========================================
Explanation:
distance = rate*time
90 = r*t
where r is the slower speed and t is the time it takes when going that slower speed.
If r is bumped up 24 mph faster, to r+24, then Santos takes t-12 hours to get there. The second equation is
90 = (r+24)(t-12)
-------------------------------------
We can solve the first equation for r to get r = 90/t
Then plug this into the second equation and do a bit of algebra
90 = (r+24)(t-12)
90 = (90/t+24)*(t-12)
90 = 90 - 1080/t + 24t - 288
90t = 90t - 1080 + 24t^2 - 288t
0 = 90t - 1080 + 24t^2 - 288t-90t
0 = 24t^2 - 288t - 1080
24t^2 - 288t - 1080 = 0
If you apply the quadratic formula, then you should get the two solutions t = -3 and t = 15. Due to time constraints, I'll skip these steps.
We'll ignore the negative t value. It makes no sense to have a negative time.
So we focus on t = 15 as the only solution.
-------------------------------------
If t = 15, then,
r = 90/t
r = 90/15
r = 6
Santos rode his bike at 6 mph at first. Going this speed means he takes 15 hours.
If he rode 24 mph faster, at 6+24 = 30 mph, then he would ride for 15-12 = 3 hours instead. Note that 90/30 = 3.
R of breaths of all people in asia in 2016? Expressing your answer in scinentific notation in the form a *10^(b) what are the values of a and b?
Answer:
[tex]a = 3.7464[/tex]
[tex]b = 16[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
Express the answer in [tex]a * 10^b[/tex]
From the question, we have:
[tex]People = 4.46 * 10^9[/tex]
[tex]Breath = 8.4 * 10^6[/tex] breath/person in a year
The number of breath is calculated by:
[tex]Overall = People * Breath[/tex]
So, we have:
[tex]Overall = 4.46 * 10^9 * 8.4 * 10^6[/tex]
Reorder
[tex]Overall = 4.46 * 8.4* 10^9 * 10^6[/tex]
[tex]Overall = 37.464* 10^{9+6}[/tex]
[tex]Overall = 37.464* 10^{15}[/tex]
Using scientific notation [tex]a * 10^b[/tex];
The value (a) must be in the following interval [tex]0 \le a \le 1[/tex]
So, we have:
[tex]Overall = 3.7464 * 10 * 10^{15[/tex]
[tex]Overall = 3.7464 * 10^{16[/tex]
By comparing the above with: [tex]a * 10^b[/tex]
[tex]a = 3.7464[/tex]
[tex]b = 16[/tex]
Please help! I will give brainliest to the first correct answer!
Answer:
A)
Step-by-step explanation:
check that the formula in A works . . .
the 7th term should be 320
a(320) = 5(2)^7-1
= 5(2)^6
= 5(64)
= 320
Santiago buys a new television for $989.76. If
the sales tax rate is 8.75%, what is the total cost
of the television?
Answer:
$1076.36
Step-by-step explanation:
The full price before tax can be represented by 1.00($989.76), and the 8.75% tax by 0.0875($989.76)
which can be combined to obtain the total cost: (1.0875)($989.76) = $1076.36
Find the value of x.
Answer:
70.86 degrees
Step-by-step explanation:
cos x = adjacent side / hypotenuse
= 2/6.1 = 0.32787
x = 70.86.
Answer:
x ≈ 70.9°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2}{6.1}[/tex] , then
x = [tex]cos^{-1}[/tex] ([tex]\frac{2}{6.1}[/tex] ) ≈ 70.9° ( to 1 dec. place )
A television shop sold a set for $799. It made a profit of $ 245.25. How much did the shop buy the television for ?
Answer:
the shop originally bought the television for $553.75
Step-by-step explanation:
this is because if they sold it for $799 and made a profit of $245.25 then you would subtract the profit from the price the TV sold for and you get $553.75
Evaluate (2x + 3) + ( x- 5) show answer pls
Step-by-step explanation:
2x +3 +x-5
3x+3+(-5)
3x +(-2)
x= -2÷3
x=-6
HOPE IT HELPEDNeed help thanks please :)
Answer:
t:
[tex] \infty , - \infty [/tex]
meaning any number can substitute t and it would be the same answer.
One batch of walnut muffins use 1 1/3 cups of walnuts.How many cups of walnuts are needed to 3 3/4 batches of muffins, answers are only 5 cups, 3 3/12 cups, 5 1/12 cups, and 4 cups, there are no 3 1/4 cups
Answer:
5 cups
Step-by-step explanation:
Let us set it up as a fraction.
[tex]\frac{\frac{11}{3}}{1}=3\frac{\frac{3}{4}}{x}[/tex]
Step 1: Divide the given values
[tex]\frac{11}{3}\div 1 \\\\=\frac{11}{3}[/tex]
Step 2: Multiply the result by the other value
[tex]3\frac{3}{4} \\\\3\frac{3}{4} \times \frac{11}{3}\\\\= 13\frac{1}{4}[/tex]
So, with this solution, the answer is [tex]13\frac{1}{4}[/tex]. However, the answer isn't included in the options provided, so that means the answer is 5 cups.
What is the reciprocal function of sine?
A. Cosine
B. Cotangent
C. Cosecant
D. Secant
Answer: its a C
Step-by-step explanation: The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.
Paul ran 12 miles in 1 hour and 36 minutes. What was Paul's average rate, in minutes per mile?
Answer:
8 miles per minute
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
8 minutes per mile
1/2 divided by 4 =__
Answer:
1/2 divided by 4 = 1/8 or 0.125
Step-by-step explanation:
1/2 divided by 4
(1/2) ÷ 4
= 1/2 × 1/4
= 1/8 or 0.125
help plzzzz i need to find the volume of the cone
Answer:
2h3-r5
Step-by-step explanation:
first 3-2=5
then 2h3-r=2h3-r5
finally 2h3-r5
Answer:
3.28653¯V7h
Step-by-step explanation:
Suppose the cost of electricity is $0.03 for each kilowatt-hour. Carlos's house runs on 11.14 kilowatt-hours a day. Find the cost of electricity for Carlos's house in one day.
I need help
An amount of $16,000 is borrowed for 8 years at 7.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Answer:
$28009.05
Step-by-step explanation:
Let us use the formula A = P(1 + r/n)^(nt)
Step 1: Convert 7.25 to decimal
[tex]7.25\% = 0.0725[/tex] in decimal form
Step 1: Percent means 'per 100'. So, 7.25% means 7.25 per 100 or simply 7.25 over 100. [tex]7.25 \div 100\\\\= \frac{7.25}{100}\\\\= 0.0725[/tex] If you divide 7.25 by 100, you'll get 0.0725 (a decimal number).Step 2: Solve with the formula
[tex]A = 16000(1 + 0.0725)^8\\\\A= 28009.05[/tex]
Step 1: Add the numbers: [tex]1+0.0725=1.0725[/tex][tex]=16000\cdot \:1.0725^8[/tex][tex]=16000\cdot \:1.75056[/tex]Step2: Multiply[tex]=28009.05068[/tex]Help pleaseee anyone??
It 's c my friend
okayyyyyyyyyyyyyyy
PLS HELP ME!!!!!!!!!!
Answer:
1) yes, SAS
2) yes, AAS
3) yes, SAS
4) not enough information to know
Step-by-step explanation:
Please solve this for me!
4c + 36 divided by 3 + 4(1 + 2) if c = 5
Answer:4 or 3.70
Step-by-step explanation:
well if c = 5 you should 1st do 4 x 5= 20 + 36 and that equals 56
now do (1+2)=3 x 4 =12 + 3 =15
now not sure what ur answers are but i got either 4 or 3.70
Good Luck!!!
Mi papá quiere comprar una camioneta que cuesta $373,990. Tiene que dar de enganche el 28%. ¿Cuánto es lo que tiene que pagar?
Answer:
i don't speak spanish sorry
Step-by-step explanation:
Answer:
104,717
Step-by-step explanation:
multiplica 373990 por 28% es .28
There are 3 oranges, 8 peaches, and 4 apples in a fruit basket. David selected one piece of fruit at random. He was hungry and ate that fruit. He then selected a second piece of fruit. What is the probability that he selects two peaches?
Answer:
Probabilty[First and second fruit is peach without replacement] = 0.267 (Approx.)
Step-by-step explanation:
Given:
Number of oranges = 3
Number of peach = 8
Number of apple = 4
Find:
Probabilty[First and second fruit is peach without replacement]
Computation:
Probablity of an event = Number of favourable outcomes / Number of outcomes
Probabilty[First fruit is peach] = 8 / [3 + 8 + 4]
Probabilty[First fruit is peach] = 8 / 15
Probabilty[Second fruit is peach] = [8-1] / [3 + 8 + 4 - 1]
Probabilty[Second fruit is peach] = 7 / 14
Probabilty[Second fruit is peach] = 1 / 2
Probabilty[First and second fruit is peach without replacement] = Probabilty[First fruit is peach] x Probabilty[Second fruit is peach]
Probabilty[First and second fruit is peach without replacement] = [8/15][1/2]
Probabilty[First and second fruit is peach without replacement] = 8 / 30
Probabilty[First and second fruit is peach without replacement] = 0.267 (Approx.)
What is the length of the missing leg?
Answer:
a = 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
a = a
b = 8
c = 10
Step 2: Solve for a
Substitute in variables [Pythagorean Theorem]: a² + 8² = 10²Evaluate exponents: a² + 64 = 100[Subtraction Property of Equality] Subtract 64 on both sides: a² = 36[Equality Property] Square root both sides: a = 6Draw a box-and-whisker plot of the data. 37, 34, 26, 33, 38, 36, 30
I don’t know how to do this
Answer:
x-10
Step-by-step explanation:
If a function is defined by the equation y=-5x+1 and the domain is the set {-2,0,2,4},
which set below represents the range of the function?
(1) {11, 12, 13, 14}
(3) {-10, -1,9,19)
(2) {-19, -9,1,10)
(4) {51, 53, 55, 57)
A
Identify the input values.
Since there is an even root, exclude any real numbers that result in a negative number in the radicand
The solution(s) are the domain of the function.
Mark Me Brainest
Lynn spent $21.90 at A Hill of Beans. She bought 2 fruit smoothies at a
cost of $8.90. She bought 2 bear claws at $1.75 each. The rest of the
money was spent on 2 iced mochas. What is the cost of one iced
mocha?
Answer:
$0.3
Step-by-step explanation:
8.90x2=17.8
1.75x2=3.5
17.8+3.5=21.3
21.90-21.3=0.6
0.6/2=0.3
What is the perimeter of the house is c=5
I’m marking brainliest.
Answer:
132
Step-by-step explanation:
C=5
3c - 2 = 13
2c = 10
4c + 1 = 21
4c + 2 = 22
length = (3c- 2) + (4c + 1)
length = 13 + 21
length = 34
width = (4c + 2) + (2c)
width = 22 + 10
width = 32
Perimeter
p = 2l + 2w
p = 2*34 + 2*32
p = 68 + 64
p = 132
Solve the equation. x/3=15 Shown work.
Answer:
45
Step-by-step explanation:
x/3=15
Mutiply each side by 3
x=45
Step-by-step explanation:
[tex] \frac{x}{3} = 15 \\ ✒ \: x = 15 \times 3 \\ ✒ \: x = 45[/tex]
To verify:-
[tex] \frac{x}{3} = 15 \\ ✒ \: \frac{45}{3} = 15 \\ ✒ \: 15 = 15 \\ ✒ \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Here’s the revenue and expenses for the month. Calculate whether Mia had a profit or loss
Answer:
300
Step-by-step explanation:
subract costs from revenue
HELP DUE IN 15 MINS!
Write the equation of a circle that has a center of (-3, 4) and goes through the point (2, 1).
Answer:
Step-by-step explanation:
You can find the left side of the equation for a circle easily enough. It's r^2 that's the problem. It is on the right.
Left Side
(x + 3)^2 + (y - 4)^2 = r^2
Right Side.
x1 = - 3
x2 = 2
y1 = 4
y2 = 1
Use the distance formula to get r^2
r^2 = (x2 - x1)^2 + (y2 - y1)^2
r^2 = (2 - - 3)^2 + (1 - 4)^2
r^2 = 5^2 + (-3)^2
r^2 = 25 + 9
r^2 = 34
Answer
(x + 3)^2 + (y - 4)^2 = 34
What are the solutions to the system of equations?
y=4x^2+6x−3
y=2x−3
Enter your answers in the boxes.
(_,_) and (_,_)
Answer:
(0, - 3 ) and (- 1, - 5 )
Step-by-step explanation:
Given the 2 equations
y = 4x² + 6x - 3 → (1)
y = 2x - 3 → (2)
Substitute y = 4x² + 6x - 3 into (2)
4x² + 6x - 3 = 2x - 3 ( subtract 2x - 3 from both sides )
4x² + 4x = 0 ← factor out 4x from each term
4x(x + 1) = 0
Equate each factor to zero and solve for x
4x = 0 ⇒ x = 0
x + 1 = 0 ⇒ x = - 1
Substitute these values into (2) for corresponding values of y
x = 0 : y = 2(0) - 3 = 0 - 3 = - 3 ⇒ (0, - 3 )
x = - 1 : y = 2(- 1) - 3 = - 2 - 3 = - 5 ⇒ (- 1, - 5 )
A cylinder and its dimensions are shown below.
5 in.
3.5 in.
Benton is painting the lateral surface of this cylinder. Which expression will give him
the number of square inches that he will be painting?
Answer: 2π(1.75)(5)
Step-by-step explanation:
Hoped this helped