Final answer:
The rate of speed for the slower boy is 3 km/h, while the rate of speed for the faster boy is 6 km/h.
Explanation:
The rate of speed for each of the two boys can be determined by using the formula:
Rate of speed = Distance / Time
Let's assume the rate of speed of the slower boy is 'x' km/h. Therefore, the rate of speed of the faster boy is '2x' km/h, as mentioned in the question.
For the slower boy: Distance = Speed * Time. Therefore, 3x = x * 3. Solving this equation, we get x = 0 which indicates that the slower boy is not moving.
For the faster boy: Distance = Speed * Time. Therefore, 3 * 2x = 6x.
According to the question, the total distance covered by both boys is 27 km in 3 hours. So, 6x + 3 * 2x = 27. Solving this equation, we get x = 3.
Therefore, the rate of speed for the slower boy is 3 km/h and the rate of speed for the faster boy is 6 km/h.
Two adjacent angles form a complementary relationship. One angle is twelve more than twice the other angle. Draw a picture to represent the situation. Then solve for each unknown angle measure.
Answer:
The angles are 26 and 64
Step-by-step explanation:
When two angles are complementary, what this means is that the add up to 90 degrees
Now, let’s say one of the angles is x, the other angle is 12 more than twice it; mathematically that would be 2x + 12
Since they add up to be 90, we have
x + 2x + 12 = 90
3x + 12 = 90
3x = 90-12
3x = 78
x = 78/3
x = 26
The other angle is 2x + 12 = 2(26) + 12 = 52 + 12 = 64
Two adjacent angles form a complementary relationship. One angle is twelve more than twice the other angle than the value of that two complementary angles are [tex]26^\circ[/tex] and [tex]64^\circ[/tex].
Given :
Two adjacent angles form a complementary relationship.One angle is twelve more than twice the other angle.The sum of two complementary angles is [tex]90^\circ[/tex]. Let one of the complementary angles be 'a' then the other complementary angle is (12 + 2a) according to the given data.
The mathematical expression of the sum of complimentary angles is:
a + (2a + 12) = [tex]90^\circ[/tex]
Now, open the parenthesis and further simplify the above ex[pression.
3a + 12 = 90
Subtract both sides by 12 in the above expression.
3a + 12 - 12 = 90 - 12
3a = 78
Now, divide both sides by 3 in the above expression.
a = [tex]26^\circ[/tex]
Now, the other complementary angle is (2(26) + 12 = [tex]64^\circ[/tex]).
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Challenger Elementary School has 800800 800 800 students. Every Wednesday, 12%12\% 12% 12, percent of the students stay after school for Chess Club. How many students attend Chess Club on Wednesdays?
Answer: 96 students
Step-by-step explanation:
Number of students in the school= 800
Percentage of students that stays after school for Chess = 12%
To get the number of students that attend Chess Club on Wednesdays, we multiply the percentage given by 800. This can be written as:
= 12% of 800
= 12/100 × 800
= 12 × 8
= 96 students
96 students attend Chess Club on Wednesdays.
Answer:
Step-by-step explanation:
We know that the entire school
(
100
%
)
(100%)left parenthesis, 100, percent, right parenthesis has
800
800800 students. We need to find out how many students are in Chess Club, which is
12
%
12%12, percent of the school.
Hint #2
We can first divide
800
800800 by
100
100100 to see that
8
88 students make up
1
%
1%1, percent of the school, then multiply by
12
1212 to see how many students make up
12
%
12%12, percent.
12
%
of the students
=
12
⋅
1
%
of the students
=
12
⋅
8
students
=
96
students
12%of the students
=12⋅1%of the students
=12⋅8students
=96students
Hint #3
96
9696 students attend Chess Club on Wednesdays.
the dimension of a rectangle piece of paper are 8.5 and 11 inches.veronicafolded the piece of paper along its diagonal.which measurement is closest to the lenght of the diagonal is inches?
Answer:
13.90 inches
Step-by-step explanation:
The sides of rectangle are 8.5 and 11 inches.
According to question diagonal needs to calculated.
The diagonal , and two sides of rectangle will forma a right angled triangle.
Right angle as it constitute a right angle of rectangle as well.
To understand more
construct a rectangle ABCD
then one of its diagonal will be AC if we take triangle ABC.
angle ABC will be right angled at B.
for triangle ABC . diagonal AC will be hypotenuse
So diagonal can be computed using Pythagoras theorem
which states that if a and b are two sides of right angled triangle containing the right angle then hypotenuse is given by [tex]\sqrt{a^2+b^2}[/tex].
____________________________________________
In the problem
two sides are of length 8.5 and 11 inches
So, diagonal is hypotenuse which can be calculated by [tex]\sqrt{8.5^2+11^2}\\=>\sqrt{72.25+121}\\=>\sqrt{193.25}\\=>13.90[/tex]
thus length of diagonal is 13.90 inches.
plz help will mark brainlest
Answer:
81pi meter squared
Answer:
81π m²
Step-by-step explanation:
Formula: C=2πr
The circumference of the column is 18π meters so therefore: 18π=2πr
Divide the both sides by 2π:
r= 9 meters
Now find the area:
Formula for Area: A=πr²
Therefore: A= π · 9² = 81π meters²
Which equation has x = 4 as the solution? log Subscript 4 Baseline (3 x + 4) = 2 log Subscript 3 Baseline (2 x minus 5) = 2 log Subscript x Baseline 64 = 4 log Subscript x Baseline 16 = 4
Answer:
A. log Subscript 4 Baseline (3 x + 4) = 2
Step-by-step explanation:
I graphed it.
The equation [tex]\log_4(3x + 4) = 2[/tex] has a solution of x = 4
What is an equation?An equation is an algebraic expression that is represented by the equality "=" sign
For an equation to have a solution of x = 4, the equation must be true at x = 4
From the options, we have:
[tex]\log_4(3x + 4) = 2[/tex]
Substitute 4 for x
[tex]\log_4(3*4 + 4) = 2[/tex]
[tex]\log_4(16) = 2[/tex]
Express 16 as 4^2
[tex]\log_4(4^2) = 2[/tex]
Apply the law of logarithm
[tex]2\log_4(4) = 2[/tex]
Apply the law of logarithm
[tex]2*1 = 2[/tex]
[tex]2= 2[/tex]
The value of x = 4 is true for [tex]\log_4(3x + 4) = 2[/tex].
Hence, the equation [tex]\log_4(3x + 4) = 2[/tex] has a solution of x = 4
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I need to know this plz and thank u
What is -5d+(-6)u-3?
Answer:-5d-6u-3
Step-by-step explanation:
-5d+(-6)u-3
-5d-6u-3
The data below represents the number of customers at each Slurpee Sam's Spaghetti Shop. 24, 25, 29, 30, 31, 31, 32, 34, 34. Which box plot correctly summarizes the data?
Answer:
A summary of the data is as follows;
1. Maximum = 34
2. Minimum = 24
3. The 1st quartile is 27
4. The median is or the 2nd quartile 34
5. The 3rd quartile is 33
The data is summarized in the attached box plot
Step-by-step explanation:
24, 25, 29, 30, 31, 31, 32, 34, 34
From the given data, we have the five values of a box and whisker plot as follows;
1. Maximum = 34
2. Minimum = 24
3. The 1st quartile is the [tex]\frac{9 + 1}{4} th[/tex] term or 27
4. The median (2nd quartile) is the [tex]\frac{9 + 1}{2} th[/tex] term or 34
5. The 3rd quartile is the [tex]\frac{3(9 + 1)}{4} th[/tex] term or 33
Hence the attached box plot summarizes the data.
Answer: C
Step-by-step explanation:
Surface area of a triangular prism
Answer:
96
Step-by-step explanation:
Answer: You need to use the formula to solve this equation
step-by-step explanation:
Area of a triangle= A = 1/2bh
Area of a rectangle= A = lw
Surface area of triangular prism= SA = bh + (s1 + s2 + s3)H
Use that formula to solve the problem.
I hope this helps
If you need more add my s n a p (i'll put it in the comments section) and send a picture of your work and i'll helpCould you please answer this question?
Only answer question 26
The answers are: x = 5 y = -2
Please use the elimination method to answer this question
Answer:
.
Step-by-step explanation:
3x - y = 17 .......A
10 × [x/5 + y/2] = 10 × 0
2x + 5y = 0 .......B
......A× 5 both 2 sides of equation
15x - 5y = 85 .....C
......B + ........C
2x + 15x = 0 + 85
17x = 85
x = 85/17
x = 5
put x value in ........A or .......B or ......C
you will receive y = -2
Which number is irrational?
Answer:
D. 4.12
Step-by-step explanation:
A irrational number can be a decimal, but can never be a fraction.
Find the measure of an angle between 0 and 360 that is coterminal with an angle measuring -800
Answer
280
Step-by-step explanation:
Answer:
280 then 80
Step-by-step explanation:
right on edg2020
Given kite MNOP below, which of the following conjectures, concerning the diagonals of a kite, is most likely true?
(graph attached)
A. The diagonals of a kite bisect the angles.
B. The diagonals of a kite are perpendicular.
C. The diagonals of a kite are perpendicular bisectors of each other.
D. The diagonals of a kite form four congruent triangles.
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
b
Which expression is equivalent to y•y•y•z•z•z•z?
Twelve of the 20 students in Ms. Sarno’s homeroom are female. Each month, Ms. Sarno randomly selects a student to act as “teacher’s helper.”
Which simulation best models the selection of female “teacher’s helpers” for January, February, March, and April?
A spinner, divided into 5 congruent sectors with three of the sectors representing female students, is spun 12 times.
A coin, with heads up representing female students, is flipped 4 times.
A bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement.
A number cube, with odd numbers representing female students, is rolled 12 times.
Answer:
the answerr is C
Step-by-step explanation:
A sumo wrestling ring is circular and has a circumference of 4.6\pi \text{ meters}4.6π meters4, point, 6, pi, start text, space, m, e, t, e, r, s, end text. What is the area AAA of the sumo wrestling ring in square meters? Give your answer in terms of \piπpi.
Answer:
The area of the wrestling ring is 5.29π [tex]m^2[/tex]
Step-by-step explanation:
A sumo wrestling ring is circular and has a circumference of 4.6π meters.
To find its area, we need to first find its radius.
The circumference of a circle is given as:
[tex]C = 2 \pi r[/tex]
where r = radius
Hence, the radius of the ring will be:
[tex]4.6\pi = 2\pi r\\r = 4.6 /2 = 2.3m[/tex]
The radius of the ring is 2.3 m.
The area of a circle is given as:
[tex]A = \pi r^2[/tex]
Hence, the area of the wrestling ring (in terms of π) will be:
[tex]A = \pi * 2.3^2[/tex]
[tex]A = 5.29\pi[/tex] [tex]m^2[/tex]
The area of the wrestling ring is 5.29π [tex]m^2[/tex]
A store sells 5 T-shirts for $46.45. What is the unit cost per T-shirt?
Answer:$9.29
Step-by-step explanation:For unit rate finding the value of one is the objective. Easiest way to find it is by dividing the value (the amount of money being payed) by the amount beig sold ( the 5 shirts) so basically $46.45 ÷ 5
Answer:
9.25
Step-by-step explanation:
Pleeeaase can u helppp meee thanks will mark brainliest!!
Answer:
140 cubic cm
Step-by-step explanation:
v=1/3 bh
b=1/2(3) (5) (4)=60
b=1/2(60)=30
v=1/3(60)7=420
420/3=140
hope this helps
A basketball player made 63 out 100 attempted free throws.What percent of free throws did the player mark?
Answer:
63%
Step-by-step explanation:
Answer:
63% of the free throws.
Step-by-step explanation:
It is out of 100% so any percent from 100 is just the number in this case it would be 63 Free throws.
IF U SMART I WANNA SEE U ANSWER THIS Q! 11ponits?
Answer is 1.6 pounds
.02 is not big enough to round up, so round down
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is and the equation will have .
Tomas brought $32.00 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 4 as much as the sketchbook, and the sketchbook cost 2 3 the cost of the paint set. Tomas had $4.50 left over after buying these items.
Answer:
The price of the sketchbook is $10, the price of the brush is $2.5 and the price of the paint set is $15.
Step-by-step explanation:
Let the price of the brush be b.
Let the price of the sketchbook be s.
Let the price of the paint set be p.
The brush was 1/4 as much as the sketchbook. This means that:
b = 1/4 * s = s/4_______________(1)
The sketchbook was 2/3 the cost of the paint set. This means that:
s = 2/3 * p
=> p = 3s/2 __________________(2)
Initially, he had $32.00 and after buying all the items, he had $4.50 left with him. This means that:
b + s + p + 4.50 = 32.00 ___________(3)
Put (1) and (2) in (3):
=> s/4 + s + 3s/2 + 4.50 = 32.00
Collect like terms and simplify:
11s/4 = 32.00 - 4.50 = 27.5
=> s = (27.5 * 4) / 11
s = $10
Put this back in (1) and (2):
b = 10 / 4 = $2.5
and
p = (3 * 10) / 2 = $15
The price of the sketchbook is $10, the price of the brush is $2.5 and the price of the paint set is $15.
Answer:
I want to delete my answer because the one already answered is correct.
10x + 9y = -17
10x – 2y = 16
what is the solution
Answer:
x = 1 and y = -3
Step-by-step explanation:
Subtract eqn 1 from eqn 2
11y = - 33
y = -3
Substituting y into eqn 2...
10x - 2(-3) = 16
10x +6 = 16
10x = 10
x = 1
The solution to the system of equations 10x + 9y = -17 and 10x - 2y = 16 is x = 1 and y = -3. This solution was found using the elimination method, which involved manipulating the equations to eliminate one variable and then solving for the other.
Explanation:The question is related to the system of linear equations. A set of linear equations with the same variables is known as a system of equations. Here we have two equations; 10x + 9y = -17 and 10x - 2y = 16. The solution to this system of equations is the ordered pair (x, y) that satisfies both equations. We can find this by using the method of substitution or elimination.
Here's the solution using the elimination method:
First multiply the second equation by 9 and the first one by 2.You will get:So, the solution for the system of equations is x = 1 and y = -3.
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Evaluate
17.3
% of
45.94
km
Give your answer rounded to 2 DP.
Answer: 17.3% of 45.94 km is 7.95 km
Final answer:
To find 17.3% of 45.94 km, convert the percentage to a decimal and multiply by the value in kilometers. The calculation gives you 7.94742 km, which rounded to two decimal places is 7.95 km.
Explanation:
To evaluate 17.3% of 45.94 km, you need to convert the percentage to a decimal by dividing by 100 and then multiply by the value in kilometers.
Convert the percentage to a decimal: 17.3% ÷ 100 = 0.173.
Multiply the decimal by the value in kilometers: 0.173 × 45.94 km.
Perform the multiplication to find the answer.
0.173 × 45.94 km = 7.94742 km.
Now, round the answer to two decimal places:
7.94742 km rounded to two decimal places is 7.95 km.
Find the sum of the first 7 terms of the following series, to the nearest integer.
15,3, 3/5
Answer:
19
Step-by-step explanation:
This is a geometric series.
15, 3, (3/5), ...
common ratio r = 3/15 = (1/5)
a_1 = 15
Formula for nth term: a_n = a_1 * r^(n-1)
a_n = 15 *(1/5)^(n - 1)
We want the sum of the first 7 terms.
S = a_1 * ( r^n - 1) / (r - 1)
here let n = 7
S = 15 * ( (1/5)^7 - 1 ) / ( (1/5) - 1)
S = 15 * ( (1/5)^7 - 1) / (-4/5)
S = 15 * (5/-4) * ( (1/5)^7 - 1)
S = ( -75/4 )* (-0.9999872)
S = - (-18.74976) = 18.749...
The sum is about 19
The sum of the first 7 terms of the following series is 18.74.
What is a geometric sequence?'A geometric sequence is a sequence where every term has a constant ratio to its preceding term. A geometric sequence with the first term a and the common ratio r and has a finite number of terms.'
According to the given problem,
Sequence = { 15, 3, [tex]\frac{3}{5}[/tex] }
Let the common ratio be r,
Let the first term of the sequence be a,
⇒ a × r = second term
⇒ 15 × r = 3
⇒ r = [tex]\frac{3}{15}[/tex]
⇒ r = [tex]\frac{1}{5}[/tex]
We know,
Sum of n number of terms in a geometric sequence can be represented by,
[tex]S_{n} = \frac{a(1-r^{7}) }{1-r}[/tex]
⇒ [tex]S_{7} = \frac{15(1-(\frac{1}{5})^{7} ) }{1-\frac{1}{5} }[/tex]
⇒ [tex]S_{7} = \frac{15(1-(\frac{1}{5})^{7}) }{\frac{4}{5} }[/tex]
⇒ [tex]S_{7}= \frac{5*15(1-(\frac{1}{5})^{7} ) }{4}[/tex]
⇒ [tex]S_{7}= \frac{125(0.999)}{4}[/tex]
⇒ [tex]S_{7}=\frac{74}{4}[/tex]
⇒ [tex]S_{7} = 18.74[/tex]
Hence, we can conclude, the sum of the first 7 terms of the geometric sequence is 18.74.
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Find the equation of the line described below. Write the equation in slope-intercept form, if possible, and graph the line. Contains (1,2) slope=3
Answer:
The equation of the line is y = 3x - 1
Step-by-step explanation:
In this question, we are asked to write the equation of the line using a point on the line and the slope of the line.
Mathematically, the slope-intercept form of a line can be written as;
y = mx + c
where m is the slope of the line and c is the y-intercept of the line. Now back to the question, we can see that we have all that is required for the line asides the value of the y-intercept C
To get this, we plug the values in the question into the equation of the straight line.
Here, we say y = 2, x = 1 and m = 3
2 = 3(1) + c
c = 2-3
c = -1
Thus, the equation of the line is y = 3x - 1
Solve the equation x^2-3x-10=0 by factoring
Answer:
Step-by-step explanation:
hello :
x²-3x-10=0 means : (x-5)(x+2)=0
x-5=0 or x+2=0
conclusion two solutions : 5 and -2
The solutions to the quadratic equation x² - 3x - 10 = 0 are x = 5 and x = -2.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
x² - 3x - 10 = 0
To solve the quadratic equation x² - 3x - 10 = 0 by factoring, we need to find two binomials whose product equals the quadratic equation.
x² - 3x - 10 = 0
Factor the expression x² - 3x - 10 using the AC method:
Consider a pair of integers whose product is -10 and whose sum is -3.
We use -5 and 2:
Hence:
Write the factored form using these integers:
( x - 5 )( x + 2 ) = 0
Equate each factor to zero and solve for x:
( x - 5 ) = 0
x - 5 = 0
x = 5
Also, ( x + 2 ) = 0
x + 2 = 0
x = -2
Therefore, the values of x are 5 and -2.
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you need to make p loaves of bread each loaf requires 355 grams of flour you already have 115 grams at home choose the expression you need to buy
- 3/7 divided by 3/8 equals ? write answer is simplest form.
Answer:
-1 and 1/7
Step-by-step explanation:
i dont know how to explain it sorry
Answer:
- 8/7
Step-by-step explanation:
- 3/7 divided by 3/8
- 3/7 ÷ 3/8
- 3/7 × 8/3
- 24/21 = - 8/7
Thus, - 3/7 divided by 3/8 equals - 8/7
-TheUnknownScientist
A deli that just opened was giving out free mini sandwiches. A sample of 50 likely customers was surveyed about which sandwich they preferred. The
people surveyed included 12 people who said they preferred the roast beef
Sandwich. Based on this information, how many of the first 150 sandwich
orders should the deli predict will be for roast beef?
Answer:
i think it's 36, but i'm not sure
Step-by-step explanation:
12 is 24 percent of 50, and 24 percent of 150 is 36
A ratio shows us the number of times a number contains another number. The number of people who prefer roast beef sandwiches out of 150 people is 36.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that in a sample of 50 people, 12 were the people who preferred roast beef sandwiches. Therefore, the ratio of people who prefer roast beef sandwiches to the total number of people surveyed will be,
[tex]\dfrac{\text{People who prefer roast beef sandwich}}{\text{People who were surveyed}} = \dfrac{12}{50}[/tex]
Similarly, if the ratio is applied to a group of 150 people,
[tex]\dfrac{\text{People who prefer roast beef sandwich}}{\text{People who were surveyed}} = \dfrac{12}{50}\\\\\\\dfrac{\text{People who prefer roast beef sandwich}}{\text{150}} = \dfrac{12}{50}\\\\\text{People who prefer roast beef sandwich}=36[/tex]
Hence, the number of people who prefer roast beef sandwiches out of 150 people is 36.
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