Answer:
height = 3000m
Step-by-step explanation:
In order to calculate the height reached by the airplane, you first calculate the distance traveled by the airplane in one minute. The distance is given by:
[tex]d=vt[/tex] (1)
v: speed of the airplane = 100m/s
t: time = 1 min = 60 s
you replace in the equation (1):
[tex]d=(100m/s)(60s)=6000m[/tex]
The distance traveled by the airplane while it is going up, can be considered as a hypotenuse of a rectangle triangle.
The angle at which the airplane started to fly was 30°. Then, you can use the following trigonometric relation to calculate the height:
[tex]sin(30\°)=\frac{height}{d}\\\\height=dsin(30\°)=(6000m)sin(30\°)=3000m[/tex]
hence, the height reached by the ariplane is 3000m
Jenna constructs the model to represent 3x2 + 11x – 4. An algebra tile configuration. 0 tiles are in the Factor 1 spot. 0 tiles are in the Factor 2 spot. 20 tiles are in the Product spot in 4 columns with 5 rows. First row: 3 + x squared, 1 negative x. The last 4 rows are the same: 3 + x, 1 negative. What factors does Jenna need to model for the sides? (3x + 1) and (x – 4) (3x – 1) and (x + 4) (3x – 2) and (x + 2) (3x + 2) and (x – 2)
Answer:(3x – 1) and (x + 4)
Step-by-step explanation:
Jenna needs to model the factors (3x – 1) and (x + 4) for the sides of the configuration. The correct answer would be an option (B).
What is the Factorization?Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.
The model is given in the question, as follows:
3x² + 11x – 4
Each row has a coefficient of 3 and an x term, which can be modeled with 3 tiles and 1 tile, respectively.
The first row has a constant term of -1, which can be modeled with 1 tile in the Factor 1 spot.
The second row has a constant term of 4, which can be modeled with 4 tiles in the Factor 2 spot.
So, the configuration shows the correct factors (3x – 1) and (x + 4) for the sides of the model.
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rate of change for y=5x+25
Answer:5
Step-by-step explanation:
rate of change is the same thing as slope (or m)
The required rate of change for the given equation y = 5x + 25 is 5.
Given that,
For the given equation y =5x +25 the rate of change is to be determined.
The slope of the line is the tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
What is the rate of change?The rate of change is defined as the change in value with the rest of the time is called rate of change.
Here,
The given equation,
y = 5x + 25
Differentiate the above equation with respect to x,
dy/dx = d(5x +25)/dx
dy/dx = 5dx/dx + d25/dx
dy/dx = 5 (since dx/dx =1 and d25/dx = 0)
here dy/dx is the slope of the equation or m or rate of change = 5
Thus, the required rate of change for the given equation y = 5x + 25 is 5.
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Solve 15 > -3x or 2/5 x > -2
Answer:
Step-by-step explanation:
the second one
An arc with length 5 pi over 4 inches is formed by a 15 degree central angle what is the radius of the circle
Answer:
Radius of the circle is 15 inches.
Step-by-step explanation:
Relation between length of arc, radius and the angle subtended by the arc on center is:
[tex]\theta = \dfrac{l}{r} ..... (1)[/tex]
where [tex]\theta[/tex] is the central angle in radians subtended by arc
[tex]l[/tex] is the length of arc
[tex]r[/tex] is the radius of arc
We are Given the following details:
[tex]l = \dfrac{5\pi}{4}\ inch[/tex]
[tex]\theta = 15^\circ[/tex]
We know that [tex]\pi \ radians = 180 ^\circ[/tex]
Converting [tex]\theta[/tex] to radians:
[tex]\theta =\dfrac{\pi}{180} \times 15[/tex] radians
Putting the values of [tex]\theta[/tex] and [tex]l[/tex] to find the value of [tex]r[/tex]
[tex]\dfrac{\pi}{180} \times 15 = \dfrac{5\pi}{4r}\\\Rightarrow r = \dfrac{45}{3} \\\Rightarrow r = 15 \ inches[/tex]
Hence, Radius of the circle is 15 inches.
Temperatures in °F can be converted in °C
Answer:
[tex] \frac{9c + 160}{5} [/tex]
Step-by-step explanation:
C = 5(F - 32)/9
so we do a little algebra here
9C = 5F - 160
we move both side
5F - 160 = 9C
5F = 9C + 160
so in the end
F =
[tex] \frac{9c + 160}{5} [/tex]
a = 9
b = 160
c = 5
Answer:
[tex]F=\frac{9C+160}{5}[/tex]
Step-by-step explanation:
[tex]C=\frac{5(F-32)}{9}[/tex]
Multiply both sides with 9.
[tex]9C=5(F-32)[/tex]
Use distributive property.
[tex]9C=5F-160[/tex]
Add 160 to both sides.
[tex]9C+160=5F[/tex]
Divide 5 to both sides.
[tex]\frac{9C+160}{5}=F[/tex]
Which expression is equivalent to 64 – 9x^2?
A(32)^2 – (3x)^2
B(32)^2 + (-3x)2
C(8)^2 – (3x)^2
D(8)^2 + (-3x)^2
Answer:
Option C is correct
Step-by-step explanation:
A = 64 - 9x^2
= 8^2 - (3^2)(x^2)
= 8^2 - (3x)^2
Hope this helps!
Remy wanted to measure the angle of the slide in the playground. He used a piece of folded paper that was 10°. He measured that 3 of the folded paper angles would fit in the angle made by the slide. What was the angle of the slide?
Answer:
30°
Step-by-step explanation:
Since the folded paper can fit into the slide three times, we simply have to multiply 10° by 3:
10° * 3 = 30°
The angle of the slide is 30°
Mr. Bond's monthly income is Rs. 2400 and his monthly expenditure on rent is Rs.250. The central angle of the sector representing rent expenses in the pie chart would be ……………
Answer:
[tex]x = 37.5^{\circ}[/tex]
Step-by-step explanation:
The central angle of the sector representing rent expenses in the pie chart is found by simple rule of three:
[tex]x = \frac{Rs. 250}{Rs. 2400}\times 360^{\circ}[/tex]
[tex]x = 37.5^{\circ}[/tex]
In the pie chart, the central angle of the sector reflecting rent expenses is equal to [tex]\boldsymbol{37.5^{\circ}}[/tex]
Pie ChartA pie chart is a circular statistical visual divided into slices to show numerical proportion. The arc length of each slice in a pie chart is proportionate to the quantity it shows.
Monthly income of Mr. Bond [tex]=[/tex] Rs. [tex]2400[/tex]
Monthly expenditure on rent [tex]=[/tex] Rs. [tex]250[/tex]
Central angle of the sector representing rent expenses in the pie chart [tex]=\frac{250}{2400}\times 360^{\circ}[/tex]
[tex]=\boldsymbol{37.5^{\circ}}[/tex]
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b÷7−12=8
Solve the equation
Answer:
[tex] \boxed{b = 140} [/tex]
Step-by-step explanation:
[tex] = > \frac{b}{7} - 12 = 8 \\ \\ = > \frac{b}{7} = 8 + 12 \\ \\ = > \frac{b}{7} = 20 \\ \\ = > b = 20 \times 7 \\ \\ = > b = 140[/tex]
A swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation for this function in point slope form.
Answer:
y-32=3(x-5)
Step-by-step explanation:
The swimming pool is being drained at a constant rate of 3 inches per hour, therefore:
The rate of change, Slope, m=3 inches per hourIf the depth of the water after 5 hours is 32 inches.
The depth is the dependent variable(as its values varies with time) while the time is the independent variable, we can write this as a pair (x,y)=(5, 32).
The point slope form of the equation of a line is of the form: [tex]y-y_1=m(x-x_1)\\(x_1,y_1)=(5,32), m=3\\$Substituting these values, we obtain:\\y-32=3(x-5)\\This is the equation of the function in point slope form.[/tex]
Marcus tracked the changes in his sales over a 12-
month period and graphed the results. Over which
interval was the change in Marcus's sales constant?
0 (0.4)
(0.5)
O (5, 6)
O (6. 12)
Answer:
Its B!
Step-by-step explanation:
Just passed on edge 2020
The interval between which the sales of the Marcus were constant was (0, 5) to (5, 6) and (5, 6) to (6, 12)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given, Marcus tracked the changes in his sales over a 12- month period.
we need to find at which interval was the change in Marcus's sales constant.
First we need to plot the graph, the points given to us will show us the sale of Marcus from the beginning to the end.
The rapid increment is in the number of sales for that period of time is (0, 4) and (0, 5) as we can see a straight line.
Line between point (0, 5) and (5, 6), there is a slant line therefore, which shows that were slow and constant growth in the sale of Marcus as the line is increasing upwards.
The line between the points (5, 6) and (6, 12) is also a slant line but the slope of the line is high than the previous line for points (0, 5) and (5, 6).
Constant growth between these two points and this growth was also constant but it was more rapid as compared to sales between the point (0, 5) and (5, 6).
Therefore the interval between which the sales of the Marcus were constant was (0, 5) to (5, 6) and (5, 6) to (6, 12)
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Given a right triangle with b=3 and c=5 find leg a? Show your work
Find attached to this question, the diagram of the right angle triangle
Answer:
Leg a = 4
Step-by-step explanation:
A right angle triangle has 3 sides : side a, b and c
The formula to solved for a right angle triangle =
a² + b² = c²
In that above question,
a = unknown
b = 3
c = 5
Therefore,
a² + 3² = 5²
a² = 5² - 3²
a² = 25 - 9
a² = 16
a = √16
a = 4
Therefore, leg a = 4
Circumference & Area of Circles: Question 10
In baseball, the next batter waits in the on-deck circle. If the diameter
of the on-deck circle is 5 feet, what is its approximate circumference?
(Urex= 314)
Select one
01571
o
Answer:
i got 19.625 if you round it you should get either 20 or 19.6
Step-by-step explanation:
if im wrong sorry
What is the value of a
Answer: Multiplying 3x and -x we obtain A= -3x^2
R 0,-180
is the same rotation as
R
90, 180
R 0,180
OR-90,180
R 0,90
90,180 is the same as R so it is
Express 5.09 * 10 to the -4 in standard form
Answer:
5.09 x 10^-4 = 0.000509
Step-by-step explanation:
Simply just move the decimal places 4 times to the left and fill in your zeros to get your answer. (I think this is standard form)
In Mathematics is 5n a monomial?
Answer:
yes
Step-by-step explanation:
because monomials can be numbers variables and numbers together with variables
Answer:
5n should be a monomial i think
Step-by-step explanation:
Brian rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 1.
Answer:
zero
Step-by-step explanation:
probability of getting total of 1 is zero
minimum of total can be 1+1=2
Can someone please explain to me what quadrants on a coordinate plane means, for brainliest and some points.
20/4 = X/18 What is X
Answer: 90
Step-by-step explanation: Divide 20 by 4 and Multiply the 18
The question is above please help
Answer:
i believe it's C i may be wrong
Step-by-step explanation:
The table shows the number of championsthips won by the baseball and softball leagues of three youth baseball
divisions organized by age groups.
Baseball League (B) Softball League (5)
Ages 7-9 C93
Ages 10-12M 2
Ages 13-15 (
2
if the winning team plays in the Ages 10-12 division, find the probability that the team is in the Basebal League. Answer
in terms of a reduced fraction.
a0
R(BIY)
Answer:
7/10
Step-by-step explanation:
Finding the totals of each column and row, we find:
There are 3+2+1 = 6 children in the baseball league.
There are 7+2+1 = 10 children in the softball league.
There are 3+7 = 10 children in the 7-9 division.
There are 2+2 = 4 children in the 10-12 division.
There are 1+1 = 2 children in the 13-15 division.
There are a total of 10+6 = 16 children.
We start with the information that the team is a member of the softball league. There are 10 children in this league; this is the denominator of the probability.
There are 7 children in the 7-9 division that are in the softball league. This gives us the probability 7/10.
correct me if this is wrong
uually Cxpressions
Which expressions are equal to 0 when x=-1? Check all that apply.
(4x + 5)
4(x - 1)
(5 - 4x)
40% - (-1))
(4 7 + 5)
(4x + 5)
4(x + 1)
(5 - 4x)
Intro
Answer:
Which expressions are equal to 0 when x = –1? Check all that apply.
StartFraction 4 (x plus 1) Over (4 x plus 5) EndFraction
StartFraction 4 (x minus 1) Over (5 minus 4 x) EndFraction
StartFraction 4 (x minus (minus 1)) Over (4 x plus 5) EndFraction
StartFraction 4 (x plus (minus 1)) Over (4 x plus 5) EndFraction
StartFraction 4 (x plus 1) Over (5 minus 4 x) EndFraction
Step-by-step explanation:
Suppose students are independent from one another. 63% of students are using Mr. Martin's new social media app, Mar-tin-stagram. 2 students are randomly selected. What is the probability that both of them use it? (Write answer as a decimal. Do not round)
Answer:
[tex]P(X=2) =0.3906[/tex]
Step-by-step explanation:
Proportion of students using the app, p = 63/100 = 0.63
Proportion of students not using the app, q = 1 - 0.63 = 0.37
Sample size, n = 2
Probability that the two students are using the app.
[tex]P(X = r) = nCr p^{n} q^{n-r} \\P(X = 2) = 2C2 *0.63^{2} *0.37^{2-2}\\P(X = 2) = 2C2 *0.63^{2} *0.37^{0}\\P(X=2) = 0.63^{2} \\P(X=2) =0.3906[/tex]
The graph below represents the system of equations 3x+4y=12 and 2x-y=8. A coordinate grid with 2 lines. One line passes through (0, 3) and (4, 0). The other line passes through (2, negative 4) and (4, 0). Which ordered pair is a solution to the system of equations? (0, 3) (3, 0) (4, 0) (0, 4)
Answer:
C. (4,0)
Step-by-step explanation:
Given a graph of the system of equations
3x+4y=12; and
2x-y=8.
Line 1 passes through (0, 3) and (4, 0).Line 2 passes through (2, -4) and (4, 0).We can see that both lines pass through (4,0). Therefore, (4,0) is a point of intersection of the two lines.
It is therefore a solution to the system of equations.
3 + 2(2x + 8) = 1 is equivalent to:
Answer:
x = [tex]-\frac{9}{2}[/tex]
Step-by-step explanation:
=> 3+2(2x+8) = 1
=> 3+4x+16 = 1
=> 4x+19 = 1
=> 4x = 1-19
=> 4x = -18
Dividing both sides by 4
=> x = [tex]-\frac{18}{4}[/tex]
=> x = [tex]-\frac{9}{2}[/tex]
Answer: -9/2
Step-by-step explanation:
3 + 2(2x + 8) = 1
3 + 4x + 16 = 1
19 + 4x = 1
4x = -18
x = -18/4 = -9/2
i need help with this question( just a simple equation):
3. Greta has two part-time jobs. She earns $14/h at her first job and earns $12.50/h at the second job. In one week, she earned $500.
a) Write an equation that models this information. (hint: define your variables first – what do you not know?)
Answer:
I'm pretty sure it's
14x + 12.50y = 500
Number of people for x tents if each tent can accommodate 4 people.
Answer:
4xpeople
Step-by-step explanation:
one tent accommodates 4 people
x tent will accommodate 4xpeople
Not sure
Answer:
[tex]4x[/tex]
Step-by-step explanation:
Each tent can accommodate 4 people.
1 tent is [tex]1x[/tex]
[tex]1x \times 4[/tex]
What is the median of this data set
Answer:
52.5
Step-by-step explanation:
median is where u find the middle number
put them in order first
24,28,51,54,67,70
its between 54 and 51
Solve for r.
–16r + 15 + 17 = 7(–3r + 16) − 5r
r =
Answer:
r = 8
Step-by-step explanation:
→Distribute the 7 to (-3r + 16):
-16r + 15 + 17 = 7(-3r + 16) - 5r
-16r + 15 + 17 = -21r + 112 - 5r
→Add like terms:
-16r + 32 = -26r + 112
→Add 26r to both sides:
10r + 32 = 112
→Subtract 32 from both sides:
10r = 80
→Divide both sides by 10:
r = 8
Answer:
Step-by-step explanation:
-16r +15+17= 7(-3r+16)-5r
-16r+32 = -21r +112-5r
-16r +26r=112-32
10r =80
r=80/10
r=8
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