HELP
Given right triangle ABC.
In the given right triangle, find the length of the hypotenuse, AB, if BC = 6 and AC = 5.
A.5
B.√36
C.√61
D.√11
Answers
A²+B²=C²
6²+5²=C²
36+25=C²
61=C²
√61=C
So the answer is C.
Answer:
Correct answer is option C (√61)
Step-by-step explanation:
in this question we have given a right triangle in which
∠C=[tex]90^{0}[/tex]
BC = 6 and AC = 5
we have to find the length of the hypotenuse, AB=?
To find the the hypotenuse we will apply Pythagoras theorem (According to Pythagoras theorem, "in a right angle triangle, square of hypotenuse is equal to the sum of square of other two sides")
In ΔABC by Pythagoras theorem
[tex]AB^{2}=AC^{2}+BC^{2}[/tex]...................(1)
put values of BC and AC in equation 1
[tex]AB^{2}=5^{2}+6^{2}[/tex]
[tex]AB^{2}=25+36[/tex]
[tex]AB^{2}=61[/tex]
AB=√61
Related Questions
Employee Earnings per month($) 1 1,200 2 2,600 3 1,800 4 1,450 5 3,500 6 2,800 7 12,500 8 3,200 Which measure of spread is best for the data in the table?
Answers
Answer: Interquartile range
Step-by-step explanation:
Interquartile Range:
Q3 - Q1 Find Q2 then Q3 then Q1. Then subtract Q3 and Q1.
This is the most accurate out of all measures of spread.
Hope this helps :)
The measure of spread is best for the data in the table is mean absolute deviation.
What is data table?Tables are a useful tool used to present data in an organized and easy-to-understand format. They typically consist of rows and columns that contain information, and can even be structured in more complex ways. Tables are often used in communications, research, and data analysis.
The given data is 1200, 2600, 1800, 1450, 3500, 2800, 12500 and 3200.
Mean absolute deviation (MAD) is a measure of variation in a data set, calculated by taking the average of the absolute differences between each data value and the mean. It gives an indication of how far each data point is from the mean, providing an easy way to detect the spread of the data. MAD is a useful tool for understanding the range of values within a data set, and it can be used to compare different sets of data to each other.
Therefore, the measure of spread is best for the data in the table is mean absolute deviation.
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The equation of the line of best fit of a scatter plot is y = 8x − 1. What is the slope of the equation?
Answers
If we look at y = mx + b and y = 8x -b we can see the similarities
y = mx + b
y = 8x - 1
m = slope = 8
b = y-intercept = -1
Slope = 8
Answer:
8
Step-by-step explanation:
I just took the test.
State the domain of the relation
Answers
The domain is {-2,0,1,2,3,4}, assuming there is a point at (4,6).
A store manager set up a cardboard display to advertise a new brand of perfume. The display is a square pyramid whose base is 18 inches on each side.The height of each triangular face of the pyramid is 12 inches. How much card word was used to make the display?
A. 516 B.756
C.612 D.1080
D is not the answer I tried the teacher marked it wrong
Answers
please award brainly
The surface area of the cardboard display is the sum of the area of the square base and the four triangular faces, totaling 756 square inches. This corresponds to answer B.
The student wishes to calculate he amount of cardboard used to create a square pyramid display. To find this, we need to determine the surface area of the pyramid, which includes the base and the four triangular faces.
Firstly, we calculate the area of the square base. The base length is given as 18 inches. The formula for the area of a square is side length squared:
Base area = 18 inches × 18 inches = 324 square inches.Next, we find the area of one triangular face using the formula for the area of a triangle (base × height / 2). The base of each triangle is the same as the side of the square base, and the height is given as 12 inches:
Triangular face area = (18 inches × 12 inches) / 2 = 108 square inches.Since there are four identical triangular faces, we multiply the area of one triangle by four:
Total area of triangular faces = 4 × 108 square inches = 432 square inches.Finally, we add the area of the base to the total area of the triangular faces:
Total surface area = 324 square inches (base area) + 432 square inches (triangular faces area) = 756 square inches.Therefore, the amount of cardboard used for the pyramid display is 756 square inches, which corresponds to answer B.
Simplify radical expression. Leave in radical form. the squarefoot of 7(the squarefoot of 14+the squarefoot 3)
Answers
1- You have the following radical expression given in the problem above:
(√7)(√(14)+√(3))
2- When you apply the distributive property, you obtain:
(√7)(√(14))+ (√7)(√(3))
3-Simpliying, you have:
(7√2)+(√21)
4- Therefore the answer is: (7√2)+(√21)
the function f(x)=2^x. the function f(x)= 2^x+k and K < 0. which of the following statements is true
Answers
Identify the coefficient of each term of the polynomial.
-2x+9
what is The coefficient of the first term is ....
what isThe coefficient of the second term is
Answers
The coefficient is a known number, written as a digit, whereas the variable is an unknown number, written as a letter to signify an unknown number.
So, the coefficient in the first term (or part of the equation) is -2. The coefficient in the second term is 9, and the variable in this equation is x.
Final answer:
The coefficient of the first term '-2x' in the polynomial is -2, and the coefficient of the second term '9' is 9.
Explanation:
In the polynomial -2x+9, each term has a coefficient. A coefficient is a number that multiplies the variable. The variable in the first term is x, and it is being multiplied by -2. Therefore, the coefficient of the first term is -2. The second term is a constant and does not have a variable associated with it. However, by convention, we can think of this term as 9 times x0, since any number raised to the zero power is 1. The coefficient of this constant term is 9.
At the ice-cream parlor you can choose from 4 flavors of ice cream, 2 types of sauce, and 3 different toppings when ordering a sundae. How many possible sundaes can be ordered?
Answers
the temperature at 10 am was -7°F. By noon, the temperature had dropped 12°F. By 2 pm, it had dropped another 5°F. what was the temperature at 2 pm?
Answers
6(z+2)-2(2z+5)=18 show step by step
Answers
Note:
Parenthesis, Exponents (and roots), Multiplication, Division, Addition, Subtraction)
Because you are trying to isolate the z (variable), you cannot do parenthesis. Instead, distribute 6 to z and 2, and -2 to 2z and 5
6(z + 2) = 6z + 12
-2(2z + 5) = -4z - 10
6z + 12 - 4z - 10 = 18
Next, combine like terms. Combine terms with common variables together, as well as constants.
6z - 4z = 2z
12 - 10 = 2
2z + 2 = 18
Next, isolate the z, do the opposite of PEMDAS. Note that there is an equal sign. What you do to one side, you have to do to the other.
2z + 2 = 18
subtract 2 from both sdies
2z + 2 (-2) = 18 (-2)
2z = 18 - 2
2z = 16
isolate the z, divide 2 from both sides
2z = 16
2z/2 = 16/2
z = 16/2
z = 8
8 is your answer for z
hope this helps
A taco stand sells tacos for $3.25 each. The stands expenses for the day are $210. Define your variables and write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then slice the inequality. Provide your conclusion as a complete sentence.
Answers
Let P= profit
let n= no. of tacos sold per day
Sol'n:
P= 3.25n-210
the profit needs to be positive, thus
3.25n>210
n>210/3.25
n> 64.615
they can only sell whole tacos, therefore they must sell at least 65 tacos to make a profit and that profit is:
P=3.25n-210
P=3.25*65 - 210
P= 211.25 -210
P= 1.25
$1.25 profit
One researcher wishes to estimate the mean number of hours that high school students spend watching tv on a weekday. a margin of error of 0.23 hour is desired. past studies suggest that a population standard deviation of 1.9 hours is reasonable. estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answers
Assuming a 95% confidence interval and substituting all the values;
At 95% confidence, Z = 1.96
Therefore,
0.23 = 1.96*1.9/Sqrt (N)
Sqrt (N) = 1.96*1.9/0.23
N = (1.96*1.9/0.23)^2 = 262.16 ≈ 263
Minimum sample size required is 263 students.
Answer:the answer is 236 students
Step-by-step explanation:
Which expression represents the volume of the box? use the formula v=lwh 3x+1, 2x-1 ×+2
Answers
(3x+1) by (2x-1) by (x+2) will be:
volume, V=lwh
plugging the values we get:
V=(3x+1)(2x-1)(x+2)
Expanding the above we get:
V=(3x+1)(2x^2+3x-2)
V=3x(2x^2+3x-2)+1(2x^2+3x-2)
V=6x^3+9x^2-6x+2x^2+3x-2
V=6x^3+11x^2-3x-2
Hence the expression for the volume will be:
V=6x^3+11x^2-3x-2
Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk 2 quarts of orange juice 16 cups of milk 32 oz of lemonade . how many gallons of beverages did he buy
Answers
1 pint=0.125 gallons
1 quart=0.25 gallons
1 cup = 0.0625 gallons
1 oz = 0.0078125 gallons
thus amount of :
milk bought
0.125*2=0.25 gallons
orange juice bought:
0.25*2=0.5 gallons
milk bought:
16*0.0625=1 gallon
lemonade bought:
32*0.0078125=0.25 gallons
Thus total gallons made was:
0.25+1+0.5+0.25
=2 gallons
The amount of beverages did he buy will be 2 gallons.
What is conversion?Conversion means to convert the same thing into different units.
Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk, 2 quarts of orange juice, 16 cups of milk, and 32 oz of lemonade.
We know the conversion
1 pint = 0.125 gallons
1 quart = 0.25 gallons
1 cup = 0.0625 gallons
1 oz = 0.0078125 gallons
Then the amount of beverages did he buy will be
Milk bought
0.125 x 2 = 0.25 gallons
Orange juice bought:
0.25 x 2 = 0.5 gallons
Milk bought:
16 x 0.0625 = 1 gallon
Lemonade bought:
32 x 0.0078125 = 0.25 gallons
Thus total gallons made will be
→ 0.25 + 1 + 0.5 + 0.25
→ 2 gallons
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Michelle invests $1000 at a bank offering 3% compounded quarterly. Write an equation to model the growth of the investment.
A) A = 1000(1.03)4t
B) A = 1000(1+.03
4
)t
C) A = 1000(1+.03
4
)4t
D) A = 1000((1.03)
4
)4t
Answers
is what I got
Answer:
C. [tex]1000( \frac{1+.03}{4})^{4t}[/tex]
Step-by-step explanation:
you plant 30 african violet seeds and 9 of them sprout use experimental probability to predict how many will sprout if you plant 20 seeds
Answers
Experimental probability =(number of occurrence of event)/(total number of trials made)
=9/30
=3/10
thus the number of seeds that will sprout given that 20 seeds we planted will be:
3/10×20
=6 seeds
6 seeds are required that will sprout if you plant 20 seeds.
What is the 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.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
It is given that out of 30 planted seeds only 9 of them sprouted, then
Experimental probability =(number of occurrences of the event)/(total number of trials made)
=9/30
=3/10
thus the number of seeds that will sprout given the 20 seeds we planted will be
3/10×20
=6 seeds
Therefore, 6 seeds are required that will sprout if you plant 20 seeds.
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99 POINTS!!!: if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then
what is the central angle,
what is the measure of the arc that 2 pieces together would intercept,
and the equation that represents
and circumference?
PLEASE HURRY!!!
Answers
coordinates of the center (8,5)
radius=6 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-8)²+(y-5)²=6²
b) circumference=2*pi*r-----> 2*pi*6---> 37.68 in
if 360° (full circle) has a length of---------> 37.68 in
90° (2 pieces together)---------> x
x=90*37.68/360-----> x=9.42 in
the measure of the arc that 2 pieces together would intercept is 9.42 in
c) The central angle of one slice is 45 degrees
) 20% of computer chips from a certain manufacturer are defective. if 100 computer chips are purchased, what is the approximate probability that at least 20 of them are defective
Answers
Linda bought circular table clothe that was a radius of 3 feet. What is the circmference to the nearest foot of linda's table cloth? (using Pie 3.14
Answers
[circumference]=2*pi*r
for r=3 ft
[circumference]=2*pi*3-----> 18.84 ft-------> nearest foot-----> 19 ft
the answer is
19 ft
A surveyor wants to measure the distance from the north end (point b ) to the south end (point c) of a body of water. He creates a right triangle by using point A which is 17.5 m due west of point c and at a 30 degree angle with point b. Find the distance across the lake
Answers
The distance across the body of water from point b (north end) to point c (south end) can be found using trigonometry and the sine ratio. Given that the angle is 30° and the distance from point A to point b is 17.5 m, the distance across the water (from point b to point c) is 8.75m.
Explanation:The problem at hand is a trigonometry problem which can be solved by using the sine ratio. In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the angle is given as 30°, and we are asked to find the distance from point b (north end) to point c (south end), which is the side opposite to the 30° angle. Therefore, we can set up the following equation using the sine ratio: sin(30°) = opposite/hypotenuse.
In this instance, the hypotenuse is the distance from point A to point b, which is given as 17.5 m. Thus, the equation becomes sin(30°) = distance from point b to point c / 17.5 m. Solving this for the distance from point b to point c would mean multiplying both sides by 17.5 m, giving us: distance from point b to point c = sin(30°) * 17.5 m.
Upon calculation, we find that sin(30°) equals 0.5, so therefore the distance from point b to point c, which is the distance across the body of water is 0.5 * 17.5m = 8.75 m.
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If f(x)=x-6 and g(x)=x1/2(x+3), find g(x) times f(x)
Answers
1. You have the following functions given in the problem above:
[tex]f(x)=x-6 [/tex] and [tex]g(x)=x1/2(x+3)=x(x+3)/2 [/tex]
2. You have that g(x) times f(x) can be written as g(x)*f(x). Therefore, you must multiply f(x) * g(x), as following:
[tex]g(x)*f(x)=(x-6)*x(x+3)/2 [/tex]
3. Applying the distributive property, you have:
[tex]g(x)*f(x)=( x^{3} + 3x^2 - 6x^{2} -18x)/2[/tex]
[tex]g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2 [/tex]
The answer is: [tex]g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2[/tex]
PLZ HELP ASAP CIRCLES
Answers
[tex] x^{2} -16x+ y^{2} -36=0 \\ \\ x^{2} -2(x)(8)+ y^{2} = 36 \\ \\ x^{2} -2(x)(8)+ 8^{2}+ y^{2} =36 +8^{2} \\ \\ (x-8)^{2}+y^{2}=100 [/tex]
Thus, we can say now:
Center of the circle is (8,0) and its radius is 10.
What do you notice about the median and mean?
Answers
what happens when you add 1 to a number
Answers
Leo, Kush and Mai share some money in the ratio 3:5:8
Kush receives £750 more than Leo.
Calculate total amount of money that they shared.
Answers
The ratio in which they received cash is 3:5:8
the difference in ration between Kush and Leo=£(5-3)=£2
Total ratio is: 16
thus the total amount was:
16/2×750
=£6000
Find the nth term of the sequence, then find the 20th term, 100th term and the series for each?
2/5, 1/15, -4/15,....
Answers
It's an arithmetic sequence where
[tex]a_1=\dfrac{2}{5}\ and\ d=-\dfrac{1}{3}[/tex]
nth term of the arithmetic sequence is equal:
[tex]a_n=a_1+(n-1)d[/tex]
Substitute:
[tex]a_n=\dfrac{2}{5}+(n-1)\cdot\left(-\dfrac{1}{3}\right)\\\\a_n=\dfrac{2}{5}-\dfrac{1}{3}n+\dfrac{1}{3}\\\\a_n=\dfrac{6}{15}+\dfrac{5}{15}-\dfrac{1}{3}n\\\\\boxed{a_n=\dfrac{11}{15}-\dfrac{1}{3}n}[/tex]
Other form:
[tex]a_n=\dfrac{11}{15}-\dfrac{5}{15}n\\\\\boxed{a_n=\dfrac{11-5n}{15}}[/tex]
[tex]a_{20}=\dfrac{11-5\cdot20}{15}=\dfrac{11-100}{15}=\dfrac{-89}{15}\\\\a_{100}=\dfrac{11-5\cdot100}{15}=\dfrac{11-500}{15}=\dfrac{-489}{15}=-\dfrac{163}{5}[/tex]
what is the volume of the cube shown below? 2 1/4
Answers
The volume of the given cube is 11.4 cubic units.
What is volume of cube?The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object.
The edge of the given cube is [tex]2\frac{1}{4}[/tex] =2.25 units.
We know that, the volume of a cube is a³, where a is an edge.
Here, volume = (2.25)³
= 11.390625
≈ 11.4 cubic units
Therefore, the volume of the given cube is 11.4 cubic units.
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Find f. f ''(x) = −2 + 24x − 12x2, f(0) = 4, f '(0) = 18
Answers
Answer:
f(x) = -x⁴ + 4x³ - x² + 18x + 4
Step-by-step explanation:
If we take the integral of f''(x) with respect to x, we get that f'(x)= -2x + 12x² - 4x³ + C.
Substituting in f'(0)=18, we get C=18.So, f'(x) = -2x + 12x² - 4x³ + 18.If we take the integral of f'(x) with respect to x, we get that f(x) = -x² + 4x³ - x⁴ + 18x + C.
Substituting in f(0) = 4, we get C=4.So, f(x) = -x⁴ + 4x³ - x² + 18x + 4To find the function f, we need to integrate its second derivative, then use the given initial conditions to solve for the constant of integration and find the exact function f(x).
Explanation:To find the function f, we need to integrate its second derivative. We integrate each term of the second derivative separately, using the power rule for integration. So, f''(x) = -2 + 24x - 12[tex]x^2[/tex] becomes f'(x) = -2x + 12[tex]x^2[/tex] - 4[tex]x^3[/tex] + C, where C is the constant of integration. Then, we integrate f'(x) to find f(x), again using the power rule for integration. Finally, we use the given initial conditions, f(0) = 4 and f'(0) = 18, to solve for the constant of integration and find the exact function f(x).
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PLEASE HELP -Given the graph of rectangle QUAD and its reflection.
Use the coordinates of the images' vertices, Q and Q' to algebraically find the line of reflection. In your final answer, include all of your work.
Answers
Q" is located at (6,2)
they bot h have the same Y value (2) so we know it was only a reflection across the X axis
we need to find out where on the X axis it was reflected.
the distance between -5 and 6 = 11 units
11/2 = 5.5
the reflection line was 5.5 units to the right of the original Q
so the reflection line would be X = 0.5
Answer:
Q = (-5, 2)
Q' = (6, 2)
(-5 + 6/2 , 2 + 2/2) = (1/2, 2)
Vertical line through the mid point would be x = 1/2
Jill earns $18.59 per hour. what is her gross earnings if she worked 46 hours. jill earns time and a half for overtime work.
Answers
There are a couple of ways to think about overtime pay.
1) Figure the number of overtime hours, and multiply that number by 1.5 times the base pay. (OT pay) = (OT hours)*(1.5*(base pay))
2) Figure the number of overtime hours, and multiply that number by 1.5, then by the base pay. (OT pay) = ((OT hours)*1.5)*(base pay)
You can see the product is the same, only the sequence of computation is changed.
Then Jill's gross earnings can be computed as ...
(40 h +(6 h)*1.5)*(base pay)
(49 h)*($18.59/h) = $910.91
Jill's gross earnings for 46 hours' work will be $910.91.