Answer:
3(p + 2q)(p + 3q)
Step-by-step explanation:
Factor out 3 from each term
3(p² + 5pq + 6q²) ← factor the quadratic by
Consider the factors of the q² term which sum to give the coefficient of the pq- term
The factors are + 2 and + 6, since
2 × 3 = 6 and 2 + 3 = 5, hence
3p² + 15pq + 18q²
= 3(p + 2q)(p + 3q)
The quadratic expression [tex]3p^2+15pq+18q^2[/tex] can be factorized by first taking out a factor of 3, then factorizing the remaining quadratic expression. The result is 3(p+2q)(p+3q).
Explanation:To answer your question about factorizing the quadratic expression [tex]3p^2+15pq+18q^2,[/tex] it's important we understand the factorization process.
First, we can take out a factor of 3.
So,[tex]3p^2+15pq+18q^2[/tex] = 3([tex]p^2+5pq+6q^2[/tex])
Now, we factor the quadratic expression [tex]p^2+5pq+6q^2.[/tex]
To factor it, we need to look for two numbers that multiply to 6 and add to 5. The numbers 2 and 3 fulfill this property. Therefore, we can write [tex]p^2+5pq+6q^2[/tex] = (p+2q)(p+3q)
So the factorization of the original expression is 3(p+2q)(p+3q)
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find the missing digit to make 18, 59_ divisible by 9
Hey im happy to help!
your answer here will be 4.
Hope this helps, have a great rest of your day!
Answer:
4
Step-by-step explanation:
Select ALL the correct answers.
Select all relations that represent functions.
Answer:
option A
option C
option D
Step-by-step explanation:
A function is a special relationship where each input has a unique output.
There could not be different y values for same value of x but it may have two x-values assigned to the same y-value.
So by following this definition:In option B
for x = 6
have two different outputs y = -6 and y = -1 REJECTED
In option E
for x = 0
have two different outputs y = 0.5 and y = 2 REJECTED
Which of these are less than 2.03. Choose all that apply.
Answer: The answer is A.
Step-by-step explanation: The two big things are a one, so it is 2.00, and then the last box is .02. Add .02 to 2.00, and get 2.02. That is less. 2 12/100 is basically 2.12, and the last one is either 23, or 230. But it is over or equal and not under.
Amanda rides her bike east for 10 km. Angela rides her bike 20 degrees south of east 12 km. How far apart are they? Round to the nearest tenth
Answer:
[tex]4.3\ km[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)[/tex]
we have
c-----> is the distance between Amanda and Angela
[tex]a=10\ km[/tex]
[tex]b=12\ km[/tex]
[tex]C=20\°[/tex]
substitute the values
[tex]c^{2}=10^{2}+12^{2}-2(10)(12)cos(20\°)[/tex]
[tex]c^{2}=18.4738[/tex]
[tex]c=4.3\ km[/tex]
What is the equation of the line that has a slope of 0 and passes through the point (6,-8)
[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=0(x-6)\implies y+8=0\implies y=-8[/tex]
Answer: Hello there!
we want to find the equation that passes through the point (6, -8) (where this notation stands for (x,y)) with a slope of 0.
a linear equation has the form y = ax+ b
where a is the slope and b is the intercept.
if a = 0, our equation has the form y = b (has no dependence of x)
so we have a constant equation that passes through the point (6, -8) , this means x = 6 and y = -8, but we know that y is constant:
then y = -8 = b
so our equation is y(x) = -8
i need help with this
Answer:
All you have to do is look up the formulas for each one.
Step-by-step explanation:
Plug in the numbers to the correct formulas and you should get your answer.
See the attached figure for your solution
y incpert
y=x²+4x-12
To find the intercept we need to substitute 0 for y and solve for x.
For our x-intercept you should get: (6,0), (-2,0)
For our y-intercept you should get (0,-12).
tell whether you would use multiplication or division to convert milliliters to liters. Explain your answer.
Division! Since litres is a larger unit then millimeters, the value will need to decrease to make up for the change in units. So division is needed.
To convert milliliters to liters, use division because you're converting from a smaller to a larger unit, with 1000 milliliters equaling one liter.
To convert milliliters to liters, you would use division. This is because the process involves going from a smaller unit of measurement to a larger one, and there are 1000 milliliters in one liter. Therefore, you move the decimal point three places to the left. For example, converting 60,000 milliliters to liters, you would calculate 60,000 milliliters / 1000, resulting in 60 liters.
In solving multi-step division problems with compound units or applying compound unit multiplication in word problems, it is essential to convert all values into the same units using multiplication and division. When dealing with compound unit conversions such as milliliters to liters, division helps find the total amount or cost for a given volume in liters after initially representing values in milliliters.
What is the radius of 11mm
Answer:
The radius is 5.5 mm
Step-by-step explanation:
The diameter is 11 mm
The radius is 1/2 of the diameter
1/2 d =r
1/2(11) =r
5.5 =r
The radius is 5.5 mm
The resale value of a go-cart decreases by $20 for every hour it is used. After how many hours does the value decrease by $400?
Name the following segment or point.
Given L,M,N are midpoints
Median to BC
1. Segment AM
2. Segment BL
3. Segment AS
Answer:
segment AM
Step-by-step explanation:
A median is a line segment which joins the vertex of a triangle to the midpoint of the opposite side. The median to BC is the vertex opposite it A joined to its midpoint M. The segment AM is the median.
Answer:
1. Segment AM.
Step-by-step explanation:
We have been given a triangle ABC. Points L, M and N re midpoints of the triangle. We are asked to find the median of segment BC.
We know that median of a triangle is line segment connecting the midpoint of a segment to the opposite vertex.
We can see that angle A is the opposite angle to side BC and M is the midpoint of side BC, therefore, segment AM is the median to side BC and 1st option is the correct choice.
Suppose Monica walks 1 km every 15 minutes how many meters further can she walk in one hour at this new Rate explain how you found your answer
Answer:
4 is your answer
Step-by-step explanation:
Well every 15 minutes he walks 1 step. So divide an hour which is 60minutes by 15 minutes. Then the answer to that you multiply by 1. So the equation would be (60/15)x1= and you will find the answer.
mark brainliest please :)
Answer:
4000 meters
Step-by-step explanation:
There are 60 minutes in an hour. Divide 60 by 14 and get 4. So she walks 4 km in an hour, but we want to know the answer in meters so we multiply 4 by 1000 to get 4000 meters.
PLEASE HELP!!!!! I HAVE A DEADLINE !!!!
Bob built a rocket that has a radius of 2 feet. Find the volume of the whole rocket he built. Round your answer to the nearest tenth. Show all of your work!!!
Answer:
V_rocket = 44[tex]\pi[/tex] ft^3 = 138.2 ft^3
Step-by-step explanation:
Volume of cone
V_cone = (1/3)*([tex]\pi[/tex]*(radius^2))*h
radius = 2ft
h = height of the cone = 3 ft
pi = 3.1416
V_cone = 4[tex]\pi[/tex] ft^3
Volume cylinder
V_cylin = ([tex]\pi[/tex]*(radius^2))*h_cyl
h_cyl = height of the cylinder = 10 ft
V_cylin = 40[tex]\pi[/tex] ft^3
Volume rocket
V_rocket = V_cone + V_cylin = 4[tex]\pi[/tex] ft^3 + 40[tex]\pi[/tex] ft^3
V_rocket = 44[tex]\pi[/tex] ft^3 = 138.2 ft^3
Find the cost of one item to the nearest cent. Round if necessary. a dozen donuts for $4.00
Answer:
33 cents
Step-by-step explanation:
4/12=1/3=0.33=33 cents
Answer:
= $1/3
Step-by-step explanation:
A dozen contains 12 items
Therefore;
a dozen of doughnuts contains 12 doughnuts
12 doughnuts = $ 4.00
1 doughnuts = 4/12
= $ 1/3
What is an equation for the line that passes through (-2,-3) with a slope of -1/2?
A) 4y+2x=7
B) 4y-2x=-12
C) 4y+2x=-16
D) 5y-4x=12
Answer:
C
Step-by-step explanation:
To write the equation of a line use the point slope form of a line substituting m = -1/2 and the point (-2,-3).
[tex]y -y_1 = m(x-x_1)\\y --3=-\frac{1}{2}(x--2)\\y+3 = -\frac{1}{2}(x+2)[/tex]
Convert to standard form by applying the distributive property and rearranging the terms.
[tex]y + 3 = -\frac{1}{2}(x+2)\\y+3 = -\frac{1}{2}x -1\\2y + 6 = -x -2\\x+2y + 6 = -2\\x + 2y = -8[/tex]
The equation x +2y = -8 is the same equation as 4y + 2x = -16 just doubled----> 2x + 4y = -16
What is a perfect square
Answer:
A perfect square is a shape with for 90 degree angles
Step-by-step explanation:
The square of an integer is called a perfect square. For example, 49 is a perfect square because 7² = 49. When a radicand is not a perfect square, you can estimate the square root of the radicand.
Rewrite the quadratic function in vertex form.
Y=2x^2+4x-1
Answer:
Vertex Pt (-1,-3) Y=2x^2+4x-1
Step-by-step explanation:
2[ (x+1)^2-1} - 1
2(x+1)^2-2} - 1
2(x+1)^2 - 3
The function f(x) = x2 is transformed to f(x) = 3x2. Which statement describes the effect(s) of the transformation on the graph of the original function?
A)The parabola is wider.
B)The parabola is narrower.
C)The parabola is wider and shifts 3 units up.
D)The parabola is narrower and shifts 3 units down.
Answer: B) The parabola is narrower.
Step-by-step explanation:
[tex]y=ax^2+bx+c[/tex] is the Standard form of a quadratic function, where a, b and c are coefficients ([tex]a\neq0[/tex]).
With the coefiicient "a" you can determine how narrow or wide the parabola is:
[tex]|a|>1[/tex] makes the parabola narrow.
[tex]0<|a|<1[/tex] makes the parabola wide.
Given the transformation of the parent function: [tex]f(x)=3x^2[/tex], you can identify that:
[tex]a=3[/tex]
Then:
[tex]|a|>1[/tex]
Therefore, as the parent function is multiplied by 3 and know [tex]|a|>1[/tex], the parabola if narrower than the parabola of the quadratic parent function [tex]f(x)=x^2[/tex].
Answer:
Option B - The parabola is narrower.
Step-by-step explanation:
Given : The function [tex]f(x)=x^2[/tex] is transformed to [tex]f(x)=3x^2[/tex]
To find : Which statement describes the effect(s) of the transformation on the graph of the original function?
Solution :
When the function of parabola [tex]f(x)=x^2[/tex] is transformed by 'a' unit [tex]f(x)=ax^2[/tex]
Then, [tex]|a|>1[/tex] makes the parabola narrow.
and [tex]0<|a|<1[/tex] makes the parabola wide.
On comparing with given function,
|a|=|3| >1 which is greater than 1.
Which means it makes the parabola narrow.
Therefore, the parabola is narrower.
So, Option B is correct.
Given the polynomial function below,find f(-5) f(x)=x^2-2x-7
Answer:
The answer is 28
Step-by-step explanation:
To find the answer, take the function and input the -5 for all x's.
f(x) = x^2 - 2x - 7
f(-5) = (-5)^2 - 2(-5) - 7
f(-5) = 25 + 10 - 7
f(-5) = 28
The value of f(-5) is 28 after plugging x = -5 in the polynomial f(x) = x² - 2x - 7
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial:
f(x) = x² - 2x - 7
Plug x = -5
f(-5) = (-5)² - 2(-5) - 7
f(-5) = 25 + 10 - 7
f(-5) = 28
Thus, the value of f(-5) is 28 after plugging x = -5 in the polynomial f(x) = x² - 2x - 7
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Suppose $10,000 is desposited in a bank at 3.5% annual interest. What is the interest earned after one year?
Answer:
$350
Step-by-step explanation:
The interest earned would be $353
Step-by-step explanation:See the image attached
Please help solve this problem
Answer: OPTION B.
Step-by-step explanation:
The number that are inside of the square root are called "radicands".
To subtract the expressions shown in the image attached, the radicands must be the same.
As you can see, both are equal, therefore, you can subtract the numbers that are in front of the square roots.
Then, you obtain the following result:
[tex]3\sqrt{2}-\sqrt{2}=(3-1)\sqrt{2}=2\sqrt{2}[/tex]
The answer is the option B.
Answer:
The correct answer is option B. 2√2
Step-by-step explanation:
It is given an expression, 3√2 - √2
Simplify the expression
The expression is 3√2 - √2
3√2 - √2 = √2(3 - 1) ( taking √2 as common)
= √2 x 2
= 2√2
Therefore the simplified form of given expression(3√2 - √2) is 2√2
The correct answer is option B. 2√2
Which graph below represents a non functional relationship?
graph c, because it is a curved line. The line has to be straight in order to be a function.
A function is a relationship between inputs where each input is related to exactly one output.
The graph in option D shows one-to-many which is not a function.
The graph in option D represents a non-functional relationship.
Option D is the correct answer
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example: f(x) = 2x is a function.
x = input
2x = output
We have,
A function can have two inputs and have the same output.
This property is called many-to-one function
For example f(x) = (-x)²,
x = 1, -1
f(1) = 1
f(-1) = 1
But a function can not have different outputs for the same inputs.
This property is called one-to-many function.
The given graph in the options are:
A - this graph represents a functional relationship.
B - this graph represents a functional relationship as many-to-one function.
C - this graph represents a functional relationship.
D - this graph represents a non-functional relationship because it is a one-to-many function
Thus,
The graph in option D shows one-to-many which is not a function.
The graph in option D represents a non-functional relationship.
Option D is the correct answer
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Substitution:
5x - y= -5
3x - 6y = 24
do u have to use the exact same number for all the substitutions?
The question involves solving a system of two linear equations, 5x - y = -5 and 3x - 6y = 24. By rearranging the first equation to find y in terms of x, and then substituting this into the second equation, we find x = -8/9. Substituting this value into y = 5x + 5, we find y = 5/9.
Explanation:The question involves a system of linear equations. You solve it using the substitution method. Here are the steps:
Rearrange the first equation, 5x - y = -5, to find y in terms of x: y = 5x + 5.Substitute y = 5x + 5 from the first equation into the second equation, 3x - 6y = 24, and solve for x. This gives: 3x - 6(5x + 5) = 24, which simplifies to -27x = 24, and further simplifies to x = -24/27 or x = -8/9.Substitute x = -8/9 into y = 5x + 5 to find the value of y. This gives y = 5*(-8/9) + 5 or y = -40/9 + 45/9, which simplifies to y = 5/9.So, the solution to the system of equations is x = -8/9 and y = 5/9.
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f(x) = |x| and g(x) = |x| + 3
The translation applied to get the graph of g(x) from the graph of f(x) = |x| and g(x) = |x| + 3
The translation applied to get the graph of g(x) from the graph of f(x) is
Answer:
The graph would move up 3.
Step-by-step explanation:
When a number is added after the absolute value brackets, the graph shifts up and down. Since it is a positive number, the shift is upwards.
Answer:
graph is shifted up by 3 units.
Step-by-step explanation:
Given : The translation applied to get the graph of g(x) from the graph of f(x) = |x| and g(x) = |x| + 3
To find : Graph of g(x).
Solution : We have given that
Parent function f(x) ans translated function g(x) = |x| + 3.
By the transformation rule : f(x) →→ f(x) + k it mean graph of f(x) shifted by k units up.
Then, graph is shifted up by 3 units.
Therefore, graph is shifted up by 3 units.
HELP ME EVERYONE PLZ
Clarissa is an artist and is making a large abstract sculpture for an exhibition.
She uses 12 pieces of glass for every pound of copper and 6.5 pounds of bronze for every 75 pieces of glass. She is using 22.5 pounds of copper in the sculpture.
How many pounds of bronze will she use in the sculpture?
A.
22.5 pounds
B.
11.54 pounds
C.
41.54 pounds
D.
23.4 pounds
Answer:
Option D. 23.4 pounds
Step-by-step explanation:
step 1
Find the pieces of glass for 22.5 pounds of copper in the sculpture.
using proportion
[tex]\frac{12}{1}=\frac{x}{22.5} \\ \\x=22.5*12\\ \\x=270\ piece\ of\ glass[/tex]
step 2
Find the pounds of bronze used in the sculpture
using proportion
[tex]\frac{6.5}{75}=\frac{x}{270} \\ \\x=270*6.5/75\\ \\x=23.4\ pounds[/tex]
Please help me (50 points)
Answer:
A. 40°
Step-by-step explanation:
Hello, there! The angle is across from (vertical to) the angle given. Therefore, the 2 angles are the same.
I hope I helped!
Let me know if you need anything else!
~ Zoe
Answer:
x = 40°, or A)
Step-by-step explanation:
The Vertical Angle Theorem states that if the angles are vertically (directly) opposite of each other, the measurements will be the same.
Therefore, if the opposite angle of x is 40, then x also = 40.
~
1/3 to 2/3 percent of change
[tex]\bf \cfrac{2}{3}\implies \cfrac{1+1}{3}\implies \cfrac{1}{3}+\stackrel{\textit{100\%}}{\cfrac{1}{3}}\impliedby \textit{change of 100\%}[/tex]
Sally's soccer team won 68% of the games they played. if they won 17 games, how many did they play?
Answer:
25
Step-by-step explanation:
Divide 17 by 68%.
Hope that helps!
Step-by-step explanation:
Let's set up a proportion.
17/x=68/100.
Now if we solve for x it would equal to 25. They played 25 games.
Brainliest? :)
WILL MARK BRAINLIEST!!!!!!!
Please show work.
10 is 40% of what number?❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
Answer:
25
Step-by-step explanation:
10*100/40
10*100= 1000
1000/40= 25
Answer:
x=25
explanation:
so we have 40% of x, x =10
40/100 x, x=10
multiplying both sides by 100 and dividing both sides by 40
x=25
calculator check~
10x100÷40 which also gives you the answer of 25
❤️ hope this helps -bangtanboys7❤️
Rewrite the quadratic function in vertex form.
Y=2x^2+4x-1
Answer:
[tex]\large\boxed{y=2(x+1)^2-3}[/tex]
Step-by-step explanation:
The vertex form of an equation of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have
[tex]y=2x^2+4x-1=2\left(x^2+2x-\dfrac{1}{2}\right)[/tex]
We must use the formula: [tex](a+b)^2=a^2+2ab+b^2\qquad(*)[/tex]
[tex]2\left(x^2+2(x)(1)-\dfrac{1}{2}\right)=2\bigg(\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-\dfrac{1}{2}\bigg)\\\\=2\left((x+1)^2-1-\dfrac{1}{2}\right)=2\left((x+1)^2-\dfrac{3}{2}\right)[/tex]
Use the distributive formula a(b + c) = ab + ac
[tex]2(x+1)^2+2\left(-\dfrac{3}{2}\right)=2(x+1)^2-3[/tex]