Answer:
The food will last for 25 days with 72 boys
Step-by-step explanation:
Proportions can be used to find the number of days the food will last for 72 boys.
60 boys in a hostel have food for 30 days.
Let x be the number of days for which the food will last
The proportion or product of both scenarios has to be same as the number of days and number of boys are proportional
Which means
[tex]60*30 = 72 * x\\x = \frac{60*30}{72}\\x = 25[/tex]
Hence,
The food will last for 25 days with 72 boys
In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle PNO = (x+14)^{\circ}m∠PNO=(x+14) ∘ , \text{m}\angle OPQ = (5x-2)^{\circ}m∠OPQ=(5x−2) ∘ , and \text{m}\angle NOP = (x-1)^{\circ}m∠NOP=(x−1) ∘ . Find \text{m}\angle OPQ.M∠OPQ.
Answer:
<OPQ = 23 degrees
Step-by-step explanation:
Given
Interior angles m∠PNO=(x+14) and m∠NOP=(x−1)
Exterior angle = m<OPQ = (5x-2)
The sum of interior angles is equal to the exterior angle, that is;
m∠PNO+m∠NOP = m<OPQ
x+14 + x-1 = 5x-2
2x + 13 = 5x-2
Collect like terms;
2x-5x = -2-13
-3x = -15
x = 15/3
x = 5
Get <OPQ
<OPQ = 5x - 2
<OPQ = 5(5)- 2
<OPQ = 25-2
<OPQ = 23 degrees
please help its the last one i need ! Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.
Answer:
See explanation
Step-by-step explanation:
The first option (4t - 8/5)... equals 16/3 t -23/5 (the fourth option in the first row)
The second option 7t - 22 (still in the first row) equals 3(3t-4)...(the third option in the second row)
The third option (still in the first row) 5(2t+1)... equals 3t + 33 (the final option in the second row)
The two options in the second row to the left equal each other
-11/4 t + 36 = (-9/2t + 3)+(7/4t + 33)
One hour after a hiker left camp, a biker set out to catch up. If the hiker traveled 3 miles per hour and the biker traveled 6 miles per hour faster, how long will it take for the biker to catch up with the hiker?
Answer:
30 minutes after biker left
Step-by-step explanation:
Given that :
Speed of hiker = 3 mph
Speed of biker = (3 +6) = 9 mph
Present Distance of hiker when the biker set out ;
Present Distance of hiker = speed * time = (3 * 1) = 3 miles
Time taken to catchup equals :
Present distance + (distance when biker set out) = bikers distance
Let time taken = x
(3 + (3 * x)) = (9 *x)
(3 + 3x) = 9x
3 + 3x = 9x
3 = 9x - 3x
3 = 6x
x = 3/6
x = 1/2 hours
x = 30 minutes
30 minutes after biker left
Answer:
0.5 hrs or 30 mins
Step-by-step explanation:
Guys is this correct? Look at the picture attached
It would be best to label the points if your turning it in. It can help people easily identify the points you've plotted.
From the looks of it, your equation is good.
The base is good and your math is right, but where did you get your height from?
If you count from point R up to line PQ you get 5 as the height.
I understand miscounting's a thing, no worries.
So if we input the correct height, we get A = 1/2 (3)(5)
1/2 * 15
7.5
The area of the polygon is 7.5 units.
I hope that helps and if you ever need any more help don't be afraid to reach out!
I need help with this .please help me
Answer:
Step-by-step explanation:
Upper left
a) 34y=15=
b) -58y=20=
c) -x=23=
d) -51=-y=
a) 34y=15
=> y= 34-15
=> y = 19
b) -58y=20
=> y= -58-20
=> y = -78
c) -x=23
=> -1x=23
=> x= 23+1
=> x= 24
d) -51= -y
=> -51= -1y
=> y= -51+1
=> y= -50
Hope it helps!
Tim has 80 coins in his piggy bank. Of these coins, 28 are nickels and the rest are quarters. What percent of the coins in the bank are quarters?
Answer:
65%
Step-by-step explanation:
Please help me. Solve for x state the properties used. 5(x - 2) - 6 = 24
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
5(x - 2) - 6 = 24
Step 2: Solve for x
Add 6 to both sides: 5(x - 2) = 30Divide 5 on both sides: x - 2 = 6Add 2 to both sides: x = 8Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 5(8 - 2) - 6 = 24Subtract: 5(6) - 6 = 24Multiply: 30 - 6 = 24Subtract: 24 = 24Here we see that 24 does indeed equal 24.
∴ x = 8 is the solution to the equation.
Please help fast as you can
Answer:
The elements of the set C will be:
C = {-2, -1, 0, 1, 2, 3, 4, 5}
In other words,
[tex]-2\le \:x<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2\le \:x<6\:\\ \:\mathrm{Interval\:Notation:}&\:[-2,\:6)\end{bmatrix}[/tex]
The solution number line is also attached below.
Step-by-step explanation:
C = {x ∈ Z | such that -2 ≤ x < 6 }
It is clear that the x ∈ Z, meaning the x belongs to the set of integers Z.
It is given that -2 ≤ x < 6.
so x must be greater than or equal to -2 and less than 6.
Therefore, the elements of the set C will be:
C = {-2, -1, 0, 1, 2, 3, 4, 5}
In other words,
[tex]-2\le \:x<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2\le \:x<6\:\\ \:\mathrm{Interval\:Notation:}&\:[-2,\:6)\end{bmatrix}[/tex]
The solution number line is also attached below.
5x + 10y > 40
Need help with this it says to graph but I know how to graph I just need help on simplifying the equation.
Answer:
x > -2y + 8
Step-by-step explanation:
How much money will we need to buy enough 12 packs for 168 people to
have 1 can each? Explain how you know.
Pls I need it now
find the value of x and the measures of the missing angles
Answer:
Step-by-step explanation:
m∠X + m∠Y + m∠Z = 180 {angle sum property of triangle}
3x + 5 + 40 +4x - 5 = 180
3x + 4x + 5 + 40 -5 = 180 {Combine like terms}
7x + 40 = 180 { subtract 40 from both sides}
7x = 180 - 40
7x = 140
x = 140/7
x = 20
m∠X = 3x + 5
= 3*20 + 5
= 60 + 5
m∠X = 65
m∠Z = 4x - 5
= 4*20 - 5
= 80 - 5
m∠Z = 75
What is the simplified form of the expressions?
a. −6a2b−1
b. 5/y−3
In ΔQRS, r = 380 cm, s = 390 cm and ∠Q=48°. Find the length of q, to the nearest centimeter.
Step-by-step explanation:
Using Cosine rule, we have:
q² = r² + s² - 2(r)(s)(cosQ)
= 380² + 390² - 2(380)(390)(cos48°)
= 98169.688cm²
Hence q = 313cm. (nearest centimeter)
The required value of side q is 313 cm for the triangle ΔQRS.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
In triangle QRS side r = 380 cm, side s = 390 cm and angle Q = 48°.
To find the length of the side q,
Use cosine rule,
[tex]cos Q = \frac{(r^2 + s^2 - q^2)}{(2\times r \times s)}[/tex]
Substitute the values here,
[tex]cos 48 = \frac{(380)^2 + (390)^2- q^2}{2\times380 \times390} \\[/tex]
[tex]0.67 = \frac{144400 + 152100 - q^2}{296400}[/tex]
198,588 = 296500 - q²
q² = 97912
q = 312.90
q = 313 cm
The value of side q is 313 cm.
To know more about Triangle on:
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If Rachel can reach 91 inches high, AC = 2x, and BC= 5x+7, how tall is the object she's
reaching for (AC)?
a) 24 inches
b) 13 inches
c) 67 inches
d) 91 inches
Answer:
d 91
Step-by-step explanation:
she is reaching it perfectly at this height in the problem, its super easy
Josh runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Answer:
6 / 55 = x / 44
44*6/55= x
x = 4.8 miles
Step-by-step explanation:
Find the sum. You may find using a number line to be helpful. Victor borrowed $20.50 from his mother to go to the theater. A week later, he paid her $20.50 back. How much does he still owe her?
Subtract the amount he paid his mother back from the amount he borrowed from her:
20.50 - 20.50 = 0
He does not owe his mother any more.
ach light bulb at Hotel California is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and ninety percent of the fluorescent bulbs are switched on. If eighty percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent
Answer:
10%
Step-by-step explanation:
The computation of the percentage of bulbs that switched on incandescent is as follows;
Let us assume the incandescent be I
And, the fluorescent be F
Now the equation is
0.4I + 0.9F = 0.8 (I+F)
0.41I + 0.9F = 0.8I + 0.8F
So here
0.4I = 0.1F
Now the percentage would be for incandescent in the case of switched on is
= 0.4I ÷ 0.8(I+F) × 100
= 0.1F ÷ 1F
= 10%
Write an equation of the line passing through the point (2, 10) that is perpendicular to the line 2x+y=17.
Answer:
y = 0.5x + 9
Step-by-step explanation:
What we know:
An equation with the point (2,10) passing through it is perpendicular to the equation 2x+y=17.
The root of 2x+y=17 is (8.5, 0).
The two equations intersect at (3.2, 10.6)
Let's check if 3.2 and 10.6 work for 2x+y=17.
2(3.2) + 10.6 = 17
6.4 + 10.6 = 17, which is true.
Let's try y = 0.5x + 9, to see if we get the same output as the earlier equation.
y = 0.5(3.2) + 9
y = 1.6 + 9
y = 10.6, so 3.2 as x does work.
As a result, the perpendicular equation is y = 0.5x + 9.
A system of equations is shown on the graph below.how many solutions does this system have
Answer:
1
Step-by-step explanation:
A solution to a system of equations is the point where the 2 lines meet.
simplify:
4 x - -5х + 3x- x+2х - 7х
Answer:
6x
Step-by-step explanation:
4 x - -5х + 3x- x+2х - 7х
Combine like terms so, so since all are the same you just do the operation they want u to do..
4x + 5x= 9x
9x + 3x = 12x
12x - x = 11x
11x + 2x= 13x
13x - 7x = 6x
Hint: 2 negatives make a postitive
Hint: in there is just an "x" there is always an invisible one in it... 1x
Hope this helped!
What polynomial should be subtracted from 3x^2+4x-1 to get the difference equal to 1
=====================================================
Explanation:
Assume the polynomial we want to find is in the form Ax^2+Bx+C
The goal is to find the values of A, B, and C.
We start with 3x^2+4x-1, then we subtract off Ax^2+Bx+C. Set this equal to 1 and we get:
(3x^2+4x-1) - (Ax^2+Bx+C) = 1
3x^2+4x-1 -Ax^2-Bx-C = 0x^2 + 0x + 1
(3x^2-Ax^2) + (4x-Bx) + (-1-C) = 0x^2 + 0x + 1
(3-A)x^2 + (4-B)x + (-1-C) = 0x^2 + 0x + 1
From here we equate the coefficients of the x^2 terms together and we see that 3-A = 0 which leads to A = 3.
Do the same for the x terms to get 4-B = 0 leading to B = 4
Finally, we have -1-C = 1 lead to C = -2
The polynomial Ax^2+Bx+C becomes 3x^2+4x-2
-------------------
Checking the answer:
(3x^2+4x-1) - (Ax^2+Bx+C)
(3x^2+4x-1) - (3x^2+4x-2)
3x^2+4x-1 - 3x^2-4x+2
(3x^2-3x^2) + (4x-4x) + (-1+2)
0x^2 + 0x + 1
0 + 0 + 1
1
We get a difference of 1, so the answer is confirmed.
the pta wants to cover the wet areas of the trail with wood chips. they find that one bag of wood chips covers 3 1/2-yard section of the trail. if there is a wet section of the trail that is approximately 50 1/4 yards long, how many bags of wood chips are needed to cover the wet section of the trail?
PLEASE THIS IS DUE IN 1 HOUR
Laila is setting up a conical tent in the backyard. The height of the tallest part of the tent is 7 feet. The inside of the tent has a volume of 56 cubic feet. How many square feet are covered by the base of the tent?
Answer: 24
Step-by-step explanation:
I got it right on edge
Answer:
Answer is 24
Step-by-step explanation:
ywwww :)
#DJPP
What is the product of (2x – 1)
(3x + 3)?
Answer:
6x^2 + 3x - 3
Step-by-step explanation:
Using the FOIL method, we would multiply 2x by 3x, then multiply 2x by 3, then multiply -1 by 3x, then multiply -1 by 3. This would bring the answer to 6x^2 + 6x -3x - 3. Combine the like terms 6x and -3x and you get 6x^2 + 3x - 3
In order for the parallelogram to be a rectangle x=
Answer:
x = 2
Step-by-step explanation:
Set the two equations 13x+34 and 10x+10 together to add up to 90 on the right which should look like this 13x + 34 + 10x + 10 = 90. Combine the two x-values to get 23x and the two other numbers to get 44. Your equation should now be 23x + 44 = 90. Subtract 44 on both sides to get this equation 23x = 46. Divide 23 on both sides to get your x value which is 2.
Answer:
X is equal to 2
Step-by-step explanation:
90 = 13x + 34 + 10x + 10
Combine Like Terms:
90 = 23x + 44
Subtraction Property of Equality:
90 - 44 = 23x + 44 - 44 ---> 46 = 23x
Division Property of Equality:
46 ÷ 23 = 23x ÷ 23 ---> 2 = x
Check Your Work:90 = 13x + 34 + 10x + 10
Fill In Variables:
90 = 13(2) + 34 + 10(2) + 10
90= 26 + 34 + 20 + 10
90 = 60 + 30
90 = 90
On the number line below, P represents a number. What is the value of the opposite of that number?
Regina's father has 3 1/2 cups of pudding to divide equally among Regina and her 3 friends. How many cups of pudding does each person receive?
Answer:
The answer is .875 cups of pudding for each person
Step-by-step explanation:
To solve this problem you will have to divide 3 1/2 among 4 people.
3 1/2 divided by 4 is equal to .875
what is the value of f(5) in f(x)=-2(x+1)
Answer:
-12
Step-by-step explanation:
someone please help me with this !
Step-by-step explanation:
The coordinates of Point S(1,2)
The coordinates of point T(7,5)
length of ST=√(7-1)²+(5-2)²
|ST|=√36+9
|ST|=√45=3√5
Answer:
a) S(1,2) T(7,5)
b)3√5 = 6.7 ( approximately)
Step-by-step explanation:
Look at the picture below.
Hope you find this helpful