Factor the following polynomial. Check your answers using FOIL.
x² + 3x - 70
O(x+10) (x-7)
(x - 1)(x-9)
(x - 3)(x - 70)
(x - 10) (x + 7)
Answers
This matches the original polynomial, so we know our factoring is correct. Therefore, the answer is:
\(x^2 + 3x - 70=(x-7)(x+10)\).
What is factor?In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. In other words, a factor is a quantity that can be multiplied by another quantity to produce a given result.
For example, if we consider the number 12, its factors are 1, 2, 3, 4, 6, and 12 because they can be multiplied together to give 12.
In algebra, the term factor often refers to an algebraic expression that can be written as a product of simpler expressions. For example, the expression x^2 - 4 can be factored as (x - 2) (x + 2), which means that it can be written as the product of the two factors (x - 2) and (x + 2).
To factor the polynomial x² + 3x - 70, we need to find two factors that multiply to give -70 and add to give 3.
One way to approach this is to list all the factor pairs of -70 and look for a pair that adds up to 3:
\(-1 * 70 = -70\)
\(-2 * 35 = -70\)
\(-5 * 14 = -70\)
\(1 *-70 = -69\)
\(2 * -35 = -70\)
\(5 * -14 = -70\)
From this list, we see that -7 and 10 are the only factor pair that add up to 3. So, we can write:
\(x^2 + 3x - 70 = (x - 7)(x + 10)\)
To check our answer, we can use FOIL to expand the product of (x - 7) (x + 10):
\((x - 7)(x + 10) = x(x) + x(10) - 7(x) - 7(10)\)
\(= x^2+ 10x - 7x - 70\)
\(= x^2 + 3x - 70\)
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Related Questions
Find the horizontal and vertical asymptotes of the curve. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
y =
7x2 + x − 1/
x2 + x − 20
A) horizontal y=
B) vertical x=
Answers
A) horizontal asymptote: y = 7 B) vertical asymptote: x = -4, 5 is the required answers for horizontal and vertical asymptotes of the curve.
The horizontal asymptote of a curve is a horizontal line that the curve approaches as x approaches infinity or negative infinity. The vertical asymptote of a curve is a vertical line that the curve approaches but never crosses as x approaches a certain value. In this case, the horizontal asymptote is found by letting x approach infinity in the fraction and observing what the value of y approaches. In the limit as x approaches infinity, the x^2 term dominates and thus y approaches 7, which is the horizontal asymptote. To find the vertical asymptote, we find the values of x where the denominator equals 0 and the numerator is not equal to 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5. Thus, the vertical asymptotes are x = -4 and x = 5. To find the vertical asymptotes, we look for the values of x where the denominator of the function equals 0 and the numerator does not equal 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5, which means that x = -4 and x = 5 are the vertical asymptotes of the function. These values of x represent the values at which the function is undefined, and as x approaches these values from either side, the value of the function approaches positive or negative infinity.
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Classify the polynomial by its degree: 4m³-9x² + 10
A) 0
B) 1st
C) 2nd
D) 3rd
E) 4th
Answers
From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is _____. a. 2 b. greater than 2 c. 3 d. less than 2
Answers
Answer:
a. 2
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
Standard deviation is known to be 14.
This means that \(\sigma = 14\)
Sample of 49
This means that \(n = 49\)
The standard error of the mean is
\(s = \frac{\sigma}{\sqrt{n}} = \frac{14}{\sqrt{49}} = \frac{14}{7} = 2\)
So the correct answer is given by option a.
What is a quadrilateral
Answers
Answer: A quadrilateral is a four-sided figure.
EX: a square, a rectangle, a trapezoid, or a rhombus.
A closed plane figure or figure formed by four nonintersecting line segments which are not on the same line and connected end to end is called quadrilateral.
Look at the tape diagram below for the number of boys and the number of girls in a school. Find total number of students in the school.
Answers
Solve for q in terms of r, s, and t
Answers
Answer:
\( q = - \: \frac{s}{ tr} \)
I hope I helped you^_^
Answer:
\(s = - trq \\ \boxed{ q = - \frac{s}{tr} }\)
q = -s/tr is the right answer.Ricardo has a bag of mixed fruit snacks. In the bag, there are 12 cherry fruit snacks and 18 strawberry fruit snacks. What is the ratio of strawberry to cherry?
A.
3:2
B.
1:12
C.
2:3
Answers
Answer:
18:12 = A. 3:2
Step-by-step explanation:
Because they are equivalent ratios, they are the same, it also said ratio of strawberries to cherries so I put it in that order.
Can I please have branliest
okay thank you have a good day
What is sin 30°?
60°
2
2
1
90°
30°
3
Answers
According to the property of cofunctions, \($\sin 30^{\circ}$\) exists equivalent to
\($\cos 60^{\circ} \cdot \sin 30^{\circ}=1 / 2$\).
What is cofunction?A trigonometric function whose value for the complement of an angle exists equivalent to the value of a given trigonometric function of the angle itself the sine exists the cofunction of the cosine.
According to the property of cofunctions, \($\sin 30^{\circ}$\) exists equivalent to
\($\cos 60^{\circ} \cdot \sin 30^{\circ}=1 / 2$\).
Therefore, the correct answer is option B. 1/2.
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Guadalupe can do a job in 15 hours. If she works with lan, together they can get the job done in 10 hours. How long would it take lan to do the job alone?
Answers
Answer:
30 hours
Step-by-step explanation:
The equation we use is 1/15 + 1/x = 1/10. X being the amount of time it takes Ian alone. X works out to 30 hours which is the answer
The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (according to GolfWeek). Assume that the driving distance for these golfers is uniformly distributed over this interval. a. Give a mathematical expression for the probability density function of driving distance. b. What is the probability the driving distance for one of these golfers is less than 290 yards
Answers
Answer:
a) \(f(x) = \frac{1}{25.9}\)
b) 0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
\(P(X < x) = \frac{x - a}{b - a}\)
The probability of finding a value between c and d is:
\(P(c \leq X \leq d) = \frac{d - c}{b - a}\)
The probability of finding a value above x is:
\(P(X > x) = \frac{b - x}{b - a}\)
The probability density function of the uniform distribution is:
\(f(x) = \frac{1}{b-a}\)
The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards.
This means that \(a = 284.7, b = 310.6\).
a. Give a mathematical expression for the probability density function of driving distance.
\(f(x) = \frac{1}{b-a} = \frac{1}{310.6-284.7} = \frac{1}{25.9}\)
b. What is the probability the driving distance for one of these golfers is less than 290 yards?
\(P(X < 290) = \frac{290 - 284.7}{310.6-284.7} = 0.2046\)
0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards
A zoo is designing a giant bird cage consisting of a cylinder of radius rr feet and height hh feet with a hemisphere on top (no bottom). The material for the hemisphere costs 2020 per square foot and the material for the cylindrical sides costs 1010 per square foot; the zoo has a budget of 45004500. Find the values of rr and hh giving the birds the greatest space inside assuming the zoo stays within its budget. Note: surface of a cylinder's side 2πrh2πrh, surface of a sphere 4πr24πr2, volume of a cylinder's side πr2hπr2h, volume of a sphere 43πr343πr3
Answers
Answer:
r = 42,32 ft
h = 84.8 ft
Step-by-step explanation:
We are going to apply Lagrange multipliers method
The greatest space means maximum volume
V(cage) = Vol. of the cylinder + volume of the hemisphere
V(cylinder ) = π*r²*h
V(sphere) = (4/3)*π*r² ⇒ V(hemisphere) = (2/3)*π*r³
V(cage) = π*r²*h + (2/3)*π*r³
Associated costs:
Costs = cost of cylinder + cost of hemisphere
Area of the cylinder = Lateral area ( no bottom no top)
Area of the cylinder = 2*π*r*h
Area of hemisphere = 2*π*r²
A(r,h) = 2*π*r*h + 2*π*r²
C(r , h ) = 10* 2*π*r*h + 20* 2*π*r² C(r , h ) = 20*π*r*h + 40*π*r²
4500 = 20*π*r*h + 40*π*r²
20*π*r*h + 40*π*r² - 4500 = 0 20*π*r*h + 40*π*r² - 4500 = g(r,h)
V(cage) = π*r²*h + (2/3)*π*r³
δV/δr = 2*r*π*h + 2*π*r² δg(r,h)/δr = 20*π*h + 80*π*r
δV/δh = π*r² δg(r,h)/δh = 20*π*r
δV/δr = λ* δg(r,h)/δr
2*r*π*h + 2*π*r² = λ* 20*π*h + 80*π*r
2*r*π* ( h + r ) = 20*π* λ* ( h + 4*r)
r* ( h + r ) = 10*λ* ( h + 4*r) (1)
δV/δh = λ* δg(r,h)/δh
π*r² = 20*λ*π*r r = 20*λ (2)
20*π*r*h + 40*π*r² - 4500 = 0 (3)
We need to sole the system of equation 1 ; 2 ; 3
r = 20*λ plugging that value in equation 1
20*λ ( h + 20*λ ) = 10*λ* ( h + 4*r)
2( h + 20*λ ) = ( h + 4*20*λ)
2*h + 40*λ = h + 80*λ
h = 40*λ
20*π*r*h + 40*π*r² - 4500 = 0
20*π*20*λ*40*λ + 40*π+400λ² - 4500 = 0
16000*π*λ² + 16000*π*λ² = 4500
32000*π*λ² = 4500
320*π*λ² = 4500
λ² = 4500/1004,8 λ² = 4.48 λ = 2.12
Then
r = 20* λ r = 42,32 ft
h = 40* λ h = 84.8 ft
How many solutions does x2 - 2x + 9 = 0 have and what type are they? Do NOT find the
actual solutions.
Answers
Answer:
3
Step-by-step explanation:
3. There were 425 people at the Lincoln
County High School football game last
week. This week, 357 people attended
the game. What was the percent decrease
in attendance?
Answers
Answer:
there is a 16% percent decrease
Step-by-step explanation:
percent of change = (new value - original value) ÷ original value
= (357 - 425) / 425
= -68/425
= -0.16
there is a 16% percent decrease
Select the two equations that will help you to solve this problem:
The combined average weight of an okapi and a llama is 450 kilograms.
3 llamas, on average, weigh 190 kilograms more than an average okapi.
You want to find the average weight of each type of animal.
Answers
Answer:
An average Ilama weighs 160 kilograms and an average okapi weighs 290 kilograms.
Step-by-step explanation:
Let,
x be the average weight of a Ilamas
y be the average weight of an okapi
According to given statement;
x + y = 450 Eqn 1
3x = y + 190 Eqn 2
From Eqn 2
y = 3x - 190 Eqn 3
Putting this value of y in Eqn 1
x + (3x-190) = 450
x + 3x - 190 = 450
4x = 450 + 190
4x = 640
Dividing both sides by 4
\(\frac{4x}{4}=\frac{640}{4}\\x=160\\\)
Putting x = 160 in Eqn 3
y = 3(160) - 190
y = 480 - 190
y = 290
Hence,
An average Ilama weighs 160 kilograms and an average okapi weighs 290 kilograms.
The yearbook club had a meeting. The club has 24 people, and one-half of the club showed up for the meeting. How many people went to the meeting?
Answers
Salim had a flock of 300 chickens 15% of which are infected with a virus he plans on taking a SRS of 7 chickens to test for the virus.
Answers
Answer:0.011
Step-by-step explanation:
The probability for exact 4 chickens being infected out of the 7 is ⁷C₄(0.15)⁴(0.85)³. The correct option is (A).
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Given that,
The probability of the infected chicken is 15%.
Which can be written as,
P(infected) = 15%
= 15/100
= 0.15
Then, the probability of not getting infected chicken is,
P(not infected) = 1 - 0.15
= 0.85
The total number of chicken for test = 7.
Now, in order to find the probability of the exact 4 infected chickens, binomial distribution can be used as.
The general expression for binomial distribution is ⁿCₓpˣqⁿ⁻ˣ.
For the given case p = P(infected) and q = P(not infected), n = 7 and x = 4.
Thus, the probability is given as,
P(Exact 4 are infected) = ⁷C₄(0.15)⁴(0.85)³
Hence, the probability that exactly 4 of the 7 chickens sampled have the virus is ⁷C₄(0.15)⁴(0.85)³.
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The complete question is given as, "Salim has flock of 300 chickens, 15% of which are infected with virus: He plans on taking an SRS of 7 chickens to test for the virus_ Which of the following would find the probability that exactly 4 of the 7 chickens sampled have the virus? Choose answer: 1(0.15) '(0.85)? (0.15)*(0.85)4 300 ` (0.15)'(0.85)3 (0.15)3(0.85)4 (0.15)4(0.85)".
can someone help with this please i am bad at math
Answers
Answer:
12 dollars
Step-by-step explanation:
we know 25 shirts cost 300 dollar
so if 25 shirts --> 300
1 shirt --> 300/25
1 shirt = 12 dollars
Answer:
12 is the answer :l
Step-by-step explanation:
What is the range of the data set? *
2 points
53, 39, 123, 59, 25, 79, 88
84
53
123
98
25
Answers
Answer:
25
Step-by-step explanation:
range = largest value - smallest value (123-25)
a gift shop sells walnuts in three fourth pond bags . Ann wants to buy enough to have 4 pounds of walnuts. How many 3/4 pound bags will she need to buy?
Answers
Answer: 4 pounds is equal to 16 four-ounce (1/4 pound) increments.
To find the number of 3/4 pound bags Ann needs to buy, we can convert 16 four-ounce increments to three-fourth pound increments:
16 four-ounce increments = 16 x 4 = 64 ounces
64 ounces = 64/16 = 40 three-fourth pound increments
Therefore, Ann will need to buy 40 bags of walnuts, each weighing 3/4 of a pound.
Step-by-step explanation:
Please help me with this
Answers
The volume of rectangular prism is 90 unit³.
We can consider the 1 block = 1 unit.
Length of prism = 5 unit
width of prism = 6 unit
Height of prism = 3 unit
So, Volume of rectangular prism
= l w h
= 5 x 6 x 3
= 90 unit³
Thus, the volume of rectangular prism is 90 unit³.
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easy algebra! Just need help with this one
Answers
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? -3/4m-1/2=2+1/4m
Answers
Answer:
* 2/3 / formula then multiply the numbers then you get the answer
Each of the following describes a variable expression.
1. The area of a rectangle that is (x + 2) units long and 4 units wide.
4(x + 2)
2. The perimeter of a rectangle that is (x + 3) units long and (x + 1) units wide.
2(x + 3) + 2(x + 1)
3.
The volume of a rectangular prism that is 2 units long, 1 unit wide, and (2x + 4) units high.
2(1)(2x + 4)
which two are equivalent
Answers
Both equations are equal since they both reduce to 4x + 8 as the surface area of a rectangle with dimensions of (x + 2) units and (4 units).
what is expressions ?An expression in mathematics is made up of various elements, including numbers, variables, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can represent a single number or a group of numbers, and they can be simple or sophisticated. For instance, the phrase 3x + 2 denotes a linear equation with the variable x. The expression (x + 3)(x - 4) denotes the sum of two binomials.
given
First and third expressions are interchangeable.
the surface area of a rectangle with dimensions of (x + 2) units and (4 units).
Area is equal to length times breadth.
Area = 4x + 8x + (x + 2) x 4a rectangular prism with dimensions of 2 units long, 1 units broad, and (2x + 4) units high has a volume of 4 units.
Volume is calculated using the formula LWH.
Volume equals 2 x 1 x ((2x + 4))
Volume equals 2(2x + 4)
Volume = 4 times Plus 8
Both equations are equal since they both reduce to 4x + 8 as the surface area of a rectangle with dimensions of (x + 2) units and (4 units).
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A bike has a maximum height of 25 inches which inequality correctly represents this height?
Answers
Bike is less than or equal to 25”.
Explanation
A bike has a maximum height of 25” which means it can be less than 25” or equal to 25”.
The sign to use is ≤ less than or equal to
the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes
Answers
The standard deviation of the response time is 1.53 minutes.
What is the standard deviation of the response time?To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.
Z-score = z = (x - μ) / σ
For the lower bound of 10 minutes:
z = (10 - 13) / σ
For the upper bound of 16 minutes:
z = (16 - 13) / σ
As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.
Using z-scores, we set up equations:
(10 - 13) / σ = -1.96
(16 - 13) / σ = 1.96
Solving the first equation:
-3 / σ = -1.96
σ = -3 / -1.96
Solving the second equation:
3 / σ = 1.96
σ = 3 / 1.96
Dividing both sides by 1.96:
-3 / 1.96 = σ
1.53 = σ
Full question:
The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.
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At a hair salon, each womab is charged $15 for a cut and 35$ for a color. how much money will the salon earn if w women grt a cut and a color?
Answers
=$50
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
The salon earn if the women get a cut and a colour is $50.
What is Total amount?There are many meanings of total, but they all have something to do with completeness. A total is a whole or complete amount, and "to total" is to add numbers or to destroy something.
In math, you total numbers by adding them: the result is the total. If you add 8 and 8, the total is 16. If a car is totalled in an accident, it has been completely destroyed. A total defeat is a complete and utter defeat with no chance of recovering. The total resources of a company are all its resources, everything it has.
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
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The following are distances (in miles) traveled to the workplace by 17 employees of a certain brokerage firm.
13, 3, 16, 18, 10, 32, 9, 31, 14, 27, 1, 11, 18, 5, 6, 15, 24
Send data to calculator
Find 30th and 75th percentiles for these distances.
(a) The 30th percentile: miles
(b)
Check
The 75th percentile: miles
X
S
Answers
The 30th percentile of the data is 9 and the 75th percentile is 21.
The given data is 1, 3, 5, 6, 9, 10, 11, 13, 14, 15, 16, 18, 18, 24, 27, 31 and 32.
Here, consider 1, 3, 5, 6, 9, 10, 11, 13, 14
30th percentiles is 9.
Consider 15, 16, 18, 18, 24, 27, 31, 32
75th percentiles = (18+24)/2
= 42/2
= 21
Therefore, the 30th percentile of the data is 9 and the 75th percentile is 21.
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a dilation has center (0,0). Find the image of the point L(-4,0) for the scale factor 7.
Answers
The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.
To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.
The coordinates of the image point L' will be:
L' = (-4 × 7, 0 × 7) = (-28, 0)
Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
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Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?
Answers
Chay can use 3 bags of mulch per flower bed.
Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.
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Write four different equations that have –3 as the solution. (2 points each)
Answers
Answer:
equation 1: x-5=-8 <=> x=-3
equation 2: x-3=-6 <=> x=-3
equation 3: x.3=-9 <=> x=-3
equation 4: -9 : x=3 <=> x=-3
=> Four equations that have –3 as the solution: x=-3