To find (g * f)(x), compute f(x) and substitute it into g(x), resulting in g(f(x)) = (√{x}+3)² + 2/√(x+3). Expand and simplify as needed.
To find (g * f)(x) for the given functions f(x)=√{x}+3 and g(x)=x²+2/x, we first need to compute f(x) and then substitute the result into function g.
First, we compute f(x):
f(x)=√x+3
Now, we substitute f(x) into g(x):
g(f(x)) = (√x+3)² + 2/√(x+3)
Step-by-step calculation:
Square f(x) to get (√x+3)².Expand the squared term to x + 6√x + 9.Substitute this into g(x):An investment advisor invested &14,000 in tow accounts. One investment earned 8% annual simple interest. And the other 6.5% annual simple interest. The amount of interest earned for 1 year was $1,027 how much was invested
Answer:
Investor invested $7,800 at 8% and $6,200 at 6.5%
Step-by-step explanation:
Use formula
[tex]I=P\cdot r\cdot t,[/tex]
where
I = interest
P = principal
r = rate (as decimal)
t = time
First investment:
[tex]P_1=x\\ \\r_1=0.08\\ \\t_1=1[/tex]
then
[tex]I_1=x\cdot 0.08\cdot 1\\ \\I_1=0.08x[/tex]
Second investment:
[tex]P_2=14,000-x\\ \\r_2=0.065\\ \\t_2=1[/tex]
then
[tex]I_2=(14,000-x)\cdot 0.065\cdot 1\\ \\I_2=0.065(14,000-x)[/tex]
The amount of interest earned for 1 year was $1,027, then
[tex]I_1+I_2=1,027\\ \\0.08x+0.065(14,000-x)=1,027\\ \\0.08x+910-0.065x=1,027\\ \\0.08x-0.065x=1,027-910\\ \\0.015x=117\\ \\x=7,800\\ \\14,000-x=6,200[/tex]
Investor invested $7,800 at 8% and $6,200 at 6.5%
y= -7x proportional or non proportional
Answer:
it is proportional
Step-by-step explanation:
Proportional functions will be in the form y = kx and non-proportional functions will be in the form y = mx + b
Simplify -5/1 the slope
Answer:
Step-by-step explanation:
The only possible simplification of the slope -5/1 is -5.
Karyn cuts a length of ribbon into 4 equal pieces each 1 1/4 feet long. How long is the ribbon
Answer:
5 feet long
Plz give brainliest
Allie measured a house and its lot and made a scale drawing. She used the scale 9 inches = 5 feet. What scale factor does the drawing use
Answer:
Therefore the scale used is 1 inch : 6.667 inches
Step-by-step explanation:
i) Scale used is 9 inches = 5 feet
ii) Scale used 9 inches = 5 [tex]\times[/tex] 12 inches = 60 inches
iii) Scale used is 1 inch [tex]= \dfrac{60}{9}\hspace{0.2cm} = \hspace{0.2cm}\dfrac{20}{3} \hspace{0.2cm} = 6.667\hspace{0.2cm} inches[/tex]
iv) Therefore the scale used is 1 inch : 6.667 inches
Write the slope -intercept form of an equation of the line that passes through the given point and is parallel to the graph of the equation.
5,-5,3x+y=-2
A. y=10x+3
B. y=-3x+10
C. y=1/3x-10
D. y=-3x-10
Answer:
The equation of the required line in the slope-intercept form is
y = -3x + 10
Step-by-step explanation:
i) the required line passes through the point (5, -5)
ii) the required line is also parallel to the line 3x + y = -2 ⇒ y = -3x - 2
Therefore the slope of the given line is -3.
Therefore the slope of the required line is also -3
The equation of the required line in the slope-intercept form is
y - (-5) = -3(x - 5) ⇒ y + 5 = -3x + 15 ⇒ y = -3x + 10 ∴ 3x + y = 10.
apply the distributive property to Factor out the greatest common factor of 75+20
Final answer:
The greatest common factor of 75 and 20 is 5, and by applying the distributive property, the expression 75+20 can be factored as 5(19).
Explanation:
The greatest common factor (GCD) of 75 and 20 is 5. Applying the distributive property to factor out 5, we get:
75 + 20 = 5 × (15 + 4)
Here's the breakdown:
Find the GCD: The largest factor that divides both 75 and 20 is 5.
Divide each term by the GCD: Divide 75 by 5 to get 15 and divide 20 by 5 to get 4.
Rewrite with the GCD factored out: Combine the results from step 2 and multiply by the GCD: 5 × (15 + 4).
Therefore, the factored expression using the distributive property is 5 × (15 + 4).
Thus, the factored form of the expression 75+20 is 5(19).
What is the value of this expression
when b = 5?
6(26-4)
Answer:
6(26-4)= 132
Step-by-step explanation:
There isn't any variable in the equation
Wanda started walking along a path 27 seconds before Dave. Wanda walked at a constant rate of 3 feet per second. Face walked along the same path at a constant rate of 4.5 feet per second. Graph the system of linear equations. How long after Dave starts walking will he catch up with Wanda
Answer:
54
Step-by-step explanation:
4.5x=3(x+27)
4.5x=3x+81
1.5x=81
x=54
bless me with the answers
Answer:
5) The correct answer is D.
6) The correct answer is A.
7) m = (10 - 6)/(1 - 0) = 4/1 = 4
The correct answer is C.
8) The correct answer is B.
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the tax and the first city was 6% and the tax and the second city was 10% total hotel tax paid for two cities with $670 how much was the hotel charge in each city before tax
Answer:
The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Step-by-step explanation:
Given:
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.
The tax of the first city was 6% and the tax of the second city was 10%.
Total hotel tax paid for two cities with $670.
Now, to find the hotel charge in each city before tax.
Let the hotel charge in first city before tax be [tex]x.[/tex]
And the hotel charge in second city before tax be [tex]y.[/tex]
So, as the hotel charge of the second city was 1500 higher than the first.
Thus,
[tex]y=x-1500[/tex] ........(1)
And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.
6% of [tex]x[/tex] + 10% of [tex]y[/tex] = $670.
[tex]\frac{6x}{100} +\frac{10y}{100} =670[/tex]
[tex]0.06x+0.10y=670[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]0.06x+0.10(x-1500)=670[/tex]
[tex]0.06x+0.10x-150=670[/tex]
[tex]0.16x-150=670[/tex]
Adding both sides by 150 we get:
[tex]0.16x=820[/tex]
Dividing both sides by 0.16 we get:
[tex]x=5125.[/tex]
The hotel charge in first city before tax = $5125.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=x-1500[/tex]
[tex]y=5125-1500[/tex]
[tex]y=3625.[/tex]
The hotel charge in second city before tax = $3625.
Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Show me how you got Christmas paper that was 8 feet long and 8 ft wide and the perimeter is 32 how
Answer:
The Proof is below.
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
Step-by-step explanation:
Let the Christmas Paper have Dimensions as
Length = 8 feet
Width = 8 feet
To Show:
Perimeter of Christmas Paper = 32
Solution:
Christmas Paper is in Rectangle Shape,
Therefore Perimeter of a Rectangle is given as
[tex]Perimeter\ of\ Rectangle=2(Length+Width)[/tex]
Substituting the values we get
[tex]Perimeter=2(8+8)=2\times 16=32\ feet[/tex]
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
The perimeter of a square is calculated by adding the lengths of all four sides. An 8 ft by 8 ft square has a perimeter of 32 ft, because 8 ft multiplied by 4 (the number of sides in a square) equals 32 ft.
Explanation:This question involves understanding the concept of perimeter in the context of a square. If you have a piece of Christmas paper that is 8 feet long and 8 feet wide, you actually have a square because all sides are of equal length. To calculate the perimeter of a square, you simply add up the lengths of all four sides.
Since each side is 8 feet, the perimeter P is given by:
P = side + side + side + side
P = 8 ft + 8 ft + 8 ft + 8 ft
P = 32 ft
So, the perimeter of the Christmas paper, if shaped like a square, is 32 feet, which is simply four times the length of one side.
Please help for 60 points and brainliest for best answers!
Answer:
6. ○ [tex]\displaystyle 33,1°; 123,1°[/tex]
5. [tex]\displaystyle See\:above\:image[/tex]
4. [tex]\displaystyle See\:above\:image[/tex]
Explanation:
6. Supplementary Angles sum up to 180°, whereas complementary angles sum up 90°. So, use subtraction for both types of angles:
[tex]\displaystyle 123,1° = -56,9° + 180° \\ 33,1° = -56,9° + 90°[/tex]
* Make sure that they are in the exact same order that exercise gives you.
5. Acute Angles measure greater than 0° and less than 90°.
4. Every segment must have C in it, and you must be EXTREMELY CAREFUL of their markings [ray, segment, and line].
I am joyous to assist you anytime.
An account was overdrawn. The status of his account was -$248. He did not realize the problem and wrote another check for $73. The bank charged him $15. What was the new status of the account?
Answer:
-$336.00
Step-by-step explanation:
-$248.00+-$73.00+-$15.00=-$336.00
What is -2 1/2 + 1 1/3 in fraction form?
[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]
Solution:
Given expression is [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex].
Let us first convert mixed fraction into improper fraction.
[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{(-2\times 2) +1}{2} +\frac{(1\times 3) + 1}{3}[/tex]
[tex]=\frac{-4 +1}{2} +\frac{3 + 1}{3}[/tex]
[tex]=\frac{-3}{2} +\frac{4}{3}[/tex]
Take LCM for the denominators (LCM of 2, 3 = 6) and make the same.
[tex]=\frac{-3\times3}{2\times3} +\frac{4\times2}{3\times2}[/tex]
[tex]=\frac{-9}{6} +\frac{8}{6}[/tex]
[tex]=\frac{-1}{6}[/tex]
[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]
Hence the fraction form of [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex] is [tex]\frac{-1}{6}[/tex].
Order 3/50 4/52 7/99 11/120 17/333 least you greatest
Answer:
Step-by-step explanation:
17/333 11/120 7/99 4/52 3/50
if 4cos° + 3sin° =5 ..find sin° and cos°
please anyone
Answer:
x = 36.87 degrees.
Step-by-step explanation:
4 cos x + 3 sin x = 5
Use the Auxiliary angle method:
R sin (α + x) = R sin α cos x + R cos α sin x
Comparing coefficients:
R sin α = 4 and R cos α = 3
R sin α / R cos α = 4/3
So tan α = 4/3
α = 53,13 degrees.
Now R^2(sin^2 α + cos^2 α ) = 3^2 + 4^2 = 25
R^2 = 25
R = 5.
R sin (x + 53.13) = 5
5 sin ( x + 53.13) = 5
sin (x + 53.13) = 1
x + 53.13 = 90
x = 36.87 degrees.
is the expression 3(x + 1 1/2) equivalent to 3x + 1 1/2
Answer:
No
Step-by-step explanation:
You only distribute the 3 to the x but not to 1 1/2. In order for the two equations to be the same, you have to distribute 3 to both the x and 1 1/2. Then the answer will look like this : 3x + 4 1/2 or 3x + 9/2
The original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.
Step 1: Distribute the Number Outside the Parentheses:
To determine equivalence, distribute the 3 to both terms inside the parentheses: 3(x) + 3(1 1/2).
Step 2: Simplify Inside the Parentheses:
Multiply 3 by x: 3x.
Multiply 3 by 1 1/2: 3 × 1 + 3 × 1/2
= 3 + 1.5
= 4.5.
Step 3: Combine the Terms:
The distributed expression simplifies to 3x + 4.5.
Step 4: Evaluate the Expression in Question:
The expression provided is 3(x + 1 1/2).
The equivalent expression, as derived, is 3x + 4.5.
Step 5: Compare the Expressions:
The expression 3(x + 1 1/2) simplifies to 3x + 4.5, not 3x + 1 1/2.
Therefore, the original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.
There are 6 red marbles, 8 blue marbles, and 11 green marbles in a bag. What is the probability that you
will randomly draw either a red or a blue marble?
24%
56%
O 32%
o
10%
NEXT QUESTION
ASK FOR HELP
TURN IT IN
TERMS OF USE
Answer:
14/25
Step-by-step explanation:
p(red or blue)=6/(6+8+11) +8/(6+8+11)=6/25+8/25=14/25
Answer:
56% yall
Step-by-step explanation:
David cooks 6 cups of rice for his family. They eat 4 cups. What fraction of the rice is uneaten
Answer:
1/3
Step-by-step explanation:
David cooks 6 cups of rice and his family eats 4 cups. To find the fraction, we must first do 6-4 to get 2. We place 2 in the numerator and 6 in the denominator. We have 2/6. We can simplify 2/6 by dividing both the numerator and the denominator by 2 to get 1/3.
solve this problem
-5(1+6n)=5n-5
What are the coordinates of point A?
Answer:
by definition
The coordinates of point A are:
(cosθ , sinθ)
Whats the value of 3x+4y-10 when x=3 and y=2
First person to answer will get the brainliest
Answer:
7
Explanation:
(3)(3)+(4)(2) − 10
(3)(3)
= 9
(4)(2)
= 8
9 + 8 = 17
17 - 10 = 7
Answer:
7
Step-by-step explanation:
3(3)+4(2)-10
9+8-10
17-10
7
8. (5 + 4 - 2) * (-2) = ?
A. -14
B.-22
O c. 14
D. 22
Answer: A. -14
Step-by-step explanation:
Answer: A. -14
Step-by-step explanation: Use PEMDAS
(5+4-2) x (-2)
= (9-2) x (-2)
= 7 x (-2)
= -14
If
f
(
x
)
=
x
6
+
3
x
−
1
f(x)=x
6
+3x−1, then what is the remainder when
f
(
x
)
f(x) is divided by
x
+
1
x+1?
Consider circle c with angle 3/4 radians. If minor arc AB measures 9n inches, what is the length of
the radius of circle C? If necessary, round your answer to
the nearest inch.
6 inches
12 inches
18 inches
24 inches
The radius of circle is 12 inches
Solution:
Given that,
Consider circle c with angle [tex]\frac{3 \pi }{4} \text{ radians }[/tex]
Minor arc AB measures [tex]9 \pi[/tex] inches
Therefore, we can say,
[tex]Central\ angle\ in\ radians = \frac{3 \pi }{4}\\\\Arc\ length = 9 \pi[/tex]
To find: Radius of circle
The length of arc when angle given in radians is:
[tex]s = r \times \theta[/tex]
Where,
"s" is the arc length and "r" is the radius and [tex]\theta[/tex] is the central angle in radians
[tex]9 \pi = r \times \frac{3 \pi }{4}\\\\r = 9 \times \frac{4}{3}\\\\r = 12[/tex]
Thus the radius of circle is 12 inches
Answer:
B.) 12 inches
Step-by-step explanation:
The following chart shows a store's records of sales of stuffed toys over two months.
September
October
Teddy Bears
Teddy Bears
346
Rabbits
que
Cats
Cats
245
Horses
Other
199
Other
If the trend shown in these graphs stays constant, what percent of the market will teddy bears occupy in November? (Round
your answer to the nearest tenth.)
a. 24.8%
b. 23.4%
C. 22.5%
d. 20.7%
The percent of the market will teddy bears occupy in November is 28.47%.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Form a table as shown
Months Teddy Bears Rabbits Cats Horses Others Totals toys
September 225 275 245 260 199 1204
October 346 308 186 297 285 1422
November 467 341 127 334 371 1640
So, the percent of the market will teddy bears occupy in November
= 467 / 1640 x 100
= 0.2847 x 100
= 28.47%
Learn more about Percentage here:
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help quick pls 20 points
Answer:
your answer is 70
Step-by-step explanation:
If LO = 15x+19 and QN = 10x+2 find PN
Answer:
[tex]PN=64\ units[/tex]
Step-by-step explanation:
The complete question is
Given the quadrilateral is a rectangle, if LO = 15x+19 and QN = 10x+2 find PN
see the attached figure to better understand the problem
we know that
The diagonals of a rectangle are congruent and bisect each other
so
[tex]QN=\frac{1}{2}LO[/tex]
substitute the given values
[tex]10x+2=\frac{1}{2}(15x+19)[/tex]
solve for x
[tex]20x+4=15x+19\\20x-15x=19-4\\5x=15\\x=3[/tex]
Find the length of PN
Remember that
[tex]PN=LO[/tex] ----> diagonals of rectangle are congruent
[tex]LO=15x+19[/tex]
substitute the value of x
[tex]LO=15(3)+19=64\ units[/tex]
therefore
[tex]PN=64\ units[/tex]
Help with matrices please? Any wrong/not applicable answers will be reported and BLOCKED
m x H = [tex]\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right][/tex]
Step-by-step explanation:
Step 1; Multiply 5 with this matrix [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get a matrix [tex]\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right][/tex]
Multiply the fraction [tex]\frac{2}{5}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get [tex]\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right][/tex]
Step2; Now equate corresponding values of the matrices with each other.
-5 = [tex]\frac{-2m}{5}[/tex] and so on. By equating we get the value of m as [tex]\frac{25}{2}[/tex]
Step 3; Add the matrices to get the value of matrix m.
Adding the three matrices on the RHS we get [tex]\left[\begin{array}{ccc}2&9&-9\\\end{array}\right][/tex].
Step 4; Adding the matrices on the LHS we get the resulting matrix as H +
[tex]\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right][/tex]. Equating the matrices from step 3 and 4 we get the value of H as [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]
Step 5; Now to find the value of m x H we need to multiply the value of [tex]\frac{25}{2}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]
Step 6; Multiplying we get the matrix m x H = [ -25 [tex]\frac{75}{2}[/tex] [tex]\frac{-25}{2}[/tex] ]