Answer:
15 students
Step-by-step explanation:
To solve this question, we can set up a system of equations.
Let's start by naming our variables.
We can call the number of students that rode in a van "x".
Then, let's name the number of students that rode a bus "y".
Knowing this, we can create two equations and then solve.
For High School A, the equation would be as follows:
12x+11y=576
For High School B, it would be:
4x+9y=384
What you have to do now, is to eliminate one of the variables.
I'm going to choose to do it with elimination, but substitution also works.
I'm going to multiply the second equation by 3, so that we can subtract the equations to eliminate the x variable.
3(4x+9y=384)
Since we're multiplying 3 to both sides, the equation will remain true.
12x+27y=1152
Now, let's subtract the other equation from this one:
12x+27y=1152
- 12x+11y=576
_____________
0x+16y=576
Our new equation is:
16y=576
Divide both sides by 16 to isolate y
y=36
This means that 36 students rode in each bus.
Let's now use this info to solve for x.
We can do this by plugging in 36 for y.
4x+9y=384
4x+9(36)=384
Simplify
4x+324=384
Subtract 324 from both sides
4x=60
Divide both sides by 4
x=15
This means that 15 students rode in each van.
As I mentioned earlier, this could have also been solved by substitution.
You would have had to isolate one variable so that one of the equations read x= something or y= something
After that, you plug that in to the other equation so you're left with only one variable.
You then simplify, and plug the value back in for the other variable.
Given the nature of this question, that would have involved working with decimals, so I chose elimination instead.
Please let me know if you have any questions!
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Here, we have given that,
The senior classes at High school A and High school B planned separated trips. The number of bus and vans rented by high school class A are 12 vans and 11 buses. The number of bus and vans rented by high school class B are 4 vans and 9 buses. The total number of students in class A are 576 students. The total number of students in class B are 384 students .Let the number of students in van be 'x' and number of students in bus be 'y' .
According to the question,
Linear equation for class A
[tex]\sf{ 12x + 11y = 576 ...eq(1)}[/tex]
Linear equation for class B
[tex]\sf{ 4x + 9y = 384 ...eq(2) }[/tex]
Subtract eq(2) from eq(1) :-
[tex]\sf{ 12x + 11y -( 4x + 9y) = 576 - 384 }[/tex]
[tex]\sf{ 12x + 11y - 4x - 9y = 192 }[/tex]
[tex]\sf{ 8x + 2y = 192 }[/tex]
[tex]\sf{ 2(4x + y) = 192 }[/tex]
[tex]\sf{ 4x + y = {\dfrac{192}{2}}}[/tex]
[tex]\sf{ 4x + y = 96}[/tex]
[tex]\bold{ y = 96 - 4x ...eq(3) }[/tex]
Subsitute eq (3) in eq(1) :-
[tex]\sf{ 12x + 11( 96 - 4x) = 576 }[/tex]
[tex]\sf{ 12x + 1056 - 44x = 576 }[/tex]
[tex]\sf{ 12x - 44x = 576 - 1056}[/tex]
[tex]\sf{ -32x = - 480 }[/tex]
[tex]\sf{ x = {\dfrac{-480}{-32}}}[/tex]
[tex]\bold{ x = 15 }[/tex]
Thus, The value of x is 15 .
Now, subsitute the value of x in eq(2) :-
[tex]\sf{ 4(15) + 9y = 384 }[/tex]
[tex]\sf{ 60 + 9y = 384 }[/tex]
[tex]\sf{ 9y = 384 - 60 }[/tex]
[tex]\sf{ 9y = 324 }[/tex]
[tex]\sf{ y = {\dfrac{324}{9}}}[/tex]
[tex]\bold{ y = 36 }[/tex]
Thus, The value of y is 36
In this question, we have taken x and y are the number of students in each van and a bus.Therefore,
The number of students in each van = 15
The number of students in each bus = 36
Hence, The number of students rode in each van are 15 .
Solve the equation by factoring. 8x^2+10x-7=0
What is the solution set?
Answer:
[tex]x = - \frac{7}{4} \: \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]8 {x}^{2} + 14x - 4x - 7 = 0 \\ 2x(4x + 7) - (4x + 7) = 0 \\ (4x + 7)(2x - 1) = 0[/tex]
Answer:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given: 8x² + 10x - 7 = 0
When factoring trinomials of the form ax² + bx + c:
multiply the leading coefficient and the last term.find the product factors that add to give you the coefficient of the middle term.rewrite the polynomial with those factors replacing the middle term.1. Split the middle term:
⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]
⇒ 14, -4 [find the product factors that add to the middle term's coefficient]
⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]
2. Factor by grouping:
⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]
⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]
⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]
⟹ (4x + 7)(2x - 1) = 0
3. Separate into 2 cases:
4x + 7 = 02x - 1 = 0
Case 1:
⇒ 4x + 7 = 0 [subtract 7 from both sides]
⇒ 4x + 7 - 7 = 0 - 7
⇒ 4x = -7 [divide both sides by 4]
⇒ 4x ÷ 4 = -7 ÷ 4
⟹ x = [tex]\bold{-\dfrac{7}{4}}[/tex]
Case 2:
⇒ 2x - 1 = 0 [subtract 1 from both sides]
⇒ 2x - 1 + 1 = 0 + 1
⇒ 2x = 1 [divide both sides by 2]
⇒ 2x ÷ 2 = 1 ÷ 2
⟹ x = [tex]\bold{\dfrac{1}{2}}[/tex]
Solutions:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
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what is the mean median and mode of 3,721,23,63,27,29,95 and 23?
Answer:
Mean: 123
Median: 28
Mode: 23
Step-by-step explanation:
give brainliest
Answer:
Mean = 123, Median = 28 , Mode = 23
Step-by-step explanation:
Mean is the average of all the numbers.
Mean = [tex]\frac{3+721+23+63+27+29+95+23}{8} \\= \frac{984}{8} \\= 123[/tex]
Median is the middle most value of the numbers when arranged in ascending order. (Average of the 2 middlemost numbers if there are even number of values.)
Arranged Values: 3,23,23,27,29,63,95,721
Median = [tex]\frac{27+29}{2} \\= \frac{56}{2} \\= 28[/tex]
Mode is the value that occurs the most in the numbers.
Mode = 23
Assessment
Read, analyze, then solve each problem. Answer each question.
A. A bowl of mango jelly was poured into a 14 cm x 8 cm x 3
cm rectangular container. If the mango jelly completely filled
the container, how much mango jelly was there?
1. What is asked in the problem? __________________________
2. Show your solutions. _________________________________
3. State the final answer. ________________________________
B. Ana is cleaning a box which is 6 dm long, 4 dm wide and 15
dm tall. What is the volume of the box?
4. What is asked in the problem? __________________________
5. What are given? _____________________________________
6. State the final answer. ________________________________
C. Wenalyn baked a cassava cake which measures 18 cm x 10
cm x 4 cm. She wants to share the cake with her two
classmates so she cuts it into three parts all of the same
sizes. How much cassava cake will each of her classmates
receive?
7. Show your solutions or illustration.
8. What is the final answer? _____________________________
D. A ream of bond paper is 28 cm long, 22 cm wide and 4 cm
thick. It contains 500 sheets. If 250 sheets were removed
from the ream of bond paper, what is the volume of the
remaining sheets?
9. Write the equation. __________________________________
10.What is the final answer? ___________________________
The formula for the volume of a rectangular prism is: length x width x height
Volume of the mango jelly : 14 x 8 x 3 = 336 cm³
Volume of the cleaning box: 6 x 4 x 15 = 360 dm³
Volume of the cake each classmate would get = (18 x 10 x 4) / 3 = 240 cm³
Volume of the remaining ream of paper : (28 x 4 x 22) / 250 = 9.9 cm³
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i am BEGGING FOR HELP on this question please help IM GIVING 5 STAR AND BRAINLIEST PLEASE ANSWER QUICKLY PLEASE ⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
Answer: COSINE
Step-by-step explanation:
I PROMISE
Answer:
See below
Step-by-step explanation:
For a right triangle, with the information given, tangent function is most appropo
tan 41 = 4/x re-arrange to
x = 4 / tan(41) then x = 4.60
From a hot-air balloon, Brody measures a 39° angle of depression to a landmark
that's 532 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest hundredth of a foot if necessary.
The balloon's vertical distance above the ground is 430 feet.
What is the angle of depression?You look straight parallel to the ground. But when you have to watch something down, then you take your sight down by moving your head up.
The angle from horizontal to the point where you stopped your head is called the angle of depression.
From a hot-air balloon, Brody measures a 39° angle of depression to a landmark that's 532 feet away, measuring horizontally.
The angle of depression = 39°
The base = 532
We need to find the vertical distance consider perpendicular.
[tex]\rm Tan \theta = \dfrac{perpendicular}{base } \\\\\rm Tan 39 = \dfrac{perpendicular}{532} \\\\\rm Tan 39 \times 532 =perpendicular\\\\0.80 \times 532\\\\P = 430.80[/tex]
Therefore, the balloon's vertical distance above the ground is 430.80 feet.
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Answer:
430.81
Step-by-step explanation:
hard way
If b=7 , what is the value of the expression 2(10-b)? A.4 B.6 C.24 D. 12
Answer:
B
Step-by-step explanation:
substitute b = 7 into the expression
2(10 - b)
= 2(10 - 7)
= 2(3)
= 6
Answer:
all you have to do is substitute
B. 6
Step-by-step explanation:
2(10-7)
2(3)
6
wright the follwing in decimlal form:3/11
Answer:
3/11 in decimal form is 0.272727272727....
Step-by-step explanation:
Yw ! :)
Please Help I Don't Understand!
Answer:
3/4
Step-by-step explanation:
Scale factor is the ratio between two different triangles. They can be scaled if they are similar triangles, which they are (in this case). Since we know that these two triangles are similar, we want to match all the sides up in a way where they all have the same ratio.
NK=3 and AH = 4, so NK/AH = 3/4.
GK=6 and LH = 8, so GK/LH = 6/8 = 3/4.
GN = 15 and LA = 20, so GN/LA = 15/20 = 3/4.
We found the matching ratios, so the answer is 3/4.
Find the volume of a cone with a diameter of 10 yards and a height of 12 yards. round your answer to the nearest tenth.
6. Multiply: (x – 4)(x + 5)
(a) x2 + 5x - 20,
(b) x2 - 4x - 20,
(c) x2 - x - 20,
(d) x2 + x - 20.
Which option below demonstrates the correct interval notation for a
continuous set of all numbers between 5 and 6, including 5, but not including
6?
OA. (5,6]
OB. (5,6)
O C. [5, 6)
OD. (5, 6}
The correct interval notation for the continuous set of all numbers between 5 and 6, including 5, but not including 6 is [5, 6) option (C) is correct.
What is interval notation?It is defined as the representation of a set of values that satisfy a relation or a function. It can be represented as open brackets and close bracket the close the brackets means the value is at the close bracket also included, and open bracket means the value at the open bracket does not include.
We have:
Continuous set of all numbers between 5 and 6, including 5, but not including 6.
From the above statement we can represent the number in the interval notation:
The numbers are between 5 and 6.
(5, 6)
As it is mentioned that 5 is included and 6 is not included, then:
[5, 6)
Thus, the correct interval notation for the continuous set of all numbers between 5 and 6, including 5, but not including 6 is [5, 6) option (C) is correct.
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Cual es la regla de la sucesion de 1,4,7,10,13,16,19,
Given, a = 1
common difference = 3
Eighth term = a+(n-1)d = 1+(8-1)3
= 1 + 21 = 22
Hope this helps :)
HELP ASAPPPP 10 POINTS
If ln=12x+16 what is the length is ln units
if a= 2x-3 and b= 2x+5
determine the product of a and b by using formulae. if x=2, ab= what?
help pleasee would appreciate a lot
Answer:
a= 2x-3 b= 2x+5
ab= (2x-3)(2x+5)
= 2x*2x+ 2x*5- 3*2x- 3*5
= 4x+ 10x- 6x- 15
= 14x- 6x- 15
= 8x -15
x= 2
= 8(2)- 15
= 16-15
= 1
How to find the surface area of a hexagon?
Answer:
adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object.
Step-by-step explanation:
Express the trig ratios as fractions in simplest terms.
(Image above)
Help please
The value of the angle P and Q are equal which is equal to 36.86°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
From Δ it is obtained that;
[tex]\rm cos P = \frac{B}H} \\\\ \rm cos P = \frac{16}{20} \\\\ P=cos^{-1}\frac{16}{20} \\\\ P= 36.86 ^0[/tex]
[tex]\rm sin \ Q = \frac{12}{20} \\\\ Q= sin^{-1}(0.6) \\\\ Q= 36.86^0[/tex]
sin P= sin Q
Hence, the value of the angle P and Q are equal which is equal to 36.86°.
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i need help with this question can someone answer fast please
Answer:
Below in bold.
Step-by-step explanation:
Petra uses the expression distance = time * speed
which is (4 + h)55 where 4 + h = total time for the 2 days.
Sierra uses the same expression but for each individual day and adds them:
4*55 + 55h
= 220 + 55h.
You save 25% on a $199 television. How much do you save?
Answer:
49.75$Step-by-step explanation:
You save 25% on a $199 television. How much do you save?
25% = 1/4
so
199 : 4 = 49.75$
Answer:
You save $49.75
A minor-league hockey team had the following scores for the start of the season: 3, 6, 2, 1, 2, 3, 0, 4, 5, 1, 5, 4.
If the hockey team scores 9 goals in their next game, would the mean, median, or mode be more affected?
If the hockey team scores 9 goals in their next game, it means that; the mean would be the most affected.
How to find mean, median and mode?
We are given the data set as;
3, 6, 2, 1, 2, 3, 0, 4, 5, 1, 5, 4.
Let us rearrange in ascending order to get;
0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6.
The mean = (0 + 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5 + 6)/12 = 3
Median = (3 + 3)/2 = 3
Mode = 1, 2, 3, 3, 5
Now, if they score 9 goals in their next game, it means that;
Mean = 45/13 = 3.46
Median = 3
Mode remains the same
Thus, mean will be the most affected.
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Function k is a transformation of the parent exponential function f. what are the domain and range of function k? k(x)= 2^x
Answer:
Domain: All real numbersRange: All real numbers greater than 0Part A
Jan says that a rhombus is a parallelogram and that every parallelogram is also a rhombus. Is Jan correct? {Box}
Part B
Explain why or why not.
I NEED THE ANSWER ASAP pls
Answer:
Jan is not correct
Step-by-step explanation:
Rhombus and parallelogram both have their opposite angles to be equal and the opposite sides to be parallel but Rhombus has all its sides to be equal like the square while the parallelogram has only the opposite sides to be equal like the rectangle
1. What is the slope of a line that is parallel to the line represented by the equation y=-2/5x + 4/5
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of the line that is parallel to the line [tex]\star~\mathrm{y=-\cfrac{2}{5}x+\cfrac{4}{5}}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Parallel lines have the same slope.So let's first determine the slope of the first line, and then let's find the slope of the line that's parallel to it.
[tex]\circ\!\!\!\star\mathcal{HINT:}[/tex]
The slope is the coefficient of x.So the slope is
[tex]\star~\mathrm{-\cfrac{2}{5}}[/tex].
Can you guess the slope of the line that is parallel to the first line?
That's right! The slope is...
[tex]\star~\mathrm{-\cfrac{2}{5}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Nina and Jo both ran a 13 km race.
Nina took 2 hour 10 minutes to run the whole race.
Jo started the race 7 minutes later than Nina but caught up when they had both travelled 11 km.
If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?
We will see that Jo's speed, rounded to 2 digit places, is:
S = 6.42 km/h
How to get Jo's speed?
Remember that:
speed = distance/time.
Nina takes 2 hours and 10 minutes to finish the race, first, let's write the time in hours:
1 hour = 60 min.
Then:
10 min = (10/60) hours = 0.167 hours.
So we can write the time as:
2.167 hours.
And the distance is 13km, so her speed is:
S = 13km/2.167h = 6 km/h
The time that she takes to reach a distance of 11km (where she meets with Jo) is:
T = 11km/(6 km/h) = 1.83 hours.
Now, Jo starts 7 minutes after Nina, then the time in which he travels the 11 km is:
1.83 hours - 7 minutes.
Where:
7 min = (7min/60 min) hours = 0.117h
Then the time is:
T= 1.83h - 0.117h = 1.713 hours.
So he travels 11km in 1.713 hours, then his speed is:
S = 11km/ 1.713 hours = 6.42 km/h
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Which of the following statements is true concerning ABC below?
B
11
11
A
OA. ZB is the smallest angle.
B. ZA is the largest angle.
OC. ZA is the smallest angle.
D. ZB is the largest angle.
14
C
Angle B is the largest angle. , Option D is the correct answer.
What is an Isosceles Triangle ?A triangle that has two sides equal is called an Isosceles Triangle.
It is given in the question a triangle ABC
With BA =BC
therefore angle A is equal to angle C
In a triangle the angle opposite to the longest side is the biggest angle
Therefore angle B is the largest angle.
Option D is the correct answer.
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Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
B. ∠TRF and ∠NRLC. ∠LRE and ∠FRAStep-by-step explanation:
→ The lines TN and FL intersect each other
at the point R forming the opposite angles ∠TRF and ∠NRL
then
∠TRF and ∠NRL are verticals angles.
………………………………………………………………………
→ The lines LF and AE intersect each other
at the point R forming the opposite angles ∠LRE and ∠FRA
then
∠LRE and ∠FRA are verticals angles.
Question 5
The price of an apple is $1.25. If you get 20% discount, how much do you have to
pay?
Answer:
you will only pay one dollar I did this question before, and it was easy Please mark me brainiest please
Step-by-step explanation:
Find the term that must be added to the equation x² + 6x = 1 to make it into a
perfect square.
What is the component form of the vector whose tail is the point (-3,2) and whose head is the point (1, -6)?
Answer:
(4, -8)
Step-by-step explanation:
The components of a vector are found by subtracting the tail from the head.
__
Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)
⇒ The component form is (4, -8), or maybe 4i -8j.
_____
Additional comment
There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.
(4,-8) is the answer
HELP with this please!!
[tex]~~~~\dfrac{12}{x^2 -49} \cdot \dfrac{x^2+9x+14}{9}\\\\\\=\dfrac{4}{x^2 -7^2}\cdot \dfrac{x^2 + 7x +2x +14}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)} \cdot \dfrac{x(x+7)+2(x+7)}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)}\cdot \dfrac{(x+7)(x+2)}{3}\\\\\\=\dfrac{4(x+2)}{3(x-7)}[/tex]
Answer:
[tex]\frac{4(x + 2)}{3(x - 7)}[/tex]
Step-by-step explanation:
Hello!
We can simplify this by factoring, and cross reducing.
Simplify[tex]\frac{12}{x^2 - 49} * \frac{x^2 + 9x + 14}{9}[/tex][tex]\frac{12}{(x+7)(x - 7)} * \frac{(x + 2)(x + 7)}{9}[/tex][tex]\frac{12(x + 2)}{9(x - 7)}[/tex][tex]\frac{4(x + 2)}{3(x - 7)}[/tex]The final simplified form is [tex]\frac{4(x + 2)}{3(x - 7)}[/tex]