2(2x) + 1x = 40 or 4x + 1x = 40 is the result of combining by substitution
Solution:
Given that we have to combine 2y + 1x = 40 and y = 2x using substitution method
The substitution method for solving systems of equations involves expressing one variable in terms of another, thus removing one variable from an equation.
Given equations are:
2y + 1x = 40 -------- eqn 1
y = 2x ----------- eqn 2
We can substitute eqn 2 in eqn 1
Which means, substitute y = 2x in place of y in eqn 1
2(2x) + 1x = 40
4x + 1x = 40
5x = 40
x = 8
From eqn 2,
y = 2(8)
y = 16
Thus by combining using substitution method we found the solution
What is -1/4(×+2)+5=-×
You have decided to purchase a new Toyota 4Runner for $25,635. You have promised your daughter that the SUV will be hers when the car is worth $10,000. According to your car dealer, the SUV will depreciate in value approximately $3000 per year.
a) Write a linear equation in which y represents the total value of the car and x represents the age of the car,
The linear equation representing the value of the car as it depreciates over time is y = -3,000x + 25,635, where y is the value of the car and x is the age of the car in years.
To write a linear equation that describes the depreciation of the SUV over time, we define two variables: y represents the total value of the car at any time x, where x represents the age of the car in years.
The car is purchased for $25,635 and depreciates at a rate of $3,000 per year, which means that the value of the car decreases by a constant amount each year. We can write this situation as a linear function:
Linear Depreciation Equation:
y = -3,000x + 25,635
Here, the y-intercept is $25,635 (the value of the car at the time of purchase when x is zero), and the slope is -$3,000 (the rate at which the value of the car decreases per year).
Find the midpoint between two points on a number line if one of the points is at -7, and the other point is at 12.
Answer:
The middle point is 3
Step-by-step explanation:
Yo sup??
The mid point can be found out by taking the sum of the two values and dividing it by 2
mid point=(12+(-7))/2
=5/2=2.5
Hope this helps
Explain why dividing by a fraction results in the same answer as multiplying by its reciprocal.
Answer:
lets consider an example like
20 divided by 2/4 so we can rewrite as
2/4* x =20
so , 2* x =20*4
2* x =80
x=80/2
x=40
similarly,we can write the fraction as (20*4/2)-we can see that reciprocal of the fraction 2/4 is 4/2
x=20*4/2=80/2=40
so, we can say that dividing by a fraction results in the same answer as multiplying by its reciprocal.
The ratio of faculty members to students at a college is 1:15. If there are 675 students, then how many faculty members are there?
Answer:
The number of faculty member is 45.
Step-by-step explanation:
Ratio of faculty members to students = 1 : 15
Number of students = 675
Total = Number students + faculty members
Let the total be t
Let the faculty member be f
Representing the ratio, we have:
[tex]\frac{15}{16} * t = 675\\\frac{15t}{16} = 675\\15t = 16 * 675\\15t = 10800\\\frac{15t}{15} =\frac{10800}{15} \\t = 720[/tex]
Therefore, the total number of both the students and faculty member is 720. To get the number of faculty member:
Total = Number students + faculty members
[tex]720 = 675 + f\\f = 720 - 675\\f = 45[/tex]
The number of faculty member is 45.
A 10 metre length of Wood is marked out into 10 equal lengths. How many metres from one end is the third mark?
3 metres from one end to the third mark
Solution:
Total length of wood = 10 metre
Wood is marked into 10 equal length.
[tex]$\text{Length of each marking}=\frac{\text{Total length}}{\text{Number of marking}}[/tex]
[tex]$=\frac{10}{10}[/tex]
= 1 metre
Length of each marking = 1 metre
Number of metres from one end to third mark = 1 + 1 + 1 = 3 metre
The image of the marking is attached below.
Hence 3 metres from one end to the third mark.
Alex flies airplanes. His plane ascends 100 feet above the ground
level in 20 seconds. What is the rate of ascension in feet per second?
Answer: the answer is 5 feet per second
Step-by-step explanation:
On the calculator, click on the graph of y = 3x and trace to view the coordinates. When the x-coordinate is 4, what is the y-coordinate?
the y-coordinate corresponding to x=4 is 12.
the equation y=3x represents a linear function. A linear function is a type of mathematical relationship where the graph of the function forms a straight line.
The equation y=3x is in slope-intercept form, where y represents the dependent variable (usually plotted on the vertical axis),
x represents the independent variable (usually plotted on the horizontal axis), and 3 represents the slope of the line.
To find the y-coordinate when the x-coordinate is 4 in the equation y=3x, we need to substitute x=4 into the equation and solve for y.
Substituting x=4 into the equation y=3x,
we get: y=3×4=12
So, when x=4, y=12.
Therefore, the y-coordinate corresponding to x=4 is 12.
This means that the point on the graph of y=3x where the x-coordinate is 4 has a y-coordinate of 12.
A circular cone has volume 1200 cubic inches and radius 5 inches. What is the height of the cone, to the nearest tenth inch?
I multiply 1200 times 5 and yet 6000 because it says what is the height
The graphs of f(x) and g(x) are shown below.
On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6).
Which of the following is the graph of (g – f)(x)?
On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)
On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).
Answer:
Option C
Step-by-step explanation:
We are given that
[tex]f(x)=-x[/tex]
The line passing through the points (0,0),(-6,6) and (6,-6).
[tex]g(x)=2x[/tex]
The line passing through the points (-3,-6),(0,0) and (3,6).
We have to find the graph of (g-f)(x).
[tex](g-f)(x)=g(x)-f(x)=2x-(-x)=2x+x[/tex]
[tex](g-f)(x)=3x[/tex]
Substitute x=0
[tex](g-f)(0)=3(0)=0[/tex]
[tex](g-f)(2)=3(2)=6[/tex]
[tex](g-f)(-2)=3(-2)=-6[/tex]
[tex](g-f)(-6)=3(-6)=-18[/tex]
Option C is true.
Vocabulary How can you tell if
a
fraction is a unit fraction?
A unit fraction is a fraction with a numerator of 1 and a positive integer denominator. Identifying unit fractions involves ensuring the numerator is 1. Examples include 1/2, 1/3, and 1/5.
A unit fraction is a fraction where the numerator is always 1, and the denominator is a positive integer. This means that a fraction of the form 1/b, where b is a positive integer, qualifies as a unit fraction. For example, 1/2, 1/3, and 1/5 are unit fractions because the numerators are all 1.
When working with fractions, it's important to understand their components. The numerator (top number) represents how many parts you have, while the denominator (bottom number) tells you into how many equal parts the whole is divided. This rule helps identify unit fractions, as the numerator must always be 1.
To summarize, determining unit fractions is straightforward: check if the numerator is 1 and the denominator is a positive integer. If both conditions are met, you have a unit fraction.
Han is planning to ride his bike 24 miles.
a. If he rides at a rate of 3 miles per hour, how long will it take?
At 4 miles per hour?
At 6 miles per hour?
b. Write an equation that Han can use to find t, the time it will take to ride 24 miles, if his rate in miles
per hour is represented by r.
c. On graph paper, draw a graph that shows t in terms of r for a 24-mile ride.
Answer:
Please read the answers below.
Step-by-step explanation:
a. If he rides at a rate of 3 miles per hour, how long will it take?
Time = Distance/Rate
Time = 24/3 = 8 hours
At 4 miles per hour?
Time = 24/4 = 6 hours
At 6 miles per hour?
Time = 24/6 = 4 hours
b. Write an equation that Han can use to find t, the time it will take to ride 24 miles, if his rate in miles per hour is represented by r.
The equation is the same we used in the part a of the problem:
t = 24/r
c. On graph paper, draw a graph that shows t in terms of r for a 24-mile ride.
The graph is attached.
which is the product of 7/9 and 6?
Answer:
14/3
Step-by-step explanation:
7 x 6
9 1
7x6=42
9X1=9
42/9 or 14/3
The product of 7/9 and 6 is 14/3.
Explanation:To find the product of 7/9 and 6, multiply the numerator (7) by the number (6) and keep the denominator (9) the same.
The calculation is as follows:
(7/9) * 6
= (7 * 6)/9
= 42/9
To simplify the fraction, divide both the numerator and the denominator by their greatest common factor, which is 3.
The simplified answer is: 14/3
-3t-8+7t =34 +9t -2
Solve for t
Please give an exposition
Answer:
t = -8
Step-by-step explanation:
combine like terms, so -3t + 7t = 4t and 34 - 2 = 32
so 4t - 8 = 32 + 9t
then subtract 4t from both sides and subtract 32 from both sides. You will get: -40 = 5t.
Then divide both sides by 5 so you will get -8 = t
Answer: t= -8
Step-by-step explanation:
3t-8+7t=34+9t-2-3t+7t-8=9t+32-24t-8=9t+32t= -8300% of what number is 51
Answer:
17
Step-by-step explanation:
Let the number be x.
We know that 3x=51
If we divide both sides by three, we get x=17
17
act like there is a variable in there and youll get 17
Simplify the expression 6s + 9c - 2s
Answer:
4s+9c
Step-by-step explanation:
6s+9c-2s
-2s. -2s
4s+9
Which describes the relationship between
A. adjacent angles
B. complementary angles
C. supplementary angles
D. vertical angles
Answer:
d
Step-by-step explanation:
which doesn't round to 4.7 4.746, 4.733, 4.647, or 4.680
Answer: 4.647
Step-by-step explanation:
The 4 in the hundredths place, or before the 6, is less than 5 so it will not round the 6 to a 7, therefore making it not round to 4.7
I need accurate answer please this is my last attempt
Step-by-step explanation:
In order to rationalise the denominator, numerator and denominator must be multiplied by [tex] \sqrt[3]{9x^{10}}[/tex]
Together, teammates Pedro and Ricky got 2693 base hits last season. Pedro had 283 more
hits than Ricky. How many hits did each player have?
Answer: Pedro= 1205. Ricky= 1488
Step-by-step explanation:
It is found that Ricky hits 1202 base and Pedro hits = 1485 base
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that
Pedro + Ricky = 2693 hits
Let Ricky hits = x
So, the Pedro hits will be = x + 283
( x + 283 ) + x = 2693
2 x + 283 = 2693
2 x = 2693 - 283
2 x = 2404
x = 1202
So, the Ricky hits 1202 base
Thus Pedro hits (1202 + 283) = 1485 base
Learn more about equations here;
https://brainly.com/question/25180086
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Solve the proportional equation below:
10/2=a/a-9
a. 11.25
b. 7
c. 2
d. 1.125
To solve the given proportional equation, it simplifies to 5 = a/(a-9), leading to 4a = 45 after simplification and solving, with the solution being a = 11.25.
Explanation:To solve the proportional equation 10/2 = a/(a-9), we first simplify and then solve for a. The equation simplifies to 5 = a/(a-9). By cross-multiplication, we get 5(a - 9) = a, which simplifies to 5a - 45 = a. Bringing all terms to one side gives 4a = 45, and dividing both sides by 4 gives a = 11.25. Therefore, the correct answer is a. 11.25.
Solve for e and f please
Answer:
Step-by-step explanation:
180-78=102
102÷2=51
E=51
What is the value of x?
Answer:
9
Step-by-step explanation:
The two triangles [tex]\triangle MNP\sim \triangle RST[/tex].
Therefore the corresponding sides are proportional.
[tex]\frac{|ST|}{|PN|} =\frac{|TR|}{|MP|}[/tex]
From the diagram |MP|=4, |PN|=3, |MN|=5 |ST|=x and |TR|=12.
Let us substitute the values and solve for x.
[tex]\frac{12}{4}=\frac{x}{3}[/tex]
Multiply both sides by 3 to get:
[tex]3*\frac{12}{4}=\frac{x}{3}*3[/tex]
This implies that:
[tex]9=x[/tex]
Therefore x=9
The graph shows the number of Internet downloads of a song compared to the number of times it is played on the radio.
What can you conclude from the data? Check all that apply.
A)The number of times a song is played on the radio affects its number of downloads.
B)Increased radio play affects the download demand for all songs equally.
C)Even though there was very high radio play, the downloads of one song remained very low.
D)In general, increased radio play does not affect the number of downloads.
Answer: a,c
Step-by-step explanation:
Answer:
A .. C
Step-by-step explanation:
Write 10+0.06+0.008 in word form
Answer:
Ten plus six hundredth plus 8 thousandth equals ten and sixty-eight thousandths
Step-by-step explanation:
0.06 is in the hundredth place
0.008 is in the thousandth place
Answer:
ten plus zero point zero six plus zero point zero zero eight
Step-by-step explanation:
The ten is 10 then plus + and then 0.06 plus + 0.008
Given the system of equations, what is the solution?
3x - 2y + 10 = 0
5y = 4x + 8
{(-34/7, -16/7)}
{(-34/7, 16/7)}
{(34/7, -16/7)}
Answer:
{(-34/7, -16/7)}
Step-by-step explanation:
Rearrange values, multiply to solve for x.
(5) 2y = 3x + 10
(-2) 5y = 4x + 8
Solve for x.
10y = 15x + 50 ↓
-10y = -8x -16
Combine and evaluate.
0 = 7x + 34
Subtract 34 from both sides.
7x = -34
Divide both sides by 7.
x = [tex]\frac{-34}{7}[/tex]
Plugin x value into either equation to solve for y.
2y = (3 × [tex]\frac{-34}{7}[/tex]) + 10
2y = [tex]\frac{-102}{7}[/tex] + 10
2y = [tex]\frac{-32}{7}[/tex]
y = [tex]\frac{-16}{7}[/tex]
a scientist has a bottle that is 5/8 full of solution. he used 2/5 of the solution in the bottle for an experiment. how much of a full bottle of solution does he use?
Final answer:
The scientist used 9/40 of a full bottle of solution.
Explanation:
To find out how much of a full bottle of solution the scientist used, we first need to calculate the amount that is left in the bottle. The bottle is currently 5/8 full, and the scientist used 2/5 of the solution. To calculate the amount left, we subtract the amount used from the initial amount:
Amount Left = Initial Amount - Amount Used
To subtract fractions, we need a common denominator. The common denominator for 8 and 5 is 40:
Amount Left = 5/8 - 2/5
To subtract the fractions, we need to have the same denominator, which is 40:
Amount Left = (5/8) * (5/5) - (2/5) * (8/8)
Amount Left = 25/40 - 16/40
Amount Left = 9/40
Therefore, the scientist used 9/40 of a full bottle of solution.
y=2x – 3
4x – 3y = 7
Answer:
4x - 3(2x - 3)= 7
4x - 6x + 9 = 7
-2x + 9 = 7
-2x = -2
x = 1
y = 2(1)-3= -1
(1,-1)
Determine if the ordered pair (-2, 1) is a solution
of 2x – y=-3.
Answer: no because 2 times -2 equals -4 and -4 - 1 = -5 not -3.
There are 3 feet in 1 yard. during the first play of a football game, one player runs the ball 10 yards before stepping out of bounds. the coach records the distance in feet and yards
Answer:
30 feet
Step-by-step explanation:
3 feet times 10 years would be 30. This is because for each yard, the player travels 3 feet.
Answer:
30 feet or 10 yards
Step-by-step explanation:
feet is 1 yard so
to get 10 yards
do 3 feet times 10 to make 30 feet
split 30 feet into yards
1 yard for every 3 feet
30 divided by 3 is 10 yards