Answer:
-6
Step-by-step explanation:
f(x) = -2x - 7 and g(x) = -4x + 6
Find f(-5)
f(-5) = -2(-5) -7 = 10-7 = 3
The find g(3)
g(3) = -4(3) +6
= -12 +6 =-6
g(f(-5)) = -6
Please help me determine the general equation for the graph above as well as solve for a. Thank you.
Observe that the x coords of the roots of a polynomial are,
[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]
Which can be put into form,
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
with data
[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]
Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,
[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]
and a will be "lost" in the process.
If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.
Hope this helps :)
Question 6 of 10
Which situation shows a constant rate of change?
A. The number of tickets sold compared with the number of minutes
before a football game
B. The height of a bird over time
C. The cost of a bunch of grapes compared with its weight
D. The outside temperature compared with the time of day
SUBMI
a) the cost of a bunch of grapes compared with its weight
GRAAAAAAAAAAAAAAAAAAAAAAAAAAAAPES!!!!!
solve for x please help (show ur work)
Answer:
x = -3
Step-by-step explanation:
12 -4x-5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from each side
12-9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
Answer:
x = -3
Step-by-step explanation:
12 - 4x - 5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from both sides
12 - 12 - 9x = 39 - 12
-9x = 27
Divide both sides by -9
-9x/-9 = 27/-9
x = -3
I need help ASAP please please please
Answer:
n=39/5
Step-by-step explanation:
24=5(n-3)
24=5n-15
-5n= -15-24
-5n=39
n= 39/5
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
1. (02.01)
Solve -4(x + 10) - 6 = -3(x - 2). (1 point)
-40
-46
-52
52
Answer:
-52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Answer: -52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red then blue).
Answer:
4/27
Step-by-step explanation:
total number of marbles=9
probability of red=4/9
since you returned the first marble, the total number of marbles remains the same
prob(Blue)=(3/9)=1/3
P(red then blue)=(4/9)*(1/3)
=4/27
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
If a $6 per unit tax is introduced in this market, then the new equilibrium quantity will be
Answer:
soory i dont know just report me if you angry
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
The expression y + y + 2y is equivalent to ??
because ??
Answer:
4y
They would have the same value if a number was substituted for y
Step-by-step explanation:
y+y+2y =
Combine like terms
4y
These are all like terms
They would have the same value if a number was substituted for y
Let y = 5
5+5+2(5) = 5+5+10 = 20
4(5) =20
Lesson 1 Skills Practice
Lines For Exercises 1-12, use the figure at the right. In that figure, line m is parallel.
Classify each pair of angles as alternate interior, alternate exterior, or corresponding.
Pictures Below.
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Answer:
alternate interior: (2, 4), (3, 5)alternate exterior: (1, 7), (43°, 6)corresponding: (1, 5), (2, 6), (3, 7), alternate interior: (2, 4), (3, 5)corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)4)
Step-by-step explanation:
In this geometry, "corresponding" angles are in the same direction from the point of intersection of the transversal with the parallel line.
"Alternate" refers to angles on opposite sides of the transversal. "Interior" and "exterior" refer to angles between and outside of the parallel lines, respectively.
Here, we list all angle pairs in each classification, so you can answer questions 1-12 based on this list.
alternate interior: (2, 4), (3, 5)
alternate exterior: (1, 7), (43°, 6)
corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)
__
Additional classifications are also used:
consecutive (same-side) interior: (2, 5), (3, 4)
consecutive (same-side) exterior: (1, 6), (43°, 7)
vertical: (1, 3), (2, 43°), (4, 6), (5, 7)
linear pairs: (1, 2), (1, 43°), (2, 3), (3, 43°), (4, 5), (4, 7), (5, 6), (6, 7)
A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs. If four eggs are selected at random, without replacement, what is the probability that all four are brown?
Answer:
The probability will 4.32%.
The probability that all four are brown is 35/8,64,501.
Given that, A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs.
What is the probability without replacement?Probability without replacement means once we draw an item, then we do not replace it back to the sample space before drawing a second item. In other words, an item cannot be drawn more than once.
If four eggs are selected at random, without replacement, the probability that all four are brown is 7/69 × 6/68 × 5/67 × 4/66
= 7/69 × 3/34 × 5/67 × 2/33
=7/23 × 1/17 × 5/67 × 1/33
=35/8,64,501
Therefore, the probability that all four are brown is 35/8,64,501.
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For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answer:
the probability of taking a clear picture of a California candor is .24
A line passes through the point (-2,4) and has a slope of 7. Write an equation for this line
Answer: y = 7x + 18
Step-by-step explanation:
y = mx + b, (-2,4), m = 7
4 = 7(-2) + b
4 = -14 + b
b = 18
y = 7x + 18
Mr Makgato sells his car for R42 000.00. The total commission is 7.2% of the selling price of which the broker receives 2 thirds and the salesperson receives the rest. How much does the broker receive?
Answer:
2016
Step-by-step explanation:
using USA dollars:
$42000 x .072 (7.2%) = 3024 total commission
3024 x 2/3 = 2016 brokers amount
Find the value of x.
Complete the Similarity statement below only if the triangles are similar.
Is -8 an irrational number?
yes or no
no bc it is not no no no no no no no
The product of two positive integer numbers is 70 and the sum of the same two numbers is 17. Find the
numbers.
Answer:
7 and 10
Step-by-step explanation:
7 * 10 = 70
7 + 10 = 17
Answer:
10 and 7
Step-by-step explanation:
call them a and b, respectively
so a*b=70 -> b=70/a
a+b=17 ->a+70/a=17 ->a=10 b =7
What is 24/9 in simplest form
Answer:
2 2/3
Step-by-step explanation:
hope this helps :)
don't be afraid to ask questions
In a nationwide survey conducted by a reputable research center, a sample of adults in a certain country were asked whether they favor a plan to break up a small collection of megabanks, which controlled about % of the banking industry; % of those sampled responded in the affirmative. According to the report, "the margin of sampling error is / percentage points with a % level of confidence." Find and interpret a % confidence interval for the percentage of all adults in the country who favor a plan to break up the megabanks.
Answer:
(42% ; 48%)
We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%
Step-by-step explanation:
The confidence interval is used to estimate the range of values for which the population value may lie at a certain level of confidence.
Given that :
Phat = 45%
Margin of error = ±3%
The confidence interval is defined as :
C. I = Phat ± margin of error
C. I = 45% ± 3%
Lower boundary :
45% - 3% = 42%
Upper boundary :
45% + 3% = 48%
C.I = (42% ; 48%)
We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%
simplify the following without using calculator
√50 + √98
Answer:
The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8
Step-by-step explanation:
√50 + √98 = √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2
(4m-n-3). 12n13
8m 20
Answer:
24n^7/m^16
Step-by-step explanation:
Just simplify and rewrite what ever you get simplify again 2 times and now make the calculation as you see every big number is a whole number and is a pair.
please help !!!!
i would really appreciate it
Answer: A
Step-by-step explanation: x=-2, y=3, z=-3
Answer:
A. -2, 3, -3
Step-by-step explanation:
x = 7 - 2y + z
y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =
= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z
13y = 63 + 8z
y = (63 + 8z)/13
2x + 2y - 3z = 11
2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11
2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11
14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11
-2×(63 + 8z)/13 - z = -3
-2×(63 + 8z) - 13z = -39
-126 - 16z - 13z = -39
-29z = 87
z = -3
y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3
x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2
At a sale this week, a desk is being sold for $312. This is a 35% discount from the original price.
What is the original price?
Answer:
$480
Step-by-step explanation:
Let original price be x
{Original price - discount amount = sale price}
So, x - (x * 35/100) = 312
x - 35x/100 = 312
100x - 35x / 100 = 312
65x/100 = 312
65x = 31200
x = 31200/65
x = $480
So I think the original price of desk was $480
The original price of the desk is $480.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, a desk is being sold for $312.
Let the original price of the desk be x.
Here, x-35% of x =312
x- 35/100 ×x=312
x-0.35x=312
0.65x=312
x=312/0.65
x=480
Therefore, the original price of the desk is $480.
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The height of a triangle is 4 yards greater than the base. The area of the triangle is 70 square yards. Find the length of the base and the height of the triangle.
9514 1404 393
Answer:
base: 10 yardsheight: 14 yardsStep-by-step explanation:
Let b represent the length of the base. Then (b+4) is the height and the area of the triangle is ...
A = 1/2bh
70 = 1/2(b)(b+4)
b² +4b -140 = 0 . . . . . multiply by 2, put in standard form
(b +14)(b -10) = 0 . . . . factor
b = 10 . . . . the positive solution
The base of the triangle is 10 yards; the height is 14 yards.
Carmen Abdul and David sent a total of 78 text messages over their cell phones during the weekend . Abdul sent 10 fewer messages then Carmen . David sent two times as many messages as Abdul how many messages did they each send?
Answer:
Carmen:27
Abdul:17
David=34
Step-by-step explanation:
Carmen+Abdul+David = 78
Carmen-Abdul=10
David=2Abdul
Carmen=Abdul+10
Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78
4Abdul=68
Abdul = 68/4=17
Carmen = 17+10=27
David = 2 * 17 = 34
27+17+34=78
I will give brainliest if you answer properly.
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
