall is standing 168168 feet from the base of a tree, and the tree casts a 180180 foot shadow. the person's shadow is 1212 feet in length. what is the height of the tree?
Answers
a glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. if a single marble is chosen at random from the jar, what is the probability that it is red
Answers
[tex] \frac{1}{10} [/tex]
You fly a hot air balloon 1.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)
Answers
Answer:
3.1
Step-by-step explanation:
If you are doing this for big ideas, the answer ended up being 3.1
I'm sorry if you wanted the work, I found the answer from something else that didn't show the work but this was the correct answer...
To find the measure of BD⌓, the visible portion of Earth's surface from a hot air balloon 1.5 miles above the ground, convert the height to kilometers and use the formula D = 112.88 km × √h to get the distance to the horizon, which is about 175.4 km. Then, calculate the semicircular distance visible by using C/2 = (π × D) / 2, which results in approximately 276.1 km for the measure of BD⌓.
Explanation:To calculate the measure of BD⌓, the portion of Earth's surface that is visible from a hot air balloon 1.5 miles above the ground, you can use the formula for the distance to the horizon, given as D = 112.88 km × √h, where h is the height above the Earth's surface. In this case, we must convert the height of 1.5 miles to kilometers before applying the formula, as the formula uses kilometers.
The conversion from miles to kilometers is 1 mile = 1.60934 kilometers, so 1.5 miles is approximately 2.414 km.
Inserting h = 2.414 km into the formula, we get:
D = 112.88 km × √2.414
D = 112.88 km × 1.5535 (approx)
D ≈ 175.4 km (rounded to the nearest tenth)
This is the straight-line distance to the horizon. To find the measure of the arc BD, which is the portion of the Earth's surface visible, we can treat this distance as the radius of a circle and calculate the circumference. However, since we are only looking at the visible part, which is a semicircle, we use half of the circumference C = π × D.
The measure of BD⌓ is therefore approximately:
C/2 = (π × 175.4 km) / 2
C/2 ≈ 276.1 km
Thus, the measure of BD⌓ to the nearest tenth is 276.1 km.
A single 6-sided dice is being rolled. What is the probability of rolling a 5 or an odd number?
Answers
S = set of all possible outcomes
S = {1,2,3,4,5,6}
E = event space
E = set of items we want to happen (rolling a 5, or rolling an odd number)
E = {1, 3, 5}
note: the event of "rolling a 5" is a subset of "rolling an odd number" because 5 is odd
n(S) = number of items in the sample space
n(S) = 6
n(E) = number of items in event space
n(E) = 3
Divide the values to get the probability
P(E) = n(E)/n(S)
P(E) = 3/6
P(E) = 1/2
P(E) = 0.50
P(E) = 50%
The answer in fraction form is 1/2
The answer in decimal form is 0.50
The answer as a percentage is 50%
These three values all represent the same idea, just written in different forms.
note: writing "P(E)" means "the probability of event E occurring", which I've defined as the event space above
Suppose a triangle has 3,4, and 5 sides.Which of the following must be true
Answers
Answer:
A. The triangle in question is a right triangle
Step-by-step explanation:
A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange?
Answers
You have to find the probabilities of them happening separately
To do this you do the amount of favorable outcomes over the total amount of outcomes
3 + 2 + 2 + 2 + 5 = 14 total fruit
The chance of Jack getting a peach is 5 / 14
The chance of Bethany getting an orange is 2 / 13 because Jack did not put the fruit back in so their is one less to choose from
You multiply the two probabilities to find the probability of them happening in a row
5/14 * 2/13 = 5/91
The answer is 5/91
Hope this helps!
simplify by 2
10/182 ÷ 2/2
5/91
5 over 91
Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line
y = 1/4x + 5
Answers
Find the slope:
y = 1/4 x + 5
Slope = 1/4
Slope of perpendicular line = -4
Substitute m = -4 into the equation:
⇒ y = -4x + b
Find y-intercept:
At point (0, 2) ⇒ y-intercept = 2
Substitute b = 2 into the equation
y = -4x + 2
Answer: y = 4x + 2
Answer:
y=-4x+2
Step-by-step explanation:
The line passes through (0,2), so chuck these numbers in and you get a value of 2 for c. If you're sharp, you might spot that this point is the y-intercept of the line since the x- coordinate is 0, this point is on the Y-axis, and you don't even have to throw numbers in.
Therefore the equation of the line is:
y = -4x + 2
Hope that was clear!
The data shows the number of grams of fat found in 9 different health bars.12, 14, 16, 16.5, 11, 18, 18, 14, 20 What is the IQR (interquartile range) for the data?
9
5
16
18
Answers
The interquartile range (IQR) for the given health bar fat content data set is 5 grams, calculated by subtracting the first quartile (13) from the third quartile (18).
To calculate the interquartile range (IQR) of the given health bar data set, first, we must organize the numbers in ascending order: 11, 12, 14, 14, 16, 16.5, 18, 18, 20. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
Find the median (the middle value) of the dataset, which will also serve as the second quartile (Q2). The median of the dataset here is 16.
To find Q1, calculate the median of the lower half of the data (not including the median of the dataset if your dataset has an odd number of values). So the lower half of the data is 11, 12, 14, 14, and the median of this is 13.
To find Q3, calculate the median of the upper half of the data. The upper half following our median is 16.5, 18, 18, 20, with a median value of 18.
The IQR is Q3 - Q1, which is 18 - 13 = 5.
Thus, the IQR for the health bars' fat content data is 5 grams.
Select the property that allows the statement 10 = y to be written y = 10.
Commutative - addition
Distributive
Associative - multiplication
Symmetric
Commutative - multiplication
Associative - addition
Identity - addition
Answers
This is the symmetric property
Hope this helps!
The property that allows the statement 10 = y to be written y = 10 is:
Symmetric
Step-by-step explanation:We know that for any set A. if a and b are two elements of the set A.
Then if a is related to b by some relation then by the symmetric property b must be related to a by the same property.
Here 10 is related to y by the equality relation.
i.e. 10=y
Hence, by the symmetric property we have that y must be related to 10 by the same equality relation.
i.e. y=10
Megan uses a credit card with a 24.9% APR compounded monthly to pay for car repairs totaling $583.75. She can pay $240 per month on the card. What will the total cost of this purchase be
Answers
Her total expense is $605.80.
the correct answer is $605.80
You roll a number cube and flip a coin. find the probability of rolling an even number and flipping heads. write your answer as a fraction in simplest form.
Answers
Hope this helped!
Final answer:
To calculate the combined probability of rolling an even number on a number cube and flipping heads on a coin, you multiply the separate probabilities of each event, which are 1/2 and 1/2 respectively, resulting in a combined probability of 1/4.
Explanation:
The probability of rolling an even number on a number cube (which is a standard six-sided die) is 3 out of 6 since there are three even numbers (2, 4, 6) and six possible outcomes overall. This simplifies to 1/2. The probability of flipping heads on a coin is 1/2 since there are two possible outcomes, heads or tails, and both are equally likely if the coin is fair.
To find the combined probability of two independent events (rolling an even number and flipping heads), you multiply the probabilities of each event together. So, the probability of rolling an even number and flipping heads is 1/2 (for the number cube) times 1/2 (for the coin), which equals 1/4 or 25%.
In the simplest form, the fraction is written as 1/4.
If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?
Answers
Answer:
The total number of students in Toby's grade is 200.
Answer:number of students who voted= 75%= 150
75% of total number of students= 150
The total number of students in Toby's grade is 200.
Step-by-step explanation:
Which of the following have the same value as the fraction below?
8/5 A.
Check all that apply.
A. 2.20
B. 220%
C. 1.60
D. 160%
Answers
Please help me out here.
Answers
When you multiply two exponents with the same base together, you can add the indexes together. For example, if you had y * y², you could make it y³, by adding the indexes of 2 and 1.
In this scenario, you can look at the last choice, where it has [tex] x^{9} [/tex] * x. You add the indexes of 9 and 1, to get [tex] \sqrt[3]{ x^{10} } [/tex]
That's equivalent to the equation given, so your answer would be the last choice.
What is the value of x in the equation x + 10 = 13?
Answers
What is the slope of a line that is parallel to the line y = x + 2?
Answers
y = x + 2
⇒ slope = 1
⇒Slope of the parallel line = 1
Answer: 1
Answer:
I’m going to assume you didn’t put the 3/4x in your equation, if you had, the answer would’ve been 3/4.
Step-by-step explanation:
REMEMBER
If the equation is parallel, it will have the same slope as the other equation parallel to it.
The difference of a number and 8 is the same as 34 less the number. find the number.
Answers
34 less the number is 34-n.
n-8=34-n
2n=34+8
2n=42
n=21
The question is a simple algebra problem. By setting up and solving the equation 'x - 8 = 34 - x', we find that the number is 21.
Explanation:The subject of this question is algebra, and involves setting up and solving an equation. Let's denote the unknown number as 'x'. Following the question, we can set up the equation as 'x - 8 = 34 - x'.
To solve the equation, let's add 'x' to both sides to get 2x - 8 = 34. Then, add 8 to both sides to get 2x = 42. Finally, divide each side by 2, so that 'x = 21'.
So, the number that satisfies the equation is 21.
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Using a straightedge, or using technology, sketch an obtuse, scalene triangle. Make sure to include your sketch in your answer.
Answers
What is the value of c when the expression 21.2x + c is equivalent to 5.3(4x − 2.6)?
Answers
To find our answer we need to work out the parenthesis. This is for instance possible using rainbow technique.
[tex]5.3(4x - 2.6) = \\ 5.3 \times 4x - 5.3 \times 2.6 = \\ 21.2x - 13.78[/tex]
Therefore the value of c = - 13.78.
~ Hope this helps you!
Comparing with 21.2x + c:-
the value of c = -13.78 Answer
If the selling price is $18 and the markup is 33% what is the dollar market
Answers
20 POINTS!
Verify the identity.
Answers
[tex]R_s=\left(\dfrac{1}{\sin x}-1\right):\dfrac{\cos x}{\sin x}=\left(\dfrac{1}{\sin x}-\dfrac{\sin x}{\sin x}\right)\cdot\dfrac{\sin x}{\cos x}\\\\=\dfrac{1-\sin x}{\sin x}\cdot\dfrac{\sin x}{\cos x}=\dfrac{1-\sin x}{\cos x}\cdot\dfrac{1+\sin x}{1+\sin x}=\dfrac{1-\sin^2x}{\cos x(1+\sin x)}\\\\=\dfrac{\cos^2x}{\cos x(1+\sin x)}=\dfrac{\cos x}{1+\sin x} \\\\L_s=R_s[/tex]
[tex]Used:\\\csc x=\dfrac{1}{\sin x}\\\\\cot x=\dfrac{\cos x}{\sin x}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\(a-b)(a+b)=a^2-b^2[/tex]
How do I simplify this expression
Answers
= 4x(x + 5) - 3(x + 5)
= 4x^2 + 20x - 3x - 15
= 4x^2 + 17x - 15 Answer