Answers
d° + c° = 2 · 68° = 136°
b° = 360° - (136° + 104°) = 360° - 240° = 120°
Related Questions
Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?
A) 17 miles
B) 32 miles
C) 37 miles
D) 40 miles
Answers
Answer:
D) 40 miles
Step-by-step explanation:
First we must find the distance between the mall and the house. The figure formed is a right triangle. The length of the side from the mall to the house forms the hypotenuse of the triangle. We can use the Pythagorean theorem to find the length:
a² + b² = c²
The two legs of the triangle, a and b, are 15 and 8:
15² + 8² = c²
225 + 64 = c²
289 = c²
Take the square root of each side:
√289 = √(c²)
17 = c
This makes the total distance
15+8+17= 40 miles
Hey! Pretty easy once you get the hang of these problems.
So you start off with the Pythagorean Theorem. Which is : a^2 + b^2 = c^2
Then just fill it in :
15^2 + 8^2 = c^2
225 + 64 = c2
289 = c^2
17 = c
And last :
15 + 8 + 17 = 40 MILES
hoped this helped!! :))
In the diagram, the radius of the outer circle is 5cm and the area of the shaded region is 16π cm^2. What is the radius or the inner circle?
Answers
By using the area of the ring we will see that the radius of the inner circle is 3cm.
What is the radius of the inner circle?
I assume that we have some kind of ring. To get the area of the ring, we need to take the area of the circle defined by the outer radius of the ring, and subtract the area defined by the circle with the inner radius of the ring.
Remember that the area of a circle of radius R is:
A = pi*R^2
We know that:
The radius of the outer circle is 5cm, so its area is:
A = pi*(5cm)^2 = pi*25cm^2
And the area of the ring is pi*16 cm^2
Then the area of the inner circle should be such that:
pi*25cm^2 - A' = pi*16cm^2
Then, solving for A'
A' = pi*25cm^2 - pi*16cm^2 = pi*9cm^2 = pi*(3cm)^2
So the radius of the inner circle is 3cm.
If you want to learn more about circles, you can read:
https://brainly.com/question/1559324
Which of the following are solutions to the equation below?
Check all that apply.
3x^2 + 27x + 60 = 0
A. 4
B. –4
C. –5
D. 5
E. –27
Answers
3x^2+27x+60=0 divide by 3
3(x^2+9x+20)=0 simplify
3(x+4)(x+5)=0
Use the 0 property and check your work.
Answer:
The solutions are B. -4 and C. -5
Step-by-step explanation:
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For [tex]\mathrm{}\quad a=3,\:b=27,\:c=60:\quad x_{1,\:2}=\frac{-27\pm \sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}[/tex]
[tex]x_1=\frac{-27+\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_1=\frac{-27+\sqrt{9}}{2\cdot \:3}\\\\x_1=\frac{-27+3}{2\cdot \:3}\\\\x_1=\frac{-24}{6} = -4[/tex]
[tex]x_2=\frac{-27-\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_2=\frac{-27-\sqrt{9}}{2\cdot \:3}\\\\x_2=\frac{-27-3}{2\cdot \:3}\\\\x_2=-\frac{30}{6} = -5[/tex]
What are the foci of the ellipse given by the equation 100x2 + 64y2 = 6,400?
Answers
[tex]\frac{ x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]
Being:
a: Semi-major axis
b: Semi-minor axis
Our equation is:
[tex]100 x^{2} + 64y^{2} = 6400[/tex]
Multiplying this equation by:
[tex] \frac{1}{(100)(64)} [/tex]
Then:
[tex]\frac{ x^{2}}{64} + \frac{y^{2}}{100} = 1[/tex]
We can see that:
[tex]a = \sqrt{100} = 10[/tex]
[tex]b = \sqrt{64} = 8[/tex]
Then the semi-major axis is on the y-axis, and the focus are located there, so:
[tex]F_{1} = (0,c)[/tex]
[tex]F_{2} = (0,-c)[/tex]
We also know that the relation between a, b and c is:
[tex]c^{2} = a^{2} - b^{2}[/tex]
[tex]c^{2} = 100 - 64 = 36[/tex]
[tex]c = \sqrt{36} = 6[/tex]
Then, the focus are:
[tex]F_{1}(0,6)[/tex]
[tex]F_{1}(0,-6)[/tex]
Quadratic relations and comic sections unit test part 1
11. a. (0, +/- 6)
Which equation represents a parabola with a focus at (0,-2) and a directrix of y=6?
Answers
[tex]F(0,-2)[/tex]
Given that the directrix is parallel to the x-axis, then the ordinary equation is given by:
[tex](x-h)^{2} = 4p(y-k)[/tex]
We need to find V(h,k), being V the vertex.
We know that these distances are always the same, namely:
│FV│ = │VD│
Being D the directrix. Given that the focus F is on the y-axis and the directrix is parallel to the x-axis, then the vertex V will also be on this axis, so h = 0.
As │FV│ = │VD│, then:
[tex]k = \frac{6-2}{2}[/tex], that is the middle point of the segment FD, so:
V(0,2)
Now │FV│= │p│= │2-(-2)│=4
Given that the vertex and focus are below the directrix, then the parabola open down, therefore: [tex]p\ \textless \ 0[/tex]
Lastly, the equation is:
[tex]x^{2} = -4(4)(y-2) = -16y+32[/tex]
[tex]y = -\frac{ x^{2} }{16} + 2[/tex]
The equation of a parabola with a focus at (0,-2) and a directrix of y=6 is x^2 = -16(y - 2).
To find the equation of a parabola with a focus at (0,-2) and a directrix of y=6, you need to use the standard form of the equation of a parabola that opens upwards or downwards. The general form of this type of parabola is (x - h)^2 = 4p(y - k), where (h,k) is the vertex of the parabola, and p is the distance from the vertex to the focus (if the parabola opens upwards or downward) or to the directrix (if the parabola opens sideway).
Given that the focus is at (0,-2) and the directrix is at y=6, the vertex of the parabola will be located midway between them. The distance between the focus and directrix is 8 units, so the vertex will be 4 units from each, which puts the vertex at (0, 2). Therefore, h=0 and k=2.
Since the focus is below the directrix, our parabola opens downward, and the value of p is negative. The distance p is half the distance between the focus and directrix, so p=-4. Plugging these values into the general form, we get (x - 0)^2 = 4(-4)(y - 2), which simplifies to x^2 = -16(y - 2).
This is the equation that represents the desired parabola.
-9 > -2 -3/4v solve.
Answers
A class has 25 students - 15 girls and 4 boys. 5 girls and 4 boys are wearing blue. a student is picked at random. what is the probability that the studnet is either a boy or girl who is not wearing blue?
Answers
0.8 or 80%.
The question is asking for the probability that a randomly chosen student is either a boy or a girl not wearing blue. There are 25 students in total, with 15 girls and 10 boys. Out of these, 5 girls and 4 boys are wearing blue. Therefore, the number of girls not wearing blue is 15 - 5 = 10 girls. Since all boys are considered in the probability, regardless of what they wear, we have 10 boys. So, we have 10 girls not wearing blue and 10 boys, totalling 20 students that match the criteria out of 25.
The probability can be calculated as follows:
( P(\text{{boy or girl not wearing blue}}) = \frac{{\text{{number of boys and girls not wearing blue}}}}{{\text{{total number of students}}}} = frac{{20}}{{25}} = 0.8 ) or 80%.
Therefore, the probability that a student picked at random is either a boy or a girl who is not wearing blue is 0.8 or 80%.
Brainly a garden has width 13−−√ and length 713−−√. what is the perimeter of the garden in simplest radical form?
Answers
The correct answer is:
16√13.
Explanation:
The perimeter of a figure is found by adding together the lengths of all of the sides. The side lengths of this garden are: √13, √13, 7√13 and 7√13. This is because opposite sides in a rectangle are congruent.
Adding these together we have:
√13+√13+7√13+7√13 = (1+1+7+7)√13 = 16√13
solve 3√5c*7√15c^2 please show your work
Answers
21√(75c³)
21√(25 c² 3c)
21√(5² c² 3c)
21× 5c√(3c)
105c√(3c)
Graph the function f(x)=−14x−2. Use the line tool and select two points to graph.
Answers
The graph of the function (f(x) = -14x - 2) is attached below and the two points from which line passes are (-0.143,0) and (0,-2).
Given :
Equation -- f(x) = -14x - 2
The following steps can be used in order to sketch the graph of the given function:
Step 1 - Write the given function.
f(x) = -14x - 2
Step 2 - Now, evaluate the x-intercept of the above function.
0 = -14x - 2
x = -1/7
Step 3 - Now, determine the y-intercept of the given function.
f(x) = -2
Step 4 - Now, graph the equation of a line that passes through the points (-1/7,0) and (0,-2).
The graph of the function is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
An antifreeze solution freezes at -100 °c. what is the freezing point on the fahrenheit scale? -82 °f -212 °f -88 °f -73 °f -148 °f
Answers
Your answer is the last option, -148°F
The formula to convert temperatures from Celcius to Farenheit is:
(C° x 9/5) + 32 or (C° x 1.8) + 32
So to solve, plug in -100°C and follow the order of operations (PEMDAS).
(-100 x 1.8) + 32
(-180) + 32
-148
-100°C is equal to -148°F
The freezing point of the antifreeze solution in Fahrenheit is -148 °F, calculated using the formula for converting Celsius to Fahrenheit.
To convert a temperature from the Celsius scale to the Fahrenheit scale, you can use the following formula: F = (C imes 9/5) + 32, where F represents the Fahrenheit temperature, and C represents the Celsius temperature.
In this case, we are given the freezing point of an antifreeze solution, which is -100 °C. Applying the formula, we get F = (-100 x 9/5) + 32. This calculation gives us F = (-180) + 32, which simplifies to F = -148 °F.
So, the freezing point of the antifreeze solution on the Fahrenheit scale is -148 °F.
Find the length of the curve yequalsthree fifths x superscript 5 divided by 3 baseline minus three fourths x superscript 1 divided by 3 baseline plus 8 for 1less than or equalsxless than or equals27.
Answers
The exact value of the arc length of the curve is 149.4 units
How to determine the exact arc length of the curve
From the question, we have the following parameters that can be used in our computation:
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
Also, we have the interval to be
-1 ≤ x ≤ 27
This means that the x valus are
x = -1 to x = 27
The arc length of the curve can be calculated using
[tex]\text{Length} = \int\limits^a_b {\sqrt{1 + ((dy)/(dx))^2}} \, dx[/tex]
Recall that
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
So, we have
[tex]\dfrac{dy}{dy} = x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}}[/tex]
This means that
[tex]\text{Length} = \int\limits^{27}_{-1} {\sqrt{1 + (x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}})^2}} \, dx[/tex]
Using a graphing tool, we have the integrand to be
[tex]\text{Length} = \dfrac{12x^\frac{5}{3}+15\sqrt[3]{x}}{20}|\limits^{27}_{-1}[/tex]
Expand and evaluate
[tex]\text{Length} = 149.4[/tex]
Hence, the exact arc length of the curve is 149.4 units
It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
A. 5/8 + 5r = 8
B. 5/8 + 5r = 1
C. 5(5/8) = r
D. 5/8 = 5r
Answers
rate of lawn sprinklerand hose would be 5 minutes /r ( rate per minute)
we would then want to add that to the ratio of the lawn sprinkler and hose together together which would be 5 minutes for both / 8 minutes for hose
we want to add those together to equal 100 percent, which can also be written as 1
so the correct equation would be B) 5/8 + 5/r = 1
Answer:
B,5/8+5r=8
Step-by-step explanation:
A right triangle has sides if length 4,12 and 13 what is its perimeter
Answers
Answer:
29
Step-by-step explanation:
The perimeter is the sum of the side lengths:
4 + 12 + 13 = 29
The perimeter of the triangle is 29. (It is not a right triangle.)
___
A right triangle with side lengths 12 and 13 will have a short side of 5. Its perimeter is 30.
Help please !!!!!!!!!!!
Answers
*Write An inequality then solve for the width.* The length of a rectangle is 12 more than its width. what values of the width will make the perimeter less than 96 feet? (Will give brainliest to best answer)
Answers
Now, to find the perimeter of our rectangle, we are going to use the formula for the perimeter of a rectangle formula: [tex]P=2(w+l)[/tex]
where
[tex]P[/tex] is the perimeter
[tex]w[/tex] is the width
[tex]l[/tex] is the length
We know that [tex]w=x[/tex] and [tex]l=12+x[/tex], so lets replace those values in our formula:
[tex]P=2(x+12+x)[/tex]
[tex]P=2(2x+12)[/tex]
[tex]P=4x+24[/tex]
We want values of the width that will make the perimeter less than 96 feet, so lets set up our inequality:
[tex]4x+24\ \textless \ 96[/tex]
[tex]4x\ \textless \ 72[/tex]
[tex]x\ \textless \ \frac{72}{4} [/tex]
[tex]x\ \textless \ 18[/tex]
Since the width can't be zero, we can conclude that the values of the width that will make the perimeter less than 96 feet are: [tex]0\ \textless \ x\ \textless \ 18[/tex] or in interval notation: (0,18)
If a circle has a radius that is 8 cm long, how long is the circle's diameter?
Answers
Answer: just add 8 + 8 and you will get 16
A supporting goods store sells 2 fishing reels and 5 fishing rods for $243. Later, they still 8 fishing reels and 6 fishing rods for $538. Find the price of each item.
Answers
x: price of fishing reels
y: price of fishing rods
We write the system of equations:
2x + 5y = 243
8x + 6y = 538
Solving the system we have:
x = 44 $
y = $ 31
Answer:
the price of each item is:
x = 44 $
y = $ 31
2x + 5y = 243 - I'll solve this one for x.
8x + 6y = 538
2x + 5y = 243
2x = 243 - 5y
2 2
x = 121.5 - 2.5y ; substitute this in for x in the second equation
8x + 6y = 538
8 (121.5 - 2.5y) + 6y = 538
972 - 20y + 6y = 538
972 - 14y = 538
-972 -972
-14y = -434
-14 -14
y = 31
The cost of a rod (y) is $31.
x = 121.5 - 2.5y
x = 121.5 - 2.5 x 31
x = 44
The cost of a reel(x) is $44.
A clown is juggling at a circus. The path of the ball is given by the parametric equations x=2cos t+2 and y=3sin t+3. In what direction is the ball moving?
-up and to the right
-counterclockwise
-down and to the right
-clockwise
Answers
[tex] \left \{ {{x=2cost+2} \atop {y=3sint+3}} \right. [/tex]
Note that this parametric equation is an ellipse. The graph of this equation is given in figure below. So, we well substitute some values of t in the equation:
If t = 0
x = 4 and y = 3
P0(4, 3)
if t = 1
x = 3.08 and y = 5.52
P1(3.08, 5.52)
if t = 2
x = 1.16 and y = 5.72
P2(1.16, 5.72)
Finally, as shown in the figure, the answer is B. counterclockwise. Notice the trajectory that follows P0, P1 and P2.
1. B. Counterclockwise
2. C. (30,401)
3. A. t=2(x-3)
4. C. She should have taken both the positive and negative square root
5. C. y=x^2+8x-25/8
6. D. Hyperbola
7. A. Graph A
The probability that a dessert sold at a certain café contains strawberries is 26%. The probability that a dessert contains both strawberries and whipped topping is 18%. Find the probability that a randomly chosen strawberry dessert contains whipped topping. Round to the nearest tenth of a percent.
Answers
P(Whipped) = x
P(Strawberry and Whipped) = P(Strawberry).P(Whipped) = 18% = 0.18
∴ P(Whipped) = P(Strawberry and Whipped)/P(Strawberry) = 0.18/0.26 = 0.6923 = 69.23%
To nearest tenth,
P(whipped topping) = 69.2%
∴ Probability that a randomly selected desert contains whipped topping is 69.2%.
The probability that a strawberry dessert contains whipped topping is approximately 69.2%
We are given that the probability a dessert contains strawberries (P(S)) is 26%, or 0.26, and the probability that a dessert contains both strawberries and whipped topping (P(S and W)) is 18%, or 0.18.
To find the probability that a randomly chosen strawberry dessert contains whipped topping (P(W|S)), we use the conditional probability formula:
[tex]P(W|S) = \frac{P(S and W)}{P(S)}[/tex]
Substituting the given values, we get:
[tex]P(W|S) = \frac{0.18}{0.26} \approx 0.6923[/tex]
Rounding to the nearest tenth of a percent we get the probability that a randomly chosen strawberry dessert contains whipped topping to be 69.2%.
The population of a city has increased by 26 % since it was last measured. If the current population is 44,100 , what was the previous population?
Answers
The previous population of the city was 35000.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Assume the previous population to be [x].
Then, we can write -
x + 26% of x = 44100
x + 26x/100 = 44100
x + 13x/50 = 44100
(50x + 13x)/50 = 44100
63x = 44100 x 50
63x = 2205000
x = 35000
Therefore, the previous population of the city was 35000.
To solve more questions on percentage increase, visit the link below-
https://brainly.com/question/17135126
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The previous population of the city was 35,000 before experiencing a 26% increase to the current population of 44,100.
Explanation:To calculate the previous population of a city that has experienced a 26% increase to its current population of 44,100, we need to reverse the percentage increase. The formula for this is:
Previous population = Current population / (1 + Percentage increase)
In this case, the percentage increase is 26%, or 0.26 in decimal form. The calculation is:
Previous population = 44,100 / (1 + 0.26) = 44,100 / 1.26
This gives us:
Previous population = 35,000 (rounded to the nearest whole number)
Hence, the previous population of the city was approximately 35,000 before the 26% increase to the current 44,100.
Which functions have real zeros at 1 and 4? Check all that apply.
f(x) = x2 + x + 4
f(x) = x2 – 5x + 4
f(x) = x2 + 3x – 4
f(x) = –2x2 + 10x – 8
f(x) = –4x2 – 16x – 1
Answers
[tex]f(x)=-2x^2+10x-8=-2(x^2-5x+4)=-2(x^2-4x-x+4)=\\-2[x(x-4)-1(x-4)]=-2(x-4)(x-1)=0\iff x=4\ \vee\ x=1\ \text{CORRECT}\\\\f(x)=-4x^2-16x-1\to f(1)=-4\cdot1^2-16\cdot1-1=-4-16-1=-21\neq0\ :([/tex]
Answer:
[tex]\boxed{f(x)=x^2-5x+4\ and\ f(x)=-2x^2+10x-8}[/tex]
Answer:
To find the zeros of a quadratic function, use the quadratic equation, [tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]. We find that the eqautions with zeros at 1 and 4 are b) x² -5x + 4 and d) -2x² + 10x - 8.
Step-by-step explanation:
a) x² + x + 4 --
[tex]x = \frac{-1 \pm \sqrt{1^2-4*1*4} }{2*1}\\x=\frac{-1 \pm \sqrt{1-16}}{2}[/tex]
Because the discriminant (the value inside the square root) is negative, this equation does not have real zeros, so it is not the answer.
b) x² - 5x + 4 --
[tex]x = \frac{5 \pm \sqrt{(-5)^2-4*1*4}}{2*1} \\x=\frac{5 \pm \sqrt{25-16}}{2} \\x = \frac{5 \pm 3}{2}[/tex]
Now, we calculate the two zeros by adding and subtracting the 3.
[tex]x = \frac{5+3}{2} \\x= \frac{8}{2} = 4\\\\x= \frac{5-3}{2} \\x= \frac{2}{2}=1[/tex]
The zeros of this function are 1 and 4, so it is included in our answer.
c) x² + 3x - 4 --
[tex]x = \frac{-3 \pm \sqrt{3^2-4*1*-4}}{2*1} \\x = \frac{-3 \pm \sqrt{9+16}}{2} \\x= \frac{-3 \pm 5}{2}\\\\x=\frac{-3+5}{2}=1\\x=\frac{-3-5}{2} = -4[/tex]
The zeros of this function are -4 and 1, so it is not the answer.
d) -2x² + 10x - 8 --
[tex]x = \frac{-10 \pm \sqrt{10^2-4*(-2)*(-8)} }{2*(-2)} \\x=\frac{-10 \pm \sqrt{100-64} }{-4} \\x = \frac{-10 \pm 6}{-4} \\\\x=\frac{-10 + 6}{-4} =1\\x = \frac{-10-6}{-4} =4[/tex]
The zeros of this function are 1 and 4, so it is included in our answer.
what does x2 + 11x + 24 look like on a graph
Answers
I hope this helps!
x^2 + 11x + 24 can be factored to:
(x+8)(x+3)
Set both factors equal to 0 to find the roots:
x+8=0
x=-8
x+3=0
x=-3
So the graph crosses the x-axis at x = -8 and x = -3.
Next we can find the vertex of the graph. This is the point where the slope changes directions. Since the x^2 term is positive, we know the parabola is facing up (like a smile face). Therefore the vertex is a minimum value.
We can find the x value of the minima by finding the difference between the roots. Half way from -3 to -8 is -5.5.
Next we can find the y value by plugging -5.5 in for x:
y = (-5.5)^2 + 11(-5.5) + 24 = -6.25
So the vertex is at (-5.5, -6.25)
Note: Minima and maxima can be found easier by using calculus.
From these three points we can draw a pretty accurate graph of the equation. See the attached picture.
James pays $120.00 for golf clubs that are on sale fo 20% off at golf pros. At nine iron ,the same clubs cost $8.00'less than they cost at golf pros. They are on sale for 13% off
Answers
Compare your prediction with the total number of pennies on Row 1. How would you change your estimate? Is the result surprising?
Answers
Answer:
a statement that your prediction was less than or greater than the actual count
a statement about how you would change your estimation process
Step-by-step explanation:
Choose any of these two.. There both correct btw
The statements that is true about your prediction of the total pennies on rows 1-4 are statement (b) and (d).
A predictive function is one of mathematical function that helps us to know about future events based on past events. There are many types of functions that can be classified as predictive functions.
The prediction was off by greater than 1,000,000 of the actual total. After seeing the result for rows 1-4, you would indeed change your prediction for the total because it indicates a significant deviation.
Complete question
Check every statement that is true about your prediction of the total pennies on rows 1-4.
a) Your prediction was off by less than or equal to 1,000,000 of the actual total.
b) Your prediction was off by greater than 1,000,000 of the actual total.
c) After seeing the result for rows 1-4, you would change your prediction for the total.
d After seeing the results for rows 1-4, you would not change your prediction for the total.
Find the sum of the series
Answers
(3*2+1)+(3*3+1)+(3*4+1)
=(6+1)+(9+1)+(12+1)
=7+10+13
=30
Thus the sum of the series is:
30
solve the equation 4(-x+4)=12
Answers
-4x-16=12 add 16 to both sides
-4x=28 divide by -4
x=-7
The answer is x=-7
The shortest side of a right triangle measures 88 m. the lengths of the other two sides are consecutive odd integersodd integers. find the lengths of the other two sides.
Answers
x+2 - the side, that has value of consecutive odd integer of x
x+2 is the longest side, so it is a hypotenuse
(x+2)² = x²+88²
x²+4x+4 = x² + 7744
4x=7740
x= 1935
x+2=1935+2=1937
Check
1937²=1935²+88²
3751969=3751969
3. The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone. (a) Sketch the roof of the castle tower. Label the known lengths as described AND label the unknown length as x. (b) What is the slant height of the roof? SHOW YOUR WORK!
Answers
Next, you must use the Pythagorean theorem.
The theorem state a^2 + b^2 = c^2
When calculated, we get 12^2 + 16^2 = 20^2
Your answer is 20
Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. How much will Vivian pay for her surgery if it costs $9600?
2320
2420
2820
after doing the math and writing it out. it has to be one of these three answers but i do beleive that its the second answer but i need reassurance
Answers
We have been given that Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. We have been given that her surgery costs $9600 and we need to find how much will Vivian have to pay for her surgery.
Since we know that the insurance company will pay any amount after Vivian has paid $500. Therefore, the remaining amount after Vivian pays $500 as deductibles will be $9600 - $500 = $9100.
Now we know that Vivian's insurance company will pay 80% of this amount, therefore, Vivian will have to pay the 20% of $9100 in addition to the $500 she already paid.
20% of $9100 is [tex]9100\cdot \frac{20}{100} = \$1820[/tex]
Therefore, the total amount that Vivian pays for surgery is $500 + $1820 = $2320.
Therefore, the first choice given is the right answer.