Answer:
(a) 128 ft
(b) 4 s
(c) Vertex: (1, 144)
Step-by-step explanation:
Given information:
h(t) = height in feett = time in seconds after the launchPart (a)The height of the projectile at launch is the value of h(t) when t = 0 (the y-intercept).
Therefore, from inspection of the graph, the y-intercept is (0, 128).
So the height of the projectile at launch is 128 ft.
Part (b)The length of time it took for the projectile to land is the time from the beginning (when t = 0) to when the height is 0 (the x-intercept).
From inspection of the graph, the x-intercept is (4, 0)
So the length of time it took for the projectile to land is 4 s.
Part (c)The vertex is the turning point (minimum/maximum point).
Therefore, from inspection of the graph, the vertex is (1, 144).
The vertex represents the time and height at which the projectile was at its maximum. So at the time of 1 second, the projectile was at its maximum height of 144 ft.
Which of the following best describes the histogram?
The histogram is evenly distributed.
The histogram is symmetrical.
The left side of the histogram has a cluster.
The left side of the histogram is the mirror image of the right side.
histor Grammer
Step-by-step explanation:
lol bhsg HD tcvh by by by g
represent , the set of numbers between 10 to 50 when they are divided by 5 then the remainder is 2 by description method listing method and set builder method
The numbers between 10 and 50 when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.
What is set?A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
We have:
The set of numbers between 10 and 50 when they are divided by 5 then the remainder is 2
The numbers are:
12, 17, 22, 27, 32, 37, 42, 47
By description method:
1 2 3 4 5 6 7 8
12 17 22 27 32 37 42 47
By set builder form:
s = {12, 17, 22, 27, 32, 37, 42, 47}
Thus, the numbers between 10 and 50 when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.
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If the measure of angle 4 is 132°, what is the measure of angle 7?
32°
48°
132°
148°
The sum of supplementary angles is 180 degrees. The measure of angle 7 is 48 degrees
Supplementary anglesThe sum of supplementary angles is 180 degrees.
Let the supplement of the angle be "x", so that;
x + 132 = 180
Subtract 132 from both sides
x + 132 - 132 = 180 - 132
x =. 180 - 132
x = 48 degrees
Hence the measure of angle 7 is 48 degrees
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please help me ASAP
Answer:
c; 6
Step-by-step explanation:
to find the rate of change from x = 2 to x = 4 you use the (y2 - y1) / (x2 - x1) formula
so
(21 - 9) / (4 - 2)
12 / 2
6
the average rate of change is 6
Joshua has a ladder that is 15 feet long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 14.2 feet above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78 degrees. Will the ladder be safe at this height? Show your work and label the diagram
Answer:
Step-by-step explanation:
Expand: In (4a)^3
help please
Answer: 3ln4 + 3lna
Step-by-step explanation:
[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]
Answer:
C and second one is A
Write and simplify the expression equivalent to 2(7x + 3) + 9x.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression 2(7x+3)+9x.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
We need to multiply 2 times 7x and 3, and then add 9x.So, let's compute...
\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\//\\//\\\/
After performing multiplication we obtain
[tex]\star~\mathrm{14x+6+9x}[/tex]
Now add 9x:
[tex]\star~\mathrm{23x+6}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
what is pemdas? algebra 1
Answer:
p=Parentheses
e=Exponents
m=Multiplication
d=Division
a=Addition
s=Subtraction
its an order of solving a equation
There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
Answer:
What you need to remember for answering this question is that the probability of any event is the number of sample points in the event divided by the number of sample points in the sample space.
If you have multiple trials and if the sampling is with replacement then, no matter how many samples are drawn, the probabilities remain the same for each trial.
Mo buys a house for £120 000
He sells the house for £150 000
Work out the percentage profit that Mo makes.
Answer:
25%Step-by-step explanation:
The profit = 150 000 - 120 000 = 30 000
………………………………………………………
The profit percentage is :
[tex]=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Answer:
C and H
Explanation:
All others are not the same shape, they tend to be pointing in different directions.
Answer:
a c h g f
Step-by-step explanation:
which graph shows that Cindy reads about 3/4 of the time while riding in the car?
The graph that shows a unit rate of 3/4, which is the time Cindy reads while riding in the car is the graph attached below.
What is Unit Rate?Unit rate can be described as a constant or exactly how much of one quantity is per 1 unit of another quantity.
Unite rate (k) = x/y.
In the graph attached below, when x (hours driving) = 3, y (hours reading) = 4.
Therefore, unit rate = 3/4. We can then conclude that the graph that shows that Cindy reads 3/4 of the time she rides in a car is the graph attached below.
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6^2-4(3-√25)^2/|4-8|
the answer is 5 but im not sure on the steps and how to get 5, please help tysm :)
I'm going to assume you start with
[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|}[/tex]
Let's simplify some pieces of this:
[tex]6^2 = 6\times6 = 36[/tex]
[tex]\sqrt{25} = \sqrt{5^2} = 5[/tex]
[tex](3 - \sqrt{25})^2 = (3 - 5)^2 = (-2)^2 = (-2)\times(-2) = 4[/tex]
[tex]|4 - 8| = |-4| = 4[/tex]
So as a first step we can reduce this to
[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|} = \dfrac{36-4\times4}4[/tex]
Now,
[tex]36 = 9\times4[/tex]
so every term contains a factor of 4 that we can cancel:
[tex]\dfrac{36-4\times4}4 = \dfrac{9\times4-4\times4}4 = \dfrac{9-4}1 = 9-4 = \boxed{5}[/tex]
as expected.
Which pair of angles shares ray A and F as a common side?
The pair of angles that share a ray as a common side in the given diagram is: ∠FAB and ∠FAD.
What are Adjacent Angles?Adjacent angles are angles that lie adjacent or next to each other sharing a common vertex and have the same ray as a common side.
In the diagram attached below, ∠FAB and ∠FAD share a common vertex, A, and a ray FA as a common side.
Therefore, the pair of angles is: ∠FAB and ∠FAD.
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An elevator began in the 9th floor. It went down 7 floors. Then, it went up 4 floors. On which floor did it stop?
Answer: Hope this helps you!
6th floor
Step-by-step explanation:
If it starts on the 9th floor and goes down 7 floors that is:
9 (9 floors) + -7 (down 7 floors)
which is also equal to 9-7
9-7 = 2
Next, we need to go up by 4 floors starting with 2, 2+4
2+4 = 6
Brainliest?
The mean percent of childhood asthma prevalence in 43 cities is 2.25%. A random sample of 31 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.7%? Interpret this probability. Assume that σ= 1.27%.
The probability is
(Round to four decimal place)
The Probability that the mean childhood asthma prevalence for the sample is greater than 2.7% is 0.0357.
What is Probability ?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
For a Normal Distribution, the z-score formula
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]
Here X is the mean and sigma is the standard deviation.
Mean of 2.25% = 2.25
The standard deviation of 1.27%, sigma = 1.27
For Sample 31 the value of the standard deviation is
s = 1.27/√31
s = 0.2442
Substituting the values
Z = ( 2.25 -1.27)/0.2442
Z = 1.8
the p-value from the graph of z and p = 0.9643
To determine value of probability greater than X is 1 - 0.9643 = 0.0357
The Probability that the mean childhood asthma prevalence for the sample is greater than 2.7% is 0.0357.
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Find the angle of CD. Round to the nearest tenth. 12.7 cm 45.5° 9/06 cm mCD= [?]°
Using the information in the diagram, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°
Calculating the angle subtended by an arcFrom the question, we are to determine the measure of [tex]\overset{\LARGE\frown}{CD}[/tex]
Consider the right triangle
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is twice the measure of the unknown angle
Let the unknown angle in the right triangle be x
∴ The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2x
Then,
x + 90° + 45.5° = 180° (Sum of angles in a triangle)
x = 180° - 90° - 45.5°
x = 44.5°
Thus,
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2×44.5°
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 89°
Hence, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°
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write in standard form
(2×10³)+(4×10²)+(4×10¹)+(4×1)
can somebody answer this please.
c:
Answer: 2,444
Step-by-step explanation: We can find the answer to this problem by simplifying the scientific notation, and then adding. You would end up with 2,000 + 400 + 40 + 4 if done correctly. Hope this helps!
f (10) = 10/2 = 5 . how to solve this problem
Answer:
f(10) means to input x = 10 into the function.
From inspection of the given function:
[tex]\sf f(10)=\dfrac{10}{2}=5[/tex]
the "10" is the numerator of the fraction.
Therefore, swap the "10" for "x" to give the function in terms of x:
[tex]\sf f(x)=\dfrac{x}{2}[/tex]
For a function
f(x)=yx is the input or domain
y is the output or range
Here
f(10)=10/2So
x=10
y=10/2
Hence the function is
f(x)=x/2You have just invested 1,500 into a stock compounded yearly at a rate of 9%. How much money will be in your account in 60 days? (Please explain)
Answer:
1522.584
Step-by-step explanation:
1500(1+.09/12)^2=1522.584
A tank contains 180 gallons of water and 15 oz of salt. water containing a salt concentration of 17(1+15sint) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate.
the long-time behavior of the solution is an oscillation about a certain constant level. what is this level? what is the amplitude of the oscillation?
Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).
Salt flows in at a rate of
[tex]\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}[/tex]
and flows out at a rate of
[tex]\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}[/tex]
so that the net rate of change in the amount of salt in the tank is given by the linear differential equation
[tex]\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))[/tex]
Multiply both sides by the integrating factor, [tex]e^{t/180}[/tex], and rewrite the left side as the derivative of a product.
[tex]e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))[/tex]
[tex]\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))[/tex]
Integrate both sides with respect to t (integrate the right side by parts):
[tex]\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt[/tex]
[tex]\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C[/tex]
Solve for A(t) :
[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}[/tex]
The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.
[tex]\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}[/tex]
So,
[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]
Recall the angle-sum identity for cosine:
[tex]R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)[/tex]
so that we can condense the trigonometric terms in A(t). Solve for R and θ :
[tex]R \cos(\theta) = -\dfrac{66,096,000}{32,401}[/tex]
[tex]R \sin(\theta) = \dfrac{367,200}{32,401}[/tex]
Recall the Pythagorean identity and definition of tangent,
[tex]\cos^2(x) + \sin^2(x) = 1[/tex]
[tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
Then
[tex]R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}[/tex]
and
[tex]\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)[/tex]
so we can rewrite A(t) as
[tex]\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]
As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of
[tex]24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}[/tex]
and
[tex]24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}[/tex]
which is to say, with amplitude
[tex]2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}[/tex]
List the first 4 terms of a geometric sequence with the first term of 2 and a common ratio of 5.
Answer:
2, 10, 50, 250
Step-by-step explanation:
For geometric sequences, multiply the previous term by the common ratio.
Using the formula for geometric sequences [tex]a_{n} =ar^{n-1}[/tex] , with [tex]a_{n}[/tex] being the nth term (so n=4 for the fourth term), a being the first term, and r being the common ratio.
Our starting term is 2. So that is automatically the first term of the four.
Second term:
[tex]a_{2} =2*5^{2-1}=2*5^1=2*5=10[/tex]
Third term:
[tex]a_{3} =2*5^{3-1}=2*5^2=2*25=50[/tex]
Fourth term:
[tex]a_{4} =2*5^{4-1}=2*5^3=2*5*5*5=10*25=250[/tex]
The slope of a line is 3. The y intercept of the same line is -12
Complete the slope intercept form equation
Answer:
y = 3x - 12
Step-by-step explanation:
Forming the slope-intercept equation :
y = mx + b
m = slopeb = y-interceptSubstitute m = 3 and b = -12 in the equation :
y = 3x - 12Answer:
y = 3x - 12
Step-by-step explanation:
The slope intercept form of a line is y = mx + b, where m is the slope and b is the y intercept. Here, m = 3 and b = -12. Therefore, the slope intercept form for this line is y = 3x - 12.
please answer!!
Use the parabola tool to graph the quadratic function.
f(x)=3x^2+6x−24
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
See below
Step-by-step explanation:
[tex]f(x)=3x^2+6x-24\\\\f(x)=3(x^2+2x-8)\\\\f(x)+3(9)=3(x^2+2x-8+9)\\\\f(x)+27=3(x^2+2x+1)\\\\f(x)=3(x+1)^2-27[/tex]
Here, we can see that the vertex of the parabola is [tex](-1,-27)[/tex] when we compare to the equation [tex]y=(x-h)^2+k[/tex] with vertex [tex](h,k)[/tex].
A second point you could plot is the y-intercept, when [tex]x=0[/tex]:
[tex]f(0)=3(0+1)^2-27\\\\f(0)=3-27\\\\f(0)=-24[/tex]
So, your y-intercept is [tex](0,-24)[/tex].
PLEASE HELP
good answer gets brainliest
Answer:
50
Step-by-step explanation:
90+40= 130
There are 180 degrees in a triangle.
180- 130 = 50
n triangle ABC (see sketch), AD is the angle bisector of the angle A and BH is the height from side AC. The obtuse angle between BH and AD is four times the side of DAB. How big is the angle CAB?
A. 30 B.45 C.60 D.75 E.90
Answer: C
Step-by-step explanation:
We know that [tex]\angle AHB=90^{\circ}[/tex], and thus by the exterior angle theorem,
[tex]90^{\circ}+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^{\circ}[/tex]
Thus, [tex]\angle CAB=2\theta=\boxed{60^{\circ}}[/tex]
somebody please help me
Answer:
66°
Step-by-step explanation:
The angle sum theorem tells you the sum of angles in a triangle is 180°.
__
79° +x +35° = 180°
x = 180° -114° . . . . . . . . subtract 114° from both sides
x = 66° . . . . . simplify
What is the value of x?
Enter your answer in the box.
Answer:
25
Step-by-step explanation:
c^2=a^2+b^2
where c = hypotenuse
so, x^2 = 24^2+7^2
x^2 = 576 + 49
x^2 = 625
x = square root of 625
x = 25
solve 5x^2=180 algebraically
Answer:
x = ± 6
Step-by-step explanation:
Hello!
Solve[tex]5x^2 = 180[/tex][tex]x^2 = 180/5[/tex][tex]x^2 = 36[/tex][tex]\sqrt{x^2} = \sqrt{36}[/tex][tex]x = \pm 6[/tex]The value of x is 6 or -6.
Hi...
Given:
[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]
Solution:[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]
Explanation:Divide both sides by 5
[tex]\hookrightarrow{\mathtt{\frac{5x^2}{5}} = {\mathtt{\frac{180}{5}}[/tex]
Simplify:
[tex]\hookrightarrow{\mathtt{x^2 = 36}[/tex]
[tex]\hookrightarrow{\mathtt{For \: x^2 \: = f(a) \: the \: solutions \: are \: x = \sqrt{f(a)}}[/tex] , [tex]\mathtt{- \sqrt{f(a)}}[/tex]
[tex]\hookrightarrow{\mathtt{x = \sqrt{36}}[/tex] , [tex]\mathtt{x = -\sqrt{36}}[/tex]
Factor the number: 36 = 6²
[tex]\mathtt{= \sqrt{6^2}}[/tex]
Apply radical rule: [tex]\mathtt{\sqrt[n]{a^n} \: = a}[/tex]
[tex]\mathtt{\sqrt{6^2} = 6} \\\mathtt{= 6}[/tex]
- [tex]\sqrt{36} = -6[/tex]
[tex]\boxed{\fbox{\bf{x = 6 , x = -6}}}[/tex]
Hope It Helps You...
PLEASE HELP!!!!!!!!!
Answer:
CE = 4.6 ft
Step-by-step explanation:
(a)
given 2 secants drawn from an external point to the circle , then
the product of the external part of one secant and the entire secant is equal to the product of the other secant's external part and that entire secant, that is
BE × BC = AB × DB
(b)
substituting given values into the equation
BE × 10 = 3 × 18
10 BE = 54 ( divide both sides by 10 )
BE = 5.4 ft
then
CE = CB - BE = 10 - 5.4 = 4.6 ft