Car X leaves Northtown traveling at a steady rate of 55 mph. Car Y leaves 1 hour later following Car X, traveling at a steady rate of 60 mph. Which equation can be used to determine how long after Car X leaves Car Y will catch up?
The equation that can be used to determine how long after Car X leaves Car Y will catch up is D. 55x = 60(x - 1).
To determine when Car Y will catch up to Car X, we need to find the time it takes for Car Y to cover the same distance as Car X. Since Car Y leaves 1 hour later, it will travel for (x - 1) hours, where x represents the time Car X has been traveling. So, the equation would be:
D. 55x = 60(x - 1)
This equation accounts for the distance traveled by both cars over the same time frame, considering Car Y started an hour later.
Complete question : Car X leaves Northtown traveling at a steady rate of 55 mph. Car Y leaves 1 hour later following Car X, traveling at a steady rate of 60 mph. Which equation can be used to determine how long after Car X leaves Car Y will catch up? A. 55x=60x-1 B.55x=60x C.60x=55x(x-1) D.55x=60(x-1).
Gio is solving the quadratic equation by completing the square 5x^2+15x-4=0 What's should gio do first?
Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]
To solve the quadratic equation [tex]\(5x^2 + 15x - 4 = 0\)[/tex] by completing the square, Gio should follow these steps:
1. Make the Coefficient of [tex]\(x^2\) 1:[/tex]
Divide the entire equation by the coefficient of [tex]\(x^2\)[/tex] to make it equal to 1. In this case, divide the equation by 5:
[tex]\[x^2 + 3x - \frac{4}{5} = 0.\][/tex]
2. Move the Constant to the Other Side:
Move the constant term to the other side of the equation:
[tex]\[x^2 + 3x = \frac{4}{5}.\][/tex]
3. Complete the Square:
Add and subtract [tex]\((\frac{3}{2})^2\)[/tex] inside the parentheses to complete the square:
[tex]\[x^2 + 3x + (\frac{3}{2})^2 = \frac{4}{5} + (\frac{3}{2})^2.\][/tex]
4. Factor the Perfect Square Trinomial:
Factor the left side, which now is a perfect square trinomial:
[tex]\[(x + \frac{3}{2})^2 = \frac{25}{4}.\][/tex]
5. Solve for (x):
Take the square root of both sides and solve for (x):
[tex]\[x + \frac{3}{2} = \pm \frac{5}{2}.\][/tex]
6. Isolate (x):
Isolate (x) on one side to find the solutions:
[tex]\[x = -\frac{3}{2} \pm \frac{5}{2}.\][/tex]
Therefore, Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]
The sum of two consecutive integers is 65. Find the two integers.
Which letters from the table represent like terms? -2x 3 4x 1
Find the domain of the graphed function?
Answer:
The correct answer to this question is C: x > 0
Step-by-step explanation:
The cost of renting a car is $35/wk plus $0.25/mi traveled during that week. An equation to represent the cost would be y = 35 + 0.25x, where x is the number of miles traveled. If your cost was $51.25, how many miles were you charged for traveling?
To find the number of miles traveled when the total cost is $51.25, subtract the base cost from the total and divide by the per-mile rate, resulting in 65 miles traveled.
Explanation:The question asks how many miles were traveled if the total cost for renting a car was $51.25. According to the equation y = 35 + 0.25x, where y represents the total cost and x represents the miles traveled, we first need to subtract the base cost of $35 from the total cost to find out how much is charged for the mileage.
Here is how you calculate it:
Subtract the weekly rental cost from the total cost: $51.25 - $35 = $16.25. Divide the remaining cost by the cost per mile: $16.25 / $0.25 = 65 miles.
Therefore, you were charged for traveling 65 miles.
Estimates 3 2/3 \ 3 2/9
wich one of these numbers is not like the others 21,15,6,16,27
carl puts $1.10 in his piggy bank everyday in month of July (31 days)his total saving was $55.00 at the end of June what is the best estimate for his savaging at the end of June
Vanessa made 6 sandwiches for a party and cut them all into fourths. How many 1/4 sandwich pieces did she have?
Margaret uses 1 3/4 teaspoons of vanilla to make 12 cupcakes. She to wants make 30 cupcakes. how much vanilla will Margaret use?
To make 30 cupcakes Margaret needs 4.375 cups of vanilla.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Margaret uses 1 3/4 teaspoon of vanilla to make 12 cupcakes
So,
1 3/4 teaspoon vanilla ⇒ 12 cupcakes
(4×1 + 3)/4 teaspoon ⇒ 12 cupcakes
7/4 teaspoon vanilla ⇒ 12 cupcakes
Divide by 12 into both sides,
7/(4×12) teaspoon vanilla ⇒ 1 cupcake
Now multiply by 30 on both sides,
(7 × 30)/(4 × 12)teaspoon vanilla ⇒ 30 cupcake
30 cupcakes ⇒ 4.375 teaspoon vanilla.
Hence "To make 30 cupcakes Margaret needs 4.375 cups of vanilla".
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Need help with this problem
Scott has fees taken out of his bank account each month for 3 months. A total of $12 is taken from his bank account.
Drag the numbers to form the equation that represents the change in Scott's bank account each month.
( ? )( ? ) = ( ? )
3, -3, 12, -12, 1/3, -1/3, 4, -4
Show work
Is the value 75+(-75) less than zero, equal to zero, or greater than zero?
what is 3/4 of 535?????????
Order these fractions from greatest to least. 4/9 , 4/10 , 4/5
DIVIDING ALGEBRAIC FRACTIONS
2p/4p^2 divided by 6p^3/6p+3
Consider the equation 3p – 7 + p = 13. What is the resulting equation after the first step in the solution?
Find the area of a triangle that has a base of 10 inches and a height of 7 inches.
A) 8.5 in2
B) 17 in2
C) 35 in2
D) 70 in2
Answer:
C ) 35 in2
Step-by-step explanation:
i did the test
write an expression 13+ 19+ 17 using mental math
Explanation:
It is convenient to regroup the numbers, and adjust two of them to "make a ten".
= 13 + 17 + 19 . . . . rearrange (swap the order of 17 and 19)
= (10 + 3) + (-3 + 20) + 19 . . . . "make a ten" by adding or subtracting a small number. Here, those adjustments cancel—which is the point of doing it.
= 10 + 20 + 19
= 30 + 19
= 49
A number n is less than 6 units from 0. Write an absolute value inequality
The absolute value inequality which relates to the expression n is less than 6 units from 0 is |n|< 6
The absolute value which stand for 6 units From 0 can be expressed as :
|0 - 6| = 6 (absolute value of any number or expression is always positive)This means that, the number n is less than 6
Therefore, the expression can be written as :
|n| < 6. This means that the absolute value of n is less than 6.
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To write an absolute value inequality when a number n is less than 6 units from 0, use the notation |n| < 6.
Explanation:To write an absolute value inequality, we need to express the distance between the number n and 0 as less than 6 units. This can be done by using the absolute value notation: |n| < 6. In this inequality, the absolute value of n must be less than 6 units.
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Solve. 54 ÷ (4 – 1)3
One card is randomly selected from a deck of cards. find the odds against drawing a blackblack fivefive.
Factor the difference of two cubes
A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?
Compound interest formula: (image uploaded V(t) )
t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years
A. 5.9 years
B. 6.1 years
C. 23.4 years
D. 24.5 years
Compound interest is the interest generated overtime on a sum of money invested. The time it will take for the amount of money to double is 5.9 years
How to calculate the compound interest?Compound interest is the interest generated overtime on a sum of money invested. The formula for calculating compound interest is expressed as:
V(t) = P(1+r/n)^nt
where:
t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t yearsGiven the following
V(t) = 2P
r = 0.12
n = 4
Substitute
2P = P(1+0.12/4)^4t
2 = (1.03)^4t
ln2 = 4t ln(1.03)
0.6931 = 0.1182t
t = 0.6931/0.1182
t = 5.9 years
Hence the time it will take for the amount of money to double is 5.9 years
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A senior class is selling lanyards as a fundraiser. The profit for each lanyard is $0.75. Write and solve an inequality to determine the number of lanyards the class must sell to make a profit of at least $250.
Which expression is the factorization of x2 + 10x + 21?
A) (x + 3)(x + 7)
B) x + 4)(x + 6)
C) (x + 6)(x + 15)
D) (x + 7)(x + 14)
pep club members are making spirit buttons. They make 490 spirit buttons in 3 1/2 hours. Find the number of button pep club makes per hour
Answer:
140 button pep club makes per hour.
Step-by-step explanation:
Given : Pep club members are making spirit buttons. They make 490 spirit buttons in [tex]3\frac{1}{2}[/tex] hours.
To find : The number of button pep club makes per hour ?
Solution :
In [tex]3\frac{1}{2}[/tex] hours they make 490 buttons.
i.e. In 3.5 hours they make 490 buttons.
So, In 1 hours they make [tex]\frac{490}{3.5}[/tex] buttons.
In 1 hours they make 140 buttons.
Therefore, 140 button pep club makes per hour.
A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000. So far, they have spent $824,000. Which compound inequality correctly expresses how much more the publisher can spend?
$155,850 ≥ x ≤ $415,850
$155,850 ≤ x ≥ $415,850
$155,850 ≥ x ≥ $415,850
$155,850 ≤ x ≤ $415,850
Answer:
[tex]155,850 \leq x \leq 415,850[/tex]
Step-by-step explanation:
A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000.
Let x be the amount publisher can spend
So, [tex]980000\leq x \leq 1240000[/tex]
Now we are given that So far, they have spent $824,000
So, [tex](980000-824000)\leq x \leq (1240000-824000)[/tex]
[tex]156000\leq x \leq 416000[/tex]
So, Option D is true
Hence compound inequality correctly expresses how much more the publisher can spend is [tex]155,850 \leq x \leq 415,850[/tex]
If one inch represents 8 feet, what dimensions would you use to make a scale drawing of a building 34 feet by 75 feet?
Please answer and explain!
Which is true? A 4.02 > 4.1 B 4.181 < 4.118 C 4.5 > 4.49 D 4.665 > 4.67
The statements, 4.02>4.1, 4.181<4.118 and 4.665>4.67 are true. Therefore, options A, B and D are the correct answers.
How to compare to decimals?Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.
A) 4.02>4.1
Here, the statement is true.
B) 4.181<4.118
The statement 4.181<4.118 is true.
C) 4.5>4.49
The statement 4.5>4.49 is not true.
D) 4.665>4.67
The statement 4.665>4.67 is true.
Therefore, options A, B and D are the correct answers.
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