Answer:
112.76 feet
Step-by-step explanation:
This is a right triangle trig problem. We have the length of the string which serves as the hypotenuse of the triangle, and we also have the reference angle (the angle the string makes with the ground) and we are looking for the height of the height, which is also the height of the triangle, which is also the side opposite the reference angle. So it's our job now to figure out which trig ratio relates the side opposite the reference angle to the hypotenuse. That's the sin ratio (opposite/hypotenuse). Set it up like this:
[tex]sin(70)=\frac{x}{120}[/tex]
Multiply both sides by 120 and then do the math in degree mode on your calculator. That gives you that x = 112.7631145
Don't know how many decimal places you need, but there you go!
Holly has a rectangular garden that measures 12 m wide by 14 m long. She wants to increase the area to 255 m? by increasing the width and length by the same amount. What will be the length (longer dimension) of the new garden? Enter your answer in the box.
Answer:
255 square meters
Step-by-step explanation:
Present area = 12 * 14 = 168 square meters
The area has to increase by a factor of 255 / 168 = 1.5178571429
Therefore, the width and length are increased by a factor of the
square root of 1.5178571429 = 1.2320134508
So the width becomes
12 * 1.2320134508 = 14.7841614091
and the length becomes
14 * 1.2320134508 = 17.2481883107
That's roughly 14.78 by 17.25 and the area equals
14.78 * 17.25 = 255 square meters
Answer: The answer is 17
Step-by-step explanation:
There are 5 4/5 cups of milk left in a carton. Write 5 4/5 as an improper fraction. Explain what the fraction represents in this situation.
Answer:
[tex]\frac{29}{5}\ cups[/tex]
Step-by-step explanation:
we have
[tex]5\frac{4}{5} \ cups[/tex]
Convert to an improper fraction
[tex]5\frac{4}{5}=\frac{5*5+4}{5}=\frac{29}{5}\ cups[/tex]
[tex]=(\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{4}{5})\ cups[/tex]
[tex]=(1+1+1+1+1+\frac{4}{5})\ cups[/tex]
The fraction represent (25/5) cups of milk plus (4/5) cups of milk left in a carton
or
The fraction represent 5 cups of milk plus (4/5) cups of milk left in a carton
5 4/5 cups of milk is equivalent to 29/5 cups when written as an improper fraction. This represents that there are a total of 29 fifths of a cup of milk in the carton.
Explanation:To convert 5 4/5 cups of milk to an improper fraction, you multiply the whole number by the denominator of the fraction and add the numerator. Here, 5 is the whole number, 4 is the numerator, and 5 is the denominator. So, you calculate (5 × 5) + 4 = 25 + 4 = 29. Therefore, 5 4/5 cups is the same as 29/5 cups of milk in improper fraction form.
In this situation, the improper fraction 29/5 represents the total number of fifths of a cup of milk in the carton. Since there are five fifths in a whole cup, and we have 5 whole cups plus an additional 4 fifths, we have a total of 29 fifths of a cup of milk.
An elevator has a placard stating that the maximum capacity is 23252325 lblong dash—1515 passengers. So, 1515 adult male passengers can have a mean weight of up to 2325 divided by 15 equals 155 pounds.2325/15=155 pounds. If the elevator is loaded with 1515 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 155155 lb. (Assume that weights of males are normally distributed with a mean of 161 lb161 lb and a standard deviation of 31 lb31 lb.) Does this elevator appear to be safe?
Answer:
0.7734; no, it does not.
Step-by-step explanation:
To find this probability we will use a z-score. We are dealing with the probability of a sample mean being larger than a given value; this means we use the formula
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our x-bar in this problem is 155, as that is the sample mean we are trying to find the probability of. Our mean, μ, is 161 and our standard deviation, σ, is 31. Our sample size, n, is 15. This gives us
[tex]z=\frac{155-161}{31\div \sqrt{15}}=\frac{-6}{8.0042}=-0.75[/tex]
Using a z table, we see that the area under the curve less than this, corresponding with probability less than this value, is 0.2266. This means that the probability of the sample mean being larger than this is
1-0.2266 = 0.7734, or 77.34%.
Since there is a 77.34% chance of the passengers having a mean weight that is too heavy, this elevator is not safe.
The probability that the elevator is overloaded using the normal distribution principle is 0.7870
Given the Parameters :
Mean, μ = 161Standard deviation, σ = 31 Sample size, n = 15X = 155Using the relation :
Zscore = (xbar - μ) ÷ (σ/√(n))
Zscore = (155 - 161) ÷ (31/√15)
Zscore = - 0.796
The probability that lift is overloaded can be expressed thus :
P(Z ≥ - 0.796) = 1 - P(Z ≤ - 0.796)
Using a normal distribution table ; PP(Z ≤ - 0.796) = 0.2130
P(Z ≥ - 0.796) = 1 - 0.2130
P(Z ≥ - 0.796) = 0.7870
Therefore, the probability that weight is overloaded is 0.7870
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Mr. and Mrs. Pierotti are remodeling their kitchen. They need 9 square yards of covering for the floor. Jackson Interiors quoted them a price of $81 for 9 square yards of linoleum. Carpet Master told them that carpeting would cost $6 per square yard. Which is cheaper—the linoleum or the carpeting?
The carpeting would be cheaper than the linoleum.
Hope this helped :)
Pete’s parents are offering to pay him a weekly allowance for doing his chores. They’ve given him two different payment options for a period of 15 weeks.
Option 1: $20 every week
Option 2: A penny in the first week, and then double the amount from the previous week in each week after that. So, 1 penny in the first week, 2 pennies in the second week, 4 pennies in the third week, and so on.
Which one is the better option for Pete? Explain why.
Find the total of each option to see which one is better.
Option 1:
$20 every week for 15 weeks = 15 x 20 = $300 total.
Option 2:
Week 1 you have 1 penny.
Week 2 you would have 1 +2 = 3 pennies.
Week 3 you would have 3 + 4 = 7 pennies.
From this we can see a pattern of 2^x - 1 where x is the number of weeks.
So in 15 weeks he would have 2^15 - 1 = 32767 pennies.
100 pennies equal $1
32767 / 100 = $327.67
The second option is better because he ends up with more money.
Which is true about the functional relationship shown in the graph?
Answer:
D
Step-by-step explanation:
For linear graphs, we say that the y-axis (y) is a function of the x-axis (x).
The y-axis shows earnings and the x-axis shows time worked (in hours). Thus, we can say that earnings is a function of the number of hours worked.
Looking at the answer choices, D is the correct choice.
Answer:
D
Step-by-step explanation:
I got it correct on A P E X
In order to earn a year-end commission check of 20%, a sales team at a large company must generate 15% more in sales from their territory during a calendar year than was generated the previous year. If the sales team generated $20,000,000.00 in sales from their territory this year, what is the minimum amount of money they can make in commissions during the next 5 years (not including this year) if they receive a commission check each year?
Answer:c
Step-by-step explanation:
please give me brainly
Simplify the expression. log(1/7)
Answer:
d. [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]10^{\log(\frac{1}{7})}[/tex]
Recall that the common logarithm has a base of 10.
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}[/tex]
Recall also that;[tex]p^{(\log_pa)}=a[/tex]
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}=\frac{1}{7}[/tex]
In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student will have dark hair, given that the student has blue eyes?
Hint:
P(A|B)=P(A∩B) / P(B)
46%
43%
21%
67%
Answer:
The correct answer option is 43%.
Step-by-step explanation:
We are given that 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair.
We are to find the probability of a student getting selected will have dark hair with blue eyes.
P(D|B) = P(D∩B) / P(B)
Substituting the given values in it to get:
P(D|B) = 0.3 / 0.7 = 0.428
Rounding it to the nearest whole percent we get:
0.428 × 100 = 42.8% ≈ 43%
Abott simplified an expression. His work is shown below.
Step 1
Step 2
Step 3
Step 4
45.5
In which step did Abott make his first mistake?
step 1
step 2
step 3
step 4
Mark this and return
Save and Exit Next Submit
Abott make his first mistake in step 2
Further explanationCalculation operations include multiply, divide, add, substract, etc.
In mathematical operations we can use the order of operation / calculation according to the principle of PEMDAS
P: Parentheses ⇒ ( ) E: Exponents (powers, square roots, etc.)⇒√,² MD: Multiplication and Division ⇒ x and : AS: Addition and Subtraction ⇒ + and -Multiplication and division or addition and subtraction are interchangeable/rank equally so the calculations/equation operations should be done from left to right
Abbot expression :
9.5 : 0.25 + + 4(0.25+0.5) + 6
Step 1 : 9.5 : 0.25 + + 4(0.75) + 6
Step 2 : 38 + 10(0.75)
Step 3 : 38 + 7.5
Step 4 : 45.5
From the Abott steps it can be concluded that the error occurred in step 2, because the number 4 must be multiplied first with the number in parentheses (ie 0.75)
The correct steps should:
step 1: Step 1: 9.5: 0.25 + 4 (0.75) + 6
Step 2: 38 + 3 + 6
Step 3: 38 + 9
Step 4: 47
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Answer:
Its B
Step-by-step explanation:
Juan’s game board is a square with sides that are 50 cm long. The area of the large circle is about 1,963.5 square cm.
What is the geometric probability that Juan will score more than 0 points?
Answers are in the pic
Answer:
C) 0.785
Step-by-step explanation:
I am assuming that hitting the blue area will result in 0 points.
The area of said square is 50*50, which is 2500 cm².
The chances of scoring >0 points is the chance of hitting the circle.
That is 1963.5/2500.
Therefore, the chance is 0.7854, or 0.785.
Final answer:
The geometric probability that Juan will score more than 0 points is 78.54%.
Explanation:
The geometric probability is the probability associated with geometrical events, such as the probability of a point landing in a certain region. In this case, the event is Juan scoring more than 0 points on his game board. To find the geometric probability, we need to compare the area of the circle to the area of the square. The area of the square is 50 cm x 50 cm = 2500 square cm. The probability of Juan scoring more than 0 points is then the area of the circle (1963.5 square cm) divided by the area of the square (2500 square cm), which equals 0.7854 or 78.54%.
23 points help asap!
Find the unit price and choose the better buy.
80 oz bottle of cleaner for $13.60
70 oz bottle of cleaner for $13.30
90 oz bottle of cleaner for $18.00
60 oz bottle of cleaner for $10.80
Answer:
60
Step-by-step explanation:
ITS THE BEST ONE
an 80 oz bottle of cleaner for $13.60 is the better buy because usually it would be about $40 for that size bottle
A color printer prints 33 pages in 10 minutes how many pages how many pages does it print per minute
A color printer that prints 33 pages in 10 minutes prints approximately 3.3 pages per minute.
Explanation:To figure out how many pages a printer can print per minute, we need to use a simple division calculation. This color printer is said to print 33 pages in 10 minutes. To find the pages printed per minute, you would divide the total number of pages printed (33) by the total time in minutes (10). The equation would look like this: 33/10 = 3.3.
So, the color printer prints approximately 3.3 pages per minute.
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The printer prints 3.3 pages per minute.
We can use a simple division method to determine how many pages the printer prints per minute. We know that:
The printer prints 33 pages in 10 minutes.This means we need to divide the total number of pages by the total number of minutes:
Number of pages the printer prints per minute = [tex]\frac{33 pages}{10 minutes} = 3.3[/tex]
Thus, the printer prints 3.3 pages per minute.
The quarterly returns for a group of 51 mutual funds are well modeled by a Normal model with a mean of 7.4% and a standard deviation of 3.4%. Use the 68-95-99.7 Rule to find the cutoff values that would separate the following percentages of funds, rather than using technology to find the exact values. a) the highest 50% b) the highest 16% c) the lowest 2.5% d) the middle 68% a) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xless than or equals 50% B. xgreater than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% b) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xgreater than or equals nothing% B. xless than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% c) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xless than or equals nothing% B. xgreater than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% d) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.)
Answer:
A) x ≥ 0.074; B) x ≥ 0.108; C) x ≤ 0.006; D) 0.04 ≤ x ≤ 0.108
Step-by-step explanation:
68% of data will fall within 1 standard deviation of the mean; 95% of data will fall within 2 standard deviations of the mean; and 99.7% of data will fall within 3 standard deviations of the mean.
Breaking this down, we find that 34% of data fall from the mean to 1 standard deviation above the mean; 13.5% of data fall from 1 standard deviation above the mean to 2 standard deviations above the mean; 2.35% of data fall from 2 standard deviations above the mean to 3 standard deviations above the mean; and 0.15% of data fall above 3 standard deviations above the mean.
The same percentages apply to the standard deviations below the mean.
The highest 50% of data will fall from the mean to the end of the right tail. This means the inequality for the highest 50% will be x ≥ 0.074, the mean.
The highest 16% of data will fall from 1 standard deviation above the mean to the end of the right tail. This means the inequality for the highest 16% will be x ≥ 0.074+0.034, or x ≥ 0.108.
The lowest 2.5% of data will fall from 2 standard deviations below the mean to the end of the left tail. This means the inequality for the lowest 2.5% will be x ≤ 0.074-0.034-0.034, or x ≤ 0.066.
The middle 68% will fall from 1 standard deviation below the mean to 1 standard deviation above the mean; this means the inequality for the middle 68% will be
0.074-0.034 ≤ x ≤ 0.074+0.034, or
0.04 ≤ x ≤ 0.108
The cutoff values using the 68-95-99.7 Rule for the given mutual funds data are calculated. The highest 50% lies between 4.0% and 10.8%, the highest 16% lies between 0.6% and 14.2%, the lowest 2.5% lies between -2.8% and 17.8%, and the middle 68% lies between 4.0% and 10.8%.
Explanation:The cutoff values can be found using the 68-95-99.7 Rule, which states that approximately 68 percent of the data lies within one standard deviation of the mean, 95 percent lies within two standard deviations, and 99.7 percent lies within three standard deviations. With a mean of 7.4% and a standard deviation of 3.4%, we can determine the cutoff values:
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75, 87, 49, 68, 75, 84, 98 (mean, median mode or range) Please help!!
Final answer:
The mean is 83, median is 75, mode is 75, and range is 49 for the set of numbers 75, 87, 49, 68, 75, 84, 98.
Explanation:
The given set of numbers is: 75, 87, 49, 68, 75, 84, 98.
To find the mean, add up all the numbers and divide the sum by the total count of numbers: (75 + 87 + 49 + 68 + 75 + 84 + 98) / 7 = 83.
To find the median, arrange the numbers in ascending order and find the middle number: 49, 68, 75, 75, 84, 87, 98. So the median is 75.
To find the mode, identify the number that appears most frequently in the set. In this case, 75 appears twice, which is the highest frequency. Therefore, the mode is 75.
The range is calculated by subtracting the smallest number from the largest number in the set: 98 - 49 = 49.
Tom had $56. He bought a soda for $2 and 2 cookies for $3. Which expression correctly shows the total money Tom has left? A. $56 + (?$2) + (?$3) B $56 + (?$2) ? (?$3) C $56 ? (?$2) ? (?$3) D $56 ? (?$2) + (?$3)
C ($56) - ($2) - ($3)
Answer:
I believe it's A
Step-by-step explanation:
Sorry if wrong ;-;
Muriel has kept track of her income and expenses for the week in the spreadsheet below. How much was Muriel's restaurant bill? a. $17.66 b. $42.55 c. $6.35 d. $112.55
Answer:
The answer to this question is option B which is $42.55.
The above statement shows that Muriel has kept track of her income and also expenses for the week in the spreadsheet.
By using the spreadsheet, you can easily calculate the restaurant bill of Muriel. The Muriel’s restaurant bill is calculated as $42.55
Anvi designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points(p), a player may have after his or her first turn of the game?
p = 4
p = -4
|p| = 4
|p| = -4
Will mark the brainliest answer to the first person to correctly answer it
Answer: c) | p | = 4
Step-by-step explanation:
A player wins 4 (+4) or loses 4 (-4) points so you are looking for an answer that is ±4.
| p | = 4 → p = 4, p = -4
Solve for x.
x - 10 = -30
Answer:
Step-by-step explanation:
Hello, the answer is:
X = -30 + 10
X = -20
Best regards
How many 30 degree angles are in a 150 degree angle? Use repeated subtraction to solve.
150 minus 30 equals 120 but i did 150/30 and got 5
To find the number of 30 degree angles in a 150 degree angle using repeated subtraction, subtract 30 from 150 until reaching 30 and count the number of times you were able to subtract. In this case, there are four 30 degree angles in a 150 degree angle.
Explanation:To determine how many 30 degree angles are in a 150 degree angle using repeated subtraction, we start by subtracting 30 from 150 until we can no longer subtract without going negative. Each time we subtract 30, we count the number of times we were able to subtract. So, 150 - 30 = 120, 120 - 30 = 90, 90 - 30 = 60, and 60 - 30 = 30. We were able to subtract 30 four times before reaching 30, so there are four 30 degree angles in a 150 degree angle.
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What does the line x = -5 look like? Horizontal vertical tilted right upwards or tilted right downwards
Answer: Vertical Line
Step-by-step explanation: The line x = -5 is a vertical line at -5. All of the coordinates on the line have an x value of value, which results in a vertical line.
A leaky faucet wastes 2,400 gallons of water per year. How many quarts of water are wasted per month? [1 gallon = 4 quarts]
2,400÷4=600
hope this is good :)
o_________________o
Answer:
Total water wasted per month = 800 quarts
Step-by-step explanation:
A leaky faucet wastes 2,400 gallons of water per year.
Total water wasted per year = 2,400 gallons
Total water wasted per month [tex]=\frac{2400}{12}=200\texttt{ gallons}[/tex]
Given that 1 gallon = 4 quarts
That is
Total water wasted per month = 200 gallons = 200 x 4 = 800 quarts.
Total water wasted per month = 800 quarts
Consider the triangle. Find the length of the hypotenuse, c
The length of the hypotenuse is (blank) cm.
Answer:
The length of the hypotenuse is 26 cm.
Step-by-step explanation:
In order to find the hypotenuse in this right triangle you can use the Pythagoras' Theorem.
The Pythagorean Theorem tells us that the relationship in every right triangle is:
[tex]a^{2}+b^{2}=c^{2}[/tex],
See the picture attached to know what is the meaning of constants a, b and c.
In the triangle given, a = 24cm and b = 10 cm, now you can use the Pythagorean Theorem to find c or the hypotenuse.
[tex]a^{2}+b^{2}=c^{2}\\ 24^{2}+10^{2}=c^{2}\\ 576+100=c^{2}\\ c^{2}=676\\\mathrm{For\:}x^2=\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{\left(a\right)},\:\:-\sqrt{\left(a\right)}\\ x_{1}=\sqrt{676}, x_{2}=-\sqrt{676} \\ x_{1}=26, x_{2}=-26[/tex]
Because we are finding the distance between points AB, this distance cannot be negative, so the answer is the length of the hypotenuse is 26 cm.
15 Point award! :)
Can anyone help me out with this word problem?
"Underwater weddings Inc. offers two kinds of weddings, Caribbean weddings and backyard swimming pool weddings. This last weekend, the company held 5 pool weddings and 2 Caribbean weddings. If the company took in $55,000, and Backyard Pool weddings cost $10,000 less than Caribbean weddings, how much does each kind of wedding cost?"
I will mark whoever can give me an explanation as well brainliest~! Thank you, and have a great day!
The cost of each Caribbean wedding is $15,000 and the cost of each backyard swimming pool wedding is $5,000.
To solve the word problem involving Underwater Weddings Inc., we can let the cost of a Caribbean wedding be x dollars. Since a backyard swimming pool wedding costs $10,000 less, its cost would be x - 10,000 dollars.
The problem states that there were 5 pool weddings and 2 Caribbean weddings, and the total income was $55,000. This gives us the equation:
5(x - 10,000) + 2x = 55,000
Now, we solve for x:
5x - 50,000 + 2x = 55,000
7x = 55,000 + 50,000
7x = 105,000
x = 105,000 / 7
x = 15,000
Caribbean weddings cost $15,000 each.
Therefore, backyard swimming pool weddings cost $15,000 - $10,000 = $5,000 each.
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. Midpoint (15, -8), endpoint (16, -3). What is the other endpoint?
Answer:
the other endpoint is [tex](14,-13)[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
Let
[tex](x1,y1)=(16,-3)[/tex]
so
[tex](16+x2)/2=15[/tex] -----> [tex]x2=30-16=14[/tex]
[tex](-3+y2)/2=-8[/tex] -----> [tex]y2=-16+3=-13[/tex]
therefore
the other endpoint is [tex](x2,y2)=(14,-13)[/tex]
find the missing sides. Brainliest!!
Answer:
1. x = 28; y = 14√3
2. x = 9√2
Step-by-step explanation:
For these, it is helpful to remember that the side lengths of a 30°-60°-90° triangle have the ratio 1 : √3 : 2, and those of a 45°-45°-90° triangle have the ratio 1 : 1 : √2.
1. 14 is the shortest side, and x is the longest side, so ...
x = 2·14 = 28
y = (√3)·14 = 14√3
__
2. 18 is the longest side and x is the shortest side of this 45°-45°-90° triangle, so ...
x·√2 = 18
x = 18/√2 = 18·(√2)/2 = 9√2
Please help im having trouble with this one
What is the measure of ∠T, rounded to the nearest degree? 22° 33° 43° 68°
Answer:
22 degrees to the nearest degree.
Step-by-step explanation:
Use the Cosine Rule
3^2 = 5^2 + 7^2 - 2*5*7*cos T
9 = 74 - 70 cos T
cos T = (74-9)/ 70
cos T = 65/70
m < T = 21.8 degrees.
Answer:
∠T=22°
Step-by-step explanation:
Given triangle RST with sides 5 cm, 7 cm, 3 cm.
If all sides are given and find the missing angle, we use cosine rule
[tex]CosA=\frac{b^{2}+c^{2} -a^{2}}{2bc}[/tex]
Where,
sides are a, b, c and angle A, B, & C are opposite angles respectively.
So,
[tex]CosT=\frac{r^{2}+s^{2} -t^{2}}{2rs}[/tex]
[tex]cosT=\frac{25+49-9}{70}[/tex]
[tex]cosT=\frac{65}{70} =\frac{13}{14}[/tex]
T = 21.79°≈ 22°
That's the final answer.
Find the point of intersection of the lines: y = 4x + 1 and y = – 2x + 4 A. (2 , 9) B. ( 1 2, 3 ) C. (1 , 2) D. ( 1 4, 2)
Answer:
B. (1/2, 3)
Step-by-step explanation:
It is perhaps easiest to try the point values in the equations.
A — 4·2+1 = 9; -2·2 +4 ≠9 . . . . not the answer
B — 4·1/2 +1 = 3; -2·(1/2) +4 = 3 . . . . this is the answer
we need go no further since we have the answer
To find the point of intersection, solve the system of equations formed by the two lines. Substituting x=1 into either equation gives y=5. Therefore, the point of intersection is (1,5).
Explanation:To find the point of intersection of two lines, we need to solve the system of equations formed by the two lines. In this case, the equations are y = 4x + 1 and y = -2x + 4.
Setting the equations equal to each other, we have 4x + 1 = -2x + 4. Solving for x, we get x = 1.
Substituting x = 1 into either of the original equations, we find y = 4(1) + 1 = 5. Therefore, the point of intersection is (1, 5).
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A theater wants to build movable steps that they can use to go on and off the stage. The dimesions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props. How much space is inside the steps?
Answer:
The total volume of the space inside the steps is 2880 cubic inches.
Step-by-step explanation:
Given : A theater wants to build movable steps that they can use to go on and off the stage. The dimensions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props.
To find : How much space is inside the steps?
Solution :
According to question,
The image form of store props is a prism split into two rectangular prism.
Refer the attached figure below.
The bottom portion of the steps having dimension [tex]16\times 20\times 6 in[/tex]
The volume of the bottom portion is
[tex]V=l\times b\times h\\V=16\times 20\times 6\\V=1920 in^3[/tex]
The top part have a width of 8 inches as entire width of bottom is 16 inches.
Length is 20 inches.
Height of the steps is 6 inches as total height is 12 inches.
The volume of the top part is
[tex]V=l\times b\times h\\V=20\times 8\times 6\\V=960 in^3[/tex]
So, the total volume of the space inside the steps is
1920+960 = 2880 cubic inches.
Therefore, The total volume of the space inside the steps is 2880 cubic inches.
The north part of the kingdom, represented by n(x)=6x^2+x−7, is being divided by a(x)=2x+3.
Use long division to divide n(x) by a(x).
What is the quotient?
Enter your answer as an expression, using ^ to indicate exponents, if necessary.
For example, if your answer is 42x^2+53x+64, enter it like this: 42x^2+53x+64
Answer:
The correct answer is,
The quotient is 3x - 4
Step-by-step explanation:
It is given that,
n(x) = 6x^2 + x − 7
a(x) = 2x + 3
To find n(x) by a(x)
n(x) = 6x^2 + x − 7
a(x) = 2x + 3
n(x) by a(x). can be written as,
3x - 4
2x + 3 ) 6x^2 + x − 7
6x^2 + 9x
-8x - 7
-8x - 12
5
Therefore quotient = 3x - 4