Answer:
5x+6
Step-by-step explanation:
f(x) = 3x + 10
g(x) = 2x - 4
(f+ g)(x)= 3x + 10 + 2x - 4
Combine like terms
= 5x+6
I really need the help please and thank you
Asnwer: C
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A cone and a pyramid have equal heights and volumes. If the base area of the pyramid is 154cm^2, find the radius of the cone
Answer:
√154/π
Step-by-step explanation:
thể tích nón = thể tích hình chóp
1/3πr².h=1/3S.h
πr²=154(rút gọn h và 1/3)
=> r=√154/π
The radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
We have:
A cone and a pyramid have equal heights and volumes.
154 = πr²
π = 22/7
r = 7 cm
Thus, the radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.
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Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5
Solution :
Here the probability that exactly 28 out of 304 students will not graduate on time. That is
P (x = 28)
By using the normal approximation of binomial probability,
[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]
∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]
[tex]$=P(27.5 \leq x \leq 28.5)$[/tex]
That is the area between 27.5 and 28.5
Therefore, the correct option is (e). Area between 27.5 and 28.5
log, (x + y)=log, y, log, x .
Solve for question D only
Answer:
4.
Step-by-step explanation:
Change of base formula is
logb x = loga x / loga b
So logx 25 = log5 25 /log5 x
Now log5 25 = log5 5^2 = 2, so:
logx 25 = 2 / log5 x
So log5 x^2 * logx 25
= log5 x^2 * 2 /log5 x
= 2 log5 x * 2 / log5 x
= 4.
Is 3.6 a integer or a whole number?
36 is a whole number.
Answer:
The number 3.6 is a rational number.
All numbers that can be represented as fractions made of two integers (whole numbers) are considered to be
When it was built, the given stadium held 31,080 fans per game. Today, it holds 86,047. How many more fans could attend per year (12 games) compared to the year it was built?
Answer:
659604 students
Step-by-step explanation:
86047-31080=54967 more students per game
54967 students per game x 12 games = 659,604 students
Find area and perimeter of shaded regions below
Answer:
Step-by-step explanation:
ABCD is a square.
side = 24 cm
Area of square = side * side = 24 * 24 = 576 cm²
Semicircle:
d = 24 cm
r = 24/2 = 12 cm
Area of semi circle =πr²
= 3.14 * 12 * 12
= 452.16 cm²
Area of shaded region = area of square - area of semicircle + area of semicircle
= 576 - 452.16 + 452.16
= 576 cm²
Perimeter:
Circumference of semicircle = 2πr
= 2 * 3.14 * 12
= 75.36
Perimeter = 2* circumference of semicircle + 24 + 24
= 2 * 75.36 + 24 + 24
= 150.72 + 24 + 24
= 198.72 cm
Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?
howdy!!
yr answer is the third graph!
Form a polynomial whose zeros and degree are given.
Zeros: - 2, 2, 6; degree: 3
Type a polynomial with intéger coefficients and a leading coefficient of 1 in the box below.
f(x)=(Simplify your answer.)
Answer:
[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]
[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]
Step-by-step explanation:
Multiply factors.
2x + 5y = 10 into slope- intercept form
Answer:
y=-2x+10
Step-by-step explanation
Hope this helped
I’m the triangle shown we can find the angle theta as follows.
Answer:
sin = opp/hyp
cos = adj/hyp
tan = opp/adj
Find the other endpoint of the line segment with the given endpoint (-2, -2) and midpoint (3,10)
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Answer:
(8, 22)
Step-by-step explanation:
For endpoints A and B, and midpoint M, the relationship of interest is ...
B = 2M -A
B = 2(3, 10) -(-2, -2) = (6+2, 20+2)
B = (8, 22)
The other end point is (8, 22).
Given the function f(x) = 3x - 1, explain how to find the average rate of change between x = 1 and x = 4.
Step-by-step explanation:
f(1) = 3×1 - 1 = 2
f(4) = 3×4 - 1 = 12-1 = 11
so, the functional value changes 11-2=9 units on an x interval of 4-1=3 units length.
the average change rate is the total change across the x interval relative to the interval length.
that is
9/3 = 3
which is the slope (= the factor of x) in the line equation.
for a line its change rate for any point is the same constant. and that is therefore automatically also the average change rate across an interval of x values.
if the change rate would be different for different parts of the function, it would not be a straight line.
Answer:
3
Step-by-step explanation:
The average rate of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 1, 4 ] , then
f(b) = f(4) = 3(4) - 1 = 12 - 1 = 11
f(a) = f(1) = 3(1) - 1 = 3 - 1 = 2
average rate of change = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3
It used to take 20 hours to get to Los Angeles, now it takes 12 hours, how much shorter was it?
Step-by-step explanation:
It takes 20 Hours to get to Los Angeles
Now it takes 12 hours....
Therefore we subtract 20 from 12
which becomes
20 - 12= 8.
So it's 8 hours shorter
Which of the two functions below has the smallest minimum y-value?
f(x) = 4(x - 6)4 + 1
g(x) = 2x3 + 28
O A. g(x)
B. f(x).
C. The extreme minimum y-value for f(x) and g(x) is --
D. There is not enough information to determine
Answer:
Answer A
Step-by-step explanation:
[tex]\displaystyle \lim_{n \to -\infty} (3x^3+28)=-\infty\\\\minimum\ of \ f(x)=6\\\\Answer\ A[/tex]
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1825 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
1) 35 gallons by the first car 2) 40 gallons by the second car
Step-by-step explanation:
Suppose the first car used x gallons, when the second car used the rest- 75-x
If the first car's efficiency is 35 miles per galon, its milleage is 35*x, the second car's milleage is 15*(75-x). And the summary milleage is equal to 1825.
35x+15(75-x)=1825
35x+1125-15x= 1825
20x=700
x=35- gallons consumed by the first car,
75-35=40- gallons consumed by the second one
The volume of a gas with a pressure of 1.2 atm increases from 1.0 L to 4.0 L. What is the final pressure of the gas, assuming constant temperature?
(a) 1.2 atm
(b) 0.30 atm
(c) 3.3 atm
(d) 4.8 atm
(e) 1.0 atm
Answer:
(b) 0.30 atm
Step-by-step explanation:
Given data
Initial pressure= 1.2atm
Initial volume= 1.0L
Final volume= 4.0L
Final pressure= ???
Let us apply the gas formula to find the Final pressure
P1V1= P2V2
Substitute
1.2*1= x*4
Divide both sides by 4
1.2/4= x
x= 0.3atm
Hence the final pressure is 0.3 atm
14% of all Americans live in poverty. If 35 Americans are randomly selected, find the probability that
a. Exactly 3 of them live in poverty.
b. At most 7 of them live in poverty.
c. At least 4 of them live in poverty.
d. Between 1 and 8 (including 1 and 8) of them live in poverty.
Find Term 20 for the sequence a= 4 6 8 10......
4,6,8,10 are in A.P
a=4d=2[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+(20-1)2[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+19(2)[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+38[/tex]
[tex]\\ \rm\Rrightarrow a_20=42[/tex]
HURRY WILL GIVE BRANLIEST
I believe that the answers in order are: Rational, Irrational, Irrational, Irrational. I think these answers are correct, but if not, please let me know. Thanks.
Answer:
I think 0.5 and 0/100 are rational
the others are irrational
11. Find the 5th term of the sequence defined by the given rule. (1/2 point)
f(n) = 6n + 4
Answer:
34
Step-by-step explanation:
n = 5
f(5) = 6(5)+4
f(5)=34
The fifth term of the sequence is equal to 34.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,
n = 5
f(5) = 6(5)+4
f(5)=34
Therefore, the fifth term of the sequence is equal to 34.
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Write the equation of the line shown in the graph above in slope intercept form
A) y=2/3x+1
B) y=-x+2/3
C) y=-2/3x+1
D) 2x+3y=3
Answer:
C, y=-2/3x+1
Step-by-step explanation:
using points (0, 1) and (3, -1) obtained from the graph:
slope = -1-1/3-0 = -2/3
use one of the points above lets take (1, 0) and another point (x,y)
slope = y-0/x-1 = -2/3
y=-2/3x+1
A circle P is circumscribed about a regular hexagon ABCDEF
If segment AE is drawn, triangle AEF is a/n ____________ triangle. Select one:
a. isosceles
b. scalene
c. equilateral
d. right
i’ll mark u as brainliest:))
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Answer:
a. isosceles
Step-by-step explanation:
Segments EF and FA of the hexagon are the same length, so the triangle is an isosceles triangle.
Annie is opening a savings account which earns 5.2% interest, compounded continuously.
How much will she need to deposit in the account so that she has $2300 after 7 years?
Round your answer to the nearest dollar.
Do NOT round until you have calculated the final answer.
Answer:
1686.22
Step-by-step explanation:
2300=P(1+(0.052x7))
2300=P1.364
P=2300/1.364
=1686.217...
=1686.22...
=1686 FOR THE NEAREST DOLLAR
- 18 = -3x + 6
Plz help
Answer:
8 =x
Step-by-step explanation:
- 18 = -3x + 6
Subtract 6 from each side
-18-6 = -3x+6-6
-24 = -3x
Divide each side by -3
-24/-3 = -3x/-3
8 =x
Answer:
x= 8
Step-by-step explanation:
[tex]\sf{}[/tex]
=> -3x+6 = -18
=> -3x+6-6= -8-6
=> -3x= -24
=> x= 8
Which answer shows y + 2x < 4x - 3, rewritten to isolate y, and its graph?
Answer:
j7kd4uzvinxru,en gg4ukfiebcjeictijxc7t
Step-by-step explanation:
mxrICE vxxn6rj CVT ryrf NYC cfkxkeuixx BBC xu BBC yfh
London bought snacks for her team's practice. She bought a bag of apples for $2.25
and a 18-pack of juice bottles. The total cost before tax was $9.63. Write and solve an
equation which can be used to determine j, how much each bottle of juice costs?
Answer:
j = $7.38 / 18
Step-by-step explanation:
1. We have to find the total cost of a 18 juice bottles pack
= $ 9.63 - $ 2.25
= $ 7.38
2. To find how much each bottle of juice costs :
j = $ 7.38 / 18 #
What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope-intercept form
A: y= 2/5x -1/5
B: y= 2/5x +1/5
C: y= -2/5x -1/5
Answer:
y = 2/5x + 1/5
Step-by-step explanation:
y = 2/5x + b
-1 = 2/5(-3) + b
-1 = -6/5 + b
1/5 = b
Cyruer.
Pucic Or the
(a) The surface area and volume of a sphere are in the ratio of 3 : 7
cm. What is the circumference
of its great circle and volume ? Find it.
Answer:
Hello,
Step-by-step explanation:
Area of the sphere:
[tex]S=4*\pi *r^2[/tex]
Volume of the sphere:
[tex]V=\dfrac{4*\pi *r^3}{3}[/tex]
[tex]\dfrac{S}{3} =\dfrac{V}{7} \\\\\dfrac{4*\pi *r^2}{3} =\dfrac{4*\pi *r^3}{3*7} \\\\1=\dfrac{r}{7} \\\\\\r=7\\\\great \ circle: 2*\pi* r=14*\pi\\[/tex]
[tex]Volume=\dfrac{4*\pi *7^3}{3} =\dfrac{1372*\pi }{3} \approx{1436,7550...(cm^3)}[/tex]
The length of a rectangle is 7 inches
more inan its width. the area of
the rectangle is eqaul to 4 inches less
than 4 times the perimeter. Find the
length and width of the rectangle
Answer:
length = 20 inches
width = 13 inches
Step-by-step explanation:
l = length
w = width
area = l×w
perimeter = (2×l) + (2×w)
l = w + 7
l×w = 4×(2×l + 2×w) - 4
(w+7)×w = 4×(2×(w+7) + 2×w) - 4
w² + 7w = 4×(2w + 14 + 2w) - 4
w² + 7w = 8w + 56 + 8w - 4 = 16w + 52
w² - 9w - 52 = 0
the solution for a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
here we use now w instead of x.
and a=1
b=-9
c=-52
w = (9 ± sqrt(81 - -208))/2 = (9 ± sqrt(81+208))/2 =
= (9 ± sqrt(289))/2 = (9 ± 17)/2
w1 = (9+17)/2 = 26/2 = 13
w2 = (9-17)/2 = -8/2 = -4
and a negative length does not make any sense for a geometric shape.
so, only w1 = 13 applies.
l = w + 7 = 13 + 7 = 20
