The equation of the perpendicular line is y = x + 15.
How to determine the equation of the perpendicular line
In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableThe first line has a slope - 1 and the slope of the second line is:
m' = - 1 / m
m' = 1
Then, the intercept of the second line is:
b = y - m · x
b = 10 - (- 5)
b = 15
The equation of the perpendicular line is y = x + 15.
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An observation deck extends 454 feet out above a valley. The deck sits 404 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by
h=-16² +404. How long will it take for the object to be 4 feet above the valley floor?
Answer:4.12
Step-by-step explanation:
Write down the place
Value of 7 in each of these numbers 78.924531
Answer:
the place value of 7 is =70.000000
Step-by-step explanation:
Please look at the picture above and respond.
-letter words (repeated letters not allowed) can be formed from the alphabet if we require;(a) the 2nd letter to be a vowel (a, e, i, o, u)?(b) exactly one vowel?
(a) The 2nd letter to be a vowel (a, e, i, o, u) = 69000
(b) Exactly one vowel = 159600
What is a vowel ?An open sound is represented by a vowel, which is a letter. The English language has six vowels: a, e, I o, u, and occasionally y. Y can function as a consonant or a vowel depending on the context, as in the word story or yes. Vowels are a representation of open, frictionless vocal sounds.
4 letter word to be formed
Total Alphabets = 26
Repeated letters are not allowed
(a) 4 letter word, Consonant - C, vowel - V
Second letter to be a vowel
C or V = 25, V = 5, C or V = 24, C or V = 23
Number of word can form = 25 × 5 × 24 × 23 = 69000
(b) 4 letter word, in this exactly one vowel.
Number of words
V(5) × C(21) × C(20) × C(19)
C(21) × V(5) × C(20) × C(19)
C(21) × C(20) × V(5) × C(19)
C(21) × C(20) × C(19) × V(5)
Total number of words formed = 4 [5×21×20×19] = 159600
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The branch of statistical studies called descriptive statistics summarizes important aspects of a data set. True or false?.
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.
It is required to find the statement.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.
Descriptive statistics refers to the summary of important aspects of a data set.
Therefore, the branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.
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Write 0.7222… as a fraction in simplest form
Answer:
3611/5000
Step-by-step explanation:
A
(5x − 11)
(3x + 11)
find y
Please help, I’m not sure what I’m doing.
Step-by-step explanation:
Fact 1: Alternate angles are equal.
Angles, (5x-11)° and (3x+17)° are ALTERNATE angles and so,
(5x-11)° = (3x+17)°
5x - 3x = 17 + 11
2x = 28
x = 28 ÷ 2
x = 14
NB: x does NOT have the degree sign because it's NOT an angle on its own, but rather within the bracket/part of the calculation to get the angle degree.
Fact 2: Opposite angles are equal.
Y° and (3x+17)° are OPPOSITE angles
y = (3x+17)°
y = (3x14) + 17
y= 42 + 17
y = 59°
Hope this helps!
The sum of two numbers is 12. The difference of the same two numbers is -4. Find the two numbers.
Larger number
Smaller number
Answer:
let the number be x and y
Step-by-step explanation:
x+y=12
x-y=-4
here,
Given that z is a standard normal random variable, what is the probability that -2.51 z -1.53?
Probability that -2.51 < z < -1.53 = 0.057
Given that z is a standard normal random variable. Then the z - values are given by the area under standard normal curve. It can be found from the standard normal tables.
Now probability that -2.51 < z < -1.53 = P( -2.51 < z < -1.53 )
= P( -2.51 < z < 0 ) - P( -1.53 < z < 0 )
= P( 0 < z < 2.51) - P( 0 < z < 1.53 ) [Since areas are equal for same positive and negative values]
P( 0 < z < 2.51) = 0.4940
P( 0 < z < 1.53) = 0.4370
[From the normal tables]
Therefore, Probability that -2.51 < z < -1.53 = 0.4940 - 0.4370 = 0.057
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Fiona has a coupon for $3 off the price of her meal at a local fast food establishment. her favorite meal is on sale at a special rate of 10% off the combo price. if fiona paid $8.25 for her meal, before taxes, what was the original price of the meal?
The Original price of the meal was $12.16.
Discount Percent is defined as the discount given on the product per hundred .
For Example . if there is 10% discount on a price of $100.
The final amount will be $90.
Final amount paid by Fiona = $8.25
percentage discount = 10%
Let the original amount be x.
According to the question ;
x - 10% of x = 8.25
[tex]x-\frac{10}{100} *x=8.25\\ \\ \frac{100x-10x}{100} =8.25\\ \\ \frac{90x}{100} =8.25\\ \\ x=\frac{8.25*100}{90}\\ \\ x=\frac{825}{90} \\ \\ x=9.16[/tex]
Since Fiona also had a discount coupon of $3.
The original amount will be $9.16+$3=$12.16.
Therefore , The original price of the meal was $12.16.
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The constant ______ of _______ between points on a line.
The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.
How far is it between the two locations?
By calculating the sum of the absolute values of the y-coordinates, you may determine the distance between two places in different quadrants with the same x-coordinates.
What does a line's slope indicate?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Describe slope using an example?
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.Learn more about slope
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a mini bottle of water contains 8 ounces of water you need 4 1/4 gallons of water how many mini water bottles do you need
The number of mini bottles required is; 68 mini bottles
How to convert units of measurement?
We are told that a mini bottle of water contains 8 ounces of water.
Now, we are told that you require 4¹/₄ = 4.25gallons of water.
Now from conversions, we know that;
1 gallon = 128 ounces
Thus; 4.25 gallons = 4.25 * 128 = 544 ounces
Since a mini bottle of water contains 8 ounces of water, then we can say that;
Number of mini bottles required is;
544/8 = 68 mini bottles
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Distributive property for x(11+2), please????
Answer: 13x
Step-by-step explanation: Multiply x to 11 and 2
11x+2x=13x
An emplovee at an animal shelter wrote
the true conditional "If 47% of the dogs
at the shelter are female, then 53% of the
dogs are male." Can he rewrite this as a true
biconditional? Explain.
There is no way he can write a bi-conditional because there are only 2 g e n d e r s which are m a l e and f e-m a l e and as such he can't use if and only if due to the fact that all non - m a l e dogs are f e m a l e dogs and v i c e v e r s a.
What is a biconditional statement?A biconditional statement is a statement combing a conditional statement with its converse. So, one conditional is true if and only if the other is true as well.
Now, he wrote a true conditional which is "If 47% of the dogs
at the shelter are f e m a l e, then 53% of the dogs are m a l e."
Now, there is no way he can write a biconditional because there are only 2 genders which are m a l e and f e m a l e and as such he can't use "if and only if" due to the fact that all non - m a l e dogs are f e m a l e dogs and vice versa.
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Solve for x: 1 < x + 3 < 4
4 > x > 7
4 < x < 7
−2 > x > 1
−2 < x < 1
Answer:
-2 < x < 1
Step-by-step explanation:
Given inequality:
[tex]1 < x+3 < 4[/tex]
[tex]\textsf{If $a < u < b$ \;then\; $a < u$ \;and \;$u < b$}:[/tex]
Case 1
[tex]\implies 1 < x+3[/tex]
[tex]\implies 1-3 < x+3-3[/tex]
[tex]\implies -2 < x[/tex]
[tex]\implies x > -2[/tex]
Case 2
[tex]\implies x+3 < 4[/tex]
[tex]\implies x+3-3 < 4-3[/tex]
[tex]\implies x < 1[/tex]
Combine the intervals:
[tex]-2 < x < 1[/tex]
PLEASE HELP MEEEEE. EXPLAINNNN
IMAGE INCLUDED
Answer:
i thing that's the answer
Solve the simultaneous equations
y=2-5x
y = x² – 2x – 8
Answer:
Step-by-step explanation:
sub equation 1 into 2
2-5x=x²-2x-8
0=x²-2x+5x-8-2
0=x²+3x-10
0=(x-2)(x+5)
x=2 or x=-5
sub x into equation 1
y=2-5(2) or y=2-5(-5)
y=-8 y=27
In a sale, all normal prices are reduced by 20%
In the sale, the normal price of a tablet computer is reduced by 79 euros.
Work out the normal price of the tablet computer.
Which number is greater,
23
×
10
3
or
11
×
10
4
? How do you know? Show your work and explain your steps.
Answer:
A. 23×10^3
B. 11×10^4
Your answer would be B, 11x10^4.
Step-by-step explanation:
To find your answer you can evaluate each equation and compare your answers.
A:
10^3 = 1,000
23•1,000 = 23,000
B:
10^4 = 10,000
11•10,000 = 110,000
End Result:
110,000 > 23,000
Therefore your answer would be choice B.
Have a great rest of your day.
From the one and only,
Mr. Universe
Answer:
A:
10^3 = 1,000
23•1,000 = 23,000
10^4 = 10,000
11•10,000 = 110,000
110,000 > 23,000
find the gradient and y-intercept of x-2y=8
(show your working)
x-2y=8
Step-by-step explanation:
x=8+2y
The gradient is 2
Answer:
gradient = [tex]\frac{1}{2}[/tex] , y- intercept = - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope (gradient) and c is the y- intercept )
given
x - 2y = 8 ( subtract x from both sides )
- 2y = - x + 8 ( divide through by - 2 )
y = [tex]\frac{1}{2}[/tex] x - 4 ← in slope- intercept form
with gradient m = [tex]\frac{1}{2}[/tex] and y- intercept c = - 4
Please help asap the picture has everything needed to answer the question. Thank you!
Answer:
Step-by-step explanation:
f(x) = 0
then x =
-2 and +2
f(x) = 5
then x = +3 and -3
Farfalla kites owns 3 factories around the globe. In one year, the original factory can make 600 kites, and each of the other factories can make 900 kites. How many kites does Farfalla produce every year
Farfalla produces 2,400 kites every year.
The number of factories Farfalla owns around the globe = 3;
The number of kites produced by original factory every year = 600;
The number of kites produced by each of other 2 factories every year = 900;
Then the total kites produced by both other factories will be = 2 × 900 = 1800;
Now, the number of kites Farfalla produces every year is = 600 + 1800 = 2400;
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2173 rounded to neatest hundred
Answer:
2200
Step-by-step explanation:
that is the answer jf
can someone help me with this question
Answer:
50 69 600 5.2 2
Step-by-step explanation:
this is because this is simple interest i=pxrxt
5 Read what Alicia says.
The angles of this pentagon are 100°, 105°, 72°, 126° and 127°.
Explain why she must be wrong.
Answer:
all the angles of the pentagon do not add up to 540
Step-by-step explanation:
total degree in a shape
180 × (n-2) where n is the number of side
a pentagon has 5 sides so
180 × (5-2)
= 540
100+105+72+126+127= 530
all the angles of the pentagon do not add up to 540
Rent for the month $ 1,150 monthly take-home salary $ 2,685 spending for food $ 595 cash in checking account $ 550 savings account balance $ 1,990 balance of educational loan $ 2,760 current value of automobile $ 9,800 telephone bill paid for month $ 115 credit card balance $ 285 loan payment $ 180 auto insurance $ 330 household possessions $ 4,400 video equipment $ 2,600 payment for electricity $ 140 lunches/parking at work $ 230 donations $ 260 personal computer $ 1,700 value of stock investment $ 1,110 clothing purchase $ 160 restaurant spending $ 180
$22,150 is the total assets .
What is total assets?
A person or entity's total assets are all of their possessions combined. Assets are things with economic value that an owner uses over time to reap benefits. These assets are often listed in the accounting records and can be seen on the company's balance sheet if the owner is a business.Total asset = Saving account balance + current value of automobile + video equipment + personal computer + cash in checking account + household possessions + value of stock investment
= $1990 + $9800 + $2600 + $1700 + $550 + $4400 + $ 1110
= $22,150
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What is 3458 rounded to the nearest thousand
Answer:
3000
Step-by-step explanation:
If it was 3500 then it would've been 4000. However, since 3458 is below 3500 it's 3000. Hope this helps. Good luck!
The table shows the distance traveled by 4 cycleists. Sort the speeds of the riders, in miles per hour, from slowest to fastest.
The speed from slowest to the fastest is Julio; Elana; Kevin; Lorena.
Given that a table shows the distance traveled by 4 cyclists as shown in attached images.
Speed is defined as . The rate at which an object changes position in any direction. Speed is measured as the ratio between distance and time traveled.
Firstly, we will calculate the speed of Elena.
The given distance is 20(1/2) mi or it can be written as 41/2mi and the time is 2(1/4) hr or 9/4hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(41/2)/(9/4)
Speed=(41/2)×(4/9)
Speed=82/9 mi/hr.
Now, we will calculate its speed of Julio.
The given distance is 12(1/4) mi or it can be written as 49/4mi and the time is 1(1/2) hr or 3/2hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(49/4)/(3/2)
Speed=(49/4)×(2/3)
Speed=49/6 mi/hr.
Further, we will calculate the speed of Kevin.
The given distance is 20(2/3) mi or it can be written as 62/3mi and the time is 1(2/3) hr or 5/3hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(62/3)/(5/3)
Speed=(62/3)×(3/5)
Speed=62/5 mi/hr.
Furthermore, we will calculate the speed of Lorena.
The given distance is 33(1/4) mi or it can be written as 133/4mi and the time is 2(1/3) hr or 7/3hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(133/4)/(7/3)
Speed=(133/4)×(3/7)
Speed=57/4 mi/hr.
Hence, the speeds from slowest to fastest from the given table is Julio; Elana; Kevin; Lorena.
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NEED HELP 25 POINTS COME NOW
How many inches are in 5.5 miles?
Answer:
5.5 miles = 348480 inches
Step-by-step explanation:
Formula: multiply the value in miles by the conversion factor '63360'.
So, 5.5 miles = 5.5 × 63360 = 348480 inches.
Answer:
348480
Step-by-step explanation:
5.5 times 63360 = 348480
