SOLUTIONS
Giving that f(x)=3x^2-x-5, g(x)=-1 what is (f+g)(x)
[tex]\begin{gathered} f(x)=3x^2-x-5 \\ g(x)=-1 \end{gathered}[/tex][tex](f+g)(x)=f(x)+g(x)[/tex]Adding up the two function:
[tex]\begin{gathered} (3x^2-x-5)+-1 \\ simplify\text{ the bracket} \\ 3x^2-x-5-1 \\ 3x^2-x-6 \end{gathered}[/tex]Therefore the correct answer is:
[tex](f+g)(x)=3x^2-x-6[/tex]Hank has picked 1.3 pounds of berries and picks about 0.75 pounds per min. Tom has picked 2.5 pounds of berries and picks about 0.5 pounds per minute. In how many minutes where are picked at least as many pounds of berries as Tom?
Hank: 1.3 pounds at a rate of 0.75 pounds per minute
Tom: 2.5 pounds at a rate of 0.5 pounds per minute
rate is given by
r = p / t
where p is the number of pounds picked during a fixed time
The number of berries picked by Hank during a certain time is given by the following equation
[tex]H=1.3+0.75t[/tex]For Tom, the equation is the following:
[tex]T=2.5+0.5\cdot t[/tex]Now, we need to find a time t when T and H are the same
[tex]\begin{gathered} H=T \\ 1.3+0.75t=2.5+0.5t \end{gathered}[/tex]We now just need to solve for t
Let's find t step by step
[tex]\begin{gathered} 1.3\cdot\: 100+0.75t\cdot\: 100=2.5\cdot\: 100+0.5t\cdot\: 100 \\ 130+75t=250+50t \\ 130+75t-130=250+50t-130 \\ 75t=50t+120 \\ 75t-50t=50t+120-50t \\ 25t=120 \\ \frac{25t}{25}=\frac{120}{25} \\ t=\frac{24}{5} \end{gathered}[/tex]Which is the same as t=4.8
Two friends, Tanisha and Zoey, had just bought their first cars. The equation
y = 18.4x represents the number of miles, y, that Zoey can drive her car for every a
gallons of gas. The table below represents the number of miles, y, that Tanisha can
drive her car for every a gallons of gas.
Tanisha's Gas Mileage
Gallons (x) Miles (y)
Use the dropdown menu and answer-blank below to form a
true statement.
Tanisha can travel
miles
than Zoey on one gallon of gas.
Answer:
3.5
Step-by-step explanation:
rate of change=
change in x
change in y
=
20
438
=21.9
y=18.4x
Tanisha−Zoey=
\,\,21.9-18.4
21.9−18.4
=
=
3.5
3.5
9- (4x + 4) = 3x - 10 + 8x
Answer: 1=x
Step-by-step explanation:
9-4x-4=3x-10+8x
9-4+10=3x+8x+4x
15=15x
1=x
Expand the brackets :
9 - 4x - 4 = 3x - 10 + 8x
-> 9 - 4x - 4 - (3x - 10 + 8x) = 0
-> 9 - 4x - 4 - 3x + 10 - 8x = 0
-> (9 - 4 + 10) - (4x + 3x + 8x) = 0
-> 15 - 15x = 0
15x = 15
x = 1
Might be confusing so just leave a comment if you don't understand (because I do the more detailed way really ;-;)
Find the decay factor from the function y = 500(0.75)3.
The given function is:
[tex]y=500(0.75)^3[/tex]It is required to find the decay factor.
Recall that the standard form of an exponential decay function is given as:
[tex]y=a(b)^x[/tex]Where a>0, 0and b is the decay factor.
Compare the given equation to the standard form.
It can be observed that b=0.75. Hence, the decay factor is 0.75.
The answer is 0.75.5. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture?
The picture represents isosceles triangle theorem.
From the figure :
It is represented that two sides are equal.
And the angles opposite to this two equal sides are equal.
So it is a isosceles triangle.
Isosceles triangle:
If two sides of a triangle are congruent , then the angles opposite to these sides are congruent.
Therefore the picture represents isosceles triangle theorem.
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I just need to know the answer for question 12
Given:
The given inequalities are:
[tex]3x+1>7\text{ and 4x}\leq24[/tex]Solving first inequality, we get:
[tex]\begin{gathered} 3x+1>7 \\ 3x>7-1 \\ 3x>6 \\ x>\frac{6}{3} \\ x>2 \end{gathered}[/tex]Solving the second inequality, we get:
[tex]\begin{gathered} 4x\leq24 \\ x\leq\frac{24}{4} \\ x\leq6 \end{gathered}[/tex]Merging the solutions of both inequalities, we get:
[tex]\begin{gathered} x>2\text{ and x}\leq6 \\ \Rightarrow x\epsilon\text{ (2,6\rbrack} \end{gathered}[/tex]So, the graph will be a number line with an open circle at 2 and a closed circle on 6 and shading in between.
Therefore,
Option A is correct.
State the quadratic formula and multiply by the equation of Albert Einstein's theory of special relativity. Write 3-4 complete sentences to explain how you got your answer, and why this can benefit future civilizations.
Answer:
The Sacheverell Theorem of Mathematics is the answer to your question. I got this answer by using the Vasagle formula and distributing throughout the parenthesis. This can benefit future civilizations because it's an undiscovered new species in the winoculous alternate universe.
Step-by-step explanation:
I am from the year 2420 so I know. Do not doubt me.
Which equation represents the line that is parallel to y=3/4x + 7 and passes through (-12,36)?
Answer:
If it is parallel:m parallel line=m line given, so:
mparallel=3/4
And it passes through one point given, so we use the formula: y-y0=m(x-x0)
so: y-36=3/4(x+12)
y=3/4x+9+36
y=3/4x+45 is the correct answer.
What is the equation of the line that passes through the points (4, -3) and (5, 0) in point-slope form? y - 5 = -1/3(x - 0) y - 4 = -3(x + 3) y - 0 = 1/3(x - 5) y + 3 = 3(x - 4)
Answer:
d. y+3=3(x-4)
Step-by-step explanation:
graphing both points you see a slope of 3. If you continue to follow the slope of 3, you will find the y-intercept is -15.
y+3=3(x-4)
y+3=3x-12
y+3(-3)=3x-12(-3)
y=3x-15 (slope intercept form)
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
How do you graph y=4x at x=-4? What does it look like on a graph
We want to plot the graph of the equation;
[tex]y=4x[/tex]we can do this by assuming to different values of x and deriving the corresponding values of y at those points.
for x= -4;
[tex]\begin{gathered} y=4(-4) \\ y=-16 \end{gathered}[/tex]Also taking a second point.
at x = 0;
[tex]\begin{gathered} y=4(0) \\ y=0 \end{gathered}[/tex]Since the equation is a linear equation, the graph will be a straight line graph;
the graph will be a straight lin passing through the two points derived.
[tex](-4,-16)\text{ and (0,0)}[/tex]the graph of the given equation can be shown below;
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
) In triangle XYZ, angle Y is right angle, and angle X and angle Y are complementary angles.If sin x =3/5 and cos x=4/5 then what is the value of sin y?
A) 3/5
B)4/5
C) 3/4
D)4/3
The value of sin Y is 4/5. The correct option is B) 4/5
Calculating the value of the sine of an angleFrom the question, we are to determine the value of sin Y.
From the given information, we have that
sin X = 3/5
and
cos X = 4/5
Also,
We have that angle X and angle Y are complementary angles.
That is,
X + Y = 90°
From the Trigonometric ratios of complementary angles, we have that
sin Y = cos (90° - Y)
From X + Y = 90°
X = 90° - Y
Therefore,
sin Y = cos X
From the given information,
cos X = 4/5
Hence, sin Y = 4/5
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Persevere with Problems William is 3 feet 1 inch tall and would like to ride a roller coaster. Riders must be at least 42 inches tall to ride the coaster. Write an addition inequality to determine how much taller William must be to ride the coaster. Let x be the variable representing how much taller William must be.
Step-by-step explanation:
1 ft = 12 in
he is 3 ft 1 in, that is then 3×12 + 1 = 37 in tall.
so,
37 + x >= 42
and then
x >= 42 - 37
x >= 5 in
One pound is equal to 0.454 kilogram. If Jim has a mass of 50 kilograms, write an equation to represent how many pounds, p, he weighs.
Answer: p=110.1321 pounds
Step-by-step explanation:
50 divided by 0.454 is equal to 110.1321
Solve for n: 2n = n + 3 O A. 1 O O c. 3 3 OD. 5 E 6
Step 1: Problem
2n = n + 3
Step 2: Concept
Collect like terms and find the value of x.
2n = n + 3
2n - n = 3
n = 3
Step 3: Final answer
n = 3
Write a systems of equations for each problem define variables used. Please show all work.On a table are 20 coin., quarters and dimes. Their value is $3.05 how many of each kind of coin are there?
We have 20 coins in total, lets say that we have X amount od quarters(0.25 dollar) and Y amount of dimes(0.1 dollar), and in total we have $3.05, with this we can write the system:
[tex]X+Y=20[/tex]Wich means that we have 20 coins, and:
[tex]0.25X\text{ + 0.1Y=3.05}[/tex]Thats the amount of money we have.
So, from the first equation, we can isolate X, as follows:
[tex]X=20-Y[/tex]And with that we can substitute X in the second equation, as follows:
[tex]0.25X\text{ + 0.1Y=3.05 }\rightarrow\text{ }0.25(20-Y)\text{ + 0.1Y=3.05 }\rightarrow\text{ }5-0.25Y+0.1Y=3.05[/tex][tex]5-0.25Y+0.1Y=3.05\rightarrow-0.15Y=-1.95\rightarrow Y=13[/tex]So, if Y=13, we have that X=7. So 13 dimes and 7 quarters.
simplify: 3√45 -4 √225 + √200 - √50
According to the given data we have the following:
3√45 -4 √225 + √200 - √50
Then to simplify we would have to make the following:
[3 × √3 × √3 × √5] - [√5 × √5 × √5] + [√2 × √2 × √2 × √5 × √5] - [√2 × √5 × √5]
=[3 × 3 × √5] - [5 × √5] + [2 × 5 × √2] - [5 × √2]
=3√5 - 5√5 + 10√2 - 5√2
=√5(3 - 5) + √2(10 - 5)
=(-2√5) + 5√2
Therefore, the answer would be 16√5 + 75√2
Determine the inverse of the function f (x) = 2(x − 3)2 + 4.
The inverse of the function is [tex]f^-1 = \frac{1}{4}x + 2[/tex] .
What is inverse of the function ?
A function that "undoes" another function is known as an inverse in mathematics. To put it another way, if f(x) produces y, then y will produce x when y is fed into f's inverse function. A function f is said to be invertible if it has an inverse, and the inverse is represented by the symbol [tex]f^-1[/tex]
Here the given function is,
=> f(x) = 2(x-3)2+4
=> f(x) = 4(x-3)+4
=> f(x) = 4x-12+4
=> f(x) = 4x -8
Now take y= f(x) then,
=> y = f(x)=4x-8
=> y = 4x-8
Now interchange x and y then,
=> x = 4y-8
Now solve for y then,
=> x+8 = 4y
=> y= [tex]\frac{1}{4} x+ 2[/tex]
Then [tex]f^-1[/tex] = [tex]\frac{1}{4}x+ 2[/tex]
Therefore inverse of the function is [tex]f^-1 = \frac{1}{4}x + 2[/tex] .
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 8 boys and 6 girls are competing, how many different ways could the six medals possibly be given out?
As given by the question
There are given that the total number of boys is 8 and total numbers of girls is 6.
Now,
Since there are two competitions, one for boys and one for girls and we want all the possible results we will calculate the possible combination for the boys and multiply them by the possible combination for the girls.
Then,
For the boys:
[tex]\begin{gathered} \text{Boys}=\frac{8!}{(8-3!)} \\ \text{Boys}=\frac{8!}{(8-3)!} \\ \text{Boys}=\frac{8!}{(5)!} \\ \text{Boys}=\frac{8\times7\times6\times5!}{(5)!} \end{gathered}[/tex]Then,
[tex]\begin{gathered} \text{Boys}=\frac{8\times7\times6\times5!}{(5)!} \\ \text{Boys}=8\times7\times6 \\ \text{Boys}=336 \end{gathered}[/tex]Now,
For the girl:
[tex]\begin{gathered} Girl\text{s}=\frac{6!}{(6-3)!} \\ Girls\text{s}=\frac{6!}{(3)!} \\ Girls\text{s}=\frac{6\times5\times4\times3!}{(3)!} \end{gathered}[/tex]Then,
[tex]\begin{gathered} Girls\text{s}=\frac{6\times5\times4\times3!}{(3)!} \\ Girls=6\times5\times4 \\ Girls=120 \end{gathered}[/tex]Now,
A total number of possible results:
[tex]\begin{gathered} \text{result}=120\times336 \\ \text{result}=40320 \end{gathered}[/tex]Hence, the ways are 40320.
Find an expression which represents the sum of (-6x + 6) and (-3x – 7) insimplest terms.
Given an expression of (-6x +6) and (-3x - 7)
[tex]\text{The sum of the expression (-6x +6) and (-3x -7)}[/tex][tex]\begin{gathered} -6x\text{ + 6 + -3x -7 } \\ \text{collecting like terms} \\ -6x\text{ -3x + 6 - 7 } \\ -9x\text{ - 1} \end{gathered}[/tex]Hence the solution to the above expression is
[tex]-9x\text{ - 1}[/tex]100 POINTS PLE HELP ASAP
A college is currently accepting students that are both in-state and out-of-state. They plan to accept two times as many in-state students as out-of-state, and they only have space to accept 200 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
x > 0 and y > 0
0 < x ≤ 200 and y > 400
0 < x and y < 200
0 < x ≤ 200 and 0 < y ≤ 400
Answer:
option c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
0 < x and y <200
Consider the equation 2x+5y=1Identify the slope and y intercept
Solution
Given the equation 2x+5y=1
We are required to Identify the slope and y intercept
The general equation of a straight line is in the form y = mx + c
Where m = slope and c= y-intercept
To solve the problem before us, we need to re-write 2x+5y=1 in the form y = mx + c
[tex]\begin{gathered} 2x+5y=1 \\ 5y=-2x+1 \\ y=-\frac{2}{5}x+\frac{1}{5} \\ \\ Comparing\text{ the resulting equation with y=mx+c} \\ m=-\frac{2}{5},\text{ c=}\frac{1}{5} \end{gathered}[/tex]Thus, the slope = -2/5 while the y-intercept is 1/5
Absolute value can never be negative,
true or false?
Answer:
Yes, an absolute value can never be false. So, the answer is true.
please help
Fully simplify.
(-9√-63)(-√-49)
Answer:
(-9√-63)(-√-49)= (9/3)
Step-by-step explanation:
Question 12(Multiple Choice Worth 1 points)(07.04 LC)Factor completely 36x² - 49.(3x + 7)(12x-7)(3x-7)(12x+7)(6x-7)(6x-7)(6x + 7)(6x-7)
The factor the binomial
[tex]a^2-b^2[/tex]Find the square root of a and the square root of b, then put them as the product of the sum and difference of these square roots
[tex]\begin{gathered} \sqrt{a^2}=a \\ \sqrt{b^2}=b \\ a^2-b^2=(a+b)(a-b) \end{gathered}[/tex]We will use this rule to factor in the given expression
[tex]36x^2-49[/tex]Find the square root for each term
[tex]\begin{gathered} \sqrt{36x^2}=6x \\ \sqrt{49}=7 \end{gathered}[/tex]Write the two factors
[tex]36x^2-49=(6x+7)(6x-7)[/tex]The answer is the last choice (6x + 7)(6x - 7)
The product of the ages (in days) of two newborn babies Simran and Jessie in two dayswill be 48 more than the product of their ages today. How old are the babies if Jessie is 2days older than Simran?
Given that:
- The product of the ages (in days) of babies Simran and Jessie in two days
will be 48 more than the product of their ages today.
- Jessie is 2 days older than Simran.
Let be "j" Jessie's age (in days) and "s" Simran's age (in days).
You can set up the following System of Equations using the data given in the exercise:
[tex]\begin{cases}(j+2)(s+2)=js+{48} \\ j={s+2}\end{cases}[/tex]You can use the Substitution Method to solve the system:
1. Substitute the second equation into the first one:
[tex](s+2+2)(s+2)=(s+2)s+48[/tex]2. Solve for "s":
[tex](s+4)(s+2)=s^2+2s+48[/tex][tex](s)(s)+(s)(2)+(4)(s)+(4)(2)=s^2+2s+48[/tex][tex]s^2+2s+4s+8=s^2+2s+48[/tex][tex]\begin{gathered} 4s=48-8 \\ \\ s=\frac{40}{4} \\ \\ s=10 \end{gathered}[/tex]3. Substitute "s" into the second original equation and evaluate:
[tex]\begin{gathered} j=10+2 \\ j=12 \end{gathered}[/tex]Hence, the answer is: Jessie is 12 days old and Simran is 10 days old.
An arena manager tallies the number of snack items (hot dogs, nachos, and popcorn) sold at each of three concession stands in the arena.
Snack Item
Hot Dogs Nachos Popcorn Total
Concession
Stands Stand A 125 65 40 230
Stand B 218 119 52 389
Stand C 65 52 13 130
Total 408 236 105 749
What is the probability that a customer purchased popcorn, given that they purchased from stand B?
6.9%
13.4%
14.0%
49.5%
The probability that a customer purchased popcorn, given that they purchased from stand B is 13.4%.
What is termed as the probability?The term "probability" refers to the likelihood of a specific event (or set of events) occurring, explained on a linear scale from 0 (unlikelihood) to 1 (certainty), as well as as a proportion between 0 and 100%.For the given question;
The data for the selling of the snack items at arena are given;
Snack Item Hot Dogs Nachos Popcorn Total Concession
Stand A 125 65 40 230
Stand B 218 119 52 389
Stand C 65 52 13 130
Total 408 236 105 749
Now the customer purchased the popcorn from stand B.
Thus, total number of snack at stand B = 389
Total number of popcorn at stand B = 52
Thus,
Probability = favourable outcome/total outcome
Probability = 52/386
Probability % = 52/386 × 100
Probability % = 13.4%.
Thus, the probability that a customer purchased popcorn, given that they purchased from stand B is 13.4%.
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Solve the system of equations :-6x - y = -16-6x -5y = -8
The given system of equation are :
-6x - y = -16
-6x -5y = -8
On subtracting both the equation we get :
-6x -y -(-6x -5y) = -16 -(-8)
-6x -y +6x +5y = -16 +8
-6x + 6x +5y -y = -8
4y = -8
4y = -8
Divide both side by 4:
4y/4 = -8/4
y = -2
Substitute the value of y =- 2 in the any one equation:
-6x - y = -16
-6x - (-2)= -16
-6x + 2 = -16
-6x = -16 -2
-6x = -18
x = 3
Answer : x = 3, y = -2
You used `14` ounces of cheese to make `2` pizzas.
How much cheese do you need for `3` pizzas?
Answer:
You need 21 ounces of cheese for 3 pizzas.
Step-by-step explanation:
If you use 14oz for 2 pizzas, then if you divide it by 2, you have 7oz for 1 pizza.
Now multiply by 3 to get 21oz for 3 pizzas.