From the given information , we can make a rough figure as shown in attachment.
Now in the given triangle we can use following formula of sin to get the angle,
[tex] sin x = \frac{Perpendicular}{opposite} [/tex]
We can see from the figure that:
perpendicular = 8 and opposite =14.
Plugging the given values in the formula for sin x,
[tex] sin x = \frac{8}{14} [/tex]
sin x = 0.5714
to find x we have to find sin inverse of 0.5714 ,
x = sin⁻¹(0.5714)
x=34.8 degrees.
Answer : the angle that the telephone pole makes with the ground is 34.8 degrees. option D
An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:
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Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
68.3
38.4
268.8
230.4
Which of the following is a cubic binomial
A.w^3-6w^2+9
B.7a^3+4a^-2
C.-y^3+3y^5
D.x^2-2x^3
help me please. Find the values of x and y that make these triangles congruent by the HL Theorum.
A. x=2, y=1
B. x=3, y=2
C. x=1, y=2
D. x=2, y=3
What is the vertex of the parabola?
A. (-1,0)
B. (0,-3)
C. (1,-4)
D. (3,0)
Option C is correct, the vertex of the parabola is (1, -4).
What is Conic section?Any curve produced by the intersection of a plane and a right circular cone is called as Conic section.
A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The vertex is either the highest point or the lowest point on the parabola depending on whether the parabola opens upward or downward.
In this case, since the parabola opens upward, we can see that
the vertex is the lowest point on the parabola which is (1,-4).
Hence, Option C is correct, the vertex of the parabola is (1, -4).
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A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone?
Sammy is 5 feet 3 inches tall. He casts a shadow that is 31 feet 6 inches long. He is standing next to a stop sign that casts a shadow that is 40 feet 6 inches long. How tall is the stop sign in feet and inches.
https://s3.amazonaws.com/algebranation/testyourself_uploads/MAFS9/9.029.png
Answer:
x = 14
x = negative 2
x = 2
x = negative 14
Step-by-step explanation:
abcd is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC s 4y-6 and the length of CD is 8y-18, find the value of y. 30 points for brainliest!
The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.
Given :
ABCD is an isosceles trapezoid with legs AB and CD and base BC.If the length of AB is (7y - 4), the length of BC s (4y - 6) and the length of CD is (8y - 18).The two legs are of equal length In any isosceles trapezoid that means:
7y - 4 = 8y - 18
Add 18 on both sides in the above equation.
7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y
Now, subtract 7y on both sides in the above equation.
7y + 14 - 7y = 8y - 7y
Simplify the above expression in order to get the value of 'y'.
y = 14
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A flower garden is in the shape of a right triangle. One leg of the triangle is 6 ft long and the hypotenuse is 12 ft long. What is the length of the other leg?
answers
A. 10.4ft
B.12.8ft
C13ft
D14.6ft
Which of these states had a flat state income tax in 2009
Apex
A.Michigan
B.New Hampshire
C.South Carolina
D.Georgia
Answer:
The correct answer is:
Michigan.
Michigan is the state that had a flat state income tax in 2009.
Step-by-step explanation:
A flat tax (short for flat-rate tax) is a tax system with a constant marginal rate, usually applied to individual or corporate income.
Flat tax benefits higher income brackets progressively due to decline in marginal value.
The state that had a flat state income tax in 2009 is:
Michigan.
Michigan is a flat-tax state that levies a state income tax of 4.25%
20 Points!!!
For working 13 hours you earned $45.50 and $94.50 for 27 hours. What is your rate of pay in dollars per hour? a. 14 dollars per hour b. 3.50 dollars per hour c. 6.50 dollars per hour d.2.07 dollars per hour
Will give branliest!!!
Help ASAP.
Answer:
$3.50 per hour
Step-by-step explanation:
Given : For working 13 hours you earned $45.50 and $94.50 for 27 hours
To Find :What is your rate of pay in dollars per hour?
Solution :
Pay for 13 hours = $45.50
So, Pay for 1 hour = [tex]\frac{45.50}{13}[/tex]
Pay for 1 hour = [tex]3.50[/tex]
So, rate is $3.50 per hour
So, Option B is true
Hence rate of pay in dollars per hour is $3.50 per hour
what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?
A)Reflected over the x-axis and rotated 180 degrees
B)Reflected over the y-axis and rotated 180 degrees
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
D)Reflected over the y-axis and rotated 90 degrees counterclockwise
Rectangle ABCD has vertices A(-4,2), B(-4,1), C(-1,1) and D(-1,2).
1. Apply the reflection over the x-axis that has a rule
(x,y)→(x,-y).
Then
A(-4,2)→A''(-4,-2);B(-4,1)→B''(-4,-1);C(-1,1)→C''(-1,-1);D(-1,2)→D''(-1,-2).2. The second transformation is rotation by 90° counterclockwise about the origin. This transformation has a rule
(x,y)→(-y,x).
Then
A''(-4,-2)→A'(2,-4);B''(-4,-1)→B'(1,-4);C''(-1,-1)→C'(1,-1);D''(-1,-2)→D'(2,-1).As you can see these points are exactly those frome the diagram.
Answer: 1st transformation is reflection over the x-axis and second transformation is rotation by 90° counterclockwise about the origin.
Information is given about a polynomial f left parenthesis x right parenthesisf(x) whose coefficients are real numbers. find the remaining zeros of f. degree 3; zeros: negative 8 comma negative 3 minus i−8, −3−i enter the remaining zeros of f.
Evaluate the exponential expression. Write your answer as a fraction in simplest form.
(2^3)^-2
In 1985, there was 285 cell phones subscribers in the small town of centerville.After 1985, the number of subscribers increased by 75% per year. How many cell phones subscribers were in centerville in 1994 ?
Zaira spent 55 hours in 2 weeks working on a science project. she worked 32 hours the first week. Write and solve an addition equation to find the amount of time she spent working the second week.
The radius of a cylinder is increased by a factor of 5. The height is not changed.
What is the effect of the increase on the volume of the cylinder?
A) The volume of the cylinder increases by a factor of 5.
B) The volume of the cylinder increases by a factor of 25.
C) The volume of the cylinder increases by a factor of 15.
D) The volume of the cylinder increases by a factor of 10.
When the radius of a cylinder is increased by a factor of 5, the volume of the cylinder increases by a factor of 25.
Explanation:The volume of a cylinder can be calculated using the formula V = πr2h, where V is the volume, r is the radius, and h is the height. In this case, the radius of the cylinder is increased by a factor of 5, but the height remains the same. Let's consider the original radius as r and the increased radius as 5r. The volume of the original cylinder is πr2h, and the volume of the new cylinder is π(5r)2h.
Simplifying the expression for the volume of the new cylinder, we get V' = 25πr2h. Comparing the volume of the new cylinder to the volume of the original cylinder, we can see that the volume has increased by a factor of 25. Therefore, statement B is correct: The volume of the cylinder increases by a factor of 25.
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The correct answer is B) The volume of the cylinder increases by a factor of [tex]25.[/tex]
Let's analyze the relationship between the volume of a cylinder and its dimensions.
The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
[tex]\( r \)[/tex] is the radius of the cylinder,
[tex]\( h \)[/tex] is the height of the cylinder.
Given that the height [tex]\( h \)[/tex] remains unchanged, if the radius [tex]\( r \)[/tex] is increased by a factor of [tex]5[/tex], the new radius [tex]\( r' \)[/tex] becomes[tex]\( 5r \).[/tex]
Now, let's compare the volumes before and after the increase in radius:
1. Original Volume [tex](\( V_{\text{original}} \))[/tex]
[tex]\[ V_{\text{original}} = \pi r^2 h \][/tex]
2. New Volume [tex](\( V_{\text{new}} \))[/tex]
After increasing the radius by a factor of [tex]5[/tex], the new radius [tex]\( r' = 5r \)[/tex].
[tex]\[ V_{\text{new}} = \pi (5r)^2 h = \pi (25r^2) h \][/tex]
Now, compare [tex]\( V_{\text{new}} \)[/tex] with [tex]\( V_{\text{original}} \)[/tex]
[tex]\[ \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi (25r^2) h}{\pi r^2 h} = \frac{25r^2 h}{r^2 h} = 25 \][/tex]
If you answer (making sense) and explain (so I can understand) you will be awarded! Please help ASAPA
What's the explicit formula HELP
45% of 40 is 18% of what number?
Answer:
45% of 40 is 18% of 100
Step-by-step explanation:
45% of 40 is 18% of what number
First we find out what is 45% of number 40
45% times 40
[tex]\frac{45}{100} * 40= 18[/tex]
Now we find
18 = 18% of what number
Let the unknown number be x
18 = 18% * x
[tex]18= \frac{18}{100} * x[/tex]
18 = 0.18 * x
Divide by 0.18 on both sides
100= x
So 45% of 40 is 18% of 100
The complete statement is 45% of 40 is 18% of 100
How to determine the number that completes the statementFrom the question, we have the following parameters that can be used in our computation:
45% of 40 is 18% of what number
Represent the number with x
So, we have
45% of 40 is 18% of x
Express as an equation
45% of 40 = 18% of x
Next, we have
18 = 0.18x
Divide through by 0.18
x = 100
Hence, 45% of 40 is 18% of 100
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Assume that the grasshopper in the food pyramid above must eat half its body weight in grass each day. If an average-size grasshopper weighs 2 grams, and 1 blade of grass weighs 0.1grams (one tenth of a gram), how many blades of grass does the grasshopper need to eat each day?
Answer:
The grasshopper needs to eat 10 blades of grass each day.
Step-by-step explanation:
The grasshopper in the food pyramid above must eat half its body weight in grass each day.
The average weight of the grasshopper is 2 grams.
The weight of one blade of grass is 0.1 grams.
Now,
The weight of grass eating by the grasshopper per day is 1 gram.
Let us assume that the grasshopper eats the "n" number of blades of the grass.
Therefore,
[tex]\begin{aligned}n \times 0.1\;\rm{gm}&=1\;\rm{gm}\\n&=\dfrac{1}{0.1}\\n&=10\end{aligned}[/tex]
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The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
Identify the population and the sample
a.
population: 1,000,000 cartons of eggs
sample: every 50th carton in each shipment
c.
population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment
b.
population: 1,000,000 cartons of eggs
sample: the 50th carton of eggs
d.
population: 10 shipments of 1000 cartons of eggs
sample: the 50th carton of eggs
Answer:
Option c. Population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment.
Step-by-step explanation:
First we find out population :
For ten shipments of 1000 cartons of eggs. In other words in each 10 shipments there are 1000 cartons of eggs.
Therefore, 1000 × 10 = 10,000 cartons of eggs.
Population : 10,000 cartons of eggs
Now it is given that she examines every 50th carton to see how many cartons contain cracked eggs.
Hence, Sample would be every 50th carton in each shipment.
In option a and b given cartons of eggs are 1,000,000, so they would be eliminated and in option d it is given that sample is only 50th carton of eggs
Therefore, option c would be correct.
How long will it take for 750 mg of a sample of radium-225, which has a half-life of about 15 days, to decay to 68 mg?
A. ≈ 50 days
B. ≈ 54 days
C. ≈ 48 days
D. ≈ 52 days
Answer:
52 Days
Step-by-step explanation:
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.
y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)
Writing [tex]5x-2y=-6[/tex] in slope-intercept form:
[tex]5x-2y=-6\\5x+6=2y\\\frac{5x+6}{2}=y\\y=\frac{5}{2}x +3[/tex]
The slope of the line is the number before "x", which is [tex]\frac{5}{2}[/tex].
The slope of the perpendicular to this line is the negative reciprocal of this.
So the slope of perpendicular is [tex]-\frac{2}{5}[/tex].
To find the equation of the perpendicular line, we need a point. It is given as [tex](5,-4)[/tex] where [tex]x_{1}=5[/tex] and [tex]y_{1}=-4[/tex].
Now we use the point-slope form of a line to figure out the equation:
[tex]y-y_{1}=m(x-x_{1})[/tex]
Plugging in the values of [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and [tex]m=-\frac{2}{5}[/tex], gives us:
[tex]y-(-4)=-\frac{2}{5}(x-5)\\y+4=-\frac{2}{5}x+2\\y+\frac{2}{5}x=2-4\\y+\frac{2}{5}x=-2[/tex]
Multiplying everything by 5 [to get rid of the denominator] and re-arranging gives us:
[tex]y+\frac{2}{5}x=-2\\5y+2x=-10\\2x+5y=-10[/tex].
THIS IS THE SECOND OPTION.
ANSWER: [tex]2x+5y=-10[/tex]
Solve for x
Please help quick
Solve y=x^2 + 7 for x
Final Answer:
The solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are: [tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]
Explanation:
To solve the equation [tex]\( y = x^2 + 7 \)[/tex] for x, you want to isolate x on one side of the equation. Here are the steps to do so:
1. **Subtract 7 from both sides**:
To isolate the [tex]\( x^2 \)[/tex] term, we first remove the constant term on the right side by subtracting 7 from both sides of the equation.
[tex]\( y - 7 = x^2 + 7 - 7 \)[/tex]
This simplifies to:
[tex]\( y - 7 = x^2 \)[/tex]
2. **Take the square root of both sides**:
To solve for x, you need to get rid of the square on the x term. This is done by taking the square root of both sides. Remember that when you take the square root of both sides of an equation, you must consider both the positive and negative square roots.
[tex]\( \sqrt{y - 7} = \pm\sqrt{x^2} \)[/tex]
Simplifying the right side (since the square root and square operations are inverses of each other), we get:
[tex]\( \sqrt{y - 7} = \pm x \)[/tex]
3. **Solve for x**:
We now have two solutions for x, a positive and a negative one, because squaring a positive or a negative number both give a positive result. Therefore, we write:
[tex]\( x_1 = +\sqrt{y - 7} \\\\ \( x_2 = -\sqrt{y - 7} \)[/tex]
So, the solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are:
[tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]
Remember that you can only take the square root of a non-negative number in real numbers. So if y - 7 is negative, the solutions for x would be complex numbers.
Can someone help me please?
true or false 120% of a whole number is always greater than the number? and why?
the law of cosines is used to find the value of m. m2 = 272 + 182 ??? 2(27)(18)cos(28??) m2 = 729 + 324 ??? (972)cos(28??) m2 = 1053 ??? (972)cos(28??) To the nearest whole number, the value of m is .
the law of cosines establishes:
c² = a² + b² - 2 ab cos C
in this problem
a=27
b=18
C=28°
c=m
m² = 27² + 18² - 2*(27)*(18)* cos(28°)
m² = 729 + 324 - 972* cos(28°)
m² = 1053 - 972* 0.8829
m² = 194.82-------------> m=13.96-----------> 14
the answer is m=14 units
The Art Store sells three types of art pencil sets. The profit is $8.45 on watercolor pencil sets, $6.19 on pastel pencil sets and $4.62 on charcoal pencil sets. There are two branches of the Art Store. The number of sales of pencil sets for each store are shown in the table below.
Set Type
Sales for Westside Branch
Sales for Downtown Branch
watercolor
132
74
pastel
56
48
charcoal
119
126
Which store had the most profit and what was the total profit of that store?
Answer:
c
Step-by-step explanation: