Answer:
The possible values are a = -2.5 or a = 4.5.
Step-by-step explanation:
Composite function:
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this case:
[tex]f(x) = 4x^2 - 8x - 20[/tex]
[tex]g(x) = 2x + a[/tex]
So
[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]
Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So
[tex]4a^2 - 8a - 20 = 25[/tex]
[tex]4a^2 - 8a - 45 = 0[/tex]
Solving a quadratic equation, by Bhaskara:
[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]
The possible values are a = -2.5 or a = 4.5.
A circle has a circumference of 2cm. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determinec
The numerical values of the circumference and area of the circle are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
ОО
Answer:
The numerical values of the circumference and area of the circle are equal.
Can someone help me out?
Answer:
Terms:
-5x4-x-1Like Terms:
-5x and -x4 and -1Coefficients:
The coefficient of -5x is -5.The coefficient of -x is -1.Constants:
4-1You simplify the expression by combining like terms:
-5x + 4 - x - 1 = -6x + 5
(7b - 4) + (-2b + a + 1) = 7b - 4 - 2b + a + 1 = 5b + a - 3
What is the rate of change of the line on the graph
Answer:
A. ¼
Step-by-step explanation:
Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:
Where,
[tex] (4, 1) = (x_1, y_1) [/tex]
[tex] (-4, -1) = (x_2, y_2) [/tex]
Plug in the values
Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]
= [tex] \frac{-2}{-8} [/tex]
= [tex] \frac{1}{4} [/tex]
Rate of change = ¼
Solve the given system by the substitution method.
3x + y = 8
7x - 4y = 6
Answer:
[tex]{ \tt{y = 8 - 3x}} - - - (i) \\ \\ = > 7x - 4(8 - 3x) = 6 \\ 7x - 32 + 12x = 6 \\ 19x - 32 = 6 \\ 19x = 38 \\ x = 2 \\ \\ = > y = 8 - 3(2) \\ y = 2[/tex]
Compare the subtraction problems (6/8-5/8=1/8) and (6/9-7/9=-1/9) why is the answer to the first problem positive nad the answer to the second problem negative select all that apply
6/9 - 7/9 = -1/9
is a negative number.
stuck on this problem
Answer:
B
Step-by-step explanation:
When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.
B is the Answer
Answer:
c. switch the x-values and y-values in the table
Step-by-step explanation:
For any table or graph reflection over the line y=x
The rule is (x,y) ----> (y,x)
f(x) is reflected over the line y=x, so the coordinates of f(x) becomes
(-2,-31) becomes (-31,-2)
(-1,0) becomes (0,-1)
(1,2) becomes (2,1)
(2,33) becomes (33,2)
As per the rule, we switch the x-values and y-values in the table
For reflection over the line y=x , the coordinate becomes
(-31,-2)
(0,-1)
(2,1)
(33,2)
Restaurants sales totaled $38,676 for the week your customer count was $7,325 what did the average customer spend for the week
What is the equation of the line that is perpendicular to
and has the same y-intercept as the given line?
(0,0)
(5,0)
O y = x+1
O y = x+5
o y = 5x + 1
O y = 5x + 5
-6 -5 -4 -3 -2 -1
23
4 5 6
Mark this and return
Save and Exit
Nyt
Submit
Answer:
y = 5x + 1
Step-by-step explanation:
Given the coordinate points (0,1) and (5,0)
First, get the slope
Slope m =(0-1)/5-0
m = -1/5
Since the required line is perpendicular, then the required slope is;
M = -1/(-1/5)
M = 5
Since 1the y intecept id (0,1) i.e. 1
Required equation is y = mx+b
y = 5x + 1
This gives the required equation
Note that the coordinate (0,1) was used instead os (0,0)
Prove that the square of an odd number is always 1 more than a multiple of 4
Answer:
By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.
Step-by-step explanation:
For examples,
Let's consider squares of 3, 11, 25, 37 and 131.
[tex] {3}^{2} = 9[/tex]
8 is a multiple of 4, and 9 is more than 8.
[tex] {11}^{2} = 121[/tex]
120 is a multiple of 4 and 121 is one more than it.
[tex] {25}^{2} = 625[/tex]
624 is a multiple of 4 and 625 is one more than it.
[tex] {37}^{2} = 1369[/tex]
1368 is a multiple of 4 and 1369 is one more than 1368.
[tex] {131}^{2} = 17161[/tex]
17160 is a multiple of 4.
Х/10 is between 1/5
and 0.6. What could the value of x be?
Answer:
2 < x < 6
Step-by-step explanation:
x/10
1/5 = 2/10
.6 = 6/10
2 < x < 6
the campus bookshop sells exercise books and textbooks, where, the total cost of 10 exercise books and 2 textbooks is $1400.00. One also finds the total cost of 3 textbooks and 30 exercise books is $3000. Then determine the price of 1 exercise book?
Answer:
The price of 1 exercise book is $122.45.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the price of one exercise book.
y is the price of one textbook.
Total cost of 10 exercise books and 2 textbooks is $1400.00.
This means that:
[tex]10x + 2y = 1400[/tex]
Since we want x:
[tex]2y = 1400 - 10x[/tex]
[tex]y = 700 - 5x[/tex]
One also finds the total cost of 3 textbooks and 30 exercise books is $3000.
This means that:
[tex]3x + 30y = 3000[/tex]
Since [tex]y = 700 - 5x[/tex]
[tex]3x + 30(700 - 5x) = 3000[/tex]
[tex]3x + 21000 - 150x = 3000[/tex]
[tex]147x = 18000[/tex]
[tex]x = \frac{18000}{147}[/tex]
[tex]x = 122.45[/tex]
The price of 1 exercise book is $122.45.
Divide the following complex numbers:
[tex](2 + i) \div (1 - 4i)[/tex]
Answer:
[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
Step-by-step explanation:
[tex] (2 + i) \div (1 - 4i) = [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]
[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]
[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]
[tex] = \dfrac{2 + 9i - 4}{17} [/tex]
[tex] = \dfrac{-2 + 9i}{17} [/tex]
[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
simplify 6 x + 3y /3
Answer:
6x + y
Step-by-step explanation:
6x + 3y/3
6x + y
Answer:
6x + y
Step-by-step explanation:
6x + 3y / 3
cancel 3y by 3
6x + y
[tex](v+6)^{2}=2v^{2}+14v+12[/tex]
Answer:
v=-6 or 4
Step-by-step explanation:
Answer:
the answer would be 5
Step-by-step explanation:
have to do the question multiply add and divide to find your answer
Geometry Oddsseseyware
An item is regularly priced at $84. Ashley bought it on sale for 70% off the regular price.
Use the ALEKS calculator to find how much Ashley paid
Answer:
58.80
Step-by-step explanation:
84 x .7(70%) =58.80
if y = k where k is a constant and y =24 when x =6 what is the value of y when x= 5
Answer:
20
Step-by-step explanation:
y=kx
24=6k
k=4
y=4*5=20
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations.
Answer:
the operating characteristics have been solved below
Step-by-step explanation:
we have an average of 10 minutes per customers
μ = mean service rate = 60/10 = 6 customers in one hr
the average number of customers that are waiting in line
mean arrival λ = 2.5
μ = 6
[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]
= 6.25/21
= 0.2976
we calculate the average number of customers that are in the system
[tex]L=Lq+\frac{2.5}{6}[/tex]
= 0.2976+0.4167
= 0.7143
we find the average time that a customer spends in waiting
[tex]Wq=\frac{0.2976}{2.5}[/tex]
= 0.1190 hours
when converted to minutes = 0.1190*60 = 7.1424 minutes
[tex]0.1190+\frac{1}{6}[/tex]
=0.2857
probability that arriving customers would wait for the service
= 2.5÷6 = 0.4167
On a map of a town, 3 cm represents 150 m. Two points in the town are 1 km apart. How far apart are the two points on the map?
Answer:
5000 km
Step-by-step explanation:
We are given that
3 cm represents on a map of a town=150 m
Distance between two points=1 km
We have to find the distance between two points on the map.
3 cm represents on a map of a town=150 m
1 cm represents on a map of a town=150/3 m
1 km=1000 m
1 m=100 cm
[tex]1km=1000\times 100=100000 cm[/tex]
100000 cm represents on a map of a town
=[tex]\frac{150}{3}\times 100000[/tex] m
100000 cm represents on a map of a town=5000000 m
100000 cm represents on a map of a town
=[tex]\frac{5000000}{1000} km[/tex]
100000 cm represents on a map of a town=5000 km
Hence, two points are separated by 5000 km on the map.
A large on-demand, video streaming company is designing a large-scale survey to determine the mean amount of time corporate executives watch on-demand television. A small pilot survey of 10 executives indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. The estimate of the mean viewing time should be within 0.25 hour. The 95% level of confidence is to be used. How many executives should be surveyed? (Use z Distribution Table.)
How many executives should be surveyed? (Round the final answer to the next whole number.)
Answer:
554 executives should be surveyed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 3 hours.
This means that [tex]\sigma = 3[/tex]
The 95% level of confidence is to be used. How many executives should be surveyed?
n executives should be surveyed, and n is found with [tex]M = 0.25[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.25 = 1.96\frac{3}{\sqrt{n}}[/tex]
[tex]0.25\sqrt{n} = 1.96*3[/tex]
[tex]\sqrt{n} = \frac{1.96*3}{0.25}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*3}{0.25})^2[/tex]
[tex]n = 553.2[/tex]
Rounding up:
554 executives should be surveyed.
How do I make people brainliest
Answer:
you have to wait until two people answer then you click their answer to make them brainliest
Step-by-step explanation:
i dont know
blah blah blah blah blah blah blah blah blah blah blah blah
What is the length of my
?
M
3x
X + 8
7639
630
N
¿
O
A. 8
B. 4
C. 16
a
D. 12
Answer:
The length of MN is 4
Choose B
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
Help asap please!!..
Answer:
9x² - 4/3x + ¼
Step-by-step explanation:
(3x - ½)²
(3x - ½)(3x -½)
9x² - ⅔x - ⅔x + ¼
9x² - 4/3x + ¼
I need help with this word problem.
Answer:
$3.22 per square feet
Step-by-step explanation:
To solve, I usually set up an equation:
sq ft = 12 1/2 = 1
$ 40.21 x
Then, use cross multiplication.
(12 1/2)x=40.21
Divide both sides by 12 1/2 or 12.5
x = 3.2168
Round to the hundredths place [because we're dealing with money]
$3.22
I hope this helps!
Answer:
3.22 per sq ft
Step-by-step explanation:
Take the total cost and divide by the amount of tiles
40.21 / 12.5
3.2168 per sq ft
Rounding to the nearest cent
3.22 per sq ft
Find the slope of the line that passes through the two points. 4,4 & 4,9
HELPPPPPPP
Answer:
is 22
Step-by-step explanation:
Answer:
It doesn't have a slope?
Step-by-step explanation:
Knowing that the slope equation is y2-y1/x2-x1
9-4 5
----- = ------ = 0
4-4 0
this means that the slope is 0...
Need help on last question
Answer:
Step-by-step explanation:
so let the equation equal 13
13 = 3[tex]x^{3}[/tex]-12x+13
so when ever 3[tex]x^{3}[/tex]-12x=0 then this is equation is true, soooo
x (3[tex]x^{2}[/tex] - 12) =0
so when x = 0 this is true, but also when
3[tex]x^{2}[/tex]-12=0 also
3[tex]x^{2}[/tex] = 12
[tex]x^{2}[/tex] = 4
x = 2
so when x = 2 or -2 or 0 , then this is true
what was the original price of the car? MUST SHOW ALL STEPS OF THE PROCESS.
Answer:
19219.48
Step-by-step explanation:
16540x0.162+16540
The original price would be 100%
It was marked down 16.2%
100 % - 16.2% = 83.8%
The price you paid was 83.8% of the original price.
To find the original price divide the amount you paid by the percentage of the original price:
16,540 / 0.838 = 19.737.47
Original price: $19,737.47
Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.
Answer:
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class.
This means that in her statistics class, Marla got 70% of her test correct.
When Marla took the SAT exam, she scored at the 70th percentile in mathematics.
This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.
Explain the difference in these two scores.
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Sketch the graph of y = 2(x – 2)2 and identify the axis of symmetry
Answer:
x = 2
Step-by-step explanation:
The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2
