The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46
Step-by-step explanation:
The equation of a line is y = m x + b, where
m is the slope of the line, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are 2 points lie on the lineb is the y-intercept, to get it substitute x and y in the equation by the coordinates of one of the 2 given points∵ The line contains the points (4.6 , -8) and (6.6 , 2.2)
∴ [tex]x_{1}[/tex] = 4.6 and [tex]x_{2}[/tex] = 6.6
∴ [tex]y_{1}[/tex] = -8 and [tex]y_{2}[/tex] = 2.2
∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Substitute the values above in the rule of m
∴ [tex]m=\frac{2.2-(-8)}{6.6-4.6}=\frac{2.2+8}{2}=\frac{10.2}{2}=5.1[/tex]
∴ The slope of the line is 5.1
∵ The equation of a line is y = m x + b
Substitute m by 5.1
∴ y = 5.1 x + b
To find b substitute x and y by the coordinates of point (4.6 , -8) OR point (6.6 , 2.2)
∵ x = 6.6 and y = 2.2
∴ 2.2 = 5.1(6.6) + b
∴ 2.2 = 33.66 + b
- Subtract 33.66 from both sides
∴ -31.46 = b
∴ y = 5.1 x + (-31.46)
∴ y = 5.1 x - 31.46
The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46
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Elliot is standing at the top of a store escalator that leads to the ground floor below. The angle of depression from the top of the escalator to the floor is 42.51 degree, and the escalator is 16 feet long. How far the top of the escalator from the ground floor? Round your answer to the nearest foot.
A. 41 feet
B. 17 feet
C. 12 feet
D. 11 feet
Answer:
The answer is 11
Step-by-step explanation:
Final answer:
The distance between the top of the escalator and the ground floor is approximately 12 feet.
Explanation:
To find the distance between the top of the escalator and the ground floor, we can use trigonometry. We have the length of the escalator (16 feet) and the angle of depression (42.51 degrees). The distance we need to find is the opposite side of the right triangle formed by the top of the escalator, the floor, and the length of the escalator. We can use the sine function to find this distance.
The formula is sin(angle) = opposite/hypotenuse. Plugging in the values, we get sin(42.51) = opposite/16. Solving for opposite, we have opposite = sin(42.51) * 16.
Using a calculator, we find that opposite ≈ 12.014 feet. Rounding to the nearest foot, the distance between the top of the escalator and the ground floor is approximately 12 feet.
Michael's father brought him a 16-foot board to cut into shelves for his bedroom. Michael plans to cut the board into 11 equal size lengths for his shelves.
The saw blade that Michael will use to cut the board will change the length of the board by -0.125 inches for each cut. How will this affect the total length of the board?
Answer:
The remaining wood will be 1.25 inches shorter.
Step-by-step explanation:
Only 10 cuts are required to cut the board into 11 equally sized lengths. Thus, the length of the board after these cuts have been made will be
10(0.125 inches), or 1.25 inches, shorter.
By making 10 cuts, the total length of the board will be reduced by 1.25 inches due to the saw blade reduction. After converting this to feet, Michael will have approximately 15.896 feet of board left.
Explanation:Michael has a 16-foot board that he plans on cutting into 11 equal lengths. This means he will need to make 10 cuts (as the 11th 'cut' is actually the end of the board not actually needing a cut). The saw blade will decrease the length of the board by -0.125 inches for each cut. To solve this, we multiply the number of cuts by the length that will be reduced by the saw blade. That gives us 10 x -0.125 = -1.25 inches. That means that the total usable length of the board will be reduced by 1.25 inches. We need to convert this to feet since the original length of the board is in feet. There are 12 inches in foot, so -1.25 inches is about -0.104 feet. Thus, the total length of the board after all the cuts will be 16 - 0.104, or approximately 15.896 feet.
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Mrs. Bailey had 12 pieces of candy. She gave away some candy and has 3 pieces left. What is the percent decrease of candy? PLEASE SHOW YOUR WORK. thank you
Mrs. Bailey had a 75% decrease in the number of candies she had after giving away 9 out of the original 12 pieces.
Explanation:To calculate the percent decrease of candy Mrs. Bailey had, we begin by identifying the initial amount and the final amount of candy. Mrs. Bailey started with 12 pieces and ended with 3 pieces, which means she gave away 12 - 3 = 9 pieces of candy. To find the percent decrease, we use the formula: “part over total, times one hundred, equals percent.” Here, the “part” is the amount of candy she gave away (9), and the “total” is the original amount she had (12).
The formula for the percent decrease is:
9 / 12 × 100 = 75%
So, the percent decrease in the number of candies Mrs. Bailey had is 75%.
Which equation can be used to find the unknown length, a, in this triangle?
15 m
17 m
3+15² = 172
152 +172 - a
2² +15= 172
at 15² = 17²
Answer:
Here is the complete question.(attachment)
The correct choice is [tex]a^2+15^2=17^2[/tex]
Step-by-step explanation:
We will apply the Pythagoras formula to calculate the perpendicular length (a).
Pythagoras formula [tex]=(base)^2+(perpendicular)^2=(Hypotenuse)^2[/tex]
The right angle is formed between [tex]a[/tex] and [tex]15\ m[/tex] length.
So [tex]17\ m[/tex] is the hypotenuse opposite to right angle is the longest side and called the hypotenuse.
So
[tex](a)^2+(15)^2=17^2[/tex]
[tex]a=\sqrt{17^2-15^2}= 8\ m[/tex]
So the measure of side length [tex]a[/tex] is [tex]8\ m[/tex].
That can be calculated from the option A that is [tex](a)^2+(15)^2=17^2[/tex].
Note:Please don't look to the marked answers that was wrong in the attachment.
Answer:
Yes it is A
Step-by-step explanation:
Which polynomials are in standard form?
Choose all answers that apply:
(Choice A)
5-2x
(Choice B)
x^4-8x^2-16
(Choice C)
5x^3+4x^4-3x+1
(Choice D)
None of the above
Polynomials are in standard form when their terms are written in descending order of exponents. Choice B [tex](x^4 - 8x^2 - 16)[/tex] is in standard form. The correct answer is Choice B.
A polynomial is in standard form when its terms are written in descending order of their exponents. Let's evaluate each of the choices:
(Choice A) 5 - 2x is not in standard form because the term with the x exponent should come first. The correct order should be -2x + 5.(Choice B) [tex]x^4 - 8x^2 - 16[/tex] is in standard form because the terms are in descending order of exponents: 4, 2, and 0.(Choice C) [tex]5x^3 + 4x^4 - 3x + 1[/tex] is not in standard form because the term with the highest exponent [tex](x^4)[/tex] should come first. The correct order should be [tex]4x^4 + 5x^3 - 3x + 1.[/tex](Choice D) This is incorrect because there is at least one polynomial (Choice B) that is in standard form.Therefore, the correct answer is Choice B.
2 to the 3rd power times 5 to the 2nd power
Answer:
2^3 * 5^2
2*2*2 * 5*5
8 * 25 = 200
Step-by-step explanation:
2^3 * 5^2
2*2*2 * 5*5
8 * 25 = 200
What is what is the answer for this 2x+3-x>5
Answer:
[tex]\large\boxed{x>2\to x\in(2,\ \infty)}[/tex]
Step-by-step explanation:
[tex]2x+3-x>5\qquad\text{subtract 3 from both sides}\\\\2x-x>5-3\\\\x>2[/tex]
Using only 32-cent and 20-cent stamps, Charlie put $3.36 postage on a package he sent to his sister,
He used twice as many 32-сent stamps as 20 cent stamps. Determine how many of each type of stamp
he used.
Answer:
Charlie used 4 20-cent stamps and 8 32-cent stamps.
Step-by-step explanation:
Let the number of 20 cents stamps be [tex]x[/tex]. Then, as per question, Chalie used twice as many 32-сent stamps as 20 cent stamps.
Therefore, number of 32-cent stamps is [tex]2x[/tex].
Now, total cost of the stamps is $ 3.36 = 336 cents
Cost of 1 20-cent stamp is 20 cents. So, cost of [tex]x[/tex] 20-cent stamps is [tex]20x[/tex]. Similarly, cost of [tex]2x[/tex] 32-cent stamps is [tex]32(2x)=64x[/tex]
Total cost = [tex]20x+64x=84x[/tex]
As per question,
[tex]84x=336\\x=\frac{336}{84}=4[/tex]
Number of 20-cent stamps = [tex]x = 4[/tex]
Number of 32-cent stamps = [tex]2x=2\times 4=8[/tex]
So, Charlie used 4 20-cent stamps and 8 32-cent stamps.
Answer:
No. of 32 cent stamps = 8
and that of 20 cent stamps = 4
Explanation:
Let no. of 32 cent stamps used be x and the number of 20 cent stamps used be y.
We are given that total postage on a package put by Charlie by using only 32 and 20 cent stamps is equal to $3.36.
So, since 100 cents make one dollar, $3.36 = 336 cents.
So,
32x + 20y = 336
Also we are given that Charlie used twice as many 32 cent stamps as 20 cent stamps which can be written as,
x = 2y
Substituting this equation in previous equation we get
32 [tex]\times[/tex]2y + 20y = 336
=> 64y + 20y = 336
=> 84y = 336
=>y = 4
Putting the value of y in x = 2y we get x = 2*4 = 8
So, no. of 32 cent stamps = 8 and that of 20 cent stamps = 4
The following table list two investment plans, A and B. Given this information, determine which investment is an ordinary annuity
and the future value of the ordinary annuity after one year, given that both investments, A and B, compound interest monthly at
the rate of 3.5%. Round to the nearest cent.
Sept.
oct.
Nov
a.
b.
C.
d.
Jan Feb Mar Apr May Jun Jul Aug Sept.
350 350 350 350 350 350 350 350 350 350 350
350 350 350 350 350 350 350 350 350 350 350
Investment A is an ordinary annuity with $3.918.03 in the account after 1 year
Investment B is an ordinary annuity with $3,918.03 in the account after 1 year
Investment A is an ordinary annuity with $3,906.64 in the account after 1 year
Investment B is an ordinary annuity with $3,906.64 in the account after 1 year
Answer:
its D my man go the answer sheet
Step-by-step explanation:
Answer:
d.
Investment B is an ordinary annuity with $3,906.64 in the account after 1 year
Step-by-step explanation:
Enter the equation of the line in slope-intercept form. Slope is − 1 /2 , and (−3, 4) is on the line. The equation of the line is y =
Answer:
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex], thus
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (- 3, 4) into the partial equation
4 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 4 - [tex]\frac{3}{2}[/tex] = [tex]\frac{5}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex] ← equation of line
Answer:The equation of the line is;
Step-by-step explanation:
How can you describe the graph of the equation y = m
+ b?
Answer:
Step-by-step explanation:
y=mx+b is the formula for slope y-intercept form.
Monica and fill each have part-time jobs Monica makes twice as much money in a week as Phil if the total of their weekly earnings is 825 how much does each person make
Monica makes $550 and Phil makes $275 per week
Step-by-step explanation:
Monica and Phil each have part-time jobs
Monica makes twice as much money in a week as PhilThe total of their weekly earnings is $825We need to find how much each person makes
Assume that Phil makes $x in a week
∵ Phil makes $x per week
∵ Monica makes twice as much money in a week as Phil
∴ Monica makes = $2x per week
∵ The total of their weekly earnings is 825
- Add their weekly earnings
∴ x + 2x = 825
- Add the like terms
∴ 3x = 825
- Divide both sides by 3
∴ x = 275
- Find 2x
∴ 2x = 2(275) = 550
Monica makes $550 and Phil makes $275 per week
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The 300 students at a school voted on four possibilities for an end-of-the-year event. The results are shown in the graph below.How many more students wanted to go to an amusement park than to a baseball game?
Step-by-step explanation:
44-18=26
if 300=100 percent
? =26 percent
26×300=7800
7800÷100=78
the answer is 78 students
Find the prime factorization of 70
Answer:
2*5*7
Step-by-step explanation:
2*5=10
10*7=70
what is the first step when using order of operations
Answer:
If there are parentheses, then you solve what's in those first.
Step-by-step explanation:
Use PEMDAS to help you remember.
P- Parentheses
E- exponents
M- multiplication
D- division
A- addition
S- subtraction
A triangle has a perimeter of 450.
Natalie creates a scale drawing of the triangle with the scale factor 1/15.
What is the perimeter of the scale drawing?
First one to answer will get Brainleist !!!
Answer: The perimeter of the scale drawing is [tex]30[/tex].
Step-by-step explanation:
You need to analize the information provided in the exercise.
You know that the perimeter of rectangle is [tex]450[/tex] and the scale factor Natalie used to create the scale drawing, was:
[tex]scale\ factor=\frac{1}{15}[/tex]
From this you can identify that, in order to find the perimeter of the scale drawing of the triangle (Which can be represented with [tex]P_2[/tex]), you must multiply the original perimeter ((Which can be represented with [tex]P_1[/tex]), by the scale factor Natalie used.
Therefore, you get that the perimeter is:
[tex]P_{2}=\frac{1}{15}P_1\\\\P_2(\frac{1}{15})(450)\\\\P_2=30[/tex]
The seventh grade class supplied bags of snacks and beverages for the school dance They supplied19 more beverages than bags of snacks The dance was supplied with a total of 371 items.
Answer:
The number of number of bags of snacks = m = 176
The number of beverages supplied = m + 19 = 176 +9 = 185
Step-by-step explanation:
Let us assume the number of bags of snacks = m
So, the number of beverages supplied = m + 19
Total number of items supplied = 371
⇒ Number of (snacks + beverages) supplied= 371
⇒ m + (m +19) = 371
or, 2 m = 371 - 19 = 352
or, m = 352 / 2 = 176
⇒ m = 176
Hence the number of number of bags of snacks = m = 176
So, the number of beverages supplied = m + 19 = 176 +9 = 185
What is the unit price if a package of 12 candy canes cost $4?
Answer:
$1 for every 3 candy canes
The drawing will help
40 point question ....... pls urgent
the minute hand in a clock is 17cm long. find the area swept by it in 12 mins. the clock is a circle. no spamssssssssss pls
The area swept by the minute hand in 12 minutes is 181.58 cm²
Step-by-step explanation:
In the circle clock
The circumference of the circle is divided into 12 equal arcsThe central angle of each arc is 30°, because the measure of the circle is 360° and divided by 12 The central angle between each two consecutive hours is 30°There are 5 minutes between each two consecutive hours, then the central angle between each two consecutive minutes is 6° because 30° ÷ 5 = 6°When the minute hand is moved than the radius of the circle is the length of the minute handWhen the hour hand is moved than the radius of the circle is the length of the hour hand∵ The minute hand is swept by 12 minutes
∵ The central angle between each two consecutive minutes = 6°
∴ The central angle when the minute hand swept 12 minutes =
6 × 12 = 72°
∵ The area of a sector of a circle = [tex]\frac{x}{360}*\pi r^{2}[/tex] ,
where r is the radius of the circle and x is the central angle of
the sector
∵ The radius of the circle is the length of the minute hand
∵ The minute hand in a clock is 17 cm long
∴ r = 17 cm
∵ The measure of the central angle is 72°
∴ x = 72°
- Substitute these values in the rule of the area of a sector
∵ Area = [tex]\frac{72}{360}*\pi (17)^{2}[/tex]
∴ Area = 181.58 cm²
The area swept by the minute hand in 12 minutes is 181.58 cm²
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1. Write the next two terms in the pattern.
11, 18, 25, 32.
A.42. 49
B.39, 46
C.38, 45
D.40, 48
2. Find the missing term.
180. 30.5
A.1080
B.900
C.330
D.210
Answer:
1. B
2. A
Step-by-step explanation:
1. The terms seem to be increasing by a constant of 7.
11+7=18
18+7=25
25+7=32
Therefore, the next two terms should be 32+7 and 32+7+7. This equals 39 and 46.
2. The terms in this pattern are being divided by 6
180/6=30
30/6=5
In order to find the missing number before 180, we need to multiply 180 by 6. 180 times 6 is equal to 1080.
hi ur answer would be 39,46
Step-by-step explanation: here's my explanation as u can see it 11 into 18 is adding 7 and for all of them the pattern is plus 7 so u do 32+7=39 and then u do 39+7=46 and thats how u get B.39,46
what is x minus 5 equals negative 13
x-5=-13
move -5 to the other side
sign changes from -5 to+5
x-5+5=-13+5
x=-13+5
answer:
x=-8
A price was first decreased by 12%, then it was decreased again by an additional 5%. What is the percent of the total decrease?
Answer:
17% ?
Step-by-step explanation:
that seems like the most logical answer
Answer:
16.4
Step-by-step explanation:
this is right
“A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin V, which is 250 % of the daily recommend allowance of vitamin C for adults. What is 100% of the daily reccomended allowance of vitamin C for adults?”
Answer:
80 milligrams
Step-by-step explanation:
Write a proportion and solve.
200mg / 250% = x / 100%
x = 80mg
Answer fast!!!!
Match the careers with the career clusters
Answer:education and training- speech Language pathologist And curriculum developer
Government and public administration- tax auditor and federal aid coordinator
Law, public safety corrections and security- attorney and paralegal
Step-by-step explanation:
The career clusters and some example careers within each cluster are Agriculture, Food, and Natural Resources (e.g. agricultural engineer, food scientist, forester), Business, Management, and Administration (e.g. accountant, human resources specialist, operations manager), and Health Science (e.g. medical doctor, nurse, medical laboratory technologist).
Explanation:The career clusters and some example careers that fall under each cluster are as follows:
1. Agriculture, Food, and Natural ResourcesAgricultural engineerFood scientistForester2. Business, Management, and AdministrationAccountantHuman resources specialistOperations manager3. Health ScienceMedical doctorNurseMedical laboratory technologistThese are just a few examples, and there are many other careers within each career cluster.
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A fraction with a zero in the numerator equals
Answer: With any number if the 0 is at the Numerator it will always be 0
Step-by-step explanation:
If a 0 is at the Denominator it will be Undifined
Which is the largest number? 8.2, 7.98, 8 9/10, 7 8/9
Answer:
8 9/10 is the largest number
Answer:
8 9/10
Step-by-step explanation:
8 is first off larger than 7 so that rules out all the 7 numbers
And 9/10 is .9 so that would make it 8.9 which is greater than 8.2
Factor completely.
X^4-10x^2+24
Answer:
(x^2-6)(x+2)(x-2)
Step-by-step explanation:
x^4-10x^2+24
(x^2-6)(x+2)(x-2)
Use the scale drawing below to determine how wide the duck pond is.
A.
9 feet
B.
18 feet
C.
27 feet
D.
36 feet
Answer:
C 28ft on edg 2021
Robert has 20 blueberries. He has 10 more blueberries than Janessa. He has 14 fewer blueberries than Amari. How many blueberries does Janessa have? How many blueberries does Amari have?
Answer: Janessa has 10 Amari has 34
The number of blue berries with Janessa and Amari are 10 and 34 respectively.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Robert who has 20 blueberries such that he has 10 more blueberries than Janessa and 14 fewer blueberries than Amari.
Assume that the number of blue berries with Janessa and Amari are x and y respectively. We can write the following modelled equations as -
20 = x + 10
20 = y - 14
Solving, we get -
x = 10
y = 34
Therefore, the number of blue berries with Janessa and Amari are 10 and 34 respectively.
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An expression can be written in rational form by
writing it as a fraction with a denominator of
Answer:
denominator of 1
Step-by-step explanation:
An expression can be written in rational number by writing 1 in the denominator then it will become a fraction and a rational number
Answer:
A rational numbers can be defined as numbers that can be expressed as the quotient between two integers.
This means that a whole number can be expressed as a rational number by just adding 1 into its denominator
[tex]2 \implies \frac{2}{1}[/tex]
That way the whole number would be a rational number, becase 2 and 1 are integers.
Therefore, an expression can be written in rational form by writing it as a fraction with a denominator of 1.