Based on the information above, the car with 1,000 pounds more will only go 1,194 miles, and the one with 2,000 pounds more will only go 1,188 miles.
What does MPG stand for?MPG stands for miles per gallon, and refers to the distance in miles a vehicle travels for each gallon of fuel in its tank.
In general, a car consumes about 1,200 miles per gallon. However, when you add load to it, its fuel consumption is higher because it requires more force to move.
Additionally, some studies state that for every 1,000 pounds of weight added to the car, it will yield 0.5% less. So if the car has 1,000 more pounds, it's not going to go 1,200 miles per gallon, it's going to go 1,194 miles.
On the other hand, if 2,000 pounds of weight were added, the fuel economy would be 1% less, that is, it would travel 1,188 miles per gallon.
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After six weeks of the coupon offer, the owner of the restaurant needs to decide if the restaurant should continue to run the same special or offer a new one. Use the provided scatter plot to write an equation for the line of best fit.
The equation of the line of the best fit on the scatter plot is y = 150x + 598
How to determine the equation of the line of best fit?From the line in the scatter plot, we have the following points
(x,y) = (3,1048) and (6,1498)
The equation is then calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1} *(x - x_1) + y_2[/tex]
The equation becomes
[tex]y = \frac{1498 -1048}{6 - 3} *(x - 3) + 1048[/tex]
Evaluate
y = 150 *(x - 3) + 1048
Expand the bracket
y = 150x - 450 + 1048
Evaluate the sum
y = 150x + 598
Hence, the equation of the line of the best fit is y = 150x + 598
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Complete the proof to show that ABCD is a parallelogram.
PROOF:
BC ║ AD and CD ║ BA because the ________________________________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.
OPTIONS:
A) lengths of consecutive sides are not equal
B) slopes of opposite sides are equal
C) lengths of opposite sides are equal
D) slopes of consecutive sides are not equal
IMAGE:
In the proof given, BC║AD and CD║BA because: B. slopes of opposite sides are equal.
What is the Slope of Parallel Lines?If two lines are parallel, they will have the same slope value,.
Slope = rise/run.
Slope of BC = rise/run = -2/5
Slope of AD = -2/5
Slope of BA = rise/run = -6/1 = -6
Slope of BA = rise/run = -6/1 = -6
Therefore, we can conclude that BC║AD and CD║BA because: B. slopes of opposite sides are equal.
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What is the volume of the cone? cone v = one-third b h startfraction 70 over 3 endfraction pi centimeters cubed startfraction 140 over 3 endfraction pi centimeters cubed startfraction 490 over 3 endfraction pi centimeters cubed startfraction 700 over 3 endfraction pi centimeters cubed
Using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]
How to determine the volume of the cone?The volume of a cone is calculated using:
[tex]V = \frac 13\pi r^2h[/tex]
The parameters are not given.
So, we use the following assumed values
Radius, r = 5
Height, h =10
Using the assumed values, we have:
[tex]V = \frac 13\pi * 5^2 * 10[/tex]
Evaluate the product
[tex]V = \frac {250}3\pi[/tex]
Hence, using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]
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Answer: C (490/3
Step-by-step explanation:
What is cos B?
A. 8/15
B. 15/8
C. 8/17
D. 15/17
Answer:
C. 8/17
Step-by-step explanation:
Given:
Hypotenuse = 17
BC = 8
Cos (B) = leg adjacent to ∠B / hypotenuse
= BC/BA
Substitute
Cos (B) = 8/17
Hence option C is correct
Please help me thanks!
Answer: See the screenshot below.
Explanation:
We'll be using these trig functions
sine = opposite/hypotenusecosine = adjacent/hypotenusetangent = opposite/adjacentThe inverse of those help us find the angle. Notation like arcsine is the same as inverse sine denoted as [tex]\sin^{-1}[/tex] on many calculators.
The decimal results are approximate.
what is the quotient of (x^3+3x^2-4x-12) divided by (x^2+5x+6)
Answer:
x - 2
Step-by-step explanation:
x^3 + 3x^2 - 4x - 12 simplifies to (x + 2)(x - 2)(x + 3)
x^2 + 5x + 6 simplifies to (x + 2)(x + 3)
(x + 2)(x - 2)(x + 3)
(x + 2)(x + 3)
The (x + 2) and (x + 3) cancel
x - 2
Kayden Kohl
9th Grade Student
(Algebra 2)
!20 PTS!
Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). EXPLAIN IN STEPS.
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). EXPLAIN IN STEPS.
For both problems, we can use the section formula.
1) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]
2) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]
i bougth 3 bags of candy and 1 drink for 3.20 dollars. my sister bought 2 bags of candy and 4 drinks for 6.30 dollars. how much does each bag of candy and each drink cost?. may somebody explain me? please.
Answer:
Step-by-step explanation:
We can set up two equations: one for each sister:
Let C and D be the prices for a Candy bag and and Drink.
Sister 1: 3C + 1D = 3.20 [The total spent by sister 1 is the sum of 3 candy bags(C) and 1 drink (D), which comes to $3.20.]
Sister 2: 2C + 4D = 6.30 [The total spent by sister 2 is the sum of 2 candy bags(C) and 4 drinks (D), which comes to $6.30.]
We have two unknowns, C and D, BUT we have 2 equations. Therefore, we're likely going to be able to solve for C and D if we rearrange one of the equations to isolate one of the unknowns, and then use that expression in the other equation. Seems unlikely, but it always works.
I'll pick Sister 1's equation and solve for D, the price of a drink:
3C + 1D = 3.20
1D = 3.20 - 3C [This tells us the price of a drink is 3.20 - 3C]
Use this definition of 1D in Sister 2's equation:
2C + 4D = 6.30
2C + 4(3.20 - 3C) = 6.30
2C + 12.80 - 12C = 6.30
-10C = - 6.5
C = $0.65
One candy bag, C, is $0.65.
Use this value of C in any equation to find D, the cost of 1 drink. I'll pick The expression we derived above:
1D = 3.20 - 3C
1D = 3.20 - 3(0.65)
1D = 3.20 - 1.95
1D = $1.25
One drink, D, is $1.25.
===================
Check the values:
Candy Bags = $0.65 each Drinks = $1.25 each
Reported
Sister 1 2 1 2
Candy bags 3 2 $1.95 $1.30
Drinks 1 4 $1.25 $5.00
$3.20 $6.30 Calculated
$3.20 $6.30 Reported
T
help help help
help help help meeee help me help me
When i double a number i get 16400 what is the number?
Answer:
the answer is 8200
Step-by-step explanation:
8200+8200=16400
Prove that √2 is an irrational number and hence show that 3+5√3 is also irrational
Answer:
square rooted numbers like the square root of 2 are irrational because when calculated they don't equal a whole number.
Step-by-step explanation:
3+5√3 = 11.66 // not whole - irrational
√2 = 1.4 // not whole - irrational
√25 = 5 // whole - rational
A cast iron pipe used as a water main for a home has an outer diameter of 8 in. If the pipe has a thickness of 0.25 in, what volume of iron does 24 in of pipe contain? Answer in cubic inches.
Question 25 of 25
Over what interval is the function in this graph increasing?
AV
M
<-10
10
A. 6≤x≤ 10
B. -4≤x≤1
C. -10≤x≤-4
D. 1≤x≤6
The correct option is option B : -4 ≤ x ≤ 1
What is Increasing and decreasing function?
Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis. Increasing and decreasing functions are also called non-decreasing and non-increasing functions.
Here, from graph
as we can observe from x = -4 graph starts increases upto x = 1 and after that graph becomes constant.
Thus, between x belongs -4 to 1 the graph is increasing.
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2sin² theta = sin theta for - 270° ≤ 0 ≤180°
Answer:
θ = 0°
θ = 30°
θ = 150°
θ = 180°
Step-by-step explanation:
2sin² θ = sin θ
Then
2sin² θ - sin θ = 0
Then
sin θ (2sin θ - 1) = 0
Then
sin θ = 0 or 2sin θ - 1 = 0
Then
sin θ = 0 or sin θ = 1/2
…………………………………………
We have sin θ = 0 and - 270° ≤ θ ≤180°
Then
θ = 0 or θ = π = 180°
On the other hand,
sin θ = 1/2 and - 270° ≤ θ ≤180°
Then
θ = π÷6 or θ = 5π÷6
π÷6 = 30° and 5π÷6 = 150°
If AB is tangent to (circle)C at A, find BC.
The length of r if AB is tangent to circle C, forming a right triangle is 8 units.
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
From the diagram, using Pythagoras theorem:
BC² = AC² + AB²
17² = 15² + r²
r = 8 units
The length of r if AB is tangent to circle C, forming a right triangle is 8 units.
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Image is attached
Find x and y of 2 similar polygons
Answer:
11
Step-by-step explanation:
10/15=6/x-2
then solve for x
x=11
A support wire reaches from the top of a pole to a clamp on the ground. The pole is
perpendicular to the level ground and the clamp is 10 feet from the base of the pole. The
support wire makes a 68° angle with the ground. Find the length of the support wire to the
nearest foot.
The length of the support wire on the pole is 27 feet
How to determine the length of the support?The given parameters are:
Distance from the base, b = 10 feetAngle with the ground, x = 68 degreesThe length (L) of the support wire is then calculated using the following cosine function
cos(x) = b/L
This gives
cos(68) = 10/L
Make L the subject
L = 10/cos(68)
Evaluate
L = 27
Hence, the length of the support wire is 27 feet
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Solve this equation
3x - 5 = -26
3x - 5 = -26
step 1:
subtract +5 on each side because you have to do the inverse operation
step 2:
3x= -21
step 3:
now divide 3 on each side
the answer is -7
Hope this helped!
TheOneAndOnlyLara~
Answer:
x=-7.
Step-by-step explanation:
Hi student! Let me help you out.
_________________
First, add 5 to both sides.
[tex]\sf 3x=-26+5[/tex]. Upon simplifying, we obtain this.
[tex]\sf 3x=-21[/tex].
↪
Now divide both sides, by 3.
[tex]\sf x=-7[/tex]
[tex]\therefore,\sf the \quad value \quad of \quad x \quad is \quad -7[/tex]. Which is our final answer.
⇨Hope that this helped! have a great day ahead! ⇦
Best Wishes!
[tex]\star\bigstar\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}[/tex]
◆◆-Greetings!-◈◈
__________________________
Determine the value of y, if x is 2
Y=x^2+5
Answer:
y = 9
Step-by-step explanation:
y = (2)^2 + 5
y = 4 + 5
y = 9
PLEASE HELP ILL MAKE YOU THE BRAINIEST What is the value of x
[tex]~~~~~~\cos 45^{\circ} = \dfrac{\text{Base}}{\text{Hypotenuse}}\\ \\\implies \dfrac 1{\sqrt 2} = \dfrac{x}{22}\\\\\implies x = \dfrac{22}{\sqrt 2}\\\\\implies x = \dfrac{22\sqrt 2}{2}\\\\\implies x = 11\sqrt 2\\[/tex]
Review the graph of f(x). What is the function’s behavior close to the vertical asymptote x = 2? Limit of f (x) as x approaches 2 minus = infinity and limit of f (x) as x approaches 2 plus = infinity Limit of f (x) as x approaches 2 minus = infinity and limit of f (x) as x approaches 2 plus = negative infinity Limit of f (x) as x approaches 2 minus = negative infinity and limit of f (x) as x approaches 2 plus = infinity
The function's behavior at vertical asymptote x = 2 is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]
How to determine the function's behavior?The attached graph represents the missing information in the question.
From the attached graph, we have the following highlights:
At x = 2, a curve points upwardAt x = -2, another curve points downwardThis means that the limit of f(x) approaches negative infinity and positive infinity at this value of x
Hence, the function's behavior is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]
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please help giving brainliest im begging lol ⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
Answer:
see below
Step-by-step explanation:
I would use the sine function for the info given
in a right triangle sine = opp leg / hypotenuse
so sin 57 = 10.8/x
then x = 10.8 / sin 57 = 12.87
B
ED
E D
B
C
B
m
A
DE
Which rule describes the composition of
transformations that maps figure ABCDE to figure
A"B"CD"E"?
ORC.900 orm
OroRC.900
ORc1800 or
OroRC.1800
Answer: [tex]R_{C, 180^{\circ}} \circ r_{m}[/tex]
Step-by-step explanation:
The sequence is a reflection over line m followed by a rotation 180 degrees about point C.
Among all the options give the last option that is,
⇒ r m0 Rc180° , is the right answer.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Now, In the given figure ABCDE is transformed to figure A”B”C”D”E.
Hence, When a figure is reflected along a line the reflected image is at the same distance to the line as the original figure was.
The figure ABCDE is first reflected through the line m to get the figure A'B'C'D'E'.
When a figure is rotated by 180 degrees the x and y coordinates change its place and y sign is reversed.
A'B'C'D'E' is rotated by 180 degrees to come to figure A"B"C"D"E".
Hence, Among all the options give the last option that is,
⇒ r m0 Rc180° , is the right answer.
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Please help me with my math question
Answer:
<
Step-by-step explanation:
5.62x10^4=56200, 4.7x10^5=470000, so it is <.
if yassy got score of 9, what is her rank?
answer:
4nd rank
Step-by-step explanation:
I'm not sure btw.
help me please I will give you brainliest
Answer:
-17, -10, -6, -5, 3, 8 only change is between 3 and 8
Please help me with this math problem!! Will give brainliest!! :)
Answer:
x = 10
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360°
(4x + 23) + (7x - 3) + (6x - 5) + (16x + 15) = 360°
4x + 23 + 7x - 3 + 6x - 5 + 16x + 15 = 360°
Add like terms
33x + 30 = 360°
Subtract 30 from both sides
33x = 330°
x = 10
Answer:
10
Step-by-step explanation:
A quadrilateral is a four sideded figure with four angles and four vertices.we should note that the sum of angles of a quadrilateral is equal 360°
therefore,
(4x+23)+(16x+15)+(6x-5)+(7x-3)=360
30 +33x= 360
33x= 360-30
33x= 330
dividing through by 33
x= 330/33
x= 10
• function notation•
these are so confusing
Answer:
15
Step-by-step explanation:
Just substitute the x for 5
In this case:
Original function: f(x) = [tex]x^{2}[/tex] - 2x
Substitute function: f(5) = [tex](5)^{2}[/tex] - 2(5)
Now solve for the substitute function
[tex](5)^{2}[/tex] - 2(5)
25 - 10
15
Therefore, f(5) is equal to 15
Prove that :
following
[tex](tan \: q \: + sec \: q) {}^{2} = \frac{1 + sin \: q \: }{1 - sin \: q \: } [/tex]
[tex]\text{L.H.S}\\\\=(\tan q + \sec q)^2\\\\\\=\left(\dfrac{\sin q}{ \cos q} + \dfrac 1{ \cos q} \right)^2\\\\\\=\left( \dfrac{1+ \sin q}{\cos q}\right)^2\\\\\\=\dfrac{(1+ \sin q)^2}{\cos^2 q}\\\\\\=\dfrac{(1+ \sin q)^2}{1-\sin^2 q}\\\\\\=\dfrac{(1 + \sin q)(1 + \sin q)}{(1+ \sin q)(1 - \sin q)}\\\\\\=\dfrac{1+ \sin q}{1- \sin q}\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Sheryl makes $7 per pair of
earrings, e, and $13 per necklace,
n, she sells. What expression
represents her total income?
The expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
Sheryl makes $7 per a pair of earrings, e, and $13 per necklace, n, she sells.
Let's suppose the total income of Sherly is T:
Then,
T = 7e + 13n
Here e is the number of earrings she sells and n is the number of necklace she sells.
T is the total income and the expression T = 7e + 13n represents the total income of Sherly.
Thus, the expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.
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