The expression is equivalent to (f circle g) (x) will be (3x+2)²+1. The correct option is D.
What is a factor?A number is obtained by dividing another number by itself without leaving a leftover. To put it another way, if multiplying two whole numbers produces a product,
The given expression is;
[tex]f(x) = 3x + 2 \\\\ g(x) = x_2 + 1[/tex]
[tex](f g)(x) =g(f(x)) =g(3x+2)=(3x+2)^2 +1[/tex]
The expression is equivalent to (f circle g) (x) will be (3x+2)²+1. Option D is correct.
To learn more about the factors refer to the link;
brainly.com/question/24182713
If you only have 36ft of fence to build with, what is the maximum area you can have?
The maximum area would be a square with 4 identical sides.
36/4 = 9
Each side would be 9 feet long.
Area = 9 x 9 = 81 square feet
Answer: 81 square feet
WILL AWARD BRAINLIEST!!! POLYNOMIALS
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
════════════════════
1.
[tex]kx^{2} + kx + \frac{25}{4}[/tex]
All you need to do is factor out [tex] \frac{1}{4}[/tex]
=[tex] \frac{4kx^{2 +} + 4kx + 25 } {4} [/tex]
if you evaluate it it will become
[tex]kx^{2} + kx + \frac{25}{4} [/tex]
────────────────────
2.
[tex] \frac{3y² + 1}{4} - \frac{y}{2} = 6[/tex]
[tex]3y² + 1 - 2y = 24[/tex]
[tex]3y² - 23 - 2y = 0[/tex]
[tex]3y² - 2y - 23 = 0[/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 3\left(-23\right)}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{4-4\times 3\left(-23\right)}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{4-12\left(-23\right)}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{4+276}}{2\times 3} [/tex]
[tex]y=\frac{-\left(-2\right)±\sqrt{280}}{2\times 3}[/tex]
[tex]y=\frac{-\left(-2\right)±2\sqrt{70}}{2\times 3}[/tex]
[tex]y=\frac{2±2\sqrt{70}}{6}[/tex]
[tex]y=\frac{2\sqrt{70}+2}{6}[/tex]
[tex]y=\frac{\sqrt{70}+1}{3}[/tex]
[tex]y=\frac{2-2\sqrt{70}}{6}[/tex]
[tex]y=\frac{1-\sqrt{70}}{3}[/tex]
[tex]y=\frac{\sqrt{70}+1}{3}[/tex]
So the answer is
[tex]y=\frac{\sqrt{70}+1}{3}[/tex]
════════════════════
Explanation:
#Carry on learning
Instructions: Find the missing side. Round your answer to the nearest tenth
Answer:
x = 39.6
Step-by-step explanation:
[tex]cos49 = \frac{26}{x} \\ \\ x = 39.6[/tex]
What is the final answer
Answer:
Step-by-step explanation:
I just came to the realization that your probably cheating. Don't cheat, it doesn't help you now or in the long run. Nevertheless, I have already outlined the method like three times. So, at the very least, attempt this question hoenstly.
A patio has dimensions of 25 feet by 35 feet. What is its area?
Answer:
3
Step-by-step explanation:
In this problem, we don't know the length or width. All we do know is that the length is 5 feet longer than the width, and that the perimeter is 54 feet. Both lengths plus both widths equals the perimeter. To solve this problem, you must give the width, the value of x.
Step 1: Draw a rectangle where the width is x and the length is x + 5.
Step 2: Find the sum of the lengths and the sum of the widths
2 times the length plus 2 times the width equals the perimeter
2(x + 5) + 2(x) = 54
Step 3: Solve for the width
2(x + 5) + 2(x) = 54
2x + 10 + 2x = 54 (Distributive Property)
4x + 10 = 54 (Group Like Terms)
4x = 44 (Subtraction Property of Equality)
4x/4 = 44/4
x = 11 (Division Property of Equality)
x = width = 11
Step 4: Solve for the length
x + 5 = length
11 + 5 = 16
Length = 16. So (3) must be the answer.
Having some trouble with this question, any help? A wire supporting a radio tower is secured to the ground 14 m from the base of the tower. If the angle between the ground and the wire is 57°, what is the height of the tower, to the nearest tenth of a metre?
By using what we know about right triangles, we will see that the height is 11.7 m.
How to find the height of the tower?We can view this as a right triangle, such that the wire is the hypotenuse of said triangle.
We know that the hypotenuse measures 14 m, and the angle between the ground and the wire si 57°. The height would be the opposite cathetus to that angle, so we can use the rule:
Sin(a) = (opposite cathetus)/hypotenuse
Replacing the values we get:
Sin(57°) = H/14m
Sin(57°)*14m = H = 11.7m
The height of the tower is 11.7 meters.
If you want to learn more about right triangles, you can read:
https://brainly.com/question/2217700
Find the area of the shaded region.
Answer:
Step-by-step explanation:
Remark
The method of finding the area of the ring is to find the area of the outer ring and subtract the area of the hole in the middle.
Outer ring
r = 10 + 4 = 14 inches
Area = pi * r^2
Outer ring area = pi * 14^2
Outer ring area = 196 pi
Inner hole
Area unshaded part = pi * r^2
r = 10
Area = pi * 10^2
Area = 100 pi
Area of the shaded part
area of the shaded part = outter circle area - inner circle area
outter circle area = 196 * pi
inner circle area = 100 pi
Area of the shaded part = 196 pi - 100 pi
Area of the shaded part = 96 pi
pi = 3.14
Area of the shaded part = 96 * 3.14
Answer area of the shaded part = 301.44
Answer area of the shaded part = 301.4 rounded to the nearest tenth
The second problem is done exactly the same way. Only the numbers have been changed. I will give you the answers to the main part of the problem and you can try and get what I got. If we disagree, be preparred to tell me what you got so I correct mine if it is wrong.
Outter Radius = 18 + 8 = 26
Area of outter circle = pi * 26^2
Area of outter circle = 676 pi
Inner Circle area hole = pi * 18^2
Inner Circle area hole = 324 pi
Area of the shaded part = outter circle - inner circle
Area of the shaded part = 676 pi - 324 pi
Area of the shaded part = 352 pi
pi = 3.14
Area of the shaded part = 352 * 3.14
Answer: area of shaded part rounded to 1 decimal place = 1105.3
The box is 12
inches wide, 18 inches
long, and has a volume
of 2,160 inches cubed.
What is the height?
*Don't forget units.
Answer:
10 inches
Step-by-step explanation:
Hope it helps ......
???????????/?//?/??????????????/
Answer:
[tex]307.876\quad cm^{2}[/tex]
Step-by-step explanation:
As, the given figure is semicircle
Area of Semicircle [tex]=\frac{\pi\ r^{2} }{2} \\[/tex]
r=14 cm
So Area is [tex]=307.876\quad cm^{2}[/tex]
Answer:
307.72 :)
Step-by-step explanation:
SEmicirlce area: 1/2(3.14r^2)
Now lets solve!!
28/2 = 14
1/2(3.14)(14^2)
1/2(3.14 x 196)
1/2(615.44)
307.72
Have an amazing day!!
Please rate and mark brainliest!!
Please Evaluate This Expression:
60 ÷ (3+7) + 7 • (9÷3)
Answer:
27
Step-by-step explanation:
60 ÷ (3+7) + 7 • (9÷3)=
60÷10+7•3=
6+7•3=
6+21=27
Find an equation for the inverse for each of the following relations. y= (2/3)x-5
Answer:
y = 3/2x + 15/2
or
y = [tex]\frac{3x+15}{2}[/tex]
Step-by-step explanation:
To solve inverse functions, switch the x and y in the equation, then
solve for y.
original equation :
y = (2/3)x - 5
switch x and y
x = (2/3)y - 5
add 5 to both sides
x + 5 = (2/3)y
Multiply both sides by the reciprical of (2/3)
(3/2)(x+5) = (3/2)(2/3)y
distribute and simplifiy
(3/2x +15/2) = y
or
y = (3/2x) +(15/2)
When Fritz drives to work his trip takes 35 minutes, but when he takes the train it takes 15 minutes. Find the distance Fritz travels to work if the train travels an average of 80 miles per hour faster than his driving. Assume that the train travels the same distance as the car.
Answer:
35 miles
Step-by-step explanation:
Let's say Fritz travels at x miles per hour via train and y miles per hour via car.
(speed of car) + 80 miles per hour = speed of train
y + 80 = x
Speed * time = distance
Speed of train * time of train = distance = speed of car * time of car
x * 15 minutes = y * 35 minutes
convert minutes to hours since miles per hour is in terms of hours
60 minutes = 1 hour
15 minutes = ? hours
multiply 15 minutes by 1 hour/60 minutes. since 60 minutes = 1 hour, we can divide both sides by 60 minutes to get 1 hour/60 minutes = 1. we can always multiply by 1, so we do that here. note that the minutes are in the denominator so the 15 minutes cross out with the 60 minutes, leaving us with only hours as our unit.
15 minutes = 15 minutes * 1 = 15 minutes * 1 hour/60 minutes = 15/60 hours = 3/12 hours
similarly, 35 minutes * 1 hour/60 minutes = 35/60 hours = 7/12 hours
x * 15 minutes = y * 35 minutes
x * 3/12 hours = y * 7/12 hours
plug y+80 in for x
(y+80) * 3/12 hours = y * 7/12 hours
(3/12) * y + 20 = (7/12) * y
subtract (3/12) * y from both sides to isolate the variable (y) and its coefficient
20 = (4/12) * y
multiply both sides by 12/4 (the inverse of the coefficient) to get rid of the coefficient
20*12/4 = y = 60
y = 60 miles per hour
x = y + 80 = 140 miles per hour
distance = x * 3/12 hours = 140 miles/hour * 3/12 hours= 35 miles
What is the quotient of 4.18*10^8/1.1*10^-2
A. 3.8*10^16
B.3.8*10^14
C.3.8*10^10
D. 3.8*10^6
(Show ur work)
Answer:
C. 3.8 x 10¹⁰
Step-by-step explanation:
Our expression :
4.18 x 10⁸ ÷ 1.1 x 10⁻²Steps to solve :
1) Take the values of the exponents of 10 and the other numbers separately.
[4.18 ÷ 1.1] × [10⁸ ÷ 10⁻²]3.8 × [10⁸⁻⁽⁻²⁾]3.8 x 10¹⁰C is the correct option.
WHAT IS [tex]\frac{P^{8} +1}{P^{4} }[/tex] WHEN [tex]P-\frac{1}{P}=11\\[/tex]
Answer:
5.4232
Step-by-step explanation:
this should be correct
A quadrilateral has two angles that measure 222° and 81°. The other two angles are in a ratio of 6:13. What are the measures of those two angles?
Answer:
Other two angles of quadrilateral measures 18° and 39°Step-by-step explanation:
Given that a quadrilateral has two angles that measure 222° and 81°.
Let other two angles of quadrilateral be 6x and 13x. We know that sum of all the angles of quadrilateral is 360°.
➝ 222 + 81 + 6x + 13x = 360°
➝ 303 + 19x = 360°
➝ 19x = 360° - 303
➝ 19x = 57
➝ x = 57/19
➝ x = 3
Hence,
6x = 6(3) = 18° 13x = 13(3) = 39°∴ Other two angles of quadrilateral measures 18° and 39°
Answer:
Measurement of other two angles are 39° and 19°
Step-by-step explanation:
Given :-
Quadrilateral has two angles of measurement 222° and 81° and the other two angles are in ratio of 6:13To find:-
The measurement of other two anglesSolution:-
Let the value of other two angles be 6x and 13x
We know , the sum of angle inside a quadrilateral is 360°
222° + 81° + 13x + 6x = 360°
19x = 360° - 303°
x = 3
So , the value of other two angles are
13 × 3 = 39°
6 × 3 = 18°
The number of sit-ups that all tenth-grade girls can do in 5 minutes is normally distributed. beth surveyed 20 of her fellow intramural tennis players, all tenth-grade girls, and determined the mean number of sit-ups they could do. can she make an inference about the population mean for all tenth-grade girls based on the sample? no, because the sample size was not big enough. no, because she did not use a simple random sample. yes, because the sample size was big enough. yes, because she used a simple random sample.
The true statement is as follows "No because she did not use a simple random sample".
What is random sampling?Random sampling is the method to choose the given samples of observation to make assumptions about the population.
It is given that
Population: All tenth-grade girls
Sample: 20 intramural tennis players
The 20 intramural tennis players cannot represent all tenth-grade girls.
This is so because the selection is biased here, and it could not be used to make inferences about the overall population. then she did not use a simple random sample.
Hence, the true statement is (b)
Read more about random sampling at:
https://brainly.com/question/1334729
Answer:
the correct answer is B.
Step-by-step explanation:
~Hope this helps! :)
Ben is climbing a tree with a lot of branches. His height off the ground at time $t$ is $2t^2-5t+29$ feet. To the nearest foot, what will his minimum height be?
Using the vertex of the quadratic equation, it is found that his minimum height will be of 25.875 feet.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the equation is:
h(t) = 2t² - 5t + 29.
Hence the coefficients are a = 2 > 0, b = -5, c = 29, and the minimum height in feet is given by:
[tex]y_v = -\frac{(-5)^2 - 4(2)(29)}{4(2)} = 25.875[/tex]
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
Ben minimum height above the ground when climbing the tree would be 25.875 feet
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given that:
h(t) = 2t² - 5t + 29
The minimum height is at h'(t) = 0, hence:
h'(t) = 4t - 5
4t - 5 = 0
t = 5/4
h(5/4) = 2(5/4)² - 5(5/4) + 29 = 25.875 feet
Ben minimum height above the ground when climbing the tree would be 25.875 feet
Find out more on equation at: https://brainly.com/question/2972832
Refer to the figure: The Triangle
Midsegment Theorem says the midpoints
(K and L) of two sides of a triangle will
result in parallel third sides such that KL is
half of MN.
A. Sketch ∆JKL and ∆JMN separately in the space below. Label all vertices.
Then explain, in detail, how you could
justify that the two triangles are similar, using the results of the Midsegment
Theorem.
What is the scale factor between the two triangles and how do you know?
Answer:
The Triangle Midsegment Theorem states that, if we connect the midpoints of any two sides of a triangle with a line segment, then that line segment satisfies the following two properties
Step-by-step explanation:
What is the correct similarity statement?
Answer:
ΔSTR ~ ΔSRQ
Step-by-step explanation:
ΔSTR ~ ΔSRQ
because we need to write the corresponding sides in the same order
ST corresponds to SR
TR corresponds to RQ
SR corresponds to SQ
If you answer this TRUTHFULLY!!! THAT MEANS NO BOTS AND NO TROLLS!!. I WILL GIVE YOU 5 STARS THANK YOU, THANK YOU ON YOUR ACC ASWELL!!! AND....100 POINTS!!!!
Answer:
pay ($), y
Step-by-step explanation:
Well, in the number of hours you work determines your pay in this case. So, pay is dependent of the number of hours.
And, the dependent variable is usually represented by y in a x,y graph.
The daily number of miles driven by a bus driver during a week are 50, 65, 78, 54, 53, 61, 79, and 78.
Which statement is true?
Both the mean and mode are appropriate measures of center.
Both the median and mode are appropriate measures of center.
Both the mean and median are appropriate measures of center.
The mode is the only appropriate measure of center.
Answer: both median and mean
Step-by-step explanation:
Answer:
C Both the mean and median are appropriate measures of center.
Step-by-step explanation:
Which equation has only one solution? |x – 5| = –1 |–6 – 2x| = 8 |5x 10| = 10 |–6x 3| = 0
The linear equation which has only one solution would be |–6x + 3| = 0
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0.
|x – 5| = –1
The absolute function cannot be equal to the negative. so we cannot solve this absolute function.
|–6 – 2x| = 8
For this absolute function, we make two equations here
-6-2x= 8 and -6-2x= 8. So we will get two solutions for x.
|5x + 10| = 10
For this absolute function, we make two equations here
5x+10= 10 and 5x+10= -10. So we will get two solutions for x
|–6x + 3| = 0
For this absolute function we make two equations
-6x+3=0 and -6x+3=-0.
Both have the same 0 on the right side. So we will get only one solution for x
Learn more about equation;
https://brainly.com/question/11888999
Answer:
the answer is D.
Step-by-step explanation:
A has no solutions
B and C have two solutions.
therefore, none of these have only one solution.
A car tyre has a diameter of 60 cm.
How far will the wheel travel in one revolution?
Answer:
Step-by-step explanation:
If 60cm is the outer diameter of the rim, then the rim without a tire would travel 188.50 (not 188.4) cm per revolution. There will of course be a tire, and the extra diameter of wheel+tire will increase the distance traveled by the bike. If e.g. the tire is 3cm from bead to outermost tread (and is properly inflated), then the extra circumference would be 2 x 3cm x pi = 18.850cm of distance traveled, for a total of just over 207.3 cm per revolution.
a 5 pack of clay pots cost $14.25. What is the unit price?
Answer:4.25
Step-by-step explanation: you divide the cost by the materials I believe (I’m sorry if it’s wrong)
Answer:
2.85
Step-by-step explanation:
In order to find a unit price (price per item), you will need to divide.
In this case, we have the numbers 14.25 and 5.
So if we divide...
14.25 ÷ 5 = 2.85
We know the unit price.
The answer is 2.85.
Brainliest please?
Segment CD is reflected across the y-axis to get segment C′D′. The coordinates of C are (−5,−5), and the coordinates of D are (0,1). What are the coordinates of D′?
Images that are reflected are mirror images of each other. The coordinate D reflected over the y-axis will give (0, 1).
What are reflections?Images that are reflected are mirror images of each other.
The reflection rule of a coordinate (x, y) over the y-axis is given as:
(x, y) - > (-x, y)
Given the coordinate CD expressed as C(-5, -5) and D(0,1), the coordinate D reflected over the y-axis will give (0, 1).
Learn more on reflection here: https://brainly.com/question/26642069
Answer:
(0, 1)
Step-by-step explanation:
The function f is given by f(x) = 2*, while the function g is given by g(x) = 4.2%.
Kiran says that the graph of g is a vertical scaling of the graph off. Mai says that the
graph of g is a horizontal shift of the graph off. Do you agree with either of them?
Explain your reasoning.
DO
I agree with Kiran that the graph of g(x) = [tex]4* 2^{x}[/tex] is a vertical scaling of the graph of f(x) = [tex]2^{x}[/tex],
Define the term scaling of the graph?Scaling of the graph refers to the process of stretching or shrinking a graph of a function either vertically or horizontally, while maintaining the shape of the graph.
If the function f is given by f(x) = [tex]2^{x}[/tex],
the function of g is given by g(x) = [tex]4* 2^{x}[/tex]
I agree with Kiran that the graph of g(x) = [tex]4* 2^{x}[/tex] is a vertical scaling of the graph of f(x) = [tex]2^{x}[/tex],
To see this, note that both functions have a base of 2 raised to the power of x. However, the function g has an additional factor of 4 multiplying [tex]2^{x}[/tex]. This means that g is 4 times larger than f for any given value of x.
On the other hand, I disagree with Mai that the graph of g is a horizontal shift of the graph of f. A horizontal shift occurs when a function is moved left or right along the x-axis. However, both f and g have the same base, so the shape of their graphs is the same. The only difference is the vertical scaling due to the additional factor of 4 in g.
To know more about graph, visit:
https://brainly.com/question/11803331
#SPJ1
Correct question here-
Robin has 10 books. There is enough space on a shelf for 4 books. In how many ways can 4 of the 10 books be
arranged on the shelf?
The number of arrangements of the books is an illustration of permutation
The books can be arranged in 5040 ways
How to determine the number of arrangements?The given parameters are:
Total books, n = 10Books to arrange, r = 4The number of arrangements is calculated as:
Ways = nPr
Substitute the given values
Ways = ¹⁰P₄
Apply the permutation formula
Ways = 10!/(10 - 4)!
Evaluate the quotient
Ways = 5040
Hence, the books can be arranged in 5040 ways
Read more about permutation at:
https://brainly.com/question/12468032
A square has an apothem measuring 2.5 cm and a perimeter of 20 cm. what is the area of the square, rounded to the nearest square centimeter? 13 cm2 25 cm2 50 cm2 100 cm2
The area of the square, which has an apothem measuring 2.5 cm and a perimeter of 20 cm is 25 cm².
What is the area of square?Area of square is the square of its side's length. It can be given as,
[tex]A=a^2[/tex]
Here, (a) is the length of the side of the square
A square has an apothem measuring 2.5 cm and a perimeter of 20 cm. The perimeter of the square is 4 times the sides of the square.
Let suppose the side of this square is a cm. thus,
[tex]4a=P\\4a=20\\a=\dfrac{20}{4}\\a=5\rm\; cm[/tex]
The area of the square is,
[tex]A=5^2\\A=25\rm\; cm^2[/tex]
Hence, the area of the square, which has an apothem measuring 2.5 cm and a perimeter of 20 cm is 25 cm².
Learn more about the area of square here;
https://brainly.com/question/1658516
Answer:
25cm
Step-by-step explanation:
e2020
Event A: lands on a number greater than 4
Event B: lands on purple
Events A and B are ______ events.
P(A or B) = ____
Answer:
disjoined am not sure abot the P(A or B)
Step-by-step explanation:
Answer:
disjointed 2/3
Step-by-step explanation:
hopeit helps
All polygons having congruent
sides and angles are described
as being
A. congruent
B. equilateral
C. regular
D. irregular
(Regular is wrong… I just tried that)