We have 15 ways to chose 2 students for the position of president and Vice President
Solution:
Given that,
There are 6 students. 2 of them are chosen for the position of president and Vice President.
To find: number of ways we have to choose the students from the 6 students
So now we have 6 students, out of which we have to choose 2 students
As we just have to select the students. We can use combinations here.
In combinations, to pick "r" items from "n" items, there will be [tex]^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}[/tex] ways
[tex]^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{n !}{(n-r) ! r !}[/tex]
Then, here we have to pick 2 out of 6:
Total students = n = 6
students to be selected = r = 2
[tex]\begin{aligned} 6 C_{2} &=\frac{6 !}{(6-2) ! 2 !} \\\\ 6 C_{2} &=\frac{6 !}{4 ! 2 !} \\\\ 6 C_{2} &=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1 \times 2 \times 1} \\\\ 6 C_{2} &=15 \end{aligned}[/tex]
Thus we have 15 ways to chose 2 students for the position of president and Vice President
Can somebody please help. FYI Math isn’t my strong suit....please help me!!!!!????
1. Let us first find the missing interior angle.
m<C+53+61=180
m<C=66 degrees
law of sines: [tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]
a,b, and c represents the lengths of the triangles and A,B, and C represents the measures of the interior angles opposite to the sides.
For the purposes of this problem let us use a shorthand version for the law of sines.
[tex]\frac{sin(B)}{b} =\frac{sin(C)}{c}\\\frac{sin(61degrees)}{b} =\frac{sin(66degrees)}{142}\\b=142sin(61degrees)/sin(66degrees)\\[/tex]
b=134.95 meters approx.
AC is equal to length b in this case so AC=134.95 meters approx.
2. law of cosines: a²=b²+c²-2bccos(A)
Let us rearrange this formula so that we can solve for cos(C) in terms of a, b, and c (the sides lengths of the triangle).
a²=b²+c²-2bccos(A)
a²-b²-c²=-2bccos(A)
[tex]\frac{a^{2}-b^{2}-c^{2}}{-2bc}[/tex]=cos(A)
cos(A)=[tex]\frac{a^{2}-b^{2}-c^{2}}{-2bc}[/tex]
Now, because we want to find measure of angle A...
cos(A)=[tex]\frac{13.7^{2}-12.2^{2}-22.1^{2}}{-2(12.2)(22.1)}[/tex]
cos(A)=0.83 approx.
A=33.52 degrees approx.
3. Solving with law of cosines.
law of cosines: a²=b²+c²-2bccos(A)
a²=16²+18²-2(16)(18)cos(52 degrees)
a²=256+324-576cos(52 degrees)
a²=580-576cos(52 degrees)
a²=225.38 approx.
a=15.01 units approx.
Solving with law of sines.
law of sines: [tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]
For the purposes of this problem let us use a shorthand version for the law of sines.
[tex]\frac{sin(71 degrees)}{18} =\frac{sin(52 degrees)}{x}\\xsin(71 degrees)=18sin(52degrees)\\x=\frac{18sin(52degrees)}{sin(71 degrees)} \\[/tex]
x=15.00 un approx.
Look at the rectangle and the square:
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answer:
Anna is incorrect.
Step-by-step explanation:
Find lengths of diagonals SQ and OM.
1. Consider right triangle SQR. By the Pythagorean theorem,[tex]SQ^2=SR^2+RQ^2\\ \\SQ^2=14^2+7^2\\ \\SQ^2=196+49\\ \\SQ^2=245\\ \\SQ=\sqrt{245}=7\sqrt{5}\ units[/tex]
2. Consider right triangle OML. By the Pythagorean theorem,
[tex]OM^2=OL^2+LM^2\\ \\OM^2=7^2+7^2\ [\text{In square LMNO, side } OL \text{has the same length as side }LM]\\ \\OM^2=49+49\\ \\OM^2=98\\ \\OM=\sqrt{98}=7\sqrt{2}\ units[/tex]
Since [tex]7\sqrt{5}\neq 2\cdot 7\sqrt{2}=7\sqrt{8},[/tex] diagonal SQ is not two times diagonal OM. Thus, Anna is incorect.
Answer:
Anna is not correct
Step-by-step explanation:
Part A: No, anna is not correct because first the rectangle (PQRS) its says that the length of (SR) is 14 inches and if cut in half at the diagonal a rectangle or a square would have 2 triangles so if A2 + B2 = C2 then if C = the length of the diagonal and A would = 14 in ( the length of the rectangle) and then B would = 7 inches which is the width of the rectangle. It concludes that 14 to the power of 2 + 7 to the power of 2 = 245 which its square root is 15.65 ( if rounded to the hundredth place)
Part B: Next, is the square (LMNO) if its length and width are both 7 inches then A2 = 7 to the power of 2 and also B2 will also = 7to the power of 2 and C2 will = will be the length of the diagonal.So, all of that 7 to the power of 2 + 7 to the power of 2 = 98 and its square root is 9.89 ( if rounded to the hundredth place) so lets just say 9.9.
Then you can see that 9.9 times 2 does not equal 15.65 so Anna was wrong.
What is an equation of a line that passes through the points (8 , -3) (8 , 4)
Answer:
[tex]\displaystyle x = 8[/tex]
Step-by-step explanation:
Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.
I am joyous to assist you anytime.
Which of the following is equivalent to
Answer:
please include more info
Step-by-step explanation:
33 POINTS!! PLEASE HELP!!
Write a situation that would model the graph below. Pay attention to the increasing, decreasing and constant parts. Watch for how the slope makes sense to the problem. Look at those units!
Make sure to include each section of the graph!
Answer:
[insert name here] drove his scooter around. When he started, his speed increased constantly to 10 mph (O-A). He cruised at 10mph for a few seconds. (A-B) Then he slowed down (B-C) and stopped for a few seconds (C-D). He then started speeding up (D-E) and cruised for a few more seconds. (E-F)
amy and brittnay spent a total of $25 for lunch. Brittanys lunch cost $3 more than amy’s did. how much did amy spend for lunch?
Answer:
Amy spent $11 for lunch.
Step-by-step explanation:
x+y=25
x+(x+3)=25
2x+3=25
2x=25-3
2x=22
x=22/2
x=11
Answer:amy spent 11 dollars.
Step-by-step explanation:I did math
A sheriff patrols several neighborhoods in her patrol car it requires 4/15 of an hour to patrol an entire neighborhood.Can a sheriff patrol 2 3 4 or 6 neighborhoods in 8/9 an hour
Answer:
3
Step-by-step explanation:
For this question, you need to make change the denominators of the fractions to be equal, making them the same lowest common denominator.
8/9 -> 40/45
4/15 -> 12/45
Since 12 goes into 40 3 1/3 times, he can patrol that many neighborhoods in 8/9's of an hour, which is rounded to 3 because he doesn't have enough time for 4.
To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value. The answer is 10/3, which means the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour.
Explanation:To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value.
Given that it takes 4/15 of an hour to patrol a single neighborhood, we can divide 8/9 by 4/15.
To divide fractions, we multiply by the reciprocal, so 8/9 ÷ 4/15 becomes 8/9 × 15/4. Multiplying across, we get (8 × 15) / (9 × 4) = 120 / 36 = 10 / 3.
How do you solve the following for x?
Answer:
Step-by-step explanation:
Is called a letter that stands for the number
Answer:
Step-by-step explanation:
√10x - 1 = 7
Square both sides,
10x - 1 = 7²
10x - 1 = 49
10x = 49 + 1
10x = 50
x = 50/10
x=5
Create a compound inequality for the following word problem. The sum of four times a number and eight is between zero and twelve
Answer:
[tex]0\leq 4x+8\leq 12[/tex]
Step-by-step explanation:
Compound inequality contain at least 2 or more inequality which is separated by "either" or "or". The end result has to satisfy both the inequality to be correct.
Now, creating compound inequality.
Lets assume a number "x" to create inequality.
As per given word problem: The sum of four times a number and eight.
∴[tex]4\times x + 8[/tex] = [tex]4x+8[/tex]
Next, as given the equation has to be between zero and twelve.
∴ [tex]0\leq 4x+8\leq 12[/tex]
∴ We have the inequality for word problem is [tex]0\leq 4x+8\leq 12[/tex].
The compound inequality that represents the given word problem is [tex]\( 0 < 4x + 8 < 12 \).[/tex]
To create a compound inequality for the given word problem, we need to translate the words into a mathematical expression. The problem states that "the sum of four times a number and eight is between zero and twelve." Let's break this down:
1. Identify the variable: The problem is asking about "a number," which we will represent with the variable [tex]\( x \).[/tex]
2. Translate "four times a number" into a mathematical expression: This phrase becomes [tex]\( 4x \).[/tex]
3. Translate "the sum of four times a number and eight" into a mathematical expression: This phrase adds 8 to the previous expression, resulting in[tex]\( 4x + 8 \).[/tex]
4. Translate "is between zero and twelve" into a mathematical inequality: This phrase indicates that the expression [tex]\( 4x + 8 \)[/tex] should be greater than zero and less than twelve. In mathematical terms, this is written as two separate inequalities:[tex]- \( 4x + 8 > 0 \)- \( 4x + 8 < 12 \)5.[/tex] Combine the two inequalities into a compound inequality: Since we want both conditions to be true at the same time, we use the logical "and" to combine them. The compound inequality is then:[tex]\( 0 < 4x + 8 < 12 \[/tex] )This compound inequality states that the expression [tex]\( 4x + 8 \)[/tex] should yield a value that is greater than 0 and less than 12, which accurately represents the conditions given in the word problem.
a line intersects the points (3,-4) and (1,2) what is the slope intercept equation for this line
Answer:
y = - 3x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, - 4) and (x₂, y₂ ) = (1, 2)
m = [tex]\frac{2+4}{1-3}[/tex] = [tex]\frac{6}{-2}[/tex] = - 3, thus
y = - 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 2), then
2 = - 3 + c ⇒ c = 2 + 3 = 5
y = - 3x + 5 ← equation of line
Answer:
y=-3x+5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-(-4))/(1-3)
m=(2+4)/-2
m=6/-2
m=-3
y-y1=m(x-x1)
y-(-4)=-3(x-3)
y+4=-3(x-3)
y=-3x+9-4
y=-3x+5
I need help please and thank you!!
Answer:3/8 as a fraction and 3/8%
Step-by-step explanation:
A rhombus, COAL is centered at the origin. The longer diagonal is on the y-axis and has a
length of 27m. The shorter diagonal is on the x-axis and has a length of has diagonals with
length 19m. Determine the coordinates of the vertices.
Answer with Step-by-step explanation:
We are given that
COAL is a rhombus .
CA and LO are the diagonals of rhombus COAL.
CA=27 m
OL=19 m
We know that
Diagonals of rhombus are bisect to each other.
Let P(0,0) be the intersecting point of diagonals
Therefore, CP=PA
LP=PO
Length PO=[tex]\frac{1}{2}LO=\frac{19}{2}=9.5 m[/tex]
Length of CP=[tex]\frac{1}{2}PA=\farc{1}{2}(27)=13.5 m[/tex]
Let C([tex]0,y_2),O(x_1,0),A(0,y_1) \;and\;L(x_2,0)[/tex].
Distance formula:[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
[tex]CP=\sqrt{(0-0)^2+(0-y_2)^2}=13.5[/tex]
[tex]\sqrt{y^2_2}=13.5[/tex]
[tex]y_2=\pm 13.5[/tex]
C(0,13.5) or (0,-13.5)
[tex]\sqrt{(y_2-y_1)^2}=27[/tex]
Substitute the value [tex]y_2=13.5[/tex]
[tex]\sqrt{13.5-y_1}=27[/tex]
[tex]13.5-y_1=\pm 27[/tex]
[tex]y_1=13.5-27=-13.5[/tex]
A(0,-13.5)
[tex]13.5-y_1=-27[/tex]
[tex]y_1=13.5+27=40.5[/tex]
A(0,40.5)
Substitute [tex]y_2=-13.5[/tex]
[tex]\sqrt{(-13.5-y_1)^2}=27[/tex]
[tex]-13.5-y_1=\pm 27[/tex]
[tex]-13.5-y_1=27[/tex]
[tex]y_1=-13.5-27=-40.5[/tex]
A(0,-40.5)
[tex]-13.5-y_1=-27[/tex]
[tex]y_1=-13.5+27=13.5[/tex]
A(0,13.5)
[tex]LP=\sqrt{(x_2-0)^2}=9.5[/tex]
[tex]\sqrt{x^2_2}=9.5[/tex]
[tex]x_2=\pm 9.5[/tex]
L(9.5,0) or L(-9.5,0)
[tex]\sqrt{x_2-x_1)^2}=19[/tex]
[tex](9.5-x_1)^2}=19[/tex]
[tex]9.5-x_1=\pm 19[/tex]
[tex]9.5-x_1=19[/tex]
[tex]x_1=9.5-19=-9.5[/tex]
[tex]9.5-x_1=-19[/tex]
[tex]x_1=9.5+19=28.5[/tex]
[tex](-9.5-x_1)=19[/tex]
[tex]-9.5-x_1=\pm 19[/tex]
[tex]-9.5-x_1=19[/tex]
[tex]x_1=-9.5-19=-28.5[/tex]
[tex]-9.5-x_1=-19[/tex]
[tex]-9.5+19=x_1[/tex]
[tex]x_1=9.5[/tex]
O(-9.5,0) or O(28.5,0) or (-28.5,0) or (9.5,0)
URGENT: FIFTEEN POINTS
What is 3452380952/100000000000 fully reduced?
Good evening ,
Answer:
Look at the photo below for the Answer.
:)
Answer:
431547619 / 12500000000
0.03452380 …
Step-by-step explanation:
Both are the simplified versions of 3452380952/100000000000.
The answer above is also correct! I hope this helps you!
- sincerelynini
Which point is 10 units from (2,5)
Answer:
All the points on (x - 2)² + (y - 5)² = 100
Step-by-step explanation:
It should be the circle with its center on point (2,5) and radius is 10.
(h , k) : center of circle (2,5) h = 2 k = 5
r: radius r = 10
Circle: (x - h)² + (y - k)² = r²
(x - 2)² + (y - 5)² = 100
Answer:
Below.
Step-by-step explanation:
There are many .
Two are (2+10, 5) = (12,5) and (2,5+10) = (2, 15).
If the weight of a package is multiplied by 4/5 the result is 30 pounds. Find the weight of the package
Answer:
weight * (4 / 5) = 30
weight * .8 = 30
weight = 30 / .8
weight = 37.5 pounds
Step-by-step explanation:
Santa's elves are selling
cookies for a bale sale. On
the first day, they sold 120
peppermint cookies and 30
cinnamon sugar cookies for a
total of $81. The next day
they made $60 by selling 70
peppermint cookies and 60
cinnamon sugar cookies.
Find the cost of each cookie.
cost of one peppermint cookies = $ 0.6
cost of one cinnamon sugar cookies = $ 0.3
Solution:Let "p" be the cost of one peppermint cookies
Let "c" be the cost of one cinnamon sugar cookies
To find: cost of each cookie
On the first day, they sold 120 peppermint cookies and 30 cinnamon sugar cookies for a total of $81We can frame a equation as:
120 peppermint cookies x cost of one peppermint cookies + 30 cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 81
[tex]120 \times p + 30 \times c = 81[/tex]
120p + 30c = 81 --------- eqn 1
The next day they made $60 by selling 70 peppermint cookies and 60 cinnamon sugar cookies70 peppermint cookies x cost of one peppermint cookies + 60 cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 60
[tex]70 \times p + 60 \times c = 60[/tex]
70p + 60c = 60 --------- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "p" and "c"
Multiply eqn 1 by 2
240p + 60c = 162 --- eqn 3
Subtract eqn 2 from eqn 3
240p + 60c = 162
70p + 60c = 60
(-) -------------------------
170p = 102
p = 0.6Substitute p = 0.6 in eqn 1
120p + 30c = 81
120(0.6) + 30c = 81
72 + 30c = 81
30c = 9
c = 0.3Summarizing the results:
cost of one peppermint cookies = $ 0.6
cost of one cinnamon sugar cookies = $ 0.3
The gardeners at Middleton Place Gardens want to plant a total of 45 white and pink hydrangeas in one flower bed. In another flower bed, they want to plant 119 hydrangeas. In this bed, they want 2 times the number of white hydrangeas and 3 times the number of pink hydrangeas as in the first bed. Use a system of equations to find how many white and how many pink hydrangeas the gardeners should buy altogether.
The gardeners should buy 48 white and 116 pink hydrangeas altogether
Step-by-step explanation:
The given is:
The gardeners at Middleton Place Gardens want to plant a total of 45 white and pink hydrangeas in one flower bedIn another flower bed, they want to plant 119 hydrangeas, in this bed, they want 2 times the number of white hydrangeas and 3 times the number of pink hydrangeas as in the first bedWe need to find how many white and how many pink hydrangeas the gardeners should buy altogether
Assume that the number of white hydrangeas is x and the number of pink hydrangeas in the first bed
∵ The first bed has x white hydrangeas
∵ The first bed has y pink hydrangeas
∵ The total of white and pink hydrangeas in 1st bed is 45
- Equate the sum of x and y by 45
∴ x + y = 45 ⇒ (1)
∵ In the 2nd bed the number of the white hydrangeas is 2 times
as in the 1st bed
∵ The number of the pink hydrangeas is 3 times as in the 1st bed
∵ The number of the hydrangeas in the 2nd bed is 119
- Multiply x by 2 and y by 3, then add the products and equate
the sum by 119
∴ 2x + 3y = 119 ⇒ (2)
Now let us solve the system of equations
Multiply equation (1) by -3 to eliminate y
∵ -3x - 3y = -135 ⇒ (3)
- Add equations (2) and (3)
∴ -x = -16
- Divide both sides by -1
∴ x = 16
- Substitute the value of x in equation (1) to find y
∵ 16 + y = 45
- Subtract 16 from both sides
∴ y = 29
∵ The number of the white hydrangeas in the 1st bed is x
∵ The number of the white hydrangeas in the 2nd bed is 2x
∴ The total number of the white hydrangeas = x + 2x = 3x
∵ x = 16
∴ The total number of the white hydrangeas = 3(16) = 48
∵ The number of the pink hydrangeas in the 1st bed is y
∵ The number of the pink hydrangeas in the 2nd bed is 3y
∴ The total number of the pink hydrangeas = y + 3y = 4y
∵ y = 29
∴ The total number of the pink hydrangeas = 4(29) = 116
The gardeners should buy 48 white and 116 pink hydrangeas altogether
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
#LearnwithBrainly
20 pts and brainiest if correct
We have 1 square with side length 8 inches, and 4 triangles with a base length of 8 inches and a height of 15.
Surface area = (8 × 8) + 4(0.5 × 8 × 15)
The first part of this equation is the area of the square
The second part is the area of a triangle, multiplied by 4 (because there are 4 triangles)
= 64 + 4(60)
= 64 + 240
= 304 in²
The total surface area is 304 square inches.
Let me know if you need any clarifications, thanks!
At this rate, how many dresses does Lucy sew in one hour?
Answer: Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.
Step-by-step explanation:
The complete question is:
"Lucy is a dress maker. She sew [tex]\frac{4}{7}[/tex] of a dress in [tex]\frac{3}{4}[/tex] hour. At this rate, how many dresses does Lucy sew in one hour?"
Let "x" represents the number of dresses that Lucy sews in one hour.
You need to analize the information given in the exercise.
According to the exercise, you know that, in [tex]\frac{3}{4}[/tex] hour, Lucy sews [tex]\frac{4}{7}[/tex] of a dress.
Then, knowing this data, you can set up the following proportion:
[tex]\frac{\frac{4}{7}}{\frac{3}{4}}=\frac{x}{1}[/tex]
Therefore, you must solve for "x" in order to find the he number of dresses that Lucy sew in one hour.
You get this result:
[tex](1)(\frac{4*4}{7*4})=x\\\\x=(1)(\frac{16}{21})\\\\x=\frac{16}{21}[/tex]
Then, Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.
Given the rectangle below with length 8 and width 6
a) construct the midpoints of all four sides of the rectangle.
b) connect the midpoints to form another quadrilateral. What type of quadrilateral is formed? Justify your answer.
c) find the area of the quadrilateral you formed.
( There is a picture of a rectangle below. I'm willing to give all my points away.)
Answer:
a) Given in attachment.
b) Quadrilateral formed is a rhombus. Because length of all the sides are equal and angle between adjacent sides is not 90°.
c) 24 unit².
Step-by-step explanation:
Let rectangle be ABCD with length 8 and width 6
And mid-points be E,F,G,H
Now, join the mid-points .
we know that angle between adjacent sides in a rectangle is 90°.
⇒ ΔFAE forms a right angle triangle with 90° at A.
By, pythagoras theorem , EF² = AF² + AE²
⇒ EF² = 3² + 4² = 25
⇒ EF = 5;
In the same way, FG = GH = HE = 5
⇒ the quadrilateral is either square or rhombus.
Now, from ΔFAE, sin(∠AEF) = [tex]\frac{4}{5}[/tex]
(sinФ = opposite side / hypotenuse)
⇒ ∠AEF = 53°;
In similar manner;
∠DEH = 53° . Now ∠FEH = 180 - 53 - 53 = 74° (sum of angles on a straight line is 180°)
⇒ the quadrilateral is rhombus has angle between adjacent sides is 53° and not 90°.
Now, to find the area of rhombus, join EG and FH. And name the intersection point as J.
consider ΔEJF,
it is a right angled triangle at J, and also quadrilateral AFJE forms rectangle, as diagonals intersect perpendicular in a rhombus.
⇒ FJ = 3 and EJ = 4.
⇒ area of this triangle = 1/2 × base × height
= 1/2 × EJ × JF = 1/2 × 3 ×4 = 6
similarly triangles FJG, GJH, HJE.
⇒ area of rhombus = 6+6+6+6 = 24.
A question on a math test was to find the value of 15.12 divided by 2.4 Steve said the answer is 0.63 what mistake might Steve have made
Answer:
2.133333
Step-by-step explanation:
He didn't simplify it
Answer:
Step-by-step explanation:
She might have not moved the decimal point in the right direction/right spaces
I just need some help on number 7
Answer:
18 feet
Step-by-step explanation:
1 inch = 6 feet
3 * 6 = 18
PLEASE answer this I put the graph in the picture
There are 2000 pounds in 1 ton. How many tons is 7500 pounds?
Answer:
3 pounds and 3/4th of a pound
Step-by-step explanation:
2000 x 3 is 6000 and you have 1500 left
you can divide 2000 equally by 4 and get 500.
Multiply 500x3 and get 1500
(the 3 and the 4 is how i got the fraction)
6000+1500 = 7500
boom big brain answer good luck
In this question, we know that 1 ton = 2000
We're trying to find how many tons is 7500 tons.
In order to find your answer, you would divide 7500 by 2000 in order to know how many tons there are.
Divide:
7500 ÷ 2000 = 3.75
This means that there are 3.75 tons in 7500 pounds
Answer:
3.75 tons
The area of a triangle is given by the formula A=1/2bh. Solve this equation for the height, h, in terms of the base, b, and area, A.
The equation for the height, h, in terms of the base, b, and area, A is [tex]h = \frac{2A}{b}[/tex]
Solution:
Given that area of a triangle is given by the formula:
[tex]A = \frac{1}{2}bh[/tex]
Where,
A is the area of triangle
b is the base of triangle
h is the height of triangle
We have to find the equation for height in terms of base and area
So we have to arrange the equation in such a way that height can be found by using area and base
Given formula is:
[tex]A = \frac{1}{2}bh[/tex]
Keep "h" alone in L.H.S and move the other terms to other side of formula
[tex]A = \frac{bh}{2}\\\\2A = bh\\\\h = \frac{2A}{b}[/tex]
Thus height is expressed in terms of base and area
Let f(x) = 3x^2 – 8x + 5 and let g(x) = 2x – 8. Find
f(x) – g(x).
A.3x2 – 10x – 3
B.3x2 – 10x + 13
C.5x2 – 10x + 13
D.5x2 – 10x - 3
Answer:
B. 3x² – 10x + 13
Step-by-step explanation:
given:
f(x) = 3x² – 8x + 5
g(x) = 2x – 8
f(x) - g(x)
= (3x² – 8x + 5) - (2x – 8)
= 3x² – 8x + 5 - 2x + 8
= 3x² – 10x + 13
What is the solution to 5x-8y=-45 9x-8y=49
To find the solution to the system of equations 5x - 8y = -45 and 9x - 8y = 49, you can solve by elimination. The solution is x = 23.5 and y = 20.3125.
Explanation:To find the solution to the system of equations:
5x - 8y = -45
9x - 8y = 49
Subtract the second equation from the first equation to eliminate y. This gives you 5x - 9x = -45 - 49, which simplifies to -4x = -94.Solve for x by dividing both sides of the equation by -4. This gives you x = -94/-4, or x = 23.5.Substitute the value of x into one of the original equations to solve for y. Using the first equation, we have 5(23.5) - 8y = -45. Simplifying this equation gives you 117.5 - 8y = -45.Subtract 117.5 from both sides of the equation to isolate -8y. This gives you -8y = -45 - 117.5, which simplifies to -8y = -162.5.Solve for y by dividing both sides of the equation by -8. This gives you y = -162.5/-8, or y = 20.3125.What is 5 3/7 - 2 1/5?
Answer:
3 8/35 is the answer your welcome
What is the value of n in the diagram below?
Step-by-step explanation:
Picture############
Maria is planning a party. Nancy, her friend, suggests that she
should order 3 pizzas for every 7 people. If she is expecting 21
people at the party, how many pizzas should she order?
Answer:
9 pizzas
Step-by-step explanation:
Maria is planning a party. She should order 3 pizzas for every 7 people. Let x be the number of pizzas Maria will order for 21 people, then
3 pizzas - 7 people
x pizzas - 21 people
Write a proportion:
[tex]\dfrac{3}{x}=\dfrac{7}{21}[/tex]
Cross multiply:
[tex]7\cdot x=21\cdot 3\\ \\7x=63\\ \\x=\dfrac{63}{7}=9\ pizzas[/tex]