Answer: Like terms
Example: 7x+9x are like terms because they both have an x with the same exponent of 1. We can combine them to get 7x+9x = 16x. This is like saying you have 7 boxes and you add on 9 boxes to get a total of 16 boxes.
Like terms are terms that have the identical variables and exponents. They can be combined or simplified in an expression. An example of like terms is 3x2 and 2x2 in the expression 3x2 + 2x2.
Explanation:Terms that have the same variables with the same exponents on the variables are called like terms. In other words, like terms can be combined together because they have identical variable parts. For instance, in the expression 3x2 + 2x2, 3x2 and 2x2 are like terms because they both contain the variable x raised to the power of 2. Therefore, they can be simplified or added together, resulting in 5x2.
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Assume that a varies directly as b. What is the constant of proportionality if a = 8 when b = 2?
k = 16
k = 4
k=1/4
k=6
Answer:
k = 4
Step-by-step explanation:
Given that a varies directly as b then the equation relating them is
a = kb ← k is the constant of variation
To find k use the condition a = 8 when b = 2
k = [tex]\frac{a}{b}[/tex] = [tex]\frac{8}{2}[/tex] = 4
Answer:
K = 4
Step-by-step explanation:
Given that varies a directly as b then the equation relating them is
Simply implies that a is directly proportional to b, that is increase in a will cause increase in, and decrease in a will cause decrease in b, and vice versa, where k remains constant.
a α b
a = kb, where k is constant
To find k use the condition a = 8 when b = 2, we make k the subject of the formular
K = a/b
K = 8/2
K = 4
Shelly wanted to buy a shirt for $25 and a skirt for $20.When she got to the check out stand, they added 8% tax to her total. About how much tax did she pay?
Answer:
$3.60
Step-by-step explanation:
25+20=45 (because you need the tax of both)
0.8(45)=3.60 (finding the tax amount)
What is the percent of 108 is 81
consider the equation y=16-x. which of the following statements is true
a. x is a function of y, but y is not a function of x.
b. y is a function of x, but x is not a function of y.
c. both x is a function of y and y is a function of x.
d. neither x is a function of y, nor is a function of x
Answer:
C. Both x is a function of y and y is a function of x
Step-by-step explanation:
A function is a relationship which assigns to each input (from the domain) value, a unique output (from the range).
y is a function of x means x is from domain, y is from range
x is a function of y means y is from domain, x is from range
1. Given [tex]y=16-x[/tex]
y is a function of x because for each x there is exactly one y corresponding to this x.
2. Rewrite [tex]y=16-x[/tex] expressing x in terms of y:
[tex]y-16=-x\\ \\-x=y-16\\ \\x=16-y[/tex]
x is a function of y because for each y there is exactly one x corresponding to this x.
Final answer:
In the equation y = 16 - x, both x and y are functions of each other since each variable can be expressed as having a unique output for each input of the other. The correct answer is c. both x is a function of y and y is a function of x.
Explanation:
To determine which statement is true regarding the equation y = 16 - x, we need to understand the concept of a function. A function, in mathematical terms, is a relationship between two sets that assigns to each element of the first set exactly one element of the second set. In simpler terms, for a variable to be a function of another variable, each input should give us exactly one output. This leads us to the vertical line test, which is a visual way to determine if a curve is a graph of a function of x.
Looking at the given equation, y is expressed in terms of x, implying that for each value of x, there is exactly one value of y. This satisfies the definition of a function, so y is a function of x. Conversely, if we solve the equation for x, we get x = 16 - y, which similarly means that for each value of y, there is exactly one value of x, so x is also a function of y.
Given these points, the correct answer is c. both x is a function of y and y is a function of x. This is because each variable can be expressed as having a unique output for each input of the other variable, therefore both variables are functions of each other.
The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and Plan 2 charges $19 per month plus $0.04 per call.If you have Plan 2 for 4 months and make 20 calls a month, how much will your total bill be?
Answer:
$79.20
Step-by-step explanation:
fixed charged of $19 x 4 months = $76.00
additional charged of $0.04 x 20 = $0.80 x 4 months = $3.20
Therefore, $76.00 + $3.20 = $79.20
Ralph’s annual income is about $32,000. Based on his expenses illustrated in the graph below, roughly how much should Ralph expect to pay in taxes this year?
The answer is $11200.
Answer:
$11,200 or its D
Step-by-step explanation:
got it right on edge
The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y. x=1,y=0.5
Please help me!!
Answer:
y = 0.5x
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 1, y = 0.5
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5
y = 0.5x ← equation of variation
Answer: 0.5
Step-by-step explanation:
One number is 5 times another number the difference between the two numbers is 1460 what is the two numbers
Answer:
The two numbers are -365 and -1825.
Step-by-step explanation:
5x=y
x-y=1460
--------------
x-5x=1460
-4x=1460
x=1460/-4
x=-365
-365-y=1460
y=-365-1460=-1825
Finley's pumpkin had a mass of 6.56.56, point, 5 kilograms (\text{kg})(kg)left parenthesis, start text, k, g, end text, right parenthesis before he carved it. After carving it, the pumpkin had a mass of 3.9\,\text{kg}3.9kg3, point, 9, start text, k, g, end text.
What was the percent decrease in the mass of the pumpkin?
The percent decrease in the mass of Finley's pumpkin after carving is approximately 40.55%.
To calculate the percent decrease in the mass of Finley's pumpkin after carving, use the following formula:
Percent Decrease = ((Original Mass - New Mass) / Original Mass) 100%
First, let's find the decrease in mass.
Decrease in Mass = Original Mass - New Mass = 6.56 kg - 3.9 kg = 2.66 kg
Then, calculate the percent decrease:
Percent Decrease = (2.66 kg / 6.56 kg) 100% = 40.55%
The percent decrease in the mass of the pumpkin after carving is approximately 40.55%.
In the image shown, line n is a transversal cutting lines l and m.
∠3 = 2x + 30
∠5 = 3x + 1
What is the measure of ∠5?
Answer:
88°
Step-by-step explanation:
Alternate interior angles are congruent. So, set the angles equal to each other and solve for x.
2x + 30 = 3x + 1
x = 29
So, ∠5 = 3x + 1 = 3(29) + 1 = 88°
Answer:
94
Step-by-step explanation:
had question on usa test prep
Please answer this correctly
Answer:
60 minutes
Step-by-step explanation:
There are 3 feet in a yard, so a football field is 300 feet long.
Dive 300 by 5 to find the total minutes.
300 / 5 = 60
Answer:
1 hour
Step-by-step explanation:
100 yards = 300 feet
300 / 5 = 60
60 min = 1 hour
Answer: It would take 1 hour for sloths to walk across a 100-yard football field.
jay spent 3/8ths of his life working for a company, if jay has been working for his current company for 15 years, how old is he ?
Answer:
40
Step-by-step explanation:
if 3/8 equals 15 that means 1/8 equals 5 because 15/3=5. now if we multiply 5 by 8 then we get 40 years
If jay has been working for his current company for 15 years, then his age is 40 years.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, jay spent 3/8ths of his life working for a company and he has been working for his current company for 15 years.
Assuming Jay's age to be x years.
∴ (3/8) of x is 15 years.
(3/8)x = 15.
x = 15×(8/3).
x = 40.
So, Jay's age is 40 years.
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Choose all that are correct given the equation: y=1/4 x + 9
A.y=7.25 when x = -7
B.y=7 when x = -8
C.y=8.5 when x =-4
D.y=10.25 when x = 5
Answer: Option A, Option B, Option D.
Step-by-step explanation:
Let's check each option.
A. Substitute [tex]x=-7[/tex] into the equation and evaluate in order to find the value of "y". This is:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-7) + 9\\\\y=7.25[/tex]
B. Substitute [tex]x=-8[/tex] into the equation and evaluate in order to find the value of "y". Then:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-8) + 9\\\\y=7[/tex]
C. Substitute [tex]x=-4[/tex] into the equation and evaluate to find the value of "y":
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-4) + 9\\\\y=8[/tex]
D. Substitute [tex]x=5[/tex] into the equation and then evaluate in order to find the value of "y". You get that this is:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(5) + 9\\\\y=10.25[/tex]
Then, the correct options are: Option A, Option B, Option D.
Find the inequality represented by the graph
Answer:
[tex]y\leq -\frac{1}{3}x+1[/tex]
Step-by-step explanation:
Given:
From the graph, the x and y intercepts are at the points (3, 0) and (0, 1) respectively.
Now, for a line with two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex], the slope is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1,y_1)=(3,0)\ and\ (x_2,y_2)=(0,1)[/tex]. Therefore,
[tex]m=\frac{1-0}{0-3}=-\frac{1}{3}[/tex]
Now, y-intercept is [tex]b=1[/tex]
Therefore, the standard form of a line is of the form: [tex]y=mx+b[/tex]. So, the equation of the line on the graph is:
[tex]y=-\frac{1}{3}x+1[/tex]
Now, from the graph, the region is below the line including all the points on the line. Therefore, the inequality used is less than or equal to. This gives,
[tex]y\leq -\frac{1}{3}x+1[/tex]
Write a unit rate for the situation. Round to the nearest hundredth if necessary.
Traveling 212 km in 6h
Answer:
35.33 km/h.
Step-by-step explanation:
Given: Distance= 212 km.
Times= 6 hours
Now, finding unit rate (speed) for the situation.
Formula; Speed= [tex]\frac{Distance}{time}[/tex]
Speed (rate)= [tex]\frac{212}{6} = 35.3333\ km/h[/tex]
Speed (rate)= 35.3333≅ 35.33 km/h (nearest hundredth).
∴ Rate of the unit is 35.33 km/h
$132 in the ratio 2 : 3 : 6
Answer:
24:36:72
Step-by-step explanation:
multiply 2,3,and 6 by 12 and you got the ratio 24:36:72, which adds to 132
Juanita organizes her magazines into 3 equal piles. She has a total of 18 magazines. How many magazines are in each pile
Final answer:
Juanita has 18 magazines and wants to divide them into 3 equal piles. By dividing the total number of magazines (18) by the number of piles (3), we find that there will be 6 magazines in each pile.
Explanation:
The question asked by the student is a simple division problem in which Juanita needs to organize her magazines into 3 equal piles, and she has a total of 18 magazines. To find out how many magazines are in each pile, we divide the total number of magazines by the number of piles.
To solve this, we perform the following calculation:
Write down the total number of magazines: 18Write down the number of piles: 3Divide the total number of magazines by the number of piles: 18 \/ 3 The result is the number of magazines per pile.So, the calculation is 18 \/ 3 = 6 magazines per pile.
find the equation of the line that has a slope of -1 and passes through the point (2,1)
Answer:
y-1=-x+2
Step-by-step explanation:
m=-1
y-1=-1(x-2)
y-1=-x+2
On a recent day, 8 euros were worth $9 and 24 euros were worth 27.
This question is incomplete, here is the complete question:
On a recent day, 8 euros were worth $9 and 24 euros were worth $27. Write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars.
The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x
Step-by-step explanation:
On a resent day;
8 euros were worth $924 euros were worth $27We need to write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars
∵ The form of the equation is y = kx, where x is the number of
euros and y is the value in dollars
∵ 8 euros were worth $9
∴ (8 , 9) is an ordered pair belong to the equation
∵ 24 euros were worth $27
∴ (24 , 27) is another ordered pair belong to the equation
To find k substitute x and y in the equation by the coordinates of one of these two points
∵ x = 8 and y = 9
∵ y = kx
∴ 9 = 8k
- Divide both sides by 8
∴ 1.125 = k
- Substitute the value of k in the equation
∴ y = 1.125 x
To check the equation substitute x by the x coordinate of the 2nd point if it gives the same value of the y-coordinate of the point then the equation is true
∵ x = 24
∵ y = 1.125 x
∴ y = 1.125(24)
∴ y = 27 the same value of the y-coordinate of the point
∴ The equation is true
The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x
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What is 3y-12=4x+8 in Point-Slope form and graphed but the line needs to pass through (-2,4)
Answer:
The equation of the line in point slope form is equal to
[tex](y-4)=\frac{4}{3}(x+2)[/tex]
The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a line in point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]3y-12=4x+8[/tex]
Convert to point slope form
Factor 3 left side and factor 4 right side
[tex]3(y-4)=4(x+2)[/tex]
Divide by 3 both sides
[tex](y-4)=\frac{4}{3}(x+2)[/tex]
In this equation
the point is (-2,4)
the slope is [tex]m=\frac{4}{3}[/tex]
using a graphing tool
The graph in the attached figure
20 points for this question
Find the least common multiple of x-1 and 1-x
Good evening ,
Step-by-step explanation:
we know that, x-1 = (-1)×(1-x) and 1-x=(-1)×(x-1)
then each of 1-x and x-1 is a multiple of the other one,
if x>1 then x-1>0 and 1-x<0 then x-1>1-x
therefore in this case the least common multiple of x-1 and 1-x is x-1.
if x<1 then x-1<0 and 1-x>0 Then 1-x>x-1
therefore in this case the least common multiple of x-1 and 1-x is 1-x.
:)
Please help!!
In the triangle below, what is the cosine of 60°?
30
Ο
-
-
Ο
Ο
-
Ο
ω
Answer:
C. 1/2
Step-by-step explanation:
SOHCAHTOA
Cosine is adjacent over hypotenuse. For the angle that is 60 the adjacent is 1 and the hypotenuse is 2.
I figured it out, its B A
If A = {4, 7, 10, 13, 17} and B = {3, 5, 7, 9}, then which of the following statements is false?
Ø A
B B
B A
Solve
2x + 3y =2/3
3x - 4y = 18
Answer:
[tex]\displaystyle [3\frac{1}{3}, -2][/tex]
Step-by-step explanation:
{2x + 3y = ⅔
{3x - 4y = 18
¾[3x - 4y = 18]
{2x + 3y = ⅔
{2¼x - 3y = 13½
____________
[tex]\displaystyle \frac{4\frac{1}{4}x}{4\frac{1}{4}} = \frac{14\frac{1}{6}}{4\frac{1}{4}} \\ \\[/tex]
[tex]\displaystyle x = 3\frac{1}{3}[/tex][Plug this back into both equations above to get the y-coordinate of −2]; [tex]-2 = y[/tex]
I am joyous to assist you anytime.
The system of equations is solved using the elimination method. By multiplying the equations to align the coefficients and adding them to eliminate y, x is found to be 3.3333. Plugging x back into one of the original equations then gives y as -2.0000.
Explanation:To solve the system of equations:
2x + 3y = 2/33x - 4y = 18we can use the method of substitution or elimination. Let's use elimination in this case:
First, we multiply the first equation by 4 and the second equation by 3 so that the coefficients of y have the same magnitude but opposite signs:
(4)(2x + 3y) = (4)(2/3) → 8x + 12y = 8/3(3)(3x - 4y) = (3)(18) → 9x - 12y = 54Next, we add the two equations together to eliminate y:
8x + 12y + 9x - 12y = 8/3 + 54
17x = 54 + 8/3
17x = 54 + 2.6667
17x = 56.6667
Now we divide both sides by 17 to solve for x:
x = 56.6667 / 17
x = 3.3333
With x found, we can now substitute it back into one of the original equations to find y. We'll use the first equation for this example:
2x + 3y = 2/3
Substitute x:
2(3.3333) + 3y = 2/3
6.6666 + 3y = 2/3
3y = 2/3 - 6.6666
3y = -6.0000
Now divide both sides by 3 to solve for y:
y = -6.0000 / 3
y = -2.0000
The solution to the system is x = 3.3333 and y = -2.0000.
A) Miss Brown is reading two books every three weeks she has read 12 Books so far how many weeks has she been reading so far ? B) If Miss Brown wants to finish reading 12 books in 15 weeks what would you tell her to change?
Ms. Brown has been reading for 18 weeks so far.
To find out how many weeks Ms. Brown has been reading so far, we can set up a proportion based on the rate at which she reads books.
Ms. Brown reads 2 books every 3 weeks, so we can write this as the ratio:
[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} \][/tex]
Now, we can set up a proportion to find out how many weeks she has been reading to reach a total of 12 books.
Let ( x) represent the number of weeks she has been reading so far. So, we set up the proportion:
[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} = \frac{12 \text{ books}}{x \text{ weeks}} \][/tex]
Now, we can solve for ( x ) by cross-multiplying:
[tex]\[ 2 \times x = 3 \times 12 \][/tex]
[tex]\[ 2x = 36 \][/tex]
Divide both sides by 2 to solve for ( x ):
[tex]\[ x = \frac{36}{2} \][/tex]
[tex]\[ x = 18 \][/tex]
So, Ms. Brown has been reading for 18 weeks so far.
complete question given below:
Ms. Brown is reading 2 books every 3 weeks. She has read 12 books so tar. How many weeks has she been reading so far?
Two fractions are given. For each one, write its decimal equivalent and determine if the decimal is terminating or non terminating 9/20 and 4/15
Answer:
9/20 yes, 4/15 not. See below
Step-by-step explanation:
Pick 9/20 and multiply numerator and denominator by 5:
9/20 = 45/100
We know that if we divide a number by 100 we need to move the coma as two places left, so:
9/20 = 45/100 = 0.45
And this is a terminal decimal as we know where it ends.
On the other hand if we pick 4/15 let try to divide it (here I will do it 'manually'):
4 |_ 15
we can divide 4 by 15, so we use 40 and begin with a comma
40 |_ 15
0.
15 enters 2 times in 40 with a rest of 10, so:
40 |_ 15
30 0.2
100
100 divided by 15 is 6 and we have 10 as rest again, and again and again...
40 |_ 15
30 0.266.....
100
100
....
So, we will have 0.266666666666666 infinitely. The decimal for 4/15 is non terminating and is 0.26666666666666666...
The triangle shown below has an area of 50units squared. Find the missing side.
This solution uses the formula for the area of a triangle together with the Pythagorean theorem to determine the length of the missing side in a right triangle. Assuming one side and the area of the triangle are given, the step involves rearranging the area formula to solve for the missing side. The Pythagorean theorem guarantees the accuracy of this method.
Explanation:The subject of this question is Mathematics. The grade of this question is Middle School. Based on the information given, we are asked to find a missing side of a triangle with a given area.
Since this is a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as x² + y² = h².
Assuming we know one side and the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height = 50. If we know one of the other sides, let's say 'y', we can solve for the other side 'x' by rearranging this formula to solve for 'x', then substituting the known values.
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The total cost of renting a vacation
home includes a deposit and a daily
rental fee of $125. A family rents a
vacation home for 5 days and pays $700.
Assume the relationship is linear. Find
and interpret the rate of change and the
initial value.
Answer:
y=125x+75
Step-by-step explanation:
Y= 125x+B
700=125(5)+B
700=625+B
700-625=625-625+B
75=B
The initial value, or deposit, for the vacation home is $75. The rate of change, or the cost per day, is $125. This constitutes a linear relationship where the total cost increases by a constant daily fee as the number of rental days increases.
Explanation:In this problem, the total cost of the vacation home equals the deposit plus (daily rental fee * number of days). The total cost came out to be $700 when the family rented the home for 5 days. Given that the daily rental rate is $125, that means that the cost of the rental alone was $125 * 5 = $625.
Subtract the cost of the rental from the total cost to find the deposit: $700 - $625 = $75. Therefore, the initial value is $75, which represents the deposit.
The rate of change, which is the cost per day, is $125. This means for every additional day the family rents the vacation home, they are charged an additional $125. So the relationship is linear because the total cost increases by a constant rate - the daily fee - as the number of days increases.
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Please find the answer and explain how you got it
Answer:
m∠NQP=74°
Step-by-step explanation:
we know that
The measure of the interior angles in a triangle must be equal to 180 degrees
In this problem
In the triangle NPQ
m∠N+m∠P+m∠Q=180°
we have
m∠N=(2x)°
m∠P=(34)°
m∠Q=(2x+2)°
substitute the values
[tex](2x)\°+(34)\°+(2x+2)\°=180\°[/tex]
solve for x
[tex](4x+36)\°=180\°[/tex]
[tex]4x=180-36[/tex]
[tex]4x=144[/tex]
[tex]x=36[/tex]
Find the measure of angle NQP
we know that
m∠NQP=m∠Q=(2x+2)°
substitute the value of x
m∠NQP=(2(36)+2)=74°
Hassan keeps picking playing cards out of a standard deck of 52 cards, hoping that he will draw a queen. There are four queens in the deck. After looking at each card, he places it back in the deck. What is the probability that Hassan will draw a Queen in the first seven attempts?
A.) 43%
B.) 46%
C.) 57%
D.) 68%
Answer:43%
Step-by-step explanation:
just finished test
Answer:
C.) 57%Step-by-step explanation:
The events describe is about picking a card, and placing it back into the deck. This means that the total number of event won't change in each trial.
We know that there are 4 queens of 52 cards. So, the probability of picking a card and be a queen is
[tex]P=\frac{4}{52}=\frac{1}{13}[/tex]
However, in this case, we have to apply the experimental probability definition, because we have several attempts. This experimental probability is defined as the ratio between the time the event occurs (4) and the total number of trials (7). That is
[tex]P_{exp}=\frac{4}{7}=0.57 \ (or \ 57\%)[/tex]
Therefore, the right answer is C.