Answer:
[tex]x = 10[/tex]. In other words, there number of girls is [tex]10[/tex].
Step-by-step explanation:
The average of a number of measurements is equal to the sum of these measurements over the number of measurements.
[tex]\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}[/tex].
Rewrite to obtain:
[tex]\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}[/tex].
For this question:
[tex]\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}[/tex].
[tex]\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}[/tex].
Therefore:
[tex]\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}[/tex].
On the other hand, there are [tex](15 + x)[/tex] boys and girls in total. Using the formula for average:
[tex]\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}[/tex].
From the question, this average should be equal to [tex]123[/tex]. In other words:
[tex]\displaystyle \frac{1875 + 120\, x}{15 + x} = 123[/tex].
Solve this equation for [tex]x[/tex] to obtain:
[tex]1875 + 120\, x= 123\, (15 + x)[/tex].
[tex](123 - 120)\, x = 1875 - 123 \times 15[/tex].
[tex]x = 10[/tex].
In other words, the number of girls here is [tex]10[/tex].
4 times the difference of a number and 12 is 120
Answer:
the answer is 42
Step-by-step explanation:
let the number be ''x''
the difference between ''x'' and 12 can be written as
x - 12
4 times means multiplied by 4, so
4 (x - 12) = 120
4x - 48 = 120
4x = 120 + 48
4x = 168
x = 168/4
x = 42
Find the DISTANCES of AB and CD to determine if AB is congruent to CD. A(-7,1) B(-4,-3) C(3,-5) D(7,-2)
Answer:
Step-by-step explanation:
The formula for calculating the distance between 2 points is expressd as;
D = √(x₂-x₁)²+(y₂-y₁)²
Given the coordinates A(-7,1) B(-4,-3) C(3,-5) D(7,-2)
The disyance AB will be expressed as
AB = √(x₂-x₁)²+(y₂-y₁)²
Given the coordinates A(-7,1) B(-4,-3)
AB = √(-4-(-7))²+(-3-1)²
AB = √(-4+7)²+(-4)²
AB = √3²+4²
AB = √25
AB = 5
For CD with coordinates C(3,-5) D(7,-2)
CD = √(7-3)²+(-2-(-5))²
CD = √(4)²+3²
CD = √16+9
CD = √25
CD = 5
Congruent sides are sides that are equal. Hence since AB is equal to CD, this means that the distances AB and CD are congruent
The cube of the difference of a number and 9.
Answer:
Hey there!
Let x be the number.
Thus, we have [tex](x-9)^3[/tex]
Hope this helps :)
16) Find the width of a rectangle whose area is (x^2 +16x+48) ft^2 and whose
length is (x+4) ft.
Answer: x+12
We know that the area is length * width. Since length is x+4, we know
(x+4) * something = x^2+16x+48.
To find that something, note that 48 (from the right side) = 4 (from the left side) * 12. Why is this important? Well, then we know that the something is x+12.
This is because (x+4) * (x+12) = x^2 + 16x + 48. But just focus on this part: 48. Even if we put like 3x+12 or something, that would work out to 3x^2+28x+48. It's 48 every time.
Hope that helped,
-sirswagger21
A 11/16-inch-long bolt is used in a machine. What is the length of the bolt written as a decimal? (Please help)
Answer:
0.6875
Step-by-step explanation:
11 divide 16 and you get 0.6875
Answer:
The answer is 11/16=0.6875.
Line l contains the points A(2, 2) and B(3,6). Line k contains the points C(0,5) and D(1,9).
Are lines land k parallel? Justify your response.
Answer:
Yes, line L and line K are parallel because the slopes are equal.
Step-by-step explanation:
From the question given:
Line L contains point A(2, 2) and B(3, 6)
Line K contains point C(0, 5) and D(1, 9)
To know if the lines are parallel, we need to determine the slope of each line.
The slope of each line can be obtained as follow:
1. Determination of the slope of line L.
Line L contains point A(2, 2) and B(3, 6)
x1 coordinate = 2
x2 coordinate = 3
y1 coordinate = 2
y2 coordinate = 6
Slope = Chang in y coordinate / change in x coordinate
Slope = y2 - y1 / x2 - x1
Slope = 6 - 2 / 3 - 2
Slope = 4/1
Slope = 4
Therefore, the slope of line L is 4.
2. Determination of the slope of line K.
Line K contains point C(0, 5) and D(1, 9)
x1 coordinate = 0
x2 coordinate = 1
y1 coordinate = 5
y2 coordinate = 9
Slope = Chang in y coordinate / change in x coordinate
Slope = y2 - y1 / x2 - x1
Slope = 9 - 5 / 1 - 0
Slope = 4/1
Slope = 4
Therefore, the slope of line K is 4.
Summary
Line >>>>>>>>>>> Slope
L >>>>>>>>>>>>> 4
K >>>>>>>>>>>>> 4
From the above calculations, we can see that line L and line K has the same slope.
Therefore, line L and line K are parallel.
Draw two lines and a transversal...
picture:
=================================================
Explanation:
It might help to move either line m or line n to make them parallel to one another. This isn't required but it might help to see the answer better.
Angles 1 and 2 are between lines m and n, so they are interior angles. They are alternate interior angles as they are on alternate sides of the transversal line.
Angles 2 and 3 are on the same side of the transversal, and both are above their adjacent parallel line counterpart, so they are corresponding angles.
Angles 3 and 4 are outside the interior region, and they alternate on either side of the transversal. They are alternate exterior angles.
Angles 1 and 4 are corresponding for similar reasons as angles 2 and 3 are.
-------------
Notes:
Drawing A has angles 1 and 2 be alternate interior, but angles 2 and 3 are not corresponding (they're vertical angles)Drawing C is a similar story as drawing A, just things have been rearranged.Drawing D has angle 1 as an exterior angle, so it cannot be an alternate interior angle.In circle C, r = 32units what is the area of circle C
Answer:
1024π, 3215.36
Step-by-step explanation:
The formula for the area of a circle is πr^2
R is the radius, which is already given to us. We need to find r^2
32x32=1024
1024π
We can leave it in terms of pi or we can solve it out.
1024x3.14=3215.36
1024π, 3215.36
Answer:
see below
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi * 32^2
A =1024 pi units^2
If we use pi = 3.14
A = 3215.36 units^2
If we use the pi button
A =3216.990877 units^2
Given: AB ∥ DC , m CB =62°, m∠DAB=104° Find: m∠DEA, m∠ADB
Answer:
Step-by-step explanation:
sum of angles of parallelogram=360 degrees
adjacent angles add up to 180 degrees (supplementary angles)
Angle A=104 (DAB=104)
Angle D=180-104=76 degrees (angle ADB)
Angle B=60 degrees
Angle C=180-60=120 (DCB)
Select the expression equivalent to(6x + 5)-(4x – 6).
this is a very dumb question but what is -1^2? my calculator says its -1 but isnt -1*-1 = 1???? im very confused plzz help
Answer:
yes; -1² is 1.
if you put -1 in parentheses, like this (-1)², then it comes out as 1
Answer:
it is 1
Step-by-step explanation:
you have to put the number between parenthesis to give you the right answer. the calculator actually taking the minus sign separate from 1 because no brackets . Try (-1)²
What is 2x-6 = 3x+1-X-7 and you have to regroup/ divide by number next to x?
Answer:
infinite solutions
Step-by-step explanation:
2x-6 = 3x+1-X-7
Combine like terms
2x-6 = 3x-x +1-7
2x-6 = 2x -6
subtract 2x from each side
-6 = -6
Since this is a true statement, x can be any real number
A certain right triangle with integer side lengths has perimeter $72$. What is its area?
Answer: 216 square units
====================================================
Explanation:
A common pythagorean triple you may be familiar with is the 3-4-5 right triangle. This has two legs of 3 and 4, and a hypotenuse of 5. The perimeter is 3+4+5 = 7+5 = 12. Note how this is a factor of 72.
If we multiply the perimeter (12) by 6, then 12*6 = 72. So we have scaled the triangle by a factor of 6. Each length is 6 times longer
the side length 3 becomes 3*6 = 18
the side length 4 becomes 4*6 = 24
the side length 5 becomes 5*6 = 30
The new perimeter is 18+24+30 = 42+30 = 72
The last step is to find the area. The two legs of this triangle are the base and height
area = 0.5*base*height
area = 0.5*18*24
area = 9*24
area = 216
-----
Or you could find the area of the 3-4-5 right triangle to get
area = 0.5*base*height = 0.5*3*4 = 6
then multiply by 36 to get 6*36 = 216. The 36 is the square of the scale factor 6 we applied above. The new lengths are 6 times longer, so the new area is 6^2 = 36 times larger.
Referring to the Fig. in Question #3, evaluate the expression shown when a = 3, b = 8, c = 4 Please help.
Answer:
[tex]\huge\boxed{4}[/tex]
Step-by-step explanation:
=> [tex]\sqrt{b^2-4ac}[/tex]
Given that a = 3 , b = 8 and c = 4
=> [tex]\sqrt{(8)^2-4(3)(4)}[/tex]
=> [tex]\sqrt{64-48}[/tex]
=> [tex]\sqrt{16}[/tex]
=> 4
How do you do question 12? Options:
A 4
B 1/4
C -1/4
D -4
Answer:
it is D
Step-by-step explanation:
after leaving home for school, it had taken you 15 minutes to walk 1000 feet. if your destination is a total of 1200 feet from home, about how many minutes do you have left to walk?
Answer: 3 min
Step-by-step explanation:
Step 1. Find the constant speed
you walked 1000 feet in 15 min
1000 ft/ 15min=200/3 ft / min
Step 2. Apply the constant speed to the left distance
You already walked 1000 feet and it is total 1200 feet
1200-1000=200 feet left
distance ÷ speed=time
200 ÷ (200/3)=3 min
Hope this helps!! :)
Please let me know if you have any question
The temperature is -3°F at 7 A.M. During the next three hours, the temperature increases 13°F. What is the temperature at 10 AM?
A -16°F
B-16°F
C- 10°F
D-10°F
WILL MARK BRAINLIEST AND 20 POINTS Determine algebraically whether each of the following functions is even, odd, or neither. f(x) = x^2 - x
Answer:
Neither
Step-by-step explanation:
The function is neither because if it was even it would follow the rules of:
[tex]f(-x)=f(x)[/tex]
and if it was odd it would follow the rules of:
[tex]-f(x)=f(-x)[/tex]
but instead it follows the rule:
[tex]-f(x)\neq f(-x))\\[/tex]
Lea left home and drove toward the ferry office at an average speed of 22 km.H. Trevon left at the same time and drove in the opposite direction with an average speed of 43 km/h. How long does Trevon need to drive before they are 65 km apart?
Answer:
1 hour
Step-by-step explanation:
Lea's speed = 22km/hr
Trevon's speed = 43km/hr in a direction opposite Lea's
How long does Trevon needs to drive before they are 65km apart.
Note : both took at the same time and in opposite direction.
Recall : speed = distance / time
Distance = speed * time
Distance between them = 65km
Let Trevon's distance = D2 = 43 * t
Lea's distance = D1 = 22 * t
t is the same since they both left at the same time.
D2 + D1 = 65
43t + 22t = 65
65t = 65
t = 65/65
t = 1 hour
please help me out guys.
Answer:
| 5x| = 0
Step-by-step explanation:
Absolute values have two solutions, one positive and one negative
The exception to this rule is when it is equal to zero
+0 = -0 = 0
5x = 0
x =0
19. Write the perimeter of the rectangle as a
simplified expression.
x - 3
7x + 1
Answer:
16x - 5
Step-by-step explanation:
2(x-3) + 2(7x+1) since there are 4 sides, 2 which have the same dimensions
2x - 6 + 14x + 1 = 16x - 5
The simplified expression of the perimeter of the rectangle should be 16x - 4.
Given that
x - 37x + 1We know that
The perimeter of the rectangle be
= 2(length + breadth)
= 2(x - 3 + 7x +1)
= 2x - 6 + 14x + 2
= 16x - 4
Therefore we can conclude that the simplified expression of the perimeter of the rectangle should be 16x - 4.
Learn more about the rectangle here: brainly.com/question/20733283
Help needed ASAP will give brainliest!
find x such that 2x^2 +2x=12
Answer:
2 and -3
Step-by-step explanation:
2x^2=4x
4x+2x=12
6x=12
how many times does 6 go into 12?
right, 2 times!
x=2
---
2x^2+2x-12=0
x^2+x-6=0
(x+3)(x-2)=0
X=-3 and 2
Michael wrote a novel that sells for $20 dollars each. He received a bonus of $50,000 to sign the contract to write the book, and he receives 9% commission on each book sale. If he sells 10,000
books how much will he make? Clearly show your work
I need help please.ASAP
Answer:
20
Step-by-step explanation:
I do not know how to explain it for you thanks
Some one help? Im confused with this part of geometry just tell me what answer
Answer:
the answer is actually PS (7x - 7)
Hoped that I helped
A sequence is defined below.
f(0) = 7
f(n) = 2f(n - 1) - 3 for n > 1, where n is an integer
What is the third number in the sequence?
Answer:
35
Step-by-step explanation:
f(0) = 7
f(1) = 2f(0) - 3 = 11
f(2) = 2f(1) - 3 = 19
f(3) = 2f(2) - 3 = 35
A snack mix recipe uses a ratio of 3/4 pound of dried apples to 1/2 pound of dried pears. What amount of dried apples would be needed per pound of dried pears?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
According to the question, data provided in the question is as follows
Given ratio
[tex]\frac{3}{4}[/tex] a pound of direct apples
[tex]\frac{1}{2}[/tex] a pound of dried pears
We can right
[tex]\frac{3}{4} : \frac{1}{2}[/tex]
Now we multiplied it to determine the amount of dried apples that required per pound of dried pears
[tex]\frac{3}{4} \times \frac{1}{2}[/tex]
[tex]\frac{3}{8}[/tex]
Hence the above is the answer and the same is to be considered by taking the pound of direct applies to pound of direct pears so that the correct amount could arrive
The amount of dried apple needed per pound of dried pear is 3/8
The question tells us that
3/4 pound of dried apples : 1/2 pound of dried pears
We are asked to find the amount of dried apples needed per pound of dried pears. To do this, we multiply both ratio together to get it in 1. This means that
3/4 * 1/2 = 3/8.
This then mean that for every pound of dried pear, 3/8 pound of dried apple was mixed.
see more here https://brainly.com/question/13419413
One airplane is located 200 km north and 50 km east of an airport. A second plane at the same altitude is located 30 km north and 100 km north and 100 km west.
The distance between the planes is closest to:
A. 150 km
B. 200 km
C. 300 km
D. 350 km
E. 400 km
Answer:
B. 200 km
Step-by-step explanation:
You can use the Pythagorean theorem for this question. First, you must find a and b. You can do this by finding the distance between North and South, and East and West. For this specific equation, you'd use 200 North - 30 North to get 170 miles on the y-axis. Then, you'd do 50 East + 100 West to get 150 kilometers distance on the x-axis. Now that you have 170 and 150, you can begin the equation
170^2 + 150^2 = c^2
28900 + 22500 = c^2
51400 = c^2
√51400 = √c^2
~226 = c
They are approximately 226 kilometers apart, and 226 is closest to 200, which is B.
While writing this, I felt like I wasn't explaining well. Please feel free to ask for clarification if you need.
The distance between the planes is closest to 200km
You can use the Pythagorean theorem for this question.
First, we need to find a and b. This is gotten by calculating the distance between North and South, and the East and West. From the question, we can say that, 200 North - 30 North gives 170 miles with respect to the y-axis. In the same vein, we know that 50 East + 100 West gives us 150 kilometers which is with respect to the x-axis.
Since we have found our a and b to be 170 and 150, we then use Pythagoras to find the answer to the equation.
170² + 150² = c²
28900 + 22500 = c²
c² = 51400
c =[tex]\sqrt{51400}[/tex]
c = ±226 km.
Since we can't have distance in negative, then our answer is 226 km. The answer asked us to find the closest distance, and thus, our answer is 200km.
Learn more about Pythagoras theorem here https://brainly.com/question/15138986
Is -8/5 a rational number
Answer:
yes
Step-by-step explanation:
i think