Answer:
The value of function (g o f) (2) is 24 . option D
Step-by-step explanation:
Given function as :
f(x) = [tex]\frac{10}{x}[/tex] - 1
And g(x) = 7 x - 4
So ,
(g o f) (x) = 7 ( [tex]\frac{10}{x}[/tex] - 1 ) - 4
Or, (g o f) (x) = [tex]\frac{70}{x}[/tex] - 7 - 4
Or, (g o f) (x) = [tex]\frac{70}{x}[/tex] - 11
So, For x = 2
I,e (g o f) (2) = [tex]\frac{70}{2}[/tex] - 11
Or, (g o f) (2) = 35 - 11
∴ (g o f) (2) = 24
Hence The value of function (g o f) (2) is 24 . Answer ( option D )
Which is the graph of 2x + 3y > -3?
Answer:
The third one
Step-by-step explanation:
You can plug the equation into Desmos and it graphs the equation for you, it's actually really helpful if you have more questions like this.
Answer:
C
Step-by-step explanation:
can someone solve this
-4x − 7y = 21
find the y intercept
Answer:
[tex]\displaystyle [0, -3][/tex]
Step-by-step explanation:
The y-intercept is when zero is set to x, so you will end up with this:
[tex]\displaystyle -\frac{21}{7} = -\frac{7y}{7} \\ \\ -3 = y[/tex]
I am joyous to assist you anytime.
The solution to the given system of linear equations lies in which quadrant?
Ex-3y = 6
1 x+y=2
Quadrant III
Quadrant !
- 5
4
-3 -2
1
2
3
4
5
X
Quadrant III
| Quadrant IV
? 17
Answer:
The solution to the given systems of linear equation is {3, -1} lies in IV Quadrant.
Step-by-step explanation:
Given:
x-3y = 6 ........( 1 )
x+y=2 ........( 2 )
To find :
x = ?
y = ?
Solution:
Let solve the above equation to get the solutions.
Eliminate X by subtracting the two equations equation 1 minus equation 2
[tex](x-3y) - (x+y) = 6 - 2\\-4y = 4\\\therefore y=-1[/tex]
Now substitute for y = -1 in equation 2 we get
[tex]x+(-1)=2\\\therefore x = 2+1\\\therefore x = 3[/tex]
Therefore, solution set is {3, -1}
In
I Quadrant {x,y} = {+,+}......both the coordinates are positive.
II Quadrant {x,y} = {-,+}.....X coordinate is negative and Y coordinate is positive.
III Quadrant {x,y} = {-,-}......both the coordinates are negative.
IV Quadrant {x,y} = {+,-}.....X coordinate is positive and Y coordinate is negative. {3,-1}
Point A on the graph is the solution.
Answer:
For those who want a quick answer. Its D on edge
Step-by-step explanation:
A book was on sale for 40% off its original price. If
the sale price of the book was $18.00, what was the
original price of the book? (Assume there is no sales
tax.)
A) $7.20
B) $10.80
C) $30.00
D) $45.00
Answer:
Option (c) $30.00
Explanation:
Let the original price be $x
Given the rate of discount is 40%
Selling (or sale) price of the book is = $18
The original price is calculated by the formula,
Selling Price = Original Price(1 – r%)
Substituting the values in the above equation,
[tex]18 = x (1-\frac{40}{100})[/tex]
[tex]18 = x (\frac{60}{100})[/tex]
[tex]x=\frac{1800}{60}[/tex]
Therefore, x = 30
Hence, option (c)is correct
The original price of the book was $30.00, which, after a 40% discount, results in the $18.00 sale price. To find the original price, divide the sale price by 0.60 (which represents the remaining 60% after the discount). So the correct option is C.
Explanation:To find the original price of the book before the sale, you need to consider that the sale price represents 60% of the original price, because the book was discounted by 40%. The calculation that needs to be done is to divide the sale price by 0.60.
Here are the steps:
Represent the sale price: $18.00Determine the percentage of the original price that $18.00 corresponds to 100% - 40% = 60%.Convert the percentage to a decimal to perform the calculation: 60% = 0.60.Divide the sale price by the decimal equivalent of the percentage: $18.00 / 0.60 = $30.00.Therefore, the original price of the book was $30.00.
what is the formula for a semicircle
Answer:
Area = πr^2/2, and Perimeter πr+2r
Step-by-step explanation:
so the formula for a circle is πr^2, and a semicircle is half of a circle....... so we do the formula of a circle, πr^2, divided by 2 to get the area of it, πr^2/2. now we kind of do the same thing for perimeter. we do the circumference/2, so 2πr/2, or πr but we need to add the bottom of the semicircle so we add 2r to it . so this whole equation would be πr+2r.
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = -5t^2 + 20t + 4 gives the height h, in meters, of the ball t seconds after it is launched.
A. What equation can be used to tell whether the ball reaches a height of 12 m ?
B. Does the ball reach a height of 12m? (yes or no)
The maximum height reached is greater than 12m, hence the ball reach a height of 12m
The height of the toy cannon all launched is expressed as [tex]h(t) = -5t^2 + 20t + 4[/tex]
h is the height reached by the ball
t is the time taken by the ball to reach its maximum height
A) In order to determine whether the ball reached the height of 12m, we will have to substitute h = 12 into the formula as shown:
[tex]12= -5t^2 + 20t + 4\\ -5t^2 + 20t + 4 -12=0\\ 5t^2 - 20t +8=0\\[/tex]
Hence the equation that can be used to tell whether the ball reaches a height of 12 is [tex]5t^2-20t+8=0[/tex]
B) At the maximum height
dh/dt = 0
-10t + 20 = 0
-10t = -20
t = 20/10
t = 2
Get the maximum height reached
h(2) = -5(2)^2 + 20t + 4
h(2) = -5(4) + 20t + 4
h(2) = -20 + 20(2) + 4
h(2) = -20+40+4
h(2) = 24 m
Since the maximum height reached is greater than 12m, hence the ball reach a height of 12m
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To determine whether the ball reaches a height of 12 meters, we set the height equation equal to 12 and solve the quadratic equation. Upon solving, we find that the ball reaches 12 meters, hence the answer to whether the ball reaches 12 meters is yes.
Explanation:To determine whether the toy cannon ball reaches a height of 12 meters, we can set the height equation h(t) equal to 12 meters:
12 = -5t^2 + 20t + 4.
To solve for t, we need to rearrange the equation and solve the resulting quadratic equation:
0 = -5t^2 + 20t + 4 - 12
0 = -5t^2 + 20t - 8
This is the equation that can be used to tell whether the ball reaches a height of 12 meters. To determine if the ball does reach 12 meters, we solve for the roots of the equation:
-5t^2 + 20t - 8 = 0
Using the quadratic formula, we find the possible values for t. If there are real, positive solutions, it means the ball does reach 12 meters at those times.
Upon solving, we find that the ball indeed reaches a height of 12 meters because there are real, positive solutions for t.
Therefore, the answer to Part B is yes; the ball does reach a height of 12 meters.
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evey y-value is the sum of one half of x and 15
Answer:
y = 1/2 x + 15
Step-by-step explanation:
The equation for the word problem is y = 1/2 x + 15.
"one half" is 1/2
sum means addition
Simplify 2x-2y +5z-2x-y+3z
Answer:
-3y+8z
Step-by-step explanation:
Add like terms which would be 2x-2x, -27-y, 5z+3z.
Answer:
-y+8z
Step-by-step explanation
mason calculated sales tax on his clothing purchase 5.57375 round to the nearest hundredth
Answer:
The nearest hundredth is 5.57. Hope I helped! ☺
QA is tangent to circle M at point D and the m angle QMD=40 what is the measure of angle MQA?
Answer:
the answer is MQA =130°
Wen u draw a parallel line with respect to MD through Q, the angle between the line become 40 degree - alternate angles
so the rest is 90 degree, therefore 90 + 40 = 130 degree
Answer:
∠MQA = 130°
Step-by-step explanation:
∠MDQ = 90° ( angle between tangent and radius )
Given ∠QMD = 40°, then
∠MQD = 180° - (90 + 40)° = 180° - 130° = 50° ( sum of angles in a triangle )
∠MQD and ∠MQA form a straight angle and are supplementary, thus
∠MQA = 180° - 50° = 130°
OR
The external angle of a triangle is equal to the sum of the 2 opposite interior angles
∠MQA is an exterior angle of the triangle, thus
∠MQA = 90° + 40° = 130°
Someone help me please!
12a = 28 ÷ 2/3
Answer:
a = 3.5
Step-by-step explanation:
12a = 28 ÷ 2/3
12a = 28 × 3/2
a = 28 × 3/2 ÷ 12
a = 3.5
Answer:
a = 3.5
Step-by-step explanation:
12a = 28 ÷ 2/3
12a = 28 × 3/2
a = 28 × 3/2 ÷ 12
a = 3.5
A parabolà can be drawn given a focus of (7,9) and a
directrix of y = 5. Write the equation of the parabola
in any form.
from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".
keeping in mind the vertex is half-way between these two fellows, Check the picture below.
[tex]\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \begin{cases} h = 7\\ k = 7\\ p = 2 \end{cases}\implies 4(2)(y-7)=(x-7)^2\implies 8(y-7)=(x-7)^2 \\\\\\ y-7=\cfrac{1}{8}(x-7)^2\implies \boxed{y=\cfrac{1}{8}(x-7)^2+7}[/tex]
Final answer:
The equation of the parabola with a focus of (7,9) and a directrix of y = 5 can be written as (x-7)^2 = 16(y-5).
Explanation:
The equation of a parabola in standard form is given by:
(x-h)^2=4p(y-k)
Where (h,k) is the vertex of the parabola and p is the distance from the vertex to the focus and to the directrix. In this case, the focus is (7,9) and the directrix is y = 5. To find the equation of the parabola, we need to determine the value of p.
From the given information, we can see that the focus is a point on the parabola and the directrix is a line that is perpendicular to the axis of symmetry and does not pass through the vertex. Therefore, the distance from the vertex to the focus is equal to the distance from the vertex to the directrix. In other words, the value of p is the distance from the vertex to the line y = 5.
Since the directrix is a horizontal line, the vertex of the parabola is on the line y = 5. Therefore, k = 5. The distance from the vertex to the line y = 5 is equal to the distance from the vertex to the focus, which is p. Therefore, we have:
p = 9 - 5 = 4
So the equation of the parabola is:
(x-7)^2 = 4 * 4(y-5)
Simplifying, we get:
(x-7)^2 = 16(y-5)
Therefore, the equation of the parabola is (x-7)^2 = 16(y-5).
if 11 oranges cost $2.35, what is the cost of 18
Answer:
$3.8
Step-by-step explanation:
2.35/11=0.2136
0.2136*18=3.8448
Your friend has improved in his math class. On his first test he scored 50 points, and then he scored 53, 56, 59, and 62 points on his next 4 tests. His tests continued to improve following this pattern. If he took 15 tests, how many points did he score on the last test?
Answer:
95
Step-by-step explanation:
We need to add up by 3 from 50 until we get the 15th number so we do this:
1. 53
2. 56
3. 59
4. 62
5. 65
6. 68
7. 71
8. 74
9. 77
10. 80
11. 83
12. 86
13. 89
14. 92
15. 95
The 15th term is 92.
What is an Arithmetic Sequence ?A sequence of numbers where each number is linked with its consecutive term by a fixed number is called Arithmetic Sequence.
It is given that
The test score results are
50 , 53 , 56 , 59 , 32 ..................
The common difference is 3
Then the nth term is given by
Tn = a₁ + (n-1)d
a₁ is the first term = 50
n = 15
Then the 15th term is
T₁₅ = 50 + (15-1) * 3
T₁₅ = 92
The 15th term is 92.
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Solve: -7(3+6x)=9(-5x+7)
Answer:
x=28
Step-by-step explanation:
-7(3+6x)=9(-5x+7)
-21-42x=-45x+63
-21-42x-(-45x)=63
-21-42x+45x=63
-21+3x=63
3x=63-(-21)
3x=63+21
3x=84
x=84/3
x=28
Compare and contrast linear and exponential functions
Answer:
A linear function is one that is changing at a constant rate as well as it changes. As for a exponential function is one that changes at a rate that's always proportional to the value of the function.
Answer:
a linear function is in which the rate of change is constant, and because you are adding the same amount every time in the graph, the change is the same. In an exponential function, it’s where your graph is not constant, the rate of change increases, or decreases because you are adding or subtracting more each time.
Step-by-step explanation:
hope it helps
A 12 cm x 2 cm rectangle sits inside a circle with radius of 8 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
Diagram was not given.
Still I had drawn it, hope may it will helpful to you. So as per my diagram I had solved the sum.
The area of the shaded region is 176.96 ≈ 178 cm²
Step-by-step explanation:
Given:
radius of the circle = r = 8 cm
length of the rectangle = L = 12 cm
breadth of the rectangle = B = 2 cm
To Find:
Area of shaded region = ?
Solution:
[tex]\textrm{Area of rectangle} = Length\times Breadth\\= L\times B\\= 12\times 2\\= 24\ cm^{2}[/tex]
[tex]\textrm{Area of Circle} = \pi \times (radius)^{2} \\=\pi \times r^{2}\\=3.14\times 8^{2}\\=200.96\ cm^{2}[/tex]
Now, The Area of Shaded region will be
[tex]\textrm{Area of Shaded region}=\textrm{Area of Circle}-\textrm{Area of Rectangle}\\=200.96 - 24\\=176.96\ cm^{2} \\=178\ cm^{2}\........... \textrm{Rounded to tenth}[/tex]
The area of the shaded region is 176.96 ≈ 178 cm²
Answer:
177.06
Step-by-step explanation:
i got it wrong on khan academy
Reiko started a business selling home medical supplies. She spent $ 5200 to obtain her merchandise, and it cost her $550 per week for general expenses. She earns $900 per week in sales. What is the minimum number of weeks it will take Reiko to make a profit?
Answer:
The minimum number of weeks is 15 weeks after that it will take Reiko to make profit.
Step-by-step explanation:
Reiko spent $5200 to obtain her merchandise and it cost her $550 per week for general expenses.
So, the total cost for her business after w weeks will be
C = 5200 + 550w ........ (1)
Now, she earns $900 per week in sales.
So, after w weeks her total earning is given by
E = 900w ......... (2)
Now, the number of weeks after that the cost and earning will be equal, will be given by
5200 + 550w = 900w
⇒ 350w = 5200
⇒ w = 14.85
So, the minimum number of weeks is 15 weeks after that it will take Reiko to make a profit. (Answer)
Answer:
900w>6500+550w
2x+3y=7 3x-y=5 find the value of x and y
Answer:
that seem hard but it is 123times 6
Step-by-step explanation:
123×6
Answer:
x=2, y=1. (2, 1).
Step-by-step explanation:
2x+3y=7
3x-y=5
-------------
y=3x-5
2x+3(3x-5)=7
2x+9x-15=7
11x-15=7
11x=7+15
11x=22
x=22/11=2
y=3(2)-5=6-5=1
Find the distance between (-8,-2) and (7,6)
Answer:
23 grids
Step-by-step explanation:
|-8|+7=8+7=15
|-2|+6=2+6=8
15+8=23
The length of a rectangle is 7 yd more than double the width, and the area of the rectangle is 99 yd^2. find the dimensions of the rectangle.
Answer:
w(2w+7) = 99
2w^2 + 7w - 99 = 0
( 2w - 11 )(w + 9 ) = 0
w+9=0 results in negative measures
2w-11 = 0
2w = 11
w = 11/2 = 5.5
L = 2w + 7 = 18
Simplify: 9x - (-19 + 11x)
i’m really bad at math so please help.
Answer:
-2x+19
Step-by-step explanation:
9x-(-19+11x)=9x+19-11x=-2x+19
Answer:
-2x + 19
Step-by-step explanation:
9x - (-19 + 11x)
Distribute the (-) sign
9x + 19 - 11x
9x - 11x + 19
Simplify
-2x + 19
I’ll make u the brainliest if right
Answer:
38
Step-by-step explanation:
To evaluate h(8) substitute x = 8 into h(x)
h(8) = 5(8) - 2 = 40 - 2 = 38
Answer:
38
Step-by-step explanation:
What are ordered pairs for 4x - 2y = 10
Answer:
(0,−5),(1,−3),(2,−1)
Step-by-step explanation:
3)June 2019-In the diagram below of AABC, D is a
point on BA, E is a point on BC, and DE is drawn.
If BD = 5, DA= 12, and BE = 7, what is the length of
BC so that AC || DE?
Answer:
BC = 23.8
Step-by-step explanation:
See the diagram attached.
Given AC ║ DE and BD = 5, DA = 12 and BE = 7.
We have to find BC.
Since, AC ║ DE, so, Δ ABC and Δ DBE are similar.
If two triangles are similar then the ratio of their corresponding sides remains the same.
Hence, [tex]\frac{BD}{BA} = \frac{BE}{BC}[/tex]
⇒ [tex]\frac{5}{12 + 5} = \frac{7}{BC}[/tex]
⇒ [tex]BC = \frac{7 \times 17}{5} = 23.8[/tex] (Answer)
Answer:
23.8
Step-by-step explanation:
Tracy’s trip she traveled 2884 miles her trip took 7 days find a unit rate to represent the average miles she traveled per day during the trip
Answer:
Average miles travelled per day =412.
Step-by-step explanation:
If Tracy travels 2884 in 7 days, then to know the average miles she travelled per day, we just have to divide 2884 into the 7 days.[tex]\frac{2884}{7} =412[/tex], then she travelled on average 412 miles per day.the answer to 0.92 into a percentage
Answer:
92%
Step-by-step explanation:
This is because all you have to do to turn a decimal into percentage is to move the decimal over 2 spots, and drop the Zero.
From a plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35 degrees and 25 degrees. How far apart are the two ships?
Answer:
189.8 m
Step-by-step explanation:
See the diagram attached.
Now, the plane is at B and the two ships are at C and at D.
So, angle of depression of C from B is ∠ OBC = ∠ ACB = 35°
Again, the angle of depression of D from B is ∠ OBD = ∠ ADB = 25° ,
Now, from the right triangle Δ ACB,
[tex]\tan 35 = \frac{AB}{AC} = \frac{265}{AC}[/tex]
⇒ [tex]AC = \frac{265}{\tan 35} = 378.5[/tex] m.
Similarly, from the right triangle Δ ADB,
[tex]\tan 25 = \frac{AB}{AD} = \frac{265}{AD}[/tex]
⇒ [tex]AD = \frac{265}{\tan 25} = 568.3[/tex] m.
Hence, the distance between the ships = CD = AD - AC = 568.3 - 378.5 = 189.8 m (Approx.) (Answer)
The distance apart is the two ships is 189.8 meters.
Given
A plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35 degrees and 25 degrees.
What is the angle of depression?The angle of elevation, the angle of depression is the angle at which you would draw a line from a point on a horizontal line to intersect another point that falls below the line.
The plane is at B and the two ships are at C and at D.
Then,
The angle of depression of C from B is ∠ OBC = ∠ ACB = 35°.
And the angle of depression of D from B is ∠ OBD = ∠ ADB = 25°.
From the right triangle Δ ACB,
[tex]\rm Tan35= \dfrac{AB}{AC}\\\\ AC= \dfrac{265}{Tan35}\\\\AC = \dfrac{265}{0.70}\\\\AC =378.57[/tex]
Again in the right triangle Δ ADB,
[tex]\rm Tan 25=\dfrac{AB}{AD}\\\\AD =\dfrac{265}{Tan25}\\\\ AD = \dfrac{265}{0.46}\\\\AD =569.30[/tex]
Therefore,
The distance apart are the two ships is;
= 568.3 - 378.5 = 189.8 m
Hence, the distance apart is the two ships is 189.8 meters.
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Write an equation in point slope form line passing through (-4,3), (3,-4)
Answer:
y-3=-(x+4)
Step-by-step explanation:
Point Slope Form: y-y1=m(x-x1)
Where m=slope and (x1, y1) is a point on the line.
m=(y2-y1)/(x2-x1)
m=(-4-3)/(3-(-4))=-7/(3+4)=-7/7=-1
y-3=-1(x-(-4))
y-3=-(x+4)
two families bought tickets for a game. one family paid $71 for 6 adults and 2 children. another family paid $56.50 for 4 children and 3 adults. how much do the tickets cost.
Answer:
Adult Ticket cost $9.50 and Children Ticket cost $7.00
Step-by-step explanation:
Let single adult tickets cost "a" and single children ticket cost "c"
6 adult and 2 children ticket is $71, we can write:
6a + 2c = 71
Also,
3 adult and 4 children tickets cost $56.50, so we can write:
3a + 4c = 56.5
We multiply 2nd equation by "-2", to get:
-2 * (3a + 4c = 56.5) = -6a -8c = -113
Now we add this equation with 1st and eliminate a and solve for c:
6a + 2c = 71
-6a -8c = -113
-------------------
-6c = -42
c = -42/-6
c = 7
To find a, we can plug this into 1st equation and then get our answer.
6a + 2c = 71
6a + 2(7) = 71
6a + 14 = 71
6a = 57
a = 57/6
a = 9.5
Hence,
Adult Ticket cost $9.50 and Children Ticket cost $7.00