Answer:
y = 13x
Step-by-step explanation:
First we need to take the number miles the Johnson family drove and divide it to the number of gallons of gasoline used to find how many miles per gallon
Miles per gallon = 52/4
Miles per gallon = 13
Now that we know how many miles per gallon, let's make an equation to find how much they can travel on a full tank of 15 gallons.
Let y = number of miles traveled
Let x = number of gallons
y = 13x
Now let's see how much they can travel in 15 gallons.
y = 13x
y = 13(15)
y = 195 miles
So the Johnson family can drive 195 miles on a full tank of 15 gallons of gasoline.
Find the center of the circle that can be circumscribed about Triangle EFG with E(2, 2), F(2, -2), and G(6,-2).
The center of the circle that can be circumscribed about Triangle EFG with E(2,2), F(2,-2), and G(6,-2) is (2, -2).
Explanation:To find the center of the circle circumscribed about triangle EFG, we can first find the midpoint of EF and the midpoint of FG.
These midpoints will lie on the perpendicular bisectors of EF and FG respectively.
The intersection of these bisectors will give us the center of the circle. Let's calculate it step-by-step:
Step 1: Find the midpoint of EF.
Midpoint of EF = ((2+2)/2, (2-2)/2) = (2, 0).
Step 2: Find the midpoint of FG.
Midpoint of FG = ((2+6)/2, (-2-2)/2) = (4, -2).
Step 3: Find the equation of the perpendicular bisector of EF.
The slope of EF = (0 - 2)/(2 - 2) = undefined. The midpoint of EF is (2, 0).
Hence, the equation of the perpendicular bisector of EF is x = 2.
Step 4: Find the equation of the perpendicular bisector of FG.
The slope of FG = (-2 - (-2))/(6 - 2) = 0. The midpoint of FG is (4, -2).
Hence, the equation of the perpendicular bisector of FG is y = -2.
Step 5: Solve the equations of the perpendicular bisectors to find the center of the circle. Since x = 2 and y = -2, the center of the circle is (2, -2).
Final answer:
To find the center of the circle that can be circumscribed about Triangle EFG, use the midpoint formula and equations of the perpendicular bisectors.
Explanation:
To find the center of the circle that can be circumscribed about Triangle EFG with coordinates E(2, 2), F(2, -2), and G(6,-2), we can use the following steps:
Find the midpoint of each side of the triangle, which will be the center of the circle.
Use the midpoint formula to find the coordinates of the midpoints of EF and FG.
The center of the circle will be the point where the perpendicular bisectors of each side intersect.
Find the equation of the perpendicular bisectors of EF and FG.
Solve the system of equations formed by the equations of the perpendicular bisectors to find the coordinates of the center of the circle.
The center of the circle that can be circumscribed about Triangle EFG is (-2/3, -4/3).
Check my answers please thank you
16-20 are correct. Remember to mark the first #20 as A
The last #20 is wrong. The answer is B. 95 minutes.
10:55 - 11:00 = 5 minutes
11:00 - 12:00 = 60 minutes
12:00 - 12:30 = 30 minutes
Total = 95 minutes
Lisa’s test grades are 79, 89, and 90.
What is Lisa’s test average?
Answer: 86
Step-by-step explanation: You would add up all the numbers, then divide by the amount of numbers there are.
For example
79+89+90=258
Since there are three numbers(79,89,90) you would divide 258 by 3 and would get 86.
Hopes this helps
The height of one right circular cylinder is 7 centimeters and it’s radius is 2 centimeters. The height of the second right circular cylinder is 28 centimeters and it’s radius is also 2 centimeters. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder? Please Explain!!
Volume of a cylinder
[tex]\pi \times {r}^{2} \times h[/tex]
larger cylinder: r=2, h=28
volume of larger cylinder lets say (V) :
[tex]\pi \times {2}^{2} \times28 \\ = 4 \times 28\pi =112\pi[/tex]
vokume of smaller cylinder lets say (v): r=2, h=7
[tex]\pi \times {2}^{2} \times 7 \\ = 4 \times 7\pi = 28\pi[/tex]
so the ratio= volume of largercylinder/ volume of smaller
[tex]ratio = \frac{112\pi}{28\pi} \\ = \frac{4}{1} [/tex]
so in ratio terms the
Ans: 4:1
The ratio of the volume of the larger cylinder to the smaller cylinder is 4:1, calculated using the volume formula for cylinders, V = πr²h.
To calculate the ratio of the volumes of two cylinders, we need to use the formula for the volume of a cylinder, V = (πh), where r is the radius and h is the height.
For the first cylinder with a height of 7 cm and a radius of 2 cm, the volume is V₁ = 3.14 (2 cm) (7 cm) = 88.36 cm³.
For the second cylinder with a height of 28 cm and the same radius, the volume is V₂ = 3.14 (2 cm) (28 cm) = 353.44 cm³.
The ratio of V2 to V1 is then 353.44 cm³ / 88.36 cm³, which simplifies to 4:1.
help me please with an explanation please!!!
well there’s 360 degrees in one circle so it’s just 270/360 which is 1/4 . you’re welcome and brainliest would be nice ty
Answer:
¾
Step-by-step explanation:
Your diagram shows that moving the hand 270° covered three of the divisions of the circle.
A circle consists of four equal parts, and you covered three of them.
Thus, 270° is ¾ of a complete turn.
Data was collected of students’ hair color and gender. The results are in the table below.
Answer:
Step-by-step explanation:
Part One
Number of girls with blonde hair = 6
Total number of students = 40
% = 6/40 * 100% = 15%
Part Two
Number of Red Headed boys = 2
Just read the chart.
Part Three
The Chance that black hair is 4/40 = 0.1 or 1 in 10
fine the value of m-8 when m=15
Answer:
23
Step-by-step explanation:
15+8=23
Answer:
7
Step-by-step explanation:
um thats just 15-8
Identify if each of triangles below is congruent or not. Remember that the diagram may not be drawn to scale. Justify your conclusion.
Answer: ¨A¨ is congruent due to SSS. ¨B¨ is not because corresponding sides are not congruent. ¨D¨ is congruent due to AA. Can´t see all of ¨C¨
Step-by-step explanation:
Identify the vertex of the graph. Tell whether it is a minimum or maximum.
(-2,-3); maximum
(-2,-3); minimum
(-3,-2); maximum
(-3,-2); minimum
ANSWER
(-2,-3); minimum
EXPLANATION
The vertex is the minimum or maximum point on a parabola.
The graph of the function opens upwards.
Therefore the vertex will be the minimum point on the graph.
From the graph, the minimum point is (-2,-3).
Therefore the vertex is (-2,-3).
The second choice is correct.
Emma’s total bill for dinner was $20. The cost of her dessert was 30% of the total bill. What was the cost of her dessert?
$6 was her dessert. you do 20x0.3=6
A concession stand sells apple cider for $3.35 a cup and donuts for $2.45 each, on Saturday the stand sold 126 items and made $362.70 how many cups of apple cider did the stand sell
52 cups.
3.35 times 52 equals 174.20
2.45 times 77 equals 188.60
So 52 cups of apple cider were sold in total.
Answer:
The number of cups of apple cider sold was 60 cups
Step-by-step explanation:
We will develop equations to solve this problem.
Let a= price for a cup of apple cider in dollars
Let b= price for a donut in dollars
Let x = number for cups of apple cider sold
Let y= number of donuts sold
Let z = number of items sold on the day = 126 items
Let v = total money made = $362.70
Lets write two equations. One in terms of the amount of items sold of cups of apple cider and donuts, and one in terms of how much money was made for selling cups of apple cider and donuts.
z = x + y
x = z- y (1)
v = ax + by (2)
we substitute equation 1 in to equation 2
v = a(z-y) +by = az -ay +by = az +y(b-a)
solve for y
y = (v-az)/(b-a) = (362.70 - 3.35×126)/(2.45-3.35) = 66 donuts were sold
therefore x = z-y = 126-66 = 60 cups of apple cider were sold
I will give 15 points
Part A:
Mowing lawns: 1= $12 2= $24 3=$36 4= $48 5= $60
Walking dogs: 1= $9 2= $18 3= $27 4= $36 5= $45
I hope this helps you.
Part A:
-Chart one-
1-12
2-24
3-36
4-48
5-60
-Chart two-
1-9
2-18
3-27
4-36
5-45
Part B:
Plot these with circles (1,12), (2,24), (3,36), (4,48), (5,60)
Plot these with squares (1,9), (2,18), (3,27), (4,36), (5,45)
Solve the exponential equation. Write the exact answer with natural logarithms and then approximate the result correct to three decimal places.
[tex]5^{1-x} =2^{x}[/tex]
I was able to start it, but I somehow got [tex]log_{5}2=0[/tex], and I don't think that's right.
Answer:
Fraction form: x = ln(5)/ln(10)
Decimal form: 0.69897000
please mark brainliest
HELP ASAP PLS!!
Which triangle is a translation of triangle ABC?
A) DEF
B) GHI
C) JKL
D) MNO
Answer:
the answer would be JKL
Step-by-step explanation:
Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively. Which statement is true about lines a and b?
(2x+3y)+(4x+9y) how do I simplify it
Answer: the answer is 6x + 12y
Step-by-step explanation:
6x+12y will be the answer for this!
in the equation y=4x-7, what is the value of y when x=2?
Answer:
-56Step-by-step explanation:
y=4x-7= x=2y=4(2)-7
y=(4)(2)(−7)
Answer:
y=−56
Value of y when x = 2 is 1.
What is an equation?
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given equation
y = 4x-7
Value of y when x = 2
Substitute x = 2 in above equation
[tex]y = 4 \times 2 -7[/tex]
[tex]y=8-7[/tex]
y = 1
Value of y when x = 2 is 1.
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A kayak rental company charges a $15 fee to rent a kayak plus $3.50 per hour. Which equation represents the function for the total cost, c, to rent a kayak for h hours?
A. c=3.5x+15
B. c=3.5x-15
C. c=-3.5x+15
D. c=-3.5x-15
Final answer:
The correct equation is c=3.5h+15, where c is the total rental cost and h is the number of hours the kayak is rented. The equation includes a fixed fee of $15 and a variable hourly rate of $3.50. The correct answer is option (A).
Explanation:
The equation representing the function for the total cost c, to rent a kayak for h hours, is A. c=3.5h+15. This equation consists of a fixed cost and a variable cost.
The fixed cost, or y-intercept, is the initial $15 fee required to rent the kayak, which is represented when h=0. The variable cost, or slope, is $3.50 per hour of rental, indicating that for each additional hour h, the cost increases by this amount.
Which expression is equivalent to (3^2)^-2
Answer: 1/81
First you simplify it to 3^-4
Then express it with a positive exponent which goes to 1/3^4
Then evaluate it to 1/81
Answer:
The expression which is equivalent to the given expression is given by :
[tex]\bf\frac{1}{81}[/tex]
Step-by-step explanation:
The expression is given to be :
[tex](3^{2})^{-2}[/tex]
Now, we need to find a expression which is equivalent to this given expression.
[tex](3^{2})^{-2}\\\\\implies (3\times 3)^{-2}\\\\\implies (9)^{-2}\\\\\implies\frac{1}{(9)^2}\\\\ \implies \frac{1}{81}[/tex]
Hence, The expression which is equivalent to the given expression is given by :
[tex]\bf\frac{1}{81}[/tex]
Mark launches a toy rocket with an initial vertical velocity of 25ft/s from a platform that is at ground level. how long will the toy rocket be in the air?
Answer:
A
Step-by-step explanation:
First: C is incorrect. It is using the value of acceleration due to gravity in the metric system.
Second: the 16 must be opposite in sign from the 25. That makes B and D incorrect.
Answer: A
Find the base and height of a rectangle with vertices (–4, 7), (–2, 7), (–2, 1), and (–4, 1). The height is units. The base is units.
ANSWER
The height is 6 units.
The base is 2 units.
EXPLANATION
The given rectangle has vertices (–4, 7), (–2, 7), (–2, 1), and (–4, 1).
To find the height of the rectangle, we use the points (-2,7) and (-2,1) or
(-4,7) and (-4,1) because they form the vertical side of the rectangle.
The height is
[tex]|7-1|=6 units[/tex]
To find the base, use the points (-2,7) and (-4,7) or (-2,1) and (-4,1).
The base is
[tex]|-2--4|=2 units[/tex]
Answer: The base is 2 units and the height is 6 units.
Step-by-step explanation:
You can plot the points (-4, 7), (-2, 7), (-2, 1), and (-4, 1) and obtain the rectangle shown in the figure attached.
As you can see in the figure, the distance between the points of the base is:
[tex]d=\sqrt{(-2-(-4))^2+(1-1)^2}\\d=2[/tex]
Then the lenght of the base is 2 units
The distance between the points of the height is:
[tex]d=\sqrt{(-2-(-2))^2+(1-7)^2}\\d=6[/tex]
Then the height is 6 units
Match the following.
1 .
absolute value
the distance from zero on the number line
2 .
inequality
the number of units between two numbers or points, regardless of direction
3 .
opposite numbers
two numbers that are the same distance from zero on the number line but in opposite directions
4 .
distance
sentence showing a relationship between numbers that are not necessarily equal; uses the symbols >, <, ≥, ≤, or ≠
Answer:
Distance - The number of units between two numbers or points, regardless of direction.
Inequality - Sentence showing a relationship between numbers that are not necessarily equal; uses the symbols >, <, ≥, ≤, or ≠
Opposite numbers - Two numbers that are the same distance from zero on the number line but in opposite directions.
Absolute Value - The distance from zero on the number line.
The question matches mathematics concepts like absolute value, inequality, opposite numbers, and distance.
Explanation:Absolute value: the distance from zero on the number line.Inequality: a sentence showing a relationship between numbers that are not necessarily equal; uses symbols like >, <, ≥, ≤, or ≠.Opposite numbers: two numbers that are the same distance from zero on the number line but in opposite directions.Distance: the number of units between two numbers or points, regardless of direction.Learn more about Mathematics here:https://brainly.com/question/26854035
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17,076 ÷ 29
Plz help me solve this is so urgent wiil give brainliest
i think it is 588 but I am not 100percent sure
Answer:
588.827
Step-by-step explanation:
In a geometry class,the girl to boy ratio is 10 to 2.if there are a total of 24 students,how many girls are there?
Answer:
20 girls.
Step-by-step explanation:
The girl to boy ratio is 10 to 2.
Insert the multiplier m and write an equation for the total number of students:
10 m + 2 m = 24, or
12 m = 24. Then m = 2.
The number of girls is 10(m) = 10 m = 10(2) = 20.
The number of boys is 2(m) = 4
Note that 20 (girls) + 4 (boys) = 24 (students), as specified.
Note that 20/4 = 10/2, which is the given ratio.
Answer:
20 girls
Step-by-step explanation:
if there are 10 girls to 2 boys when you doble it you get 20 girls to 4 boys but when you add 20 and 4 together you get 24 students
Find the slope of the line
Answer:
4/5
Step-by-step explanation:
Answer: [tex]m= \frac{4}{5}[/tex] or [tex]m= 0.8[/tex]
(0,0) = (x1,y1)
(5,4) = (x2,y2)
Slope= [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{4-0}{5-0}[/tex]
= [tex]\frac{4}{5}[/tex]
As decimal
= [tex]0.8[/tex]
10.5 Tangents. Hw 20
Answer:
Refer to step-by-step.
Step-by-step explanation:
1. x = 4
x + 3 = 7
x = 7-3
x = 4
2. x = 25
We need to use the Pythagorean theorem to find x.
a² + b² = c²
15² + 20² = x²
225 + 400 = x²
652 = x²
√652 = √x²
x = 25
3. x = 12
Line NP and Line QP will have the same measurement.
x = 12
4. x = 29.41
We need to use the Pythagorean theorem to find x.
a² + b² = c²
24² + 17² = x²
576 + 289 = x²
865 = x²
√865 = √x²
x = 29.41
5. NO
We apply the Pythagorean theorem to find if they are tangent.
a² + b² = c²
9² + 40² = 41²
81 + 1600 = 2500
1681 = 2500 NO
6. NO
a² + b² = c²
4² + 12² = 13²
16 + 144 = 169
160 = 169 NO
7. NO
a² + b² = c²
20² + 21² = 28²
400 + 441 = 784
841 = 784 NO
8. YES
a² + b² = c²
14² + 48² = 50²
196 + 2304 = 2500
2500 = 2500 YES
Add 9 to me. Then multiply by 3. If you subtract 16 the add 7, you get 27. What number am I?
Answer:
Step-by-step explanation:
3 because :
3+9=12
12×3=36
36-16=20
20+7=27
EMERGENCY
The graph represents function 1, and the equation represents function 2.
Function:
y = 8x + 12
How much more is the rate of change of function 2 than the rate of change of function 1?
Answer:
The rate of change is 8 more for function 2 than it is for function 1.
Step-by-step explanation:
Function 1 is a horizontal line, which has a slope of 0. Slope is the same as rate of change.
Function 2 has a slope of 8 (since it is the coefficient of x.
As a result, we know that function 2's rate of change is 8 higher than that of function 1.
PLEASE HELP QUICKLY
Which is the graph of y =
√x-5-1 ?
graph A
graph B
graph C
graph D
Answer:
Step-by-step explanation:
Answer:
The answer is graph D.
Your welcome:))))
18% of 120 to 12% of 120
Answer: 18% of 120 is 21.6
And, 12% of 120 is 14.4
* Both of their work is below:)
* Hopefully this helps:)!! Mark me the brainliest:)!!
∞ 234483279c20∞
Answer:
18% of 120 to 12% of 12021.6 to 14.4Step-by-step explanation:
18% of 120
Convert 18% to a decimal by dividing by 100:
18 / 100 = 0.18
120 * 0.18 = 21.6
12% of 120
Convert 12% to a decimal by dividing by 100:
18 / 100 = 0.12
120 * 0.12 = 14.4
18% of 120 to 12% of 12021.6 to 14.4