Answers
Work Shown:
a = x, b = 3, c = 4
a^2 + b^2 = c^2 ... pythagorean theorem
x^2 + (3)^2 = (4)^2
x^2 + 9 = 16
x^2 = 16 - 9
x^2 = 7
x = sqrt(7)
x = 2.64575131106459
x = 2.6
In a right triangle with one leg of length 3, the other leg of length 4, and the hypotenuse of length x, the Pythagorean theorem formula (3² + 4² = x²) gives the length of x as √25, or 5 units.
Explanation:In Mathematics, a right triangle has one angle that is a right angle (90 degrees). In these triangles, the Pythagorean theorem applies, which says that the square of the length of the longest side (hypotenuse) is equal to the sum of squares of the other two sides (legs).
If x is a leg of the triangle, then its length can be found by rearranging the Pythagorean theorem formula. If the length of one leg is 3, the other is 4, and the length of the hypotenuse is x, then the equation is: 3² + 4² = x².
That simplifies to 9 + 16 = x², and further to x² = 25. Taking the square root of both sides gives us the length of x as 5 units.
Learn more about Pythagorean Theorem here:https://brainly.com/question/19649203
#SPJ2
Related Questions
PLS HELP I'll mark brainlest!
i need the process too!
Answers
Answer:
19. 1400 ft^2
20. 1680 + 112pi m^3
For 20, a decimal answer would be 2031.86
Step-by-step explanation:
19. Lateral surface area refers to the area without including any horizontal planes(the tops and the bottoms - hence the name lateral). The lateral surface area of this prism is simply 5 equivalent rectangles. Each rectangle has an area of 280(14*20). Thus, the answer is 280*5 = 1400 [tex]ft^{2}[/tex]
20. The volume of a shape such as this(where the horizontal planes are always the same shape) can be calculated by the area of the base times the height. In this case, the area of the base is the semi circle (area of [tex]\frac{4*4*\pi}{2}[/tex]). The area of the rectangle is 15 * 8 = 120. Adding these together gets you 120 + 8pi. Multiplying this by the height of 14 gets you 1680 + 112[tex]\pi[/tex] [tex]m^3[/tex]
a mountain bike tire has a diameter of 26 inches to the nearest foot how far does the tire travel when it makes 32 revolutions and does this require circumference and area?
Answers
The distance it covers in 32 revolution is 217.9 ft .
Step-by-step explanation:
Given,
The diameter of the tire of the bike = 26 in
The radius (r) = 13 in
To find the distance it travels in 32 revolutions.
To find the revolution we need to find the circumference.
Formula
The circumference of a circle = 2πr
Now,
The circumference of a circle = 2×[tex]\frac{22}{7}[/tex]×13 in
= 81.71 in (approx)
The distance it covers in 32 revolution is = 81.71×32 in
= 2614.85 in
We know that 1 ft = 12 inch
2614.85 in = 2614.85 ÷ 12 ft = 217.9 ft (approx)
Which of the following equations contains the point (8,5) and is perpendicular to the line y=2x-3
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 3 ← is in slope- intercept form
with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex], thus
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (8, 5) into the partial equation
5 = - 4 + c ⇒ c = 5 + 4 = 9
y = - [tex]\frac{1}{2}[/tex] x + 9 ← equation of line
Joe needs to replace the carpet in his living room and hallway with hardwood flooring. A floor plan is shown below. what is the total area of the floor plan? Each box of flooring contains 2.05 square meters of flooring. How many boxes should Joe buy? One box costs $54.80. How much will the flooring cost?If Joe gets a coupon for 20% off, how much would the flooring cost?
Answers
Answer:
A. Area total= 30 m2
B. 14 boxes
C. 596.40
D. 477.12
Step-by-step explanation:
A, 3.2 (1.5) A=4.8 A=6(4.2)= 30m2
B= 30/2.5= 13.95= 14 boxes
C. 12(42.6)= 596.40
D= 80/100= x/596.4 = 477.12
The total area Joe needs to cover with hardwood flooring would determine the number of boxes of flooring he should buy. Assuming the area is 100 square meters, Joe would need 49 boxes, which would cost $2,685.20 without a discount, and $2,148.16 after a 20% discount.
To determine the total area that Joe needs to floor and the number of boxes of flooring he should buy, we need to calculate the square meters of the combined living room and hallway. Unfortunately, the floor plan measurements are not provided in the question, so let's assume we have those measurements. For example, if the living room and hallway together are 100 square meters, Joe will divide the total area by the area covered by one box of flooring to find out how many boxes he needs.
The calculation for the number of boxes is as follows: total area divided by area per box. If each box contains 2.05 square meters of flooring, and the total area is 100 square meters, Joe would need 48.78 boxes. Since he can't buy a fraction of a box, he would need to purchase 49 boxes.
To find the total cost, we multiply the number of boxes by the cost per box. At $54.80 per box, the cost for 49 boxes is $2,685.20. With a 20 percent discount, the new cost is 80 percent of the original cost, which would be $2,148.16 (0.80 x 2,685.20).
There are 10 pens and 15 pencils in a box. If a student selects two of them at random,
then what is the probability of selecting a pen and then a pencil?
Answers
Answer:
0.25
Step-by-step explanation:
Given:
Number of pens in a box = 10
Number of pencils in a box = 15
To find: probability of selecting a pen and then a pencil
Solution:
Probability refers to the chance of occurring of some event.
Probability of selecting a pen and then a pencil = (Probability of selecting a pen) × (Probability of selecting a pencil given that a pen has already been drawn)
[tex]=\frac{10}{25}\times \frac{15}{24}=\frac{150}{600}=\frac{1}{4}=0.25[/tex]
Probabilities are used to determine the chances of events
The probability of selecting a pen and then a pencil is 1/4
The samples are given as:
[tex]Pen = 10[/tex]
[tex]Pencil = 15[/tex]
The total number of items in the box is:
[tex]Box = 10 + 15[/tex]
[tex]Box = 25[/tex]
The required probability is then calculated as:
P = P(Pen) * P(Pencil)
So, we have:
[tex]P =\frac{10}{25} \times \frac{15}{24}[/tex]
Evaluate the product
[tex]P =\frac{150}{600}[/tex]
Simplify
[tex]P =\frac{1}{4}[/tex]
Hence, the required probability is 1/4
Read more about probabilities at:
https://brainly.com/question/15246027
4 5 6 7 8 9 10
TIME REMAINING
50:40
Gustavo is in a contest where he will win one of four possible prizes. He creates a four-part spinner to represent the four prizes that he has an equal chance of winning: a video game system, a bicycle, a watch, and a gift card. He spins the spinner several times to demonstrate the likelihood of winning a certain prize.
What is true about Gustavo’s data collection?
Gustavo used an experiment where the data is qualitative.
Gustavo used an experiment where the data is quantitative.
Gustavo used a simulation where the data is qualitative.
Gustavo used a simulation where the data is quantitative.
Answers
Answer:
The answer is qualitative as the prices to be won are different.
Hope this helps
What’s the largest fraction you can make using the numbers 1,2,3,4,5
Answers
Answer:
5/1
Step-by-step explanation:
Please mark me brainliest
In March in Austin, Texas, the temperatures for 7 consecutive days were 20°C, 22°C, 20°C, 24°C, 21°C, 26°C, and 23°C. What was the median of the temperatures for these days?
A) 20°C
B) 21°C
C) 22°C
D) 23°C
Answers
Jake purchased a box of 1000 candy guitar lollipops to sell bakery for $20 how much did he pay for each lollipop?
Answers
Answer:
50 Cents each i was thinking a dollar but its actually 50 cents:)
Step-by-step explanation:
He paid 5 dollars per lollipop
G(x)=x^2-10x+24 if graphed on a coordinate plane where would it cross the x axis
Answers
Answer: x^2-10x+24 crosses the x-axis at (4,0) and (6,0)
Step-by-step explanation: (4)^2-10(4)+24 = 0, (6)^2-10(6)+24 = 0.
what is the volume of this right triangular pyramid?
Answers
Answer:
2736
Step-by-step explanation:
Formula is 1/3 x base area x height
The volume of the right triangular pyramid is [tex]\(2736 \text{ cm}^3\).[/tex] Therefore, option a is correct.
To find the volume of a right triangular pyramid, you can use the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
The base area of a right triangular pyramid is given by the formula for the area of a triangle:
[tex]\[ \text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \][/tex]
Given the dimensions of the right triangular pyramid as [tex]\(36 \text{ cm}\), \(19 \text{ cm}\), and \(24 \text{ cm}\), we have:[/tex]
Base:[tex]\(19 \text{ cm}\)[/tex]
Height of the triangle: [tex]\(36 \text{ cm}\)[/tex]
Height of the pyramid: [tex]\(24 \text{ cm}\)[/tex]
First, let's find the base area:
[tex]\[ \text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 19 \times 36 \]\[ \text{Base Area} = \frac{1}{2} \times 19 \times 36 = 342 \text{ cm}^2 \][/tex]
Now, let's calculate the volume of the pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 342 \times 24 \][/tex]
[tex]\[ V = \frac{1}{3} \times 342 \times 24 = 2736 \text{ cm}^3 \][/tex]
So, the volume of the right triangular pyramid is [tex]\(2736 \text{ cm}^3\).[/tex]
what is the slope of the line (-4,-4) and (1,4)
Answers
Answer:
8/5
Step-by-step explanation:
To find the slope given two points
m = (y2-y1)/(x2-x1)
= (4- -4)/(1 - -4)
= (4+4)/(1+4)
=8/5
Answer: answer is 8/5
Step-by-step explanation:
HELP NOW PLZ!!! IM IN A QUIZ!!! IM GIVING BRAINLIEST AND 15 POINTS!!!!
Vikram is studying the square pyramid below. A square pyramid. The square base has side lengths of 34.2 inches. The triangular sides have a height of 28.4 inches and length of 33.2 inches. To find the surface area of the pyramid, in square inches, Vikram wrote (33.2) (34.2) + 4 (one-half (34.2) (28.4)). What error did Vikram make?
A) He used the same expression for the area of all four lateral faces.
B) He used the wrong expression to represent the area of the base of the pyramid.
C) He used the wrong value as the height when he found the area of the lateral faces.
D) He used an expression for surface area that only finds the total area of three faces.
Answers
Answer:
He used the wrong expression to represent the area of the base of the pyramid.
Step-by-step explanation:
i just took it yesterday
Vikram made an error in the expression to represent the area of the base of the pyramid. So, Option B is correct.
What is the surface area of a square pyramid?The surface area of a square pyramid is given by the formula,
[tex]SA=s^2+4(\frac{1}{2}bh)[/tex]
Where, s-length of the side of the square, b- length of the base,
and h- the height of the pyramid.
Given data:The square base had a side of length s=34.2 inches
The height h=28.4 inches
Calculating the surface area:The surface area is given by the expression:
[tex]SA=s^2+4(\frac{1}{2}bh)[/tex]
On substituting the values
[tex]SA=(34.2)^2+4(\frac{1}{2}(34.2)(28.4))[/tex]
But Vikram wrote,
[tex]SA=(33.2)(34.2)+4(\frac{1}{2}(34.2)(28.4))[/tex]
So, he used the wrong expression for the area of the base of the pyramid.
Therefore, option B is correct.
Learn more about the surface area of the pyramid here:
https://brainly.com/question/15928093
#SPJ2
which shapes belongs to only one of Rraoul's group
Answers
Answer: only the parallelogram rhombus.
Step-by-step explanation:
Explain the Error: Corey writes the equation y =_ 85x and finds that he needs 16 cups of onions. Describe and correct his error
Answers
Answer:
32.50
Step-by-step explanation:
Item 10
Evaluate the expression. Write your answer in scientific notation.
(4.2×10^8)+(5.9×10^9)=
Answers
Answer:
1420000005.9
Step-by-step explanation:
(4.2*10^8)+(5.9+10^9)
(4.2*100000000)+(5.9+100000000)
420000000+1000000005.9
1420000005.9
which number is a factor of 10
Answers
Answer: The factors of 10 are 1,2,5,10
Step-by-step explanation:
1•10
2•5
Factors are numbers that the given number (10) can be divided by. In this case, your answers is 1 and 10 and 2 and 5
The following are the temperatures in °C for the first 10 days in January: -5, 0.7, -1.9, 3.5, -9.2, 7.1, -0.6 ,-8.7 ,2.2 ,0.6 Calculate the range.
Answers
Answer:
The range is -16.3
Step-by-step explanation:
The range is the highest number minus the lowest number and if we take a look at this data -5, 0.7, -1.9, 3.5, -9.2, 7.1, -0.6 ,-8.7 ,2.2 ,0.6, we can see that the lowest value is -9.2 and the highest value is 7.1, so we have to minus the lower value from the higher value
-9.2 - 7.1 = -16.3
The range is -16.3
Wayne has 16 3/4 gallons in his car. If he used 2/5 of the gas in his car, how many gallons does he have left
Answers
Answer:
Wayne has 10.05 gallons left.
Step-by-step explanation:
16 3/4 times 2/5 is 6.7
16 3/4 minus 6.7 is 10.05
Wayne has 327/20 gallons of fuel left in his car.
What is a fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator.The number on the bottom of the line is called the denominator.
Now it is given that,
Amount of fuel in the car = 16 3/4 gallons = 67/4 gallons
Amount of fuel used = 2/5 gallons
Therefore,
Amount of fuel left in the car = Amount of fuel in the car - Amount of fuel used
⇒ Amount of fuel left in the car = 67/4 - 2/5
⇒ Amount of fuel left in the car = 327/20 gallons
Thus, Wayne has 327/20 gallons of fuel left in his car.
To learn more about fractions:
https://brainly.com/question/15200890
#SPJ2
The number of seconds in any hour has an order of magnitude of 3.
O A. True
O B. False
Answers
Answer:
A. True
Step-by-step explanation:
I could be wrong
True, The number of seconds in any hour has an order of magnitude of 3.
What is order of magnitude?The order of magnitude is the power of 10, a number is raised to when it's in scientific notation.
Given,
No. of seconds in an hour = 3600 seconds
In scientific notation
No. of seconds in an hour = 3.6 × 10³ seconds
Here, 10 is being raised to the third power.
Hence, The number of seconds in any hour has order of magnitude of 3.
Learn more about order of magnitude here:
https://brainly.com/question/4953281
#SPJ6
From the table below, determine whether the data shows an exponential function. Explain why or why not
1 x 1 3 6 9 12
1 y 1 1 1 2 4 1 8
a. No, the domain values are at regular intervals.
b. No; a different value is added to each range value.
C. No; there is no relationship between the x value and its corresponding y value.
d. Yes; the domain values are at regular intervals and the range values have a common factor 2
Please select the best answer from the choices provided
Answers
Final answer:
The data provided do not represent an exponential function, as there is no constant ratio between y-values for evenly spaced x-values. The correct answer among the given options is 'c' suggesting there is no clear relationship between the x and y values.
Explanation:
From the provided data, it is not clear whether there is an exponential relationship between the x and y values. To determine whether a set of data represents an exponential function, we typically look for a constant ratio between successive y-values when the x-values are evenly spaced. In other words, as x increases by regular intervals, the y values should be multiplied by a constant factor if the relationship is exponential. However, the y-values listed (1, 1, 1, 2, 4, 1, 8) do not show a common factor between each term. Therefore, the data do not represent an exponential relationship, making option 'd' incorrect.
Let's evaluate the other options:
a. No, the domain values are at regular intervals: This is a characteristic of an exponential function, but the range values must also have a common factor, which they do not in this case.
b. No; a different value is added to each range value: This could suggest a linear or polynomial relationship rather than an exponential one. However, without additional context or a pattern in the additions, we cannot be certain of this either.
c. No; there is no relationship between the x value and its corresponding y value: Based on the erratic pattern of y-values, this option seems the most accurate as it suggests that the data does not correspond to any clear mathematical relationship.
The best choice given the options is likely 'c' as it accurately describes the lack of consistent relationship between x and y values necessary for a function to be exponential.
Can anyone help with question one I keep getting 2:5
Answers
Answer:
B= 2:7
Step-by-step explanation:
First add all the marbles.
16+12+4+10
16+12=28
28+4=32+10=42
There are 12 white.
Simplify
12:42= 6:21=2:7
B
Step-by-step explanation:
Because 16+12+4+10= 42
so you have 12 white marble and you have 42 marbles in total so
12 : 42 simplified would be 2 : 7
You were just adding all the other colors and leaving out the white ones but you have to add them all together.
Use the scale factor to find the area of the enlarged figure. Explain your steps.
A small rectangle has a length of 8 and width of 4. A large rectangle has a length of 25.6 and width of a.
Answers
The answer is The scale factor of the enlargement is 3.2. Square the scale factor to get 10.24. Find the area of the original figure, which is 32. Multiply 32 and 10.24 to get the area of the enlarged figure, which is 327.68. I took the asinmate
The area of the enlarged figure is 327.68 units²
What is scaling ?
It is the method to resize drawing with comparing to true size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.
It is given that :
A small rectangle has a length of 8 and width of 4 and a large rectangle has a length of 25.6 and width of a, then
The area of the small rectangle is :
area = length · width
area = (8)(4) = 32 units²
The scale factor is ...
scale factor = greater length / smaller length
= 25.6/8
= 3.2
The area of the greater rectangle will be equals to the small rectangle area multiplied by the square of the scale factor:
(32 units²)(3.2²) = 327.68 units²
Therefore, the area of the enlarged figure is 327.68 units²
Read more about scaling at:
https://brainly.com/question/12750330
#SPJ5
The diameter of a circle is 8 kilometers. What is the angle measure of an arc kilometers long?
Answers
55
Step-by-step explanation:
Graph the funtion f(x) - -3x + 6
Answers
Answer:
The y intercept is 6 and the slope is -3.
Please see the attached graph.
12x+9−20x
HELP ME PLEASE
Answers
Answer:
− 8x+9
Step-by-step explanation:
Sharon cut a board into 4 pieces of equal size to make a table. Which fraction of the whole board does each piece represent?
Answers
Answer:
1/4
Step-by-step explanation:
Since a board is cut into four parts and we are to determine the fraction for each piece
So it will be 1/total number of pieces
Which will be 1/4
So the fraction for each board will be 1/4
Can someone do 15?!?!?
Answers
Given:
The given triangle is a right triangle.
The length of the hypotenuse is 31 units.
The length of the leg is 23 units.
One of the angle is x.
We need to determine the value of x.
Value of x:
The value of x can be determined using the trigonometric ratio.
Thus, we have;
[tex]sin \ \theta=\frac{opp}{hyp}[/tex]
Substituting [tex]\theta=x[/tex], the side opposite to the angle x measures 23 units and the hypotenuse is 31.
Thus, we have;
[tex]sin \ x=\frac{23}{31}[/tex]
Dividing, we get;
[tex]sin \ x=0.74[/tex]
Taking [tex]sin ^{-1}[/tex] on both sides of the equation, we get;
[tex]x=sin^{-1}(0.74)[/tex]
[tex]x=47.7[/tex]
Rounding off to the nearest whole integer, we get;
[tex]x=48[/tex]
Thus, the value of x is 48°
Hence, Option c is the correct answer.
Seven candidates are running for three different class offices: president, vice president,
and secretary. In how many ways can the offices be filled with these candidates?
Answers
Work Shown:
7 ways to pick the president.
6 ways to pick the VP
5 ways to pick the secretary
7*6*5 = 210 ways to pick the three people from a pool of seven. Order matters because the positions are different. Note the count down from 7 to 6 to 5 which indicates that any given person cannot run for more than one office.
You can use the permutation formula with n = 7 and r = 3
The permutation formula is [tex]_n P_r = \frac{n!}{(n-r)!}[/tex] where the exclamation marks represent factorials.
There are 210 distinct ways to assign seven candidates to three different class offices (president, vice president, and secretary), based on permutation principles.
The question involves finding out in how many ways three different class offices (president, vice president, and secretary) can be filled from a pool of seven candidates. This is a permutations problem because the order in which the candidates are chosen matters (as the offices are distinct). To solve this, we use the permutation formula. For the first office, you have 7 choices (any of the 7 candidates can fill it). Once the first position is filled, you are left with 6 candidates for the second office. Similarly, after filling the second office, there are 5 candidates left for the third office.
Therefore, the total number of ways to fill these positions is the product of these choices, which is calculated as:
7 × 6 × 5 = 210 ways.
This means there are 210 distinct ways to assign these seven candidates to the three available class offices, assuming no candidate can hold more than one office simultaneously.
John is painting a picture.He has green, red, yellow, purple, orange and blue paint. He wants to use four different colors on this picture. If order does not matter, how many ways can John pick four colors for his picture, if one of them is green?
a
6
b
15
c
10
d
4
Answers
Answer:
c) 10
Step-by-step explanation:
You do 5 C 3 ( because you are choosing 3 from the remaining 5).
5C3 = 5!/(3!2!) = 10
Answer:
C 10
Step-by-step explanation:
He has 6 colours to choose 3 from.
One of them is green, so he just needs to choose 2 from the remaining 5.
That's,
5C2 = 10