Answer:24
Step-by-step explanation:
Small scooters cost £80 and large scooters cost £130. A school buys few scooters for the playground for £1000. How many of the smaller and larger scooter did they buy?
Answer:
Small scooters = 6
Large scooters = 4
Step-by-step explanation:
Let S represents small scooter and L represents large scooter
The cost of a small scooter is £80
Mathematically, the cost of S number of small scooters is
80S
The cost of a large scooter is £130
Mathematically, the cost of L number of large scooters is
130L
The total amount spent on both scooters is £1000
Mathematically,
80S + 130L = 1000
So we have 2 unknowns and only 1 equation. Therefore, we have use trial and error method .
Trial and Error Method:
80S + 130L = 1000
80S = 1000 - 130L
S = (1000 - 130L)/80
Let’s suppose they bought 1 large scooter
S = (1000 - 130(1))/80
S = 10.875
Number of scooters cannot be in fraction so 1 doesn’t work
Let’s suppose they bought 2 large scooter s
S = (1000 - 130(2))/80
S = 9.25
Number of scooters cannot be in fraction so 2 doesn’t work
Let’s suppose they bought 3 large scooter s
S = (1000 - 130(3))/80
S = 7.625
Number of scooters cannot be in fraction so 3 doesn’t work
Let’s suppose they bought 4 large scooters
S = (1000 - 130(4))/80
S = 6
So that means they bought 6 small scooters and 4 large scooters.
Similarly, other combinations for scooters don’t work since they yield either fractional value or negative value which cannot be correct.
Therefore, the only possible combination of small and large scooters is
6 Small scooters
4 Large scooters
Verification:
80S + 130L = 1000
80(6) + 130(4) = 1000
480 + 520 = 1000
1000 = 1000 (satisfied)
PLZZZZ HELP MEEEEE I WILL GIVE BRAINLIST ‼️‼️‼️‼️‼️‼️‼️‼️‼️
Answer:
|-3| - |6| = 9
| 6 - -3| = | 6+3| = 9
Step-by-step explanation:
The distance between points is given by
d = sqrt( (x2 -x1) ^2 + (y2-y1) ^2 )
Since the y coordinates are the same
d = sqrt( (x2 -x1) ^2 )
d = sqrt( x2-x1)^2)
Or the distance between the two points
The distance between them is 9 units
|-3| - |6| = 9
| 6 - -3| = | 6+3| = 9
What is the decimal multiplier to increase by 4.1%?
Answer:
1.041.
Step-by-step explanation:
4.1 % = 4.1 / 100 = 0.041 as a decimal fraction.
So ehen we increase a quantity by 4.1% we multiply by 1.041.
NEED HELP ASAP!!!!!
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Answer:
20,000 is the length of the book with 20,000 pages.
Saturn is 8.867 × 108 miles away from the Sun. Uranus is 1.787 × 109 miles away from the Sun. Approximately how many times farther is Uranus from the Sun than Saturn is?
A. 0.2 times
B. 2 times
C. 20 times
D. 200 times
Answer:
Uranus is approximately 5 times farther from the sun than Saturn. The smallest zero is x = -10 as its the left-most value on a number line.
Step-by-step explanation:
Saturn:8.867 x 108 = 957. 636
Uranus: 1.787 x 109 = 194.783
b. 2 times
Answer:
a = 0.2 times
Can someone help me on this please
(sin5-sin15+sin25-sin35)/(cos5-cos15-cos25+cos35) =cot10
Answer:
Step-by-step explanation:
(sin5-sin15+sin25-sin 35)/(cos 5-cos 15+cos 25 +cos 35)[tex]=\frac{-(sin 35-sin 5)+(sin 25-sin 15)}{(cos 35+cos 5)-(cos 25+cos 15)} \\[/tex]
[tex]=\frac{-2 cos \frac{35+5}{2}sin \frac{35-5}{2}+2 cos \frac{25+15}{2} sin \frac{25-15}{2} }{2cos \frac{35+5}{2}cos \frac{35-5}{2}-2cos \frac{25+15}{2} cos \frac{25-15}{2} }[/tex]
[tex]=\frac{-cos 20 sin 15+cos 20 sin 5}{cos 20 cos 15-cos 20 cos 5} \\[/tex]
[tex]=\frac{- cos 20(sin 15-sin 5)}{cos 20(cos 15-cos 5)}[/tex]
[tex]=\frac{-(sin 15-sin 5)}{cos 15-cos 5)} \\=\frac{-2cos \frac{15+5}{2}sin \frac{15-5}{2} }{-2 sin \frac{15+5}{2}sin \frac{15-5}{2} } } }[/tex]
[tex]=\frac{cos 10 sin 5}{sin 10 sin 5}[/tex]
[tex]=\frac{cos 10}{sin 10}[/tex]
=cot 10
Please can someone help! I will mark you branliest!
This year (10 years after you first took out the loan), you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $112,681 left to pay on your loan. Your house is now valued at $190,000. Your current situation How much of the original loan have you paid off? (i.E, how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
Answer:
The below is the first of paragraph in the question which is missing:
Suppose that 10 years ago you bought a home for $150,000, paying 10% as a down payment, and financing the rest at 8% interest for 30 years.
$22,319.00
Step-by-step explanation:
In order to determine the portion of the original loan that has been paid off,we need to ascertain the original loan amount as below:
loan amount=purchase price of the home-down payment
purchase price is $150,000
down-payment =10%*$150,000=$15,000
loan amount=$150,000-$15,000=$135,000
If the loan amount has reduced to $112,681,hence the loan amount paid off is the difference between the original loan amount and the balance now:
original loan paid off=$135,000-$112,681=$22,319.00
Solve for x in the equation 2 x squared + 3 x minus 7 = x squared + 5 x + 39.
Answer:
its D
Step-by-step explanation:
on edge
A rhombus has side lengths of 25. What could be the lengths of the diagonals? *
Answer:
0 < x < 50
Step-by-step explanation:
We start out with a square (which IS a rhombus for all sides are equal in
length. That's when the diagonals are equal in length, which, by the
Pythagorean theorem equal to
5*√2
C^2=a^2+b^2
=25^2+25^2
Factorise
c^2=25^2 × 2
c=square root of 25^2 × 2
That is
c=√25^2 × 2
=5×√2
As we decrease the angle on the bottom left and increase the angle on
the bottom right, the green diagonal increases to 25+25 or 50, but never gets to 50. The red diagonal shrinks to 0 but never gets to 0.
the lengths of a diagonal can only be in the open interval from 0 to 50. In interval notation that is (0,50) or 0 < x < 50.
Answer:
Minimum value: 0, Maximum value: 50
Step-by-step explanation:
A rhombus is a quadrilateral with side of same length but different angle pairs. Let consider the following rhombus (See attachment). It is known that sum of all angles in quadrilateral is equal to 360°. The length of each diagonal is, respectively:
[tex]d_{1} = 2\cdot l\cdot \sin 0.5\alpha[/tex]
[tex]d_{2} = 2\cdot l \cdot \sin (90-0.5\alpha)[/tex]
[tex]d_{2} = 2\cdot l \cdot (\sin 90^{\circ}\cdot \cos 0.5\alpha - \cos 90 \cdot \sin 0.5\alpha)[/tex]
[tex]d_{2} = 2\cdot l \cdot \cos 0.5\alpha[/tex]
Each expression shows that value of a diagonal changes at the expense of the other one inasmuch angle changes. The minimum and maximum values of any of the diagonal occur when trigonometric functions are equal to 0 and 1, respectively.
Minimum value: [tex]d_{min} = 0[/tex], Maximum value: [tex]d_{max} = 2\cdot l = 2 \cdot (25) = 50[/tex]
find the values of t6 and d for the arithmetic sequence with t6= 4 and t10= -4
Answer:
t1 = 14 d= -2
Step-by-step explanation:
tn = t1 + d ( n-1)
t6 = t1 + d(6-1)
4 = t1+ 5d
t10 = t1 +d (10-1)
-4 = t1 +d9
Take the two equations and subtract to eliminate a1
4 = t1+ 5d
- (-4 = t1 +d9)
-------------------------
4 = t1+ 5d
+4 =- t1 -d9
-------------------------
8 = -4d
Divide each side by -4
8/-4 = -4d/-4
-2 =d
Now we can find t1
4 = t1+ 5d
4 = t1 + 5(-2)
4 = t1 -10
Add 10 to each side
4+10 = t1
14 = t1
Answer:
A
Step-by-step explanation:
t1 = a
tn = a + (n-1)d
t6 = a + 5d = 4
a = 4 - 5d
t10 = a + 9d = -4
4 - 5d + 9d = -4
-8 = 4d
d = -2
a = 4 - 5(-2)
= 4 + 10
= 14
The perimeter of the triangular park shown on the right is 12x - 6. . What is the missing length?
Answer:
8x-4
Step-by-step explanation:
3x-3+x+1+?=12x-6
4x-2+?=12x-6
4x+?=12x-4
?=8x-4
Therefore, 8x-4
Evaluate cosθ when sinθ = -7/8 and θ is in Quadrant IV.
Answer:
cosθ= [tex] \frac{ \sqrt{15} }{8} [/tex]
Step-by-step explanation:
Please see attached picture for full solution.
In the 4th quadrant, the cosine of an angle is positive.
The opposite side takes the negative sign in -⅞ since it is below the x-axis. Likewise, we reject [tex]x = - \sqrt{15} [/tex] since x lies on the right side of the y axis.
What is the length of the missing side? Hint: use the Pythagorean Theorem.
Answer: To find the missing length= WX= √9^2+12^2
WX= 15
Step-by-step explanation:
Bryan's hockey team is purchasing jerseys. The company charges $ 250 for a onetime set-up fee and $ 23 for each printed jersey. Expression represents the total cost of x number of jerseys for the team?
Answer:
$250 + $23x
Step-by-step explanation:
One time set-up fee for jerseys = $250
cost of one jersey = $23
therefore, cost x jersey = cost of one jersey*x = 23x
Total cost for this deal will be sum of One time set-up fee for jerseys and cost x jersey
Total cost = One time set-up fee for jerseys + cost x jersey
Total cost = $250 + $23x
Expression represents the total cost of x number of jerseys for the team is $250 + $23x.
Of 25 test scores, 8 are less than or equal to 75. What is the percentile rank of a test score of 75?
a. 8
b. 17
c. 32
d. 68
How to add polynomials in brackets
PLZ HELP!
Round your answer to the nearest hundredth.
A
9
7
?
B.
С
Answer:
Angle B = 51.06 degrees
Step-by-step explanation:
arcsin(7/9)=Angle B
Therefore, Angle B = 51.06 degrees
65 m
16 m
b
What is the length of the missing leg?
Answer:3,969[tex]^{2}[/tex](squared) or 63
Step-by-step explanation:
First you must plug the answers into the equation A[tex]^{2}[/tex] + B[tex]^{2}[/tex]=C[tex]^{2}[/tex]
Then you square the numbers. example: 2[tex]^{2}[/tex]=2 x 2=4
After that you subtract from both sides of the equation to get the variable by itself. Example: 4+b[tex]^{2}[/tex]=10
-4 -4
b[tex]^{2}[/tex]=10
After that you square both sides or you could say answer[tex]^{2}[/tex]
Which data collections are considered a census? Select all that apply.
a. Ally wants to find out the favorite food of students in her math class, so she surveys the first
ten students who walk into class.
b. Isaac wants to find out the least favorite school subject of the students in his science class, so
he surveys all the students in science class.
c. Malik wants to find out how much time seventh graders in his school spend doing homework
each night, so he surveys the 13-year-old boys in the seventh grade.
d. Emily wants to find out how much time soccer players on her team spend practicing on their
own each week, so she surveys each girl on the team.
e. Lucas wants to find out the favorite song of the singers in his school chorus, so he surveys his
close friends in the chorus.
Answer: Choice B.
Step-by-step explanation:
Censuses are complete data collections of every member of a population.
For example, the U.S. Census occurs every 10 years and documents every member of the American population.
Choice A only surveys the first ten students; this is not a complete census.
Choice B surveys all the students in the targeted data group. This is a census.
Choice C only surveys the male students, even though there are female students in his data group. This is not a census.
Choice D only surveys the girls on the soccer team, even though there may be boys on the team as well. This is not a census.
Choice E only surveys his friends in the chorus, even though there may have been people that were not his close friends. This is not a census.
Only choice B is a complete census.
Answer:
choice B
Step-by-step explanation:
because choice b is the only complete census
Solve the triangle m<N= 118°, m<P= 33° and m=15. Round to the nearest tenth. Please show work.
Answer:
M = 29
27.31838095 = n
16.8511209 = p
Step-by-step explanation:
M = 180 -33-118 = 29
We can use the rule of sines
sin A sin B sin C
------------ = ---------- = ------------
a b c
sin 118 sin 29
------------ = ----------
n 15
Using cross products
15 sin 118 = n sin 29
Divide by sin 29
15 sin 118 / sin 29 = n
27.31838095 = n
sin 33 sin 29
------------ = ----------
p 15
Using cross products
15 sin 33 = p sin 29
Divide by sin 29
15 sin 33 / sin 29 = p
16.8511209 = p
Find the meeting point of these two rights: y = 5x - 6 and y = -4x + 3
The meeting point is (1, - 1).
Look at the attachment to see.
Happy to help!
Solve the following: a) 3x2+ 4 9.5 b) 7+2x 5
Answer:
a= 55.5
b= 45
hope it is helpful for u
Please help, this is worth a lot to me
If the height of a parallelogram is 4 times more than it’s base, and the area is 221 sq in, what is the base and height?
Answer:
Base = 13in
Height = 17in
Step-by-step explanation:
Step-by-step explanation:
height of a parallelogram = 4 times more than it’s base
Let height = H
Base = B
H = 4 + B
area of the parallelogram = 221 in²
area of the parallelogram = base × height
221 = B × H = B × (4+B)
221 = 4B + B²
B² + 4B - 221 = 0
Using almighty formula to find B
See attachment for explanation
From the calculation:
Since the dimension of the parallelogram can't be negative, B = 13in
Height = B + 4 = 13+4
Height = 17in
Answer:
Base = 13 inches
Height = 17 inches
Step-by-step explanation:
The formula to find the area of a parallelogram = Base × Height
Let's represent Base = B
Height = H
From the question, the height is 4 times more than the Base
Height(H) = B + 4
Area = 221 square inches
Therefore, area of a parallelogram = Base × Height
221 sq in = B ×( B+4)
221 sq in = B² + 4B
B² + 4B - 221 = 0
We would solve the quadratic equation using factorisation method. Hence,
B² + 17B - 13B - 221 = 0
(B²+ 17B) - (13B - 221) = 0
B(B + 17) - 13(B + 17) = 0
(B + 17) (B - 13) = 0
B + 17 = 0
B = - 17
Or
B - 13 = 0
B = 13.
From the above calculation, since B = Base
B = -17 inches Or 13 inches
The base of a parallelogram cannot be negative, hence , The Base of the Parallelogram = 13 inches.
We are told that the height of the Parallelogram is 4 times more than the Base. This was represented but the equation
B + 4 = H
Since B = 13 :
13 + 4 = H
Height(H) = 17 inches.
Therefore, The base of the Parallelogram is 13 inches while the height of the Parallelogram is 17 inches.
A skydiver descends at 20 1 3 kilometers per hour after deploying their parachute. Which of the following expressions represents the change in the skydiver's altitude if they descend for 4 7 of an hour?
1250mph you'd tear through the crust of the earth and create a supervolcano to end all of us.
Step-by-step explanation:
Never fall that fast when parachuting, only you can prevent supervolcanoes.
Please help!!! Idk how to do this.
Answer:
Hello! I think x= 1.6 or 1.3 in this situation
Step-by-step explanation:
The fact that the number 7 on the left quadrilateral is 6.3, and the 4's are 3.6, I have come to the conclusion that x equals either 1.6 or 1.3.
In the figure, find m∠ABD if m∠ABC = 85° and m∠DBC = 61°.
Question 3 options:
A)
24°
B)
5°
C)
146°
D)
29°
Answer:
A. 24°
Step-by-step explanation:
ABC is 85° which is the whole angle. DBC is a part of ABC and is 61°. If we do 85-61=24. The answer would be 24°.
PLZ MARK BRAINLIEST!!!
If m ∠ABC=85° and m ∠DBC=61° then m angle ABD=24°. Hence the option A is correct.
What is an angle?
An angle is the figure formed by two sides of a figure , sharing a common endpoint, called the vertex of the angle.
How to determine angle between lines?From the given figure we can conclude that ∠ABD=∠ABC-∠DBC.
We have been given that m ∠ABC=85° and m ∠DBC=61°
∠ABC=85/m and ∠DBC=61/m
Put in the above equation
∠ABD=∠ABC-∠DBC
∠ABD=85/m-61/m
=24/m
we have been find m ∠ABD so we have to multiply 24/m by m is 24°.
Hence the value of m angle ABD=24 degrees.
Learn more about angles at https://brainly.com/question/25716982
#SPJ2
An animal shelter houses dogs, cats, and rabbits. There are 126 animals at the shelter. Of the animals, 13 are cats. Three fourths of the remaining animals are dogs. How many of the animals are rabbits? Show your work.
Answer:
28 rabbits
Step-by-step explanation:
From the statement, you can write the following:
d+c+r= 126
d=dogs
c= cats
r= rabits
Then, you have that there are 13 cats and that three fourths of the remaining animals are dogs:
c=13
d=(126-13)*(3/4)= 113*(3/4)= 85
Now, you can isolate r, to find the number of rabbits:
r=126-d-c
r= 126-85-13
r= 28
According to this, the are 28 rabbits.
Answer:
pppoooooiiinnttssss
Step-by-step explanation: