Using proportions, it is found that the average speed of the motorcycle is of 64 km/h.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, in one and one-quarter hours, that is, [tex]\frac{1} + \frac{1}{4} = 1.25[/tex] hours, the car traveled 20 km farther, hence the number of km/h by which the car is faster is given by:
f = 20/1.25 = 16 km/h.
The car's velocity was of 80 km/h, hence the average speed of the motorcycle is given by:
m = 80 km/h - 16 km/h = 64 km/h.
More can be learned about proportions at https://brainly.com/question/24372153
An architect creates a scale model of a building with a scale of 5 cm =4 m. If the actual building is 32 m tall, how tall is the scale model?
A.8
B.25.6
C.33
D.40
The height of the building on the scale model created by the architect is 40 centimeters long.
What is scale factor?Scale factor is the factor which is used to enlarge or smaller the original figure.
Scale factor is the ratio of representation measurement of the figure to the original figures.
The architect creates a scale model of a building with a scale of,
[tex]\rm 5 \;cm =4 \; m[/tex]
As, one meter is equal to 100 centimeters. Thus, the scale factor used by the architect for the building is,
[tex]r=\dfrac{5}{400}\\r=\dfrac{1}{80}[/tex]
Now the actual building is 32 m tall. Let suppose the height of the building on the model is x meters. Thus, the scale factor for this can be given as,
[tex]r=\dfrac{x}{3200}[/tex]
Now, both the scale factor are of the same model. Therefore,
[tex]\dfrac{x}{3200}=\dfrac{1}{80}\\x=40\rm cm[/tex]
Hence, the height of the building on the scale model created by the architect is 40 centimeters long.
Learn more about the scale factor here;
https://brainly.com/question/10253650
what is the vertex of f(x)=x2+10x+7
What are the domain and range of the relation given in the table?
y
X
5
5
10
9
15
-1
19
5
32
domain: {10, 15, 19, 32} range: {-1, 5, 9}
domain: {-1,5, 9} range: {10, 15, 19, 32}
O
domain: {10, 15, 19, 32} range: {yly € R}
O domain: {z|3 ER} range:{-1, 5, 9}
Answer:
domain: {10, 15, 19, 32} range: {-1, 5, 9}
Step-by-step explanation:
the x values are the domain, while all the y values are the range
Please help with this asappppppppll
We are given with a circle and we need to find the equation of the circle , but first let's recall that , the equation of a circle with radius 'r' and centre at (h,k) is given by [tex]{\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}[/tex]
Now , here as as the circle cuts the +ve x-axis at (9,0) . So , it's radius is 9 units or the 2nd way is to measure the distance from centre of the circle to the point where the circle cuts the graph , as the centre is at Origin , so here (h,k) = (0,0) .Which means that the centre is located at the point whose coordinates are (0,0) which is also known as origin . Now , finding the equation of the circle :-
[tex]{:\implies \quad \sf (x-0)^{2}+(y-0)^{2}=(9)^{2}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x^{2}+y^{2}=81}}}[/tex]
This is the required equation of Circle
1) Change the rate, 45 miles per 5 gallons to a unit rate per gallon.
Answer:
9
Step-by-step explanation:
45 mph per 5 gallons
45 ÷ 5
or
45/5
=
9
Unit Rate per Gallon is 9
A fireperson needs to use a ladder of 25 feet in length to rescue a cat that has become
stuck in a tree. The tree is 50 feet high, and the cat is 15 feet off the ground straight up in the
trunk of the tree. How far from the bottom of the tree will the ladder have to be in order to
reach the point at which the cat is?
A.15
B.20
C.25
D.30
E.135
Answer:
A, because the cat is only 15 feet in the air and the TREE is 50 feet
whats the answer to 3 sqaured plus 2x equals 7
Answer:
Step-by-step explanation: 3²+12²=x² simplifies to 9+144=x² so 153=x² or x²=153.
Which statement about the hyperbola is true?
Answer:
The point is (3,0) is a vertex.
true statements for this hyperbola:
The focus for this hyperbola is at (5,0) and (-5,0)The point is (3,0) is a vertex.The transverse axis passes through (0,0)Transverse endpoint axis is more, which is not visible in this graph.Jason is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee is $25 and the one-time joining fee is $100. Make a table of values and then write an equation for C,C, in terms of t,t, representing the total cost of the gym membership over tt months. Number
Answer:
C = 100 + 25t
Step-by-step explanation:
where is the nokia and who has it
Answer:
Headquarters in Espoo since September 2019
Founded 12 May 1865 in Tampere, Grand Duchy of Finland Russian Empire
Founders Fredrik Idestam Leo Mechelin Eduard Polón
Headquarters Espoo , Finland
Area served Worldwide
19 more rows
Step-by-step explanation:
Jim is running a race against his best friend Ryan. Jim runs at a rate of 6 miles per hour while Ryan runs at a rate of 11 miles in 2 hours. Which person is running the fastest
Answer:
Its Jim
Step-by-step explanation:
I got Ryan running at 5 1/2 miles per hour, while Jim runs at 6 miles per hour.
Help me asap please I need this now
Answer:
D
Step-by-step explanation:
Because y intercept is -25
so in D it says - 25
Multiply the expressions below. Then simplify if possible. a. 2x(3x – 4) b. (x+3)(2x-5) C. (2x + 5)(2x – 5) d. X(2x + 1)(x-3)
Answer:
a) 6x² - 8x
b) 2x² + x - 15
c) 4x² - 25
d) 2x³ + 7x² - 3x
Step-by-step explanation:
a) 2x (3x - 4)
brackets means multiplication or into
base on the question
2x * 3x = 6x^2
and
2x * (-4) = -8x
therefore
6x² - 8x
is the answer
b) (x + 3) (2x - 5)
clear brackets with (x + 3)
i. x * (2x - 5) = 2x^2 - 5x
ii. +3 * (2x - 5) = 6x - 15
add i add ii
2x² - 5x + 6x - 15
if u noticed, there are similar figures 6x and 5x, so we take like term
2x² + x - 15 answer
c) (2x + 5) (2x - 5)
clear bracket
i. 2x * (2x - 5) = 4x² - 10x
ii. 5 * (2x - 5) = 10x - 25
add i and ii
4x² - 10x + 10x - 25
collect terms
4x² - 25 answer
d) x (2x + 1) (x - 3)
I) first we deal with x(2x+1)
x * (2x + 1) = (2x² + x)
II) then we find the multiplication of
(2x² + x) (x - 3)
i. 2x² * (x - 3) = 2x³ - 6x²
ii. x * (x - 3) = x² - 3x
add i and ii
2x³ - 6x² + x² - 3x
collect terms
2x³ - 5x² - 3x
Find the radius of a circle with:
Circumference of 24 pi cm
Answer:
r ≈ 3.82
Step-by-step explanation:
Using the formula:
C = [tex]2\pi r[/tex]
We rearrange to get r as the subject:
r = [tex]\frac{C}{2\pi }[/tex]
r = 24÷(2×[tex]\pi[/tex])
r ≈ 3.82
What is the 8th term of the geometric sequence with this explicit formula?
an = 6.(-2)(n-1)
Answer:
-768
….......
Substitute n = 8 into the explicit formula
[tex]a_{8} = 6[/tex] × [tex](-2)^{7}[/tex]= [tex]6[/tex] × [tex]-128[/tex]
= -768
A credit of $35 and a debit of $40 are applied to your bank account. What integer represent integer represents "a credit of $35" if zero represents the original balance
29
Which expression represents the product of 3 and (n + 1.8) ?
A 5.55
B 9.15n
C 3.75 + 1.8
D 3.75 + 5.4
Answer:
D
Step-by-step explanation:
it is a strange question. but I guess its meaning is to identify an expression that is structured in the same way as the generic basic expression.
3×(n + 1.8)
after doing the multiplication this gives us
3n + 3×1.8 = 3n + 5.4
so, the only answer option including 5.4 is D.
it would mean that 3n = 3.75. n = 1.25
but just to show you how strange this question is, let's have a look at the other answer options :
is 5.55 = 3n + 5.4 ?
it would mean
0.15 = 3n
n = 0.05
so, formally, this is also an expression that represents the original expression.
9.15n = 3n + 5.4
6.15n = 5.4
n = 5.4/6.15 = 0.87804878...
so, formally, this is also an expression that represents the original expression.
3.75 + 1.8 = 3n + 5.4
5.55 = 3n + 5.4
and we are back to A and therefore, formally, this is also an expression that represents the original expression.
so, many greetings from me to your teacher. he/she has to be more careful about how to phrase questions.
because here, formally, all 4 answers are theoretically correct.
Select the statement that describes the expression 6 + (8 ÷ 2) − 3.
6 times the quotient of 8 and 2, then subtract 3
Add 6 to the product of 8 and 2, then subtract 3
Add 6 to the difference of 8 and 2, then subtract 3
Add 6 to the quotient of 8 and 2, then subtract 3
Answer:
add 6 to the quotient of 8 and 2 by the subtraction of 3
Answer:
add 6 to the quotient of 8 and 2 by the subtraction of 3
Step-by-step explanation:
Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
In class, pairs of students were given numbers to work with. In each pair, one student found the greatest common factor and the other student found the least common multiple.
Jess and Nate were given the numbers 8 and 12.
Jess found that the greatest common factor is 4.
Nate found that the least common multiple is 48.
One of these students made a mistake.
Which student made a mistake?
What number should the student have found instead?
Answer:
Nate made a mistake. He should have got 24 as Least common factor.
Step-by-step explanation:
Given number are 8 and 12.
To find the GCF or LCF we have to list multiples.
For LCF
List the multiples of each number until at least one of the multiples appears on all lists.Find the smallest number that is on all of the lists.This number is the LCM.For GCF
List the multiples of each number until at least one of the multiples appears on all lists.Find the Biggest number that is on all of the lists.This number is the GCFThe least common multiple of 8 and 12 is 24.
The Greatest common multiply of 8 and 12 is 4.
Hence, Nate is wrong. Nate should have found 24.
[RevyBreeze]
You are decorating a cake with 15 roses. You want an equal number of roses in each of the 3 rows on the cake. Which equation would you use to find the number of roses, r, in each row?
a) For AQMNO use the Triangle Proportionality Theorem to solve for x. OMN
Answer:
x = 12 unitsperimeter = 113 unitsGiven for big triangle:
MN = 36MO = 3x + 9 + 15 = 3x + 24Given for small triangle:
side 1 : 36 - 9 = 27side 2 : 3x + 9setting up proportionality:
[tex]\hookrightarrow \sf \dfrac{36}{3x+24} = \dfrac{27}{3x+9}[/tex]
[tex]\hookrightarrow \sf 36(3x+9) = 27(3x+24)[/tex]
[tex]\hookrightarrow \sf 108x+324 = 81x+648[/tex]
[tex]\hookrightarrow \sf 108x-81x = 648-324[/tex]
[tex]\hookrightarrow \sf 27x = 324[/tex]
[tex]\hookrightarrow \sf x = 12[/tex]
Perimeter of the triangle:
36 + 17 + 15 + 3x + 9
36 + 17 + 15 + 3(12) + 9
113 units
Answer:
x = 12
perimeter = 113 units
Step-by-step explanation:
Triangle Proportionality Theorem states that if a line parallel to one side of the triangle intersects the other two sides, then it divides the sides into proportional corresponding segments.
[tex]\implies 3x+9 : 15 = (36-9) : 9[/tex]
[tex]\implies 3x+9 : 15 = 27 : 9[/tex]
[tex]\implies \dfrac{3x+9}{15}= \dfrac{27}{9}[/tex]
[tex]\implies 3x+9 = 45[/tex]
[tex]\implies 3x = 36[/tex]
[tex]\implies x = 12[/tex]
Perimeter = [tex]3x+9 + 15 + 17 + 36[/tex]
Substituting [tex]x = 12[/tex]:
⇒ perimeter = 3(12) + 9 + 15 + 17 + 36
= 113
The value of which of these expressions is closest to e?
Heres the answer i couldnt find this
Answer:
c
Step-by-step explanation:
Find the exact value of the remaining trigonometric functions given: Tan x = Undefined Sin x > 0
(I’ve been having some trouble understanding this one—please explain, if possible!)
Answer:
sin(x) = 1cos(x) = 0cot(x) = 0csc(x) = 1sec(x) = undefinedStep-by-step explanation:
The tangent function can be considered to be the ratio of the sine and cosine functions:
tan(x) = sin(x)/cos(x)
It will be undefined where cos(x) = 0. The values of x where that occurs are odd multiples of π. The smallest such multiple is x=π/2. The value of the sine function there is positive: sin(π/2) = 1.
The corresponding trig function values are ...
tan(x) = undefined (where sin(x) >0)
sin(x) = 1
cos(x) = 0
__
And the reciprocal function values at x=π/2 are ...
cot(x) = 0 . . . . . . 1/tan(x)
csc(x) = 1 . . . . . . .1/sin(x)
sec(x) = undefined . . . . . 1/cos(x)
11. Daisy is calculating her assets. She has $10,000 in gold and silver jewelry, and $50,000 in her savings. She has paid $20,000 of her $150,000 house. She has also pain
$10,000 of the $45,000 car she bought last year.
O $285,000
O $80,000
O $255,000
O $90,000
Answer:
C is the answer because if u add all the numbers up and subtract how much she has paid so far u get 255,000
Answer: $90,000
Step-by-step explanation: just did the test
5. What percent of students are between 5’5” and 5’ 11”?
Answer:
97%
Step-by-step explanation:
Answer:
the answer is 5 hope this helps have a great day
Step-by-step explanation:
5-4(2-x)=17
5-4(-x+2)=17
5-4(-x+2)=17
5+4x-8=17
5+4x-8=17
-3+4x=17
4x-3=17
4x-3+3=17+3
4x=20
4x/4=20/4
x=5
Factor 48-8x to identify the equivalent expressions.
Answer:
The final answer is 8(6-x)
⇒ Given value: 48−8x
⇒ find: equivalent expression
⇒ Solution: 48−8x = 8(6−x)
[tex].[/tex]
What type of problem can be modeled and solved with a linear system?
Answer:
real-world problems.
Step-by-step explanation:
A bouquet has 30 flowers. The size of the bouquet is decreased by a factor of 3. How many flowers remain
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
10
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Step-by-step explanation:
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
First let know what we are doing..
Given:
A bouquet has 30 flowers
Size of bouquet decrease by a factor of 3
How many flowers remains
Note;
The term "decreased by a factor" means to divide.
Solve;
Thus, 30/3 = 10
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
[RevyBreeze]
A radio is on sale for $76.50 at a 15% discount. What was the original selling price?
Please show the solution and checking, it’s urgent
Answer:
87.975
Step-by-step explanation:
76.5 x 15% = 11.475
76.5 + 11.475 = 87.975
Kanesha wants to find out if people in her community would support turning an unused park into a dog park. Which populations would be appropriate to sample for the survey?
people who live near the unused park
parents of small children in the community
children attending the local school
owners of local businesses
A. People who live near the unused park
Step-by-step explanation:
It would be best to ask people who live near the unused park since they would most likely be the ones using it.
Answer:
A
Step-by-step explanation:
because they would have better fun for their kids and it wouls probably cost less
