Answer: We can plot the given points on a coordinate plane where each unit represents 2 miles:
y
| E(1,2)
|
| M(-4,2)
|
|
|H(-4,-1) F(1,-1)
|___________________
x
Now we can see that the distance between the football field (F) and the high school (H) is 5 units in the x direction and 1 unit in the y direction, which corresponds to a distance of 5 x 2 = 10 miles in the x direction and 1 x 2 = 2 miles in the y direction. Using the Pythagorean theorem, we can find the distance between the two points:
distance = sqrt((10)^2 + (2)^2)
= sqrt(104)
So the distance between the football field and the high school is approximately 10.198 miles. Therefore, the statement that is true is:
"The distance between the football field and the high school is approximately 10.198 miles."
Step-by-step explanation:
24. A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table.
According to this data, which was the most likely distribution of the colors of candies in the bag before it was opened?
A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange
B. 300 red, 250 blue, 200 green, 100 yellow, and 150 orange
C. 200 red, 200 blue, 200 green, 200 yellow, and 200 orange
D. 200 red, 200 blue, 200 green, 100 yellow, and 100 orange
The most likely distribution of the colors of candies in the bag before it was opened A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange.
What is distribution?Distribution is the process of making a product or service available for use or consumption by a consumer or business. It involves the movement of a product or service from the producer to the customer or end user. Distribution channels can include direct sales, wholesalers, retailers, online stores, or a combination of all of these. Distribution involves the coordination of activities related to the transfer of goods and services, including storage, shipping, return policies, and customer service. Distribution is a key element of the marketing mix, allowing companies to reach their target markets and meet customer needs.
This is the most likely distribution of the colors of candies in the bag before it was opened because it is the closest to the total number of candies that were in the bag to begin with: 1,000. This distribution has a total of 1,000 candies, which is the same as the amount of candies that were in the bag before it was opened.
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So NL + y = 5. What would NL be?
NL would be 3.1 cm
What are similar triangles?
These are set of triangles which have some common relations on comparing their corresponding properties. But similarity of the triangles does not imply that they are congruent.
From triangle PQN, applying the trigonometric function. We have;
Tan θ = opposite/ adjacent
Tan 60 = 3.2/ y
1.7321 = 3.2/ y
y = 3.2/ 1.7321
= 1.8475
y = 1.9 cm
To determine the value of NL,
NL + y = 5
NL = 5 - y
= 5 - 1.9
= 3.1
NL = 3.1 cm
The value of NL would be 3.1 cm.
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Kaitlyn was asked to solve for the unknown. The problem
shows that n + 6 = 13. Her steps are shown below.
She started with 6 tiles.
Then she added tiles as she counted up to 13.
Kaitlyn realized that she added 7 more tiles to her
original 6 in order to make 13.
The unknown number is 7.
How could Kaitlyn check her work? Check all that
apply.
She could substitute 7 for n and add.
She could subtract 6 from 13 and check that the
answer is 7.
She could subtract 7 from 13 and check that the
answer is 7.
She could substitute 6 for n and add.
She could put all the tiles in 1 pile and count them
to see if there are 13.
Answer:
Step-by-step explanation:
The following methods can be used by Kaitlyn to check her work:
She could substitute 7 for n and add.
This is a valid way to check her work as she found the value of the unknown to be 7, so substituting 7 for n should give her the same result.
She could subtract 6 from 13 and check that the answer is 7.
This is also a valid way to check her work as n + 6 = 13 can be rewritten as n = 13 - 6, which simplifies to n = 7.
She could put all the tiles in 1 pile and count them to see if there are 13.
This is a practical way to check her work, as she started with 6 tiles and added 7 more to make 13, so there should be a total of 13 tiles. Counting all the tiles would confirm this.
Therefore, the correct options are:
She could substitute 7 for n and add.
She could subtract 6 from 13 and check that the answer is 7.
She could put all the tiles in 1 pile and count them to see if there are 13.
Suppose that 10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
a. Let's consider your existing mortgage:
i. How much money did you pay as your down payment?
ii. How much money was your mortgage (loan) for?
iii. What is your current monthly payment?
iv. How much total interest will you pay over the life of the loan?
b. This year, you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.
i. How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
ii. How much money have you paid to the loan company so far?
iii. How much interest have you paid so far?
iv. How much equity do you have in your home (equity is value minus remaining debt)
i. The down payment is $11,000
ii. The mortgage (loan) was for $99,000.
iii. The current monthly payment is $471.15.
iv. Total interest is $169,334.00.
Down payment:The down payment is the initial payment made when purchasing a home, typically expressed as a percentage of the total purchase price.
Mortgage (loan):In the given problem, the mortgage (loan) is the amount of money borrowed to purchase the home, which is equal to the purchase price of the home minus the down payment.
Here we have
Problem 1:
10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
The down payment was 10% of the purchase price of the home
=> Down payment = 10% of $110,000
= [10/100] × $110,000 = $11,000
∴ You will be paid $11,000 as your down payment.
Amount borrowed = the purchase price of the home - Down payment
=> Amount borrowed = $110,000 - $11,000 = $99,000
∴ Your mortgage (loan) was for $99,000.
To calculate the current monthly payment, use the formula for the monthly payment of a fixed-rate mortgage:
P = (A / D) x (r / 12)
Where:
A = amount borrowed
D = discount factor, i.e calculated as (1 - (1 + r / 12)⁻ⁿ)
r = monthly interest rate,
n = total number of payments,
=> P = ($99,000 /124.4) x 0.0075 = $471.15
∴ The current monthly payment is $471.15.
The formula for total interest = (P x n) - A
=> Total interest = ($471.15 x 360) - $99,000 = $169,334.00
∴ You will pay a total of $169,334.00 in interest over the life of the loan.
Therefore,
i. The down payment is $11,000
ii. The mortgage (loan) was for $99,000.
iii. The current monthly payment is $471.15.
iv. Total interest is $169,334.00.
Problem 2
This year, you check your loan balance. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.
i. Amount paid off = Original loan amount - Current loan balance
Original loan amount = $99,000
Current loan balance = $88,536
Amount paid off = $99,000 - $88,536
Amount paid off = $10,464
∴ you have paid off $10,464 of the loan.
ii. Total paid = Monthly payment x Number of payments
P = ($99,000 / 207.483) x 0.0075
P ≈ $471.15
The number of payments is the number of months since you took out the loan. Since the loan was taken out 10 years ago, or 120 months ago, the number of payments is 120.
Total paid = $471.15 x 120
Total paid = $56,538
∴ you have paid $56,538 to the loan company so far.
iii. To determine how much interest you have paid so far, we need to subtract the amount paid off from the total amount paid:
Interest paid = Total paid - Amount paid off
Interest paid = $56,538 - $10,464
Interest paid = $46,074
∴ you have paid $46,074 in interest so far.
iv. Equity = Current value of the home - Current loan balance
Equity = $150,000 - $88,536
Equity = $61,464
∴ you have $61,464 of equity in your home.
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A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 2425 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week? (100 points!)
Answer:
Step-by-step explanation:
Let's assume that the first car used x gallons of gas during the week, then the second car used (75 - x) gallons of gas because the total gas consumption by both cars is 75 gallons.
The first car's fuel efficiency is 30 miles per gallon, so it traveled (30x) miles during the week.
The second car's fuel efficiency is 35 miles per gallon, so it traveled (35(75 - x)) miles during the week.
The total distance traveled by both cars is given as 2425 miles, so we can set up the equation:
30x + 35(75 - x) = 2425
Expanding the equation:
30x + 2625 - 35x = 2425
Simplifying:
-5x = -200
x = 40
Therefore, the first car used 40 gallons of gas during the week, and the second car used (75 - 40) = 35 gallons of gas during the week.
Answer: Car 1 used 40 gallons and car 2 used 35 gallons.
Step-by-step explanation: In this problem, we will use a system of equations to reach our answer. We can let x be the gallons consumed by the first car, and y be the gallons consumed by the second car(these are both for one particular week only). We know the total consumption of gas is 75 gallons so the gallons consumed by car 1 and car 2 have to add up to 75. We can then create the equation x+y=75. We know that car 1 has an efficiency of 30 miles per gallon and 35 miles per gallon for car 2. The miles produced by x gallons in car 1 can be represented by 30x=# of miles. we can use 35y = # of miles for car 2. We know the combined total of miles from both cars is 2425 so we can make the equation 30x+35y=2425 miles. Now that we have our equations, we can simply solve them to find our answers.
x+y=75
x=75-y Isolating a variable
30x+35y=2425
30(75-y)+35y=2425 Substituting the variable we isolated
2250-30y+35y=2425
2250+5y=2425
5y=175
y=35
x+(35)=75
x=40
y=35 and x=40
Car 1 used 40 gallons and car 2 used 35 gallons.
Hope this helps!
Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
The expression represents the prime factorization of 192 is 2×2×2×2×2×2×3. Therefore, option C is the correct answer.
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given number is 192.
The prime factorization is process of writing the given number into product of prime numbers.
Here, 192= 2×2×2×2×2×2×3
Therefore, option C is the correct answer.
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f(x)=x^2 −x−1 Over which interval does f have an average rate of change of zero?
Answer:
C. -1 < x < 2.
Step-by-step explanation:
Change to vertex form to find the axis of symmetry:
x^2 − x −1
= (x - 0.5)^2 - 0.25 - 1
= (x - 0.5)^2 - 1.25.
Thus the graph is symmetrical about x = 0.5.
So the interval must be equal lengths either side of x = 0.5.
That would be -1 < x < 2.
Can someone help create a frequency distribution with 5 classes using this data? Please I’d you can include the frequency
The required frequency distribution table is below in the solution part.
What is the relative frequency of the data?The relative frequency of the data is the ratio of the given frequency to the total frequency in the observation.
To create a frequency distribution with 5 classes, we first need to find the range of the data, which is the difference between the largest and smallest values:
Range = 10
Next, we divide the range by the number of classes we want (5) to get the class width:
Class width = Range / Number of classes
Class width = 10 / 5
Class width = 2
Now, we can create the frequency distribution table:
Class Frequency
0-1 5
2-3 29
4-5 16
6-7 14
8-9 2
10-11 2
___________________
Total 73
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Schedule K-1 (Form 8865) (irs.gov) use this form provided to Natalie Maloney
Schedule K-1 (Form 8865) is used to report the partner's share of income, deductions, credits, and other items for the tax year of a foreign partnership.
Some guidelines for completing the form:Identification information: Fill out the partnership's name, employer identification number (EIN), and address.
Partner's identifying information: Fill out the partner's name, identifying number (usually their taxpayer identification number or TIN), address, and their percentage of ownership in the partnership.
Income items: Report the partner's share of ordinary income, net rental income, gain or loss from the sale of property, and other income items on lines 1-7. Make sure to also include any foreign source income or deductions.
Deductions: Report the partner's share of partnership deductions, such as business expenses, depreciation, and depletion, on lines 8-15.
Credits: Report the partner's share of any foreign taxes paid or other credits on lines 16-21.
Other items: Report any other items that are required to be reported on Schedule K-1, such as guaranteed payments, charitable contributions, and Section 743(b) adjustments, on lines 22-27.
At-risk limitation: If the partnership is engaged in an activity subject to the at-risk rules, report the partner's share of the at-risk limitation on line 28.
Passive activity limitation: If the partnership is engaged in a passive activity, report the partner's share of the passive activity limitation on line 29.
P.S Your question is incomplete, so I gave a general overview of the tax form for better understanding.
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need help now i have like so much questions that need to be done
The measure of angle ABC in the triangle inscribed in the circle is given as follows:
m < ABC = 84º.
How to obtain the angle measure?The sum of the measures of the interior angles of a triangle is of 180º.
The internal angles for the triangle are given as follows:
<A = 48º.<ABC.<C = 48º -> congruent to angle A, as segments AB and AC both represent the radius of the circle, as they are a segment connecting a point on the circumference of the circle to the center.Then the measure of angle ABC is obtained as follows:
m < ABC + 2 x 48 = 180
m < ABC = 180 - 96
m < ABC = 84º.
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I need help anyone please ?!!!!!!!
Answer:its a
Step-by-step explanation:you did it wrong
Find an equation of the straight line passing through the points (4, 3) and (2, -5).
The equation of the straight line is 4x -y = 13. It is general form of equation of a line.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of several points that are endlessly extended in opposite directions. Two points in a two-dimensional plane determine it. Collinear points are described as two points that are on the same line.
The equation of a line that passes through the points (x₁, y₁) and (x₂, y₂) is
y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).
The coordinates of the points are (4, 3) and (2, -5).
The slope of the line is (-5-3)/(2-4)
=-8/-2
= 4
The equation of line is
y - 3 = 4(x - 4)
→ y - 3 = 4x - 16
→ 4x -y = 13
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Solve:
|-6x|=30
no solution
x = 6 and x=10
x = -5 and x =5
x= -1 and x=-4
Answer:
x = -5 and x =5
Step-by-step explanation:
However, we notice that the solutions -5 and 5 satisfy the original equation in case 2, because |-6(-5)| = 30 and |-6(5)| = 30 is true. Therefore, the two solutions that satisfy the original equation in both cases are x = 5 and x = -5.
Hence, the solution to the equation |-6x| = 30 is x = 5 and x = -5.
Tamika wants to use a sheet of fiberboard 19 inches long to create a skateboard ramp with a 20° angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary. Student Help Vid Next Question> Your Solution:
Using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.
What is meant by elevatiοn?The height abοve οr belοw a specified reference pοint, mοst frequently a reference geοid, which is a mathematical representatiοn οf the Earth's sea level as an equipοtential gravitatiοnal surface, determines a lοcatiοn's elevatiοn.
A frequently used idea in relatiοn tο height and distance is the angle οf elevatiοn, particularly in trigοnοmetry. It is described as a relatiοnship between an οblique line frοm the οbserver's eye tο an item abοve his eye and the hοrizοntal plane.
This angle eventually develοps abοve the surface. The angle οf elevatiοn is made in such a way that it is abοve the οbserver's eye, as the name suggests.
Using the given infοrmatiοn, we drew a right triangle as given belοw.
The hypοtenuse οf the triangle is the length οf the sheet.
The angle οf elevatiοn is 20°.
The base οf the triangle is the grοund.
The hypοtenuse l = 19 inches
Angle Ф = 20°
We have tο find the elevatiοn h.
sin Ф = h/l
sin 20 = h/19
0.342 = h /19
h = 6.49 inches
Therefοre using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.
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If the model is 18 inches long and the actual locomotive is 72 feet long, what is the similarity transformation to map from the model to the actual locomotive? Express the answer using the notation x* ax, where x is a measurement on the model and ax is the corresponding measurement on the actual locomotive.
Answer:
(1/48)ax
Step-by-step explanation:
We can use the proportion of the lengths of the model and the actual locomotive to determine the scale factor for this similarity transformation.
The model is 18 inches long, which is equivalent to 1.5 feet (since 1 foot = 12 inches). The actual locomotive is 72 feet long. So, the scale factor can be calculated as:
scale factor = actual length / model length
scale factor = 72 feet / 1.5 feet
scale factor = 48
This means that each measurement on the model is 1/48th the size of the corresponding measurement on the actual locomotive. We can express this similarity transformation using the notation x* ax as: x* (1/48)ax
So, if a measurement on the model is x, the corresponding measurement on the actual locomotive would be (1/48)ax.
Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 5.2 years and a standard deviation of 1 years.
The figure below shows the distribution of lifetimes of fluorescent lightbulbs.
Calculate the probability that a randomly chosen Fluorescent lighbulb lifetime will be between 3.2 and 6.2.
Answer:
Step-by-step explanation:
To solve this problem, we need to standardize the values using z-scores and then find the area under the standard normal distribution curve between those z-scores.
First, we need to find the z-scores for the values 3.2 and 6.2 using the formula:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
For x = 3.2:
z = (3.2 - 5.2) / 1 = -2
For x = 6.2:
z = (6.2 - 5.2) / 1 = 1
Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. The area represents the probability of a randomly chosen Fluorescent lighbulb lifetime being between 3.2 and 6.2.
Using a standard normal distribution table, we can find that the area between z = -2 and z = 1 is approximately 0.8186.
Therefore, the probability that a randomly chosen Fluorescent lighbulb lifetime will be between 3.2 and 6.2 is approximately 0.8186 or 81.86%.
Determine if the triangle pictured below is a right triangle.
(30 points)
Answer: Yes
Step-by-step explanation: Even though the sides might be different because there is little detail in this illustration, you actually have to predict, and if it looks as straight up as it is here, it counts as right. (Also, if you have a tool like a protractor, you could use that to measure it.)
How would you graph f(x)=x+3 ? And could you leave an explanation?
Answer:
Step-by-step explanation:
To graph the function f(x) = x + 3, we need to plot a series of points that satisfy the equation. We can do this by picking some values of x and then finding the corresponding values of f(x).
For example, when x = 0, f(x) = 0 + 3 = 3. So we have the point (0, 3) on our graph.
Similarly, when x = 1, f(x) = 1 + 3 = 4. So we have the point (1, 4) on our graph.
We can continue this process for other values of x, and we'll get more points on the graph. For example, when x = -1, f(x) = -1 + 3 = 2. So we have the point (-1, 2) on our graph.
Once we have enough points, we can connect them with a straight line to get the graph of the function. In this case, we'll notice that the graph is a line with a slope of 1 and y-intercept of 3. The slope of the line tells us how much y changes when x increases by 1, and in this case, it changes by 1 unit.
So, to graph f(x) = x + 3, we can start by plotting the point (0, 3) and then draw a line that passes through this point and has a slope of 1. We can use a straightedge or ruler to draw the line as accurately as possible. The resulting graph will be a straight line that intersects the y-axis at the point (0, 3) and has a slope of 1.
Find the missing value of 15,17,___,28,39:mean 23
Step-by-step explanation:
The sum of the given numbers is:
15 + 17 + x + 28 + 39 = 99 + x
To find the missing value, we can use the formula for the mean (average):
mean = (sum of numbers) / (number of numbers)
Substituting the given values:
23 = (15 + 17 + x + 28 + 39) / 5
Multiplying both sides by 5:
115 = 15 + 17 + x + 28 + 39
Simplifying:
x + 99 = 115
x = 16
Therefore, the missing value is 16.
Determine if the three side lengths could form a triangle 3,7,9 acute,right, or obtuse
Answer:
The triangle is acute.
Step-by-step explanation:
To determine whether the side lengths of 3, 7, and 9 can form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check if this condition is satisfied for the given side lengths:
3 + 7 = 10 > 9, so the sum of the two smaller sides is greater than the largest side.
7 + 9 = 16 > 3, so the sum of the two smaller sides is greater than the largest side.
3 + 9 = 12 > 7, so the sum of the two smaller sides is greater than the largest side.
Since all three inequalities are true, we can conclude that the given side lengths of 3, 7, and 9 can form a triangle.
To determine whether the triangle is acute, right, or obtuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's first determine which side is the longest. Since 9 is the largest side length, it must be the hypotenuse if the triangle is right-angled.
However, using the Pythagorean theorem, we can see that:
3^2 + 7^2 = 58 < 9^2, so the triangle is not right-angled.
Therefore, the triangle must be either acute or obtuse. To determine which one, we can use the law of cosines, which states that in any triangle:
c^2 = a^2 + b^2 - 2ab*cos(C)
where a, b, and c are the side lengths, and C is the angle opposite to side c.
Let's apply this formula to the triangle with side lengths 3, 7, and 9:
9^2 = 3^2 + 7^2 - 2(3)(7)*cos(C)
81 = 58 - 42*cos(C)
cos(C) = (58 - 81)/(-42) = 0.5476
C = cos^(-1)(0.5476) = 56.69 degrees
Therefore, the largest angle in the triangle is approximately 56.69 degrees. Since this angle is less than 90 degrees, we can conclude that the triangle is acute.
Answer:
obtuse angled triangle
Step-by-step explanation:
for the sides to form a triangle
the sum of any 2 sides must be greater than the third side.
3 + 7 = 10 > 9
3 + 9 = 12 > 7
7 + 9 = 16 > 3
then the 3 sides 3 , 7 , 9 will form a triangle
given 3 sides a , b , c with c the longest side
• if a² + b² = c² ⇒ right triangle
• if a² + b² > c² ⇒ acute angled triangle
• if a² + b² < c² ⇒ obtuse angled triangle
here a = 3 , b = 7 , c = 9
a² + b² = 3² + 7² = 9 + 49 = 58
c² = 9² = 81
since a² + b² < c²
then triangle is obtuse
Consider the parabola represented by this equation.
4x2 + 4x + 2y + 1 = 0
Which features are features of the parabola?
0
opens down
opens to the left
directrix at y = ㅎ
vertex at (-1,0)
directrix at x =
02/00
HELPPPP MEEEW
Answer:
a) opens down
c) directrix at y = 1/8
d) vertex at (-1/2,0)
Step-by-step explanation:
Starting from the given equation:
4x^2 + 4x + 2y + 1 = 0
We can rearrange to obtain the standard form of the equation of a parabola:
2(y + 1/2) = -4(x + 1/2)^2 + 1
(y + 1/2) = -2(x + 1/2)^2 + 1/2
Comparing to the standard form:
(y - k) = a(x - h)^2
We can see that the vertex of this parabola is at the point (-1/2, -1/2).
Next, we can find the axis of symmetry by noting that the parabola is symmetric about a vertical line passing through the vertex. This line is given by:
x = -1/2
We can also determine whether the parabola opens upward or downward by looking at the sign of the coefficient a. In this case, a = -2, so the parabola opens downward.
The distance between the vertex and the directrix is given by |1/(4a)|. Therefore, the distance between the vertex (-1/2, -1/2) and the directrix is:
|1/(4(-2))| = 1/8
So the directrix of the parabola is the horizontal line y = 1/8.
Therefore, the correct options are:
a) opens down
c) directrix at y = 1/8
d) vertex at (-1/2,0)
The other options are incorrect:
b) The parabola does not open to the left.
e) The directrix is not a vertical line at x = -3/8.
2. Is AP'Q'R' a 180° rotation about the origin of APQR?
Explain.
4
t
2
20
2
d
P
R
2 4
4.
R
à x*
8
It should be noted that AP'Q'R' a 180° rotation about the origin of APQR.
How to explain the rotationIt should be noted that to perform a 180° rotation about the origin, one has to draw the original figure and label its coordinates and draw the origin and label it O.
One can also use the following formula to find the coordinates of the image of a point (x,y) after a 180° rotation about the origin:
(x', y') = (-x, -y)
Here, P'Q'R' represents the coordinates of the image of the point PQR. We simply take the negative of the original x and y coordinates to find the new coordinates after the rotation.
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Q.5. Joseph has a small library at home that currently has 50 books. Each week, his family buys
him five books to add to the library. Which inequality can be used to find w, the number
of weeks when Joseph will have more than 125 books?
A. 50w +5 > 125
B. 5w+50 > 125
C. 50w +5 < 125
D. 5w+50 < 125
Answer:
To solve this problem, we need to set up an inequality that represents the situation where Joseph will have more than 125 books.
Let w be the number of weeks.
At the end of w weeks, Joseph will have 50 + 5w books (since he adds five books to his library every week).
To find the inequality that represents having more than 125 books, we can set up the following equation:
50 + 5w > 125
Simplifying this inequality:
5w > 75
w > 15
Therefore, the inequality that represents the situation where Joseph will have more than 125 books is:
5w + 50 > 125
The answer is B.
En la ciudad de trujillo se determinó que el 46% de la población ne llee la revista A, que el 60% ne lee la revista B y el 58% lee A o B pero no ambas. Si 63000 personas leen A y B.¿Cuántas personas hay en Trujillo?
Answer: Para resolver el ejercicio se plantea un diagrama de conjuntos, en el
cual se representan un conjunto A y B ( Ver dibujo adjunto ) .
b +x = 46% a + x = 60% a + b = 58%
Al sumar las dos ecuaciones :
b + x = 46%
a + x= 60%
--------------------------
a + b +2x = 106%
58% + 2x = 106%
2x = 106% - 58%
2x = 48%
x = 48%/2
x = 24% no leen ninguna de las dos revistas
c = 63000 personas que leen A y B
se llama al total de personas y :
y * 18% = 63000 personas
y = 63000 / 18%
y = 63000/0.18 = 350000 son las personas hay en Trujillo
Please help I only have part A incorrect I can’t figure it out
By similarity ratio of triangles, we have;
ΔPQR ∼ ΔPSR ∼ ΔRSQ
PS/PR = PR/PQ
PQ/RQ = RQ/SQ
How to solve similar triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Thus, applying the concept of similar triangle ratio we can say that;
ΔPQR ∼ ΔPSR ∼ ΔRSQ
Similarly, by similarity ratio of triangles, we have;
PS/PR = PR/PQ
We also have;
PQ/RQ = RQ/SQ
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Find the slope of the line passing through each of the following pairs of points (-6,-5) (-4,-3)
The Slope of the line is 1.
The slope of a line:The slope of a line is a numerical value that shows the stiffness or direction of the line. The formula used to find the Slope of the line is given by
Slope (m) = [ y₂ - y₁] / [ x₂ - x₁]Where (x₁, y₁) and (x₂, y₂) are pairs of points that pass through the line.
Here we have
The pair of points (-6, -5) and (-4, -3)
By using the formula,
The slope of the line = [ y₂ - y₁] / [ x₂ - x₁]
= [ -3 - (-5) ] / [ -4 - (-6) ]
= [ -3 + 5 ]/ [ -4 + 6 ]
= [ 2/2] = 1
Therefore
The Slope of the line is 1.
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Solve x2 +7=71
giving the positive and negative solutions.
[tex]x^{2} +7=71 \iff x^{2} =71-7[/tex]
[tex]x^{2} = 64 \iff x^{2} = 8^{2}[/tex]
[tex]x_{1} = - 8, \ x_{2} = 8[/tex]
A class has 34 students. In how many different ways can five students form a group for an activity?
Therefore, there are 278,256 different ways for 5 students to form a group from a class of 34 students.
A math factorial has what meaning?Factorial, followed by an exclamation point, is the sum of all positive integers that are less than or equal to a specific positive integer in mathematics. Factorial seven is therefore represented by the symbol 7!, which is made up of the letters 1 2 3 4 5 and 7. By definition, factororial 0 is equal to 1.
The number of ways to form a group of 5 students out of a class of 34 students can be calculated using the combination formula:
C(34, 5) = 34! / (5! (34-5)!) = (34 × 33 × 32 × 31 × 30) / (5 × 4 × 3 × 2 × 1) = 278,256.
Therefore, there are 278,256 different ways for 5 students to form a group from a class of 34 students.
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Sam is collecting money for an animal shelter. He collects $150.00 each day for 6 days. The shelter will use 35% of the money he collects to buy pet food. The rest of the money will be used to buy cleaning supplies.
How much of the money that Sam collects will be used to buy cleaning supplies?
According to the solving Sam will spend $585.00 of the money he collects on cleaning materials.
What do the percentages mean?%, a relative figure signifying hundredths of any amount. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Mathematical percentile is a related topic.
According to the given information:Sam collects $150.00 each day for 6 days, so the total amount he collects is:
$150.00/day x 6 days = $900.00
The shelter will use 35% of the money he collects to buy pet food. To find out how much money will be used to buy pet food, we can multiply the total amount Sam collects by 35% (or 0.35):
$900.00 x 0.35 = $315.00
So, $315.00 of the money that Sam collects will be used to buy pet food. To find out how much money will be used to buy cleaning supplies, we can subtract the amount used to buy pet food from the total amount collected:
$900.00 - $315.00 = $585.00
$585.00 of the money that Sam collects will be used to buy cleaning supplies.
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Keenan jumped 3 times every 18 minutes. At that rate, how many would he jump in 24 minutes?
Answer:
4 jumps in 24 minutes
Step-by-step explanation:
Rate: 1 jump every 6 minutes
24/6 = 4
