Answers
Answer:
see explanation
Step-by-step explanation:
In 13 - 17
Consider the factors of the constant term which sum to give the coefficient of the x- term
13
x² - x - 42 = (x - 7)(x + 6)
15
x² + x - 6 = (x + 3)(x - 2)
17
x² - 27x + 50 = (x - 25)(x - 2)
19
r² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
r² - 25
= r² - 5² = (r - 5)(r + 5)
1. (x+6)(x-7)
2. (x+3)(x-2)
3. (x-2)(x-25)
4. (x-5)(x+5)
I hope it helps
Related Questions
what type of number is the square root of 5
Answers
Answer:
Irrational
Step-by-step explanation:
root of 5 = 2.23606797749978969640917366873127623544061835961152572427089…
This number never ends. Another term for it would be a recurring decimal, but it is not exact. Anyway, the square root of 5 is irrational since it is not defined to stop. Even if it was rounded, it would not be exact.
Hope this Helps.
Find the total surface area of this triangular prism
Answers
Answer :
T.S.A = 200 cm²
What is the inverse of the given function?
Answers
Answer: -7, -1, 5, -5
Step-by-step explanation:
In order to find the inverse, swap the x's and y's and solve for y.
[tex]y=\dfrac{5x+1}{-x+7}\\\\\\\underline{Swap\ the\ x's\ and\ y's}:\\x=\dfrac{5y+1}{-y+7}\\\\\\\underline{\text{Multiply both sides by -y+1 to clear the denominator}}:\\x(-y+7)=5y+1\\-xy+7x=5y+1\\\\\\\underline{\text{Add xy and subtract 1 from both sides}}:\\7x-1=xy+5y\\\\\\\underline{\text{Factor out the y from the right side}}:\\7x-1=y(x+5)\\\\\\\underline{\text{Divide x+5 from both sides}}:\\\dfrac{7x-1}{x+5}=y[/tex]
Since the boxes you need to fill in show -x in the denominator, multiply the equation by -1/-1:
[tex]y=\dfrac{-1}{-1}\bigg(\dfrac{7x+1}{x+5}\bigg)\\\\\\\large\boxed{f^{-1}(x)=\dfrac{-7x-1}{-x-5}\qquad for\ x \neq -5}[/tex]
can someone help me?
Answers
I think the outlier is 9
The mean is 3.75
The range is 8
Explanation:
I’m not too sure if these are correct but the mean is the sum of everything divided by the number of numbers there are or in this case 20 and the range is found by subtracting the highest number with the lowest number or in this case 9-1 which is 8
A fair dice and unbaised coin are tossed once.what is the probability of obtaining 3 and a tail
Answers
Answer:
1/4 & 1/2
Step-by-step explanation:
4 sides to the dice
2 sides to coin
Answer:1/12
Step-by-step explanation:
The probability of getting a three on a fair die is 1/6
The probability of getting tails on an unbiased coin is 1/2
Then the probability of getting a three on a fair die and tails on an unbiased coin is 1/6 x1/2=1/12
Two congruent circles centered at points A and B each pass through the other circle's
center. The line containing both A and B is extended to intersect the circles at
points C and D. The circles intersect at two points, one of which is E. What is the degree
measure of angle CED?
Answers
Answer:
60°
Step-by-step explanation:
We know triangle ABC is an equilateral triangle, since all of its side measures are the radii of the circles. That means angle BAC is 60°. Likewise, angle BAD is 60°, so arc CD is 120°.
The measure of inscribed angle CED is half the measure of the intercepted arc CD, so is ...
∠CED = 120°/2
∠CED = 60°
PLZZZZZZZZZ HLPPPPPPPP MEEEEEEEEEEE
which of the following is made up of one base and a vertex not in the same plane as the base? check all that apply
a. cone
b. prism
c. cylinder
d. pyramid
Answers
Answer:
a. cone. Since it's the only shape with one base and a vertex not on the same plane
need helpppp with this one
Answers
Answer:
Step-by-step explanation:
brodha,,,
ur answer is
c)) 2sinxcosx
The vertex form of a quadratic function is f(x) = a(x - 1)2 + k. What is the vertex of each function? Match the function
rule with the coordinates of its vertex.
f(x) = 9(x + 5)2 - 6
(6,9)
f(x) = 6(x + 9)2 - 5
(5,6)
f(x) = 9(x - 5)2 + 6
(-9.-5)
f(x) = 6(x - 5)2 - 9
U (-5,-6)
(5.-9)
f(x) = 5(x - 6) +9
Done
Intro
Answers
Answer:
f(x) = 9(x + 5)2 - 6 (-5,-6)
f(x) = 6(x + 9)2 - 5 (-9,-5)
f(x) = 9(x - 5)2 + 6 (5,6)
f(x) = 6(x - 5)2 - 9. (5,-9)
f(x) = 5(x - 6) +9. (6,9)
Step-by-step explanation:
To find the vertex: for the x-coordinate, take the "h" in the parentheses (x + h) and reverse its sign. For the y-coordinate, use the "k" term as-is.
The coordinates of the vertex of the equations are:
f(x) = 9(x + 5)^2 - 6; Vertex = (-5,-6)f(x) = 6(x + 9)^2 - 5; Vertex = (-9,-5)f(x) = 9(x - 5)2 + 6; Vertex =(5,6)f(x) = 6(x - 5)^2 - 9; Vertex = (5,-9)f(x) = 5(x - 6) +9; Vertex = (6,9)How to determine the vertex of the quadratic functions?The vertex form of the quadratic function is given as:
y = a(x -h)^2 + k
Where:
Vertex = (h,k)
Using the above highlight, the coordinates of the vertex of the equations would be:
f(x) = 9(x + 5)^2 - 6
Vertex = (-5,-6)
f(x) = 6(x + 9)^2 - 5
Vertex = (-9,-5)
f(x) = 9(x - 5)2 + 6
Vertex =(5,6)
f(x) = 6(x - 5)^2 - 9
Vertex = (5,-9)
f(x) = 5(x - 6) +9
Vertex = (6,9)
Read more about vertex quadratic functions at:
https://brainly.com/question/1480401
A survey asks teachers and students whether they would like the new school mascot to be a shark or a moose. This table shows the results. Which statement is true? A. There is no difference between the preferences of students and teachers. B. "Shark" is more popular with students, but "moose" is more popular with teachers. C. "Moose" is more popular with students, but "shark" is more popular with teachers. D. "Moose" is equally popular with students and teachers.
Answers
Answer:
The correct statement is (D).
Step-by-step explanation:
Compute the probabilities for the data provided:
Probability students preferring sharks:
[tex]P(\text{Students preferring sharks})=\frac{90}{95}=0.947[/tex]
Probability teachers preferring sharks:
[tex]P(\text{Teachers preferring sharks})=\frac{5}{95}=0.053[/tex]
Probability students preferring moose:
[tex]P(\text{Students preferring moose})=\frac{10}{20}=0.50[/tex]
Probability teachers preferring moose:
[tex]P(\text{Teachers preferring moose})=\frac{10}{20}=0.50[/tex]
From the above computations it can be concluded that:
Shark is more popular with students.Moose is equally popular with students and teachers.Thus, the correct statement is (D).
Answer: Just did it and the answer is “Shark”...
Step-by-step explanation:
Here is a set of data 2.4 1.6 3.2 0.3 1.5 a. calculate the mean b. each new piece of data is now doubled, calculate the new mean c. each new piece of data is now doubled, calculate the new mean
Answers
Answer:
a) mean=1,8 b) mean=3.6 c) mean=7.2
Step-by-step explanation:
a) 2.4 +1.6+ 3.2+ 0.3+ 1.5=9
9/5=1.8
b) 4.8+3.2+6.4+0.6+3=18
18/5=3.6
c)9.6+6.4+12.8+1.2+6=36
36/5=7.2
Answer:mean is 1.8
Step-by-step explanation:
Add all up divide by 5
In the figure below, if m∠2=(18x+6)° and m∠3=(21x+18)° then m∠2= ____ .
Answers
Answer:
m∠2 = 78°
Step-by-step explanation:
Two lines 'l' and 'm' are parallel and another line 'n' is a transverse.
Since ∠2 and ∠3 are the consecutive interior angles,
Therefore, sum of these angles will be 180°.
m∠2 + m∠3 = 180°
(18x + 6)° + (21x + 18)° = 180°
(18x + 21x) + ( 6 + 18) = 180
39x + 24 = 180
39x = 180 - 24
39x = 156
x = [tex]\frac{156}{39}[/tex]
x = 4
Since, m∠2 = (18x + 6)°
By substituting the value of x = 4,
m∠2 = (18×4) + 6
= 72 + 6
= 78°
Therefore, measure of angle 2 is 78°.
Please help...Simplify 10^-8.
Answers
The exponent numerical expression 10⁻⁸ in the simplified form will be 1/10⁸.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The exponent numerical expression is given below.
⇒ 10⁻⁸
We know that a⁻ⁿ = 1/aⁿ. Then the expression is written as,
⇒ 10⁻⁸
⇒ 1 / 10⁸
The exponent numerical expression 10⁻⁸ in the simplified form will be 1/10⁸.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
Given the following number line, what number could be A if XY - ZA?
X
Y Z
-6
A. -5
B. -1
C. 5
D. 6
Answers
Answer:
C. 5
Step-by-step explanation:
XY= -1-(-5)= 4
ZA= A-1= 4 ⇒ A=1+4= 5
A=5
If you are examining a triangle with given measurements for one leg and the hypotenuse, how will you determine the measure of the unknown leg? Explain.
Answers
Answer:
It depends
Step-by-step explanation:
If you are given a right triangle, you use Pythagorean Theorem: a² + b² = c²
If you are given an angle but its not a right triangle, you can use either Law of Sines: [tex]\frac{A}{sin(a)} = \frac{B}{sin(B)} = \frac{C}{sin(C)}[/tex] or Law of Cosines: [tex]c^2 = a^2 + b^2 -2abcosC[/tex].
Answer:
Sample Response: Create and label a diagram. Then, using the Pythagorean theorem, substitute the values for corresponding variables into the theorem and solve by applying inverse operations.
Step-by-step explanation:
Edge 2021
ABCD ~ QRST
Find the missing side length, n.
B.
C
8
R
n
S
А
D
T
12.
9
n = [?]
Answers
Answer:
n = 6
Step-by-step explanation:
The left side is 8/12 = 2/3 the length of the bottom, so ...
n = (2/3)(9)
n = 6
What is the relationship between angles A and B? They are congruent. They are complementary. They are supplementary. There is no relationship between them.
Answers
An image is attached to complete the question.
Answer:
The correct option is B
They are complementary.
Step-by-step explanation:
Angle A, and angle B in the attached image sum up to ninety degrees.
Two angles are said to be complementary if they add up to make ninety degrees. This characteristic makes us conclude that the two given angles, which are 59°, and 31°, have the sum: 59° + 31° = 90°, and are therefore, complementary.
The correct option is B.
If the attachment is not what completes your question, then knowing the meanings of supplementary angles, and congruent angles, is enough to help decide what option to choose.
Supplementary angles are angles that sum up to make one hundred and eighty degrees. (180°)
Congruent angles are angles that have the same shape and size.
Answer:
They are complementary.
Step-by-step explanation:
See attachment for the missing figure.
As in the figure, its the right angle triangle.
∠A+∠B=90° ( by complementary angles )
Lets verify now,
59°+31°=90° is correct
Angle A and Angle B are complementary angles
Can I get some help with this?
Answers
Answer:
x = 37 degrees
Step-by-step explanation:
Let the unknown angle be x
So,
Tan x = [tex]\frac{opposite}{Adjacent}[/tex]
Opposite = 3, Adjacent = 4
Tan x = [tex]\frac{3}{4}[/tex]
Tan x = 0.75
x = [tex]tan ^{-1} 0.75[/tex]
x = 37 degrees
PLZ HELP ME ☻ [tex]\[\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 2, \quad \frac{yz}{y + z} = 3\][/tex] Solve system of equations
Answers
Answer:
[tex]x=\frac{12}{7} \\y=\frac{12}{5} \\z=-12[/tex]
Step-by-step explanation:
Let's re-write the equations in order to get the variables as separated in independent terms as possible \:
First equation:
[tex]\frac{xy}{x+y} =1\\xy=x+y\\1=\frac{x+y}{xy} \\1=\frac{1}{y} +\frac{1}{x}[/tex]
Second equation:
[tex]\frac{xz}{x+z} =2\\xz=2\,(x+z)\\\frac{1}{2} =\frac{x+z}{xz} \\\frac{1}{2} =\frac{1}{z} +\frac{1}{x}[/tex]
Third equation:
[tex]\frac{yz}{y+z} =3\\yz=3\,(y+z)\\\frac{1}{3} =\frac{y+z}{yz} \\\frac{1}{3}=\frac{1}{z} +\frac{1}{y}[/tex]
Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":
[tex]1=\frac{1}{y} +\frac{1}{x} \\-\\\frac{1}{3} =\frac{1}{z} +\frac{1}{y}\\\frac{2}{3} =\frac{1}{x} -\frac{1}{z}[/tex]
Combine this last expression term by term with the reduced equation 2, and solve for "x" :
[tex]\frac{2}{3} =\frac{1}{x} -\frac{1}{z} \\+\\\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\ \\\frac{7}{6} =\frac{2}{x}\\ \\x=\frac{12}{7}[/tex]
Now we use this value for "x" back in equation 1 to solve for "y":
[tex]1=\frac{1}{y} +\frac{1}{x} \\1=\frac{1}{y} +\frac{7}{12}\\1-\frac{7}{12}=\frac{1}{y} \\ \\\frac{1}{y} =\frac{5}{12} \\y=\frac{12}{5}[/tex]
And finally we solve for the third unknown "z":
[tex]\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\\\\frac{1}{2} =\frac{1}{z} +\frac{7}{12} \\\\\frac{1}{z} =\frac{1}{2}-\frac{7}{12} \\\\\frac{1}{z} =-\frac{1}{12}\\z=-12[/tex]
Rápido y fácil, trigonometría. Urgente porfavor
Answers
Answer:
The angle [tex]\theta[/tex] measures approximately [tex]28.81^o[/tex]
Step-by-step explanation:
Since this problem involves the finding of an angle in a right angle triangle for which we know the opposite side and the adjacent side, the trigonometric function that relates them is the tangent:
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Then, for our case we get a starting equation that reads:
[tex]tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{7.7}{14}[/tex]
and for which we need to solve for [tex]\theta[/tex]. Then we use the arctangent function to get the final answer:
[tex]tan(\theta)=\frac{7.7}{14} \\\theta=arctan(\frac{7.7}{14})\\\theta= 28.81^o[/tex]
Antoine has a solid, spherical ball of clay with a radius of 5 cm. If he shapes it into a solid, cone–shaped figure with a radius of 2 cm, what will the height of the cone be?
Answers
Answer:
Step-by-step explanation:
We'll call height h.
The equations of a cone and sphere are:
Cones: 1/3 * base area * h
Spheres: 4/3 π * r³
The base area of a cone would be the area of a circle equation:
π * r² = π * 2² = 4π.
Because you're converting from sphere to cone, you would set their equations equal to each other.
1/3 * 4π * h = 4/3 π * 5³
Next, isolate h.
h = (4/3 π * 5³)/(1/3 * 4π)
h = 125
Hope this helps!
Answer:125
Step-by-step explanation:
Mustafa’s soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit? 5n – 300 = 1,500 5n + 300 = 1,500 5n – 200 + 100n = 1,500 5n – 100 – 200n = 1,500
Answers
Answer:
(a) 5n -300 = 1500
Step-by-step explanation:
Profit is the difference between revenue and cost.
RevenueThe revenue the fundraiser will generate apparently comes only from ticket sales. At $5 each, the sale of n tickets will result in revenue of 5n dollars.
CostThe cost the team must pay will be the sum of the cost of the DJ and the cost of the decorations. The team's total cost will be ...
200 +100 = 300
ProfitThe profit is the difference between revenue and cost. The team wants that difference to be $1500, so an appropriate equation for the number of tickets to sell is ...
revenue - cost = profit
5n -300 = 1500
Answer:
5n - 300 = 1,500
Step-by-step explanation:
just got it right on edge
Circle O has a circumference of approximately 250π ft. Circle O with diameter d is shown. What is the approximate length of the diameter, d? 40 ft 80 ft 125 ft 250 ft
Answers
Answer:
250 ft
Step-by-step explanation:
circumference of circle 'C' is defined as
C = 2πr
250π = 2πr
r = 250π/2π
r= 125
d = 2r = 2×125 = 250 .
diameter of the given circle is 250 ft
The diameter of the circle is 250ft
Data;
Circumference = 250πdiameter = dCircumference of a CircleThe formula of circumference of a circle is given as
[tex]c = 2\pi r[/tex]
Let's substitute the values in here and solve
[tex]c = 2 \pi r\\250\pi = 2 \pi r\\r = 125ft[/tex]
The length of the radius is 125ft
But the length of diameter of a circle is twice the length of the radius
[tex]d = 2r\\d = 2 * 125\\d = 250ft[/tex]
The diameter of the circle is 250ft
Learn more on circumference of a circle here;
https://brainly.com/question/14283575
The temperature at 3:00pm was 15 degrees. At midnight the temperature was -2 degrees. What is the difference between those two temperatures
Answers
Step-by-step explanation:
(-2)-(+15)=(-17)
the difference between those two temperature s is (-17)
A movie was 3 1/2 hours long if Lilly turned of the movie off 1/4 of the way through how much time did she spend watching
Answers
Answer:
7/8 of an hour
Step-by-step explanation:
Answer:
duration of movie = 3 hours 30 minutes
= 180 + 30
= 210 minutes
Lily turned of 1/4 of the way
time she spend watching
= 1/4 × 210
= 52.5 minutes
Combine the following expressions.
Answers
Answer:
second option
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals
[tex]\sqrt{27x^{3} }[/tex]
= [tex]\sqrt{9(3)x^2.x}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{x^2}[/tex] × [tex]\sqrt{x}[/tex]
= 3 × [tex]\sqrt{3}[/tex] × x × [tex]\sqrt{x}[/tex]
= 3x[tex]\sqrt{3x}[/tex]
-------------------------------
[tex]\sqrt{12x^{3} }[/tex]
= [tex]\sqrt{4(3)x^2.x}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{x^2}[/tex] × [tex]\sqrt{x}[/tex]
= 2 × [tex]\sqrt{3}[/tex] × x × [tex]\sqrt{x}[/tex]
= 2x[tex]\sqrt{3x}[/tex]
---------------------------------------
Thus
3 × 3x[tex]\sqrt{3x}[/tex] - 2 × 2x[tex]\sqrt{3x}[/tex]
= 9x[tex]\sqrt{3x}[/tex] - 4x[tex]\sqrt{3x}[/tex]
= 5x[tex]\sqrt{3x}[/tex]
What can you about the value of a if the equation y=ax^2-8 has no solutions? Plz explain!
Answers
Answer:
If a is negative or zero there are no real solutions
Step-by-step explanation:
y=ax^2-8
Set equal to zero to find the solution
0 =ax^2-8
Add 8 to each side
8 = ax^2
Divide by a a cannot be zero or we cannot divide by it
8/a = x^2
Take the square root of each side
sqrt(8/a) = sqrt(x^2)
We need 8/a to be positive for it to have real solutions
That means a has to be positive
If a is negative or zero there are no real solutions
Chiko bought 75 shares of stock at $19.58 per share. He received dividends of $73.42 during the year. At the end of the year, his stock was valued at $22.14. (Do not use commas, percentage signs or dollar signs in your answers. Round percentage answers to the nearest tenth) What was his purchase price?
Answers
Answer: 1,468.5
Step-by-step explanation:
Hi, to answer this question we simply have to multiply the price of each share of stock ($19.58) by the number of shares of stock bought (75 ).
Mathematically speaking:
Price per share x number of shares = 19.58 x 75 = $1,468.5
His purchase price was 1,468.5
Feel free to ask for more if needed or if you did not understand something.
all of the following are acceptable ways to name the angle shown except?
Answers
Step-by-step explanation:
where is figure man
.....
Answer:
The answer is: ∠ R
A bag contains Red, Green and Yellow balls. A ball is taken at random from the bag. The probability that it is Red is 0.35 and the probability that it is Green is 0.4 Find the probability that ball selected is: one is yellow other is not red plz answer urgent
Answers
Answer:
0.25
0.65
Step-by-step explanation:
Looking at the question, we can see that we were not given the probability of selecting a yellow ball.
Hence the probability of this is;
1-0.35-0.4 = 1-0.75 = 0.25
The probability that the selected ball is yellow is 0.25
The probability that it is not red means it is either yellow or green
What this means is that we add the probability of yellow to the probability of green
= 0.25 + 0.4 = 0.65