Given the functions f(x) = x ^ 2 + 3x - 1 and g(x) = - 2x + 3 determine the value of (f + g)(- 2)
Answers
Start by finding (f+g)(x)
[tex](f+g)(x)=(x^2+3x-1)+(-2x+3)[/tex]simplify the equation
[tex]\begin{gathered} (f+g)(x)=x^2+(3x-2x)-1+3 \\ (f+g)(x)=x^2+x+2 \end{gathered}[/tex]then, replace x by -2
[tex]\begin{gathered} (f+g)(-2)=(-2)^2+(-2)+2 \\ (f+g)(-2)=4-2+2 \\ (f+g)(-2)=4 \end{gathered}[/tex]Related Questions
In ΔVWX, m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2. Find m∠W.
Answers
The measure of angle W in the triangle is 29 degrees
How to determine the measure of angle W?The definition of the angles are given as
m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2)
Where the triangle is given as
Triangle VWX
The sum of angles in a triangle is 180 degrees
This means that
V + W + X = 180
Substitute the known values in the above equation
So, we have
6x - 4 + x + 12 + 3x + 2 = 180
Evaluate the like terms
10x = 170
Divide by 10
x = 17
Substitute x = 17 in m∠W=(x+12)
So, we have
m∠W=(17+12)
Evaluate
m∠W = 29
Hence, the angle W is 29 degrees
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Dilate trianglesDraw the image of AABC under a dilation whose center is A and scale factor is
Answers
Since the dilation is centered at vertex A, the coordinates of A' are the same of A.
Then, to find the coordinates of B, let's multiply the distance AB by the scale factor:
[tex]\begin{gathered} AB=12.6\\ \\ A^{\prime}B^{\prime}=12.6\cdot\frac{1}{4}=3.15 \end{gathered}[/tex]Doing the same for AC, we have:
[tex]A^{\prime}C^{\prime}=AC\cdot\frac{1}{4}=11.3\cdot\frac{1}{4}=2.825[/tex]The points B' and C' are on the sides AB and AC, respectively.
Knowing this, let's draw the image A'B'C':
Since AB = BC, we also have A'B' = B'C' = 3.15.
Find the lateral surface area and volume of the object in picture below
Answers
So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
Leila triples her recipe that calls for 2/5 of a cup of flour. Leila has 1 cup of flour. Does she have enough to triple her recipe?
no
yes
Answers
Answer:
No
Step-by-step explanation:
3 × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex] cups required to triple her recipe
she only has 1 cup
so does not have enough to triple her recipe
Answer:
No
Step-by-step explanation:
If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.
Write an equation for a rational function with:
Vertical asymptotes at x = -5 and x =
-6
x intercepts at x = -3 and x = -4
y intercept at 4
Answers
Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.
What is Rational Function?
Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.
So this will be a rational function with the vertical asymptotes given by the denominators:
(x + 5) and (x + 6).
The x-intercepts will be provided by the numerator,
which will be:
a(x + 3)(x + 4)
The letter an is a constant.
Given that (0,4) is the y intercept, we have:
4 = a(0+3)(0+4) / (0+5)(0+6)
4= 12a / 30
12a = 120
now,
a = 120/12,
a = 10,
and a = 1.
Now,
a(x+3)(x+4) / (x+5)(x+6) = 0
10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0
Hence, We have the following equation for a rational function:
10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.
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A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.
Answers
Solution
Step 1
Given data for C(x), the bakery's pricing
[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]Required
Step 1
To find the cost of 8 hot cocoa bombs
[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]Step 2
To find the cost of 18 hot cocoa bombs
[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3To find the C(30)
[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]Step 4
What C(30) represents.
C(30) represents the cost of ordering 30 hot cocoa bombs which is $105
A plane intersects both bases of a cylinder, passing through the center of each baseof the cylinder. What geometric figure will be formed from this intersection?
Answers
When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.
I need help, I did 1-2b, but i do not mind someone answering it either way so I can double check, but I am mainly stuck with 2c and if someone can tell me the answer and as to why, it would mean a lot and you can get brainlest if it is the right answer :)(Not a multiple choice question)
Answers
Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.
The given function :
[tex]f(x)=x^4-4x^3-x^2+12x-2[/tex]In the graph of the f(x) , the least value of x of the given curve is : (-0.939)
and the f(x) at x = (-0.939) is -10.065
The absolute minimum value is (x,y) = (-0.939, -10.065)
To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)
Answer : (x, y) = (-0.94, -10.07)
how many ones equal 4 tens
Answers
We have to find the number of ones in 4 tens.
As we know that, there are 10 ones in a 10.
Therefore, in 4 tens, the total number of ones would be 1 x 4 x 10 = 40
Write a multiplication expression to represent each situation. Then find each product and explain its meaning. Ethan burns 650 calories when he runs for 1 hour. Suppose he runs 5 hours in one week.
Answers
We know that
• Ethan burns 650 calories per hour.
If he runs 5 hours we just have to multiply this time with the given rate.
[tex]650\cdot5=3,250[/tex]Therefore, Ethan burns 3,250 calories in 5 hours.4(px+1)=64The value of x when p is -5 is ?
Answers
Answer:
x = -3
Explanation:
Given the equation:
[tex]4\left(px+1\right)=64[/tex]We are required to find the value of x when p is -5.
[tex]\begin{gathered} 4\left(px+1\right)=64\colon p=-5 \\ 4\left(-5x+1\right)=64 \\ -20x+4=64 \\ -20x=64-4 \\ -20x=60 \\ \text{Divide both sides by -20} \\ x=\frac{60}{-20} \\ x=-3 \end{gathered}[/tex]Michael earns (2x3 + 3x) every month. His wife earns (3x2 + 6) every month. x represents the number of days they work in a month. What is the total earnings in a month?2x3 - 3x2 + 3x - 62x3 + 3x2 + 3x + 66x5 + 21x3 + 18x(2x3 + 3x) / (3x2 + 6)
Answers
From the question, we can derive the following:
Micheal earns 2x³ + 3x
His wife earns 3x² + 6
If x represents the number of days they work, in a month, we are asked to find the total earnings in a month.
So we will have:
(2x³ + 3x) + (3x² + 6)
Adding up the two earnings:
2x³ + 3x² + 3x + 6
So, (2x³ + 3x² + 3x + 6) is the total earnings in a month.
So the correct answer is the second option wich is (2x³ + 3x² + 3x + 6).
Suppose that $2000 is invested at a rate of 2.8%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 5 years.Do not round any intermediate computations, and round your answer to the nearest cent.
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Solution:
Given the amount invested, P; the rate, r, at which it was invested and the time, t, it was invested.
Thus,
[tex]\begin{gathered} p=2000, \\ \\ r=2.8\text{ \%}=0.028 \\ \\ t=5 \end{gathered}[/tex]Then, we would solve for the total amount, A, using the formula;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ Where; \\ n=4 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} A=2000(1+\frac{0.028}{4})^{(4)(5)} \\ \\ A=2000(1.007)^{20} \\ \\ A=2299.43 \end{gathered}[/tex]ANSWER: $2,299.43
The distance to the nearest exit door is less than 200 feet.
Answers
ANSWER
d < 200
EXPLANATION
If d is the distance to the nearest exit door, and this distance is less than 200 feet, then the inequality to represent this situation is d < 200.
Use the Distibutive Property: Expand -3(x + 3)
Answers
The distributive property of multiplication states the following:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]So, for the given expression, we have:
[tex]-3(x+3)=(-3)\cdot x+(-3)\cdot3=-3x-9[/tex]Given the measure -845°, which answer choice correctly gives an angle measure coterminal with the given angle and on the interval,0 < 0 < 360
Answers
Given the measure -845° we can find its coterminal measure on the interval, [0,360) below
Explanation
For angles measured in degrees
[tex]\begin{gathered} β=α±360*k,where\text{ }k\text{ }is\text{ }a\text{ }positive\text{ }integer \\ -845°=\frac{-169}{36}π≈-4.694π \\ Coterminal\text{ }angle\text{ }in\text{ \lbrack}0,360°)range:\text{ 235\degree, located in the third quadrant.} \end{gathered}[/tex]Answer: Option A
Tasty Subs acquired a food-service truck on October 1, 2024, for $23,100. The company estimates a residual value of $1,500 and a six-year service life. Required:Calculate depreciation expense using the straight-line method for 2024 and 2025, assuming a December 31 year-end.
Answers
The company estimates a residual value of $1,500 and a six-year service life.
It is given that,
Cost of truck delivery = $ 23100
Salvage value = $ 1500
Useful life = 6 years
Depreciation expenses by using the straight-line method are calculated as,
[tex]Depreciation\text{ expenses p.a = }\frac{cost\text{ - salvage value }}{useful\text{ life}}[/tex]Substituting the value in the formula,
[tex]\begin{gathered} Depreciation\text{ expenses p.a = }\frac{23100\text{ - 1500}}{6} \\ Depreciation\text{ expenses p.a = }\frac{21600}{6} \\ Depreciation\text{ expenses p.a = 3600} \end{gathered}[/tex]Thu
New York City is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 2 vans and 6 buses with 244 students. High School B rented and filled 4 vans
and 7 buses with 298 students. Every van had the same number of students in it as did the buses.
Find the number of students in each van and in each bus.
Answers
There are eight students in each van and 38 students are in each bus.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of students fit into a van would be v
And the number of students fit into a bus would be b
School A:
2v + 6b = 244 ...(i)
2v = 244 - 6b
v = 122 - 3b
School B:
4v + 7b = 298 ...(ii)
Substitute the value of v = 122 - 3b in the equation (ii),
4(122 - 3b) + 7b = 298
Solve for b to get b = 38.
Substitute the value of b = 38 in equation (i),
2v + 6(38) = 244
2v + 228 = 244
2v = 16
v = 8
Therefore, eight students are in each van and 38 students are in each bus.
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which of the following liner equations passes through points (-1,5) and (1,5)?
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Hence, the correct option is Option D. None of the choices are correct.
The change in the value of a stock is represented by the rational number -5.90 describe in words what this means
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The change in the value of a stock which is represented by the rational number -5.90 means that the stock decreased by 5.90 units.
Whenever we use negative value to describe change, it means that the value of that particular entity that been decreased by that number.
On the contrary, If we are using positive value to describe change, it means that the value of that particular entity that been increased by that number.
For example:- The change in total money possessed by Daniel is $ 50 means there is an increase of $ 50 in the money with Daniel.
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7.5 is 15% of what number?
Answers
Let the number be x. So equation for x is,
[tex]\begin{gathered} \frac{15}{100}\cdot x=7.5 \\ x=\frac{7.5\cdot100}{15} \\ =\frac{750}{15} \\ =50 \end{gathered}[/tex]The number is 50.
Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
Answers
The probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is .
in the question ,
it is given that
the waiting time is randomly distributed between 0 and 6 minutes .
Since it is uniformly distributed , the Uniform distribution have two bounds a and b .
The probability of finding the value greater than x can be calculated using the formula .
P(X>x) = (b-x)/(b-a)
Given that , the waiting time is Uniformly distributed 0 and 6 minutes , we get a=0 and b=6,
Substituting the values in the Probability formula , we get
P(X>2.25) = (6-2.25)/(6-0)
= 3.75/6
= 0.625
Therefore , the probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is 0.625.
The given question is incomplete , the complete question is
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
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David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.(Not sure if I'm expressing this correctly.)c = amount spent350 - c = 235c= 115
Answers
Given:
David had $350. After shopping, he was left with $235.
Required:
If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.
Explanation:
We know c is the amount spent
So,
Available amount = Total amount - spent amount
235 = 350 - c
c= 350 - 235
c = 115
Answer:
Hence, David spent $115.
find the slope of the line that passes through (10,2) and (2,10)
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Give the first four terms of the geometric sequence for which A1 = -7 and r = -4.07 7 7 74, 16, 64, 256 -7,28, -112, 448 -7, -11, -15, -1928. -112, 448. - 1792
Answers
Given:
[tex]\begin{gathered} firstterm(a_1\text{) = -7} \\ \text{common ratio (r) = -4} \end{gathered}[/tex]Required: First four terms
The nth term of a geometric sequence :
[tex]a_{n\text{ }}=a_1\text{ }\times r^{n-1}[/tex]Hence, we can obtain the next four terms by substituting
[tex]\begin{gathered} \text{when n = 1, a}_1\text{ = -7} \\ n=2,a_2\text{ =-7 }\times(-4)^{2\text{ - 1}} \\ a_2\text{ = -7 }\times\text{ -4} \\ =\text{ 28} \\ \\ \text{when n =3, a}_3\text{ = -7 }\times(-4)^{3\text{ -1 }} \\ a_3\text{ = -7 }\times\text{ 16} \\ =\text{ -112} \\ \\ \text{when n = 4, a}_4\text{ = }-7\text{ }\times(-4)^{4-1} \\ a_4\text{ = -7 }\times\text{ -64} \\ =\text{ 448} \end{gathered}[/tex]v+1.6>-5.5
nnnnnnnnnnnn
Answers
Answer:
v > -7.1
Step-by-step explanation:
What is 58 divided into 7275
Answers
Answer:125.431034
Step-by-step explanation:
Find the interest odf the loan using banker's ruleP - $350,- = 4.8%, t = 150 days
Answers
i = P r T
interest: i
Principal = $350
Interest rate : 4.8% (in decimal form, 4.8/100 = 0.048)
time = t = days/365 = 150/360
Replacing:
i= 350 (0.048) (150/360) = 7
Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find AU (BNC).{
Answers
Solution:
Given that;
[tex]\begin{gathered} A=\left\{0,2,4,6\right\} \\ B=\left\{1,2,3,4,5\right\} \\ C=\left\{1,3,5,7\right\} \end{gathered}[/tex]For B∩C, i.e . common elements between bot sets
[tex]B\cap C=\lbrace1,3,5\rbrace[/tex]Then, A∪(B∪C), i.e. all the elements in A and B∩C
[tex]A∪\left(B∪C\right)=\lbrace0,1,2,3,4,5,6\rbrace[/tex]Hence, A∪(B∪C) is
[tex]\begin{equation*} \lbrace0,1,2,3,4,5,6\rbrace \end{equation*}[/tex]Hello, I need help completing this math problem. I will include a picture. Thank you so much!
Answers
From the given picture, we can see that the figure is a right triangle, so we can apply Pythagorean theorem, that is,
[tex]5^2+8^2=x^2[/tex]where x denotes the missing length. Then, our equation give us
[tex]\begin{gathered} x^2=25+64 \\ x^2=89 \end{gathered}[/tex]By taking square root to both side, we have
[tex]\begin{gathered} x=\sqrt[]{89} \\ x=9.4339 \end{gathered}[/tex]Therefore, by rounding this result to the nearest tenth, the answer is 9.4 ft