Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
A car covers the distance between two cities in 6 hours.
A van covers the same distance in 5.5 hours.
The speed of the van is 4 km per hour faster than the speed of car.
Let assume that
Speed of the car be x km per hour
So,
Speed of van is x + 4 km per hour.
Let further assume that
Distance between two cities be y km.
We know, Distance covered = Speed × Time.
➢ Now, Distance (y) covered by car at the speed of x km per hour in 6 hours is
[tex]\rm :\longmapsto\:\boxed{\tt{ y = 6x}} - - - - (1)[/tex]
➢ Also, Distance (y) covered by van at the speed of x + 4 km per hour in 5.5 hours is
[tex]\rm :\longmapsto\:\boxed{\tt{ y = 5.5(x + 4)}} - - - - (2)[/tex]
So, from equation (1) and (2), we have
[tex]\rm :\longmapsto\:6x = 5.5(x + 4)[/tex]
[tex]\rm :\longmapsto\:6x = 5.5x + 22[/tex]
[tex]\rm :\longmapsto\:6x - 5.5x = 22[/tex]
[tex]\rm :\longmapsto\:0.5x = 22[/tex]
[tex]\rm :\longmapsto\:\dfrac{5}{10} \times x = 22[/tex]
[tex]\rm :\longmapsto\:\dfrac{1}{2} \times x = 22[/tex]
[tex]\bf\implies \:x = 44[/tex]
On substituting the value of x, in equation (1), we have
[tex]\rm :\longmapsto\:y = 6 \times 44[/tex]
[tex]\bf\implies \:y = 264[/tex]
So,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Distance \: between \: cities = 264 \: km} \\ \\ &\sf{Speed \: of \: car \: = \: 44 \: km \: per \: hour}\\ \\ &\sf{Speed \: of \: van \: = \: 48 \: km \: per \: hour} \end{cases}\end{gathered}\end{gathered}[/tex]
b^(3) * b^(4) write without exponents
Answer:
(b×b×b)×(b×b×b×b)
Step-by-step explanation:
Writing the equation out is the only way to remove the exponents.
HELPPPP PLEASEEEE!!!!
Answer:
B
Step-by-step explanation:
what are the x and y intercepts of the equation -2x +3y=10
Answer:
Step-by-step explanation:
To find the x-intercept, let y = 0 and solve the resulting equation for x:
-2x + 3(0) = 10, or -2x = 10. This results in x = -5; the x-intercept is (-5, 0).
To find the y-intercept, let x = 0 and solve for y: -2(0) + 3y = 10, or y = 10/3.
The y-intercept is (0, 10/3).
if 18 out of 40 snacks are sweet how many sweet snacks will there be per 100 snacks
Answer:
45 sweet snacks
Step-by-step explanation:
100/40 = 2.5 time more (how many more snacks total)
18 x 2.5 = 45
Answer:
45
Step-by-step explanation:
18 out of 40 is 45%
45% of 100 is 45
How many numbers x between 1 and 100 (inclusive) have the property that x2+x3 is a perfect square?
(Please help. I'm suffering)
=========================================================
Explanation:
Factor the given expression
x^2+x^3
x^2*1+x^2*x
x^2(1+x)
x^2(x+1)
We end up with something where the factor x^2 is a perfect square regardless of whatever we replace x with from the set {1,2,3,...,99,100}.
In short, we don't need to worry about the x^2 portion.
--------------------
The only thing of importance is the x+1 factor.
The x+1 must be a perfect square so that the original expression is as well.
Let's say M is some perfect square between 1 and 100. That means M belongs to the set of values
{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
If we want M+1 to be a perfect square, then we'll need to subtract 1 from each item in that set above to counteract the "plus 1" in "M+1".
Subtract 1 from each item to end up with this modified set
{0, 3, 8, 15, 24, 35, 48, 63, 80, 99}
--------------------
Every item mentioned in that second set will make x^2+x^3 to be a perfect square.
For example, let's pick x = 15
x^2(x+1) = 15^2*(15+1)
x^2(x+1) = 15^2*16
x^2(x+1) = 15^2*4^2
x^2(x+1) = (15*4)^2
x^2(x+1) = 60^2
This confirms that x^2+x^3 is a perfect square for x = 15. I'll let you check the other values.
There are 10 values in the set {1^2,2^2,...,9^2,10^2} = {1,2,...,81,100}. There are also 10 values in the set {0,3,8, ..., 80, 99} we got earlier. The cardinality hasn't changed. However, we'll kick out 0 because it's not between 1 and 100. So we end up with 9 as our final answer.
--------------------
To summarize, there are 9 values of x that make x^2+x^3 a perfect square, where x is some whole number between 1 and 100 inclusive.
[tex]\frac{1}{2}[/tex](-1.4m+0.4)= |?|m+0.2
What number makes the expression equivalent?
what do you have to do
100 points
.
I know the answer I just need explanation as to why this is the answer!
The question:
3. Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
The answer:
Student A is Wrong and student B is correct!
The work of the students:
You are given line AB and point C. Construct a line parallel to line AB that passes through point C.
Student A Steps:
Draw a line that intersects points B and C.
Draw a line through point C and point G.
Keep the compass at the same width, and place it on point C.
Keeping the compass at the same width, place it on point F.
Mark the intersection of the two arcs as point G.
Open the compass to the width between points D and E.
Place the compass on point B, and swing an arc that crosses line AB and line BC. Label the points D and E.
Swing an arc that crosses line BC, and label the point F.
Swing an arc that intersects the arc created from line BC at point C.
Student B steps:
Draw a line that intersects points B and C.
Place the compass on point B, and swing an arc that crosses line AB and line BC. Label the points D and E.
Keep the compass at the same width, and place it on point C.
Swing an arc that crosses line BC, and label the point F.
Open the compass to the width between points D and E.
Keeping the compass at the same width, place it on point F.
Swing an arc that intersects the arc created from line BC at point C.
Mark the intersection of the two arcs as point G.
Draw a line through point C and point G.
Student A is wrong and Student B is correct.
How?
Direction is saying to construct a line that passes through C The last step is enough to describe that A is wrong.Its saying to swing an arc(Should be line).On the other hand Student B has done correct By passing point through C and G it satisfies our required construction.A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
x =
Answer:
2/3 My guy
Step-by-step explanation:
Answer:
The completeness property for points in the plane tells us two things
Exactly one point in the plane is named given the numbers of the ordered pair and
Exactly one ordered pair of numbers names a given point in the plane.
To graph a point one draws a dot at the coordinates that corresponds to the ordered pair. It's always a good idea to start at the origin. The x-coordinate tells you have many steps you have to take to the right (positive) or left (negative). And the y-coordinate tells you have many steps to move up (positive) or down (negative).
To find out the coordinates of a point in the coordinate system you do the opposite. Begin at the point and follow a vertical line either up or down to the x-axis. There is your x-coordinate. And then do the same but following a horizontal line to find the y-coordinate.
A relation is a set of ordered pairs. The first coordinate (usually the x-coordinate) is called the domain and the second (usually the y-coordinate) is called the range. If you remember from earlier chapters the domain contains values that correspond to the independent variable whereas the range contains values corresponding to the dependent variable.
Step-by-step explanation:
1. Which is the meaning of the inequality - 6 < x in words?
Negative 6 is less than or equal to a.
Negative 6 is not equal to .
Negative 6 is greater than 3
Negative 6 is less than 2.
Answer:
first choice
Step-by-step explanation:
Part E
? Question
How would the situation change if the interest on Emma's credit card were compounded annually
rather than monthly, and she didn't make any payments toward the balance?
Select the correct answer from each drop-down menu.
After 4 years, Emma would owe approximately $ M for her original purchase of $300.
It would take around years for her balance to increase from $300 to $450.
Answer:
$525
2.9 years
Step-by-step explanation:
This question is about financial management. It is to be noted that it would take around 2.9 years for her balance to increase from $300 to $450.
What is the calculation for the above?Note that according to the question,
After 4 years, Emma would owe about $525 for her original purchase of $300.
The equation will be:
300 * (1 + x)[tex]^{4}[/tex] = 525 (This is based on the compound interest formula_
⇒ (1+x)[tex]^{4}[/tex] = 7/4 (If we divide both sides by 300)
Hence
x = 0.1502
= 15.02%
When the balance ups from $300 to $450,
We can state that:
300 * ( 1+ 15.02%) [tex]^{y}[/tex] = 450
⇒ Hence, y = 2.9 years.
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A long tunnel has the shape of a rectangular prism. It is about 100 cm high, 10 m wide and 1 km long. What is the volume of the tunnel expressed as an exponent?
A. 10^4 m3
B. 1000 cm3
C. 1 km3
D. 10^3 m3
Write the equation of a line passing through point (9, 7) and is parallel toy=43x+6. (Place your answer in slope intercept form and do not use spaces in your answer).
I don't know I don't know
help me please !!!!!!!!!!
1) 2m-1=3m
2) 2m=1+m
3) 3= 1+m
4) -2+m=1
5) 2+m=3
6) m-1=2
Hope this helped you- have a good day bro cya)
The product of a number and 9,
increased by 4, is 58. Find the
nurnber.
solve the following eqation: 4m - 12 = 0
Answer:
m=3
Step-by-step explanation:
Move the 12 over to the other side so it will be 4m=12, then divide each side by 4 to get m=3
Answer:
m=3
Step-by-step explanation:
4m-12=0
4m-12+12=0+12
4m=12
4m/4 =12\4
m=3
Write a two column proof of the statement. If 9k - 5 = 7k + 3, then k = 4.
Step-by-step explanation:
9k-5=7k+3
9k-7k=3+5
2k =8
k=4
if you work 35.6 hours and get paid $7.85 a hour how much is that in total
Answer:
$279.46
Step-by-step explanation:
to solve this equation you have to multiply 35.6 to 7.85
35.6 * 0.05 = 1.78
35.6 * 0.8 = 28.48
35.6 * 7 = 249.2
1.78 + 28.48 + 249.2 = $279.46
AGAIN LAST BUT NOT LEAST
This is for the smarty pants
and the person knows who I am talking bout
Answer:
Mr. Smarty Pants here
Distance between some points
A and B = 2
B and C = 5
C and B = 5
Four points that are 7 away from another point
-2,1
5,-6
5,8
12,1
Distance between some points
4
Arithmetic sequence for a1=5
Answer:
a =5that is the answer ok
If the expression is expanded, what is the coefficient of x? 4(3x+5)
Answer:
12
Step-by-step explanation:
4 ( 3x + 5 )
= 4 ( 3x ) + 4 ( 5 )
= 12x + 20
The coefficient of x in 12x is 12.
Choose the fraction that is equal to:
0.8 repeating A)8/9 B)6/7 C)8/10 D)2/25
Answer:
A) 8/9
Step-by-step explanation:
8 divided by 9 is 0.88888888888888888888889 on a calculator
The fraction that is equal to 8/9. Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
⇒ 0.8888...
Convert the decimal number into a fraction number, then we have
Let x = 0.8888..., then
10x = 8.888....
10x - x = 8.8888.... - 0.8888...
9x = 8
x = 8/9
The fraction that is equal to 8/9. Then the correct option is A.
More about the Algebra link is given below.
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Answer 6-7 thanks!!!!
please show work tyvm 4+3x6x(4-3³)²
Answer:
9526
Step-by-step explanation:
simplify 3^3+27
4+3*6(4-27)^2
simplify: 4-27+ -23
4+3*6(-23)^2
since the power of 2 is even it will be a positive
4+3*6*23^2
simplify: 23^2 to 529
4+3*6*529
simplify 3*6 to 18
4+18*529
then simplify 18*529 to 4+9522
and 4+9522= 9526
Can y’all help with 5 and 6 please !
I don’t know why I don’t get it-
Check Your Understanding HELP ASAP!!!
Answer:
B. [tex]9(\frac{4}{5} * \frac{1}{3})[/tex]
Step-by-step explanation:
In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
As the associate property is switching the numbers in the parentheses, B is the answer as it switched the [tex]\frac{1}{3} and \frac{4}{5}[/tex] while keeping the equation the same, and not editing any information that would change the outcome (answer) of the problem.
Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?A table showing Rate in mile per hour, Time in hours, and Distance in miles. The first row shows First Car and has 60, t, and 60 t. The second row shows Second Car and has, 55, t, and 55 t.60t – 55t = 060t + 55t = 160t + 55t = 15060t – 55t = 150
Answer:
your equation should be 60t + 55t =150
Answer:
The answer is C!
Step-by-step explanation:
Please help me solve this
Answer:
Step-by-step explanation:
This number is much larger than 1. You need to start at the decimal and move left (that's how scientific notation works for numbers larger than 1.)
So the answer is 1.0054 * 10 ^7
The person doing this started at the 1 and moved right until he/she hit the decimal. Wrong direction.
I can’t figure out how to solve 2(x+1) = 2x+1
Answer:
[tex]2(x + 1) = 2x + 1 \\ 2x + 2 = 2x + 1 \\ collecting \: like \: terms \\ 2x - 2x = 1 - 2 \\ 1x = - 1 \\ x = - \frac{1}{1} \: \: or \: \: x = - 1[/tex]
Answer:
-1
Step-by-step explanation:
find the volume and surface area of prism
Follow up from the attachment.
Figure 2
Surface area:319cm²
Volume:184cm²
A water park has pools, slides, and rides that, in total, make use of 8.7\times 10^{6}8.7×10 6 gallons of water. They plan to add a ride that would make use of an additional 4.8\times 10^{3}4.8×10 3 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
Answer:
as i said i would go with 93-51=42
Step-by-step explanation:
8.7*10.6=92.22 and 8.7*10+6=93
4.8*10.3=49.44 and 4.8*10+3=51
so i am thinking that you would add 93+51 which equals 144...
or you could try 93*51 but your gunna get 4,743
or try 93-51 which is 42
or try 93 diveded by 51 which is 1.8235294117647058
I would go with 93-51=42!
hope this helped:)
After the new attraction is constructed, the park will have used 8704.8 × 10³ total gallons of water.
What is Algebra?Algebra is the study of mathematical symbols, while logic is the manipulation of those signifiers.
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS principle. To answer the problem properly and accurately, this rule must be followed.
A water park uses 8.7 × 10⁶ gallons of water in total for its pools, slides, and attractions. They intend to include a ride that will use an extra 4.8 × 10³ gallons of water.
After the new attraction is constructed, the park will have used the total gallons of water is given as,
⇒ 8.7 × 10⁶ + 4.8 × 10³
⇒ 8700 × 10³ + 4.8 × 10³
⇒ 8704.8 × 10³
After the new attraction is constructed, the park will have used 8704.8 × 10³ total gallons of water.
More about the Algebra link is given below.
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