Answer:
His original speed was 60 mph.
Step-by-step explanation:
The average speed formula is shown below:
speed = distance / time
For the first leg of the trip Mr. Blue drove at a speed of "x" mph, for a distance of 105 miles, therefore the time that took to complete the trip is:
time 1 = distance / speed
time 1 = 105 / x h
On the second leg of the trip Mr. Blue drove faster at a speed of "x + 10" mph, so the time it took him to complete the trip was 15 minutes less, therfore:
time 2 = time1 - (15/60) = (105/x) - 0.25 = (105 - 0.25*x)/x h
Applyint the time and speed from the second leg to the average speed formula we have:
x + 10 = {105/[(105 - 0.25*x)/x]}
x + 10 = 105*x/(105 - 0.25*x)
(x + 10)*(105 - 0.25*x) = 105*x
105*x + 1050 -0.25*x² - 2.5*x = 105*x
-0.25*x² -2.5*x + 1050 = 0 /(-0.25)
x² + 10*x - 4200 = 0
x1 = [-(10) + sqrt((10)² - 4*(1)*(-4200))]/2 = 60
x2 = [-(10) - sqrt((10)² - 4*(1)*(-4200))]/2 = -70
Since his speed couldn't be negative the only possible value was 60 mph.
Answer:
60 mph
Step-by-step explanation:
If a vertical plane slices a cylinder perpendicular to both its bases, what cross section is formed?
rectangle
square
circle
triangle
You deposit $1500 in a bank account that pays 4% annual interest. Find the balance
after 6 years if the interest is compounded monthly. Round to the nearest cent.
Growth
Answer:
To calculate the balance after 6 years with monthly compounding, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = the final amount (balance) after t years
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $1500
r = 4% = 0.04 (as a decimal)
n = 12 (compounded monthly)
t = 6 years
Plugging in the values, we get:
A = 1500 * (1 + 0.04/12)^(12*6)
Calculating the right-hand side:
A = 1500 * (1 + 0.003333)^72
A = 1500 * (1.003333)^72
A ≈ 1500 * 1.265032
A ≈ $1897.55
Therefore, the balance after 6 years with monthly compounding, rounded to the nearest cent, is approximately $1897.55.
Mr. Wong cuts a coil of wire into two pieces in the ratio of 3:4. The length of the longer piece is 32 centimeters. What is the total length of the coil of wire?
Answer:
56 cm
Step-by-step explanation:
The ratio of the lengths of the pieces is 3:4.
The longer piece is 32 cm.
We set up a proportion to find the length of the smaller piece.
Let the length of the smaller piece be x.
3 is to 4 as x is to 32
3/4 = x/32
4x = 3 * 32
4x = 96
x = 24
The smaller piece is 24 cm.
24 cm + 32 cm = 56 cm
Answer: 56 centimeters long.
Step-by-step explanation:
You can find the other value in a ratio by dividing the value given by its corresponding value in the ratio, then multiplying the quotient by the other value in the ratio.
32 is the longer piece, and 4 is longer than 3.
32 / 4 = 8.
8 * 3 = 24
The shorter piece is 24 centimeters long.
The total length of the coil is 24 + 32, or 56 centimeters long.
A parallelogram has a base of 8.5 cm and a height of 6 cm. What is the area of the parallelogram
Answer:
51cm^2
Step-by-step explanation:
The formula for the area of a parallelogram is : [tex]base*height[/tex]
To work out the area of a parallelogram you would simply multiply the base of 8.5 by the height of 6, this gives you 51cm^2. This is because the formula for the area of a parallelogram is base multiplied by the height.
1) Multiply 8.5 by 6.
[tex]8.5*6=51cm^2[/tex]
Which word or words best complete the sentence? Two intersecting lines are _____ in the same plane.
Answer:
Two intersecting lines are co-planar in the same plane.
Hope this helps!
:)
Answer:
the answer is always
Step-by-step explanation:
I just took the quiz and got it right.
9. You have a globe that has a diameter of 22 inches. Find the volume of
your globe. Use 3.14 for pi and round your answer to the nearest whole
number.
A) 523 cubic inches
B) 44,580 cubic inches
C) 7,235 cubic inches
D) 5,572 cubic inches
Answer:
D
Step-by-step explanation:
4/3 * pi * r^3 is the formula.
7. How would you solve this equation: 9x = 153? *
Multiply
Divide
Add
Subtract
You would need to DIVIDE by 9
Answer:
x=17
Step-by-step explanation:
divide both sides of the equation by 9
a boy is older than his sister by 3 years five years ago, the ratio of their ages was 4 : 3 find his present.
Answer:
five years ago -- boy- x+3 years
sister --- x
ratio-- 4:3 so difference is 3 years
4-3-- 1 1--3
five years ago --- sister :3*3--9 brother : 4*3--12
present : sister 14 years and brother 17 years old
Step-by-step explanation:
What kind of Polynomial is this?
8b
A. Binomial
B. Monomial
C. Trinomial
What kind of polynomial is this?
2a^2 + 3b + c
A. Trinomial
B. Monomial
C. Binomial
The perimeter of a square is equal to the circumference of a circle with a radius of 10 cm.
What is the area of the square? (Round to the nearest tenth.)
Answer:
C = 2*3.14*10 = 62.8 cm = P of square
Area=1/16 * p2
=
246.49 cm2
Extending Patterns What is the value of y when x = 0? When x = 0, y = .
HURRY PLS
Answer: 0
Step-by-step explanation: it would only be a different number if there’s an equation like y=2x 3
0000000000000000000000
Step-by-step explanation:
There were 144 people in attendance at the school football game last Friday. This week there were 346 people in attendance at the school football game.What is the percent of change from last week to this week?Round your answer to the nearest whole number
Answer: 140%
Step-by-step explanation:
STEP 1: FIND THE CHANGE IN # OF PEOPLE:
initial # of people: 144
final # of people: 346
change in # of people = (final - initial)
change in # of people = (346 - 144)
change in # of people = 202
STEP 2: FIND THE % CHANGE
202/144 = x/100
(100)(202/144) = x
100(1.4) = x
140% = x
Answer:
140 %
Step-by-step explanation:
(346-144)/144 * 100
(202/144) * 100
-2(3a+1) = 5(1+a)
What is a? And how do get the answer?
Just solve the equation
Given:
-2(3a+1) = 5(1+a)
-6a - 2 = 5 + 5a
11 a = -7
a = -7/11
Answer:
a = -7/11
Step-by-step explanation:
Distribute -2 and 5 through the parentheses, -6a - 2 = 5 + 5a
Move the Variable and constant to a proper side, -6a - 5a = 5 + 2
Calculate like terms, -11a = 7
Divide both sides of the equation by -11, a = -7/11
Final answer, a = -7/11
For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?
Answer:
k = 21
Step-by-step explanation:
[tex]xy = k\\\\Plugging\: x = 7\: and\: y = 3,\: we\; find:\\7\times 3 = k\\21 = k\\\huge\red{\boxed{k = 21}}\\[/tex]
A cylinder has a circular base with diameter of 20 inches. What is the volume of this cylinder with the height of 11 inches?
HELP PLEASE
Answer:
3455.75
Step-by-step explanation:
-(8x) . 3x^2 please help
Answer:
− 24 x 3
This is if you multiply the expressions
If the soccer team paid $5 for 15 hamburger, then what is the price of one hamburger?
Answer:
$0.33 per hamburger
Step-by-step explanation:
You know that the team paid $5 for 15 hamburgers, then you need to divide the cost of all the hamburgers, ($5) by the number of hamburgers. 5/15 = 0.33 repeating. This means that they paid $0.33 per hamburger.
Answer:The answer is 80
5, 10, 15, 20, 25, 30, 35,40, 45, 50, 55, 60, 65, 70, 75, 80.
Devon started the week with $50 in his checking account. On Monday he took $20 out of the
account. On Tuesday, the balance of Devon's account changed to $0. Which value best
represents the change to his account balance on Tuesday?
Answer:
see below
Step-by-step explanation:
Starting with 50
Took out 20
50-20 = 30
Then the balance was 0
We need to subtract 30 to get to get to 0
30-30 = 0
Taking out 30
Withdrawing 30
Spending 30
All are ways of indicating taking out 30 dollars
Answer:
On Tuesday, Devon took 30 dollars out of his checking account.
Step-by-step explanation:
Starting with: $50 - Ending with $0
Monday: took out $20 or in other words -20 50-20=30
Tuesday: undetermined, but since that was his last day, it would correspond with $0 so, he must've took out $30 and then ended up with none in the end.
30-30=0
So, he took 30 dollars out on tuesday.
how many ounces are equal to 7 pounds
Answer:
112
Step-by-step explanation:
multiply the mass value by 16
Answer:
112 ounces are in 7 pounds
Step-by-step explanation:
because there are 16 ounces in 1 pound if you multiply 16 by 7 you will get 112 oz.
What is a mixed number betweeen 3 3/11 and 3 2/5
Answer:
3 4/11.
Step-by-step explanation:
3/11 = 15/55
2/5 = 22/55
So a number in between could be 20/55
= 4/11.
So the mixed number could be 3 4/11.
pls help i give u brainliest and 5 stars
Answer:
20+20+6+6+30+30=112cm^2
Step-by-step explanation:
Answer:
112 meters squared
Step-by-step explanation:
Surface Area = 2×(3×2 + 3×10 + 2×10) = 112 meters squared
find an equation for the line that passes through the points (5, -4) and (1, -2)
Answer:
y=-3/2x-.5
Step-by-step explanation:
(5,-4) and (1,-2)
Step 1: find slope:
-4-2/5-1=-6/4=-3/2
y=mx+b
y=-3/2x+b
2.: Plug in point
(1,-2)
-2=-3/2*1+b
-2=-3/2+b
-2+3/2=b
b=-.5
please solve this I am stuck
is it
(x+3)² - x?
I may be wrong x
Solve the simultaneous equations
2x - 3y = 18
5x + 9y = -10
Answer:
2x - 3y = 18 (1)
5x + 9y = -10 (2)
<=>
Multiply both sides of (1) by 5, and multiply both sides of (2) by 2, then:
10x - 15y = 90
10x + 18y = -20
Subtract (2) to (1):
=> 33y = -110 => y = -110/33
Substitute y back into (1):
=> 2*x - 3*(-110/33) = 18
=> 2*x + 10 = 18
=> 2*x = 8
=> x = 4
=> Solution: x = 4, y = -110/33
Hope this helps!
:)
Answer: x=4 y= -10/3
Step-by-step explanation:
Look at the attachment. It should explain.
Morgan's grandmother orders her groceries online and has them delivered to her house.
Her bill is $120. She has a coupon for 20% off and plans to give the delivery driver a
15% tip.
Answer: The total price of the groceries, including discount and tips $110.4
Step-by-step explanation:
What is the value of the following expression for a = -1 and b = 4?
13a^-3 b^-1
A. -13/4
B. -52
C. -4/13
D. -156
Well, if a = -1 and b = 4 then when we plug in the values of a and b into the expression we get:
[tex]13(-1)^{-3}\cdot4^{-1}[/tex].
Then simplify it:
[tex]-13\cdot1/4=-\frac{13}{4}[/tex].
The answer is A.
Hope this helps.
Step-by-step explanation:
Step 1: Substitute -1 for a and 4 for b
[tex]13 * (-1)^-^3 * (4)^-^1[/tex]
[tex]13 * (-1) * \frac{1}{4}[/tex]
[tex]-\frac{13}{4}[/tex]
Answer: Option A, [tex]-\frac{13}{4}[/tex]
what is the greatest common factor 30y^8 + 10y^4
Answer: 10y^4
Since it can go 10y^4(3y^4+1)
Step-by-step explanation:
Answer:
10y^4
Step-by-step explanation:
in order to solve you would have to find the prime factors of each term i order to find the GCF.
hope this helped ;)
Combine like terms to create an equivalent expression
-3.6 - 1.9t + 1.2 + 5.1t
Answer:
3.2t-2.4
Step-by-step explanation:
-3.6 - 1.9t + 1.2 + 5.1t
Combine like terms
-3.6+ 1.2 - 1.9t +5.1t
-2.4 + 3.2t
Answer: 3.2t-2.4
Step-by-step explanation:
First thing you need to do is do -1.9t+5.1t= 3.2t. Then you do -3.6+1.2= -1.2.
Then put all this together and you get 3.2t-1.2. (do not do 3.2t+-1.2 this incorrect because we left the subtracting sign
ray cuts out a figure that has 4 equal sides and no right angles. what is the best name for the figure?
Answer:
Trapezoid
Step-by-step explanation:
None
Answer:
trapezoid
Step-by-step explanation:
(01.01)
Evaluate −15 + (−4). (1 point)
Group of answer choices
Answer: -19
Step-by-step explanation: when ur adding two negatives it's gonna equal a negative