Answer:
[tex] \displaystyle y _{ \text{parallel}} = \frac{5}{6} x- 2[/tex]
Step-by-step explanation:
we are given a equation of line
[tex] \displaystyle y = \frac{5}{6} x - 10[/tex]
we want to figure out the line Parallel to the given line and passes through (12,8)
to figure out the parallel line we need to figure out two things one is the Slope of the parallel line another is the y-intercept of the parallel line
figuring out the slope of the parallel line is easy because we know that parallel lines have the same slope therefore,
[tex] \displaystyle m _{ \text{parallel}} = \frac{5}{6} [/tex]
now we need to figure out the y-intercept and the equation to do so we can consider the following formula:
[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]
we the point where the parallel line passes i.e [tex](x_1,y_1)=(12,8)[/tex] and we already got that the slope is ⅚ thus substitute:
[tex] \displaystyle y - 8= \frac{5}{6} (x- 12)[/tex]
we can figure out the equation by simplifying the above equation to slope-intercept form in order to do so
distribute:
[tex] \displaystyle y - 8= \frac{5}{6} x- \frac{5}{6} \times 12[/tex]
reduce fraction:
[tex] \displaystyle y - 8= \frac{5}{6} x- 5 \times 2[/tex]
simplify multiplication:
[tex] \displaystyle y - 8= \frac{5}{6} x- 10[/tex]
add 8 to both sides:
[tex] \displaystyle y = \frac{5}{6} x- 2[/tex]
and we are done!
emma is planning a surprise party. she is considering.......
Answer:
Step-by-step explanation:
what is she considering? I would need more information to complete the probolem
Answer:
Nothing...
Step-by-step explanation: Do you have choices, because if you do, please edit your question so I could help you :)
a flying object's height in the sky can be represented by the equation d= 30+vt+[tex]4t^2\\[/tex] where d is the height in feet, v is the velocity in feet per second, and t is the time in seconds. how long has the flying object been traveling if it has a velocity of 8 feet per second and has risen to a height of 126 ft?
a). 4 seconds
b). 6 seconds
c). 8 seconds
d). 16 seconds
Answer:
t=4 seconds
Step-by-step explanation:
The equation given to us is
d=30 + vt + 4t²
d=126 feet
v= 8 ft per second
to find t =?
Now putting the values in the above equation gives
126 = 30 + 8t + 4t²
126 - 30 = 8t + 4t²
96 = 8t + 4t²
Dividing the whole equation by 4
[tex]\frac{96}{4}=\frac{8t}{4}+\frac{4t^{2} }{4}[/tex]
it will become
24 = 2t + t²
taking 24 to other sides of equality
0 = 2t + t² -24
t²+2t-24=0
Now we will do mid term breaking of the eqaution
t²+6t-4t-24=0
taking common from the equation
t(t+6)-4(t+6)=0
(t+6)(t-4)=0
so it becomes
t+6 = 0 or t-4 =0
t =-6 or t = 4 seconds
as time can not be negative
so t=4 seconds
Given: ∆AKL, AK = 9 m∠K = 90° m∠A = 60° Find: P∆AKL The area of ∆AKL
The perimeter (P∆AKL) of triangle AKL is 21.294 m, and the area is 20.25 m². Triangle AKL is a 30-60-90 triangle, with sides in the ratio 1:√3:2, allowing for straightforward calculations of the perimeter and area using the given side lengths and right triangle properties.
Explanation:To find the perimeter (P∆AKL) and the area of triangle AKL (∆AKL), we can use the properties of a right triangle. Since we have one angle of 60°, and the right angle 90°, the remaining angle must be 30°. With this information, we recognize that triangle AKL is a 30-60-90 special right triangle.
For a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. Knowing one side, AK (the side opposite the 60° angle), is 9 m, we determine the side opposite the 30° angle (AL) is half that length, so AL = 9m / 2 = 4.5 m. The side opposite the 90° angle (KL) is √3 times the side opposite the 30° angle, so KL = 4.5m * √3 = 7.794 m.
Now we can find the perimeter (P) by adding all the sides:
AK + AL + KL = 9m + 4.5m + 7.794m = 21.294 mThe area (A) of a right triangle is (½)*base*height.
A = (½) * AK * AL = (½) * 9m * 4.5m = 20.25 m²A traveling circus brings along everything it needs for its shows in big trucks.
a. the circus audience sits in rows around the performing ring. there are 9 seats in each row. how many rows will need to be set up if 513 people are expected to attend the show? can the rows be divided into a number of equal sections? explain how you find your answer.
b. circus horses eat about 250 pounds of horse food per week. about how many pounds of food does a circus horse eat each day? explain. (hint: 1 week = 7 days)
Answer :
(a) The number of rows need will be, 57 rows.
(b) The amount in pounds of food a circus horse eat each day is, 35.71 pounds.
Step-by-step explanation :
Part A:
As we are given that the there are 9 seats in each row that means 9 people can sit in each row.
Now we have to determine the number of rows will need to be set up if 513 people are expected to attend the show.
As, 9 people can sit in 1 row
So, 513 people can sit in [tex]\frac{513}{9}=57[/tex] row
Thus, the number of rows need will be, 57 rows.
Yes, the rows be divided into a number of equal sections as, 3 rows would be 19 sections or, 19 rows would be 3 sections.
Part B:
As we are given that circus horses eat about 250 pounds of horse food per week. Now we have to determine the amount in pounds of food does a circus horse eat each day.
Given : 1 week = 7 days
As, in 1 week the circus horses eat about 250 pounds of horse food
or, in 7 days the circus horses eat about 250 pounds of horse food
So, in 1 day the circus horses eat about [tex]\frac{1day}{7day}{\times 250=35.71[/tex] pounds of horse food
Thus, the amount in pounds of food a circus horse eat each day is, 35.71 pounds.
Huilan is 9 years older than Thomas. The sum of their ages is 53 . What is Thomas's age?
Answer:
The answer is 43. Hope this helps!!!!!
Step-by-step explanation:
Answer:
The correct answer is that Thomas's age is 44.
Step-by-step explanation:
If the sum of their ages is 53 and Huilan is 9 years older all we have to do is subtract 9 from 53, which equals 44.
Hope this helps,
Davinia.
50 POINTS!!!!!!!!!
The base (b) of the triangle is _ units.
A) 3 B) 5 C) 8 D) 13
The height (h) of the triangle is units.
A) 3 B) 5 C) 8 D) 13
The area of the triangle is square units.
A) 5 B) 7.5 C) 15 D) 30
I WILL KNOW IF YOU ARE WRONG!!!!!!!
Answer: the base is: 3 units
The height is: 5 units
The area is: 7.5 units
Step-by-step explanation: I just answered this question ❤️
The base of triangle is, 3 units
The height of triangle is, 5 units
And, The area of triangle is, 7.5 units²
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in image.
Now, We get by graph of triangle;
The base of triangle is, 3 units
The height of triangle is, 5 units
We know that;
⇒ Area of triangle = 1/2 × base × height
⇒ Area of triangle = 1/2 × 3 × 5
⇒ Area of triangle = 7.5 units²
Thus, The base of triangle is, 3 units
The height of triangle is, 5 units
And, The area of triangle is, 7.5 units²
Learn more about the triangle visit;
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There are 6,000 products at the store in one hour, 425 products are sold how products are left
Answer:
5575
Step-by-step explanation:
its just subtraction you take the 6000 and subtract 425 and thats how you get whats left they try to trick you using the time im guessing correct me if im wrong
Find the tan(Θ) of an angle in standard position if the terminal side passes through the point (4, -8).
See the attached explanation and diagram.
Tricia made a 56% on her science test. If she got 14 problems correct, how many questions were on the test?
Answer:
25
Step-by-step explanation:
let x questions on the text, so we get:
56/100=14/x, 4/100=1/x,
x=25
When you roll a standard number cube once, what is the probability of rolling a number divisible by 3?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
On a standard cube there are the numbers 1, 2, 3, 4, 5, 6
Only 2 are divisible by 3, that is 3 and 6, hence
P(divisible by 3 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
This table can be used to organize Raj’s credit card balances and payments over 6 months. The annual percentage rate on the card is 18%.
Raj’s Credit Card Payments
(Month) (Balance) (Payment) (Interest Rate) (Interest Charged)
1 $500 $100 0.015 $6.00
2 - $50 0.015 -
3 - $50 0.015 -
4 - $50 0.015 -
5 - $50 0.015 -
6 - $50 0.015 -
What is the amount of total interest charged for the first 6 months?
Answer: 25.90
Step-by-step explanation:
Edge
The total interest charged for the first 6 months is $36.00.
Explanation:The total interest charged for the first 6 months can be calculated by adding up the interest charged for each month. From the table, we can see that the interest charged for each month is $6.00. Since there are 6 months, we can calculate the total interest charged as follows:
Total Interest Charged = Interest Charged per Month x Number of Months
Total Interest Charged = $6.00 x 6
Total Interest Charged = $36.00
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The swimsuit is on sale for 25% off its original price. If the original price was $58. What is the sale price?
Compare the volume of a square pyramid to the volume of a square prism with the same base and height as the pyramid.
Answer:
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
Step-by-step explanation:
The volume of a square pyramid is given by the formula
V = 1/3 s^2 h
where s is the side length of the base
The volume of a square prism given by the formula
V = s^2 h
where s is the side length of the base
So dividing the two, taking the pyramid on top
1/3 s^2 h
---------------------
s^2 h
If the bases are the same, then the side lengths are the same and we know the heights are the same. We will cancel them from the top and the bottom.
1/3
---------------------
1
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
Step-by-step explanation:
The volume of a square pyramid is given by the formula
V = 1/3 s^2 h
where s is the side length of the base
The volume of a square prism given by the formula
V = s^2 h
where s is the side length of the base
So dividing the two, taking the pyramid on top
1/3 s^2 h
---------------------
s^2 h
If the bases are the same, then the side lengths are the same and we know the heights are the same. We will cancel them from the top and the bottom.
1/3
---------------------
1
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
What is the probability of spinning a 2 on a spinner that has 8 equal sides numbered 1-8 and rolling a 3 on a die
Answer:
1/48
Step-by-step explanation:
To find the probability of 2 independent events, we multiply their probabilities together.
Probability of getting a 2 on the spinner, 1 of 8 spots
1/8 =
Probability of getting a 3 on the die, 1 of 6
1/6 =
Multiply these probabilities together
1/8 * 1/6 = 1/48
63÷10 63÷10^2 63÷10^3. Please answer these equation and type the answer in the space below in the comment section THX and have a awesome day:)
A tiger can eat food that weighs up to 15% of its body weight if a tiger can I eat 75 lb of food how much does a Tiger Way
How would you name line segment AH?
Answer:
last one
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
At a county fair, 9 people out of 1,000 earned a perfect score in a carnival game. What decimal represents the number of people who earned a perfect score?
Answer:
Decimal represents the number of people who earned a perfect score is 0.009 .
Step-by-step explanation:
As given
At a county fair, 9 people out of 1,000 earned a perfect score in a carnival game.
[tex]Number\ of\ people\ who\ earned\ a\ perfect\ score = \frac{People\ who\ earned\ perfect\ score}{Total\ number\ people}[/tex]
people who earned a perfect score = 9
Total number of people = 1000
Put in the above
[tex]Number\ of\ people\ who\ earned\ a\ perfect\ score = \frac{9}{1000}[/tex]
Number of people who earned a perfect score = 0.009
Therefore decimal represents the number of people who earned a perfect score is 0.009 .
To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.
Select one answer.
If we let μ1, μ 2, and μ 3 be the mean verbal reasoning scores for students who attended secondary school, vocational school, and primary school only, respectively, the appropriate hypotheses in this case are:
a. H0: μ1 = μ2 = μ3
Ha: μ1, μ2, μ3, are not all equal
b. H0: μ1, μ2, μ3, are not all equal
Ha: μ1 = μ2 = μ3
c. H0: μ1 = μ2 = μ3
Ha: μ1 μ μ2 μ μ3
d. H0: μ1 μ μ2 μ μ3
Ha: μ1 = μ2 = μ3
e. None of the above are correct.
The correct hypotheses are:
b. [tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) and \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
To determine the appropriate hypotheses for testing the relationship between the type of school attended and verbal reasoning scores for Irish students, we first need to understand the nature of the comparison being made.
We have three groups of students: those who attended secondary school, vocational school, and primary school only. We want to investigate if there is a difference in the mean verbal reasoning scores among these groups.
The null hypothesis [tex](\(H_0\)) states that there is no difference in the mean verbal reasoning scores among the three types of schools, expressed as \( \mu_1 = \mu_2 = \mu_3 \), where \( \mu_1 \), \( \mu_2 \), and \( \mu_3 \)[/tex] are the population means for students attending secondary school, vocational school, and primary school only, respectively.
The alternative hypothesis [tex](\(H_a\)) suggests that at least one of the population means is different from the others, expressed as \( \mu_1, \mu_2, \mu_3 \)[/tex] are not all equal.
Option b correctly represents these hypotheses:
[tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
This formulation allows for the testing of differences in mean verbal reasoning scores across the three types of schools. The null hypothesis assumes equality among the means, while the alternative hypothesis considers the possibility of inequality.
Anthony has 18 stickers.He wants to give 3 to each of his friends.How many friends can he give stickers to?
Thirty-six of the students in the school choir like to sing solos. These 36 students make up 24% of the choir. How many students are in the choir?
Answer:
150
Step-by-step explanation:
We can write a proportion to find the total amount in the choir using the information given. A proportion is two equivalent ratios set equal to each other.
[tex]\frac{24}{100}=\frac{36}{y}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
24y=100(36)
24y=3600
y=150.
There are 150 students in the choir.
HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4
Answer:
S22 for the arithmetic sequence is:
First option: 15.4
Step-by-step explanation:
a12=2.4
d=3.4
S22=?
Sn=(a1+an)n/2
n=22
S22=(a1+a22)22/2
S22=(a1+a22)11
ak=aj+(k-j)d
a12=a1+(12-1)d
2.4=a1+11(3.4)
2.4=a1+37.4
Solving for a1: Subtracting 37.4 both sides of the equation:
2.4-37.4=a1+37.4-37.4
Subtracting:
-35=a1
a1=-35
a22=a12+(22-12)d
a22=2.4+10(3.4)
a22=2.4+34
a22=36.4
S22=(a1+a22)11
S22=(-35+36.4)11
S22=(1.4)11
S22=15.4
A total of 56 students signed up to play in a flag football league. If each team has 10 students, how many more students will need to sign up so all of the students can be on a team?
Final answer:
A total of 4 more students need to sign up for all 56 students to be placed on teams of 10 in the flag football league.
Explanation:
The question is asking how many additional students will need to sign up to ensure that all students can participate in a flag football league, with the stipulation that each team is made up of 10 students. With 56 students currently signed up, we can divide this number by the team size to see how many complete teams can be formed:
56 students ÷ 10 students per team = 5 teams with 6 students left over.
To have a complete additional team, 10 students are needed. Since there are already 6 students without a team, the number of additional students required is:
10 students needed for a complete team - 6 students already signed up but not placed on a team = 4 additional students needed.
Write an explicit formula for the sequence... then find a17
Answer:
The correct answer option is: [tex]a_n=\frac{5}{2} n-\frac{11}{2}, 37[/tex].
Step-by-step explanation:
We are given the following arithmetic sequence and we are to write an explicit formula for it and the find the 17th term of the sequence:
{[tex]a_n[/tex]}={[tex]-3, -\frac{1}{2} ,2,\frac{9}{2} ,7[/tex]}
From the given options, we can put in the values of n and check if it proves to be true.
For [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex], put values of [tex]n[/tex] from 1 to 5 which the number of the term.
[tex]a_1=\frac{5}{2} (1)-\frac{11}{2}\\\\a_1=-3[/tex]
[tex]a_2=\frac{5}{2} (2)-\frac{11}{2}\\\\a_2=-\frac{1}{2}[/tex]
[tex]a_3=\frac{5}{2} (3)-\frac{11}{2}\\\\a_3=2[/tex]
[tex]a_4=\frac{5}{2} (4)-\frac{11}{2}\\\\a_4=\frac{9}{2}[/tex]
[tex]a_5=\frac{5}{2} (5)-\frac{11}{2}\\\\a_5=7[/tex]
Therefore, the formula for the given sequence is [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex].
Also, [tex]a_{17}=\frac{5}{2} (17)-\frac{11}{2}=37[/tex]
Answer: The correct one is an=5/2n-11/2,37 so A :)
Can someone please take some time to help me? I would really appreciate it. Thank you very much.
Adia plans to wallpaper her bedroom. The measurements are 10’ by 12’ with 8’ ceilings.
Part 2: If each single roll of wallpaper covers 72 square feet, how many single rolls of wallpaper will Adia need for her project?
Answer: _ single rolls (type the number only)
-------------------------------------------------------------------------------------
Adia plans to wallpaper her bedroom. The measurements are 10’ by 12’ with 8’ ceilings.
Part 3: If each single roll of wallpaper covers 72 square feet, how many double rolls of wallpaper will Adia need for her project?
Answer: _ double rolls (type the number only)
Answer:
5 single rolls or 3 double rolls.
Step-by-step explanation:
Ignoring doors and windows, we need to find the lateral surface ares. We are not papering the ceiling or floor.
The lateral surface areas = P*h
= 2(l+w) * h
= 2(10+12) * 8
= 2(22)*8
=352 ft^2
A single roll covers 72 ft^2 so we divide the number of ft^2 that we need (352^2) by the amount of a single roll
352/72 =4.88888(repeating)
Rounding up since we need to buy in full rolls.
We will need 5 rolls
Assuming a double roll will cover twice that of a single roll
2*72 = 144 ft^2
Take 572/144 =2.4444444
Rounding up since we need to buy in full rolls.
We will need to buy 3 double rolls
Adia will need 5 single rolls or 3 double rolls of wallpaper to cover her 10' by 12' bedroom with 8' ceilings.
Adia needs to calculate the amount of wallpaper needed to cover the walls of her bedroom. To find the total wall area, we calculate the perimeter of the room and multiply it by the ceiling height. The perimeter is two times the length (12 feet) plus two times the width (10 feet), giving us 44 feet. Multiplying the perimeter by the ceiling height (8 feet) gives us the total wall area: 44 feet × 8 feet = 352 square feet.
Since each single roll covers 72 square feet, dividing the total wall area by the coverage of one roll gives us the number of rolls needed: 352 square feet / 72 square feet/roll = 4.89, which means Adia will need 5 single rolls of wallpaper.
For double rolls, we need to consider that each double roll is equivalent to two single rolls.
Therefore, we divide the number of single rolls needed by 2 to get the number of double rolls: 5 single rolls / 2 = 2.5, which means Adia will need 3 double rolls (since she can't purchase half a roll, she'll have to round up).
bobby’s christmas list had 3 more than twice as many items on it than johnny’s list. johnny asked for 8 fewer items than bobby. how many items were on johnny’s (x) and bobby’s (y) christmas lists?
Answer:
Johnny had 5 items and Bobby had 13 items.
Step-by-step explanation:
Let us assume that Johnny has x items and Bobby has y items in their list.
Bobby had 3 more than twice as many items on it than Johnny. So,
[tex]\Rightarrow y=3+2x[/tex] ----------1
Johnny asked for 8 fewer items than bobby. So,
[tex]\Rightarrow y-8=x[/tex] -----------2
Putting the value of x from equation 2 in equation 1, we get
[tex]\Rightarrow y=3+2(y-8)[/tex]
[tex]\Rightarrow y=3+2y-16[/tex]
[tex]\Rightarrow 2y-y=16-3[/tex]
[tex]\Rightarrow y=13[/tex]
Putting the value of y in equation 2,
[tex]\Rightarrow 13-8=x[/tex]
[tex]\Rightarrow x=5[/tex]
So, Johnny had 5 items and Bobby had 13 items.
A market buys mixed nuts at $15 per pound.They want to make a 20% profit. What would you pay for 1 pound of nuts
Answer:
Step-by-step explanation:
100% = $15
20% = 1.2*15 = $18
Quick check
A jet ski company charges a flat fee of $26 plus $3.25 per hour to rent a jet ski another company charges a fee of $24 plus $3.50 per hour to rent the same jet ski find number of hours for which the cost are the same round your number to the nearest whole hour
Answer: 8 hours
Step-by-step explanation:
Company 1: 3.25x + 26
Company 2: 3.50x + 24
3.50x + 24 = 3.25x + 26
0.25x +24 = 26 subtracted 3.25x from both sides
0.25x = 2 subtracted 24 from both sides
x = 8 divided both sides by 0.25
Check:
Company 1: 3.25x + 26 = 3.25(8) + 26 = $52
Company 2: 3.50x + 24 = 3.50(8) + 24 = $52
Calculate the sum of the infinite series
Answer:
[tex]\frac{40}{3}[/tex]
Step-by-step explanation:
Here a= 20, r = -1/2
Here, the absolute value of r is 1/2 which is less than 1. So, the series converges.
The sum of an infinite geometric series is given by
S = [tex]\frac{a}{1-r}[/tex]
Substituting the values in the above equation, we have
[tex]S = \frac{20}{1-(-1/2)} =\frac{20}{3/2} =\frac{40}{3}[/tex]
∴ The sum of the given infinite series is 40/3
Answer:
A. 40/3 hope thats helpful
Identify the domain of the graphed function.
Answer:
(-4,-2) U (-2,4]
Step-by-step explanation:
Domain is the set of x values for which the function is defined.
We look at the x values on the graph
the graph starts at -4 and we have a hole at x=-4
For a hole we use parenthesis
Graph starts at -4 and ends at -2. Both -4 and -2 have hole, so we use parenthesis.
So interval is (-4,-2)
From -2 to 4 , there is no hole or break in between. the graph is continuous from -2 to 4
so interval is (-2, 4]
combine both intervals
(-4,-2) U (-2,4]
Answer:
B. (-4,-2) (-2,4)