Answer:Yes
Step-by-step explanation:A=16 B=30 C=34
16*16= 256 30*30=900 34*34=1156
256+900=1156
Answer:
let's check first is it Right Triangle because we can do it using Pythagorean theorem:
let's sides 16 and 30 be legs, and 34 hypotenuse
1156=1156...so, this is true and your triangle IS Right Triangle
but, it is also a scalene triangle with a right angle
Step-by-step explanation:
PLS PLS PLS PLS PLS PLS HELP!!!!! FIRST TO ANSWER CORRECTLY GETS MARKED THE BRAINLIEST!!!!!
Answer:
5 [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
A thirty minute TV program means that is the total.
If each commercial is 2 1/2 minutes long then we multiply that my three (for each of the times they show a commercial)
2 1/2 * 3 = 7 1/2 minutes (That's the commercials)
30 (Total) - 7 1/2 = 22 1/2 (That all the entertainment segments together)
Since there is 4 segments we divide 22 1/2 by 4
(22 1/2) / 4 = 5.625 or 5 and 5/8
Amara needs 454545 kilograms of meat to feed her 222 pet dragons each day. Each pet dragon eats the same amount of meat. How many kilograms of meat does Amara need to feed 444 pet dragons each day?
Answer:
Amara need to feed 909090 kg of 444 pet dragons each day.
Step-by-step explanation:
Given:
454545 Kg of meat among the 222 pet dragons.
To Find:
Kg of meat required for 444 pets.
Solution:
Here Total of 222 pets eat 454545 meat
Assume that each dragon eat same amount of kg of meat
So each dragon will eat =454545/222 kg of meat
=2047.5 kg of meat for one dragon
We have 444 dragons so they will consume as
444*2047.5 kg of meat
=909090 k g of meat required for the 444 dragons .
OR you can also try as ,
There are total 222 given pets and 444 to be calculated ,
So 444 is twice of 222
Hence requirement for meat will be twice so
222 requires 454545 kg of meat
Hence by relationship
444 will require twice of 454545 i.e
444 will require 909090 kg of meat.
Answer:
20747.5
Step-by-step explanation:
Lucas spends 72 minutes cleaning his room. This is 8 times as long as it takes him to wash the dishes. How long does it take Lucas to wash the dishes?
Answer:
It takes Lucas 9 minutes to wash the dishes
Step-by-step explanation:
In this question, we are tasked with calculating the number of minutes it will take Lucas to wash the dishes given the amount of time he spends on cleaning his room.
since we do not know the amount of time it will take, we can represent this with t
Now what information do we have? we are told that this time t multiplied by 8 will be equal to the time in minutes he takes to clean his room.
Hence, mathematically, we have 8t = 72 minutes
t = 72/8
t = 9 minutes
John makes 35% of his free throw shots sue makes 40% of her free throw shot What is the possibility that John And sue both miss their shots
Answer:
The possibility that John And sue both miss their shots = 0.39
Step-by-step explanation:
John makes 35% of his free throw shots = 0.35
The probability of John missing his shot = 0.65
Sue makes 40% of her free throw shot = 0.4
The probability of Sue missing his shot = 0.6
The possibility that John And sue both miss their shots = 0.65 (0.6)
= 0.39
0). Where is Point B on the number line?
Answer: point B should be the 2nd number on the number line.
Step-by-step explanation:
the answer is shove it up your whole
hAHA JK ITS B
PLEASE HELP!!!! Write the equation of a parabola with vertex (2,-1) and directrix y=-3.
Please show work and put your equation in graphing/vertex form.
Answer:
y = 1/8(x -2)^2 -1
Step-by-step explanation:
The vertex form of the equation of a parabola can be written as ...
y = (1/(4p))(x -h)^2 +k
for vertex (h, k) and vertex-to-directrix distance p. Here, the vertex has a y-value of -1, and the directrix has a y-value of -3, so the distance between them is -1 -(-3) = 2, and the desired equation with vertex (2, -1) is ...
y = 1/8(x -2)^2 -1
_____
Comment on the graph
One description of a parabola is that it is the locus of points equidistant from the focus and the directrix. I like to show that a point on the parabola (not the vertex) meets that requirement. That is what the dashed orange lines are for in the diagram. You can easily see that each has length 4.
pls help! i’m not sure if the answer i chose is the right 1.
A restaurant investigated the correlation between prices and the number of customers. The linear model below represents this situation, where x is the average meal price [in dollars], and y is the number of daily customers. Interpret the slope. A. The average number of daily customers is 18. B. The average price per meal is $18. C. If the average meal price decreases by $1, the number of daily customers decreases by 18. D. If the average meal price increases by $1, the number of daily customers decreases by 18.
Answer: correct answer is D
That is, If the average meal price increases by $1, the number of daily customers decreases by 18.
Step-by-step explanation:
Given that the linear model below represents this situation, where x is the average meal price (in dollars), and y is the number of daily customers. Interpret the slope.
y = 437 - 18x
Since x = the average meal price.
and
y is the number of daily customers.
Let x = 1
Y = 437 - 18 = 419
If x = 2 then
Y = 437 - 36 = 401
The difference between the number of daily customers is
419 - 401 = 18
Therefore, If the average meal price increases by $1, the number of daily customers decreases by 18.
Tessa bought stock in a restaurant for $103.00. Her stock is now worth $126.69. What is the percentage increase of the value of Tessa's stock?
Answer:
23%
Step-by-step explanation:
use this image to help, leave comments if any questions
The original price of a shirt was $20. It was decreased to $15. What is the percent decrease of the price of this shirt?
Answer:
25%
Step-by-step explanation:
20 - 15 = 5
5 / 20 = .25
.25 x 100 / 100 =
25/100
25%
Feel free to let me know if you need more help! :)
18. At a store, a pack of six turkey burgers costs $5.00. A pack of six buns costs $3.00. One pack of turkey burgers and
one pack of buns serve one table of people at Tessa's barbecue. Iff) = 5x represents the total cost of x packs of
turkey burgers and if g(x) = 3x represents the total cost of x packs of buns, which function can Tessa use to determine
the total cost of servingx tables of people at her barbeque?
A. (x)=f(x) -9(x) B1(x) =F ch(x) = f(s) +g(x) D. (x) = f(x) - g(x)
Answer:
I would say add it up
Step-by-step explanation:
Answer:
Step-by-step explanation:
The correct answer would be C - h(x) = f(x) + g(x). The total cost for serving everyone at the barbecue would consist of adding the cost of both the buns and turkey burgers.
Y = A system of equations. Y equals StartFraction 2 over 3 EndFraction x plus 1. Y equals negative StartFraction 2 over 3 EndFraction x minus 1x + 1 and y = x – 1
Final answer:
To solve the system of equations, you can substitute the value of y in terms of x from the third equation into the first two equations.
Explanation:
The system of equations given is:
Y = ½x + 1
Y = -½x - x + 1
y = x - 1
To solve these equations, we can substitute the value of y in terms of x from the third equation into the first two equations:
Substituting y = x - 1 into Y = ½x + 1:
Y = ½(x - 1) + 1
Simplifying, we get:
Y = ½x - ½ + 1
Substituting y = x - 1 into Y = -½x - x + 1:
Y = -½(x - 1) - (x - 1) + 1
Simplifying, we get:
Y = -½x + ½ + 1
Therefore, the system of equations can be simplified to:
Y = ½x - ½ + 1
Y = -½x + ½ + 1
PLZ HELP ME UNDERSTAND
Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.
A. 0 = 2x2 – 7x – 9
B. 0 = x2 – 4x + 4
C. 0 = 4x2 – 3x – 1
D. 0 = x2 – 2x – 8
E. 0 = 3x2 + 5x + 3
Answer:
A. 0 = 2x2 – 7x – 9C. 0 = 4x2 – 3x – 1D. 0 = x2 – 2x – 8Quadratic equations will have two real number solutions that are
A. 0 = 2x2 – 7x – 9
C. 0 = 4x2 – 3x – 1
D. 0 = x2 – 2x – 8
What are quadratic equations and examples?In a quadratic equation, the variable x is an unknown value, for which we need to find the solution. Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc.
How do you solve quadratic equations?Solving Quadratic Equations
Put all terms on one side of the equal sign, leaving zero on the other side.Factor.Set each factor equal to zero.Solve each of these equations.Check by inserting your answer in the original equation.Learn more about quadratic equations here: https://brainly.com/question/8649555
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Jalen is trying to set a pole that is 10 feet long into the ground so that it is perpendicular with
the horizontal surface. Jalen locates a point 6 feet from the base of the pole, a C, and labels
it A He then measures the distance from point A to point What distance, to the nearest
tenth of a foot does Jalen need for the pole to be perpendicular? Justify,
10 font long board and an 18 foot long board. To make the ramp
isht triangle. How long should
Answer:
Step-by-step explanation:
The distance of point A from the top of the pole that will make the pole be perpendicular position to the ground
so, for the pole to be in perpendicular position it must obey Pythagorean theorem
Then, using Pythagoras theorem
c² = a² + b²
x² = 10² + 6²
x² = 100 + 36
x² = 136
x = √136
x = 11.662ft
To nearest tenth
x = 11.7 ft.
So, the pole must be at a distance of 11.7 ft from the top of the pole to point A.
To justify,
10 font long board and an 18 foot long board. To make the ramp right triangle. How long should ramp
So, to calculate the ramp, which is the hypotenuse we will still apply Pythagorean theorem
Then, using Pythagoras theorem
c² = a² + b²
x² = 10² + 18²
x² = 100 + 324
x² = 424
x = √424
x = 20.59 ft
To nearest tenth
x = 20.6 ft.
So, the ramp is 20.6 ft long
Jalen needs to measure 8 feet from point A to the base of the pole to set it perpendicularly to the ground.
To make the pole perpendicular to the ground, Jalen needs to measure the distance from point A to the base of the pole, which forms a right angle at point B.
Using the Pythagorean theorem: Distance AB = √((10)^2 - (6)^2) = √(100 - 36) = √64 = 8 feet.
Therefore, Jalen needs to measure 8 feet from point A to the base of the pole for it to be positioned perpendicularly.
Frank, who lives in Texas, and his sister Lilly, who lives in Japan, correspond regularly. From what he can tell from the postmarks on both his and his sister's letters, it appears that it takes longer for Lilly's mal from Japan to reach him in Texas than it does for his letters from Texas to reach her in Japan. When Frank called his post office to ask if there was a reason for this, the postmaster told him that the delivery time of letters in both directions should be the same. Frank and his sister decided to collect data to see if letters from Japan to Texas take longer to be delivered than letters from Texas to Japan. They recorded the delivery time in days. After convincing themselves that the assumptions were reasonable, they performed a two-sample t-test and obtained the following computer output. Two sample T for To Texas vs To Japan Mean 8.74 6.75 StDev 2.92 SE Mean 0.84 0.85 To Tesas To Japan 95% CI for To Texas - mu To Japan: (-0.53.4.51) T-Test mu To Texas mu To Japun (s): T 1.66 P-0058 DF-18 Using a significance level of 0.05, which of the following statements best describes the conclusion that can be drawn from these data? There is convincing evidence that there is no difference in the mean delivery times. There is convincing evidence that there is a difference in the mean delivery times. There is convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan. There is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan. The t-test cannot be used for sample sizes that are this small.
Based on the results of the two-sample t-test, which yielded a p-value of 0.058 (larger than the significance level of 0.05), there isn't strong enough evidence to conclude that the mean delivery time from Japan to Texas is greater than that from Texas to Japan.
Explanation:From the computer output of the two-sample t-test, we can see that the p-value given is 0.058. This p-value is used to determine the statistical significance of the results. Since the p-value is greater than the chosen significance level of 0.05, we fail to reject the null hypothesis. Keep in mind, that failing to reject the null hypothesis does not prove it to be true, it simply suggests that we do not have strong enough evidence against it.
Therefore, the conclusion that can be made from the data is: There is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan.
This means that while Frank and Lilly may have observed different delivery times, according to this data and the chosen significance level, those differences may as well be due to chance and not due to a true difference in mail delivery times.
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The two-sample t-test results indicate that there is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan. Thus, the difference in delivery times is not statistically significant at the 5% level.
To analyze the data collected by Frank and Lilly regarding the delivery times of their letters, a two-sample t-test was performed. The t-test results are summarized in the following way:
Mean delivery time to Texas: 8.74 daysMean delivery time to Japan: 6.75 daysStandard Deviation to Texas: 2.92Standard Deviation to Japan: 2.92P-value: 0.058Confidence Interval: (-0.53, 4.51)The P-value of 0.058 is greater than the significance level of 0.05, suggesting that there is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan. Therefore, we fail to reject the null hypothesis, meaning that the difference in delivery times is not statistically significant at the 5% level.
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2
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Which data set has a median of 15?
o 7, 16, 14, 16, 11, 7, 17
18,9, 19, 16, 6, 20. 13
• 9, 17, 13, 15, 16, 8, 12
18, 15, 11, 14, 19, 15, 6
Answer:
{13, 23, 11, 16, 15, 10, 26}
Step-by-step explanation:
The "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. The middle number is 15, so the median is 15.
plzzzz lmk if it was right and give me the brainliest
THX so muchhhhh
Answer:
The answer would be the last one. 18, 15, 11, 14, 19, 6
Here's Why:
To find the median, you must first put these numbers in order from least to greatest.
Least ----> Greatest
6, 11, 14, 15, 15, 18, 19
The next step is to find the middle number. In this case, the middle number is 15, therefore, you're median is 15.
6, 11, 14, 15, 15, 18, 19
(: hope this answers your question
The time it takes people to read a certain book is normally distributed with a mean of 147 minutes and a standard deviation of 12 minutes.
Approximately what percent of people take between 123 and 171 minutes to read the book?
Approximately 95.44% of people take between 123 and 171 minutes to read the book.
To find the percentage of people who take between 123 and 171 minutes to read the book, we'll use the properties of the normal distribution.
First, we need to find the z-scores for both 123 and 171 minutes using the formula:
[tex]\[ z = \frac{{X - \mu}}{{\sigma}} \][/tex]
Where:
-[tex]\( X \)[/tex] is the value (in minutes),
-[tex]\( \mu \)[/tex] is the mean (147 minutes),
- [tex]\( \sigma \)[/tex] is the standard deviation (12 minutes).
For 123 minutes:
[tex]\[ z_1 = \frac{{123 - 147}}{{12}} = -2 \][/tex]
For 171 minutes:
[tex]\[ z_2 = \frac{{171 - 147}}{{12}} = 2 \][/tex]
Now, we'll use a standard normal distribution table or calculator to find the percentage of values between these z-scores. For a standard normal distribution, approximately 95.44% of the data falls within ±2 standard deviations from the mean.
So, to find the percentage of people who take between 123 and 171 minutes, we subtract the percentage outside this range from 100%:
[tex]\[ \% = 100 - (100 - 95.44) = 95.44\% \][/tex]
Approximately 95.44% of people take between 123 and 171 minutes to read the book.
P(t) = 21,000 (4/7)^t/3
Answer:
3
Step-by-step explanation:
Diana has a 32 ounce bag of mixed nuts: 1/2 of the mix is peanuts, 1/9 of the mix is Brazil nuts, and 1/12 of the mix is cashews. How many of the bag are cashews
Answer:
2.67 ounce of cashews are in the mix.
Step-by-step explanation:
Since we are dealing with a 32 ounce bag of mixed nuts and 1/12 of this bag is cashews (1/12 of the mix),
Then:
1/12 × 32 ounce = The actual quantity of cashew nuts in the mix.
= 1/12 × 32
= 32/12
= 2.67 ounce of cashews are in the bag.
Answer:
2.666ounce is contained in the bag
Step-by-step explanation:
Given that 32 ounce of bag has mixed nuts of which 1/12 of this bag contain cashews.
(1/12 of the entire mix),
Hence,
1/12 × 32 ounce
= 1/12 × 32
= 32/12
= 2.666ounce of cashews are in the bag.
Bethanine left at 3:00 in the afternoon and walked 3/10 of a mile to Bridget's house. Laney walked 36/100 of a mile to Bridget's house. How far did Bethanie and Laney walk altogether? Determine if there is extra or missing inform
Answer:
Bethanie and Laney walked a total of = 0.66 miles or ([tex]\frac{33}{50}[/tex]th of a mile)
Step-by-step explanation:
Bethanie walked 3/10th of a mile
Laney walked 36/100th of a mile
Lets divide and convert them to decimal:
3 divided by 10 gives us 0.30
36 divided by 100 gives 0.36
Total they walked:
0.30 + 0.36 = 0.66 miles
That would be (in fraction):
66/100 = 33/50 of a mile
What are two numbers that equal to 28 in multiplication
Answer:
7*4
14*2
Step-by-step explanation:
Answer:
Answers will vary
Step-by-step explanation:
There are many possibilities, especially if you're going beyond whole numbers, meaning decimals work as well
Whole numbers
1 and 28
2 and 14
4 and 7
Decimals
3 and 9.33 or 9 1/3
5 and 5.6
6 and 4.67 or 4 2/3
8 and 3.5
9 and 3.11
10 and 2.8
These are just a few simple ones, it gets even more complicated if you have two numbers both with decimals
If ∆XYZ ~ ∆RST, find the value of x.
Answer:
x = 12
Step-by-step explanation:
[tex]\frac{xy}{rs}[/tex] = [tex]\frac{xz}{rt}[/tex]
[tex]\frac{5x - 3}{3x + 2} = \frac{60}{40}[/tex]
20x - 12 = 18x + 12
2x = 24
x = 12
The value of x from the given similar triangles is 12.
Given that, ∆XYZ ~ ∆RST.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From ∆XYZ and ∆RST, we have
XY/RS = XZ/RT
⇒ (5x-3)/(3x+2)= 60/40
⇒ (5x-3)/(3x+2)=3/2
⇒ 2(5x-3)=3(3x+2)
⇒ 10x-6=9x+6
⇒ 10x-9x=6+6
⇒ x=12
Hence, the value of x from the given similar triangles is 12.
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Amelia is 3 years older than Caleb, and Caleb is 2 years more than half of Amelia's age. The system of equations represents this situation. A = 3 + C C = 2 + 0.5A How old is Amelia? How old is Caleb?
Step-by-step explanation:
Simple
If Amelia is 10 years old and so half of Amelia age = 5
Caleb is 2 years more so = 5 + 2 = 7
It means Caleb age = 7
And Amelia age = 10
Kyle has picked 5 1/3 bushels of apples. He wants to know how many more bushels,b, of apples he needs to pick to have 9 bushels in all. Part A: Write an equation to describe this situation. Part B: How many more bushels does Kyle need to pick? Show your work, *
Answer:
Step-by-step explanation:
Kyle has picked 5 1/3 bushels of apples
He want to pick b more bushels of apple to have 9 bushels in all
A) 5[tex]\frac{1}{3}[/tex] + b = 9 bushels
b) b = 9 - 5 [tex]\frac{1}{3}[/tex] = 3 [tex]\frac{2}{3}[/tex]
- Part A: The equation is [tex]\(\frac{16}{3} + b = 9\).[/tex]
- Part B: Kyle needs to pick [tex]\(3 \frac{2}{3}\)[/tex] more bushels of apples.
Let's break down the problem step by step.
Part A: Write an Equation
Kyle has already picked 5 1/3 bushels of apples. He wants to have a total of 9 bushels. We need to find out how many more bushels, b , he needs to pick.
First, convert the mixed number 5 1/3 into an improper fraction:
[tex]\[ 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \][/tex]
Now we can write the equation for the total number of bushels he wants:
[tex]\[ \frac{16}{3} + b = 9 \][/tex]
Part B: Solve the Equation
To find b, we solve the equation:
[tex]\[ \frac{16}{3} + b = 9 \][/tex]
Subtract [tex]\(\frac{16}{3}\)[/tex] from both sides of the equation to isolate b :
[tex]\[ b = 9 - \frac{16}{3} \][/tex]
Convert 9 to a fraction with the same denominator as [tex]\(\frac{16}{3}\):[/tex]
[tex]\[ 9 = \frac{9 \times 3}{3} = \frac{27}{3} \][/tex]
Now perform the subtraction:
[tex]\[ b = \frac{27}{3} - \frac{16}{3} = \frac{27 - 16}{3} = \frac{11}{3} \][/tex]
Convert [tex]\(\frac{11}{3}\)[/tex] back to a mixed number if needed:
[tex]\[ \frac{11}{3} = 3 \frac{2}{3} \][/tex]
So, Kyle needs to pick:
[tex]\[ b = 3 \frac{2}{3} \text{ bushels} \][/tex]
Summary
- Part A: The equation is [tex]\(\frac{16}{3} + b = 9\).[/tex]
- Part B: Kyle needs to pick [tex]\(3 \frac{2}{3}\)[/tex] more bushels of apples.
The following are the weights,in pounds, of some dogs at a kennel: 36,45,29,39,51,49.
find median:
suppose one of the weights were given in kilograms.Can you still find median.
Answer:
Median = 42 pounds
Step-by-step explanation:
It is given that the following are the weights,in pounds, of some dogs at a kennel: 36,45,29,39,51,49.
Arrange the data in ascending order.
29, 36, 39, 45, 49, 51
Total number of terms = 6 (even)
So, the formula for median is
[tex]Median=\dfrac{\frac{n}{2}\text{th term}+(\frac{n}{2}+1)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{\frac{6}{2}\text{th term}+(\frac{6}{2}+1)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{3\text{rd term}+4\text{th term}}{2}[/tex]
[tex]Median=\dfrac{39+45}{2}[/tex]
[tex]Median=42[/tex]
Hence, the median weight is 42 pounds.
To find the median, units of the data should be same. If one of the weights were given in kilograms, then we cannot find median.
Three cards are drawn from a standard deck of 52 cards without replacement. Find the probability that the first card is an ace, the second card is a three, and the third card is a jack.
Answer:
[tex]4.82\cdot 10^{-4}[/tex]
Step-by-step explanation:
In a deck of cart, we have:
a = 4 (aces)
t = 4 (three)
j = 4 (jacks)
And the total number of cards in the deck is
n = 52
So, the probability of drawing an ace as first cart is:
[tex]p(a)=\frac{a}{n}=\frac{4}{52}=\frac{1}{13}=0.0769[/tex]
At the second drawing, the ace is not replaced within the deck. So the number of cards left in the deck is
[tex]n-1=51[/tex]
Therefore, the probability of drawing a three at the 2nd draw is
[tex]p(t)=\frac{t}{n-1}=\frac{4}{51}=0.0784[/tex]
Then, at the third draw, the previous 2 cards are not replaced, so there are now
[tex]n-2=50[/tex]
cards in the deck. So, the probability of drawing a jack is
[tex]p(j)=\frac{j}{n-2}=\frac{4}{50}=0.08[/tex]
Therefore, the total probability of drawing an ace, a three and then a jack is:
[tex]p(atj)=p(a)\cdot p(j) \cdot p(t)=0.0769\cdot 0.0784 \cdot 0.08 =4.82\cdot 10^{-4}[/tex]
A ladder 20 feet long leans against a building forming and angle of 46 degrees with the level ground. To the nearest foot how far away is the foot of the ladder to the building
Answer:
The distance of the foot of the ladder to the building is 14 ft.
Step-by-step explanation:
The length of ladder = 20 ft
Angle formed by ladder with level ground, θ = 46
We are required to find out the distance of the foot of the ladder from the building
The above question can be found out by using trigonometric relations as follows;
[tex]Cos\theta = \frac{Adjacent\, side \, to\, angle}{Hypothenus\, side \, of\, triangle}[/tex]
The adjacent side of the right triangle formed by the ladder the building and the ground is the distance of the foot of the ladder from the building
The hypotenuse side is the length of the ladder = 20 ft
Therefore;
Adjacent side of triangle = Hypotenuse × cosθ
∴ Distance of the foot of the ladder from the building = Hypotenuse × cosθ
Distance of the foot of the ladder from the building = 20 ft × cos(56)
Distance of the foot of the ladder from the building = 13.893 ft
To the nearest foot, the distance of the foot of the ladder to the building = 14 ft.
the equation is x^2+(y+5)^2=81. find the center and radius
Answer:
The center is (0,-5) and the radius is 9
Step-by-step explanation:
The equation of a circle can be given by
(x-h)^2 + (y-k) ^2 = r^2
where (h,k) is the center and r is the radius
(x-0)^2 + (y- -5) ^2 = 9^2
The center is (0,-5) and the radius is 9
Is the sequence geometric? If so, find the common ratio and the next two terms.
1,2,4,8,..
Answer:
16, and 32
Step-by-step explanation:
The common ratio are be multiply by 2.
Find the angle measures given the figure is a rhombus.
The measure of angle 1 in the rhombus is determined as 74⁰.
How to calculate the measure of angle 1?
The measure of angle 1 is calculated by applying the following formula as shown below;
Each diagonal of a rhombus bisects the angle through which it passes.
Also, the opposite angles of a rhombus are equal.
The missing angles of the rhombus is calculated as follows;
(32 + 32) + 4(∠1) = 360 (sum of angles in a rhombus)
64 + 4∠1 = 360
4∠1 = 360 - 64
4∠1 = 296
∠1 = 296 / 4
∠1 = 74⁰
From the diagonal of the rhombus given, we calculated the value of angle 1 as ∠1 = 74⁰.