We have been given that there are about 1.61 kilometers in 1 miles.
Let x represent a distance measured in kilometers and y represent the same distance measured in miles.
We can set two equations from the given information as:
[tex]x=\frac{1}{1.16}*y[/tex] (Number of kilometers in terms of number of miles)
[tex]y=1.61*x[/tex] (Number of miles in terms of number of kilometers)
Therefore, [tex]x=\frac{1}{1.16} y[/tex] and [tex]y=1.61*x[/tex] will be our equations.
To relate a distance measured in kilometers and miles, two equations can be written: y = 1.61x and x = 0.62y.
Explanation:To write equations that relate a distance measured in kilometers and the same distance measured in miles, we can use the conversion factor between kilometers and miles. Based on the given information, 1 mile is equivalent to 1.61 kilometers. So, the first equation would be: y = 1.61x, where x represents the distance in kilometers and y represents the distance in miles. To find the equation in the opposite direction, we can use the inverse of the conversion factor, which is 1 divided by 1.61. So, the second equation would be: x = 0.62y.
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7-3x=x-4(2+x)
helppp
What are the converse, inverse and contrapositive of the statement? Which statements are true? Statement: If the figure is square, then the figure is quadrilateral
The converse, the inverse, and the contrapositive of the statement
"If the figure is square, then the figure is a quadrilateral." is given below.
We have,
The statement: "If the figure is square, then the figure is a quadrilateral."
Converse:
The converse of the statement switches the "if" and "then" parts of the original statement.
Converse: If the figure is a quadrilateral, then the figure is square.
Inverse:
The inverse of the statement negates both the "if" and "then" parts of the original statement.
Inverse: If the figure is not square, then the figure is not a quadrilateral.
Contrapositive:
The contrapositive of the statement also switches the "if" and "then" parts and negates both of them.
Contrapositive: If the figure is not a quadrilateral, then the figure is not square.
Thus,
Converse: If the figure is a quadrilateral, then the figure is square.
Inverse: If the figure is not square, then the figure is not a quadrilateral.
Contrapositive: If the figure is not a quadrilateral, then the figure is not square.
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50 POINTS! Arrange the steps to solve this problem. 9 steps. 50 POINTS!
[tex]\left\{\begin{array}{ccc}x+y=-2\\2x-3y=-9\end{array}\right\\\\\text{multiply the first equation by 3}\\3(x+y)=3(-2)\qquad|\text{use distributive property}\\3x+3y=-6\\\\\underline{+\left\{\begin{array}{ccc}3x+3y=-6\\2x-3y=-9\end{array}\right}\qquad\text{add 3x+3y=-6 to 2x-3y=-9, and solve for x}\\.\qquad5x=-15\qquad|:5\\.\qquad x=-3\\\\\text{Substitute the value of x in the first equation (x+y=-2)}\\\\-3+y=-2\qquad|+3\\y=1\\\\\text{The solution for the system of equations is (-3, 1)}[/tex]
Answer:
...
Step-by-step explanation:
Car dealerships claim to make most of their money from servicing cars. In a certain month, an Acura dealership sold fifteen less used cars than twice the number of new cars. In the smae month, they serviced fifty more than twelve times the number of new cars sold. If the dealership either sold or services a total of 335 cars that month, how many new cars were sold that month? How many use? How many serviced?
Answer:
New cars sold = 20,
Used cars sold = 25
Cars serviced = 290
Step-by-step explanation:
In a month they sold fifteen less used cars than twice the number of new cars.
Lets say 'x' number of new cars were sold, then:
The number of used car sold is:
[tex]2\times x-15=2x-15[/tex]
In the same month they serviced fifty more than twelve times the number of new cars sold. So the number of cars serviced is:
[tex]12\times x+50=12x+50[/tex]
Altogether they sold or serviced 335 cars, so the sum of all the cars sold and serviced should be 335:
[tex]x+(2x-15)+(12x+15)=335[/tex]
Solving for 'x' we get:
[tex]x+2x+12x-15+50=335[/tex]
[tex]15x+35=335[/tex]
[tex]15x=335-35=300[/tex]
[tex]x=\frac{300}{15}=20[/tex]
Therefore, the number of new cars sold in that month is 20.
Number of used car sold [tex]=2x-15=2\times 20-15=40-15=25[/tex]
Number of cars serviced [tex]=12\times x+50=12\times20+50=240+50=290[/tex]
We can also cross check by summing them up:
[tex]290+25+20=335[/tex]
Evaluate –4 – w for w = –7
i think the answer might be 3
The answer is 3. Have a great day!
Which of the inequalities represents the statement, "Two times a number x, less 15, is greater than or equal to 4 times the number y"? A) 2x - 15 ≤ 4y B) 2x - 15 ≥ 4y C) 2x + 15 ≤ 4y D) 15 - 2x ≤ 4y
Therefore, the best and most correct answer among the choices provided by the question is the fourth choice "15 - 2x ≥ 4y". I hope my answer has come to your help.
Answer:
Step-by-step explanation: B) 2x - 15 ≥ 4y is the correct answer
Please help. Thanks!
B. The equation of this line is x = 3.
E. This graph is not a function because the value x = 3 is assigned to more than one y-value.
Colton solved an equation incorrectly, as shown below:
Step 1: x − 13 = 26
Step 2: x = 26 − 13
Step 3: x = 39
Which statement best explains why Step 2 is incorrect in Colton’s solution?
He did not subtract 13 from 26.
He did not multiply 26 by 13.
He did not add 13 to 26.
He did not divide 26 by 13.
Answer:
He did not add 13 to 26.
Step-by-step explanation:
Given : Step 1: x − 13 = 26
Step 2: x = 26 − 13
Step 3: x = 39
To Find: Which statement best explains why Step 2 is incorrect in Colton’s solution?
Solution:
Correct steps
Step 1:[tex]x- 13 = 26[/tex]
Step 2:[tex]x = 26+13[/tex]
Step 3:[tex]x = 39[/tex]
So, this concludes that He did not add 13 to 26 in step 2
So, Option C is correct.
Hence He did not add 13 to 26.
Answer:
he did not add 13 to 26
Step-by-step explanation:
choosing the 6 winning lottery numbers when the numbers are chosen at random from 0 to 9 A) 1/1,000,000 B) 1/100,000 C) 1/10,000,000 D) 531,441
Answer:
A 1/1,000,000
Step-by-step explanation:
Choose the graph below that correctly represents the equation 2x + 4y = 24.
A. line through the points 0 comma 6 and 12 comma 0
B. line through the points 0 comma negative 6 and 12 comma 0
C. line through the points 0 comma negative 12 and 6 comma 0
D. line through the points 0 comma 12 and 6 comma 0
a line through the point (0, 6 )
to find a point on the line, choose any value of x , substitute into the equation and solve for y
x = 0 : 0 + 4y = 24 ( divide both sides by 4 )
y = [tex]\frac{24}{4}[/tex] = 6
hence line goes through (0, 6 )
The correct graph that represents the equation 2x + 4y = 24 is option A, which shows a line through the points (0, 6) and (12, 0).
Explanation:The equation 2x + 4y = 24 can be rearranged to y = -0.5x + 6. This means that the equation represents a linear function with a slope of -0.5 and a y-intercept of 6.
Option A, which shows a line through the points (0, 6) and (12, 0), is the correct graph since it satisfies the equation. The slope is -0.5 and the y-intercept is 6.
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Help!! I have no clue
okay so you just plug in the x and ys. x is the first number, y is the second. then you just do them all out
So we know that an ordered pair looks like (x,y), right? For this inequality, we're supposed to plug in the values of x and y. If it isn't true, then the inequality does not represent the ordered pair.
First option: (0,1)
[tex]2x + 3y \geq -1[/tex] --> [tex]2(0) + 3(1) \geq -1[/tex] --> [tex]5 \geq -1[/tex]
So this option is correct.
Second option: (-2,1)
[tex]2x + 3y \geq -1 --> 2(-2) + 3(1) \geq -1[/tex]
--> [tex]-4 + 3 \geq -1 --> -1 \geq -1[/tex]
This is also correct.
Third option: (-6,0)
[tex]2(-6) + 3(0) \geq -1 --> -12 \geq -1[/tex]
This is not true, so this option is not correct.
Fourth option: (0,-1)
[tex]2(0) + 3(-1) \geq -1 --> -3 \geq -1[/tex]
This is not correct.
Fifth option: (2,-1)
[tex]2(2) + 3(-1) \geq -1 --> 4 - 3 \geq -1[/tex]
This is correct.
if ( 6^2) ^x =1 what is the value of x
Evaluate the algebraic expression for the given variable
-x- -3,x=-5
What is f(–3) for the function f(a) = –2a2 – 5a + 4?
Answer:
The value of f(-3) is 1.
Step-by-step explanation:
Given expression,
[tex]f(a)=-2a^2-5a+4----------(1)[/tex]
For finding the value of f(-3),
Put a = - 3 in equation (1),
We get,
[tex]f(-3)=-2(-3)^2-5(-3)+4[/tex]
[tex]=-2(9)+15+4[/tex]
[tex]=-18+19[/tex]
[tex]=1[/tex]
Hence, the value of f(-3) is 1 for the given function.
Choose a fraction that makes the following sentence true. 0.1 is a rational number because it can be written as ___.
a. 1/10
b. 1/9
c. 0.1
d. 1/11
gUYS I FOUND THE RIGHT ANSWER ITS 1/9 ON GOD I JUST GOT IT RIGHT
The decimal 0.1 is a rational number because it can be expressed as the fraction 1/10, which is the correct answer to the student's question.
Explanation:The student asked to choose a fraction that correctly completes the sentence: 0.1 is a rational number because it can be written as ___. The correct choice is 1/10. This is because the decimal 0.1 can be converted directly to the fraction 1/10 by placing the digit 1 in the numerator and 10 in the denominator, which signifies the decimal's place value. Rational numbers are those that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
which expression represents “seventeen more than one-fourth y”
hello again
17-1/49 is your correct answer thank you and have a great day please mark me as brainliest if can
Answer:
Expression which represents “seventeen more than one-fourth y” is:
[tex]\dfrac{1}{4}y+17[/tex]
Step-by-step explanation:
We have to find a expression which represents
“seventeen more than one-fourth y”
one-fourth y= [tex]\dfrac{1}{4}y[/tex]
So, seventeen more than one-fourth y= [tex]\dfrac{1}{4}y+17[/tex]
Hence, expression which represents “seventeen more than one-fourth y” is:
[tex]\dfrac{1}{4}y+17[/tex]
Evaluate (a + b)2 for a = 2 and b = 3
f(a,b) = 2(a+b)
f(2,3) = 2(2+3)
f(2,3) = 2(5)
f(2,3) = 10
What is the value of the discrimination for the quadratic equation 0=2x2+x-3
Remark
The formula for a discriminate is b² - 4*a*c
a = 2
b = 1
c = - 3
So the discriminate =
D = (1)² - 4*2*(-3)
D = 1 - - 24
D = 25
Sole the equation for the indicated variable.
zm= a+b/a, for a
zm= a+b/a, for a
Switch sides to have a on left side
a+b/a=zm
Now multiply both sides by a
A+b= zm(a)
A+b= ama
Now subtract azm both sides
A+b-azm=0
Subtract b both sides
A-azm= -b
Factor out a from ask
A(1 -zm)= -b
Divide each term by 1 - zm to get
A= - b/1-zm
a rock fell from a cliff at 108 feet high and landed on an embankment feet from the ground. find the amount if time it would have taken the rock to fall.
To solve this problem we will directly use the formula:
[tex]h=\frac{1}{2}gt^2[/tex]..........Equation 1
where symbols have their usual meanings.
Here g=32.2 ft/s^2 and h=108 feet
Therefore, from Equation 1 we will get:
[tex]t=\sqrt{\frac{2h}{g}}[/tex]....Equation 2
Plugging in the values in Equation 2 we get:
[tex]t=\sqrt{\frac{2\times 108}{32.2}}\approx 2.59[/tex] seconds.
Therefore, the amount of time it would have taken the rock to fall is 2.59 seconds.
is 1000 a perfect cube?
Think of a cube with side lengths of 10.
The volume of the cube will be L*W*H = 10*10*10 = 1000
This volume of 1000 is what we consider a perfect cube.
Answer: yes
10*10*10=[tex]10^{3}[/tex]
10*10*10=1,000
1,000 is a perfect cube, because 10^3 is 1,000.
I hope this helps :)
****BRAINLIEST GOES TO THE FIRST CORRECT ANSWER****
The two equations are vertical angles, which mean they are equal.
Set each equation to equal each other and solve for x.
3x-3 = 6(x-10)
Simplify the right side:
3x-3 = 6x-60
Subtract 3x from each side:
-3 = 3x - 60
Add 60 to each side:
57 = 3x
Divide both sides by 3:
x = 57 / 3
x = 19
The lateral surface area of cone A is equal to the lateral surface area of cylinder B.
True or false
Answer:
TRUE
Step-by-step explanation:
Lateral area of cone is given by: πrl
where r is the radius and l is the slant height
Here r=r and l=2h
Hence, lateral area of cone A= π×r×2h
= 2πrh
Lateral area of cylinder is given by: 2πrh
where r is the radius and h is the height
Lateral area of cylinder B=2πrh
Clearly, both the lateral areas are equal
Hence, the statement that:The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is:
True
22.48 rounded to the nearest whole number
ANSWER
22
EXPLANATION
22.48 rounded to the nearest whole number is 22.
The reason is that the 4 after the decimal point is less than 5 so we won't round up.
Answer:
The round off number is 22.
Step-by-step explanation:
The number = 22.48
Nearest whole number = 22
Explanation:
A whole number is any number which is without any decimal or fraction.The question was to round off the nearest of 22.48.Now the rule is that if the number left to decimal is 5 or more than 5, round of the number by adding 1 to the number right to the decimal. If the number left to decimal is 4 or less than 4 then round off number simply by removing all left to decimal.Now in our question there was 4 left to decimal. So we apply the second rule and the rounded off number will be 22.Select and place the symbol that will make the statement true -|y| ? |-y|
It's [tex]\leq[/tex]
The correct symbol to make the statement -|y|? |-y| true is '=', because the absolute value of 'y' and '-y' are always equal, regardless of whether 'y' is positive or negative.
Explanation:The correct symbol to make the statement true is '='. This is because the absolute value of any number, positive or negative, is always positive, or zero in the case of zero itself. So no matter what value 'y' takes on, |-y| and |y| will always be equal.
For example, let's consider that y = -5. Then |-5| = 5 and |5| = 5. Here |-y| and |y| are equal.
If y = 5, then |-5| = 5 and |5| = 5. Here too, |-y| and |y| are equal. Therefore, no matter if 'y' is positive or negative, the absolute value of 'y' and '-y' are always equal.
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What is the slope and y intercept of y= 3
the slope is 0 over 1 and the y-intercept is 3
The steps for solving the equation 2x-3=7
Step 1: Add 3 to both sides.
2x-3+3=7+3
2x=10
Step 2: Divide both sides by 2.
2x/2=10/2
x=5
Standard Form 2x-10=0
Factorization 2(x -5)=0
Solution x=10/2=5
Graph the equation on the coordinate plane.
y=−2x
Use editing software or windows paint to edit dots, thanks!
Solution :
Given, the equation [tex]y=-2x[/tex].
To graph the equation on the coordinate plane, we first need to derive the different points of the equation [tex]y=-2x[/tex],
[tex]at\:\;x=0\Rightarrow y= -2(0)=0\\\\at\:\;x=1\Rightarrow y= -2(1)=-2\\\\at\:\;x=2\Rightarrow y= -2(2)=-4\\\\at\:\;x=3\Rightarrow y= -2(3)=-6\\\\at\:\;x=-1\Rightarrow y= -2(-1)=2\\\\at\:\;x=-2\Rightarrow y= -2(-2)=4\\\\at\:\;x=-3\Rightarrow y= -2(-3)=6[/tex]
The graph plotted using these points is shown in the figure,
Triangle ABC has vertices at A(−1 , 2), B(4, 2), and C(3, −1). Classify the triangle according to the side lengths.
A) equilateral
B) isosceles
C) right
D) scalene
Answer:
B) Isosceles
Step-by-step explanation:
The given triangle has vertices at A(-1,2), B(4,2) and C(3,-1).
We must first determine the length of the sides of the triangle, before we can classify it.
We apply the distance formula to find length of the sides.
[tex]|AB|=\sqrt{(4--1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{(4+1)^2+(2-2)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{5^2+(0)^2}[/tex]
[tex]\Rightarrow |AB|=\sqrt{25}[/tex]
[tex]\Rightarrow |AB|=5 units[/tex].
The length of side BC
[tex]|BC|=\sqrt{(3-4)^2+(-1-2)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |BC|=\sqrt{1+9}[/tex]
[tex]\Rightarrow |BC|=\sqrt{10}[/tex]
The length of side AC
[tex]|AC|=\sqrt{(3--1)^2+(-1-2)^2}[/tex]
We simplify to obtain;
[tex]|AC|=\sqrt{(3+1)^2+(-3)^2}[/tex]
[tex]\Rightarrow |AC|=\sqrt{(4)^2+(-3)^2}[/tex]
[tex]|AC|=\sqrt{16+9}[/tex]
[tex]|AC|=\sqrt{25}[/tex]
[tex]|AC|=5\:units[/tex]
Since [tex]|AC|=5\:units=|AB|[/tex], the given triangle is an isosceles triangle.
The correct answer is
Answer:
B) isosceles
Step-by-step explanation:
11.Bentley Manufacturing Company wants to rent a private club for its annual dance. The total cost will be $1,045. If the committee charges $9.50 per person, how many people need to attend the dance in order to cover the cost?
Answer:
110 people need to attend the dance in order to cover the cost.
Step-by-step explanation:
Bentley Manufacturing Company wants to rent a private club for its annual dance.
The total cost will be $1,045.
The committee charges $9.50 per person.
So, let the total number of persons attending be = x
So, this situation can be represented as:
[tex]9.50x=1045[/tex]
This gives x = 110
So, 110 people need to attend the dance in order to cover the cost.