Given :-
The car arrives from city A to city B in 3 hours.Speed is increased by 20% .To find :-
The new time taken .Solution :-
Let us assume the distance between A and B be x and the initial speed by y . After 20% increase in the speed , new speed will be ,
[tex]\blue{\dashrightarrow} [/tex] Speed = 120y/100
[tex]\blue{\dashrightarrow} [/tex] Speed = 6/5y
• According to the Question ,
[tex]\red{\dashrightarrow} [/tex] Distance = Speed * Time
[tex]\blue{\dashrightarrow} [/tex] x = y * 3 hrs
[tex]\red{\dashrightarrow} [/tex] x = 3y
And ,
[tex]\blue{\dashrightarrow} [/tex] t = Distance/Speed
[tex]\red{\dashrightarrow} [/tex] t = x ÷ (6y/5)
[tex]\blue{\dashrightarrow} [/tex] t = 5x/6y
[tex]\red{\dashrightarrow} [/tex] t = 5 (3y)/6y
[tex]\blue{\dashrightarrow} [/tex] t = 5/2 hrs
[tex]\red{\dashrightarrow} [/tex] t = 2.5 hrs
Hence now it will take 2.5 hrs to go from A to B .
Answer:
Step-by-step explanation:
Let's say the distance between A and B is 3 miles (3, because I see a need to divide the distance by 3 hours to determine the car's speed). The actual distance makes no difference in the answer, since it is asking for a relative speed change (20%).
We find the speed to be 3 miles/3 hours, or 1 mph. A 20% increase in speed would be (1.20)(1) = 1.20 mph.
We can find the time for a 1.2 mph car to go 3 miles by:
(3 miles)/(1.2 mph) = 2.5 hours
=====
[Note that if we assumed a different distance, say 6 miles, we'd get the same result:
6 miles/3 hours = 2 mph
1.2*2 = 2.4 mph
New time = 6/2.4 = 2.5 hours; same as before]
What is an equation of the line that passes through the points (-7, 7) and (3, 7)(
Answer:
y=7
Step-by-step explanation:
The slope is (7-7)/(3+7) = 0. So, the line is a horizontal line.
The y value of both points is 7.
p(x)=x-3
g(x) = 2x-5
Find the following.
(p ° q)(5)= and (q ° p)(5)=
Answer:
(p∘q)(5) = 2
(q∘p)(5) = -1
Step-by-step explanation:
The composition of functions can be written a little differently, perhaps making it easier to understand.
(p∘q)(x) = p(q(x))
(p∘q)(5) = p(q(5)) = p(2·5 -5) = p(5) = 5 -3
(p∘q)(5) = 2
__
(q∘p)(5) = q(p(5)) = q(2) = 2·2 -5
(q∘p)(5) = -1
Help pllsssssss to find the vAlue of a
Answer:
a = 11
Step-by-step explanation:
As all angles on a straight line must add up to 180°:
(9a + 6) + 75 = 180
9a + 6 + 75 = 180
9a + 81 = 180
Subtract 81 from both sides of the equation:
9a + 81 - 81 = 180 - 81
9a = 99
Divide both sides by 9 to isolate a:
9a ÷ 9 = 99 ÷ 9
a = 11
Hope this helps!
Answer:
[tex]a=11[/tex]
Step-by-step explanation:
These are supplementary angles, meaning they together make up the whole measure of the angle of a straight line. A straight line is 180°, so the sum of these has to be 180° too:
[tex](9a+6)+75=180[/tex]
Then just solve for a:
[tex]9a+6+75=180\\9a+81=180\\9a=99\\a=11[/tex]
The designers of a new website expect the number of visitors to the site to double each month. There were 600 visits to the site the first month. Which function can be used to predict the number of visitors during month m
The exponential function used to predict the number of visitors during month m is [tex]y = 600(2)^m[/tex]
An exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the factor.
Let y represent the number of visitors during month m.
There were 600 visits to the site the first month and they double each month, hence:
a = 600, b = 2
The exponential function is given by:
[tex]y = 600(2)^m[/tex]
Find out more on exponential function at: brainly.com/question/2456547
Help help hep help help math
Answer:
Angle 5
Step-by-step explanation:
4/10 proportional to 6/15
Answer:
Nooooooo
Step-by-step explanation:
7(2+3x)+8, 12+3(8+x), and (7x+2)3+8x
Answer:
The first answer is 21x+22.
Second answer is 36+3x.
Third answer is 29x+6.
Step-by-step explanation:
I just simplified
QUESTION 4 PLEASE HELP ME ASAP
Answer:
Part 1: The entry fee is $5
Part 2: Each minute costs 25 cents
Step-by-step explanation:
In the expression, the '+5' represents the fee added to '.25m' the cost per each minute.
YOU’RE GETTING a brainlist if you answer these!!!!: If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?
If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?
Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?
Answer:
Where's the picture?
Step-by-step explanation:
Tomika uses 6 1/9 inches of wire to make a necklace and 3 1/3 inches of wire to make a bracelet. How many necklace and bracelet sets can she make if she uses 28 1/3 inches of wire in all?
Answer:
3
Step-by-step explanation:
please i need help on this question
the rectangular gable is 8 feet tall the area of the gable is 120 square feet, what is the length of the base
X is y% of what number?
Answer:
42
Step-by-step explanation:
yeah-ya.......... right?
Van is watching birds in his backyard. There are 9 sparrows or 45% sparrows. How many birds are in his backyard?
Answer:
11
Step-by-step explanation:
How Much Percentage is 7 out of 45.99?
Answer: 0.152207 %
Step-by-step explanation: divide the amount by the total to get the percentage.
A shed has dimensions of 12m in length and 5 m in width. Both the length and width are increased by the same amount in order to increase the floor area by more than double the original area?
The amount by which the length and width of a shed can be increased to
more than double the area, depends on the initial dimensions.
The amount that can be added to both the length and the width to increase the floor area by more than double the original area is more than 3 meters.Reasons:
The given parameters of the shed are;
The length of the shed = 12 m
Width of the shed = 5 m
The amount by which the length and the width are increased = The same amount
The new area after the increase in the length and width of the shed = More than double the initial area
Required:
The amount of increase in the length.
Solution:
Let the amount by which the length and width are increased = x
We have;
Initial area of the shed = 12 m × 5 m = 60 m²
The new area = (12 + x) × (5 + x) > 2 × 60
By multiplication, we get;
(12 + x) × (5 + x) = x² + 17·x + 60 > 2 × 60 = 120
x² + 17·x + 60 - 120 > 120 - 120 = 0
x² + 17·x - 60 > 0
By factorization, we get;
(x + 20)·(x - 3) > 0
x > -20, or x > 3
The increase (positive) amount of the solution is x > 3
Therefore, the amount by which both the length and the width can be increased to more than double the area is x > 3 meters
Learn more about the area of a rectangle here:
https://brainly.com/question/16410706
write a two column proof. given: ab is congruent to ed, ca is congruent to ce; ac bisects bd. Prove abc is congruent edc.
Given that, AB ≅ ED, CA ≅ CE, and AC bisects BD, the two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.
What is the SSS Congruence Theorem?The side-side congruence theorem (SSS) states that if two triangles has three pairs of sides that are congruent to each other, then both triangles are congruent.
We are given the following information:
AB ≅ EDCA ≅ CEAC bisects BDSince AC bisects BD, therefore the third pair of sides of ΔABC and ΔEDC, BC and CD, will be congruent.
Therefore, it implies that both triangles has three pairs of congruent sides (AB ≅ ED, CA ≅ CE, and BC ≅ CD), which meets the criterion of the SSS Congruence Theorem.
Therefore, ΔABC ≅ ΔEDC by SSS Congruence Theorem.
The two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.Learn more about the SSS Congruence Theorem on:
https://brainly.com/question/19262620
Evaluate the integral:
Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then
∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt
… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt
… = 7 ∫ √(1 - sin²(t)) cos(t) dt
… = 7 ∫ √(cos²(t)) cos(t) dt
We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so
√(cos²(t)) = |cos(t)| = cos(t)
and the integral reduces to
… = 7 ∫ cos²(t) dt
Recall the half-angle identity for cosine:
cos²(t) = (1 + cos(2t))/2
Then the integral is
… = 7/2 ∫ (1 + cos(2t)) dt
… = 7/2 (t + 1/2 sin(2t)) + C
… = 7t/2 + 7/4 sin(2t) + C
Get the antiderivative back in terms of x. Recall the double angle identity for sine:
sin(2t) = 2 sin(t) cos(t)
We have t = arcsin(x/√7), which gives
sin(t) = sin(arcsin(x/√7)) = x/√7
cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7
Then
∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C
… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C
An angle measures 152° more than the measure of its supplementary angle. What is the measure of each angle?
° and
°
Answer:
14° and 166°
Step-by-step explanation:
Ok, so a supplementary angle is 180°.
Let's say one angle is x and the other angle is x+152.
We know these angles add up to a supplementary angle (180°) so...
x+(x+152)=180
x+x+152=180
2x+152=180
2x=28
x=14
So now we know one angle is 14°, we also know the other angle is x+152, knowing that x=14 we can plug it in 14+152= 166° for the other angle.
Hope this helps :)
Can u help me with my homework
can retainers still fit w a small gap?
Answer:
Retainers have been designed to be used as an end of treatment to help retain your teeth in their new position. ... These are removable and fixed retainers. The reason why retainers can't be used to close a gap is because they are fitted at the end of treatment and are made to fit the straight teeth mould.
hope it help u
itz by Riddhi
Answer:
yes
Step-by-step explanation:
Green Valley High School recently completed an expansion. Of the new classrooms, 11 are math
classrooms, 8 are science classrooms, and 6 are history classrooms. If a single classroom is picked at
random, what is the probability that the classroom is for math or history?
Answer: 68%
Step-by-step explanation:
The best way to do this is add up the number of math and history rooms, and divide that by the total number of rooms.
There are 17 total math and history rooms, and 25 rooms total.
17/25 = .68
Multiply that by 100 to get the percent and the answer is 68%
A’= _ , _
B’= _ , _
C’= _ , _
Answer:
if it's only translated left 3, then it should be A (-5, -1) B (-1, -1) and C (-1, 2)
8/9 write simplified
How many 4/5are in 1
Answer:
If your gonna ask it on groups its one group
The triangle below is equilateral. Find the length of side x in simplest radical
form with a rational denominator.
Answer:
[tex]\frac{4\sqrt{3} }3}[/tex]
Step-by-step explanation:
Since it is an equilaterla triangle, we can see the side opposite to that of side length 4 is 60 degrees. Since the other angle is a right angle (90 degrees), we can find that the other side is 30 degrees (the degrees add up to 180). We can also see that this is a 30-60-90. We can see that the side x, through the identity (you can find 30-60-90 identity online), we see that the side x is [tex]\frac{4}{\sqrt{3}}[/tex]. However, it is also asking us to simplify this, so we multiply the top and bottom by [tex]\sqrt{3}[/tex] and get [tex]\frac{4}{\sqrt{3} } = \frac{4\sqrt{3} }{3}[/tex]
How do u write x/7=14 in algebra tiles
Answer:
98 is the answer.
Step-by-step explanation:
x/7 = 14
=> 14 × 7 = 7 × x/7
=> x = 98
Therefore, 98 is the answer.
Hoped this helped.
Over a lengh of 101 inches the hight changes 5" what is the angle?
Answer:
2.83°
Step-by-step explanation:
The tangent of an angle is the ratio of rise to run.
θ = arctan(5/101) ≈ 2.83°
_____
We assume the length is referring to the horizontal distance.
If it is the distance along the path, then the angle is ...
θ = arcsin(5/101) ≈ 2.84°
Find the difference (6d+5) - (2-3d)
Answer:
(9d+3)
Step-by-step explanation:
(6d+5)-(2-3d)
>(6d+5)+(-2+3d)
>{(6d+3d)+(5-2)}
=(9d+3)
I need a step by step explanation as well as work
Answer:
x = 2
m = 15/4
a = 5/4
Step-by-step explanation:
When the "base" lines are parallel, all of the triangles are similar. That means corresponding segments are proportional, including corresponding parts of segments.
We see that x corresponds to a partial segment marked 3. That same top-bottom correspondence has another pair of segments marked 2 and 3. That means x=2.
x/3 = 2/3 ⇒ x = 2
__
The segments marked 'm' and 'a' are "whole side" segments, so we need to put those in proportions with corresponding whole sides. If we use the bottom side, we find ...
a/3 = 5/(3+6+3) = 5/12 ⇒ a = 5/4 = 1 1/4 . . . . . multiply by 3
and
m/(6+3) = 5/12 ⇒ m = 15/4 = 3 3/4 . . . . . multiply by 9
__
x = 2
m = 15/4
a = 5/4