Final answer:
The second car, starting 1/2 hour late and traveling at 55 miles per hour, will take 2.25 hours to catch up to the first car. This means it will catch up before the first car, traveling at 45 miles per hour, reaches the destination 135 miles away in 3 hours.
Explanation:
The question involves calculating the time it will take for the second car, traveling at an average speed of 55 miles per hour and starting 1/2 hour later, to catch up to the first car, which left on time traveling at an average speed of 45 miles per hour to a destination 135 miles away. To solve this, we need to find when both cars have traveled the same distance.
First, calculate the distance the first car has traveled by the time the second car starts: Distance = Speed × Time, which is 45 miles/hour × 0.5 hours = 22.5 miles. This means the second car starts 22.5 miles behind the first car.To catch up, the second car needs to cover this 22.5-mile gap in addition to the same distance covered by the first car moving forward. The relative speed at which it's catching up to the first car is the difference in their speeds: 55 miles/hour - 45 miles/hour = 10 miles/hour. Thus, the time to catch up is calculated as Time = Distance / Speed, which in this case is 22.5 miles / 10 miles/hour = 2.25 hours.Finally, since the first car travels at 45 miles per hour, we calculate if it arrives before being caught: Time of travel for the first car to reach 135 miles is 135 miles / 45 miles per hour = 3 hours. Since 2.25 hours (the catch-up time) is less than 3 hours (the travel time to the destination), the second car will indeed catch up to the first car before it arrives at the football game.
Can someone help me with this sat question
Answer:
2,-2
Step-by-step explanation:
makito answered 70 pecent of 30 test quedtions correctly how many questions did he answer correctly
Answer:
21
Step-by-step explanation:
Millie needs the average height of the plants she is buying to be at least 73 inches.She has selected three plants that are 70,71,and 72 inches tall. Write and solve an inequality that Millie could use to determine the possible heights of her fourth plant
Which values make this equation true?
(5x^7 y^2)(-4x^4 y^5)=-20x^a y^b
A.) a=11, b=7
B.) a=11, b=10
C.) a=28, b=7
D.) a=28, b=10
When multiplying terms with exponents, just add the exponents together.
You have x^7 and x^4, so 7 +4 = 11
Y^2 and Y^5 = 2+5 = 7
so it would be -20x^11 y^7
The answer is A.) a=11, b=7
What is the solution to the system of equations?
y = x – 10
2x + y = 4
(–8, 6)
(–6, 16)
(6, –8)
(16, –6)
Answer:
The solution is the point (6,-8)
Step-by-step explanation:
we have that
The first equation is [tex]y=(1/3)x-10[/tex] instead [tex]y=x-10[/tex]
[tex]y=(1/3)x-10[/tex] -----> equation A
[tex]2x+y=4[/tex] -----> equation B
Solve the system of equations by substitution
Substitute equation A in equation B and solve for x
[tex]2x+[(1/3)x-10]=4[/tex]
[tex](7/3)x=14[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=(1/3)(6)-10=-8[/tex]
therefore
The solution is the point (6,-8)
What is the value of x?
Answer:
The value of x is 68 degrees!
Step-by-step explanation:
In this question, we have an isosceles triangle because of Base Angles Theorem. The 2 sides are congruent, which means its an isosceles and that the Base angles are congruent. So far, we know that 2 angles are equal to 112 degrees. Due to Sum Angles Theorem, we can go 180-112 to get 68 degrees!
Answer:
x=68
Step-by-step explanation:
Since this is an isosceles triangle, the bottom two angles are the same value, 56 degrees. The three angles of a triangle add to 180 degrees.
56+56+ x = 180
Combine like terms
112 +x = 180
Subtract 112 from each side
112-122 +x = 180 -112
x =68
what is the value of x
enter your answer in the box
Answer:
x = 19
Step-by-step explanation:
3x - 3 = 6(x - 10)
3x - 3 = 6x - 60
+3 +3
3x = 6x - 57
- 6x
- 3x = -57
= 19
Answer:
x = 19Step-by-step explanation:
[tex](3x-3)^{0} =\left[6(x-10)] ^{0}\\[/tex] (opposite angle)
[tex]3x-3=6(x-10)\\ 3x-3=6x-60\\ 60-3=6x-3x\\ 57=3x\\ \frac{57}{3} =x\\ 19=x[/tex]
this property says you can rewrite 3 x (4+5) as (3x4) +(3 x 5).
Answer:
distributive property
Step-by-step explanation:
Distributive property says that x(y + z) = (x*y) + (x *z)
The property used in the given expression is
Distributive property of multiplication over addition.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distributive property of multiplication over addition states that,
a(b + c) = a x b + a x c
Now,
3(4 + 5) = (3 x 4) + (3 x 5)
This is the Distributive property of multiplication over addition.
Thus,
The property of distributive multiplication over addition is used.
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You can buy 5 stickers for 3$. Write a proportion that gives you the cost of c if you buy 12 stickers.
Answer:
$7.20
Step-by-step explanation:
I got u bro, Divide the price of the stickers by the number of stickers ($3/5=$.60) multiply the price of one sticker by the number of stickers ($.60x12=) :)
Final answer:
The cost of 12 stickers can be found by writing the proportion 5 stickers/3 dollars = 12 stickers/c dollars and solving for c, which yields c = 7.2. Thus, 12 stickers cost $7.20.
Explanation:
The student is asked to write a proportion to determine the cost c if they buy 12 stickers when the known price is 5 stickers for $3. To set up the proportion, we can compare the number of stickers to the cost. We have one ratio of 5 stickers to $3, and we need to find the equivalent ratio for 12 stickers to $c. The proportion can be represented as:
5 stickers / 3 dollars = 12 stickers / c dollars
Now we cross-multiply to solve for c:
5 * c = 3 * 12
c = (3 * 12) / 5
c = 36 / 5
c = 7.2
Therefore, the cost c of 12 stickers is $7.20.
3/4 is considered a real and rational number
Answer:
It is a rational number and real number
Explanation:
it is a real number because it can become .75 and that is a real number.
it is a rational number because assume that 3/4 is a rational number. Since every rational number can be expressed as a/b form which do not have any common factor so we can say that a/b = 3/4 Squaring both side we get: a2/b2 = 9/16 a2 = (9/16) b2 Or we can say b2 = a2(16/9) a2 is divided by 9. So we can say that a is divided by 9. It implies that there exist some number c such that a/9 = c a = 9c By squaring both side we get a2 = 81 c2 Put the value of a2 from the equation a2 = (9/16) b2 we get: (9/16)b2 = 81c2 this tends to b2/ 9 = 16 c2 It implies that b2 is divided by 9. So we can say that b is divided by 9. This implies that a and b have a common factor 9. Since a and b have common factor therefore 3/4 is not a irrational number. Hence 3/4 is a rational number.
Good luck
Please mark me brainliest
Answer:
3/4 is a rational number and also a real number
Step-by-step explanation:
to prove 3/4 is real
3/4 is a fraction. It is a proper fraction since denominator is grater than numerator.
3/4 can be written as 0.75 which is terminating decimal.
Therefore 3/4 is a real number
To prove 3/4 is a rational number
3/4 is the form of p/q.
Therefore 3/4 is a rational number.
What’s the area of this rounded to the nearest one’s place?
Answer:
I think I might be terribly wrong but 160,728 ft
Step-by-step explanation:
Answer:
503
Step-by-step explanation:
To find the area of a cirlce it is pi x 2 x the radius squared.
Since,this is a semi-circle you dived by 2 afterwards.
So [tex]\pi x 160 x 2 /2[/tex] is 502.857142857
Round that to the nearest one that is 503 ft squared.
Which of the following is a solution to the inequality 7-1/5x>0?
[tex]7-\dfrac{1}{5}x>0\qquad\text{subtract 7 from both sides}\\\\-\dfrac{1}{5}x>-7\qquad\text{change the signs}\\\\\dfrac{1}{5}x<7\qquad\text{multiply both sides by 5}\\\\\boxed{x<35}[/tex]
Which table shows a proportional relationship?
Answer:
the answer is the last one
Step-by-step explanation:
i drew all the example and i would say that the last one came out having a proportional relationship.
tell me if i got it right!
sasha is reading a novel wth 427 pages. she has read 276 pages. what percentage has she read?
Final answer:
Sasha has read approximately 64.66% of the novel by dividing the number of pages she read (276) by the total number of pages (427), and then multiplying the result by 100.
Explanation:
To find out what percentage of the novel Sasha has read, we need to use the formula for percentage:
Percentage = (Part / Whole) × 100
Sasha has read 276 pages of a 427-page novel. So, in this case, the part is 276, and the whole is 427.
Now we calculate:
Divide the number of pages read by the total number of pages: 276 / 427.Multiply the result by 100 to get the percentage: (276 / 427) × 100.Let's do the math:
276 divided by 427 is approximately 0.6466.Multiplying 0.6466 by 100 gives us approximately 64.66%.Therefore, Sasha has read about 64.66% of the novel.
The shallowest section of an underground tunnel is -50 feet. The deepest section of the tunnel is -135 feet. How many feet below the shallowest section is the deepest section
A. -95 feet
B. - 185 feet
C. 85 feet
D. 195 feet
Answer:
The answer would be c)85 FEET
Step-by-step explanation:You start with the deepest section(-135) and add the shallowest point(50). the result is an 85 foot difference.
Answer: c 85ft
Step-by-step explanation:
The area of a rectangular mirror is 15 15/16 square feet. The width of the mirror is 3 3/4 feet. If there is a 5 foot tall space on the wall to hang the mirror, will it fit? Explain. _________ fit because the height is ______ feet.
Answer: The mirror will fit because the height of the mirror is 4 feet.
Step-by-step explanation:
we just divide 15 by 3 3/4 and get the answer of 4.
Yes, the mirror will fit on the wall because its height is approximately 4.25 feet, which is less than the 5-foot tall space on the wall.
Explanation:To determine whether the mirror will fit, we need to calculate its height. Since the area of a rectangle is given by the formula Area = Height × Width, we can find the height by rearranging the formula to Height = Area ÷ Width.
The given area of the mirror is 15 15/16 square feet and the given width is 3 3/4 feet.
After performing the division, we get the height of the mirror to be approximately 4.25 feet.
Since the space on the wall is 5 foot tall and the height of the mirror is less than this, the mirror will fit on the wall. So, the answer is: Yes, it will fit because the height is 4.25 feet.
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Factor the expression over the complex numbers.
x2+25
[tex]Use\\\\a^2-b^2=(a-b)(a+b)\\\\i=\sqrt{-1}\to i^2=-1\\------------------------\\\\x^2+25=x^2+5^2=x^2-(-5^2)=x^2-(5i)^2\\\\\boxed{x^2+25=(x-5i)(x+5i)}[/tex]
What is the distance between the points (12,-8) and (-14,20)
Answer:
The approximate distance between the points is 38.2
Step-by-step explanation:
The distance between these two points is a diagonal line. In order to solve this problem, you need to plot your points and form a right triangle. The overall distance from one point to another on the x-axis is 26 (12-(-14)), and the overall distance from one point to another on the y-axis is 28 (20-(-8)). These two distances will form a right angle at (-14,-8). The distances on the x and y axis are the 'legs' of the triangle and the distance between the given points in the problem represents the hypotenuse. Using the pythagorean theorem (a^2 +b^2 = c^2), we can substitute in our values of 'a' and 'b' to get 28^2 + 26^2 = c^2, or 784 + 676= 1460, therefor the square root of 1460 is approximately 38.2.
So to find the distance between these two points, we are going to be plugging them into the Distance Formula and solving as such:
[tex]D=\sqrt{(12-(-14))^2+(-8-20)^2}\\D=\sqrt{(26)^2+(-28)^2}\\D=\sqrt{676+784}\\D=\sqrt{1460}[/tex]
Now, with this radical we can simplify it using the product rule of radicals (√ab = √a × √b) as such:
[tex]\sqrt{1460}=\sqrt{10*146}=\sqrt{5*2*2*73}=2*\sqrt{73*5}=2\sqrt{365}[/tex]
Answer:In short:
Exact distance: √1460 or 2√365 unitsApproximate Distance (rounded to the hundreths): 38.21 unitsAn electrician has $120 to spend on interior light fixtures. the wholesale price for 13-watt low-energy lamp is $4. The price for a high-energy lamp is $5. write an expression for how much the electrician spends for A units of the low-energy lamp and B units of the high-energy lamp.
complete the table for the electrician's purchase. assume that all of the $120 is spent
To find the expression for the cost of low-energy lamps and high-energy lamps, use the expressions 4A and 5B respectively. To find the values of A and B that make the total cost equal $120, solve the equation 4A + 5B = 120.
Explanation:To write an expression for how much the electrician spends on low-energy lamps and high-energy lamps, we can use the following expressions:
Cost of low-energy lamps: 4A
Cost of high-energy lamps: 5B
To complete the table, we need to calculate the values of A and B such that the total cost equals $120. Since all of the $120 is spent, the expression for the total cost would be:
Total cost: 4A + 5B = 120
We can solve this equation to find the values of A and B.
Please help, ASAP:
Five liters of a20% salt solution was mixed with five liters of a70% salt solution. Find the concentration of salt in the mixed solution?
Answer: 45%
Step-by-step explanation:
[tex]\underline{\qquad \qquad\quad|\text{Quantity}|\quad\%\quad|\text\quad{Qty } \times\text{\%}\qquad}\\\underline{\text{Solution A }|\text{5 liters}\quad|\text{0.20}\quad|5\times0.20=1.00}\\\underline{\text{Solution B }|\text{5 liters}\quad|\text{0.70}\quad|5\times0.70=3.50}\\\text{Mixture }\quad|\text{ 10 liters }|\quad\text{x}\quad|\qquad\text{4.50}[/tex]
10x = 4.50
x = .45
= 45%
Please help me!!!!! PLeASe Also I will be giving Brailiest
Answer:
x = 75
y = 105
Step-by-step explanation:
Remark
You can find y in two different ways.
One
You can recall that y is the sum of the 2 interior angles not connected to it. Those angles are called the remote interior angles. Or
Two
You can add the three angles to 180 and solve for x. Then since x and y are supplementary, you can find y.
Solution
One
y = 60 + 45
y = 105 Answer
Two
x + 60 + 45 = 180 All triangles have 180 degrees. Solve for x.
x + 105 = 180 Subtract 105 from both sides
x = 180 - 105 Combine
x = 75 Find an equation that relates x and y
x + y = 180 x and y are supplementary they add to 180
75 + y = 180 Subtract 75 from both sides.
y = 180 - 75 Combine
y = 105
kristin spent &131 on shirts. Fancy shorts cost $28 and plain shorts cost $15. if she bought a total of 7 then how many of each kind did she buy?
Answer:
3 fancy shorts
4 plain
Step-by-step explanation:
By setting up equations for the total cost and the number of shorts purchased, we find that Kristin bought 2 fancy shorts at $28 each and 5 plain shorts at $15 each.
To solve the problem, let's denote the number of fancy shorts Kristin bought as F and the number of plain shorts as P. The problem gives us two conditions: Kristin spent a total of $131 on shorts, and she bought a total of 7 shorts. Fancy shorts cost $28 each, and plain shorts cost $15 each.
Now, we can set up two equations based on this information:
For the total cost: 28F + 15P = 131 (1)For the total number of shorts: F + P = 7 (2)Using equation (2), we can express P as P = 7 - F and substitute this into equation (1) to solve for F:
28F + 15(7 - F) = 131
Simplify the equation:
28F + 105 - 15F = 131
13F = 26
F = 2
Now that we have the value for F, we can use it to find P:
P = 7 - F
P = 7 - 2
P = 5
Kristin bought 2 fancy shorts and 5 plain shorts.
6(3c - 5d +6) using distributive property
Expanding, you get 6(3c) - 6(5d) + 6(6) = 18c - 30d +36
Answer:
18c - 30d +36
Step-by-step explanation:
6(3c - 5d +6)
When we use the distributive property, we distribute the 6 to all the terms inside the parentheses
6*3c - 6*5d +6*6
18c - 30d +36
Quincy is trying to estimate the height of a tree in his backyard. He measures the tree’s shadow as 12 ft. He stands near the tree and measures his own shadow as 3 ft. Quincy knows that he is about 5 ft tall. He estimates the height of the tree by following these steps
Answer:
The tree is 20 ft tall.
Step-by-step explanation:
We can use ratio's to solve this problem. Take the height of the object over the shadow length.
5 ft x ft
----------- = ----------------
3ft 12 ft
Using cross products
5*12 = 3*x
60 = 3x
Divide by 3 on each side
60/3 = 3x/3
20 =x
The tree is 20 ft tall.
The expression 50w+400 represents the amount of money Jenny has in her savings account after an unknown number of weeks. How much money does Jenny originally have in her savings account? Which part of the equation represents the amount of money she will put away each week? Explain your answers.
Answer:
400 originally, and 50 dollars a week from there!!
Step-by-step explanation:
Since the 50 is followed by the variable "w", and the w stands for week, we can believe that Jenny makes 50 dollars a week.
Because the 400 was in the her account to begin with, we know this is the amount she originally had!
which number, when placed in the box, will make the equation true?
[tex] {?}^{2} = \sqrt{64} [/tex]
A.
[tex] \sqrt{8} [/tex]
B.
[tex] \sqrt{32} [/tex]
C. 16
D. 32
[tex]\mathsf{\heartsuit\;\; (\sqrt{8})^2 = \sqrt{64}}\\\\\mathsf{\heartsuit\;\; [(8)^\frac{1}{2}]^2 = \sqrt{(8)^2}}\\\\\mathsf{\heartsuit\;\; (8)^\frac{2}{2} = [(8)^2]^\frac{1}{2}}\\\\\mathsf{\heartsuit\;\; 8 = [8]^\frac{2}{2}}\\\\\mathsf{\heartsuit\;\; 8 = 8}\\\\\mathsf{\heartsuit\;\; Option\;(A)\;is\;the\;Answer}[/tex]
The number which will make the equation true, when placed in the box is: A. √8.
How to solve for the unknown number?In order to determine the unknown number, we would assign a variable (x) to the unknown number and then evaluate the resulting algebraic equation as follows:
x² = √64
x² = 8
Taking the square root of both sides, we have:
x = √8.
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is y=19x-5 proportional?
If x and y are proportional, then y : a = constant.
[tex]\dfrac{y}{x}=a\to y=ax[/tex] ← the equation
We have y = 19x - 5. It's not a proportional.
The coordinates of point b
Answer:
(3, -1) PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Solve for y.
50/90-y=5/18
Answer:
y = 5/18
Step-by-step explanation:
50/90-y=5/18
Lets simplify our fractions
50/90 = 5/9 (divide top and bottom by 10)
5/9 - y = 5/18
Subtract 5/9 from each side
5/9 -5/9 -y = 5/18 - 5/9
-y = 5/18 - 5/9
We need to get a common denominator of 18
-y = 5/18 - 5/9 *2/2
-y = 5/18 -10/18
-y = -5/18
Multiply each side by -1
-1*-y = -5/18 * -1
y = 5/18
A rectangle with vertices A(6, 0), K(0,0), L(0,9), and M(6, 9) is rotated around the x-axis. To the nearest tenth of a cubic unit, what is the volume of the resulting three-dimensional figure? Approximate as 3.14.
Answer:
1526.0 cubic units
Step-by-step explanation:
Rotating rectangle AKLM you will get cylinder with height KA and base radius KL. From the given data
[tex]KA=\sqrt{(6-0)^2+(0-0)^2}=6,\\ \\KL=\sqrt{(0-0)^2+(9-0)^2}=9.[/tex]
The volume of the cylinder is
[tex]V_{cylinder}=\pi r^2\cdot H.[/tex]
Then
[tex]V_{cylinder}=\pi \cdot 9^2\cdot 6=486\pi \approx 1526.0\ un^3.[/tex]