Answer:
A) [tex]y=-\frac{1}{20}x+20[/tex]
B) 14 gallons of gasoline
A linear function that relates the amount of gasoline to the traveling distance is : y = - (1/20)x + 20 and the gallons of gasoline left after you drive 120 miles will be 10 gallons.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is a table shows the amount of gasoline [g] (in gallons) left in your tank after you travel [m] miles.
The given table is -
Miles [m] Gallons [g]
0 20
20 19
40 18
60 17
We can write the linear function as -
y = mx + c
We can write the slope as -
m = {(19 - 20)/(20 - 0)}
m = (- 1/20)
At [x] = 0, then [y] = 20. So, the equation will be -
y = (-1/20)x + 20
y = - (1/20)x + 20
At [x] = 120 miles -
y(120) = (-1/20 x 200) + 20
y(120) = - 10 + 20
y(120) = 10 gallons
Therefore, a linear function that relates the amount of gasoline to the traveling distance is - y = - (1/20)x + 20 and the gallons of gasoline left after you drive 120 miles will be 10 gallons.
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Plz help I dont know
Given: ΔABC, AB=12, m∠A=60°,m∠C=45°, AB =8 Find the perimeter of ΔABC
Answer:
The perimeter of ΔABC is 43 units
Step-by-step explanation:
An illustrative diagram is shown in the attachment below.
To find the perimeter of the triangle, we will first determine the length of the unknown sides.
First, we can determine /BC/ using the Sine rule
From Sine rule
[tex]\frac{SinA}{a} = \frac{SinB}{b} = \frac{SinC}{c}[/tex]
∴ [tex]\frac{SinA}{a} = \frac{SinC}{c}[/tex]
In the diagram, [tex]a = /BC/[/tex] and [tex]c = /AB/ = 12[/tex]
m∠A=60° and m∠C=45°
∴ [tex]\frac{Sin60}{/BC/} = \frac{Sin45}{12}[/tex]
[tex]/BC/ = \frac{12 \times Sin60}{Sin45}[/tex]
[tex]/BC/ = 6\sqrt{6}[/tex]
To find /AC/, will first determine m∠B
m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)
60° +m∠B + 45° = 180°
m∠B + 105° = 180°
m∠B = 180° - 105°
m∠B = 75°
Also, using the sine rule
[tex]\frac{SinB}{b} = \frac{SinC}{c}[/tex]
From the diagram, [tex]b = /AC/[/tex]
[tex]\frac{Sin75}{/AC/} = \frac{Sin45}{12}[/tex]
[tex]/AC/ = \frac{12 \times Sin75}{Sin45}[/tex]
[tex]/AC/ = 6 + 6\sqrt{3}[/tex]
Now,
The perimeter of ΔABC = /AB/ + /BC/ + /AC/
= [tex]12 + 6\sqrt{6} + 6+6\sqrt{3}[/tex]
= 43.09 units
≅ 43 units
Hence, the perimeter of ΔABC is 43 units.
Answer:
Using the figure above, if AB = RT and ∠R = 70°, then ________.
ΔABC ~ ΔRTS
m ∠ S = 50°
ΔABC ≅ ΔRTS
m ∠ S = 60°
Step-by-step explanation:
The average credit card rate for new users is nearly 15%. Suppose you buy a $120 pair of shoes
using a brand-new credit card. If you are not able to make any payments on your credit card,
how much money will you owe 4 years after you purchased the shoes?
Answer:
$480
Step-by-step explanation:
A, B, and C are pegs on the bank of a canal which has
parallel straight sides. C and D are directly opposite
each other. AB = 30 m and BC = 140 m.
When I walk from A directly away from the bank,
I reach a point E, 25 m from A, such that E, B, and
D line up. How wide is the canal?
Answer:
116.67 m
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are equal and the ratio of their sides are in the same proportion.
From the image attached:
∠A = ∠C = 90° (right angled triangle).
∠ABE = ∠CBD (vertically opposite angles are equal to each other)
The angle-angle similarity postulate states that If two angles of one triangle are equal to two angles of another triangle, then both triangles must be similar. Hence:
Since, ∠A = ∠C and ∠ABE = ∠CBD, we can say that ΔABE and ΔCBD are similar triangles. Since they are similar, the ratio of their corresponding sides is equal. Therefore:
BC / AB = CD / AE
BC = 140 m, AB = 30 m, AE = 25 m
substituting:
140 / 30 = CD / 25
CD = (140 / 30) * 25
CD = 116.67 m
The width of the canal = CD = 116.67 m
1. The sum of the interior angles of a regular polygon is 1080°.
Part A: Classify the polygon by the number of sides.
A. 6
B. 8
COS)
C. 10
D. 11
Part B: What is the measure of one interior angle of the polygon? Write your answer to the nearest whole
degree.
degrees
Answer:
8 sides
each interior angle is 135°
Step-by-step explanation:
letters cost $1 each to send in the mail and packages cost $5 each the equation x + 5y = 25 describes how many letters and packages you can send for $25 find the y intercept and explain what it means
Answer:
y is the packages in the equation
[tex]7x - 6x = [/tex]
Answer:
x
7x-6x=x
7-6=1 but instead of putting the one there it would just be x depending on your teacher they'd mark it wrong if you put the 1.
Describe the data for a correlational research study and explain how these data are different from the data obtained in experimental and nonexperimental studies, which also evaluate relationships between two variables. A correlational study satisfies which conditions?
Answer:
Step-by-step explanation:
need asap‼️
Which phrase could be best represented by the algebraic expression
NO
-8?
Choose the correct answer below.
O A. the quotient of 9 and a number z
OB. 8 less than a number z
OC. 8 less than the quotient of z divided by 9
OD. the difference between a number z and 8
Answer:
oc
Step-by-step explanation:
m n
When Sandy and Allen's mother decorates the house for a holiday by herself, it takes her 5 hours. When both Sandy and Allen help, the three can finish the job in 2.5 hours. When only Allen helps his mother decorate, it takes the two 3.5 hours. How long would it take Sandy to decorate the house by herself?
Answer:
8 3/4
Step-by-step explanation:
time for all work:
Mother - 5 hours
Mother + Sandy + Allen - 2.5 hours
Mother + Allen - 3.5 hours
Sandy - x
In 1 hour
Mother - 1/5
Mother + Sandy + Allen - 2/5
Mother + Allen - 2/7
Sandy - 1/x
(M+S+A) - S = (M+A)
2/5 - 1/x = 2/7
solve equation
x = 8 3/4 hours
Hope this helps :)
The number of hours that Sandy took to decorate the house by herself will be 8.75 hours.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
At the point when Sandy and Allen's mom designs the house for a vacation without help from anyone else, it requires her 5 hours. At the point when both Sandy and Allen help, the three can complete the task in 2.5 hours. At the point when just Allen assists his mom with finishing, it requires two 3.5 hours.
Let 'M', 'S', and 'A' be the number of hours of mother, Sandy, and Allen. Then the equations are given as,
M = 5 ...1
1/M + 1/S + 1/A = 1/2.5 ...2
1/M + 1/A = 1/3.5 ....3
From equations 2 and 3, then we have
1/3.5 + 1/S = 1/2.5
1/S = 1/2.5 - 1/3.5
1/S = 4 / 35
S = 35/ 4
S = 8.75 hours
The number of hours that Sandy took to decorate the house by herself will be 8.75 hours.
More about the solution of the equation link is given below.
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How to select south Africa in countries
Answer:
what what 7-Eleven would 7th you have
rectangle has an area of x2 + 3x — 4 and a width of x— 1. What is the length of the rectangle?
Answer:
x+4
Step-by-step explanation:
If you plug in the answer choices (x+4, x-4, x+2, x-2) into (x-1) (insert solution), x+4 gives you x^2+3x-4. :)
What is the equation of the line that passes through the point (4,−2) and has a slope of −2?
Answer:y=-2x+6
Step-by-step explanation:
You want to find the equation for a line that passes through the point (4,-2) and has a slope of -2.
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was -2. So you can right away fill in the equation for a line somewhat to read:
y=-2x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(4,-2). When x of the line is 4, y of the line must be -2.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: . b is what we want, the -2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,-2).
So, why not plug in for x the number 4 and for y the number -2? This will allow us to solve for b for the particular line that passes through the point you gave!.
(4,-2). y=mx+b or -2=-2 × 4+b, or solving for b: b=-2-(-2)(4). b=6.
look at image. plssss help
Answer: B
Step-by-step explanation:
Since the 3 on the outside of the parenthesis is positive, none of the signs change on the inside of the parenthesis when you distribute the 3.
Answer:
The answer is B)
[tex] \frac{3}{5} x - \frac{3}{7} [/tex]
Can someone help I willl give brainliest
Answer:
87˚
Step-by-step explanation:
Since they have equal angles we can make this equation:
3x + 57 = 8x + 7
5x = 50
x = 10
now we can substite x back into one of the equations
8x + 7
8(10) + 7
80 + 7
87
A restaurant has a sign by the front door that says, "Maximum occupancy: 75 people."
What percentage of its capacity is 84 people?
Answer:
112%
Step-by-step explanation:
The percentage of its capacity is calculated as
Number of people / Maximum Occupancy × 100%
Number of people = 84 people
Maximum Occupancy = 75 people
Hence:
84 people /75 people × 100
= 1.12 × 100
= 112%
Therefore, the percentage of its capacity that is 84 people is 112 %
Please answer this correctly without making mistakes.I want ace expert and genius people to answer this correctly without making mistakes
What is this problem solve ? 2(n-1) +4n=2(3n-1)
Answer:
Any value will work
Step-by-step explanation:
2n - 2 + 4n = 6n - 2 -> 6n - 2 = 6n - 2 -> 0 = 0. Any value will work
Answer:
infinitely many solutions
Step-by-step explanation:
i ready
What is the answer???
The exterior angles of an octagon Are X, 2X, 3X, 4X, 5X, 6x, 7X and 8X. What is the size of the smallest interior angle of this octagon?
A. 10
B.45
C.80
D.100
Answer:
Hence, the smallest interior angle of this octagon is 100
Step-by-step explanation:
Final answer 100
What is the equivalent fraction of 6/8 with 32 as the new denominator
If /is an explanatory variable and m is the corresponding response variable, which of these would be represented by the horizontal axis on a scatterplot? O A. Neither /nor m B. 1 C. m D. Both / and m??
Answer: The explanatory variable goes in the horizontal axis.
Step-by-step explanation:
The explanatory variable is the variable that can be manipulated in an experiment. This is also called (and more commonly) the independent variable. This is the variable we usually "input" in a system, with the objective of observing the change in the response variable (also called the dependent variable, because it depends on the independent variable).
Usually, we write the explanatory variable on the horizontal axis and the response variable on the y-axis.
Then the correct answer would be C: /.
This is only because m is defined ONLY as a response variable, there are a lot of experiments with two variables, where we can use each of the variables as the explanatory variable.
And also there are some cases where in order to make the graph easier to read, we do not use the explanatory variable in the horizontal axis, instead, we may use some transformation or something alike, but those are really special cases.
10+(-6)
What is it please tell me
Answer:
4
Step-by-step explanation:
Answer:
The answer is 4
Step-by-step explanation:
I learnt this in 7th grade.
Sneha drinks a 27-ounce energy drink containing 137 calories per 9 ounces. How many calories did she drink?
Answer: 411
Step-by-step explanation:
A bakery can make 320 cookies in 2 hours. At this rate, how many cookies can they make in 5 hours?
800
800800
800800
800800
800800
800800
800800
800800
800800
800800
800800
800800
800800
800800
800800
800
Express 55 miles per hour in kilometers per hour?
help please
solve for x
Answer:
x = 17
Step-by-step explanation:
4x-10 and 58 are alternate interior angles since the lines are parallel
Alternate interior angles are equal.
4x-10 = 58
Add 10 to each side
4x-10 +10 = 58+10
4x = 68
Divide each side by 4
4x/4 = 68/4
x = 17
Answer:
17
i did the math at home.
Please help ASAP it’s due tomorrow
Answer:The answer is 14x-25=115 (B)
Step-by-step explanation:
he bought a certain amount of shirts, each being 14 dollars. So 14(how ever many shirts)- 25(the coupon) = Sales price
Answer:
b. 14x-25=115
Step-by-step explanation:
14 dollars each and 25 discount
the "each" here means the cost per cloth is 14, and total cost of the clothes Marco buy will increase depend on the amount of clothes.
Thus, it is 14x
The 25 discount represent that NO MATTER how many clothes Marco purchase, he only gets a discount of 25. It is a independent value.
Total clothes bought - discount = total amount of money spent.
Thus, it is 14x-25=115
Randi estimates the sum of 6.8 x 5.2 as 11. Is this a reasonable estimate? Why?
it isnt reasonable estimate. 6.8 is about 7 and 5.2 is about 5, and 7+5=12, not 11
A square shaped backyard has an area of 144 square yards where the length and width are the same. Another rectangular shaped backyard with the same area has a width of 8 yards and a length of 18 yards. The length x (in yards) and the width y (in yards) shows either direct or inverse variation. What is the equation that relates x and y?
Answer:
5y and 8x
Step-by-step explanation:
The chart shows Jolene's tutoring schedule. Today she worked with both math and
chorus students. When is the next time Jolene will tutor both subjects on the same
day?
Subject. Frequency
Math Every2Days Chorus
Every 5 Days
Pls help urgent
Answer:
10
Step-by-step explanation:
5x2=10
Answer:
10
Step-by-step explanation:
5 times 2 equals 10
