Answer:
the following 3 equations are equivalent :
• x + 1 = 4
• 2 + x = 5
• -5 + x = -2
Step-by-step explanation:
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
-5 + x = - 2
Let’s take this equation :
x + 1 = 4
=======
By Adding 1 to both sides of the equation we get :
x + 1 + 1 = 4 + 1
⇔ x + 2 = 5
⇔ 2 + x = 5
Then the equations x + 1 = 4 and 2 + x = 5 are equivalent.
…………………………………………………………………
On the other hand ,if we subtract 6 from both sides
of the equation x + 1 = 4 we get :
x + 1 - 6 = 4 - 6
⇔ x - 5 = -2
⇔ -5 + x = -2
Then the equations x + 1 = 4 and -5 + x = -2 are equivalent.
Answer:
A. 2 + x = 5
B. x + 1 = 4
E. -5 + x = -2
Step-by-step explanation:
right on edg, hope it helps ya'll.
Right triangle J K L is shown. Line L J has a positive slope. A dotted and horizontal line is drawn to point J to form an angle of 53 degrees.
What is the measure of the angle of elevation from point L to point J?
37°
45°
53°
137°
Considering the sum of the internal angles of the triangle, the angle of elevation from point L to point J is of 37º.
What is the sum of the internal angles of a triangle?The sum of the internal angles of a triangle is of 180º.
In this problem, the angles are:
90º, 53º, x
Hence:
90 + 53 + x = 180
x = 180 - 143
x = 37º
The angle of elevation from point L to point J is of 37º.
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Answer:
53*
Step-by-step explanation:
took on edge
i have no idea whats going on. PLEASE HELPPP
Answer:
36 meters
Step-by-step explanation:
You are given an angle and the length of the side adjacent. You want to find the length of the side opposite, so the relevant trig relation is ...
Tan = Opposite/Adjacent
SetupThe height of Yuri's balcony is the sum of the heights of Kim's balcony and the height of Yuri's balcony above that. Each of those height is the side opposite a given angle in a right triangle. These can be found by solving the tangent relation for the opposite side:
Tan = Opposite/Adjacent
(Adjacent)(Tan) = Opposite
height of Kim's balcony = (30 m)tan(40°)
height above Kim's balcony = (30 m)tan(20°)
__
height of Yuri's balcony = height of Kim's + height above Kim's
height of Yuri's balcony = (30 m)tan(40°) +(30 m)tan(20°)
height of Yuri's balcony = (30 m)(tan(40°) +tan(20°))
Evaluationheight of Yuri's balcony ≈ (30 m)(0.8391 +0.3640) ≈ 36.092 m
The height of Yuri's balcony is about 36 meters.
= {y: y is a multiple of 3, 5 < y < 10}
Answer:
Step-by-step explanation:
6 and 9
If f(x) = x-2, what is f¹(x)?
f¹(x) = 9x + 18
ƒ²¹(x) = x + 2
f¹(x) = 9x+2
ƒ¹ (x) = -2x +
Interchange x and y
[tex]\\ \tt\leadsto x=\dfrac{1}{9}y-2[/tex]
Solve for y[tex]\\ \tt\leadsto \dfrac{1}{9}y=x+2[/tex]
[tex]\\ \tt\leadsto y=9(x+2)[/tex]
[tex]\\ \tt\leadsto y=9x+18[/tex]
That's the inverse[tex]\\ \tt\leadsto f^{-1}(x)=9x+18[/tex]
Answer:
[tex]f^{-1}(x)=9x+18[/tex]
Step-by-step explanation:
[tex]f^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is its reflection in the line y = x.
Given function:
[tex]f(x)=\dfrac{1}{9}x-2[/tex]
To find the inverse of the given function:
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=\dfrac{1}{9}x-2[/tex]
Rearrange the equation to make x the subject:
[tex]\implies y+2=\dfrac{1}{9}x[/tex]
[tex]\implies 9(y+2)=x[/tex]
[tex]\implies x=9y+18[/tex]
Replace x with [tex]f^{-1}(x)[/tex] and y with x:
[tex]\implies f^{-1}(x)=9x+18[/tex]
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The manager of a food store noted that for every 20 persons who visit the store, they sell 6 burgers at $2.35 each, 8 aerated drinks at $1.60 each, and 4 pack of fries at $ 2.00 each. To the nearest cent, what is the average (arithmetic mean) amount of sales per person who comes in?
Two poles of different heights are used for a climbing event and need to be secured to the ground using wires. The shorter pole is 6.0 m tall and the wire is secured 8.0 m from the base of the pole. If wire of the taller pole is 16.0 m long. Determine the height of the taller pole
Answer:
12.8 m.
Step-by-step explanation:
The length of the wire on the shorter pole (AC)
= √(6^2+8^2)
= √100
= 10 m.
The 2 triangles are similar so
10/16 = 8/x where x is height of taller pole.
10x = 128
x = 12.8m
10 points + BRAINEST
[tex]\textbf{Heya !}[/tex]
basic math tips -»
"of" means multiply
[tex]\sf{\cfrac{1}{10}\cdot\cfrac{5}{1}}[/tex]
multiply the numerators and denominators times each other -»
[tex]\sf{\cfrac{5}{10}}[/tex]
reduce:-
[tex]\sf{\cfrac{1}{2}}[/tex]
`hope it was helpful to u ~
Find the measure of the indicated angle to the nearest degree 35 and 28
The missing indicated angle of the given right angle triangle is; 39°
How to use trigonometric ratios?We can see in the attached image showing the missing figure that it is a right angle triangle and as such we can find the missing angle via trigonometric ratios. In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles
The trigonometric ratios we can use are as follows;
sin x = opposite/adjacent = opp/hyp
cos x = adjacent/hypotenuse = adj/hyp
tan x = opposite/adjacent = opp/adj
Now, we see that the missing angle lies on the side with a length of 28. Thus, adjacent side = 28 and opposite side of it = 23. Thus;
tan x = opposite/adjacent = 23/28
x = tan⁻¹(23/28)
x = tan⁻¹(0.8214)
x = 39.4° ≈ 39°
Thus, we can conclude that the measure of the indicated angle to the nearest degree 35 and 28 is calculated as 39°.
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A construction company is repaving a damaged road. So far, they have repaved a total of 55,721 centimeters of the road. Today, they repaved 34,066 centimeters of the road. How many centimeters of the road had they repaved before today?
Answer:
21655
Step-by-step explanation:
minus the values
A school system is reducing the amount of dumpster loads of trash removed each week. in week 5, there were 60 dumpster loads of waste removed. in week 10, there were 40 dumpster loads removed. assume that the reduction in the amount of waste each week is linear. write an equation in function form to show the amount of trash removed each week. f(x) = −4x 60 f(x) = 4x 60 f(x) = −4x 80 f(x) = 4x 80
The equation in function form is f(x)=-4x+80.
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
We can find the equation in function form as shown below:
We have given two points (5,60) and (10,40)
Slope of line
m = (40-60)/ (10-5)
m=-20/5
m=-4
Equation in slope intercept form
(y-y1) =m(x-x1)
(y-60) =-4(x-5)
y-60=-4x+20
y=-4x+20+60
y=-4x+80
y=f(x)
f(x)=-4x+80
Hence, the equation in function form is f(x)=-4x+80.
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From a functionalist view point, the U.S. economic system would be seriously strained if we completely eliminated poverty level wages.
It is true that the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."
What is poverty level wages?The poverty level wages stipulates the lowest or minimum possible wages that a person can be paid in a functional economy. The maintenance of the poverty level wages helps the economy to remain functional and afloat.
Thus, it is a true statement that; From a functionalist view point, the U.S. economic system would be seriously strained if we completely eliminated poverty level wages."
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What is the relation between the variables in the equation
a. varies inversely as y
b.xvaries directly as y
Please select the best answer from the choices provided
O
O
A
B
C
O
y
-7?
c. y varies directly as x¹
d. y varies inversely as ¹
The relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y
How to determine the relation between the variables in the equation?The complete question is added as an attachment
From the attached figure, we have the following equation
x^4/y = 7
Multiply both sides of the equation by y
x^4 = 7y
The above represents a direct variation from x^4 to y.
Where 7 represents the variation constant
Hence, the relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y
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What ia an equation of the line that is parallel to y=3x-8 and passes through the point (4,-5)?
Answer:
y = 3x - 17
========================
Given liney = 3x - 8Parallel lines have equal slopes, so its equation is in the form of:
y = 3x + bSince it passes through the points (4 , - 5), find the value of the y-intercept b by substituting x- and y- coordinates into this equation:
- 5 = 3*4 + b- 5 = 12 + bb = -5 - 12b = - 17The equation of the parallel line is:
y = 3x - 17A DVD player costs $96.34, with sales tax included. What is the original price of the DVD player if the sales tax rate is 8.25%?
The original price of the DVD player if the sales tax rate is 8.25% is $88.79
Sales taxCost of DVD player including tax = $96.34Sales tax = 8.25%Original cost = 8.25%Total cost = original cost + (sales tax × original cost
96.34 = x + (8.5% × x)
96.34 = x + (0.085 × x)
96.34 = x + 0.085x
96.34 = 1.085x
x = 96.34 / 1.085
x = 88.7926267281105
Approximately,
x = $88.79
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You decide to buy a laptop for $750. You make a down payment of $150 and the company will allow you to pay off the remainder in 12 payments over the next year at 13.5% interest with a finance charge of $25. Make a table of all payments over the next year including the initial down payment and finance charge. Show the difference between paying in cash for the laptop and this financial arrangement. Show all equations and calculations you used. Explain the benefits and downsides of financing your laptop and describe when you would advise someone to finance this kind of purchase. Upload your payment table and answers below.
Total amount paid over the next year including the initial down payment and finance charge = $856
The difference between paying in cash for the laptop and this financial arrangement = $106
Cost of laptop=$750
Down payment=$150
Finance charges = $25
Remaining amount =$600
Amount for 1 month including 13.5 % interest=600/12*13.5/100+600/12
=$56.75
Total amount paid over the next year including the initial down payment and finance charge = 56.75*12+150+25 = $ 856
The difference between paying in cash for the laptop and this financial arrangement = $106
Benefits of financing laptop:
A costly laptop can be yours without having to pay in full.
Bank loans and conventional credit card services are not required.
Numerous retailers provide rewards, flexible payment plans, zero-interest rates, and other benefits.
Downsides of financing laptop:
It's dangerous to borrow money because late payments might result in fees and excessive interest rates.
A credit score may suffer if there is no interest charged.
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4 2/7 - 2 1/3 =
4,5 - 2 5/8 =
5 2/8 - 15% =
Thanks for answer!
The simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.
What are the simplified form of the expression?1) 4 2/7 - 2 1/3
First we convert the mixed fraction 4 2/7 and 2 1/3 into an improper fraction.
4 2/7 = (7×4 + 2 )/7 = 30/7
2 1/3 = (3×2 + 1 )/3 = 7/3
Hence,
30/7 - 7/3
( 30×3 - 7×7 )/21
( 90 - 49 )/21
41/21
2) 4.5 - 2 5/8
First we convert both 4.5 and 2 5/8 into an improper fraction.
4.5 = 4 5/10 = (4×10 + 5)/10 = 45/10 = 9/2
2 5/8 = (2×8 + 5 )/8 = 21/8
Hence,
9/2 - 21/8
(9×8 - 21×2 )/16
(72 - 42 )/16
30/16
15/8
3) 5 2/8 - 15%
First we convert both 5 2/8 and 15% into an improper and proper fraction respectively.
5 2/8 = (5×8 + 2)/8 = 42/8 = 21/4
15% = 15/100 = 3/20
Hence
21/4 - 3/20
(21×20 - 3×4 )/80
(420 - 12 )/80
408/80
51/10
Therefore, the simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.
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PLEASE HELP 50 POINTS
I think for the first part 505 m and 53.1 degrees (Like they wrote, you need to repeat it) and same goes for the drcond part. In the last part, I think you need to add the directions. HOPE IT HELPS
*TIP: you can delete the answer the second person gave you to be able to recive more answers :)
Find the length of BC¯¯¯¯¯¯¯¯
Answer:
B
Step-by-step explanation:
I love trig lol,
Assuming you know trig, Cos(17)=BC/42
Cos(17)*42=BC
Cos(17)~0.956
0.956*42=40.152=BC
Since this is a approximation, B is the closest to our estimate.
Which equation is the inverse of 5y+4= (x+3)² +?
1
6 11
10
O y = x² +/
1/2 X+
7
Oy=3± √√5x+2
O-5y-4 = -(x+3)²--1/2
7
O y=-3± √√5x+2
Answer:
-5y-4=-(x+3)2-1/(2)
Step-by-step explanation:
ANSWER: It's D
Have a great day!!!
Please if anyone no math I really need help
Answer:
c
Step-by-step explanation:
option a (x-4) translates the graph 4 units right, not down
option b (x)-4 translates the graph 4 units down, not left
option c (x)+4 translates the graph 4 units up, so it is correct
option d (x+4) translates the graph 4 units left, not right
if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down
if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left
Can someone help me with these problems please!!
a.
i. In standard form y = 5x² - 20x + 27ii. The y intercept is (0, 27)iii. Find the graph in the attachmentb.
i. In standard form is y = 3x² + 6x + 15ii. The y-intercept is (0, 15)iii. Find the graph in the attachmentWhat is a quadratic function?A quadratic function is a function of the form y = ax² + bx + c
a. i. How to write the quadratic function y = 5(x - 2)² + 7 in standard form?To write y = 5(x - 2)² + 7, we expand the bracket and simplify.
So, y = 5(x - 2)² + 7
y = 5(x² - 4x + 4) + 7
y = 5x² - 20x + 20 + 7
y = 5x² - 20x + 27
So, the quadratic function y = 5(x - 2)² + 7 in standard form is y = 5x² - 20x + 27
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 5x² - 20x + 27
y(0) = 5(0)² - 20(0) + 27
y(0) = 0 - 0 + 27
y(0) = 27
The y intercept is (0, 27)
iii. The graph of y = 5(x - 2)² + 7Find the graph in the attachment
b. i. How to write the quadratic function y = 3(x + 1)² + 12 in standard form?To write y = 3(x + 1)² + 12, we expand the bracket and simplify.
So, y = 3(x + 1)² + 12
y = 3(x² + 2x + 1) + 12
y = 3x² + 6x + 3 + 12
y = 3x² + 6x + 15
So, the quadratic function y = 3(x + 1)² + 12 in standard form is y = 3x² + 6x + 15
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 3x² + 6x + 15
y(0) = 3(0)² - 6(0) + 15
y(0) = 0 - 0 + 15
y(0) = 15
The y-intercept is (0, 15)
iii. The graph of y = 3(x + 1)² + 12Find the graph in the attachment
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Solve the equation below by factorising.
2x^2- 10x= 0
Answer:
x = 0 , x = 5
Step-by-step explanation:
2x² - 10x = 0 ← factor out 2x from each term on the left side
2x(x - 5) = 0
equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x - 5 = 0 ⇒ x = 5
what is the solution to the system of equation -4+3y=-3
Answer:
[tex]\huge\boxed{\sf y = 1/3}[/tex]
Step-by-step explanation:
Given equation:-4 + 3y = -3
Add 4 to both sides
3y = -3 + 4
3y = 1
Divide 3 to both sides
y = 1/3[tex]\rule[225]{225}{2}[/tex]
Find the equivalent expression of 20a + 28b.
Answer:
4 (5a + 7b)
Don't worry I helped my brother with this.
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
The surface area of the composite figure is equal to 233.6 square centimeters.
How to determine the surface area of a solid
The surface area is the area of all faces of a solid. Since the surface area of the figure is a combination of triangles and quadrilaterals, we must sum all the areas to determine the surface area of the figure. Now we proceed to determine this:
A = 4 · (1/2) · (3 cm) · (2 cm) + 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (2 cm) + 2 · (8 cm) · (3.6 cm)
A = 233.6 cm²
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How long must a ladder be to reach the top of a 12-foot wall if the bottom of the ladder is placed 3 feet from the base of the wall
Answer: 13 feet
Step-by-step explanation:
Answer:
12.37 ft
Step-by-step explanation:
Hypotenuse(c): the ladder
Cathetus: the wall (a=12) and the floor (b=3)
Equation:
[tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]c^{2} =(12)^{2}+ (3)^{2} =144+9[/tex]
[tex]c^{2} =153[/tex]
[tex]c=\sqrt{153}[/tex]
[tex]c=12.37[/tex]
The ladder is 12.37 feet long
Hope this helps
How many different ways are there to choose a dozen donuts from the 4 varities at a donut shop so that you get atleast one donut of every variety g
There are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop. (at least one donut of every variety must be selected)
How to calculate the number of ways to select items?There are 'r' items from 'n' different varieties (repetition allowed). Then, the number of ways to select items is given by
The number of ways = [tex]_{n+r-1}C_r[/tex]
Where the combination [tex]_{n}C_r[/tex] is calculated as
[tex]_{n}C_r=\frac{n!}{r!(n-r)!}[/tex]
Calculation:It is given that there are 4 varieties of donuts in a shop. I.e., n = 4
Number of donuts to be selected r = 12 (one dozen)
And also given that at least one donut of every variety has to be selected.
Since there are 4 varieties, at least one from each of these means the count is 4.
So, the remaining number of donuts to be selected is 12 - 4 = 8.
So, r becomes 8 i.e., r = 8
On substituting,
the number of ways of selecting the remaining 8 donuts = [tex]_{4+8-1}C_4[/tex]
⇒ [tex]_{11}C_4[/tex]
⇒ [tex]\frac{11!}{4!(11-4)!}[/tex]
⇒ [tex]\frac{11!}{(4!)(7!)}[/tex]
⇒ 330
Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.
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Alek is taking an inventory of styles of compression bandages for work. Here is the data he has collected.
The individuals in this data set that can be gotten is B) Compression bandage styles and this data set contains A) 3 variables, 1 of which is categorical.
What is categorical variable ?A categorical variables serve as the variable type that posses two or more categories.
This categories could be nominal variable, however considering the data , we can see that the first two are quantitative data and the data are:
WidthTotal lengthColorTHE COMPLETE QUESTION IS:
Alek is taking an inventory of styles of compression bandages for work. Here is the data he has collected.
The individuals in this data set are:Choose 1 answer:
A) Blood Centers
B) Compression bandage styles
C) Nurses
This data set contains:Choose 1 Answer:
A) 3 variables, 1 of which is categorical
B) 3 variables, 3 of which are categorical
C) 6 variables, 1 of which categorical
D) 6 variables, 3 of which are categorical
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A math club is researching a golf tournament fund-raiser. it will cost $1,000 to host the tournament. if it rains, the club will lose the investment. if it is sunny, it is expected that the club will collect $4,500 from the participants. if the chance of rain is 20%, what is the expected value for the tournament?
The expected value of tournament is $2600.
According to the statement
we have given that the tournament will cost $1000 and if it is sunny, it is expected that the club will collect $4,500 from the participants. And we have to find the expected value of a tournament.
So, we know that the
Cost of hosting the tournament : $1,000
If it rains, the club will lose the investment: $ -1,000
If it is sunny, the club will collect $4,500 ;
From all this the profit they will get
profit: 4,500 - 1000 = 3,500
And
There is a chance of 20% then
The club will loss the investment is
-1000*20 = -200
And
Effect on their profit if there is a rain then
3500*80 = 2800
then
The expected value of tournament is 2800-200=2600.
So,The expected value of tournament is $2600.
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Answer:
C
Step-by-step explanation:
on edge
A population has a mean of μ= 35 and a standard deviation of σ = 5. after 3 points are added to every score in the population, what are the new values for the mean and standard deviation?
The new values for the mean and the standard deviation are 38 and 5 respectively.
The mean of a population is given as [tex]\mu = \frac{\sum_{N}^{i}x_i}{N}[/tex] and its standard deviation is given as [tex]\sigma = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}}[/tex].
In the question, we are given that a population has a mean of μ = 35 and a standard deviation of σ = 5, and are asked for the new values for the mean and standard deviation when 3 points are added to every score in the population.
We let the new population formed be over the variable k.
Thus, [tex]k_i = x_i + 3[/tex], for all i from 1 to N.
Thus, the new mean can be calculated as:
[tex]\mu_k = \frac{\sum_{N}^{i}k_i}{N}\\\mu_k = \frac{\sum_{N}^{i}(x_i + 3)}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i + 3N}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i}{N} + 3\\\mu_k = \mu + 3\\\mu_k = 35 + 3 = 38 [Since, \mu = 35].[/tex]
Thus, the new mean is 38.
Thus, the new standard deviation can be calculated as:
[tex]\sigma_k = \sqrt{\frac{\sum_{N}^{i}(k_i-\mu_k)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i + 3-38)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-35)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}} [Since, \mu = 35]\\\sigma_k = \sigma = 5.[/tex]
Thus, the new standard deviation is 5.
Thus, the new values for the mean and the standard deviation are 38 and 5 respectively.
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