Answer:
[tex](x^2+5)*(x-3)[/tex]
Step-by-step explanation:
In grouping method factoring, you must have to split the middle term in a way that the product of two terms in middle must be equal to the product of two terms at the edges of equation. Remember you have to consider the resultant signs as well as the magnitude of both products.
Now in the case given above,
[tex]x^3-3x^2+5x-15[/tex]
the result is [tex]-15x^3[/tex]
Note that the magnitude is 15x^3 and sign is '-' for both products.
Now taking out the common terms, equation becomes;
[tex]x^2(x-3)+5(x-3)[/tex]
Taking out (x-3) as common, now the factorized version we have is:
[tex](x-3)(x^2+5)[/tex]
I’m trying to find the missing fraction for this 1/3 + blank =7/12
[tex]\dfrac{1}{3}+x=\dfrac{1}{12}\\\\\dfrac{4}{12}+x=\dfrac{1}{12}\\\\x=-\dfrac{3}{12}=-\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
The LCD here is 12. Subtract 1/3, or 4/12, from 7/12, to obtain the missing fraction. 7/12 - 4/12 = 3/12, or 1/4. The missing fraction is 1/4.
Need help on the stretch problem.
Step-by-step explanation:
ΔACX is an isosceles triangle, so ∠AXC = ∠XAC. We'll call the measure of this angle x°.
∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180. That means ∠BXC = 180 − x.
ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB. We'll call the measure of this angle y°.
Angles of a triangle add up to 180, so:
y + y + (180 − x) = 180
2y = x
y = x/2
∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.
x + y = 90
x + x/2 = 90
3/2 x = 90
x = 60
Therefore, ∠AXC = ∠XAC = 60°.
Wilhich expression is equivalent to 3x/x+1 divided by x+1
Answer:
3x over x+1 MULTIPLIED by 1 over x+1 Letter choice will be A On ingenuity
Step-by-step explanation:
For this case we must find an expression equivalent to:
[tex]\frac {\frac {3x} {x + 1}} {x + 1}[/tex]
Applying double C we have:
[tex]\frac {3x} {(x + 1) (x + 1)} =\\\frac {3x} {(x + 1) ^ 2}[/tex]
Finally, an equivalent expression is:
[tex]\frac {3x} {(x + 1) ^ 2}[/tex]
Answer:
[tex]\frac {3x} {(x + 1) ^ 2}[/tex]
Need help in number 9. Thanks for helping
Answer:
A 6/7
Step-by-step explanation:
3/4 ÷ 7/8
Copy dot flip
3/4 * 8/7
The numerator is 3*8 = 24
The denominator is 4*7 = 28
24/28
Divide the top and botto by 4
6/7
90 divided by20 plus 5 multiply by 5
If point C is inside AvB, then __+m CvB= m AvB
Answer: OPTION A
Step-by-step explanation:
It is important to remember the "Angle Addition Postulate" in order to solve this exercise.
You have this larger angle:
[tex]\angle AVB[/tex]
According to the "Angle Addition Postulate", if the point "C" is in the interior of [tex]\angle AVB[/tex], then the measure of this angle can be obtained by adding the angle [tex]\angle AVC[/tex] and the angle [tex]\angle CVB[/tex].
You can observe in the figure that:
[tex]m\angle AVC=39\°\\\\\mangle CVB=23\°[/tex]
Then you get that:
[tex]m\angle AVC+m\angle CVB=m\angle AVB\\\\39\°+23\°=62\°[/tex]
Therefore, the correct answer is Option A.
Answer:answer is actually C
The following box plot shows the class scores on a particular math test:
box plot with number line titled percent with 50 as the minimum, 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum
Which of the following data sets is represented in the box plot?
{40, 50, 50, 77, 77, 100}
{0, 50, 60, 75, 85, 100}
{50, 60, 60, 75, 75, 85, 85, 100}
{60, 65, 70, 75, 85, 85, 85}
Answer:
Choice C
Step-by-step explanation:
Because,
50 is min
75 is middle
100 is max
The correct data set is {50, 60, 60, 75, 75, 85, 85, 100}
Given,
The box plot with number line titled percent with 50 as the minimum, 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.
We need to determine the following data sets are represented in the box plot.
Let us segregate the following data set by taking the help of a minimum value.
Now, we require a data set that has a minimum value of 50.
There is only one data set given in the option that is a minimum value of 50.
Thus, data set is {50, 60, 60, 75, 75, 85, 85, 100}.
Cross-checked the above data set with more information that is already given in the question.
We required 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.
Thus, all the above requirements are fulfilled by the data set {50, 60, 60, 75, 75, 85, 85, 100}.
Hence, the correct data set is {50, 60, 60, 75, 75, 85, 85, 100}
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Which of the following is a linear function?
Explanation
The first option indicates that equation could be put in y = mx + b form.A linear equation is in y = mx + b format.Answer
First option: 1/3x = y - 3
What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 2x + y - 1=0?
Answer:
y=-2x+4
Step-by-step explanation:
2x+y-1=0
2x+y=0+1
2x+y=1
y=1-2x
y=-2x+1
y=mx+b where m=slope and b=y-intercept
parallel means same slope,
so the slope would still be -2.
--------------
y-y1=m(x-x1)
y-2=-2(x-1)
y=-2x+2+2
y=-2x+4
Can someone please help me out with this question??
Answer:
Hi there!
The answer to this question is: C
Farah would packs 10 outfits for a 9 day vacation.
Step-by-step explanation:
It follows the pattern having one more outfit than the number of vacation days
Which pairs of triangles appear to be congruent? Check all that apply.
Answer:
Step-by-step explanation: just did it on apex
The pairs of triangles appear to be congruent are Triangles 1 and 4, Triangles 1 and 3 and Triangles 3 and 4, that is option B, option C and option E. This can be obtained by understanding the concept of congruence.
Which are the required pairs?Congruent triangles have same size and shape.Corresponding sides and angles are equal. Two congruent triangles can overlap perfectly.In the question, Triangle 2 is larger than the other triangles.
Triangle 1, Triangle 3 and Triangle 4 appears to have the same size and shape.
Thus Triangle 1, Triangle 3 and Triangle 4 appears to be congruent to each other.
Hence the pairs of triangles appear to be congruent are Triangles 1 and 4, Triangles 1 and 3 and Triangles 3 and 4, that is option B, option C and option E.
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Please help me do question 21, 22 and 23. I am in 6th grade.
Question 21: 24 minutes
[tex]\frac{3}{\frac{3}{2} } = \frac{x}{12}[/tex]
x = [tex](\frac{3}{\frac{3}{2} })(12)[/tex]
x = 24
Question 22: 20 centimeters
x = one side of the square
x² = 25
x = 5
4x = perimeter
4(5) = perimeter
20 = perimeter
Question 23: 17 sides
Hexagon = 6 sides
Octagon = 8 sides
Triangle = 3 sides
Total amount of sides = 6 + 8 + 3
Total amount of sides = 17
Write parametric equations of the line with the equation 3x + 2y = 5.
Answer:
a. x = t, y = -[tex]\frac{3}{2}t[/tex] + [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The answer is a. x = t, y = -3/2t + 5/2
The parametric equations of the line with the equation 3x + 2y = 5 is mathematically given as
x=t
y = (5-3t)/2
What is the parametric equations of the line with the equation 3x + 2y = 5.?Question Parameter(s):
the line with the equation 3x + 2y = 5.
Generally, the equation for the equation in slope-intercept is mathematically given as
y = 3x -5/ 2
Therefore
y = (5-3t)/2
While
x=t
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Ralph is 3 times as old as Sara in 4 years Ralph will be twice as old as Sara will be then. Find Ralph’s age now.
If x represents Sarah’s age now, which of the following expressions represents Ralph’s age in four years.
3x
6x
2x+4
3x+4
Answer:
3x+4 Ralph is currently 12 years old.
Step-by-step explanation:
You can find the equation by reading the scenario given. When you read it, it says that Ralph is 3 times as old as Sara and since her current age is going to be used to represent x you will first get 3x. That automatically eliminates the second and third choice given. It then says the equation is for Ralph's age in four years which means to add four to the equation. This gives you 3x+4 as your equation.
When something is tripled and then in a few years it is doubled, it is easiest to first try the number that is being added. So in this case the number is four. When you multiply 4 by 3 you get 12. If Sara is 4 she'll turn eight in four years and if Ralph is 12 he'll turn 16 in four years. 16 divided by 2 is 8 which shows you that Ralph is currently 12
Write as percents
1) 3/5
2)7/8
3)4/25
4)27/50
Write as fractions
1)50%
2)34%
3)56%
4)33 1/3%
Answer:
1)3/5=60%
2)7/8=87.5%
3)4/25=16%
4)27/50=54%
fractions
1)50%=0.5
2)34%=0.34
3)56%=0.56
4)331/3%=1.1033
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add (4x^2-2x)+(5x-7)
Answer:
4x²+ 3x - 7
Step-by-step explanation:
(4x²-2x)+(5x-7)
= 4x²- 2x + 5x - 7
= 4x²+ 3x - 7
The sum of Expressions is 4x² +3x -7.
What is an Expression?An expression is a mathematical statement consisting of variables, constants and mathematical operators.
The sum of the expression (4x²-2x) and (5x-7) has to be determined
(4x²-2x)+(5x-7)
4x² -2x+5x -7
4x² +3x -7
Therefore, the sum of Expressions is 4x² +3x -7.
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What is the perimeter of a rectangle with a 7-inch width and a 16-inch length?
Answer:
7+16= 23
23*2=46. ..........
4. A company found that its monthly profit, P, is
given by P = -10x2 + 120x - 150 where x is the
selling price for each unit of the product.
Which of the following is the best estimate of
the maximum price per unit that the company
can charge without losing money?
A $300
C$11
B $210
D $6
Answer:
11
Step-by-step explanation:
Ok so we aren't looking to maximize profits which is equivalent to finding the vertex of the parabola.
But we want to know what is the highest number of x so that our we aren't losing money. We aren't losing money when our profit is 0.
So we are asked to solve P(x)=0 for x and take the highest x of that equation.
[tex]P(x)=0[/tex]
[tex]-10x^2+120x-150=0[/tex]
I'm going to divide both sides by -10 to make the numbers easier to work with later.
[tex]x^2-12x+15=0[/tex]
I'm going to use the quadratic formula.
[tex]x^2-12x+15=0[/tex] when compared to [tex]ax^2+bx+c=0[/tex] gives us [tex]a=1,b=-12,c=15[/tex].
We are going to plug this into our quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
[tex]x=\frac{12\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}[/tex]
[tex]x=\frac{12\pm \sqrt{144-60}}{2}[/tex]
[tex]x=\frac{12\pm \sqrt{84}}{2}[/tex]
[tex]x=\frac{12}{2} \pm \frac{\sqrt{84}}{2}[/tex]
[tex]x=6 \pm \frac{\sqrt{84}}{2}[/tex]
I'm ready to put this into my calculator.
The one with the plus gives me 10.5826 approximately.
The one with the minus gives me 1.4174 approximately.
The 10.5826 is the higher number.
So about 11 dollars.
Answer:
C $11
Step-by-step explanation:
If a company found that its monthly profit, P, is given by P = -10x2 + 120x - 150 where x is the selling price for each unit of the product, the best estimate of the maximum price per unit that the company can charge without losing money is $11.
Question 14(Multiple Choice Worth 1 points) (07.06 MC) An unknown number x is at most 30. Which graph best represents all the values of x? Number line graph with closed circle on 30 and shading to the right. Number line graph with closed circle on 30 and shading to the left. Number line graph with open circle on 30 and shading to the left. Number line graph with open circle on 30 and shading to the right
Answer:
Number line graph with closed circle on 30 and shading to the left
Step-by-step explanation:
we know that
The algebraic expression of the phrase " An unknown number x is at most 30" is equal to
[tex]x\leq 30[/tex]
The solution is the interval ------> (-∞,30]
All real numbers less than or equal to 30
Number line graph with closed circle on 30 and shading to the left
see the attached figure
The point (0,0) is a solution to which of these inequalities?
O
O
O
O
A. y - 4<3x - 5
B. y - 5< 3x - 4
C. y +5< 3x + 4
D. y + 5 < 3x - 4
Answer:
B.
Step-by-step explanation:
Let's plug in and find out.
A. y-4<3x-5 with (x,y)=(0,0)
0-4<3(0)-5
-4<-5
This is false because -5 is not bigger than -4.
B. y-5<3x-4 with (x,y)=(0,0)
0-5<3(0)-4
-5<-4
This is true because -4 is bigger than -5.
C. y+5<3x+4 with (x,y)=(0,0)
0+5<3(0)+4
5<4
This is false because 4 is not bigger than 5.
D. y+5<3x-4 with (x,y)=(0,0)
0+5<3(0)-4
5<-4
This is false because -4 is not bigger than 5.
The only true inequality I got from plugging in (0,0) for (x,y) was B so that your answer.
Hello,..... I will mark you as a brainliest
A frog is there in a 12m deep well. The frog wants to jump out of the well . Every time it jumps 3m & falls back by 1m. In how many jumps will he come out of the well ???
Remember, I will mark you as a brainliest...
Answer:
5 jumps
Step-by-step explanation:
Personally I would write it out, although there surely is a formula for it.
3 fall to 2 - 5 fall to 4 - 7 fall to 6 - 10 fall to 9 - 12.
This makes 5 jumps, since once he is out he won't fall back in.
Of the 425 tickets sold, 275 were adult tickets. What percent of the tickets were adult tickets? Round to the nearest tenth of a percent.
Answer:
64.7%
Step-by-step explanation:
Write a proportion:
275 / 425 = x / 100
x = 64.7
64.7% of the tickets were adult tickets.
What is the vertex if angle XYZ
A Vertex is the point that 2 or more lines connect.
When an angle is written given the letters of the lines/ points, the point where the lines connect are always the middle letter.
For ∠XYZ, the vertex would be point Y, because it is the middle letter.
An angle is formed by two rays that have a common endpoint which is known as the vertex of the angle
The vertex of the angle ∠XYZ is point Y
The reason the above selection is correct is as follows;
There are three methods used in naming an angle, including;
Using three capital letters with the middle letter representing the vertexUsing only one capital letter, if the angle will not be confused with other anglesUsing a small letter or number in the middle of the angle. The given angle is ∠XYZ, therefore, the middle letter, Y, is the vertex
The vertex point is Y
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What’s the vertex form of F(x)=x^2+2x-3
Answer:
[tex]\large\boxed{f(x)=(x+1)^2-4}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================[/tex]
[tex]\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================[/tex]
[tex]\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4[/tex]
The pH of a solution is a measure of how acidic it is. The greater the acidity, the lower the pH. The function f(x) = −log x gives the pH of a solution, where x is the concentration of hydrogen ions, in moles per liter.
The graph of f(x) = −log x is________________of the graph of g(x)=log x
answer options:
a: vertical translation (not correct answer)
b: horizontal translation
c: reflection in the x-axis
d: reflection in the y-axis
Answer:
c. a reflection in the x-axis.
Step-by-step explanation:
All values of log x are made negative by the transformation so it is a reflection in the x axis.
The graph of [tex]f(x) =-log x[/tex] is the reflection in the x-axis of the graph of [tex]g(x)=log x[/tex].
What is a graph?" Graph is defined as a pictorial representation of the relation between the variables in the coordinate plane along x-axis and y-axis."
According to the question,
Given function on the graph,
[tex]f(x) =-log x[/tex]
[tex]g(x)=log x[/tex]
[tex]'x'[/tex] represents the concentration of hydrogen ions, in moles per liter.
value of [tex]'x'[/tex] remain the same in both cases.
[tex]f(x)[/tex] value is negative.
[tex]g(x)[/tex] value is positive.
The graph of [tex]f(x)[/tex] lying in the first quadrant and the graph of [tex]g(x)[/tex] lying in the fourth quadrant.
Therefore, the graph of [tex]f(x)[/tex] is the reflection in the x-axis of the graph of [tex]g(x)[/tex].
Hence, Option(C) is the correct answer.
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What is the solution to the system of equations below? y = -3X+5 and y=4x-2 (1, 2) (1, –18) (–1, 8) (–1, –6)
Answer:
(1, 2 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 5 → (1)
y = 4x - 2 → (2)
Substitute y = 4x - 2 into (1)
4x - 2 = - 3x + 5 ( add 3x to both sides )
7x - 2 = 5 ( add 2 to both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = (4 × 1) - 2 = 4 - 2 = 2
Solution is (1, 2 )
Ryan is putting money into a savings account. He starts with
$450
in the savings account, and each week he adds
$30
Let S represent the total amount of money in the savings account (in dollars), and let
W represent the number of weeks Ryan has been adding money. Write an equation
relating S to W. Then use this equation to find the total amount of money in the savings account after 14 weeks.
equation=
total amount of money after 14 weeks= $?
the equation is S=30w+450
to find the answer just replace the w by 14
multiply 30 by 14 to get 420 and add 450 to it to get 870
The equation relating the total amount of money 'S' in the savings account to the number of weeks 'W' that Ryan has been saving is S = 450 + 30W. By substituting W with 14 in this equation, we find that Ryan will have $870 in his savings account after 14 weeks.
Explanation:In this case, Ryan had started with $450 in his savings account. His weekly contribution to the savings is $30. So the total amount of money 'S' in the savings account after 'W' weeks could be represented by the equation S = 450 + 30W.
Now, if you want to find out the total amount of money in the savings account after 14 weeks, just substitute W = 14 into the equation. Thus the equation becomes S = 450 + 30*14 = 450 + 420 = $870.
Therefore, Ryan will have $870 in his savings account after 14 weeks.
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Tom bought a pizza. He ate 1/3 of the pizza and gave some of it to his brother. He was then left with 1/5 of the pizza. What fraction of the pizza did Tom give his brother?
Answer:
7/15
Step-by-step explanation:
first recognise that 3/3 is a whole pizza and so is 5/5.
Secondly make all the numbers to have the same denominator
So times both denominators of the fractions together; 5x3=15
Now find 1/3 of 15. Do this by dividing 15 by 3. This equals 5.
So 1/3 is equal to 5/15
Now do the same for 1/5. 15 divided by 5, this equals 3.
So 1/5 is equal to 3/15
Now that we know that the whole pizza is 15/15
We minus 1/3 from 15.
15-5=10. So we now have 10/15 left.
now we know that 'x' is representative of the amount of pizza Tom gave to his bother.
10/15 - 3/15 = x
x = 7/15
So out of the whole pizza (15/15), tom ate 5/15 and was left with 3/15 meaning he gave 7/15 to his brother.
Final answer:
Tom ate 1/3 of the pizza and was left with 1/5 of it, so he gave away 2/15 of the pizza to his brother.
Explanation:
The question is asking which fraction of a pizza Tom gave to his brother. To find out, we know Tom ate 1/3 of the pizza and ended up with 1/5 of it. The fraction that Tom gave his brother is the difference between what he had after eating and what he was left with, thus:
1/3 - 1/5 = (5 - 3) / 15
So, 2/15 of the pizza was given to Tom's brother.
what fraction of the positive integer factors of 1000^3, are perfect squares?
Answer:
25/81
Step-by-step explanation:
1000³ = (10³)³ = 10⁹ = 2⁹ × 5⁹
For a factor to be a perfect square, the exponents must be even. For example:
2⁰ × 5⁰, 2⁰ × 5², 2² × 5⁰, etc.
There are 5 even exponents between 0 and 9 for each 2 and 5. So the number of perfect square factors is 5×5 or 25.
The total number of factors is 9×9 or 81.
So the fraction of positive integer factors that are perfect squares is 25/81.
25/81 is the fraction of the positive integer factors of 1000^3,
What is perfect square ?When you multiply an integer (a "whole" number, positive, negative, or zero) by itself, the resulting product is known as a square number, perfect square, or simply "a square." For example, 0 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 5 = 25.Perfect squares are significant because they demonstrate how to calculate the square root of a completely exact natural number. A perfect square's square root1000^3 = (10^3)^3 = 10^9 = 2^9 x 5^9
Perfect square factors have even exponents.
There are 5 even exponents between 0 and 9 for each 2 and 5.
Number of perfect square factors: 5x5 =25
Total number of factors: 9x9 =81
Fraction: 25/81
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Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour . What is Nina’s rate miles per hour if there are 5,280 feet in a mile?
Which girl bikes faster?
Answer:
Nina's rate in miles per hour is 2.7 miles/hour
Nina bikes faster
Step-by-step explanation:
we know that
1 hour=3,600 seconds
1 mile=5,280 feet
Convert feet to miles
63,360 feet=63,360/5,280=12 miles
Convert seconds to hours
3,400 sec=3,400/3,600=0.94 hours
Find Nina's rate in miles per hour
12/0.94=12.7 miles/hour
Sophia's rate in miles per hour is 10 miles/hour
Compare the rates
12.7 miles/hour > 10 miles/hour
therefore
Nina bikes faster
Answer:
12.7 mph
Nina
Step-by-step explanation: