Answer:
speed of commuter bus: 32 km
speed of passenger car : 48 mph
Step-by-step explanation:
We will use the concept of speed distance and time.
where time = distance / speed
____________________________________________________
Let the speed of commuter bus be x mph
Given that passenger car travels 16 mph faster than commuter bus.
Speed of passenger car if speed of commuter bus is x mph (x+16)mph
Distance traveled by commuter bus = 56 miles
Time taken by commuter bus to travel 56 miles = 56/X (1)
Distance traveled by passenger car = 84 miles
Time taken by passenger car to travel 84 miles = 84/(X+16) (2)
__________________________________________
It is given that time taken by both bus and car is same
so equating equation 1 and 2
we have
56/X = 84/(X+16) (by cross multiplication we have)
=> 56(X+16) = 84*X
=> 56X + 896 = 84X
=> 896 = 84X - 56 X
=> 896 = 28X
=> X = 896/28 = 32.
Therefore , speed of commuter bus is x mph or 32 km
speed of passenger car is x+16 mph = (32+16) mph = 48 mph
Final answer:
The passenger car travels at 48 mph, while the commuter bus travels at 32 mph, derived from the fact that they travel the same time but different distances.
Explanation:
To find the speeds of the passenger car and the commuter bus, we can use the formula for distance (distance = speed × time). Since both the bus and the car travel for the same amount of time, we can set up an equation to solve for their speeds based on the distances they travel.
Let x be the speed of the commuter bus in mph. Consequently, the speed of the passenger car would be x + 16 mph. According to the information given:
The bus travels 56 miles.
The car travels 84 miles.
Since they travel for the same time t, we have:
Bus: 56 miles = x × t
Car: 84 miles = (x + 16 mph) × t
Dividing the mileage of the car by the bus gives us:
[tex]\(\frac{84}{56} = \frac{(x + 16)t}{xt}\)[/tex]
[tex]\(1.5 = \frac{x + 16}{x}\)[/tex]
Multiplying by x to get rid of the fraction and then solving for x provides:
1.5x = x + 16
0.5x = 16
x = 32 mph
This means the bus travels at 32 mph and the passenger car travels at:
32 mph + 16 mph = 48 mph
Therefore, the speed of the passenger car is 48 mph and the speed of the commuter bus is 32 mph.
Orlando is making a design for a logo. He begins with a square measuring 22 inches on a side.
The second square has a side length of 17.6 inches, and the third square has a side length of
14.08 inches. Which square will be the first square with a side length of less than 10 inches?
A) fifth square
B) fourth square
C) sixth square
D) seventh square
Answer: A
Step-by-step explanation:
The first square is 22 inches on a side.
The second is 17.6 inches on a side
the third is 14.08 inches on a side.
We can suppose that we have a constant rate of decrease betwen the sides cubes, this means that:
22in*x = 17.6in
where x is the rate of scale.
x = 17.6/22 = 0.8
Now we test this with the second and third:
17.6in*0.8 = 14.08in
Ok, this works.
then the side of n-th cube can be found with the equation
L = 22*0.8^(n-1)
we can try the different options and see which one gives a value smaller than 10.
A) n = 5
L = 22*0.8^4 = 9.01
Then the correct option is A
Answer:
the answer is A i had a quiz
Step-by-step explanation:
Solve the following system:
y=1
y=-6x-5
Answer:
x = -1
y = 1
Step-by-step explanation:
Since it gives you "y", plug in the number given into the equation:
y = -6x - 5
1 = -6x - 5
Then, add 5 to both sides:
1 = -6x - 5
+5 + 5
________
6 = -6x
Divide both sides by -6:
6 = -6x
-1 = x
So now you have, x = -1 and y = 1
Work out the gradient of a line that is parallel to -2x+y-5=0
Answer:
gradient = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
Given
- 2x + y - 5 = 0 ( add 2x and 5 to both sides )
y = 2x + 5 ← in slope- intercept form
with gradient m = 2
Parallel lines have equal gradients
Gradient of parallel line is m = 2
Which expression is equivalent to 5y^-3
Answer:
Step-by-step explanation:
5
5y^-3 = ---------
y^3
A cone-shaped container has a height of 9 inches and diameter of 2.5 inches. It is filled with a
liquid that is worth $2 per cubic inch.
What is the total value of the liquid in the container?
Use 3.14 for .
Enter your answer in the box.
*pleaseee help i will mark brainliest if right*!!!!!
ps, thank you
Answer:
the total value of the liquid in the container is $29.4
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cone
The volume of a cone is expressed as
V=1/3(πr²h)
Given data
Height h= 9 inches
Radius r= diameter/2= 2.5/2= 1.25in
Substituting we have
V= 1/3(3.14)*(1.25)²*9
V= 1/3*(3.14)*14.06
V= 44.156/3
V= 14.7in³
The volume of the cone is 14.7in³
Hence If 1 in³ of liquid costs $2
14.7in³ will cost $x
x= 14.7*2
x= $29.4
What's the answer will award brainiest
Answer:
D
Step-by-step explanation:
Answer:
D?
Step-by-step explanation:
A circular pool has a radius of 10 feet. What is the areaof the surface of the water in the pool? Use 3.14 for π.
Answer:
314ft²
Step-by-step explanation:
A = πr²
A= π10²
A=100π
A=100*3.14
A=314
Hope this helps :)
Final answer:
To calculate the area of the circular pool's surface, use the formula A = πr² with π approximated as 3.14 and the given radius of 10 feet. The area is 314 square feet, as the calculation yields A = 3.14 × 100, which does not need adjustment for significant figures.
Explanation:
To find the area of the surface of the water in the circular pool with a radius of 10 feet, we use the formula for the area of a circle, which is A = πr². Let's use the given value for pi (π) as 3.14 and the radius (r) is 10 feet. So the calculation is A = 3.14 × (10 feet)².
Now, squaring the radius, we get (10 feet)² = 100 feet². Next, we multiply this by our value for pi, resulting in A = 3.14 × 100 feet² = 314 feet². Therefore, the area of the surface of the water in the pool is 314 square feet.
Recalling significant figures, since our given radius was precise to two significant figures, our final answer should also reflect two significant figures. However, since all the numbers in 314 are significant, there is no need for adjustments in this case, and the result remains 314 square feet.
5 cups of grape juice to 2 cups of apple juice
Which pair(s) of expressions are equal in value? Check all that apply.
Answer:
Where is the expressions ?
Step-by-step explanation:
Answer:
a [4.9] and [3.1]
c [-6] and [-6]
Step-by-step explanation:
Edge 2020-2021
It's right I did it
Hope that helps
Electricity City increases the price of televisions by 25%. If a television now sells for
$425, what was the original price?
Answer:
340
Step-by-step explanation:
As it was increased by 25%, $425 is 125% of the original price, so we can get back to 100% by dividing 425 by 5 [85], so 85 is 25% of the price. We can now get the original price by subtracting 85 from 425 (or you could multiply 85 by 4) which is 340
You can check this answer by multiplying 340 by 1.25
If the answer is 425, then it is correct, else, not. [it is]
the difference of a number x and 7 *
Answer:
C
Step-by-step explanation:
x-7 is the answer
Answer:
difference means subtract
x-7
C. is correct because it subtracts and the numbers are in order
Step-by-step explanation:
You have boxes that will hold 1 cubic foot, 3 cubic feet,
9 cubic feet, and 27 cubic feet of paper. What is the fewest
number of boxes you need to hold 257 cubic feet of paper?
Answer:
13 boxes
Step-by-step explanation:
To calculate the minimum number of boxes that can be had with that amount of paper, they should be kept in the largest box, that is, the 27 cubic foot box, therefore, we divide:
257/27 = 9.51
Which means that we can save the paper in 9 boxes of 27 cubic feet, now we will save the rest in the next smaller box, the 9 cubic foot box.
First let's calculate how many leftover paper:
257 - 27 * 9 = 14
Therefore, we can only use 1 box of 9 cubic feet:
14 - 9 = 5
For the remaining 5 cubic feet use 1 box of 3 cubic feet and 2 boxes of 1 cubic foot.
Therefore, in total it would be:
9 of 27 ft ^ 3 + 1 of 9 ft ^ 3 + 1 of 3 ft ^ 3 + 2 of 1 ft ^ 3 = 13
a total of 13 boxes would be the minimum
will give brainliest.
Find the value of c that makes the expression a perfect square trinomial.
You need to give us the equation first, otherwise we can't do it
:|
Nine bean plants were grown in varying amounts of light. Mark thinks that, if the light is too intense, a bean plant will not grow as
high.
Is Mark's prediction correct?
Yes; the tallest plants were the ones that got the weakest light.
No; some plants grew just as well while getting very strong light.
Yes, when the light was too strong the plants did not grow as well.
No: plants that got the strongest light were also the ones that grew best.
Answer: C) Yes, when the light was too strong the plants did not grow well
Step-by-step explanation:
What is 5x^2-6x+2 multiplied by 4x^2-3x
Depends on what x is.
Use one or more transformations to transform the pre-image (purple) onto the image (white).
Transformations in geometry include translation, rotation, reflection, and dilation, which are used to change a figure's position, orientation, or size. The appropriate transformation to use depends on the changes observed between the purple pre-image and the white image in the problem.
Explanation:In mathematics, specifically in geometry, we use transformations to move or change a figure in some way without altering its fundamental shape or size. The transformation of a pre-image onto an image can be achieved using transformations such as translation, rotation, reflection, or dilation.
To transform the purple pre-image onto the white image, firstly identify the type of transformation required. For instance, if the white image is the same size as the purple pre-image and only its position has changed, use translation. If the image is mirrored along a line, use reflection. If it's turned around a point, use rotation. If the image is an enlarged or reduced version of the original figure, use dilation.
Consequently, the precise steps depend on the type of transformation(s) required.
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Use the laws of logarithms and the values given below to evaluate the logarithmic expression.
log7=0.8451 log5=0.6990
log3=0.4771 log2=0.3010
The value of [tex]\(\log 12\)[/tex] is approximately 1.0792 based on the given logarithmic values. Option B [tex]$\approx 1.0791$[/tex]
Let's evaluate the logarithmic expression [tex]\(\log 12\)[/tex]. We'll use the given logarithmic values:
1. Recall that [tex]\(\log 12\)[/tex] represents the common logarithm (base 10 logarithm) of the number 12.
2. Apply the change of base formula:
[tex]\[ \log 12 = \frac{\log 12}{\log 10} \][/tex]
Given values:
[tex]- \(\log 12 \approx 2.4849\) (from \(\log 12\))[/tex]
[tex]- \(\log 10 \approx 2.3026\) (from \(\log 10\))[/tex]
Now calculate:
[tex]\[ \log 12 \approx \frac{2.4849}{2.3026} \][/tex]
[tex]\[ \log 12 \approx 1.0792 \][/tex]
Therefore, the value of [tex]\(\log 12\)[/tex] is approximately 1.0792.
The correct answer is b. [tex]\(\approx 1.0791\)[/tex].
The correct question is:
Use the laws of logarithms and the values given below to evaluate the logarithmic expression.
[tex]$$\begin{array}{ll}\log 7=0.8451 & \log 5=0.6990 \\\log 3=0.4771 & \log 2=0.3010\end{array}$$[/tex]
[tex]$\log 12$[/tex]
a. [tex]$\approx-1.0791$[/tex]
b. [tex]$\approx 1.0791$[/tex]
c. [tex]$\approx 3.0234$[/tex]
d. [tex]$\approx-3.0234$[/tex]
Complete the work shown to find a possible
solution of the equation.
(x - 5) +5=2
(x - 5)2 = -3
A possible solution of the equation is
Answer:
It's 14.
Step-by-step explanation:
Took it on edg 2020
Someone pls help it’s due later
Answer:
5.)Z=7
Check:
6.) False
True
Step-by-step explanation:
5z-10=25
5z-10+10=25+10
5z=35
5z/5=35/5
z=7
Check:
5(7)-10=25
35-20=25
25=25
(Love your profile picture)
Answer:
5) 7
6a) no
6b) yes
Step-by-step explanation:
5)
add 10 to both sides then divide by 5 to isolate the Z
6a) the actual answer is 4F + 12
you don't add 4 you multiply
6b) That is the answer
You see which number is the greatest common factor (GCF)
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 4r and height 4h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
Pls help WILL GIVE BRAINLIEST
Answer:
16 times
Step-by-step explanation:
Since the sides are in the same ratio, i.e
1 : 4
The cylinders are similar
(Ratio of sides)² = Ratio of areas
4² = 16
Step-by-step explanation:
Step 1: Make a ratio of the sides
Side of Cylinder A : Side of Cylinder B
1 : 4
Step 2: Find the ratio of the area
[tex]1 : 4[/tex] ← Ratio of Side
[tex](1)^2 : (4)^2[/tex] ← Ratio of Area
[tex]1 : 16[/tex] ← Ratio of Area
Answer: The area of Cylinder B is 16 times greater than Cylinder A
PLEASE HELP 30 POINTS PLEASE!!!!!
The function f(x)=−11sin(7/3x+1/6)−2 models the average rate of change in temperature of a substance monitored in an experiment. In the function, x represents the number of minutes since the commencement of the experiment and the temperature of the substance is measured in degrees Fahrenheit. Over what range of temperatures does the average rate of change in temperature fall?
The range in the average rate of change in temperature of the substance is from a low temperature of ____°F to a high of ____°F.
Answer:
-13ºF || 9ºF
Step-by-step explanation:
Answer:
-13ºF & 9ºF
Step-by-step explanation:
The range in the average rate of change in temperature of the substance is from a low temperature of -13º F to a high of 9º F.
Whats the lowest value of the range of the function shown on the graph?
Answer:
-2
Step-by-step explanation:
Answer:
Step-by-step explanation:
c
A sign is in the shape of a triangle. It has a base of 12 inches and an area of 120 square inches. What is the height of the sign?
Answer:
The height is 20
Step-by-step explanation:
This is because 120= .5x12
which equals 120= 6. Of course this is not equal so we do 120/6= 20.
Now if we insert 20 to check .5x12x20= 20 which makes the statement true
Answer: 20
Step-by-step explanation: 120 divided by 3 = 40 half of 40 is 20
Find the unknown side of the triangle when x =
12 in and y = 5 in.
Answer:
13
Step-by-step explanation:
As x and y are perpendicular - we can use pythagoras.
So, The length of side x squared + The length of side y squared = The missing length squared.
12^2=144
5^2=25
144+25=169
sqrt169=13
Answer:
Unknown side = 13 in
Step-by-step explanation:
If it is a right sided triangle, then you can use the Pythagoras theoreum.
unknown side = u
x² + y² = u²
12² + 5² = u²
u² = 144 + 25
u² = 169
u = + - SQRT(169)
{Only the positive value has a meaning}.
Unknown side = 13 in
Which expression is equivalent to
- 5/3?
Answer:
The first one! :)
Step-by-step explanation:
At the bottom of each question for example the first on it has 1 at the top then at the bottom it says 5/3 with a x.So if it does not say 5/3 it can be excluded.So it says only one 5/3.So one 5/3 is the exact same as 5/3!
And for the last one says -5/3.:)
And no im not saying 1 5/3 :(
(❁´◡`❁) (●'◡'●) ╰(*°▽°*)╯ (≧▽≦) (*/ω＼*) (^///^) ^_^ (┬┬﹏┬┬) ಥ_ಥ ಠ_ಠ
[tex]$\frac{1}{\sqrt[3]{x^{5}}}$[/tex] is equivalent to [tex]- 5/3[/tex].
The calculation of the given expression can be defined as
[tex]$\begin{aligned} \rightarrow x^{-\frac{5}{3}} &=\frac{1}{x^{\frac{5}{3}}} \\ &=\frac{1}{\sqrt[3]{x^{5}}} \end{aligned}$[/tex]
So, the final answer is "Option b".[tex]$\frac{1}{\sqrt[3]{x^{5}}}$[/tex]
What are Equivalent Fractions?Equivalent fractions are fractions that represent the same value, even though they look different. A fraction has two parts. The number on the top of the line is called the numerator which tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator and it shows the total number of equal parts the whole is divided into or the total number of equal parts which are there in a collection.To learn more about equivalent refer to:
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Helppp plzz!!! Julius is in charge of planting a peach orchard that covers 15 acres. He uses the same amount of ground space for each tree. Julius plants 25 trees in the section of the orchard called the South Hill region that measures 450 feet by 24 feet. Approximately how many trees does Julius plant in the orchard in all? (1 = 43,560 ).
A. 909
B. 1,151
C. 1,513
D. 1,746
Answer:
C
Step-by-step explanation:
Area of known planted trees: 450ft x 24ft = 10800 sq ft
total area of orchard: 43560 sq ft. x 15 acres = 653400 sq ft
653400 / 10800 = 60.5 "duplicated known areas"
25 trees in each "known area"
60.5 x 25 = 1512.5 trees
round to 1513 trees
C
I worked it out but not sure
What is the relationship between segment RS and segment RU
Answer:
I would like to answer but where is the picture for the question. Download that to this page and i will answer it. Have a great day
Step-by-step explanation:
please help thanks will mark brainliest
Answer:
12 inches
Step-by-step explanation:
W = 9 + L
WL = 252
L = 12
Answer:
l = 12
Step-by-step explanation:
Let l = length
width = l+9
The area of rectangle is
A = lw
A = l * (l+9)
252 = l^2 +9l
Subtract 252 from each side
0 = l^2 +9l -252
Factor
What 2 numbers multiply to -252 and add to 9
21*-12 = 252
21-12 = 9
0 = (l+21) (l-12)
Using the zero product property
l+21=0 l-12=0
l = -21 l = 12
We cannot have a negative length
l = 12
Solve for x: −1 < x + 3 < 5
2 < x < 8
−4 < x < 2
2 > x > 8
−4 > x > 2
Answer:
-4<x<2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ÷)
Ryan invests a sum of money in a savings account with a fixed annual interest rate of 4.31% compounded 12 times per year. After 10 years, the balance reaches $12,855.94. What was the amount of the initial investment?
Based on the information given the amount of the initial investment is $8,361.
Let P represent the amount of the initial investment
Hence,
12855.94 = P(1 + .0431/12) ^12(10)
12,855.94=P(1+0.0035917)^120
12,855.94=P(1.0035917)^120
12,855.94=P(1.53760782)
P=12,855.94/1.53760782
P=$8,360.8
P=$8,361 (Approximately)
Inconclusion the amount of the initial investment is $8,361.
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