The total number of cars both the student and the teacher made is 49
let
total cars = x
cars made by student = s
cars made by teacher = t
Total = student + teacher
x = s + t
s = 2/7x
So,
x = 2/7x + t
x - 2/7x = t
t = (7x - 2x) / 7
t = 5/7x
Similarly,
s = t - 21
s = 5/7x - 21
equate both s equation
2/7x = 5/7x - 21
2/7x - 5/7x = -21
(2x - 5x) / 7 = -21
- 3/7x = -21
x = -21 ÷ -3/7
= -21 × - 7/3
= (-21 × -7) / 3
= 147/3
x = 49
Therefore, the total number of cars both the student and the teacher made is 49
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Which functions are invertible? Select each correct answer. A coordinate graph with both horizontal and vertical axes ranging from negative 10 to 10 in increments of 2. A line is graphed with one end is in the first quadrant and the other end is in the third quadrant. The line passes through the x axis between 0 and negative 2 and it passes the y axis between 0 and 2. A coordinate graph with both x and y axes are ranging from negative 10 to 10 in increments of 2. A parabola is drawn facing down whose vertex is in the first quadrant and the parabola crosses the x axis at begin ordered pair 0 comma 0 end ordered pair and begin ordered pair 2 comma 0 end ordered pair. Parabola has arrows on both ends. An absolute value function graphed on a coordinate plane. The x and y axes range from negative 10 to 10 in increments of 2. The vertex is at begin ordered pair 0 comma negative 2 end ordered pair. The graph opens up and passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 2 comma 0 end ordered pair. Graph has arrows on both ends. Graph of a square root function on a coordinate plane. Both axes range from negative 10 to 10 in increments of 2. The curve begins at begin ordered pair 0 comma 0 end ordered pair. It increases from left to right and passes through begin ordered pair 4 comma 2 end ordered pair. Curve has an arrow on one end.
Using function concepts, it is found that:
Graph 1 (Left-top) is invertible.Graph 4(Bottom-right) is invertible.A function f(x) has an inverse if, and only if:
[tex]f(a) = f(b) \leftrightarrow a = b[/tex]
That is, each value of the output y is associated with only one value of the input x.In this problem:
In graphs 1(left-top) and 4(bottom-right), these conditions are respected, hence, they are invertible. In the parabola of graph 2(top-right), for example, y = 0 is associated with both x = 0 and x = 2, so it is not invertible.In the absolute value function is graph 3(bottom-left), for example, y = 0 is associated with both x = -2 and x = 2, so it is also not invertible.To learn more about the use of graphs to verify if a function is invertible, you can take a look at https://brainly.com/question/13160937
A plane travels 2047.5 miles in 3.5 hours. Find the plane's speed in miles per hour.
585m/hr
Step-by-step explanation:To find the plane's speed for 1 hour, we will need to divide 2,047.5 by 3.5:
2,047.5 / 3.5 = 585.
585 miles represents the speed of the plane for 1 hour.
Kameron wrote the following equation:
4x - (x - 3) = 18
Using the distributive property, what would her next step be?
Answer:
hope it helps you..........
Rico's dog weighs 64 pounds.
The dog is 3 times as heavy as he was when he was 6 months old.
Write an equation that can be used to find the dog's weight, w, when he was 6
months old.
The equation that can be used to represent the weight of the dog when he was 6 months old is 64/x.
What is the equation that can be used to represent the weight of the dog when he was 6 months old?The equation that can be used to represent the dog's current weight is: 64 = 3x
Where x represents the weight of the dog when he was 6 months old
In order to determine the value of x, divide both sides of the equation by 3
x = 64/x
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Answer:
the answer is below
Step-by-step explanation:
need helpppppp plz .
Answer:
A) x=10
Step-by-step explanation:
All the angles in a triangle will add to equal 180°.
Knowing this, we can set up an equation.
(8x+5) + (5x-1) + (4x+6)= 180°
In order to solve, we must first combine like terms. (These can be found on the left side of the equation).
8x+5x+4x= 17x
5+ (-1) + 6= 10
We can now rewrite our equation as follows:
17x+10=180°
Subtract 10 from both sides.
17x+10=180°
- 10 -10
17x=170°
Divide by 17 on both sides.
17x=170°
---- -----
17 17
x= 10°
The answer is x=10°.
The graphs of 4x+12y=8 and y=mx+5 are perpendicular. What is the value of m?
Answer:
m = 3
Step-by-step explanation:
Slope of first one is -1/3
Perpendicular therefore m = -(-1/3)^(-1) = 3
m = 3
Answer:
Given the equation line 4x+12y=8
Step-by-step explanation:
The equation is y=mx+5y=mx+5
The line passes through A(3,14)A(3,14)
Putting (x,y)=(3,14)(x,y)=(3,14), we have…
14=3m+514=3m+5
⟹3m=9⟹3m=9
⟹m=3
46. A sphere shaped bowl has a radius of 5.5 inches How much water can the bowl hold? Round to the nearest tenth.
Answer:
try 17.89 cm..then 18 for answer
please help me!!!!!!! due soon
Answer:
A
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
(4x + 11) is an exterior angle of the triangle , then
4x + 11 = 3x - 24 + 2x
4x + 11 = 5x - 24 ( subtract 5x from both sides )
- x + 11 = - 24 ( subtract 11 from both sides )
- x = - 35 ( multiply both sides by - 1 )
x = 35 → A
HELP ME PLEASEEE!!
48 degrees 96 degrees x =
Answer:
144°
96+48(further away angles)
Answer:
x = 144°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle , then
x = 48° + 96° = 144°
Question in the picture
Answer:
√85
Step-by-step explanation:
last month nick spent $50 this month he spent 60% of last month how much did nick spend
Answer:
Nick spent $30.00.
Step-by-step explanation:
60% of $50.00
60% ÷ 100 = 0.6
0.6 x 50 = 30
Answer:
30$Step-by-step explanation:
last month nick spent $50 this month he spent 60% of last month how much did nick spend?
50 : 100 * 60 =
0.5 * 60 = 30$
Noah borrowed $0.80 from his friend John five days last week to buy chips. how much does Noah owe John?
Answer:
$0.80
Step-by-step explanation:
Answer:
So Noah owes John $4.00
Step-by-step explanation:
Since Noah borrowed 80 cents from John for 5 days, you'd simply multiply 0.80 (remember to include the decimal) by 5, and you'd get 4.
Hope this helps you :)
Transversal cuts parallel lines and as shown in the diagram, and m∠4 = 55.1°. What are m∠5 and m∠7? A. m∠5 = 34.9°, and m∠7 = 145.1°. B. m∠5 = 55.1°, and m∠7 = 34.9°. C. m∠5 = 124.9°, and m∠7 = 55.1°. D. m∠5 = 55.1°, and m∠7 = 124.9°. E. m∠5 = 34.9°, and m∠7 = 55.1°.
Answer:
m < 5 = 55.1 i think im not forsure
Step-by-step explanation:
Whenever the Transversal EF intersects parallel line AB and CD, the values of m∠5 and m∠7 are 55.1° and 124.9°, respectively.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the information provided in the question,
Since the transverse line, EF, intersects the line segment AB and CD, it creates equivalent, alternate, and other angles.
As a result, the m∠5 and m∠7 are as follows:
First, supplementary angles ∠5 and ∠7 are present. Since they add up to 180 degrees, they are equal.
Since alternate angles are equivalent, ∠5 is an alternative angle to ∠4. Therefore,
m∠5 ≅ m∠4
m∠5 = 55.1°
So,
m∠5 + m∠7 = 180°
55.1 + ∠7 = 180
∠7 = 180 - 55.1
m∠7 = 124.9°
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352 is 32% of what number?
Answer:
1100
Step-by-step explanation:
Find x, y, and z. Drag and drop the numbers into the boxes to show the value of each variable.
Answer:
x=186.68
y=140
z=233.34
Step-by-step explanation:
easy method to solve since you have the answers to pick from
first triangle. we have two sides 175 and 105 and we know that 175 have to be the largest number, its the hypotenuse. which means
y=140,
cannot be 233 or 186 because both greater than 175
now next triangle. x-y-z, we already know "y" and "z" needs to be the largest number so it has to be
z= 233.34 and finally
x=186. 67
W
Enter the value of x-21.
(x - 21)
71
I don't understand raitos please help solve math problems
Brainliest
Please do one of the above
(I would appreciate if you did more then one)
Answer:
5. 7.5m
6. 3, 925m
7. 383.9m
8 42.99m
Answer:
Step-by-step explanation:
how to solve the following system y=(1/2)x^2+2x-1 and 3x-y=1
Answer:
(0,-1),(2,5)
Step-by-step explanation:
3x-y=1
0.5[tex]x^{2}[/tex]+2x-1=y
Substitute the equation of y into the other equation
3x-(0.5[tex]x^{2}[/tex]+2x-1)=1
3x-0.5[tex]x^{2}[/tex]-2x+1=1
collect like terms
-0.5[tex]x^{2}[/tex]+x=0
Solve for x
x(-0.5x+1)=0
0=-0.5x+1
-1=-0.5x
x=2 x=0
Back substitute into the other original equation and solve for y
3(2)-y=1
6-y=1
y=5
(2,5)
3(0)-y=1
-1(-y)=-1(1)
y=-1
(0,-1)
Tony Peyton, age 20, would like to have $1,000,000 by the time he is 65 years of age. If Tony could earn 6.9% annual interest compounded monthly, how much must he invest now to have $1,000,000 by the time he is 65?
Using compound interest, it is found that he must invest $45,225 now.
Compound interest:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem:
He wants to have $1,000,000 in 65 - 20 = 45 years, hence [tex]t = 45, A(t) = 1000000[/tex].6.9% annual interest, hence [tex]r = 0.069[/tex].Compounded monthly, hence [tex]n = 12[/tex].Then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]1000000 = P\left(1 + \frac{0.069}{12}\right)^{12(45)}[/tex]
[tex]P = \frac{1000000}{(1.00575)^{540}}[/tex]
[tex]P = 45225[/tex]
He must invest $45,225 now.
To learn more about compound interest, you can take a look at https://brainly.com/question/25781328
Answer:
He must invest $45,225
y=1.5x+8 which represents the equation when solved for x?
[tex]y=1.5x+8\\\\\implies 1.5x = y-8\\\\\implies x = \dfrac{y-8}{1.5}\\\\\implies x = \dfrac{y-8}{\tfrac 32}}\\\\\implies x = \dfrac{2(y-8)}{3}\\\\\implies x = \dfrac 23 y- \dfrac{16}3[/tex]
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of OC at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. Find Q3, the third quartile.
A) 0.53
B) 0.67
C) -1.3
D) 0.82
Using the normal distribution, it is found that the third quartile is of Q3 = 0.67, hence option B is correct.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 0ºC, hence [tex]\mu = 0[/tex].The standard deviation is of 1ºC, hence [tex]\sigma = 1[/tex].The third quartile is X when Z has a p-value of 0.75, as [tex]100\frac{3}{4} = 75[/tex], hence X when Z = 0.67.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.67 = \frac{X - 0}{1}[/tex]
[tex]X = 0.67[/tex]
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find the domain of y= 2/3 square root of x+5-4
Veronica tried to solve an equation step by step.
8 = y - 4.6
8 + 4.6 = y - 4.6 +4.6 Step one
12.6 = y step two
Which step is wrong or are no steps wrong?
if f(x)=2x^2+1 and g(x)= x^2-7 find (f-g)(x)
Answer:
x² + 8
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 2x² + 1 - (x² - 7)
= 2x² + 1 - x² + 7 ← collect like terms
= x² + 8
a locker room contains 21 books. you select 7 books at random. how many different sets of books can you select
Answer:
14
Step-by-step explanation:
3x7=21 you take away 7 books you would have 14 left or 7x2
The blueprint for Moreno's living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new blueprint? (The width is 8)
Answer:
Part a) The scale of the new blueprint is
Part b) The width of the living room in the new blueprint is
Step-by-step explanation:
we know that
The scale of the original blueprint is
and
the width of the living room on the original blueprint is 6 inches
so
Find the actual width of the living room, using proportion
Find the actual length of the living room, using proportion
Find the scale of the new blueprint, divide the length of the living room on the new blueprint by the actual length of the living room
simplify
Find the width of the living room in the new blueprint, using proportion
help please I'm stuck
Step-by-step explanation:
the line was translated. in other words : it was shifted. it only changed its position. no other attribute changed.
so, the length is still 4.
which image shows a reflection?
Answer: A
Step-by-step explanation:
A)14.3
B)11
C)7.4
Plz help
Answer:
c
Step-by-step explanation: