The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.
What is the Pythagoras theorem?The theorem is given by (hyp)² = (opp)² + (adj)².This theorem applies to a right-angle triangle only.Calculation:The given triangle is a right-angle triangle.
It has two lengths. They are
length of the hypotenuse = 21
length of the adjacent or base = 13
Then, the third side i.e., the opposite side length is calculated by
(hyp)² = (opp)² + (adj)²
⇒ (21)² = (opp)² + (13)²
⇒ 441 = (opp)² + 169
⇒ (opp)² = 441 - 169 = 272
⇒ opposite side length = √272 = 16.49 ≅ 16.5
Therefore, the length of the third side is 16.5.
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how many different choices of car does a person have if a particular model comes in 11 colors and 4 styles
Answer:
44 options
Step-by-step explanation:
In order to solve this problem you would simply need to multiply the options specifics together. In this scenario, these are the color and style. Therefore since the individual can choose from 11 colors and 4 styles you simply multiply 11 by 4. This is because every single color chosen has 4 styles to choose from, meaning that all 4 styles also have 11 colors to choose from and vice versa.
11 * 4 = 44
Therefore, we see that an individual looking to buy a car has a total of 44 options to choose from.
The graph below shows the distance a car drove over a course of 18 hours. At what time did the driver end her trip?
at 20 hours
at 2 hours
at 18 hours
at 4 hours
I need help for this question
(a) Function formula of f(t) in terms of t is, f(t)=17-1.3t
(b) The domain of the function is 0 to 13.076.
(c) The range is 0 to 17
(d) 9.38 is the value exist for f(t)=4.8
(e) The correct option of this sub part is How many hours since the candle was lit when it is 4.8 inches long.
What is a Function?An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Also, the input and output are somehow connected.
Solution of sub part (a)The initial length of the candle is 17 inch. It also given that, it burns with a constant rate of 1.3 inches per hour.
After one hour since the candle was lit, the length of the candle will be (17 – 1.3) = 15.7 inch.
After two hour, since the candle was lit, the length of the candle will be (15.7-1.3) = 14.4 inch.17 - 2(1.3) can be used to represent the candle's length after two hours.
Hence, the length of the candle after t hours when it was lit can be represented by the function, f(t)=17-1.3t
Solution of sub part (b)Putting f(t)=0 in the equation, we get
0=17-1.3t
-17=-1.3t
t=13.076
Hence, The domain of the function is 0 to 13.076
Solution of sub part (c)Putting t=0 in the equation, we get
f(t)=17-1.3t
f(t)=17-1.3×0
f(t)=17
Hence, The range is 0 to 17.
Solution of sub part (d)putting f(t)=4.8 in the equation we get
4.8=17-1.3t
4.8-17=-1.3t
t=9.38
Hence, the value of t for f(t) =4.8 is 9.38.
Solution of sub part (e)When the candle was 4.8 inches long, then time taken to lit from the equation is 9.38 hours.
Hence, The correct option of this sub question is How many hours since the candle was lit when it is 4.8 inches long.
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What is the answer help
Answer: 162°
Step-by-step explanation:
To find the answer to this question, we need to find what 45% of 360 degrees (a circle) is.
First, a percent divided by 100 becomes a decimal.
45% / 100 = 0.45
Next, "of" means multiplication in mathematics.
0.45 * 360 = 162
The central angle will be 162°.
Which system of linear inequalities has the point (3, -2) in its solution set?
y < -3; y ≤ 2/3x - 4
y > -3; y ≥ 2/3x - 4
y < -3; y ≥ 2/3x - 4
y > -2; y ≤ 2/3x - 4
The system that has linear inequalities has the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.
We know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
In option B, we have
y > -3 ----> inequality A
y ≥ 2/3x - 4 ----> inequality B
In both inequality, change the values of x and y at the point (3, -2) and then compare the outcomes.
Inequality A
y > -3 ----> is true
Inequality B
y ≥ 2/3x - 4 ----> is true
Therefore
The ordered pair is a solution of the system B
As a result, the point (3, -2) in the solution set of the system with linear inequalities is y > -3; y 2/3x - 4.
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A book is bought for 350 and sold for R490. Calculate the percentage profit.
well, the profit is clearly just 490 - 350 = 140.
Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?
\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)
Three quarters of a number is 27. What is two ninths of the number?
Answer:
8
Step-by-step explanation:
let x be the number , then
\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )
3x = 108 ( divide both sides by 3 )
x = 36
the number is 36, so
\(\frac{2}{9}\) × 36 = 2 × 4 = 8
The two ninths of the number is 8
We know that Three quarters of a number is \(\frac{3}{4}\) times of a number
Hence we will assume the number x ,
\(\frac{3}{4} of x = 27\)
\(x = 27 X \frac{4}{3}\)
\(x = 36\)
Now as we know the number is 36
Therefore , the two ninths of the number assumed as y
We will multiply the number 36 by 2 and then divide by 9
Hence,
\(y = 36 X \frac{2}{9}\)
\(y = 8\)
Thus, the two ninths of the number 36 is 8
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Hi :), im really struggling with this. Just wanted to know if anyone can explain step by step for me please. Id really appreciate it.
Answer:
222
Step-by-step explanation:
What I did was calculate the area of each sides of the triangular prism.
For the two triangles:
1/2(6x5)=15 (for 1 triangle, notice there are 2 so -> 30)
For the 2 rectangles:
5x12=60 x2 = 120
For the base:
6x12=72
Add all them together we get 222
Please help me I have no clue what this is steps would be great I have a exam and I have no clue what I'm doing anyways... HELP MEEEEEE if you have time to help me with this that would be amazing.
Answer:
D. Infinitely Many Answers
Step-by-step explanation:
Simply the function -x+4(x-2)
-x+4x-8
3x-8
Notice it is the same with the the first function
Thus, they are the same function, so they intersect each other infinitely many.
Find the height of the tower using the information given in the illustration.
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
O
Problem !. Draw the Logic Circuit for:
BD + BE + D'F
Problem 2. What is the boolean Expression of F5?
B
X
Y
Z
F5
The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.
To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.
Step 1: Apply De Morgan's laws
NOT (R AND NOT P) can be simplified as (NOT R) OR P.
Step 2: Distributive property
F5 = (P AND Q) OR ((NOT R) OR P)
Step 3: Apply associative property
F5 = (P AND Q) OR (P OR (NOT R))
Step 4: Apply absorption law
F5 = P OR (P OR (NOT R))
Step 5: Apply idempotent law
F5 = P OR (NOT R)
By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.
Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.
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The question probable may be:
Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:
F5 = (P AND Q) OR (R AND NOT P)
Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?
Examples of thermal insulators include
1.)down feathers.
2.)Styrofoam.
3.)air.
4.)all of the above
Answer:
4.
Step-by-step explanation:
PLS HELP! URGENT ! 25 POINTS
Answer:
C
Step-by-step explanation:
Name 4 noncoplanar points.
Answer:
RPVN
Step-by-step explanation:BRBR
John bought a video game that was 30% off. The game was originally $60. What was the sale price of the game?
Answer:
42 dollars
Step-by-step explanation:
30% of 60 = 60 × .30 = 18
60 - 18 = 42
sales price is 42 dollars
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ax+by=(a-b), bx-ay=(a+b) Solve by using SUBSTITUTION METHOD.
The solution to the system of equations is x = (ab - a² - b)/a and y = a²/b - ab/b²
To solve the system of equations using the substitution method, we start by solving one of the equations for one variable and then substitute that expression into the other equation.
Let's solve the first equation, ax + by = (a - b), for variable x:
ax = (a - b) - by
Dividing both sides by a, we have:
x = (a - b)/a - (b/a)y
Now, we substitute this expression for x into the second equation, bx - ay = (a + b):
b((a - b)/a - (b/a)y) - ay = (a + b)
Expanding and rearranging the terms, we get:
\(ba/a - b²/a - b²y/a + by - ay = a + b\)
Simplifying further:
\(b - b²/a - b²y/a + by - ay = a + b\)
Now, we can collect like terms:
\(b - (b² + b²y)/a + by - ay = a + b\)
Rearranging and grouping the terms with y:
\((by - b²y)/a - (ay - b²y)/a = a\)
Factoring out y:
\(y(b - b²)/a - y(a - b²)/a = a\)
Now, we can divide both sides by (b - b²)/a:
y = a/((b - b²)/a) = a(a/b - b)/b
Simplifying further:
y = a²/b - ab/b²
Finally, we substitute this value of y back into the expression we found for x:
x = (a - b)/a - (b/a)(a²/b - ab/b²)
Simplifying and finding a common denominator:
x = (a - b)/a - (a² - ab)/ab
Combining the fractions:
x = (a - b - (a² - ab))/a
Expanding:
x = (a - b - a² + ab)/a
Combining like terms:
x = (ab - a² - b)/a
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What is the name for a mathematical phrase? O A. An inequality OB. An operation OC. An expression OD. An equation
PLEASE HELP! I will mark you Brainly and rate well!
Fuel Usage.
The slope can be used to represent the average rate of change, or how much one quantity changes, on average, relative to the change in another quantity. An example of a slope that changes in real-life involves units of measure such as beats per minute or kilowatts per hour.
Over a 45-day period, the amount of propane in a tank that stores propane for heating a home decrease from 500 gallons to 344 gallons.
1. Use a graph or the slope formula to show the average rate of change in the amount of propane used over the 45-day period.
2. Show all work.
3. Explain what your solution represents in the context of the situation.
Answer: this is not answer but it will help u with whoever does answer it
Step-by-step explanation:
we see here, slope is another version of finding the average rate of change. Average rate of change is finding the difference between the dependent variable (y-term) divided by the difference in the independent variable (x-term). Slope and average rate of change is exactly the same thing
Bao walked 15 miles in 6 hours. What was her walking rate in miles per hour?
Group of answer choices
2.5 miles per hour
2 miles per hour
1 mile per hour
1.5 miles per hour
The solution is, 2.5 miles per hour was her walking rate in miles per hour.
We know that,
Speed is measured as distance moved over time.
The formula for speed is speed = distance ÷ time.
To work out what the units are for speed, you need to know the units for distance and time.
In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
Here, given that,
Bao walked 15 miles in 6 hours.
so, we get,
in 6 hours = 15 miles
so, in 1 hour = 15 / 6 miles
=2.5 miles
Hence, The solution is, 2.5 miles per hour was her walking rate in miles per hour.
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The quadratic regression showing the height (f(x)), in feet, a young boy throws a ball in relation to distance (x), in feet, the ball travels is given by f(x)=−0.0116x^2+0.931x+6.6785.
How far will the ball have traveled when it hits the ground? Round your answer to the nearest whole number.
the ball will have traveled about 89 feet when it hits the ground, rounded to the nearest whole number.
To find how far the ball will have traveled when it hits the ground, we need to find the value of x that makes f(x) equal to zero. This means we need to solve the quadratic equation:
\(f(x) = -0.0116x^2+ 0.931x + 6.6785 = 0\)
There are different methods to solve a quadratic equation, such as factoring, completing the square, or using the quadratic formula. Here, we will use the quadratic formula, which can be written as:
x = (-b ± √(\(b^2\) - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation in standard form: \(ax^2 + bx+c = 0\)
In this case, we have:
a = -0.0116
b = 0.931
c = 6.6785
Putting these values into the quadratic formula, we get:
x = (-0.931 ± √(\(0.931^2\) - 4(-0.0116)(6.6785))) / 2(-0.0116)
x = (-0.931 ± √(1.2709)) / -0.0232
x = (-0.931 ± 1.1273) / -0.0232
we get two possible values for x:
x = (-0.931 + 1.1273) / -0.0232
x = 8.4487
or
x = (-0.931 - 1.1273) / -0.0232
x = 88.6336
The value x = 8.4487 implies that the ball hits the ground after traveling only about 8 feet, which is too short for a realistic throw. The value x = 88.6336 implies that the ball hits the ground after traveling about 89 feet, which is more reasonable.
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what did the ancestral puebloans do to make the growing need for housing
Answer: How did the Ancestral Puebloans adapt their housing to the building materials that were available in the arid Southwest? They built some houses of stone blocks against canyon walls and built freestanding villages of stone and adobe brick.
Step-by-step explanation:
1. Find the mean of these times that American Airlines flights used to taxi to the Los Angeles
terminal after landing from a flight: 12 min, 8 min, 21 min, 17 min, 12 min.
Answer:
14
Step-by-step explanation:
f(x) = 3x + 12, g(x) = 3x - 1;
=
=
Find (fºg)(x).
\(\text{Given that,}\\\\f(x) = 3x +12, ~ ~ g(x) = 3x -1\\\\(f \circ g)(x)\\\\=f(g(x))\\\\=f(3x-1)\\\\=3(3x-1) +12\\\\=9x - 3 +12\\\\=9x +9\\\\=9(x+1)\)
What is the measure of the angle?
The ratio of math teachers to choir teachers is 3:2 respectively. There are 12 math teachers. How many math and choir teachers are there all together?
Answer:
30
Step-by-step explanation:
\(3 + 2 = 5 \\ \frac{2}{5} \times x = 12 \\ \\ \frac{2x}{5} = 12 \\ cross \: mutiply \\ 2x = 60 \\ divde \:both \: sides \: by \: 2 \\ x = 30\)
What rigid motion maps the solid-line figure onto the dotted-line figure?
A reflection
B. rotation
C. translation
Answer:
A. Reflection
Step-by-step explanation:
I believe the answer would be reflection
Horizontal lines have a/an ______ slope?
Answer: 0
Step-by-step explanation: There is no slope on horizontal lines as they are flat.
Suppose that E and F are two events and that P(E)=0.2 and P(F|E)=0.5 What is P(E and F)?
By definition of conditional probability,
P(F | E ) = P(F and E ) / P(E )
Then
P(F and E ) = P(F | E ) P(E ) = 0.5 • 0.2 = 0.1
PLEASE HELP ILL GIVE BRAINLIEST!!!!!!
In a lab experiment, 2200 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 26 hours. How many bacteria
would there be after 17 hours, to the nearest whole number?
Answer:
3461
Step-by-step explanation:
y=d(2)^t/d
a=2200 d=26 t=17
y=2200(2)^17/26
y=3461.38562454
y=3461
16) Graph g(x) = x + 3 + 2