Answer:
[tex]\dfrac{47}{60}[/tex] sq. units.
Step-by-step explanation:
The given function is
[tex]h(x)=\dfrac{1}{7-x}[/tex]
We need to find the area between x-axis and the given function from x=2 to x=5.
Left Riemann sum formula of area:
[tex]Area=\sum_{n=0}^{N-1}f(x_n)(\Delta x_n)[/tex]
For given question,
[tex]Area=\sum_{n=2}^{5-1}f(x_n)(\Delta x_n)[/tex]
[tex]Area=\sum_{n=2}^{4}f(x_n)(\Delta x_n)[/tex]
[tex]Area=f(x_2)(3-2)+f(x_3)(4-3)+f(x_4)(5-4)[/tex]
Now,
[tex]Area=\dfrac{1}{7-2}\times (1)+\dfrac{1}{7-3}\times (1)+\dfrac{1}{7-4}\times (1)[/tex]
[tex]Area=\dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{3}[/tex]
[tex]Area=\dfrac{12+15+20}{60}[/tex]
[tex]Area=\dfrac{47}{60}[/tex]
Therefore, the required area is [tex]\dfrac{47}{60}[/tex] sq. units.
What equation represents 3 less than the product of 7 and a number is 4 more than the number
i need help in algebra
Answer: No
Step-by-step explanation:
Because there is more than one 3 in the following ordered pair. If you make this a table it will be easier.
Answer:
No
Step-by-step explanation:
It would be yes only if the output (y-value) has values one time.
There are double 2s in the output so therefore your answer would be no
Hope this helps!
Find the quotient of `((5+2i)(6-4i))/((2+i))`, and express it in the simplest form.
Answer:
4 ²/3
Step-by-step explanation:
( 5+2) ×( 6-4) / ( 2+1 )
= (7)×(2) / 3
= 4 ²/3
Which of the line segments shown in the coordinate plane are congruent?
A(-2, 3) B(5, 7) C (3, -3) D (-3,-5) E (-3, 10)
00
00
-10 8 6 4 2
2 4 6 8 10
8
69
Answer:
segments shown in the coordinate plane are congruent?
A(-2, 3) B(5, 7) C (3, -3) D (-3,-5) E (-3, 10)
00
00
-10 8 6 4 2
2 4 6 8 10
Big Brainers Unite and redeem your points!
===========================================================
Explanation:
Check out the diagram below for a visual.
The line x = 2 is a vertical line in which every point on this line has x coordinate 2. Two points on this line are (2,0) and (2,1).
The point (-2,4) is 4 units away in the horizontal direction from the line x = 2. Basically we start at (-2,4) and move 4 units to the right to arrive at (2,4). Move 4 more units to arrive at (6,4).
In short: we reflect (-2,4) over the line x = 2 and it lands on (6,4)
We see that choice C must be the answer as no other answer choices have (6,4). So if you are pressed for time, you can stop here.
-------------
Let's keep going for the sake of completeness
We'll follow the same steps for the point (-1,5).
Move 3 units to the right to go from (-1,5) to (2,5). The goal again is to reach the vertical line x = 2
Then move another 3 units to the right to arrive at (5,5)
(-1,5) reflects over x = 2 to land on (5,5).
The perimeter of a square is 4s, where s is the length of one side.
Find the perimeter of the square at the right. Show unit analysis.
7 ft
Answer:
28ft.
Step-by-step explanation:
If [tex]s[/tex] equals 7 and the perimeter equals 4 times [tex]s[/tex], then the perimeter would be 4 times 7.
pls help i need help pls
Answer:
1. x = 32°
2. x = 28°
3. x = 15°
4. x = 30°
5. x = 40°
6. x = 20°
Step-by-step explanation:
All the angles should add up to 90° as they are complementary.
could someone help me with this question.
Answer:
D
Step-by-step explanation:
The measure of an inscribed angle is half the measure of its intercepted arc, that is
∠ GHI = 0.5 × arc GI = 0.5 × 80° = 40° → D
Jayden is running laps at track practice. The track is 25 kilometers around. Jayden runs 1 lap in 2 minutes. How many minutes does it take Jayden to run 1 kilometer?
Answer:
0.08 minutes for a kilometer.
Step-by-step explanation:
If the track is 25 kilometers, and he runs 25 kilometers in 2 minutes, he runs a kilometer in 2÷25 minutes or 0.08 minutes which is 4.8 seconds.
I'm pretty sure the track isn't 25 kilometer or he can't run a lap in 2 minutes. But if so, the answer is 0.08 minutes.
which expression represents five more than one-third y?
Answer:
1/3 y +5
Step-by-step explanation:
five more than one-third y
1/3 y +5
Answer:
5+1/3y
Step-by-step explanation:
Hope it helps
Solve application using algebra. Write your equation or inequality and show your solving steps. The sum of 3 consecutive integers is 147. Find the 3 integers.
Answer:
Integers are 48, 49, 50
Step-by-step explanation:
x+(x+1)+(x+2) = 147
3x + 3 = 147
3x = 147-3
x = 144 / 3 = 48
a. 1
b. 0
c. Infinitely many
d. Cannot be determined
Answer:
0
Step-by-step explanation:
The lines are parallel, they will never intersect
Answer:
no solution ( 0)
Step-by-step explanation:
If the lines have the same slope by different y intercepts, the lines are parallel
They will never intersect, so they have no solution
Determine the unknown angle measures of ADEF.
Round to the nearest degree.
m2D
23.5
m2 =
24.3
D
33.8
F
Answer:
m∠D = 46°
m∠F = 44°
Step-by-step explanation:
cos D =base/hypo
cosD =23.5/33.8 = 0.695
so and D = 45.97°
thus angle F = 180-(90+45.97) =44.03°
Using relations in a right triangle, it is found that:
The measure of angle D is of 46º.The measure of angle F is of 44º.What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem:
The hypotenuse is of 33.8.The side opposite to angle D is of 24.3.The side opposite to angle F is of 23.5.Hence:
[tex]\sin{D} = \frac{24.3}{33.8}[/tex]
[tex]D = \sin^{-1}{\left(\frac{24.3}{33.8}\right)}[/tex]
[tex]D = 46^\circ[/tex]
[tex]\sin{F} = \frac{23.5}{33.8}[/tex]
[tex]F = \sin^{-1}{\left(\frac{23.5}{33.8}\right)}[/tex]
[tex]F = 44^\circ[/tex]
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This probability distribution shows the typical distribution of pitches thrown to a batter in a given at bat in a baseball game. Find the probability that the pitcher will throw fewer than 3 pitches to a batter.
Answer:
0.35
Step-by-step explanation:
This probability distribution is shown below:
Pitch 1 2 3 4 5
Frequency 15 20 40 15 10
Probability 0.15 0.2 0.4 0.15 0.1
The probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 3)
X is the number of pitches thrown. Therefore:
P(X < 3) = P(X = 1) or P(X = 2)
The additive rule pf probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.
P(X < 3) = P(X = 1) or P(X = 2) = P(X = 1) + P(X = 2) = 0.15 + 0.2 = 0.35
The probability that the pitcher will throw fewer than 3 pitches to a batter = 0.35
Answer:
.35
Step-by-step explanation:
A water balloon is tossed vertically from a window at an initial height (s-sub zero) of 37 feet and with an initial velocity(v-subzero) of 41 feet per second. Answer the following using the fact that h(t)=-16T^2+v-sub zer0t+s sub zero. a) Determine a formula, h)t), for the function that models the height of the water balloon at time t . b)Plot the function in Desmos in an appropriate window. Use the graph to estimate the time the water balloon lands c)Use algebra to find the exact time the water balloon lands. Show your work. No decimals in your answer. d)Determine the exact time the water balloon reaches its highest point and its height at that time. e)4 pts] Compute the average rate of change of on the intervals . Include units on your answers and write a sentence to explain the meaning of the values you found. Arc{1.5,2}____________________________. Explanation: Arc{2,2.5}____________________________. Explanation: årc{2.5,3}____________________________. Explanation:
Answer:
a) h(t) = -16t^2 +41t +37
b) see attached (3.270 seconds)
c) (41+√4049)/32 seconds
d) 1.28125 seconds; 63.265625 feet
e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47
Step-by-step explanation:
a) The formula and initial values are given. Putting those values into the formula, we get ...
h(t) = -16t^2 +41t +37
__
b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.
__
c) Using the quadratic formula, we can find the landing time as ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]
The exact landing time is (41+√4049)/32 seconds.
__
d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.
The value of the function at that point is ...
h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64
The maximum height is 4049/64 = 63.265625 feet.
__
e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...
h'(t) = -32t +41 . . . in feet per second
Then the average rates of change are ...
arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s
arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s
arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s
These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.
Answer:
(a) h(t) = -16t² + 41t + 37
(b) About 3.3 s
[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]
(d) -15 ft/s; -31 ft/s; -47 ft/s
Step-by-step explanation:
(a) The function
h(t) = -16t² + v₀t + s₀
v₀ = 41 ft·s⁻¹
s₀ = 37 ft
The function is
h(t) = -16t² + 41t + 37
(b) The graph
See Fig. 1.
It looks like the water balloon lands after about 3.3 s.
(c) Time of landing
h = -16t² + 41t + 37
a = -16; b = 41; c = 37
We can use the quadratic formula to solve the equation:
[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]
(i) Evaluate the discriminant D
D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368 = 4049
(ii) Solve for t
[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]
[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]
(d) Time and maximum height
(i) Time
The axis of symmetry (time of maximum height) is at t = -b/(2a)
[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]
(ii) Maximum height
The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37 = 63.27 ft
(e) Average rate of change
(i) Arc{1.5,2}
h(1.5) = 62.5
h(2) = 55
m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s
The water balloon has started to fall after it has reached peak height, so it is not going very fast
(ii) Arc{2,2.5}
h(2.5) =39.5
m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s
The balloon is in mid-fall, so gravity has caused it to speed up.
(iii) Arc{2.5,3}
h(3) = 16
m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s
The balloon is about to hit the ground, so it is falling at almost its maximum velocity.
Fig. 2 shows the height of the balloon at the above times.
The function of fx has been transformed to give go. Witch of the following functions represent gx?
Answer:
Sorry your mouse is blocking the fx equation. Is it x squared? I can't help you if I can't see what the equation is I'm sorry
Step-by-step explanation:
Is 1,2,3,4 a geometric sequence ?
Which linear function has the steepest slope? A) y = negative 8 x + 5 B) y minus 9 = negative 2 (x + 1) C) y = 7 x minus 3 D) y + 2 = 6 (x + 10)
y = -8x + 5
y - 9 = -2(x+1)
y - 9 = -2x - 2
y = -2x +7
y + 2 = 6(x+10)
y + 2 = 6x + 60
y = 6x + 58
The linear function has the steepest slope is y = -8x + 5
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.A)y = -8x + 5
B) y – 9 = -2(x+1)
⇒y – 9 = -2x - 2
⇒y = -2x +7
C) y=7x-3
D) y + 2 = 6(x+10)
⇒y + 2 = 6x + 60
⇒y = 6x + 58
Steepest slope is determined by the greatest value of gradient(m).
Therefore, The linear function has the steepest slope is y = -8x + 5
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The graph of g(x) is a transformation of the graph of f(x)=2x. Enter the equation for g(x) in the box. g(x) =
The -3 is not in the exponent
Explanation:
The parent function is [tex]f(x) = 2^x[/tex]. Plugging in x = 0 leads to y = 1. So the point (0,1) is on the f(x) curve. Going from (0,1) to (0,-2) is a vertical shift of 3 units downward. To represent this shift, we tack on a "-3" at the end of the f(x) function.
[tex]g(x) = f(x) - 3\\\\g(x) = 2^x - 3[/tex]
You could look at other points as well, but I find working with x = 0 is easiest.
As a check, plugging x = 0 into g(x) leads to...
[tex]g(x) = 2^x - 3\\\\g(0) = 2^0 - 3\\\\g(0) = 1 - 3\\\\g(0) = -2[/tex]
This confirms our answer.
The height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet. Find the length of the base and the height of the triangle
Answer:
Step-by-step explanation:
The length of the base is 3 feet and the height of the triangle is 6 feet.
What is the area of a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.
Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.
The dimensions of the triangle will be calculated as,
A = (1/2) x b x h
A = (1/2) x b x ( b + 3 )
54 = ( 1 / 2 ) x ( b² + 3b )
108 = ( b² + 3b )
( b² + 3b - 108) = 0
( b² + 12b -3b -108 ) = 0
(b - 3 ) ( b+ 12 ) = 0
b = 3 and b = -12 ignore negative value.
The height will be calculated as,
h = b + 3
h = 3 + 3
h = 6 feet
Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.
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Penny buys 3 bouquets of flowers for $3 each and 4 bouquets for $2 each. Which expression gives the total cost of the bouquets that Penny buys?
A.
33 + 42
B.
33 + 24
C.
33 + 4 × 2
D.
32 + 4 × 2
Its neither of the above(maybe you type something wrong?)
The total cost is
$(3 x 3 + 4 x 2)
Clara is building a triangular garden. She wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long.
Answer:
3s+15
Step-by-step explanation:
let 's' be the length of the shortest side
-> twice as long as the length of the shortest side =2s
->length of the longest side to be three more than twice as long as the length of the shortest side = 2s + 3
-> the third side= 12 feet
p = s + 12 + 2s+3
p= 3s+15
f(x) = x2 - 4x - 21.
What will the function have at the y-intercept and where would the vertex be ?
Answer:
vertex is (2,-25) Y-intercept is -21
Step-by-step explanation:
Answer: EDMENTUM USERS!
I got this correct on the tutorial. Hope this helps!
Step-by-step explanation:
Which of the binomials below is a factor of this trinomial?
X2-16x + 28
O A. x+7
O B. x2 + 7
O c. x+4
O D. X-14
Answer:
x-14
Step-by-step explanation:
The binomial which is a factor of this trinomial is (x- 14).
What is Trinomial?An algebraic expression with three terms is called a trinomial.
Examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z.
Given:
p(x) = x²-16x + 28
If x+ a is factor of any polynomial p(x) then x= -a satisfy the polynomial.
factorizing p(x)
x²-16x + 28
= x²-14x + 2x + 28
= x( x- 14) + 2 (x+ 14)
= (x- 14)(x+ 2)
Hence, the binomial is (x- 14).
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Rachel, Mario and Sanjit share some money in the ratios 4 : 3 : 9 Mario receives £96. Work out the difference between the amount received by Rachel and the amount received by Sanjit.
Answer:
Step-by-step explanation:
If Marios share is 3 parts and is £96, then
Find one part = 96/3 = 32
So,
Rachel receives = 32 x 4 = £128
Sanjay receives = 32 x 9 = £288
Hope this helps
The angle of elevation of the top of a tower from a point 100m away from the base of the tower is 45°. The angle of elevation of the top of the flag staff mounted on the top of the tower is 60°. The height of the flag staff is.......... (Use √3 =1.73)
Answer:
The height of the flag staff is 73 m
Step-by-step explanation:
Let H₁ be the height of the building.
Since the angle of elevation of the top of the tower is 45° from a point 100 m away from the base of the tower,
From tan45° = H₁/100
H₁ = 100tan45° = 100 m
Let H₂ be the height of the building plus flag staff.
Since the angle of elevation of the top of the flag staff is 60° from the same point 100 m away from the base of the tower,
From tan60° = H₂/100
H₂ = 100tan60°
= 100√3
= 100 × 1.73
= 173 m.
So, the height of the flag staff is h = H₂ - H₁
= 173 m - 100 m
= 73 m.
So, the height of the flag staff is 73 m
if twice the raju age is 6 years more than raman age. if raju age is 10 years then raman age is
Someone plz help me XX
Answer:
-2<x<2
Step-by-step explanation:
its wrong but ur from britain luv innit xxx
Which coordinate grid shows Point A at (0.75, −1.50)? Coordinate grid shown from negative 2 to positive 2 on the axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 6 grid lines to the left of the y-axis and 3 grid lines above the x-axis. Coordinate grid shown from negative 2 to positive 2 on the axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 6 grid lines to the right of the y-axis and 3 grid lines below the x-axis. Coordinate grid shown from negative 2 to positive 2 on the axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 3 grid lines to the left of the y-axis and 6 grid lines above the x-axis. Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 3 grid lines to the right of the y-axis and 6 grid lines below the x-axis.
Answer:
( fraction negative 1 over 4, fraction 1 and 3 over 4 )
Step-by-step explanation:
Answer:
1st one will be it!
Step-by-step explanation:
Give an example of an angle which has a cos value between 0.3 and 0.5
Answer:
70 degrees
Step-by-step explanation:
We want to determine an angle [tex]\theta$ such that $0.3<\cos \theta<0.5[/tex]
If [tex]0.3<\cos \theta<0.5,$ then:[/tex]
[tex]\arccos 0.3< \theta<\arccos 0.5[/tex]
[tex]60^\circ<\theta<72.53^\circ[/tex]
Therefore, any angle greater than 60 degrees but less than 72.54 degrees will give a cosine value of the required range.
Example:
[tex]\cos 70^\circ =0.342[/tex]
