Enter an equivalent expression for 2x + 3 + 5x + 6 in simplest form.
Jenna has a piece of paper that is 99 3/4 square inch in Area.
It is 10 1/2 inches long.
What is the width of the piece of paper in inches?
Answer:
Width is 9 1/2 in.
Step-by-step explanation:
My reasoning is that, since youve gotten the area (99 3/4), your asked to find the width. You have the length which is 10 1/2. In this situation youre expected to divide. What you divide is 99 3/4 by 10 1/2. If you calculate this, you get a quotient of 9 1/2. I’m not very ethical at explanations, but I hope you found it helpful somehow.
A business is owned by 3 people. Mrs. Applegate owns
3
19
of the business. Mrs. Brown owns 3 times as much as
Mrs. Charles. What fractional part of the business does Mrs. Brown own?
Given:
Mrs. Applegate owns [tex]\dfrac{3}{19}[/tex] of the business.
Mrs. Brown owns 3 times as much as Mrs. Charles.
To find:
The fractional part of the business that Mrs. Brown owns.
Solution:
Let Mrs. Charles owns x part of business.
Mrs. Brown owns 3 times as much as Mrs. Charles.
Mrs. Brown owns = 3x part of business.
Mrs. Applegate owns [tex]=\dfrac{3}{19}[/tex] of the business.
[tex]x+3x+\dfrac{3}{19}=1[/tex]
[tex]4x=1-\dfrac{3}{19}[/tex]
[tex]4x=\dfrac{19-3}{19}[/tex]
[tex]4x=\dfrac{16}{19}[/tex]
Divide both sides by 4.
[tex]x=\dfrac{16}{4\times 19}[/tex]
[tex]x=\dfrac{4}{19}[/tex]
Now,
Mrs. Brown owns [tex]=3\times x[/tex]
[tex]=3\times \dfrac{4}{19}[/tex]
[tex]=\dfrac{12}{19}[/tex]
Therefore, Mrs. Brown owns [tex]\dfrac{12}{19}[/tex] of the business.
1/x+x/2=11/6 transformable to quadratic equations
Note: Consider we need to find the solution of given equation.
Given:
The equation is
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
To find:
The solution of the equation.
Solution:
We have,
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
[tex]\dfrac{2+x^2}{2x}=\dfrac{11}{6}[/tex]
By cross multiplication, we get
[tex]6(2+x^2)=11(2x)[/tex]
[tex]12+6x^2=22x[/tex]
[tex]6x^2-22x+12=0[/tex]
[tex]2(3x^2-11x+6)=0[/tex]
Divide both sides by 2.
[tex]3x^2-11x+6=0[/tex]
Splitting the middle term, we get
[tex]3x^2-9x-2x+6=0[/tex]
[tex]3x(x-3)-2(x-3)=0[/tex]
[tex](x-3)(3x-2)=0[/tex]
Using zero product property, we get
[tex]x-3=0[/tex] and [tex]3x-2=0[/tex]
[tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex]
Therefore, the solutions of the given equation are [tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex].
Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).
Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
We are given the algebraic equation: 1/x+x/2=11/6
Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.
LCD(x,2,6) = 6x
Multiply all through the fractions by 6x
(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)
6 + 3x² = 11x
Rewriting the equation:
3x² - 11x + 6 = 0
Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
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Describe how the graph of y=2xy=2x is the SAME as the graph of y=2x-7y=2x−7.
Select all statements that are true.
They both have a slope of 2.
They cross the x-axis at the same point.
They are parallel to each other.
They have the same slope.
They are in the same location.
They cross the y-axis at the same point.
Answer:
-They both have a slope of 2.
-They are parallel to each other.
-They have the same slope.
Step-by-step explanation:
The 2 equations are;
y = 2x and y = 2x - 7
Now, from slope intercept equation,
y = mx + c
Where m is slope and c is the intercept on the y-axis
From the 2 equations y = 2x and y = 2x - 7, Comparing with y = mx + c, we can see they both have a slope of 2.
For 2 lines to have same slope, it means that they are parallel and have different y-intercepts.
They should cross the x-axis when y = 0.
But at x = 0,we have;
y = 2x = 0. And x = 0
Also,for y = 2x - 7 is y = 2x - 7 = 0
2x = 7 and x = 7/2.
Thus,they don't cross the x - axis at the same point
Looking at the options, we can see that there are 3 correct ones from what we've described above namely;
-They both have a slope of 2.
-They are parallel to each other.
-They have the same slope.
Answer:
its
Step-by-step explanation:
The larger of two numbers is 4 more than 2 times the smaller number. If the sum of the two numbers is 28, what is the larger number
Answer:
The larger number is 20.
Step-by-step explanation:
Let x and y be the two numbers.
y = 2x + 4
x + y = 28
So x + 2x + 4 = 28
3x = 24
x = 8
y = 20
Mr Thompson wants to cut a 5-ft rope into a 1/4-ft sections how many 1/4 sections will he have
Answer:
20 pieces of rope
Step-by-step explanation:
Mr. Thompson has a 5-ft rope. If he cuts the rope into 1/4-ft pieces, that means for every foot, there are 4 pieces of rope. There are 5-ft of rope, so we multiply 5 and 4 to get the number of pieces of rope.
5 x 4 = 20 pieces of rope.
I hope that this helps! :)
Please give me the correct answer.
Answer:
[tex] -m + 6 = 3m + 14 [/tex]
Step-by-step explanation:
Given:
[tex] -(m - 6) = 3m + 14 [/tex]
Required:
Multiply (m - 6) by -1.
Solution:
To multiply (m - 6) by -1, we would be applying the distributive property. This means that we would multiply each term in the parentheses by -1.
Thus:
[tex] -1(m) -1(-6) = 3m + 14 [/tex]
The result would be:
[tex] -m + 6 = 3m + 14 [/tex] (negative times negative = positive)
A store owner uses pieces of tape to paint a window advertisement. The letters are slanted at an 80 degree angle. What is the measure of angle 1?
Answer:
∠1 is 180° − 80° = 100°.
Step-by-step explanation:
Using the corresponding angles, the 80° angle is congruent to the angle that is supplementary to ∠1, as shown. The measure of ∠1 is 180° − 80° = 100°.
The measure of ∠b comes to be 100°.
As we know,
In window advertisement,
∠b and 80° are supplementary angles to each other.
What are the supplementary angles?When the sum of Two angles is 180°, each angle is said to be the supplement of the other angle.
As ∠b +80° =180°
∠b = 180°-80°
∠b = 100°.
Therefore, The measure of ∠b comes to be 100°.
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pleasee heelllppp asapppp ugghhh its for a testtt plzzzzzz
Answer:
The answer is 1
Answer:
i think -3
Step-by-step explanation:
Help I Dont Understand?
Look at image please help me ASAP
Answer:
[tex]\frac{-3 y^{11} }{x}[/tex]
Solve.
4(y + 4) = 32
Answer:
y = 4
Step-by-step explanation:
4*y = 4y
4*4 = 16
4y+16=32
to get 4y alone, we subtract 16 from 32.
32-16 = 16
4y = 16
to get y alone, we divide 4 by 16
16/ 4 = 4
so, y = 4
Answer: y=4
Step-by-step explanation:
4(y+4)=32
Divide both sides by 4
y+4=8
Subtract 4 from both sides
y=4
bla lee la. la la lee bla
Answer:laaa vidas so las vi vi ras ony laa viras so las vi vi ras
Step-by-step explanation:laaaa vidas so las vi vi ras boty hastice hastice sola vi vi rasss*birb falling*
help meh plss :) i don't know the answer
Answer:
33 1/3
Step-by-step explanation:
which function has the range (-infinity,-2]U[0,infinity)?
a. y=cos(x+1)
b. y=csc(x)-1
c. y=sec(x)+1
d. y=cot(2x)-1
Answer:
y= csc(x)+1
Step-by-step explanation:
A P E X
cosec(X) + 1 has the range (-infinity,-2]U[0,infinity)
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
As, the given range (-infinity,-2]U[0,infinity) well satisfied the cosec(X) + 1
Generally, Range of Cosec x is, (-∞,-1] ∪ [1,∞).
So,
Range of Cosec (x) +1 will be ,
= (-∞,-1+1] ∪ [1+1,∞).
= (-∞, 0] ∪ [2,∞)
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Please please please help quickly!
Um th eanswer is 56-64-34-3402-30 = 19038
what is the answer to this problem: A(-4,-5), B(-2,-3), C(4,-3), D(6,-2), E(6,6), F(-1,6), G(-4,2). Find the length of BC.
Answer:
Length of BC is 6.
Step-by-step explanation:
B is at (-2,-3) and C is at (4,-3)
Length BC
[tex]=\sqrt{((-3--3)^{2} +(4--2)^{2} }=\sqrt{6^{2}} =6[/tex]
What are the solutions to the quadratic equation 4(x + 2)2 = 36 x = −11 and x = 7 x = −7 and x = 11 x = −5 and x = 1 x = −1 and x = 5
Answer:
c
Step-by-step explanation:
edge2020
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
What is a Quadratic Equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
4(x + 2)² = 36
4( x(x + 2) + 2(x+2) ) = 36
4( x² + 2x + 2x + 4 ) = 36
4( x² + 4x + 4 ) = 36
4x² + 16x + 16 = 36
4x² + 16x + 16 - 36 = 0
4x² + 16x - 20 = 0
We can further simply ( divide through by 4 )
x² + 4x - 5 = 0
Hence,
a = 1b = 4c = -5x = (-b±√(b² - 4ac)) / (2a)
x = (-4±√(4² - (4 × 1 × -5)) / (2×1)
x = (-4±√(16 - (-20)) / (2)
x = (-4±√(16 + 20)) / (2)
x = (-4±√(36)) / 2
x = (-4±6)) / 2
Hence
x = (-4-6)) / 2 and x = (-4+6)) / 2
x = -10/2 and x = 2/2
x = -5 and x = 1
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
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Pls help me, im not understand this
Answer:
Step-by-step explanation:
Sasha purchased paint that will cover 400 square feet per gallon. Sasha needs to paint a 4704-square-foot surface with 2 coats of paint.
How many gallons of paint will she need for this project?
A.11
B.12
C.23
D.24
Answer:
D. 24
Explanation:
First you would need to find how many you need for one coat.
400 times 12 = 4,800
(That will give you a little extra paint)
Then just double 12 to get two coats and you would get D.
Have a nice day!
Hope this helped.
What is the slope of this line?
5
1/5
-1/5
-5
Answer:
1/5
Step-by-step explanation:
You do rise over run so your rise is 1 and your run is 5 so the answer is 1/5.
And it is positive because it is pointed to the right side.
Hope this helps
describe and correct the error a student made when finding the function rule for the data in the table
I don't know if you still need the answer, but it's in the picture
The correct statement is; B. When x increases by 1, y increases by 9. The function rule is y = 9x + 1
What is linear function?A linear function is represented as: y = mx + c
Where m is the slope and b is the intercept the value of y, when x = 0
From the given table, we have the following observations that;
As x increases by 1
The value of y increases by 9 and the slope of the table is 9
So, we have been given m = 9
Then y = 9x + c
Since an increment of 1 in the value of x will result in an increment of 9 in the value of y which means that; If x is reduced by 1, the corresponding value of y would reduce by 9.
When x = 1 then y = 10
This means that y = 9x + 1
The correct statement is; B. When x increases by 1, y increases by 9. The function rule is y = 9x + 1
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the wheels on a bicycle have a circumference of 4 feet. if the bicycle travels 48 feet how many rotations does it make?
Answer:
12
Step-by-step explanation:
48 divided by 4 is 12
hectare is equal to 2.471 acres. A land developer buys a hectare of land to build homes. Each home will be built on 0.25 acres of land. How many homes can the land developer build on the hectare of space?
Answer:
2.221
Step-by-step explanation:
Multiply the divisor and the dividend by the same power of 10 so that the divisor is a whole number. To check if your answer is reasonable, estimate the quotient by rounding the divisor and dividend to the nearest whole numbers.
ANSWER:
try 2.721....................
PLS help me asap
A motorboat moves across a lake at a constant speed. When it begins, it is 64
km from the shore. After 17 minutes, it is 30 km from the shore. Which
function describes the motorboat's distance from the shore?
The answer
A. y= 2x+64
B. y=-2x+64
C. y=-17x+ 30
D. y=-17x+64
Answer:
y=-2x+64 i think
Step-by-step explanation:
which of the following would you expect to have the highest interest? a 5-year CD a 10-year CD and online savings account or savings account at a Traditional Bank
Answer:10-year CD
Step-by-step explanation:
No
What is the equation of the line shown in this graph?
Answer:
y= 1
Step-by-step explanation:
Use y=mx +b
We have no slope so its just y= b
y=1
Which is the graph of f(x) = 2 Square root negative X
Answer:
the graph is (0,2)
Step-by-step explanation:
please helppp ppppñpñp
Answer:
I tried my best to explain it, hope it helps!
Step-by-step explanation:
