The perimeter of a rectangle is 36 inches, and the area is 65 square inches. find the length and width of the rectangle.
If your car travels 290 miles and uses 8.2 gallons, how many miles per gallon did you get? (round your answer to three decimal places.)
State the missing reasons in this flow proof.
Given: angle 5 = 40, angle 2 = 140.
Prove: a is parallel to b.
Statements:
angle 5 = 40 a. ____________.
angle 2 = 140 b. _____________.
angle 5 and angle 2 are supplementary angles c.________.
Angle 5 and angle 2 are same-side interior angles d._________.
a is a parallel to b e._______
The provided statements are either given information, interpretations from the given diagram or applying rules of geometry such as the definitions of supplementary angles and the Same-Side Interior Angles Theorem.
Explanation:The missing reasons in this geometric proof are as follows:
a. Given: The fact that angle 5 = 40 is simply provided, it's the given information in the question.
b. Given: Similarly, the measurement of angle 2 being 140 is given information.
c. Definition of supplementary angles: Angle 5 and angle 2 are supplementary because the sum of their measure equals 180 (40+140).
d. Interpretation of the diagram: Without a diagram, it's difficult to be precise, but if angle 5 and angle 2 are indicated as same-side interior angles, then this inference comes from interpreting the diagram.
e. Same-Side Interior Angles Theorem: Lastly, if the same-side interior angles are supplementary, then the lines are parallel. This is a rule encapsulated by the same-side interior angles theorem.
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Given the function f(x)=x2+2x+1, find: f(2b)
Given the function f(x)=x2+2x+1, find: f( 2a−3/5 )
PLS HELP!!!
A copy center offers its customers two different pricing plans for black and white photocopies of 8.5 in. by 11 in. pages. Customers can either pay $0.08 per page or pay $7.50 for a discount card that lowers the cost to $0.05 per page. Write and solve an equation to find the number of photocopies for which the cost of each plan is the same.
.08c = .05c + 7.50; c = 250
.05c = .08c + 7.50; c = 22.5
.08c = .05c – 7.50; c = 250
7.50 = .08c + .05c; c = 58
Answer:
.08c=.05c-7.50; c=250
Step-by-step explanation:
What is the relationship between the sine and cosine of complementary angles in a right triangle? Please give an example to support your answer.
Final answer:
The sine and cosine of complementary angles in a right triangle are equal to each other but reversed, because the opposite side for one angle is the adjacent side for the other, relative to the hypotenuse.
Explanation:
The relationship between the sine and cosine of complementary angles in a right triangle is that they are equal to each other but reversed. If one angle is x and its complementary angle is 90° - x (because complementary angles add up to 90°), then the sine of x is equal to the cosine of its complementary angle, and vice versa.
This is because, in a right triangle, the side that is the opposite side for one angle becomes the adjacent side for the complementary angle, relative to the hypotenuse which remains the same for both angles.
For example, in a right triangle with one acute angle of 30°, its complementary angle is 60°. The sine of 30° is 1/2, and the cosine of 60° is also 1/2. Similarly, the cosine of 30° is [tex]\sqrt{3/2[/tex], and the sine of 60° is [tex]\sqrt{3/2[/tex] shows a complementary relationship.
In 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be. Find their ages now.
Answer: The present age of Harry is 2 years and that of Jim is 6 years.
Step-by-step explanation: Given that in 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be.
We are to find the present ages of Harry and Jim.
Let x and y represents the present ages of Harry and Jim respectively.
Then, according to the given information, we have
[tex]x+4=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y+2=2(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of y from equation (i) in equation (ii), we get
[tex]y+2=2x+4\\\\\Rightarrow x+4+2=2x+4\\\\\Rightarrow 2x-x=2\\\\\Rightarrow x=2.[/tex]
From equation (i), we get
[tex]y=x+4=2+4=6.[/tex]
Thus, the present age of Harry is 2 years and that of Jim is 6 years.
How do you find the quadratic equation of a parabola with the vertex and x intercept?
WXY is an isosceles triangle with line WX congruent to line WY. if WX is 3 more than four times x, XY is 7 less than five times x, and WY is 66 less than seven times x, find x and the measure of each side.
Answer:
x=10
Step-by-step explanation:
part 1:
4x+3=5x-7
(subtract 4x from 5x to get 1x and add 7 to 3 to get 10)
1x=10
x=10
part 2:
WX=4(10)+3=43
XY=5(10)-7=43
WY=7(10)-66=4
An isosceles triangle, have two congruent sides.
The value of x is 23The measure of each side is 95, 95 and 108From the question, we have the following highlights
[tex]\mathbf{WX = WY}[/tex]
[tex]\mathbf{WX = 3 + 4x}[/tex]
[tex]\mathbf{XY = 5x - 7}[/tex]
[tex]\mathbf{WY = 7x - 66}[/tex]
(a) Find x
We have:
[tex]\mathbf{WX = WY}[/tex]
Substitute values for WX and WY
[tex]\mathbf{3 + 4x = 7x - 66}[/tex]
Collect like terms
[tex]\mathbf{7x - 4x = 3 + 66}[/tex]
[tex]\mathbf{3x = 69}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 23}[/tex]
Hence, the value of x is 23
(b) The measure of each side
Substitute 23 for x in:
[tex]\mathbf{WX = 3 + 4x}[/tex]
[tex]\mathbf{XY = 5x - 7}[/tex]
[tex]\mathbf{WY = 7x - 66}[/tex]
[tex]\mathbf{W = 3 + 4 \times 23}[/tex]
[tex]\mathbf{W = 95}[/tex]
[tex]\mathbf{XY = 5x - 7}[/tex]
[tex]\mathbf{XY = 5 \times 23 - 7}[/tex]
[tex]\mathbf{XY = 108}[/tex]
[tex]\mathbf{WY = 7x - 66}[/tex]
[tex]\mathbf{WY = 7 \times 23 - 66}[/tex]
[tex]\mathbf{WY = 95}[/tex]
Hence, the measure of each side is 95, 95 and 108
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What equation is graphed in this figure?
A.y-4=-1/3(x+2)
B.y-3=1/3(x+1)
C.y+2=-3(x-1)
D.y-5=3(x-1)
Using synthetic division, what is the quotient (2x3 − 2x − 12) ÷ (x − 2)? 2x2 + 4x + 6 2x2 − 4x + 6 2x2 + 4x − 6 2x2 + 4x − 6 + 1 over the quantity of x minus 2
The answer to your question would be 2x^2+4x+6
Answer:
[tex]\text{The quotient is }2x^2+4x+6[/tex]
Step-by-step explanation:
Given the dividend and divisor we have to find the remainder using synthetic division.
The given polynomial [tex]2x^3-2x-12[/tex] is divided by (x-2).
Step 1: Set up the synthetic division.
The dividend goes on the inside of the box.
Step 2: Bring down the leading coefficient to the bottom row.
Step 3: Multiply c i.e 2 by the value just written on the bottom row.
Step 4: Add the column created in step 3 and write the sum in the bottom row.
Repeat steps 1-4 until the last column.
From the last row the remainder becomes
[tex]2x^2+4x+6[/tex]
Hence, option A is correct.
Simplify square root of negative 48.
a) negative 4 square root of 3
b) 4 square root of negative 3
c) 4 i square root of 3
d) 4 square root of 3 i
Answer:
C. 4 i square root of 3
Step-by-step explanation:
Fabian has a savings account balance of $1,374.73. The interest rate on the account is %3.9 compounded twice a year. If he opened the account nine years ago, what was the value of his deposit?
The leg of a right triangle is 3 units and the hypotenuse is 7 units. What is the length, in units, of the other leg of the triangle?
4
Square root of 40
Square root of 58
10
7^2 = 3^2 +x^2
49 = 9 +x^2
x^2 = 49-9 =40
x = square root of 40
Answer:
the square root of 40 is the answer your looking for
Step-by-step explanation:
Terms and coefficients of 7p - 3r + 6 - 5s
The terms and coefficients of the expression 7p - 3r + 6 - 5s are 7p, -3r, 6, and -5s, with coefficients of 7, -3, no coefficient, and -5 respectively.
Explanation:The terms and coefficients of the expression 7p - 3r + 6 - 5s are:
The term 7p has a coefficient of 7.The term -3r has a coefficient of -3.The term 6 is a constant and does not have a coefficient.The term -5s has a coefficient of -5.Learn more about Terms and Coefficients here:https://brainly.com/question/23992956
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Solve each system by graphing or using a table
Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges $12 to wash a car and $15 to wash a truck. In 270 minutes, Evan made $105 washing cars and trucks. How many trucks did Evan wash? 2 trucks 3 trucks 4 trucks 5 trucks
Factor -8x^3-2x^2-12x-12x-3
Find the measure of an angle whose measure is 60 degrees more than the measure of its complement
Answer:
75⁰
Step-by-step explanation:
Angle = x
Complement = 90 - x
Given:
x = 90 - x + 60
2x = 150
x = 75⁰
is that ok?? i just want to make sure, thanks
write an equation of the line that passes through the given point(-2,5) and is parallel to the given line 2y=4x-6
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Sally has 42 coins, all dimes and nickels, that have a total value of $3.00. How many nickels does she have?
Sally has 24 nickels.
Explanation:To determine the number of nickels Sally has, we can set up a system of equations using the given information. Let's assume Sally has x nickels and (42 - x) dimes. The value of the nickels is 5x cents, and the value of the dimes is 10(42 - x) cents. We can set up the equation: 5x + 10(42 - x) = 300 (since the total value is $3.00).
Simplifying the equation, we get: 5x + 420 - 10x = 300. Combining like terms, we have: -5x + 420 = 300. Subtracting 420 from both sides gives us: -5x = -120. Dividing both sides by -5, we find x = 24.
Therefore, Sally has 24 nickels.
Find the value of y in the equation
What does it mean to be “in the black?”
Answer: c you have more credits then debts
Step-by-step explanation:
Identify the expression that is equivalent by distributive property of5(2x+3)A 10x +3B 10x + 5C 10x +15
Plz can I help me with math
What is the lowest common multiple of (3^2 x 8^4) and (3^3 and 8^3) ?
Help me and how to do this??
25 POINTS PLS HURRY!!!
How does the graph of g(x)=0.25⌊x⌋ differ from the graph of f(x)=⌊x⌋?
Multiplying by 0.25 shifts the graph of g(x)=0.25⌊x⌋ up 0.25 unit.
Multiplying by 0.25 shifts the graph of g(x)=0.25⌊x⌋ right 0.25 unit.
Multiplying by 0.25 shifts the graph of g(x)=0.25⌊x⌋ down 0.25 unit.
Multiplying by 0.25 compresses the graph of g(x)=0.25⌊x⌋ vertically by a factor of 0.25.
Answer:
The answer is d
Step-by-step explanation:
evaluate g(x)=3x+1 over the domain of g, {0,1,2,3}. What is the range of g?