[tex] \: \Large \mathbb{SOLUTION:}[/tex]
[tex] \: \: \rm{ {7x}^{2} + 4x - {x}^{2}}[/tex]
[tex] \: \: \text{Reorder and gather like terms}[/tex]
[tex] \: \: \rm{( {7x}^{2} - {x}^{2} ) + 4x}[/tex]
[tex] \: \: \text{Collect coeffiecients of like terms}[/tex]
[tex] \: \: \rm{(7 - 1) {x}^{2} + 4x}[/tex]
[tex] \: \: \text{Calculate the sum or difference}[/tex]
[tex] \: \: \rm{ \underline{ \underline{ {6x}^{2} + 4x}}}[/tex]
[tex] \rm{6x {}^{2} + 4x}[/tex]
Solution:Collect like terms
[tex] \red{7x {}^{2} } + 4x \red{ - x {}^{2} }[/tex]
[tex] \red{6x {}^{2} } + 4x [/tex]
What is the slope of a line perpendicular to the line whose equation is 4x+5y=354x+5y=35. Fully simplify your answer.
The perpendicular slope is expressed as the negative reciprocal of the slope or − 1 m. In this scenario, the slope, or m, is −4 so the slope of the perpendicular line is − 1 −4 which simplifies to 1 4
Work out the area of the shaded shape.
3cm
4cm
I don’t understand this so if anyone can help?
Answer:
0.84
4.48
5.32
Step-by-step explanation:
5. One positive number is 3 greater than another positive number. When 12 is added to the square of the smaller number, the result is the same as four times the larger number. Find the two numbers.
Answer:
4, 7
Step-by-step explanation:
x = y + 3
y² + 12 = 4x
using the first equation in the second
y² + 12 = 4(y + 3) = 4y + 12
y² = 4y
y = 4
x = y + 3 = 4 + 3 = 7
PLEASE HELP FAST!!
Select true or false:
The function -3(x + 2)(x - 5)³ > 0, when x < -2 or x > 5.
O True
O False
Answer:
false
Step-by-step explanation:
what is an equivalent fraction -9 - (-4 1/3)
Answer:
Step-by-step explanation:12
If x represents a number, then write an expression
for the product of one more than the number with
one less than the number.
The value of algebraic expression for given is (x + 1)(x - 1)
What is an Algebraic expression?An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
A group of phrases containing letters and numbers that are joined using addition (+), subtraction (-), multiplication (*), and division (**) are known as algebraic expressions.
Let the number be x
Expression for given statement will be -
(x + 1)(x - 1)
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Solve for x.
3x = 6x-2
x=2|3
x=3/2
x=2
Answer:
2/3
Step-by-step explanation:
What is the slope of a line that passes through points (0,7) and (-3,0)
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{0 - 7}{ - 3 - 0} \\ m = \frac{ - 7}{ - 3} \\ m = \frac{7}{3} [/tex]
PLEASE GIVE BRAINLIEST
When two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is?
When two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.
We need to find the type of correlation when two variables vary along with each other but the data points are loosely scattered around the line of best fit.
What are scatterplots?A scatter plot helps find the relationship between two variables. This relationship is referred to as a correlation. Based on the correlation, scatter plots can be classified as follows.
Scatter plot for the positive correlationScatter plot for negative correlationScatter plot for null correlationA weak positive correlation indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.
Therefore, when two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.
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During a pudding eating contest, Jackie ate five and a half pudding
cups. His sister ate two and a quarter pudding cups. How many pudding
cups did they eat altogether?
PLS HELP ME BY SHOWING STEP BY STEP, THE EQUATION AND THATS IT PLS HELP IM DESPERATE!!
True or False: In –6x – 20 = –2x + 4(1 – 3x)
Given [tex]-6x-20[/tex]
Proof that it is equal to the [tex]-2x + 4(1 - 3x)[/tex] or not
[tex]-2x + 4(1 - 3x)[/tex]
Distribute
[tex]-2x+ 4-12x[/tex]
[tex]4-14x[/tex]
Not equal to the [tex]-6x-20[/tex] [tex]\neq[/tex] [tex]4-14x[/tex]
So, it is false
What is Distribute in math?
To "distribute" anything is to divide it up or to give someone a piece of it.
What does the mathematical distributive property mean then?
The distributive property is the distributive law of multiplication over operations in fundamental arithmetic, such as addition and subtraction.
Distributive property: What Is It?
This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.
In other words, an expression of the type A (B + C) can be resolved as A (B + C) = AB + AC in accordance with the distributive property.
This characteristic also holds for subtraction.
A(B-C) = AB-AC
This demonstrates that the other two operands share operand A.
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(HELP) The town of Miami is mapped on a coordinate
grid with the origin being at City Hall. Jordan's house
is located at the point (-5, 7) and Ca'Miyah's house is
located at (-2, 3). To the nearest tenth, How far is it
from Jordan's house to Ca'Miyah's house?
(51)
Answer: 5.2
Step-by-step explanation:
If we put both points on a grid, Jordan's house would be 4 points above and 3 points to the left of Ca'Miyah's. We can plug these two amounts into the pythagorean theorem to find the distance between the houses: 4^2 + 3^2 = x^2. If we solve this equation, we get 5.196, which rounds to 5.2.
Hope this helps!
Please Help!
Find the dimensions of an American football field. The length is 200ft. more than the width, and the perimeter is 1,040ft. Find the length and width. Use the perimeter formula P=2L+2W
The width and length of the field are 160ft and 200ft respectively
When both the given variables are related to each other, we are required to consider one variable as x and the other as a function of x to solve accordingly
Let the width of the football field be 'x' ft.
then according to given data,
length= 200 ft more than width= (x+200)ft
According to given,
Perimeter of the given field =2L+2W=1040
where L is length and W is the width
Now putting the values of length and width earlier derived, we get:
2(x)+2(x+200) =1040
2x+2x+400=1040
4x+400=1040
4x=1040-400
4x=640
x=160ft
Now, the width of the field= x=160ft
length of the field= x+200=160+200=360ft
Hence the length and the width of the field are 160ft and 360ft
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Here is a list of fractions.
15
20
3344
3
One of these fractions is not equivalent to
4
Write down this fraction.
12
16
26
32
21
28
Answer:
So bassiccalyy the answer is 3344/3 because it is not equivalent to 4
“ – 9(11 – 18) – 5.5”
pls pls pls helppp!!! will give brainliest!!!!
Answer:
x = 64
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees, so the missing angle in the triangle on the right has an angle measurement of 180 - 47 - 81 = 52 degrees.
Since the angle and the rightmost angle in the triangle on the right are vertical angles. They are congruent.
Finally, since the triangle on the left is an isosceles triangle and the base angles, the angles on the top left and bottom left, are congruent and therefore their angle measures are both x degrees. So, 2x + 52 = 180 and x = 64.
find both area and perimeter of square its length is 16 cm
Answer:
Perimeter=16cm
Area=16cm
Step-by-step explanation:
we know that all 4 sides of square are equal. So,
Length of 4 sides of square= 16cm
Length of 1 side of square= 16/4cm=4cm
Now that we have found the length of single side of square, by using the formula of area and perimeter we can get of square like this:
Perimeter= 4 times the length of square
or,Perimeter= 4*4
Therefore,Perimeter=16 cm
Now,
Area=square of length of side
or,Area=4^2
Therefore, Area=16 cm
Absolute value equations : solve for all values of y in the simplest form.
21=|7y|
All values of y in the simplest form are 3 and -3
How to solve for all values of y in the simplest form?The equation is given as
21 = |7y|
The above equation is an absolute value equation
When the above equation is expanded, we have the following equations
So, we have
-21 = 7y and 21 = 7y
Divide both sides of the equations by 7
So, we have
-3 = y and 3 = y
Rewrite as
So, we have
y = -3 and y = 3
Hence, all values of y in the simplest form are 3 and -3
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Given the quantities a=3.7m, b=3.7s, c=80m/s, what is the value of the quantity d=a^3/cb^2?
The value of the quantity d is 0.0462 m^2/s.
Here,
The quantities a=3.7m, b=3.7s, c=80m/s.
We have to find the value of d = a^3/cb^2
What is quantity?
A quantity is an amount, number, or measurement that answers the question 'how much?' Quantities can be expressed in numbers or non-standard units.
Now,
The quantities a=3.7m, b=3.7s, c=80m/s.
The value of d;
[tex]d = \frac{a^{3} }{cb^{2} }[/tex]
[tex]d = \frac{3.7*3.7*3.7 }{80 * 3.7^{2} }[/tex]
[tex]d = \frac{3.7}{80}[/tex]
[tex]d = 0.0462[/tex]
Hence, The value of the quantity d is 0.0462 m^2/s.
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Of the students at Milton Middle School, 143 are girls. If 55% of the students are girls, how many total students are there at Milton Middle school?
A.
260
B.
325
C.
195
D.
130
The students in Mr. Bishop's class have written 28 poems. They are putting their poems together to make a poetry book. They put 4 poems on each page. So far, the students have made 5 pages. How many pages do they still need to make? ____ pages
Solve the equation, and enter the solutions from least to greatest. If there is only one solution, enter "n.a." for the second solution. or Reset Nextelect the correct answer from each drop-down menu. Consider this expression. The simplest form of the expression has in the numerator and in the denominator. 1/x+1/x-10=x-9/x-10
We need to know how to solve quadratic equation for this problem. The solution of the equation is x=1 and x=10.
An equation that has a variable with maximum degree two is called a quadratic equation. A quadratic equation can be solved by factorization method. Factorization method is a method where we group the variables together to find common factors among them. The common factors give the solution of the equation. Since a quadratic equation has variable of degree two it has two solutions. The roots of a quadratic equation can be real and unequal, real and equal or imaginary. If we solve the given equation we get a quadratic equation.
[tex]\frac{1}{x} +\frac{1}{x-10} =\frac{x-9}{x-10} \\\frac{x-10+x}{x(x-10)} =\frac{x-9}{x-10} \\2x-10=x(x-9)\\2x-10=x^{2} -9x[/tex]
[tex]x^{2} -9x-2x+10=0\\x^{2} -11x+10=0\\x^{2} -10x-x+10=0\\x(x-10)-1(x-10)=0\\(x-1)(x-10)=0\\[/tex]
Therefore the solution of the equation is x=1 and x=10.
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Write an equation for each line.
y-intercept-5/2, x-intercept-1/3
a.y = -5/2x -1/3
c. y = 2.5x + 7.5
b. y = 7.5x + 2.5
d. y = "-7.5x" - 2.5
The equation of the line is y = -7.5x - 2.5
How to determine the equation of the line?The given parameters are
y-intercept = -5/2
x-intercept = -1/3
A linear equation is represented s
y = mx + c
Where
c = y-intercept = -5/2
So, we have:
y = mx - 5/2
The equation x-intercept = -1/3 means that
y = 0 and x = -1/3
So, we have
0 = -1/3m - 5/2
This gives
1/3m = -5/2
Evaluate
m = -15/2
Substitute m = -15/2 in y = mx - 5/2
y = -15/2x - 5/2
Rewrite as
y = -7.5x - 2.5
Hence, the equation of the line is y = -7.5x - 2.5
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PLS Help.............................
Answer:
Top to bottom
1
30
9
45
Step-by-step explanation:
Thang decided to borrow $7000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 5%. How much interest will Thang pay
Answer:
He will pay $1,050 interest
Step-by-step explanation:
5% interest is paid every year for 3 years
5% * 3(years) = 15%
7000 * 15% = $1,050
$1,050
360 miles traveled on 12 gallons of gasoline? (write each rate as a unit rate)
The unit rate is 30 miles per gallon
How to calculate the unit rate ?The number of miles travelled is 360 miles
The number of gallons is 12 gallons
Therefore the unit rate can be calculated as follows
Unit rate= 360/12
= 30
Hence the unit rate is 30 miles per gallon
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A group of friends wants to go to the amusement park. they have $154.25 to spend on parking and admission. parking is $11.25, and tickets cost $35.75 per person, including tax. how many people can go to the amusement park?
4 people can go to the amusement park.
Let the number of people that can go to amusement park be x.
The parking fee will be paid once only, while cost of ticket will be multiplied based on the number of people.
Forming equation as per the given information in question -
11.25 + 35.75 × x = 154.25
Solving the equation as per the operators -
Shifting 11.25 to Right Hand Side of the equation
35.75x = 154.25 - 11.25
Performing subtraction on Right Hand Side of the equation
35.75x = 143
Shifting 35.75 to Right Hand Side of the equation
x = 143 ÷ 35.75
Performing division on Right Hand Side of the equation
x = 4
Therefore, 4 people can go to the amusement park.
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please help with question 20! thank you. it’s similar to a previous question i asked but i’m still not too sure how to approach it. thank you.
Answer:
118
Step-by-step explanation:
The key piece of information to focus on is that there are around 120 fruits. 15 is the biggest of the given divisors, and the gaps between multiples of 15 is the greatest (compared to 4 and 6) which will narrow down our options. Therefore we can first try approaching the problem by finding multiples of 15 that are close to 120.
The question says that when the number (let's call it A) is divided by 15, it leaves 13. Therefore we can express A as such:
A-13 = 15x OR 15x + 13 = A
Where 'x' represents a whole number showing that the number is divisible by 15.
The closest multiples of 15 to 120 are 105 (15*7), 120 (15*8), and 135 (15*9).
A is one of these numbers + 13, let's see which ones are closest:
105+13 = 118, 120+13 = 133, 135+13 = 148
118 is very close to 120, so let's check it with the other numbers:
118/4 = 29 r 2
118/6 = 19 r 4
The exact number of fruits is 118.
Hope this helped!
Answer:
118
Step-by-step explanation:
We are told that there are about 120 fruits.
Fruits divided equally among 4 students
Multiples of 4: 4, 8, 12, ... 112, 116, 120, 124, ...
Therefore, 116, 120 and 124 are closest to 120.
Add the given remainder of 2 to these numbers:
116 + 2 = 118120 + 2 = 122124 + 2 = 126Fruits divided equally among 6 students
Multiples of 6: 6, 12, 18, ... 108, 114, 120, 126 ...
Therefore, 114, 120 and 126 are closest to 120.
Add the given remainder of 4 to these numbers:
114 + 4 = 118120 + 4 = 124126 + 4 = 130Fruits divided equally among 15 students
Multiples of 15: 15, 30, 45, ... 105, 120, 135, ...
Therefore, 105, 120 and 135 are closest to 120.
Add the given remainder of 13 to these numbers:
105 + 13 = 118120 + 13 = 133135 + 13 = 148Therefore, as the total of 118 fruits is common to all three groups the exact number of fruits is 118.
Check
Divide 118 by each group of students:
118 ÷ 4 = 29 r 2118 ÷ 6 = 19 r 4118 ÷ 15 = 7 r 13As the remainders concur with the given amount of fruit left over for each group of students, this verifies that the exact number of fruits is 118.
1. Which two points lie on a line with slope 2/3? A. (2, 0) and (3,0)
B. (3, –4) and (1, 2)
C. (0, 0) and (2, 3)
D. (–3, 2) and (0, 4)
2. What is the slope of the line that passes through the given points?
(6, –1) and (–3, –1)
A. undefined
B. 0
C. – 2/3
D. – 3/2
If you know the answers to the rest of the quick check please share them!
1. The two points that lie on a line with a slope of 2/3 are: D. (–3, 2) and (0, 4)
2. The slope is: B. 0.
How to Find the Slope of a Line?The formula for finding the slope of a line is:
Slope (m) = change in y/change in x
1. To find the two points that has a slope of 2/3, calculate the slope of each of them:
Slope for A = (0 - 0)/(3 - 2) = 0
Slope for B = (-4 - 2)/(3 - 1) = -3
Slope for C = (3 - 0)/(2 - 0) = 3/2
Slope for D = (4 - 2)/(0 -(-3)) = 2/3
Therefore, the two points that lie on a line with a slope of 2/3 are: D. (–3, 2) and (0, 4)
2. Slope of the line = change in y / change in x = (-1 -(-1))/(-3 - 6)
Slope (m) = 0/-9
Slope (m) = 0
The slope is: B. 0.
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