Step-by-step explanation:
step 1. 6x - 30 = 2(x + 33)
step 2. 6x - 30 = 2x + 66
step 3. 4x = 96
step 4. x = 24.
step 5. mNMO = x + 33 = 24 + 33 = 57°.
A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is pi/6, and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
Answer:
0.533 miles/min
Step-by-step explanation:
Calculate how fast the balloon is rising at the moment : dy /dt
location from the lift-off point = 4 miles
angle between the observer's line-of-sight and the horizontal ( ∅ ) = \(\frac{\pi }{6}\)
d∅ / dt = 0.1 rad/min
tan ∅ = y / 4
derivate
sec^2 ∅ . d∅ / dt = 1/4 . dy/dt
= sec^2 \(\frac{\pi }{6}\) . 0.1 = 1/4 . dy/dt
= ( sec^2 0.5238 * 0.1 ) * 4 = dy/dt
dy/dt = 8 / 15 miles/min
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three statements that are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² .......equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
Based on the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
By comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x - 0)² + (y - 0)² = 3²
x² + y² = 9.
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$120; Markup: 35%
What's the final price? pls show how u got the answer...
Answer: 162
Step-by-step explanation:
So you will need to find the Markup. The original cost is $120.
Divide the number by 100 is 1.2. $1.2 is 1% of the $120.Now times the number by 35. $1.2 x 35 is $42.Finally, add the number. 120 + 42 = 162.I hope this is the answer you are looking for.
i need help, this is for a final
Step-by-step explanation:
Since the two triangles are similar
Then the ratio of sides are equal
Then MK:ML =JH:JI
Sub in this and you will get x =64.1
Rule start at 6 2/3 subtract 1 1/4 show work
Answer:
3 11/12
Step-by-step explanation:
6 2/3 convert into improper = 20/3 - 11/4
find common denominator which would be 12
new equation: 80/12 - 33/12
and now subtract which would be 47/12 and turn that into mixed fraction and youll get 3 11/12
what is the value of 2/3 the power of 3
Answer:
The answer is 2 hope this helped!
Step-by-step explanation:
The null hypothesis and the alternate hypothesis are: H0: The frequencies are equal. H1: The frequencies are not equal. Category f0 A 10 B 30 C 30 D 10 State the decision rule, using the 0.05 significance level. (Round your answer to 3 decimal places.) Compute the value of chi-square. (Round your answer to 2 decimal place.) What is your decision regarding H0
Answer:
Reject H0
Step-by-step explanation:
Given :
H0: The frequencies are equal. H1: The frequencies are not equal
Category f0 A 10 B 30 C 30 D 10
Total f0 = (10 + 30 + 30 + 10) = 80
Expected frequency is the same for all categories :
Expected frequency = 1/4 * 80 = 20
χ² = Σ(observed - Expected)² / Expected
χ² = (10-20)^2 / 20 + (30-20)^2 /20 + (30-20)^2 / 20 + (10-20)^2 / 20
χ² = (5 + 5 + 5 + 5) = 20
Pvalue = 0.00017
Pvalue < α
Create a real-world problem involving a cube - Use a perfect cube as its volume - Show using cube roots to find one edge
PART A
A box of sugar has equal lengths of 6 inches. Calculate the volume of sugar that can fill the box.
The volume of the box can be calculated using the cubic volume formula given to be:
\(V=l^3\)Therefore, the volume of the box of sugar is calculated to be:
\(\begin{gathered} V=6^3 \\ V=216\text{ cubic inches} \end{gathered}\)PART B
An ice cube is said to contain a volume of 8 cubic inches of water. What will be the length of one side of the cube?
The length of the cube can be calculated using the formula:
\(l=\sqrt[3]{V}\)Hence, we can solve to be:
\(\begin{gathered} l=\sqrt[3]{8} \\ l=2\text{ inches} \end{gathered}\)Which estimated solution is closest to the actual solution shown in the graph?
Question 7 options:
(3,3)
(6,1)
(0,2)
(4,5)
(7,7)
(4,3)
(2,4)
Answer:
(7) (2, 4)
Step-by-step explanation:
You want to know which of the offered points is closest to the point of intersection of the two graphed lines.
SolutionThe point of intersection can be read from the graph as approximately (2 1/3, 3 3/4). The nearest grid intersection to that point is (2, 4), which is the last point on the list of choices.
(2, 4) is closest to the actual solution
__
Additional comment
You can see this, too, by graphing the offered choices. There are none closer than (2, 4).
Please help and thank you
Daniella: Were you thinking of perpendicular lines?
Ori: It seems like you've got the basic idea, but your definition could be more precise.
Kaori: Yes! Well done. Here, have a cookie. You've earned it.
Find the volume of a pyramid with a square base, where the perimeter of the base is
12.8 m and the height of the pyramid is 12.5 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:
12.5
Step-by-step explanation:
how many atoms of each element are in the formula Pb3(PO4)4
I need help on this problem please?
Answer:
yes ur friend is correct
Step-by-step explanation:
because the value of x .
The diagram only shows that angles M and B are supplementary ( add up to 180 degrees) and that angel 4x is adjacent to angel M.However, there is no information about the measure of angle B or angel M, so we cannot determine the value of x
What is the area for the problem
Using the area formula for composite figures, we can find the value of the area of the figure to be 39mm².
What do you mean by composite figures?The area that any composite shape covers is known as the area of composite shapes. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These shapes or figures can be constructed from a different variety of shapes that includes triangles, squares, quadrilaterals, etc.
To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.
Here in the question,
We can divide the figure into 2 rectangles.
One rectangle with length, l = 8mm and breadth, b = 3mm.
Area of the rectangle = l × b = 8 × 3 = 24mm².
Now, in the 2nd rectangle:
Length, l = 5mm
Breadth, b = 3mm.
Area of the rectangle = l × b = 5 × 3 = 15mm².
Total area of the figure = 24 + 15 = 39mm².
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A puzzle has 1080 pieces. How many pieces are 80% of the puzzle?
Answer:
864
Step-by-step explanation:
80/100 simplified is 4/5
so you do 4/5 of 1080
which is 1080 divided by 5 that is 216
and then 216 x 4 which is 864
Which unit of measurement is part of the metric system?
O quart
O kilogram
O foot
O pound
Answer:
2. kilograms
Step-by-step explanation:
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\( \huge{ \rm{Question:}}\)
7. If a figure measures 7 centimeters high, 3 centimeters wide and 2 centimeters deep, what is the volume of the figure?
\( \huge{ \rm{Answer:}}\)
The volume of the figure is 42.
Step-by-step explanation:
= 2 x 7 x 3
= 14 x 3
= 42
HOPE THIS HELPS^^
©s is inversely proportional to t.
When s 0.9, t = 5
Work out t when s = 90
0.9 * 100 = 90
5 * 100 = 500
t = 500
Answer:
Step-by-step explanation:
0,9÷90=0,01
t= 5×0,01=0,05
PLEASE HELP!!
solve for substitution
y+4=x
10x+2y+16
Using the substitution the system of equations y + 4 = x and 10x + 2y + 16 is solved to be
x = 8/3y = -4/3How to solve the system of equationsSubstitution involves replacing a value with it's equal
The given equation include
y + 4 = x
10x + 2y + 16
substituting x = y + 4 into 10x + 2y + 16
10x + 2y + 16
= 10(y + 4) + 2y + 16
= 10y + 40 + 2y + 16
collecting like terms
= 12y + 16
12y = -16
y = -16/12
y = -4/3
substituting y = -4/3 into x = y + 4
x = -4/3 + 4
x = 8/3
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Find the missing angle measures
Answer:
\(120^{\circ}, 120^{\circ}, 60^{\circ}, 60^{\circ}\)
Step-by-step explanation:
The angles of a quadrilateral add to \(360^{\circ}\).
\(2h+2h+h+h=360 \\ \\ 6h=360 \\ \\ h=60 \implies 2h=120\)
Find x in the given figure.
Write the equation of the line in slope intercept form that: has a slope of m=1/2 and goes through the point (2, -3) please help.
Answer:
\(y =\frac{1}{2}x -4\)
Step-by-step explanation:
m = (1/2) ; (2 , -3)
y -y1 = m(x - x1)
\(y - [-3] = \frac{1}{2}(x - 2)\\\\y + 3 = \frac{1}{2}x - 2 *\frac{1}{2}\\\\y + 3 = \frac{1}{2}x -1\\\\y = \frac{1}{2}x - 1 - 3\\y =\frac{1}{2}x -4\)
Factor the expression d2-8d +16
Find the area of this shape
Answer:
12.5
Step-by-step explanation:
(7.5+2.5)x2.5/2
Answer:
12.5 units ^2
Step-by-step explanation:
This figure is a trapezoid
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h
where b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 2.5+ 7.5) *2.5
= 1/2 ( 10) * 2.5
=12.5 units ^2
Which sequence could be partially defined by the recursive f (n + 1) = f(n) + 2.5 for n > 1?
Answer:
Step-by-step explanation:
f(n + 1) = f(n) + 2.5
f(1) = -10
f(2) = f(1) + 2.5 = -10 + 2.5 = -7.5
f(3) = f(2) + 2.5 = -7.5 + 2.5 = -5
f(4) = f(3) + 2.5 = -5 + 2.5 = -2.5
(b) You need to raise a total of $600 for your trip. There are 10 days before you leave. You estimate that youwill be able to sell 15 cans of soda per day. How much should you charge for each can?Set up the problem:Ix 1Answer:$per can
The Solution:
To raise a total $600 in 10 days with an estimate of selling 15 cans of soda per day.
To find the amount you should charge for each can is:
\(\frac{\text{ \$600}}{\text{ 10 days}}\times\frac{\text{ 1 day}}{\text{ 15 cans per day}}=\frac{600}{150}=\text{ \$4}\)Therefore, the correct answer is $4 for each can of soda.
Can someone please teach me how to solve this question step-by-step?
Answer:
\(\frac{1}{12}\)
Step-by-step explanation:
1) Construct a probability tree (check the attachment).
1.1) Change the given items/values into fractions. In this case, there are 3 entrees, each with a probability of \(\frac{1}{3}\) because the probability of selecting a hamburger (an example that could be applied to other options too) is 1 out of the 3 options. Likewise is the case with sides and drinks; the probability of selecting fries (or vegetable) out of the two options is \(\frac{1}{2}\), and the probability of selecting milk (or juice) out of the two options is \(\frac{1}{2}\).
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Zaire keeps track of the number of frisbee golf holes on which he makes par or better. The
table shows the number of holes Zaire has played during his round so far. If the ratio of holes
with par or better to total holes played is equal to 0.8, on how many of the holes has Zaire
made par or better?
Answer:
1.80
Step-by-step explanation:
Zaire has made par or better on 12 holes out of 15 that he has played.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
If the ratio of holes with par or better to total holes played is equal to 0.8, it means that Zaire has made par or better on 80% of the holes he has played.
Let's set up an equation to solve for the number of holes with par or better:
N/15 = 0.8
To solve for N, we can cross-multiply:
N = 15 x 0.8
N = 12
Therefore, Zaire has made par or better on 12 holes out of 15 that he has played.
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The graph of f(x) is shown.
For what values of x does f(x)=0?
Answer: X = -4, 0, 2
Step-by-step explanation:
Wherever the line touches the x-axis the f(x) or y = 0
Question 1 of 5 Find the difference. (12m + 1) - (5m - 4) O A. 7m + 5 O B. 17m-3 O C. 17m+ 5 D. 7 m - 3
Answer: 7m + 5
Step-by-step explanation:
Distribute the Negative Sign:
=12m+1+−1(5m−4)
=12m+1+−1(5m)+(−1)(−4)
=12m+1+−5m+4
Combine Like Terms:
=12m+1+−5m+4
=(12m+−5m)+(1+4)
=7m+5