Answer:
2 sqrt(2x-1)
Step-by-step explanation:
f(x) = sqrt(x+7)
g(x) = 8x-11
f(g(x))=
Place g(x) in for x in the function f(x)
f(g(x)) = sqrt( 8x-11 +7)
= sqrt( 8x -4)
Factor out 4
= sqrt( 4(2x-1)
= 2 sqrt(2x-1)
[tex]\\ \sf\longmapsto f(x)=\sqrt{x+7}[/tex]
[tex]\\ \sf\longmapsto g(x)=8x-11[/tex]
g(x) will be put on the place of x[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-11+7}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-4}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{4(2x-1)}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=2\sqrt{2x-1}[/tex]
The base and height of a right triangle are 20 inches and 15 inches. Find the length of the hypotenuse.
Using the Pythagorean theorem:
Hypotenuse = sqrt( 20^2 + 15^2)
Hypotenuse = sqrt( 400 + 225)
Hypotenuse = sqrt(625)
Hypotenuse = 25
Answer: 25 inches
Answer:
25 inches
Step-by-step explanation:
We can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
20^2 + 15^2 = c^2
400 +225 = c^2
625=c^2
Taking the square root of each side
sqrt(625) = sqrt(c^2)
25 = c
Can someone please help
Answer:
[tex]162.07[/tex]
Step-by-step explanation:
An image that creates represents this situation has been attached to this answer. As one can see, the diagram models the situation, the angle of depression represents the angle between the horizon line and the line of sight. The horizon line and the tower form a right angle (a (90) degree angle). This means that the angle of depression is complementary to the angle of sight. Therefore, one can state the following:
[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]
Substitute,
[tex](angle\ of\ depression) + (angle\ of \ sight)=90[/tex]
[tex](m<ABD)+(m<DBC)=90[/tex]
[tex]42+(m<DBC)=90[/tex]
Inverse operations,
[tex]42+(m<DBC)=90[/tex]
[tex]m<DBC=48[/tex]
Now one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are a series of ratios that describe the relationship between the sides and angles in a right triangle. These ratios are as follows:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Bear in mind, the terms (opposite) and (adjacent) are subjective, and change depending on the reference angle. However, the term (hypotenuse) refers to the side opposite the right angle and is constant regardless of the reference angle.
In this case, one has found an angle in the triangle, one is given the measure of the side opposite this angle, and one is asked to find the side adjacent to this angle. Therefore, it would make the most sense to use the ratio tangent (tan).
[tex]tan(\theta)=\frac{opposite}{adjacnet}[/tex]
Substitute,
[tex]tan(48)=\frac{180}{adjacent}[/tex]
Inverse operations,
[tex]tan(48)=\frac{180}{adjacent}[/tex]
[tex]adjacent=\frac{180}{tan(48)}[/tex]
[tex]adjacent=162.07[/tex]
Which of the following contains a variable?
A. He scored a 95 on the test.
B. The bug crawled 15 inches per second.
C. The area is 56 square centimeters.
D. Ana is 3 years older than Mark.
Answer:
D. Ana is 3 years older than Mark.
Step-by-step explanation:
We do not know how old Mark is. That is the variable
UR SO COOL IF UOU ANSWERRR PLEASE ANSWERRRR
Answer:
1/6 is less than 1/2
Step-by-step explanation:
1/6 is close to 0
8/9 is close to 1
1/6 is less than 1/2
please me in the math
[tex]6 {x}^{6} + 6 {x}^{4} + 6 {x}^{2} and \: \\ 4 {x}^{6} - 4 {x}^{x} \\ it \: is \: lcm[/tex]
Answer:
I'm sorry I'm not good at math
Step-by-step explanation:
sorry
1. Which of the following expressions are equivalent to? Select all that apply. A. 31 . 36 B. 31 . 35 C. 3-2 . 3-4 D. 32 . 3-8 E. 3 • 3-6 F.3-1 . 3-5
Answer: A and C
Step-by-step explanation:
please help,
all i have is 16 x 33 = 528cm2 ?!!!
Answer:
732 m^2
Step-by-step explanation:
Find the area of the full rectangle
33*24 =792
Find the area of the triangle
24-16 = 8
33 -18 =15
The area of the triangle is
A = 1/2 bh = 1/2 ( 15)(8) = 60
Subtract the triangle from the rectangle
792 - 70=732 m^2
Answer:
732 [tex]m^2[/tex]
Step-by-step explanation:
First we can find the area of the shape if the triangle wasn't there. That would be:
24×33=792.
Then, we can find the area of the triangle to subtract that from the total.
The formula for the area of a triangle is [tex]A=\frac{1}{2} bh[/tex].
So [tex]A=\frac{1}{2} (8)(15)[/tex]
I found the base of the triangle by subtracting 16 from 24.
I found the height of the triangle by subtracting 18 from 33.
Now, solve the equation.
[tex]A=\frac{1}{2}( 120)[/tex]
A=60
Then finally, Subtract 60 from 792.
You get 732.
I hope this helps!
the distance between the points (tan a, 1) , (0,2)
Answer:
Answer
Step-by-step explanation:
please like and mark me brainlist
What is the value of c
Answer:
if im not mistaken its 121
Step-by-step explanation:
Answer:
99°
Step-by-step explanation:
The interior angle sum of any 5 sided polygon is 540°.
540-53 = 487 - 137 = 350 - 105 = 245- 146 = 99°
Who can help me with problem 2 you can earn 11 points
Answer:
m∠ADC = 90°
5x-5 = 90
x = 19
Step-by-step explanation:
what is the value of a if va- vh is equals to 1
Answer:
[tex] \displaystyle a = \frac{1+vh}{v}[/tex]
Step-by-step explanation:
we want to figure out a value of a for the following condition
[tex] \displaystyle va - vh = 1[/tex]
to do so factor out v;
[tex] \displaystyle v (a - h )= 1[/tex]
divide both sides by v which yields:
[tex] \displaystyle \frac{(a-h) \cancel{(v)}}{ \cancel{v}}= \frac{1}{v} [/tex]
therefore,
[tex] \displaystyle a-h = { \frac{1}{v}}[/tex]
now,add h to both sides:
[tex] \displaystyle a = \frac{1}{v}+h[/tex]
further simplification if necessary:
[tex] \displaystyle a =\boxed{ \frac{1+vh}{v}}[/tex]
factor out of v
[tex]\sf{v(a-h)=1 }[/tex]Dividing both sides by (v)
[tex]\sf{\dfrac{v(a-h)}{(v)}=\dfrac{1}{(v)} }[/tex]cancel out (v)
[tex]\sf{\dfrac{\cancel{v}(a-h)}{\cancel{(v)}}=\dfrac{1}{(v)} }[/tex][tex]\sf{ a-h=\dfrac{1}{v} }[/tex]
add h in both sides
[tex]\sf{a-h+h=\dfrac{1}{v}+h }[/tex]cancelout h
[tex]\sf{a-\cancel{h}+\cancel{h}=\dfrac{1}{v}+h }[/tex] [tex]\sf{a=\dfrac{1}{v}+h }[/tex] [tex]\boxed{\sf{a=\dfrac{1+vh}{v} } }[/tex][tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Therefore:-the value of a if va- vh is equals to 1 is [tex]\bold{\dfrac{1+vh}{v} }[/tex]
SP= 328, Profit = Rs 29
[tex]sp = 328 \\ p = 29 \\ cp = .... \\ \\ p = sp - cp \\ 29 = 328 - cp \\ cp = 328 + 29 \\ cp = 357[/tex]
Rational between √16 and √17
Answer:
41/10
Explanation:
sqrt16 = 4
sqrt17 = 4.12
4.1 = 41/10 and 4<4.1<4.12
Choose the graph that correctly corresponds to the equation y = −4
Answer:
e
Step-by-step explanation:
the graph should look something like this
-0.6the decimal in equivalent fraction form
[tex]\sf \: If \: the \: question \: is \: to \: convert \: - 0.6 \\ \sf \: to \: its\: equivalent \: fractional \: form \: then ⟹[/tex]
[tex]\sf \: - 0.6 \\ \sf= \frac{ - 6}{10} (direct \: fractional \: form) \\ \sf = \frac{ - 3}{5} (in \: simplified \: form)[/tex]
Which angles are adjacent to each other?
• Angle KGD and Angle AEB
• Angle BEC and Angle AEB
• Angle AEB and Angle ECU
• Angle JCI and Angle KGD
Answer:
Step-by-step explanation:
adjacent angles have a common vertex and a common ray
∠BEC and ∠AEB (common vertex E common ray EB)
please! can somebody help me?
Step-by-step explanation:
The depth of the water is increasing by 2 feet each minute.
Can someone help me by please
=============================================================
Explanation:
10% in decimal form is 0.10
25% in decimal form is 0.25
The jump from 0.10 to 0.25 is "times 2.5" since (0.25)/(0.10) = 2.5
This means that we have 2.5 times as many apples compared to oranges.
If we have 2 oranges, as mentioned in every answer choice, then we must have 2*2.5 = 5 apples.
Based on this, the answer is either A or B.
----------------
65% turns into 0.65
The jump from 0.10 to 0.65 is 6.5 since (0.65)/(0.10) = 6.5
So we have 6.5 times as many pears as oranges.
If we had 2 oranges, then we have 2*6.5 = 13 pears
----------------
To summarize, we have:
2 oranges, 5 apples, 13 pears.
The answer is therefore choice A
A macaroni and cheese recipe calls for 's of a 2 % pound block of cheese. How many pounds
are needed?
Mr. Williams ask to buy 1/2 of a pan of brownies that is 2/3 full. What fraction of the original pan does he buy?
4/6
Mr. williams wants to buy 4/6
Answer:
there is some missing information here
if the pas is a dozen brownies
1/2 of a pan is 6 2/3 of 6 would be "4"
how much mac-n-cheese are being made?
that information would be needed to solve this
Step-by-step explanation:
The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?
y – 20
y – 14
y – 8
y – 6
Answer:
Step-by-step explanation:
If we divide 24 by 6, we get 4, which is the other factor of 24 when given the one factor of 6. Same goes here. In order to find out what the other factor of [tex]y^2-10y+24=0[/tex] is when given one factor of y - 4, we simply divide the second degree polynomial by y - 4 to get the quotient. The quotient, then, is the other factor. Synthetic division is the easiest way to do this.
If y - 4 is the factor, then by the Zero Product Property, y - 4 = 0 and y = 4. Setting up synthetic division:
4| 1 -10 24
____________
The rule is to start by bringing down the first term, multiplying it by the number outside, then putting that product up under the next term in line:
4| 1 -10 24
4
1
Then add the column, multiply the sum by the number outside, and put that product up under the next term in line:
4| 1 -10 24
4 -24
1 -6
And add the last column and that is the remainder. We get a 0 remainder. That means that y - 4 goes evenly into the polynomial and the other factor we are looking for is found in the numbers under the addition line. These numbers are the leading coefficients of the depressed polynomial, the polynomial that serves as the other factor: 1y - 6.
Therefore, the 2 factors that multiply together to give us [tex]y^2-10y+24=0[/tex] are (y - 4)(y - 6) and we can check ourselves by multiplying this out by FOILing to see if the result is the polynomial we started with. It is, so we're all done!
Answer:
its ( y-6 )
Step-by-step explanation:
well if you use the FOIL method you will get that answer. also i took the test and got a 100 so there u go.
PLEASE HELP!! would this be symmetric or reflexive property?
Answer: It's "reflexive" because the equation is equal on both sides
Step-by-step explanation: The reason it isn't symmetric property, is because the variables are mismatched (it's not the same on both sides.)
Hope this helped!!
Help would be greatly appreciated
Answer:2/pi
Step-by-step explanation:
First, name the points. Top Left will be A, Top Right will be B, Bottom Right will be C, and Bottom Left will be D. Now, the area of ABCD is 4. Then, we have to find the area of the circle. The center to the midpoint of AB is 1. The length of the midpoint of AB to B is 1. So, using the Pythagorean Theorem, it will be 1^2 + 1^2 = 2, then it will be sqrt2. Finding the area of the circle will be easy now that we have the radius. sqrt2*sqrt2*pi = 2pi. So, it will be 4/2pi, and simplified, it will be 2/pi.
Solve for x. Round to the nearest tenth of a degree, if necessary. Please HELP!
Answer:
x = 29.5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos x = adj side/ hypotenuse
cos x = 67/77
Taking the inverse cos of each side
cos^-1( cos x) = cos^-1 (67/77)
x = 29.52626525
To the nearest tenth
x = 29.5
Abram completes one lap of a go-cart track every 40 seconds. Joshua completes one lap of the same track every 30 seconds. Suppose Abram and Joshua cross the starting line at the same time.
a. How many seconds will pass before they cross the starting line at the same time again?
b. How many laps will Abram have completed in that time?
c. How many laps will Joshua have completed in that time?
Answer:
Below in bold.
Step-by-step explanation:
a. This is the Lowest common multiple of 30 and 40 which is
120 seconds.
b. In 120 seconds Abram had completed 120/40
= 3 laps.
c. Joshua completed 120/30 = 4 laps.
Answer:
Step-by-step explanation:
A, Lowest common mutiple of 30 and un is 120 seconds
(40x3 = 120, 30x4 = 120)
6.120/40 = 3 laPs Abram did 3 laps.
L. 120/30 = u laPs Jeshya did u laps
I needddd help it’s urgenttttt!!!!
Two towns A and B are 220km apart. A bus left town A at 11.00 AM and travelled towards town B at 60km/hr. At the same time, a van left town B for town A and travelled at 80km/hr. The van stopped for a total of 45 minutes on the way before meeting the bus. Calculate the distance covered by the bus before meeting the van. Please show clear working and explanation to get a brainlist !!!
Answer:
Sa / Va = time traveled by bus a
Sb / Vb + 3/4 = time traveled by van b
Sa / Va = Sb / Vb + 3/4 times traveled are the same
= (220 - Sa) / Vb + 3/4
Sa ( 1 / Va + 1 / Vb) = 220 / 80 + 3/4
Sa (140 / 4800) = 3.5
Sa = 120 km
Check: 120 km / 60 km/hr = 2 hr = Ta
Sb = 1.25 * 80 = 100 km traveling for 1.25 hrs
What is this equation rewritten in logarithmic form?
9X = 3
A. log 3 = x
B. log, 3 = 9
C. log3 9 = x
D. log3 x = 9
Answer:
A. log9 3=x
Step-by-step explanation:
The logarithmic form with base 9 is log₉ 3 = x.
The correct option is A.
The equation 9ˣ = 3 can be rewritten in logarithmic form by identifying the base and the result of the exponential operation. In this case, the base is 9, the result is 3, and the exponent is x.
The logarithmic form with base 9 is log₉ 3 = x.
Option A, log₉ 3 = x, is the correct representation of the equation in logarithmic form.
The logarithmic form states that the logarithm of a number (3 in this case) to a specific base (9 in this case) is equal to the exponent (x in this case).
In the equation, 9ˣ = 3, the logarithmic form log₉ 3 = x indicates that the logarithm of 3 with base 9 is equal to x. This means that 3 is the result of raising 9 to the power of x.
Therefore, option A, log₉ 3 = x, is the correct answer representing the equation 9ˣ = 3 in logarithmic form.
To learn more about the logarithms;
brainly.com/question/28346542
#SPJ6
Solve the equation for x: (4x+38) + (2x-18)=180
Answer:
80/3
Step-by-step explanation:
try mathw4y it helps alot.
Answer:
x = 80/3
Step-by-step explanation:
(4x+38) + (2x-18)=180
Combine like terms
6x +20 = 180
Subtract 20 from each side
6x+20 -20 = 180-20
6x = 160
Divide by 6
6x/6 = 160/6
x = 80/3
In △MNP , point Q is between points M and N, and point R is between points N and P. Point H is the incenter of the triangle, HQ⊥MN, and HR ⊥NP. QN=36 and HN=39 . What is HR ? Enter your answer in the box.
Answer:
15
Step-by-step explanation:
The given parameters are represented by drawing the triangle with the details given using MS Visio
The point Q is located between points M and N in ΔMNP
The point R is located between points N and P in ΔMNP
The incenter of the triangle = H
Line HQ is perpendicular to side MN on ΔMNP
Line HR is perpendicular to side NP on ΔMNP
The length of the segment QN = 36
The length of the segment HN = 39
By Pythagoras' theorem, HQ = √((HN)² - (QN)²)
∴ HQ = √(39² - 36²) = 15
HQ = 15
Given that H is the incenter of ΔMNP, the lengths of the perpendicular from H to the sides of the triangle are equal to the radius of the inscribed circle of the triangle
Therefore, the radius lengths are HQ, and HR
∴ HR = HQ = 15
HR = 15.
!!ASAP!!
1.
25
40
75
2.
40
75
140
Answer:
C= 40
D= 75
Alternate interior angle
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Hope it helps...
Have a great day!!!
