From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
Like and unlike terms in algebraic expression:In algebraic terms, the terms that contain the same variable and the same power or degree are called like terms, In algebraic like terms, the numerical coefficients can vary but are not variables.
Here are some examples of like terms and unlike terms,
4x and 9x are like terms
3x²y and 10x²y are like terms
2xy and 10yx are like terms
3x and 19y are unlike terms [ ∵ variable is different ]
2xyz and 2xy are unlike terms [ ∵ variables is missing in 2nd term ]
Here we have a set of algebraic terms that can be classified as given below
=> 3x and x - like terms
=> 1/4 and 0.5 - like terms
=> –m and 8m - like terms
=> –xy² and 2xy² - like terms
=> y and y² - unlike terms [ ∵ powers are not same ]
=> 4xy and –5x²y - unlike term [ ∵ powers are not same ]
=> m and n - unlike term [ ∵ variables are not same ]
=> –7 and 6 like terms
Therefore,
From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
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The complete Question
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? Choose all that apply.
=> 3x and x
=> 1/4 and 0.5
=> –m and 8m
=> –xy² and 2xy²
=> y and y²
=> 4xy and –5x²y
=> m and n
=> –7 and 6
If the sale of jacket is 160 what is the original price before the 80 percent
Julie made 7 out every 10 baskets she attempted during a basketball game. If she attempted to make 30 baskets, how many did she make?
Answer: 21
Step-by-step explanation:
If she makes 7 out of 10 shots she makes 70% of her shots (7/10 x 100 = 70%)
So if she makes 30 shots, 21 will go in the basket
(30)(0.70) = 21
What are the solutions to the following system?
StartLayout Enlarged left-brace 1st row negative 2 x squared + y = negative 5 2nd row y = negative 3 x squared + 5 EndLayout
The given system of equations has solutions (-2, -1) and (-2, -1) respectively.
Solving system of equationsCalculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations.
Finding the value of the variable that makes the condition of all the given equations true is how we solve an equation system.
Given the system of equation below:
-2x² + y = -5
y = -3x² +5
Substitute equation 2 into 1 to have:
-2x² + (-3x+5) = -5
-2x²-3x² +5 = -5
-2x²-3x² +10=0
-5x² = -10
x² = 10/5
x² = 2
x = ±√2
If x = -√2
y = -3x² +5
y = -3(2) + 5
y = -1
If x = √2
y = -3x² +5
y = -3(2) + 5
y = -1
Hence the solutions to the given system of equations are (-√2, -1) and (√2, -1).
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Local stores have donated 30 packets of flower seeds and 105 packets
of vegetable seeds. Carter wants to know what portion of the seeds are
flower seeds. Write a fraction to represent the ratio of flower seeds to the
total amount of seeds. Then, write the fraction as a decimal number.
The ratio of flower seeds to the total amount of seeds is 2/7 = 0.2857.
What is meant by GCF?The greatest common divisor of two or more numbers that are not all equal to zero is the largest positive integer that divides each of the integers. This term is used in mathematics. The symbol represents the two integers x and y's greatest common factor. The GCF of two or more numbers is the greatest number among all the common factors of the given numbers.
Given that,
The local stores have donated 30 packets of flower seeds and 105 packets of vegetable seeds.
30/105
We have to find the GCF of 30 and 105=15
30/15=2
105/15=7
So, the answer is 2/7
The ratio of flower seeds to the total amount of seeds is 2/7.
By converting fractions as a decimal number we get,
2/7=0.2857
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a bag contains 10 red marbles, 5 white marbles, and 6 blue marbles. you draw 5 marbles out at random, without replacement. what is the probability that exactly two marbles are red?
The probability that exactly two marbles are red, is 0.365.
In the given question we have to find the probability that exactly two marbles are red.
A bag contains 10 red marbles, 5 white marbles, and 6 blue marbles.
Total marbles is
10+5+6=21
We draw 5 marbles out at random, without replacement.
Marbles taken out =5
Total possibility of taking 5 marbles out of 21 marbles is [tex]^{21}C_{5}[/tex].
Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
So [tex]^{21}C_{5}=\frac{21!}{5!(21-5)!}[/tex]
[tex]^{21}C_{5}=\frac{21!}{5!16!}[/tex]
[tex]^{21}C_{5}=\frac{21\times20\times19\times18\times17\times16!}{5\times4\times3\times2\times1\times16!}[/tex]
Simplifying
[tex]^{21}C_{5}[/tex] =7×19×9×17
[tex]^{21}C_{5}[/tex] = 20,349
Probability of exactly two marbles are red is
Possible out comes of exactly two red marbles equal to 2 red and other color marble 3.
Total red marbles are 10. So [tex]^{10}C_{2}[/tex]
The remaining marble except red marble is 11. So [tex]^{11}C_{3}[/tex]
[tex]=^{10}C_{2}\times^{11}C_{3}[/tex]
Simplifying
[tex]=\frac{10!}{2!(10-2)!}\times\frac{11!}{3!(11-3)!}[/tex]
[tex]=\frac{10!}{2!8!}\times\frac{11!}{3!8!}[/tex]
[tex]=\frac{10\times9\times8!}{2\times1\times8!}\times\frac{11\times10\times9\times8!}{3\times2\times1\times8!}[/tex]
=5×9×11×5×3
=7,425
So the probability that exactly two marbles are red
P(R)=7,425/20,349
P(R)=0.365
Hence, the probability that exactly two marbles are red, is 0.365.
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Write a function for the tranformations described below:
"The cubic function shifts 7 units right and 5 units up."
The function for the transformation "The cubic function shifts 7 units right and 5 units up. is written as f(x) = (x - 7)^3 + 5.
How to write the function for the given transformationLet the cubic function be = f(x) = x^3
The transformation required include shifts 7 units right and 5 units up
shifting 7 units to the right is achieved by subtracting 7 units from x in the function hence f(x) = (x - 7)^3
moving 5 units up is achieved by adding 5 units to the function hence
f(x) = (x - 7)^3 + 5
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Find the slope (3,-20),(5,8)
Answer: 14
Explanation:
(3, -20) (5, 8)
x1 y1 x2 y2
[tex]\frac{y2 - y1}{x2 -x1}[/tex]
[tex]\frac{8 - -20}{5-3}[/tex] = [tex]\frac{8+20}{5-3} = \frac{28}{2} = 14[/tex]
Finn wants to buy a sweater for $29.50 and jeans for $42.50 if the sales tax rate is 8.25% what will be the amount of cell taxes on finn’s purchase
The amount of cell taxes on finn’s purchase is $5.94.
How to calculate the value of the tax?Since Finn wants to buy a sweater for $29.50 and jeans for $42.50, the total cost will be:
= $29.50 + $42.50
= $72
If the sales tax rate is 8.25%, the amount on tax will be:
= Tax rate × Total cost
= 8.25% × $72
= $5.94
The tax is $5.94.
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isaac owns a trucking company. for every truck that goes out, isaac must pay the driver $19 per hour of driving and also has an expense of $1.50 per mile driven for gas and maintenance. on one particular day, the driver drove an average of 30 miles per hour and isaac's total expenses for the driver, gas and truck maintenance were $512. write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. define the variables that you use to write the system.
8 hours the driver worked and 240 miles the truck drove.
Assume that the truck traveled y miles per hour. and that the driver worked x hours per day.
The equations describing the provided issue will be
19x + 1.50 y = 512
y = 30x
y = 19 x + 1.50 y = 30 x + 1.50 y
When we enter the second equation into the first one, we get,
19 x + 1.50 (30 x) = 512
19x+ 45x = 512
64x = 512
x = 8
y = 240
The vehicle traveled 240 miles, and the driver put in eight hours' worth of work.
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Question Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7
Answer:
y=3x-13
Step-by-step explanation:
Since the parallel equations have equal slope.
The equation of line parallel to y=3x+7 will be y=3x+k.
(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13
HELP MEEEEEE PLEASEEEEE
unable to see the graph
1. 6:N=2:5
2. 5:3=N:6
3. N:20=5:10
4. 1:4=2:N
Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answer:
153.9 units squared
Step-by-step explanation:
A = pi*r^2
A = pi* 7^2
A = pi* 49
A = 153.9
Write an equation of the line passing through the point $A\left(-6,\ 5\right)$ that is parallel to the line $y\ =\ \frac{1}{2\ }x-7$
.
The equation of the line through the point (-6,5) and parallel to the line is y=[tex]\frac{1}{2}[/tex]x-7 is y=[tex]\frac{1}{2}[/tex]x+8.
What is equation of line ?
Any location with an x and y axis can have a line equation constructed using the slope of the line. To build a line with a certain point, one uses the equation for a straight line. Any two points can be used to find the slope. Slope is the part of a straight line that is steep.
Here the given equation is y=[tex]\frac{1}{2}[/tex]x-7
We know that equation of line is y=mx+c , where m = slope.
Then slope of given line is m= 1/2 . Now the line is parallel to given line so slope of the equation is also equal.
=> slope m=1/2.
Now the given point [tex](x_1,y_1)=(-6,5)[/tex] .
Using equation of the line is ,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-5 = 1/2(x+6)
=> 2y-10=x+6
=>2y=x+16
=>y=[tex]\frac{1}{2}[/tex]x+8
Hence the equation of the line is y=[tex]\frac{1}{2}[/tex]x+8.
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9) Give the following expression in index form
a) √3
For the given expression √3, its index form is written as ( 3 )¹/² .
As given in the question,
Given expression is equal to :
√3
Standard form of writing expression in index form is given by:
√ ( square root ) will express the value in index form as 1 / 2 in the exponent.
√x = ( x ) ¹/²
Here x = 3 substitute the value of x in the standard way of index form we have:
Index form of the given expression is written as :
√3
= ( 3 )¹/²
Therefore, for the given expression √3, its index form is written as ( 3 )¹/² .
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Complete the equation describing how
and y are related.
XOL2345
911 13 15
1
y
7
17
y = [? ]x + [ ]
Enter the answer that
belongs in [?].
The equation that describing how x and y are related is y = 2x + 7
From the given table we have to choose two points
The first point = (1, 9)
The second point = (2, 11)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (11-9) / 2 - 1
= 2 / 1
= 2
From the table
At x = 0 the value of y = 7
Therefore the y intercept = 7
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Then,
y = 2x + 7
Hence, the equation that describing how x and y are related is y = 2x + 7
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expand and simplify (x+5)(x-3)
The simplified expression is x² + 2x - 15.
We are given a mathematical expression. The expression has two terms. The first term is (x + 5) and the second term is (x - 3). The terms are multiplied by each other to obtain the final expression. Let the resulting expression be represented by the variable "E". The expression has been solved below.
E = (x + 5)(x - 3)
We will use the distributive property.
E = x*(x - 3) + 5*(x - 3)
E = x*x - x*3 + 5*x - 5*3
E = x² - 3x + 5x - 15
E = x² + 2x - 15
Hence, the expanded and simplified form of the given expression is x² + 2x - 15.
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Question 12 (10 points)
If AWXY is equilateral and AWZY is isosceles, find each missing measure. Answers may be used more than once!
angle 1 =
angle 2 =
angle 3 =
angle 4 =
angle 5 =
The measure of all the angles is given below :
angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°
Given, ΔWXY is an equilateral triangle and ΔWZY is an isosceles triangle.
We have to find the measure of all the angles,
As, ΔWXY is an equilateral triangle
so, ∠WXY = ∠XYW = ∠YWX = 60°
Now, let ∠WZY = ∠WYZ = x and ∠ZWY = y
so, on applying angle sum property, we get
2x + y =180°
so, y = 60°
and 2x = 120°
x = 60°
Hence, angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°
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How do i write the equation
Answer:
[tex]y=-\frac{1}{5}x[/tex]
Step-by-step explanation:
Start by finding the slope of the line. Slope is defined as the RISE over the RUN. Find two points on the line with clear coordinate pairs. The line clearly passes through the origin, and the point (5,-1). To get from one point to the other, I have to go DOWN 1 unit. This is the RISE. The rise is -1 because I am going down. I also have to go RIGHT 5 units. This is the RUN. Slope is rise divided by run. Since a positive number divided by a negative number is a negative number, I move the negative sign outside the fraction: [tex]-\frac{1}{5}[/tex]. This is the slope!
The line crosses the y-axis at 0, so the y-intercept is 0.
Point-slope form is a way to write linear equations. It looks like this:
[tex]y=mx+b[/tex]
The letter m represents the slope, and the letter b represents the y-intercept. Let's plug in the values we found for those respectively:
[tex]y=-\frac{1}{5}x+0[/tex]
This simplifies to the equation below! This is the equation of the line!
[tex]y=-\frac{1}{5}x[/tex]
A, B & C lie on a straight line. G, B & F lie on a different straight line. D, E & F lie on a straight line parallel to AC. DEB = 104°. GBA = 24°. Work out EBF.
The measure of angle EBF is 80° .
In the question ,
it is given that ,
point A, B and C lie on a straight line .
and G , B and F lie on a different straight line .
angle GBA = 24° so ,
GBA + GBC = 180° ...because linear pair
So , GBC = 180 - 24 = 156°
angle CBF = 24° ......because vertically opposite angles are equal .
from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,
156° = ABE + EBF .....(1)
Since the line AC and DF are parallel and BE is the transversal
So , angle DEB + angle ABE = 180°
104° + ABE = 180°
ABE = 180-104
ABE = 76°
Substituting ABE = 76° in the equation (1) ,
we get ,
156 = 76+ EBF
EBF = 156 - 76
EBF = 80°
Therefore , The measure of angle EBF is 80° .
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A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times. How many times can you expect to land on yellow if you spin the spinner 100 times?
20 times can you expect to land on yellow if you spin the spinner 100 times.
Given:
A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times.
10 times spinning = landed on yellow 2 times.
divide by 10 on both sides
1 time spinning = landed on yellow 2/10 times
1 time = 1/5 times
multiply by 100 on both sides
1 time * 100 = 1/5*100 landed on yellow
100 times spinning = 20 times landed on yellow.
Therefore 20 times can you expect to land on yellow if you spin the spinner 100 times.
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1. Giuseppe is 74 inches tall, and Raymond is 6 feet 1 inch tall. Who is
taller? Explain.
Answer: Giuseppe is taller.
Step-by-step explanation:
Giuseppe is 74 inches tall, and we know that 12 inches is one foot, so 74/12 is ~6.1677777... versus 6.1.
Another way you can check this is by converting feet to inches. So 6 feet 1 inch would be (6 x 12) + 1 which is ~73.
please help me find the zero of y=-5x+5
Answer:
1
Step-by-step explanation:
To find the zero of an equation you set the equation equal to 0
That means you do this:
-5x+5=0
Then you solve for x
-5x=-5
x = -5/-5
x= 1
Solve :
22r^2+1144r-7656=0
Fill in the equation for the missing components of the line through (3, 5) and (8, 10)
"ENTER ANSWER AS A DECIMAL
y-5=__(x-3)
The equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)
The first point = (3, 5)
The second point = (8, 10)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (10-5) / (8-3)
= 5 /5
= 1
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope of the line
Consider the point (3, 5)
Substitute the values in the equation
y-5 = 1(x-3)
Hence, the equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)
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Ralph hit a softball into the air with an initial upward velocity of 48 feet per
second. The height h in feet of the ball above the ground can be modeled by
h = -16t² +48t + 3, where t is the time in seconds after Ralph hit th
softball.
What is the realistic domain for this function?
Answer:
domain: [0, (6+√39)/4] ≈ [0, 3.06125]
Step-by-step explanation:
You want the realistic domain of a height function h = -16t² +48t + 3.
DomainThe given polynomial is defined for all values of t. Since it represents height above the ground, and after the ball is thrown, only function values in the first quadrant are of interest: h ≥ 0, t ≥ 0.
The height becomes zero at t = (6+√39)/4 ≈ 3.061 seconds after the ball is hit. Hence the realistic domain is [0, (6+√39)/4], the interval in which the ball is above ground.
__
Additional comment
We can solve this using the "completing the square" method.
t^2 -3t = 3/16 . . . . . . divide by -16, add 3/16
(t -3/2)^2 = 3/16 +9/4 . . . . . add 9/4 to complete the square
t = 3/2 ± √(39/16) = (6 ± √39)/4 . . . . . . take the square root, add 3/2
Only the positive value of the solution is applicable to this problem. That value is ...
h = 0 at t = (6 +√39)/4 ≈ 3.061249
Write down the factors of 28 Then,write down the prme factors of 28
the factors of 28 are : 1, 2, 4, 7, 14, and 28.
the prime factors of 28 are : 2, 2, and 7.
Find the value of the expression (2x − 12) + (xy-10) for x = 8 and y = 2.
-
O-8
O 6
O-10
02
The value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.
According to the question,
We have the following expression:
(2x − 12) + (1/2xy-10)
Now, the values of x and y are given to be 8 and 2 respectively.
So, we will put these values of x and y in the given expression:
(2*8-12)+(1/2*8*2-10)
First, we will use multiplication:
(16-12)+(8-10)
4+(-2)
(Note that when two integers are of different signs then the integers are subtracted but the sign in the result is of the larger integer.)
4-2
2
Hence, the value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.
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(b) Let m be the number of minutes it takes for the two
towers to contain the same number of gallons. Set
up and solve an equation for m.
Answer:
y = mx + b
PLEASE GIVE BRAINLIEST THANK YOU!!!
Daniel has saved $2,000 in a savings account that earns 0. 5% interest annually. What will most likely happen to the purchasing power of his savings over time?.
Daniel's purchasing power will decrease because the interest rate is lower than the historical rate of inflation.
Purchasing power can be portrayed as the quantity of labor and products that a unit of cash or an amount of cash can buy. The connection between financing cost and inflation rate influences the buying force of a saving record.
At the point when the loan cost is higher than the inflation rate, purchasing power increments. Yet, when the interest rate is lower than the expansion rate, buying power falls. For example, In the United States for the 12 months ending April 2022, the annual inflation rate was 8.3%. Since the 0.5% annual interest rate being earned by Daniel is lower than the 8.3% annual inflation rate, the most likely thing to happen to the purchasing power of his savings over time is to fall.
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