The parallelogram ABCD with vertices A(-8, 5), B(-7, 8), C(-1,6), and D(-2, 3) is a rectangle as two sides are equal, so option A is correct.
What is parallelogram?A unique kind of quadrilateral created by parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but for it to be a parallelogram, its opposite sides must be parallel.
Given data:
The parallelogram ABCD with vertices A(-8, 5), B(-7, 8), C(-1,6), and D(-2, 3),
Calculate the distance of sides as shown below
[tex]AB = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB = [tex]\sqrt{[-7-(-8)]^2 + (8-5)^2}[/tex]
AB = √(1² + 3²)
AB = √10
Calculate
BC = [tex]\sqrt{[-1-(-7)]^2+(6 - 8)^2}[/tex]
BC = √(36 + 4)
BC = √40 or 2√10
Similarly,
CD = √10
And AD = 2√10
Here AB = CD and BC = AD, opposite sides equal, so it is a rectangle. Therefore, the parallelogram ABCD with vertices A(-8, 5), B(-7, 8), C(-1,6), and D(-2, 3) is a rectangle as two sides are equal.
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A line passes through the points (4, -1) and (2, 3). What is the slope of the line?
Answer:
-2
Step-by-step explanation:
We can find slope by using change in y over change in x, as shown:
3-(-1) = 4, and 2-4=-2, and 4/-2 = -2, so our answer is -2.
Khalid has 2 bags of cornmeal that each contain 25 servings. One serving is 3/4 cup. Khalid is making muffins that require 2.5 cups of cornmeal per batch. What is the maximum number of batches of muffins that Khalid can make using cornmeal?
Using ratios and proportions, he can make 15 batch of muffins from 2 bags of cornmeal
What are Ratios and ProportionsRatio is used for comparing two quantities of the same kind. The ratio formula for two numbers, a and b is expressed as a : b or a/b. When two or more ratios are equal, they are said to be in proportion. The concept of ratio and proportion is based on fractions.
Proportion refers to the equality of two ratios. Two equivalent ratios are always in proportion. Proportions are denoted by the symbol (: :) and they help us to solve for unknown quantities. In other words, proportion is an equation or statement that is used to depict that the two ratios or fractions are equivalent.
In this problem, we know that he has 2 bags of cornmeal
1 bag of cornmeal = 25 serving
2 bags = x
x = 2 * 25 = 50 servings
When making muffins, he needs 2.5 cups in a batch
But 3/4 cup = 1 serving
x cups = 50 serving
x = 50 * 3/4
x = 37.5 cups
1 batch = 2.5 cups
x batch = 37.5 cups
x = 37.5 / 2.5
x = 15 batch
He can make a 15 batches
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Question 1:
Joe and Sara are each running a 5k. In the age/ability group that Joe is running in, the average run time is 22:30 minutes/seconds with a standard deviation of 4 minutes. In the age/ability group that Sara is running in, the average run time is 31:15 minutes/seconds with a standard deviation of 6 minutes.
Joe's run time is 19:45. Sara's run time is 28:20. Compute the z-scores for each and thus make a claim about who ran a better race compared to their age/ability group.
Question 2:
Suppose a data set has a mean 50 and standard deviation 5. If the Z-score of a data value is -2, what is the actual score?
1. The z-scores are given as follows:
Joe: Z = -0.6875.Sara: Z = -0.49.Due to the lower z-score, Joe had a better time.
2. The actual score is of 40.
What are z-scores?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.Considering the mean and the standard deviation for his distribution, and also that 15 seconds = 0.25 minutes, the z-score for Joe is obtained as follows:
Z = (19.75 - 22.5)/4
Z = -0.6875.
For Sara, the z-score is calculated as follows:
Z = (28.33 - 31.25)/6
Z = -0.49.
Joe had a better time, as his lower z-score means that a lower percentage of runners spent less time than him, that is, a lower percentage of runners ran faster than him.
For item 2, the actual score is calculated as follows:
-2 = (X - 50)/5
X - 50 = -10
X = 40.
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Suppose that sin(a) = 4/6 and cos(b) =1/5 define in the first quadrant, determine cos(a-b). (round to 4 decimal places)
The value of the cosine of the angle of (a - b) will be 0.80.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
It is a function that repeats itself in a particular time interval.
Suppose that sin(a) = 4/6 and cos(b) = 1/5.
Then the value of 'a' is given as,
sin(a) = 4/6
sin(a) = 2/3
a = 41.81°
Then the value of 'b' is given as,
cos(b) = 1/5
b = 78.46°
Then the value of the cosine of the angle of (a - b) will be given as,
⇒ cos(41.81° - 78.46°)
⇒ cos(-36.65°)
⇒ cos 36.65°
⇒ 0.80
The value of the cosine of the angle of (a - b) will be 0.80.
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If n represents a power of 10, what is the value of n when 0.006 is rounded to the nearest power of 10?
Enter your answer in the box.
Answer:
The value of n is [tex]10^{-3}[/tex]
What is log function?
The logarithm (log) function is a mathematical function used to determine the logarithm of a number. The logarithm of a number is the exponent to which a particular base must be raised in order to produce that number. For example, the logarithm of 8 with base 2 is equal to 3 because 2 to the third power is 8. In mathematics, the logarithm of a number can be expressed as logbX, where b is the base and X is the number.
Step-by-step explanation:
We can write -
0.006 = 6 x 10^-3
10ⁿ = 6 x 10^-3
[tex]10^{n+3}[/tex] = 6
log([tex]10^{n+3}[/tex]) = log(6)
(n + 3) log 10 = log (6)
n +3 = log(6)/log(10)
n + 3 = 0.78
n = -3 + 0.78
n = -3 (approx.)
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Please answer soon!!
Which angles are coterminal with 3л/2?
Select each correct answer.
A. 11л/2
B. -л/-2
C. -7л/-2
D. л/2
Answer:
A, C
Step-by-step explanation:
You want to know which answer choices are angles that are coterminal with 3π/2.
CoterminalAngles are coterminal when their terminal rays lie in the same position. In general, any angle will be coterminal with angles that are an integer multiple of 2π added to the original.
That is, an angle is coterminal with all angles that have the same value modulo 2π.
For the given angle and each of the answer choices, the attachment calculates the coefficient of π modulo 2. The ones that match the given angle are ...
A. 11π/2 mod 2π = 3π/2
C. -7π/-2 mod 2π = 3π/2
__
Additional comment
Both -π/-2 and π/2 match the angle π/2, which is not the same as 3π/2.
Of course, the minus signs in numerator and denominator cancel, so -7π/-2 is the same as 7π/2.
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COMMON IDENTITIES IN VECTOR ANALYSIS
How do i prove that .......... if F, G, and H are scalar fields?
The cross product or the curl of F, G, and H are zero so they are scaler fields.
What are dot products and cross products?The cosine of the angle between the vectors and their magnitude are combined to form the dot product.
The dot product is represented by A.B = ABCos θ.
The sine of the angle between the vectors and their magnitude are combined to form the cross-product.
The cross product is represented by A×B = ABSin θ.
Given, F × (G × H) = (F . H)G - H(F .G).
∴ F × (G × H) = (FHcosФG) - H(FGcosФ).
F × (G × H) = FGHcosФ - FGHcosФ.
F × (G × H) = 0.
We know that cross-product is the curl of a vector field and if the curl is zero it is a scalar field.
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PLEASE HELP
Two swimming pools are being drained so that they can be repaired. The two equations below describe the depth of the two pools, d, as a function of time in hours, t.
d=5 - 1/4t. d=7 - 1/3t
Ted wants to know when the two pools will reach the same depth. He solves the system by equating the two equations for d and then solving for t. The solution he finds is t = 24, so he concludes that after 24 hours the pools will be the same depth. Is Ted’s conclusion reasonable? Why or why not?
A. Yes, Ted’s conclusion is reasonable. Setting the two equations equal and solving for t will solve for the time when the two pools are at the same depth.
B. Yes, Ted’s conclusion is reasonable. Substituting into both equations yields the same value for d, which is the depth of the pools.
C. No, Ted’s conclusion is not reasonable. Ted failed to take into account the limits on the domain and range of the two functions.
D. No, Ted’s conclusion is not reasonable. Ted made a math error when he was finding a common denominator when solving for t.
Yes, Ted’s conclusion is reasonable.
Setting the two equations equal and solving for t will solve for the time when the two pools are at the same depth.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement made up of two expressions connected by an equal sign.
We have,
d = 5 - (1/4)t ____(1)
d = 7 - (1/3)t ____(2)
Now,
The time at which the depth d is the same.
Make (1) and (2) equal.
5 - (1/4)t = 7 - (1/3)t
(1/3)t - (1/4)t = 7 - 5
(4t - 3t)/12 = 2
t = 2 x 12
t = 24
Thus,
Yes, Ted’s conclusion is reasonable.
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n baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
a. Tasha, because she has the lowest ratio since 0.9 > 0.8
b. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
c. Jana, because she has the lowest ratio since 0.9 > 0.8
d. Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
The player that has a ratio that means they have a better batting average is B. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
How to illustrate the ratio?From the information Illustrated, the ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most.
For the season so far, Jana has hit the ball 12 times out of 15 attempts. This will be:
= 12/15
= 0.8
Tasha has hit the ball 9 times out of 10 attempts. This will be:
= 9/10
= 0.9
The player that has a ratio that means they have a better batting average is Tasha.
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0.0000000536 in scientific notation
Answer: 5.36 × [tex]10^{-8}[/tex]
Step-by-step explanation:
5.36 × [tex]10^{-8}[/tex]
A Consumer with a 10 years loan, will have to make 125 payments.
A. True
B. False
Answer:
False
Step-by-step explanation:
Assuming monthly payments
12 payments per year X 10 years = 120 payments
A TPN solution contains 8.25 % amino acids it. If the patient needs 75 grams of protein per day, how much of the TPN solution should the patient receive per day?
The patient should receive 909 mL of the TPN solution per day.
To determine the amount of the TPN solution the patient should receive per day, we need to use the following formula:
amount of TPN solution = (grams of protein needed / percentage of amino acids in TPN solution) × 100
In this case, we are given that the TPN solution contains 8.25% amino acids and that the patient needs 75 grams of protein per day. Substituting these values into the formula, we get:
amount of TPN solution = (75 / 8.25) × 100
amount of TPN solution = 9.09 × 100
amount of TPN solution = 909 mL
Therefore, the patient should receive 909 mL of the TPN solution per day.
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In the following lever system, what is the clockwise torque? 40 N. 9m. 3m. 80 N.
Answer:
Counter Clockwise Torque = 360 Nm
Clockwise Torque = 240 Nm
Step-by-step explanation:
Solve equation:
0=2n+6n
Answer: 0=8n
Step-by-step explanation: Add 2n+6n = 8n, so 0=8n
Answer:
0
Step-by-step explanation:
0=2n+6n
add 2n + 6n =8n
0=8n
divide both sides by 8 and you get 0
I'm not sure though unless it's 0=8n
Please help me on this.
Andrew buys 8 bottles of cranberry juice at the corner store for a total cost of $5.68. If each bottle costs the same amount, how much is 6 bottles of juice?
What is the value of x in |6|=x
Answer and Step-by-step explanation: I used demos and got (6,0) as my answer.
Tom wants to know whether a new chest of drawers will fit next to his bed. The chest of drawers would like to buy is 70 centimeters wide.He knows that the room is 86 inches wide. The bed is 67
inches wide. Will the chest fit next to bed?
Answer:
no
Step-by-step explanation:
Tom wants to know if a 70 cm chest will fit in the space left by a 67 in bed in a room 86 in wide.
Available spaceThe space available is 86 in -67 in = 19 in.
Space neededAn approximate conversion between cm and inches is that 10 cm corresponds to about 4 in. Then 70 cm will correspond to 7×4 = 28 inches, much too wide for a 19-inch space.
The chest will not fit next to the bed.
Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint. Elena has 2/3 cup of white paint. How much purple paint can she make?
Elena can make 20/3 cups of purple paint
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.
Since Elena has 2/3 cup of white paint. then;
1 1/2 cups of red paint (1 1/2=1.5)
1/2 cup of white paint (1/2=0.5)
Then the ratio is 3:1.5:0.5
Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)
Let x the number of cups of purple paint
5/ 0.5 = x / (2/5)
x = 20/3 cups of purple paint
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1. Shelby had $33.00. Then,
Now, she wants to spend all of her
money on some ice cream cones
that cost $3.00. How many ice
cream cones can she buy?
Answer:11 cones
Step-by-step explanation: She can by 11 since $3x 11 =$33
16. Model Real Life Your aunt and uncle
buy 2 personal watercrafts for $3,495
each. They make 10 equal payments
for the watercrafts. What is the amount
of each payment?
7
TR
The amount of each payment is $699.
What is payment?
Payment refers to the exchange of something of value as a condition of a contract. While one party pays money and receives something else of value, the other party gets paid in return for delivering a good or service. Physical currency was once the most common form of payment, but nowadays most forms of payment use technology.
Given: Buy 2 personal watercrafts for $3,495 each.
So, the price for 2 watercrafts is, 2 x $3495 = $6990
They make 10 equal payments for the watercrafts.
So each payment is of $6990/10 = $699.
Hence, the amount of each payment is $699.
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I think of a number,take away 4 and multiply the result by 2.
The number that is thought in the form of expression will be 2x - 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let the number be 'x'. Then the expression is given as,
⇒ (x - 4) × 2
Simplify the expression, then we have
⇒ (x - 4) × 2
⇒ 2x - 4
The number that is thought in the form of expression will be 2x - 4.
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please help!!!!!!!!!!!!!!!!!!
Answer:
1x2=2 3x3x1=3
Step-by-step explanation:
What is the remainder when 7x^4+6x^3−9x^2−32x+95 is divided by x+1?
Only enter a number
The required quotient is given as [tex]7x^3-x^2-8x-24[/tex] and the remainder term is 119
In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}[/tex] .
What is synthetic division?It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.
Here,
When performing synthetic division of polynomials, the terms in the product that remain as fractions are referred to as the division's remainder, whereas the polynomial is referred to as the division's quotient.
[tex]= \frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}\\=7x^3-x^2-8x-24+\frac{119}{x+1}[/tex]
Thus, the required quotient is given as [tex]7x^3-x^2-8x-24[/tex] and the remainder term is 119
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a coach took his team out for pizza after their last game. there were 14 players so they had to sit in smaller groups at different tables. six players sat at one table and got 4 small pizzas to share equally. the other 8 players sat at a different table and got 6 small pizzas to share equally. afterwards one of the players said it wasnt fair because some kids got more pizza do u agree?
Yes, it wasn't fair because some kids got more pizza.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A coach took his team out for pizza after their last game.
There were 14 players, so they had to sit in smaller groups at different tables.
Six players sat at one table and got 4 small pizzas to share equally.
Each of them got = 4/6 = 0.67
The other 8 players sat at a different table and got 6 small pizzas to share equally.
Each of them got = 6/8 = 0.75
0.75 > 0.67
Therefore, some kids got more pizza.
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PLEASE I REALLY NEED HELP!!! 100 points if answer right
y=1/3x+4 is perpendicular to y=-3x-4,
y=2/5x-7 is perpendicular to y=-5/2x+7,
y=-5/2x+8 is perpendicular to y=2/5x+6,
y=-2x+6 is perpendicular to y=1/2x+3 and
y=7/5x-9 is perpendicular to y=-5/7x-11.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We know that the product of slopes of perpendicular lines is -1.
mM=-1
m is slope of one line and M is the slope of perpendicular line.
M=-1/m
y=1/3x+4
The perpendicular line is y=-3x-4
y=2/5x-7
The perpendicular line is y=-5/2x+7
y=-5/2x+8
The perpendicular line is y=2/5x+6
y=-2x+6
The perpendicular line is y=1/2x+3
y=7/5x-9
The perpendicular line is y=-5/7x-11.
Hence, the lines with corresponding perpendicular lines are
y=1/3x+4---> y=-3x-4
y=2/5x-7-----> y=-5/2x+7
y=-5/2x+8----->y=2/5x+6
y=-2x+6---->y=1/2x+3
y=7/5x-9-----> y=-5/7x-11.
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IMAGE ATTACHED PLEASE HELP PLEASE
Answer: first one
Step-by-step explanation: when u divide the equation to (x+2) and (x-1)
My Truck Takes 50 Gallons of gas. I used 20⅔ gallons on Monday. 9¼ on Tuesday. And 2½ on Wednesday. How many Gallons of gas do i still have in my truck?
Answer:
17 7/12 gallons of gas.
Step-by-step explanation:
Set the fractions to like denominators. It'll make it a hell of a lot easier to add.
20 2/3rds = 20 8/12
9 1/4ths = 9 3/12
2 1/2 = 2 6/12
Adding those together gets you 31 17/12 which is 32 5/12 simplified.
Take that fraction and subtract it from your 50 gallons and it'll get you 17 7/12
2y+x=-15 and x=3y substitution method
Answer:x = -9, y = -3
Step-by-step explanation:
Shelby is walking through her favorite store and sees a shirt she likes being sold for $80.00. She then notices the store is having a 45% off sale on all items. Excited to purchase the shirt, she grabs it and goes to the cash register. As she’s taking out her wallet, she finds a coupon for 25% off (that is applied after the store’s sale). What is the final price of the shirt that Shelby pays after the two discounts?
a. $9.00
b. $33.00
c. $28.00
d. $52.00
first we go 45+25=70 so now 80-70=$10.00
Did you mess up one of the answer because I did it two ways and got 10.00?