Answers
The two binomials that create this trinomial are
(x-12)(x-2)
the answer would be x^2 - 14x +24
Answer:
[tex](x-12)[/tex] is a factor
Step-by-step explanation:
[tex]x^2-14x+24[/tex]
The product is 24 and sum is [tex]-14[/tex]
To factor it we need to find out two factors whose product is 24 and sum is [tex]-14[/tex]
[tex]-12 \cdot -2= 24[/tex]
[tex]-12 +(-2)= -14[/tex]
Two factors are [tex]-12 , -2[/tex]
[tex]x^2-14x+24[/tex]
[tex](x-12)(x-2)[/tex]
[tex](x-12)[/tex] is a factor
Related Questions
spiders can walk on walls write the statement in if then form
Answers
If then because statements are much like they seem.
Express the Set -4x-6<2x+6 using interval notation
Answers
there's a parentheses at 2, (2, because "x" is greater than, not equal to, but greater than 2.
there's a parentheses at +∞), because ∞ is just a conceptual way to say it keeps on going, so is never reached.
Find the area of the following circle. Use = 3.14
r = 5 yd.
Answers
The formula s= sa/6 gives the length of the side, s, of a cube with the surface area, sa. How much longer is the side of the cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters ?
Answers
they're on a ratio of 3:2, so if the small is 2, the large one is 3, and if the small one is 120, the large one is 180.
on a 3:2 ratio, 3 is larger than 2 by 1 unit, 1 is 50% of 2, or half, so the longer side is 50% larger.
Answer with explanation:
Side of cube = S
Surface Area of Cube = S.A
Relation between Side of a cube and surface area
[tex]S=\frac{S.A}{6}[/tex]
→If surface area of cube =180 Square meters
Side of cube (S)
[tex]S_{1}=\frac{180}{6}\\\\=30[/tex] meters
→ If surface area of cube =120 Square meters
Side of cube (S)
[tex]S_{2}=\frac{120}{6}\\\\=20[/tex] meters
[tex]S_{1}-S_{2}=30 -20=10\\\\S_{1}=S_{2}+10[/tex]
Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.
10 x 6 tens-unit form and standard form
Answers
Answer:
Standard form: 600
Unit form: 6 hundreds.
Step-by-step explanation:
We have been given a number [tex]10\times 6[/tex]-tens. We are asked to write our given number in unit form and standard form.
To write our given number in standard form, we will expand our given number as shown below:
6-tens [tex]6\times 10=60[/tex]
[tex]10\times 6[/tex]-tens would be [tex]10\times 60=600[/tex]
Therefore, our given number in standard form would be 600.
We know that unit form is writing a number using place value units.
We can see that our given number has 0 ones, 0 tens and 6 hundreds.
Therefore, our given number in unit form would be 6 hundreds.
We have that the Tens unit form of 10 x 6 and Standard form is mathematically
[tex]6*10^1[/tex]
6tens
From the question we are told that
10 x 6
10 x 6=60
Standard form is a number, between 1 and 10 multiplied by a power of 10
Generally the equation for the Standard form is mathematically given as
x*10^y
Therefore
the Standard form of 10 x 6 is mathematically given as
[tex]6*10^1[/tex]
And
Generally the equation for the Tens unit form of 10 x 6 is mathematically given as
x*tens(10)
Tens-unit form is mathematically given as
6tens
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(01.02) Choose the best definition for the following term: variable
Answers
A "Variable" is an inconsistent set of numbers. This set is subjected to change over time. The most common set or best demonstration would be an "input-output' Variable.
x = 0
y = 1 + 2x Substitute x = 0
y = 1 + 2(0) Any number times 0 is 0
y = 1 + 0 Simplify
y = 1
I hope this could help.
The perimeter of a square is 26.46 inches. What is the side length of the square?
Answers
Normally it would be:
P=s1+s2+s3+s4
for a square its simply
P=4s
26.46=4S
6.615=S
Each side is 6.615 inches
The side length of a square whose perimeter is 26.46 inches can be calculated by dividing the given perimeter by 4 (the number of sides in a square), resulting in a side length of approximately 6.615 inches.
Explanation:The subject of this question is Mathematics, with the specific topic being measurement and geometry. This question is applicable to Middle School grade levels. The student seeks to determine the side length of a square, knowing the perimeter is 26.46 inches.
To find the side length, we need to recall the formula for the perimeter of a square: P = 4s, where P represents the perimeter and s represents the length of a side. The student's square has a perimeter of 26.46 inches, so the equation would be 26.46 = 4s.
To isolate the value of s, we divide both sides of the equation by 4. This gives us: s = 26.46/4. Upon doing the division, we find that each side of the square is approximately 6.615 inches.
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A customer pays $3.27 for oranges and $4.76 for pears. How many pounds of fruit does the customer buy?
Answers
3.27/1.09=3lbs. of oranges
then take 4.76 and divide that by 1.19 (for the pears)
4.76/1.19=4lbs. of pears
add 4+3 to get how many lbs. in all
4+3=7
A total of 7 pounds of fruit does the customer buy.
Given that, a customer pays $3.27 for oranges and $4.76 for pears.
The cost of 1 pound orages=$1.09 and the cost of 1 pound pears=$1.19
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of pounds of oranges =3.27/1.09=3 pounds
The number of pounds of pears =4.76/1.19=4 pounds
Total weight=3+4=7 pounds
Therefore, a total of 7 pounds of fruit does the customer buy.
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How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?
Answers
now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it? well (90/100) * y, or 0.9y.
now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it? (100/100) * x, or 1x or just x.
we know whatever "x" and "y" amounts are, they -> x + 6 = y
and we also know that x + 1.2 = 0.9y
[tex]\bf \begin{array}{lccclll} &\stackrel{gallons}{acid}&\stackrel{acid~\%}{quantity}&\stackrel{acid~gallons}{quantity}\\ &------&------&------\\ \textit{pure acid}&x&1.00&x\\ \textit{20\% sol'n}&6&0.20&1.2\\ ------&------&------&------\\\ mixture&y&0.90&0.9y \end{array} \\\\\\ \begin{cases} x+6=\boxed{y}\\ x+1.2=0.9y\\ ----------\\ x+1.2=0.9\left( \boxed{x+6} \right) \end{cases} \\\\\\ x+1.2=0.9x+5.4\implies x-0.9x=5.4-1.2\implies 0.1x=4.2 \\\\\\ x=\cfrac{4.2}{0.1}\implies x=\stackrel{gallons}{42}[/tex]
To get a 90% acid solution, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution.
Explanation:To solve this problem, we can use the formula for concentration:
Concentration = (Volume of pure acid) / (Total volume of solution)
Let x represent the volume of pure acid to be added. We know that the total volume of the solution after adding the pure acid is 6 gallons + x gallons. We also know that the concentration of the 20% acid solution is 0.2.
Using the formula, we can set up the equation:
0.9 = x / (6 + x)
Multiplying both sides of the equation by (6 + x), we get:
0.9(6 + x) = x
Simplifying the equation, we have:
5.4 + 0.9x = x
Subtracting 0.9x from both sides of the equation, we get:
5.4 = 0.1x
Dividing both sides of the equation by 0.1, we get:
54 = x
Therefore, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution to get a 90% acid solution.
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The table of values below represents a linear function and shows the height of a tree since it was transplanted. What was the height of the tree when it was transplanted?
Answers
The height of the tree when it was transplanted was:
4 feet
Step-by-step explanation:As we could observe that the given table represents a linear function.
The table is given as follows:
Year since it was 4 4.5 5
transplanted
Height (Feet) 12 13 14
We will find the linear function.
Let y denotes height and x denote year since it was transplanted.
We know that any linear function passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here let (a,b)=(4,12) and (c,d)=(5,14)
Hence, the linear function is calculated as follows:
[tex]y-12=\dfrac{14-12}{5-4}\times (x-4)\\\\\\y-12=2(x-4)\\\\\\y-12=2x-8\\\\\\y=2x-8+12\\\\\\y=2x+4[/tex]
Now the height of tree when it was transplanted is the value of y when x=0
Hence, when x=0 we have:
y=4
Hence, the height was:
4 feet
Solve for x.y = mx+b
Answers
- _ + _
m m
this is the answer
Solve for x means to isolate x.
y - b = mx
We now divide both sides by m to isolate x.
(y - b)/m = x
Find the vertex of the parabola whose equation is y = x2 - 4x + 6.
Answers
Vertex Formula: [tex]x = \frac{-b}{2a}[/tex]
[tex]y = x^2 - 4x + 6 [/tex]
b = (-4)
a = 1
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-4)}{2(1)}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
So the vertex x point is at 2 so (x,y) = (2,y)
Now lets find the y by inserting 2 where the x is located in the equation:
[tex]y = x^2 - 4x + 6[/tex]
[tex]y = 2^2 - 4(2) + 6[/tex]
[tex]y = 4 - 8 + 6[/tex]
[tex]y = 2[/tex]
Now that we found the y for the vertex, we have (x,y) = (2,2) and (2,2) is our vertex. We can graph the equation to and see (2,2) is correct.
Carol ate 2/5 of the cake. Dima ate 3/5 of the REMAINING CAKE, mom ate the rest.
How many times more did Carol eat compared to Dima? PLEASE EXPLAIN, GIVING BRAINLIEST, PLEASE HELP.
Answers
What percentage of 3000 is 330
Answers
Answer:
11
Step-by-step explanation:
find the next three terms in the geometric sequence: 4, -12, 36, -108
Answers
Use the premises and conclusion to answer the questions. Premises: If an angle measure is less than 90°, then the angle is an acute angle. The measure of angle ∠B is 48°. Conclusion: ∠B is an acute angle. Is the argument valid? Why or why not? The argument is not valid because the conclusion does not follow from the premises. The argument is not valid because the premises are not true. The argument is valid by the law of syllogism. The argument is valid by the law of detachment.
Answers
If p and q are 2 propositions (or statements, or assertions) then,
Statement 1: If p, then q.
Statement 2: p
Conclusion: q
That is, if q follows from p, and if p is true, then q is true.
Statement 1: If angle ∠B measure is less than 90°, then ∠B is an acute angle.
Statement 2: The measure of angle ∠B is 48°
Conclusion: ∠B is an acute angle
Answer: The argument is valid by the law of detachment.
A salesperson's commission rate is 5 %. What is the commission from the sale of $ 44,000 worth of furnaces? Use pencil and paper. Suppose sales would double. What would be true about the commission? Explain without using any calculations.
Answers
5% = 0.05
0.05 * 44,000 = 2,200
So the salesperson makes 2,200 dollars from the sale of 44,000.
If sales doubled, then she would make the double amount.
a. The commission from the sale of $ 44,000 worth of furnaces is $1,800
b. Commission would double as well.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
We are given that salesperson's commission rate is 5 %
Then Commission paid on $36,000 worth of furnaces with a rate of 5% is:
= Amount of sales x commission rate
= 36,000 x 5%
= $1,800
If the sales were to double, the commission would be based on double the amount so it would double;
= 36,000 x 2
= $72,000
Commission = 72,000 x 5%
= $3,600
therefore Commission is doubled.
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There are 24 student's in a science class. Mr. Sato will give each pair of student's 3 magnets. So far, Mr. Sato has given 9 pairs of students their 3 magnets. How many more magnets does Mr. Sato need zo.that each pair of student's habe exactly 3 magnets?
Answers
9 pairs already got their magnets. 12 - 9 = 3 pairs still need magnets.
each pair gets 3 magnets. So he needs 3*3 = 9 more magnets
Cody filled a container with 7 3/16 quarts of iced tea. how many 1/4 quart glasses can be served from the container
Answers
[tex]\bf \stackrel{mixed}{7\frac{3}{16}}\implies \cfrac{7\cdot 16+3}{16}\implies \stackrel{improper}{\cfrac{115}{16}} \\\\\\ \textit{how many times does }\frac{1}{4}\textit{ go into }\frac{115}{16}? \\\\\\ \cfrac{\quad \frac{115}{16}\quad }{\frac{1}{4}}\implies \cfrac{115}{16}\cdot \cfrac{4}{1}\implies \cfrac{115}{4}\implies 28\frac{3}{4}[/tex]
Solve the system 2x-2y=10 4x-5y=17
Answers
4x-4y=20,
given:4x-5y=17
y=3
pluck it in
2x-6=10
move the 6 to the right
2x=16
divide
x=8
y=3
Equation 2) 4x - 5y = 17
Multiply ALL of equation 1 by 2.
1) 2(2x - 2y = 10)
Simplify.
1) 4x - 4y = 20
2) 4x - 5y = 17
Subtract equations from one another.
y = 3
Plug in 3 for y in the first equation.
1) 2x - 2y = 10
2x - 2(3) = 10
Simplify.
2x - 6 = 10
Add 6 to both side.s
2x = 16
Divide both sides by 2.
x = 8
------------------------------------
Check your work by plugging in 8 for x, and 3 for y into the original equations.
2x - 2y = 10 & 4x - 5y = 17
1) 2x - 2y = 10
2(8) - 2(3) = 10
Simplify.
16 - 6 = 10
10 = 10
2) 4x - 5y = 17
4(8) - 5(3) = 17
Simplify.
32 - 15 = 17
17 = 17
Therefore, x = 8, y = 3
~Hope I helped!~
how to round 254 to the nearest hundred
Answers
If the tens place is 5 or above round it to 300, if it is 4 or below round it down to 200.
The tens value is 5 so you would round 254 to 300.
The gas tank in the car holds 20 gallons of gasoline. You used up 4 gallons and 1 quart on your trip. How much gasoline is left in the tank?
Answers
20-4.25
=15.75
There is 15.75, or 15 3/4, gallons of gasoline left in the tank.
The correct answer is:
Total capacity of tank in quarts:
20 gallons = 20 × 4 = 80 quarts
Gasoline used in quarts:
4 gallons 1 quart = (4 × 4) + 1 = 17 quarts
Gasoline left in the tank in quarts:
80 − 17 = 63 quarts
Gasoline left in the tank in gallons and quarts:
63 quarts = 63 ÷ 4 = 15 remainder 3 = 15 gallons 3 quarts
How many kilometers could the red car travel in 12 hours?
Answers
a 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. how many containers of sugar will the 9 pound bag create?
Answers
well
[tex]\bf 9 \div \frac{2}{3}\implies \cfrac{9}{\frac{2}{3}}\implies \cfrac{\quad \frac{9}{1}\quad }{\frac{2}{3}}\implies \cfrac{9}{1}\cdot \cfrac{3}{2}\implies \cfrac{27}{2} \\\\\\ \textit{2 goes \underline{13 times} into 27, with a \underline{remainder of 1}}\implies 13\frac{1}{2}[/tex]
Answer:
13 1/2
Step-by-step explanation:
382 & 3/10 - 191 & 87/100= WHAT?
Answers
Given the values of the derivative f′(x) in the table and that f(0)=150, find or estimate f(x) for x=0,2,4,6.
Answers
To find or estimate f(x) for x=0,2,4,6, integrate the given derivative f'(x) with respect to x to find the constant term. Then, add each value of f'(x) in the table to the constant term to obtain the values of f(x) for x=0,2,4,6.
Explanation:To find or estimate f(x) for x=0,2,4,6, we need to use the values of the derivative f'(x) given in the table. Since f'(x) represents the rate of change of f(x) at different values of x, we can use the derivative to find or estimate the values of f(x). Given that f(0) = 150, we can start by finding the constant term of the function using this initial condition.
To find the constant term, we need to integrate the derivative f'(x) with respect to x. This will give us the original function f(x).Integrating f'(x) gives us f(x) = 150 + C, where C is the constant term we need to find.Next, we can use the given values of f'(x) in the table to find or estimate the corresponding values of f(x) for x=0,2,4,6.Let's assume that the third column in the table represents the values of f'(x) at different values of x. We can add each value to the constant term C to obtain the values of f(x) for x=0,2,4,6.Therefore, by integrating f'(x) and adding the constant term, we can find or estimate the values of f(x) for x=0,2,4,6.
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Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of vector QP
Answers
P = (-4,11)
Q = (-5,8)
The x-component of vector QP is
-4 - (-5) = 1
The y-component of vector QP is
11 - 8 = 3
The vector QP is
(1,3) or
[tex]\vec{QP} = \hat{i} + 3\hat{j}[/tex]
The magnitude of the vector is
√(1² + 3²) = √(10)
Answer:
[tex]\vec{QP} = \hat{i}+3\hat{j} \,\, or \,\, (1,3)[/tex]
The magnitude is √(10).
Answer:
<1, 3>, square root of ten
Step-by-step explanation:
Barb’s class has 18 bikes .tim’s class has some rows of bikes with 5 bikes in each row. Tim’s class has more bikes than barb’s class. How many rows of bikes could tim’s class have?
Answers
A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem. (b) Label the upper right vertex of the rectangle (x,y) and indicate the lengths of the sides of the rectangle. (c) Express the area A as a function of x and state the domain of A. (d) Calculate the derviative of A and solve for the critical values. (e) What is the largest area the rectangle can have?
Answers
Answer:
(a) see attached(b) width: 2x; height: y = 9-x²(c) A=2x(9-x²) . . . 0 ≤ x ≤ 3(d) dA/dx = -6x² +18; x=±√3(e) 12√3 units²Step-by-step explanation:
(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.
(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.
(c) As with any rectangle, the area is the product of length and width:
... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this
... A = -2x³ +18x . . . . . expanded form suitable for differentiation
A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.
(d) The derivative of A with respect to x is ...
... A' = -6x² +18
This is defined everywhere, so the critical values will be where A' = 0.
... 0 = -6x² +18
... 3 = x² . . . . . . . divide by -6, add 3
... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A
(e) The rectangle will have its largest area where x=√3. That area is ...
... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)
... A = 12√3 . . . . square units . . . . ≈ 20.785 units²
The parabola y = 9 - x^2 is graphed, and a rectangle's vertices and area calculations are superimposed on it. The derivative of the area function gives critical values, determining the maximum area is 18 square units.
Explanation:To solve this problem, we must utilize quadratic equations, Two-Dimensional (x-y) Graphing, and calculus.
(a) To begin, we need to draw a graph of the parabolic equation y = 9 - x^2. The vertex of the parabola is at the point (0,9) since the x-coordinate of the vertex is -b/2a in a general quadratic equation of the form y = ax^2 + bx + c, and here a = -1 and b = 0.
(b) For the rectangle, the upper right vertex is at point (x, y=(9 - x^2)), with base length 2x and height (9 - x^2).
(c) The area (A=base * height) of the rectangle is then given by A = 2x * (9 - x^2). The domain of A is specified by the values of x for which A is defined. Here A is defined for all x ∈ (-∞, ∞).
(d) The derivative of A with respect to x is A’ = 2(9 - 3x^2), which can be set equal to zero, the solution of which gives critical values x = ±√3.
(e) By the second derivative test or comparing values at the endpoints and critical points, you can determine that the largest area is 18 square units when x = √3.
Therefore,
b) The upper right vertex is at point (x, y=(9 - x^2)), with base length 2x and height (9 - x^2).
c) Here, A is defined for all x ∈ (-∞, ∞).
d) The solution of which gives critical values x = ±√3.
e) The largest area is 18 square units.
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help!! me asap!! please!!