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A cab charges 1.45 for the flat fee and 0.55 for each mile. Write and solve an inequality to determine how many miles Ariel can travel if she has 35 dollars to spend
Given the system of equations, what is the solution?
x + 2y = 7
x - 2y = -1
(A.) {(-8, -12)}
(B.) {(3, 2)}
(C.) {(-4, 6)}
Final answer:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 is found by eliminating y, yielding x=3 and y=2, which is option B, (3, 2).
Explanation:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 can be found by adding or subtracting the two equations to eliminate one of the variables. By adding the two equations, we eliminate y and get 2x = 6, which results in x = 3. Substituting x = 3 back into either of the original equations yields y = 2. Therefore, the solution to the system is (3, 2), which corresponds to option B.
six times the reciprocal of a number equals 2 times the reciprocal of 6. find the number.
The length of a rectangle is twice its width. if the area of the rectangle is 162 m2 , find its perimeter.
The width of the rectangle is 9m and the length is 18m. The perimeter of the rectangle is 54m.
Explanation:Let's assume the width of the rectangle as 'w'. According to the given information, the length would be twice the width, so the length can be represented as '2w'.
The formula for the area of a rectangle is length multiplied by width, which can be written as 'A = lw', where 'A' is the area. By substituting the given area value of 162m2, the equation becomes '162 = 2w * w'.
Solving this equation, we get 'w = 9m' which represents the width. The length can be found by doubling the width, so the length is '2 * 9m = 18m'.
The perimeter of a rectangle can be calculated using the formula 'P = 2(l + w)', where 'P' is the perimeter, 'l' is the length, and 'w' is the width. Plugging in the values, the perimeter of the rectangle is 'P = 2(18m + 9m) = 54m'.
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Let f ( x ) = 2 x − 1 , g ( x ) = 3 x , and h ( x ) = x ^2 + 1 , what is g (h ( 24 ) ) ?
At the beginning of the year Jason had $80 in his savings account. Each month he added $15 to his account. Write in expression for the amount of money and Jason saving account each month. Then use the expression to find the amount of money in his account at the end of the year
Find an equation of the line that satisfies the given conditions. through (−5, −13); perpendicular to the line passing through (−2, −1) and (2, −3)
HIJK is a rectangle. Find the value of x and the length of each diagonal. HJ=x and IK= 2x-7
The value of x will be equal to 7 for the two diagonals HJ and IK.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position. A geometer is a mathematician who works in the field of geometry.
Given that the length of each diagonal is HJ=x and IK= 2x-7
HJ and IK are diagonals.
By definition of the rectangle, the diagonals are congruent or equal.
HJ=IK
x=2x-7
-x+x=2x-x-7
0=x-7
0+7=x-7+7
7=x and 2x-7=2 (7)-7=14-7=7
For the two diagonals, the value of x is 7.
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a model rocket is 3 inches long. the real rocket is 120 feet long. what is the unit rate that describes the relationship of the real rocket to the model rocket? a.360 ft/in. b.360 in./ft c.40 in./ft d.40 ft/in.
How many 3 digit positive integers are odd and do not contain the digit 5?
How can you use distance and slope formulas to classify quadrilaterals?
A radio station plays 3 1/2 minutes of commercials every 1/4 hour. At this rate, how many minutes of commercials does this radio station play in one hour?
2(x+3) + 6 = 3x - 9 written in word form? HELP!!!
A parabola has vertex (2, 3) and contains the point (0, 0). find an equation that represents this parabola.
The required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
The parabola equation into the vertex form:
(y-k) = a(x-h)²
Where (h,k) are the x and y-coordinates of the vertex.
The parabola has vertex (2, 3) which is given in the question
Here h = 2,and k = 3
Substitute the values of h = 2 and k = 3 in the above equation
y - 3 = a(x - 2)²
y = a(x - 2)² + 3
If the parabola contains the point (0, 0)
Substitute the point (0, 0) in the above equation
0 = a((-2)² + 3
4a = -3
a = -3/4
Thus, the equation becomes y = (-3/4)(x - 2)² + 3
Hence, the required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
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Find the equation in standard form of the line with slope − 4 7 -47 that passes through the point ( 2 , 5 ) (2,5)
Factor polynomial 2x^2-11x+15
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▹ Answer
(2x - 5) * (x - 3)
▹ Step-by-Step Explanation
2x² - 11x + 15
Rewrite:
2x² - 5x - 6x + 15
Factor:
x(2x - 5) - 6x + 15
x(2x - 5) - 3(2x - 5)
Factor:
(2x - 5) * (x - 3)
Hope this helps!
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Two angles are supplementary. one angle measures 12 degrees less than 5 times the other. find the measure of each angle
The measures of the two supplementary angles are 32 degrees and 148 degrees, respectively.
Explanation:The question is about finding the measures of two supplementary angles given the relationship between them. Supplementary angles are two angles whose measures add up to 180 degrees. If we let x be the measure of the first angle, then the measure of the second angle is 5x - 12 degrees, according to the problem statement.
Since the angles are supplementary, we can set up the following equation: x + (5x - 12) = 180. This simplifies to 6x - 12 = 180. Solving for x gives us x = 32, so the first angle measures 32 degrees.
Substitute x = 32 into the equation for the second angle gives us: 5x - 12 = 5(32) - 12 = 148 degrees. Therefore, the two angles measure 32 degrees and 148 degrees, respectively.
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***PLEASE HELP*** ***50 POINTS***
Construct a system of two linear equations where (−2, 3) is a solution to the first equation but not to the second equation, and where (5, −2) is the solution to your system.
You need to write the equations of your system and graph them on the same graph.
Explain how your graph shows that your system satisfies the 2 required conditions.
see attached picture:
Chad bought 8 pounds of strawberries for $25.25. What is the cost, c, of 1 pound of strawberries?
Math quest after a winter storm, the depth of the snow on cherry street was 10 \text{ cm}10 cm10, space, c, m. but then, the snow started melting at a rate of \dfrac{1}{3} \text{ cm}31 cmstart fraction, 1, divided by, 3, end fraction, space, c, m per hour.what was the depth of the snow on cherry street after 333 hours?
We are given that the initial depth of snow is 10 cm while the rate of melting is 1/3 cm per hour. So the melted ice after 3 hours is:
melted = (1/3 cm/hr) * 3 hours = 1 cm
Hence the depth left is:
depth = 10 cm – 1 cm = 9 cm
Answer:
9 cm
Answer:
9 cm.
Step-by-step explanation:
Let x be the number of hours.
We have been given that after a winter storm, the depth of the snow on cherry street was 10 cm. Then, the snow started melting at a rate of [tex]\frac{1}{3}[/tex], so the snow melted in x hours will be [tex]\frac{1}{3}x[/tex].
Since initially there was 10 cm of snow, so the depth of snow after x hours will be:
[tex]10-\frac{1}{3}x[/tex]
To find the depth of snow after 3 hours we will substitute [tex]x=3[/tex] in our expression.
[tex]10-\frac{1}{3}\times 3[/tex]
[tex]10-1[/tex]
[tex]9[/tex]
Therefore, the depth of the snow on cherry street after 3 hours will be 9 cm.
Which of the following does not have a measure of 40 degrees?
∠AOX
∠DOA
∠COA
Answer:
the correct answer is C) COA
Sam's bedroom has a perimeter of 46 feet. If the length of the bedroom is 11 feet, what is the width of the bedroom?
Which expression means 7 more than a number?
A.
d × 7
B.
d + 7
C.
d ÷ 7
D.
d – 7
Can you write a linear inequality whose solution contains only points with positive x-values and y-values? why or why not?
Yes, a linear inequality can be written whose solution contains only points with positive x-values and y-values.
Explanation:A linear inequality is a mathematical statement that expresses a relationship between two linear expressions using inequality symbols (>, <, ≥, or ≤). It describes a region of values that satisfy the inequality, often represented on a coordinate plane as a shaded area.
Yes, a linear inequality can be written whose solution contains only points with positive x-values and y-values. One example of such an inequality is y > 0. This inequality represents all the points above the x-axis in the coordinate plane, where both x-values and y-values are positive.
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Plz answer ASAPPP tyyy
Multiply. (−4−7i)(3−5i)
Morgan needs gas for her jeep, which gets 26 miles per gallon for gas mileage. When she stops at the gas station, she already has 10 gallons of gas in her tank. She buys more gas for $1.60 per gallon. If Morgan spends $21 on gas, what is the total distance she could travel? Round, if necessary, to the nearest tenth.
Answer:
The answer 601.3 miles.
Step-by-step explanation:
Assume that the set s has 8 elements. how many subsets of s have at most 2 elements?
Solve 10x-3=6x+85 give a reason to justify each statement
10x-3 = 6x+85
add 3 to each side
10x=6x+88
subtract 66x from each side
4x = 88
divide 88 by 4 to get x
x - 88/4 = 22
x = 22