Answer:
-1
Step-by-step explanation:
3 • 7 = 21
Find two factors of 21 whose sum equals the coefficient of the middle term, which is -1 .
-21 + -1 = -22
-1 + -21 = -22
1 + 21 = 22
21 + 1 = 22
Answer:
Can not be factorized further
Step-by-step explanation:
Here we are asked to factorize the expression [tex]3x^2+x+7[/tex]
In order to factorize a quadratic polynomial , we have to follow the following steps.
step 1. We have to find the product of coefficient of [tex]x^2[/tex] and the constant term. In this case the coefficient of [tex]x^2[/tex] is 3 and constant term is 7. Hence the product is 3*7=21
Step 2: Now we have to find all the possible factors of this product. In our case the factors will be
21=1*21
21=3*7
Step 3: We have to select one pair of those factors such that their sum or difference is equal to the coefficient of middle term that is [tex]x[/tex] . In this case it is 1. And we can see that in our polynomial , none of the pair gives you 1 either as sum or difference.
As there does not exist any such pair , it can not be further factorize.
Need help please !!!
Answer:
option C is the correct answer
Step-by-step explanation:
The trigonometric equation you are using has a general form
y = A* tan w*(x - r)
Where
A is the amplitude of the function
w is the frequency rad/s
r is the phase shift
In your case
A = -2
The frequency is
w = (2*pi)/period
period = pi/4
w = 8
r = -pi/2
y = -2* cos 8*(x + pi/2)
An account earns simple interest.
$2000 at 3.5% for 4 years
a. Find the interest earned.
$280
b. Find the balance of the account.
$
Answer:
$2280
Step-by-step explanation:
I see you've already found part a, which is to find the amount of interest earned. The next part is easy, to find the balance of the account after four years, just add the interest you've found back to the principal (the original size of the account or loan). $2000 + $280 equals $2280.
The interest earned on the account is $280. The balance of the account after 4 years is $2280.
Explanation:To find the interest earned on the account, we use the formula for simple interest:
I = PRT
where:
I is the interest P is the principal amount (the initial amount of money) R is the rate of interest T is the time in years
Substituting the given values:
I = $2000 * 3.5/100 * 4 = $280
To find the balance of the account, we add the interest earned to the principal:
Balance = P + I = $2000 + $280 = $2280
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An animal shelter has a total of 275 animals composed of dogs and cats. The number of cats is 5 more than one half of the number of dogs. How many dogs are in the shelter?
Answer: There are 180 dogs in the shelter.
Step-by-step explanation:
Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.
You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:
[tex]d+c=275[/tex]
If the number of cats is 5 more than one half of the number of dogs, you can express it with:
[tex]c=\frac{d}{2}+5[/tex]
Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:
[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]
what are x, y, and z? Simplest radical form.
Answer:
x=5, y=22.36, z=11.18
Step-by-step explanation:
Use mean extremes
10^2=sqrt(20x)
Solving x = 5
for y:
y=sqrt(20(20+5))=22.36
for z:
z=sqrt(5(20+5))=11.18
Express the area of a rectangle with length 4x^34x
3
4, x, start superscript, 3, end superscript and width 555 as a monomial.
The awnser is 20 x 3
Hope this helps!
The area of a rectangle with length 4x^3 and width 5 is expressed as the monomial 20x^3 by multiplying the length and width.
To express the area of a rectangle as a monomial when given the length and width, we simply need to multiply these two dimensions together. In this case, the rectangle has a length of 4x^3 and a width of 5. The area (A) of a rectangle is given by the formula A = length * width.
So, the area of this rectangle can be calculated as:
A = 4x^3 * 5
Now, we multiply the numerical coefficients (4 and 5) and then combine them with the variable part:
A = (4 * 5) x^3
A = 20x^3
This expression, 20x^3, represents the area of the rectangle as a monomial
!!!!!!!!!!!!!!!!!!!!!
ANSWER
A. (x+4)
EXPLANATION
The given binomial is
[tex] {x}^{2} + 12x + 32[/tex]
Split the middle term:
[tex] {x}^{2} + 8x + 4x + 32[/tex]
Factor;
[tex]x(x + 8) + 4( x + 8)[/tex]
Factor further;
[tex](x + 8)(x + 4)[/tex]
Therefore
[tex](x + 4)[/tex]
is a factor.
a different lake currently has an area of 240 square km but is shrinking each year by 6% from the previous year's area. How much area will the lake have after 13 years?
The answer is:
[tex]A(13)=107.37Km^{2}[/tex]
Why?We can calculate the area of the lake after 13 years using the following equation:
[tex]A(t)=A(initial)(1-ShrinkingRate)^{t}[/tex]
Where,
A(t), is the area after t time (years)
A(Initial), is the initial area
Shrinking Rate, is the rafe of shrinking and it's 6% or 0.06.
t, is the time
So, substituting we have:
[tex]A(13)=240(1-0.06)^{13}=240*0.447=107.37Km^{2}[/tex]
So, the are after 13 years will be:
[tex]A(13)=107.37Km^{2}[/tex]
Have a nice day!
What is the simplified expression for 4 to the power of negative 3 multiplied by 3 to the power of 4 multiplied by 4 to the power of 2 whole over 3 to the power of 5 multiplied by 4 to the power of negative 2
To simplify the expression, combine the exponents and evaluate the values to get the simplified expression 1/12.
Explanation:To simplify the expression, we can combine the exponents of the same base. Let's break it down step-by-step:
Combine the exponents of 4: (-3+2) = -1Combine the exponents of 3: (4-5) = -1Combine the exponents of 4: (2-2) = 0So, the simplified expression is 4-1 * 3-1 * 40. Any number raised to the power of 0 is equivalent to 1, so the expression can be further simplified to 4-1 * 3-1 * 1. Finally, we can evaluate the values: 4-1 = 1/4, and 3-1 = 1/3.
Therefore, the simplified expression is (1/4) * (1/3) = 1/12.
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The expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex] simplifies to [tex]\(\frac{4}{3}\).[/tex]
To simplify the expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex], follow these steps:
Combine the exponents for the similar bases using the exponent rules.For the base 4: [tex]\(4^{-3 + 2} \times 4^{2} \times 4^{2}\)[/tex]Combine into: [tex]\(4^{-3 + 2 + (-(-2))} = 4^1\)[/tex]For the base 3: [tex]\(3^4 / 3^5 = 3^{4-5} = 3^{-1}\)[/tex]Simplify the expression: [tex]\(\frac{4}{3}\)[/tex]So the simplified expression is [tex]\(\frac{4}{3}\)[/tex] .
Corrected question:
What is the simplified expression for [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex]
If p(x) = ab^x and r(x) = cd^x, then p(x) * r(x) equals
p(x) * r(x) = ab^x * cd^x
p(x) * r(x) = (a*c)*(b^x*d^x)
p(x)*r(x) = ac(bd)^x
For the last step, I used the rule that (ab)^x = a^x*b^x
Final Answer: ac(bd)^xThe product of two exponential functions p(x) = ab^x and r(x) = cd^x is calculated by following the rules of exponents in mathematics, resulting in p(x) * r(x) = a * c * (bd)^x
Explanation:The student is asking for the product of two exponential functions. If p(x) = ab^x and r(x) = cd^x, their product can be calculated as follows:
Firstly, recognize each function as an exponential. The base of the exponential in p(x) is b, and in r(x) is d. Multiply the two equations together. This can be done because the operations defined for the exponential can be applied when the base of two exponential functions are the same. Substitute p(x) and r(x) back into the equation. We get: p(x) * r(x) = ab^x * cd^x Apply the rules of exponents in math, more specifically the multiplication rule, which states that a^m * a^n = a^(m+n). So, p(x) * r(x) = a * c * (bd)^xLearn more about Multiplication of Exponential Functions here:
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Rewrite this polynomial in terms of its simplest factors using the appropriate method: x3 + x2 − 6x.
Answer: GCF = x
Step-by-step explanation:
x(x^3/x + x^2/x + -6x/x)
x(x^2 + -6)
x(x - 2)(x + 3)
Answer:
x(x + 3)(x - 2)
Step-by-step explanation:
Factor out x from each term
= x(x² + x - 6)
To factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x - term (+ 1)
The factors are + 3 and - 2, since
+ 3 × - 2 = - 6 and + 3 - 2 = + 1, hence
x² + x - 6 = (x + 3)(x - 2)
---------------------------------------
x³ + x² - 6x = x(x + 3)(x - 2) ← in factored form
A bakery used 2 cups of flour to make a full size cake If they wanted to make cake that was 0.4 the size how many cups of flour would they need.
Answer:
0.8 cup(s)
Step-by-step explanation:
2 x 0.4 = 0.8
Answer:
0.8
Step-by-step explanation:
So to get this answer you had to mulyiply the 2 cups of flour by the size you want which is 0.4 . 2(0.4)=0.8
PLEASE. HELP. ME I WILL GIVE BRAINLIEST I NEED TO ANSWER ALL OF THESE AND EXPLAIN THEM
In a week tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45 write and solve an algebraic equation to show how to find the amount that Kayla earns
Answer:
Step-by-step explanation:
Tracey Earns in week= $102.45
Tracy=2x-12.45
102.45=2x-12.45
2x= 102.45+12.45
2x=114.90
x= 114.90/2
x=$57.45
Kayla earns 57.45 dollars
The equation is n = (102.45 + 12.45) x 2.
And Kayla earns $229.8.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
In a week, Tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45.
Let n be the amount Kayla earns.
Then,
Kayla earns,
n = (102.45 + 12.45) x 2
n = $229.8
Therefore, Kayla earns $229.8.
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what is the height of a triangle with area 67.5 square meters and base 9 meters?
Answer:15
Step-by-step explanation:h=2 A/b meaning h=2 67.5/9
Answer:
h = 15 meters
Step-by-step explanation:
The area of a triangle is determined by its height multiplied by its base.
The equation is A = 1/2*bh.
Plugging in the numbers gives us 67.5 = 1/2*9h.
Dividing by 4.5 in both sides gives us that h = 67.5/4.5 = 15 meters.
how do you solve for the indicated variable. 8x+4y=12;y
Answer:
x=1
Step-by-step explanation:
8x+4y=12y
-4y -4y
8x=8y
x=1
Angles A and B are complementary. Angles A has a measure of (3x+30). Angle B has a measure of 36. What is the value of x?
Answer:
2
Step-by-step explanation:
3(2)+30=36
At an elementary school there are two fenced in areas on the playground. The small play area is
1
4
the area of the large play area. The total square footage of the two areas is 2000 ft2. What is the size of the small play area?
A) 200 ft2
B) 400 ft2
C) 800 ft2
D) 1600 ft2
Well, this is just a big guess, but probably the most sense-able, B) 400 ft²
Find the volume of the figure: an oblique cylinder next to a cube.
Answer:
[tex](2,200\pi +8,000)\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the figure is equal to the volume of cube plus the volume of the cylinder
step 1
Find the volume of the cube
The volume of the cube is equal to
[tex]V=b^{3}[/tex]
we have
[tex]b=2(10)=20\ ft[/tex] ----> the length side of the cube is equal to the diameter of the cylinder
so
[tex]V=20^{3}=8,000\ ft^{3}[/tex]
step 2
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=10\ ft[/tex]
[tex]h=42-20=22\ ft[/tex]
substitute
[tex]V=\pi (10)^{2} (22)[/tex]
[tex]V=2,200\pi\ ft^{3}[/tex]
step 3
The volume of the figure is equal to
[tex](2,200\pi +8,000)\ ft^{3}[/tex]
The volume of the figure = volume of oblique cylinder + volume of cube = 2,200π + 8,000 cubic feet.
What is the Volume of an Oblique Cylinder?Volume of oblique cylinder = πr²h [radius of cylinder = r].
The volume of the figure = volume of oblique cylinder + volume of cube = πr²h + s³
Given the following:
s = 2(10) = 20 ftr = 10 fth = 42 - 20 = 22 ftPlug in the values into πr²h + s³:
The volume of the figure = π(10²)(22) + 20³
The volume of the figure = 2,200π + 8,000 cubic feet.
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a line passing through the origin intersects the point -8 -5 what is the slope of the line
To find the slope of a line passing through the origin and a point, use the formula slope = (y2 - y1)/(x2 - x1). For a line passing through origin and the point (-8,-5), the slope is 5/8.
Explanation:The topic at hand revolves around the concept of slope and the algebra of straight lines. The slope is calculated by finding the change in y (vertical axis) over the change in x (horizontal axis). To find the slope of a line passing through the origin and the point (-8,-5), use the formula slope = (y2 - y1)/(x2 - x1).
In this case, the origin is point (0,0) and the given point is (-8,-5). So to find the slope, we substitute these values into the slope formula: slope = (-5 - 0)/(-8 - 0) = 5/8. Therefore, the slope of the line passing through the origin and the point (-8,-5) is 5/8.
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The slope of the line is 5/8.
Explanation:The slope of a line, denoted by m, represents the rate of change between the vertical and horizontal components of two points on the line.
To find the slope of a line passing through the origin and intersecting the point (-8, -5), we can use the slope formula. The slope formula is given by: m = (y2 - y1) / (x2 - x1).
Plugging in the values from the given point gives: m = (-5 - 0) / (-8 - 0)
= -5 / -8
= 5/8.
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50 POINTS PLEASE HELP ME IM RUNNING OUT OF TIME!!!!!!!!!
Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
Rx = 3 T<3,-6> r(90◦, o)
Answer:
Step-by-step explanation:
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the student council at Madison Middle School has five sixth graders 5 7 grade and 5 eight graders. 1 student council member will be selected at random to represent the school at a conference what is the probability that the selected student council member will be in the 7th grade
5/15 or 1/3 would be the correct answer
WILL MARK BRAINLIEST!!!! PLEASE HELP!!!!
X is 3
Refer to picture
Need help with #1 please it’s algebra!
Answer:
145°
Step-by-step explanation:
The angle is 90°+55°=145°
Answer: 145°
Step-by-step explanation:
The angle of straight lines is always 180°, so I took 180 and subtracted 55 from it, and then 90 to get 35. I got 90 because the x and y axis are perpendicular to each other, and the angle between perpendicular lines is always 90. 35° is the angle of the small un marked section to the left of the circles, so to get the angle of the circle-like line, I did 180-35 to get 145°.
Help plz show work plz
Answer: c) 286.5 in²
Step-by-step explanation:
S.A.= 2π r · h
= 2π (7.3/2) · 12.5
= 2π (3.65) (12.5)
= 286.5
puzzle: the quadratic code 4- 3
Answer:
The answer to 4-3 is 1.
Step-by-step explanation:
The quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.
The quadratic equation '4 - 3' is a simple algebraic equation that can be decoded as follows:
Start with the number 4.
Subtract 3 from it.
So, the decoded mathematical expression is:
4 - 3 = 1
The result is 1.
Therefore, the quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.
This demonstrates how to decode and interpret a simple algebraic expression, showing that when you subtract 3 from 4, the result is 1.
It's a basic example of performing arithmetic operations on numbers.
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The probable question may be:
Decode the quadratic expression '4 - 3' to reveal the mathematical expression it represents. Provide the complete mathematical expression that corresponds to the given quadratic code.
HELP PLEASE SOMEONE PLEASE HELP ME?!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:false
Step-by-step explanation: divide each side by 7 you get b ≤ -7. The red line needs to go the other way since it is less than
Answer:
False, it is incorrect
Step-by-step explanation:
7b≤ -49
Divide by 7
7b/7 ≤-49/7
b ≤-7
We have a closed circle at -7 (closed because of the equals)
b is less than so the lines goes to the left
8 If f(x) = x3, which of the following describes the graph of f(x + 2)? A. The graph of f(x + 2) is a horizontal shift of f(x) = x3 two units to the right. B. The graph of f(x + 2) is a vertical shift of f(x) = x3 two units up. C. The graph of f(x + 2) is a horizontal shift of f(x) = x3 two units to the left. D. The graph of f(x + 2) is a vertical shift of f(x) = x3 two units down.
Answer:
C
Step-by-step explanation:
In translating graphs of functions, we can follow 2 rules:
1. The graph of [tex]f(x)+a[/tex] is the graph of [tex]f(x)[/tex] shifted a units UP VERTICALLY and the graph of [tex]f(x)-a[/tex] is the graph of [tex]f(x)[/tex] shifted a units DOWN VERTICALLY.
2. The graph of [tex]f(x+a)[/tex] is the graph of [tex]f(x)[/tex] shifted a units to the LEFT HORIZONTALLY and the graph of [tex]f(x-a)[/tex] is the graph of [tex]f(x)[/tex] shifted a units RIGHT HORIZONTALLY.
If we understand the 2 rules above, we clearly know that f(x+2) will be a horizontal shift to the LEFT, of course, with respect to the function [tex]f(x)=x^3[/tex]. Looking at the answer choices, C is right.
Bill is going to order new jerseys for his baseball team. The jerseys will have the team logo printed on the front.
"Print It" will charge $21.50 each for the jerseys.
Using n for the number of jerseys ordered and c for the total cost in dollars, write an equation to show the total cost of the jerseys from "Print It."
Answer:
Equation: $21.50•n=c
Lines a is perpendicular to line b . Which statement about lines a and b is true ?
Answer:
The product of the slopes of line a and line is -1.
Perpendicular lines a and b intersect at a right angle, or 90 degrees. This is independent of whether they are increasing or decreasing, or their steepness on a graph.
Explanation:The statement about lines a and b that is true when they are perpendicular is that they form a 90-degree angle with each other. The concept of perpendicularity in geometry refers to lines, planes, or surfaces that intersect at a right angle.
Terms like increasing or decreasing line or the steepness of a line do not apply here as they pertain to the slope of the line in the context of a graph, which is distinct from the concept of perpendicularity.
For example, saying line A is a decreasing line while line B is an increasing line, does not describe their perpendicular relationship. Instead, they intersect or meet at a right angle (90 degrees), proving their perpendicular nature.
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If 4b-1=b, then 24b= ?
Answer:
Step-by-step explanation:
4b-1=b
3b-1=0
3b=1
b=1/3
24b=
24(1/3)=
8
Equations are expression separated by an equal sign. The value of 24b if 4b-1 = b is 8
Equation and expressionEquations are expression separated by an equal sign
Given the expresion
4b - 1 = b
Find the value of "b"
4b - b = 1
3b = 1
b = 1/3
Determine the value of 24b
24b = 24(1/3)
24b = 8
Hence the value of 24b if 4b-1 = b is 8
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