Answer:
System of linear equations
[tex]\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.[/tex]
a: adult ticket price and c: child ticket price
Step-by-step explanation:
This system of equations can be used to find the price of the adult and child tickets.
We have two equations (one for each day) and two unknowns (adult ticket price and child ticket price).
Let a: adult ticket price and c: child ticket price,
we have for the first day that 3 adult tickets and 1 child ticket adds $38:
[tex]3a+1c=38[/tex]
and for the second day we have that 2 adult tickets and 2 child tickets adds $52:
[tex]3a+2c=52[/tex]
If we write this as a system of equations, we have:
[tex]\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.[/tex]
PLLLLLLLLLLLLLLLEEEEEEEEEAAAAAAAASSSSSSSE HEEEEEEEEELP As soon as a new car that costs $25,000 is driven off the lot, it begins to depreciate at a rate of 24.9% annually. About how much money is the car worth after the second year?
Answer:
The value of the car after two years is $14,100.025
Step-by-step explanation:
Here, we want to calculate the value of a car after its second year, given the depreciation percentage.
To get the value of the car year after year at the fixed percentage level, what we do is to set up an exponential equation;
V = I(1-r)^t
where V is the present value
I is the initial value = $25,000
r is the rate = 24.9% = 24.9/100 = 0.249
t is the number of years = 2 in this case
So we substitute these values in the depreciation case and have;
V = 25000(1-0.249)^2
V = 25000(0.751)^2
V = $14,100.025
There are only r red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is Find the number of red counters and the number of green counters that were in the bag originally. ( 5 marks)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
There are only r red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7 The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13
Find the number of red counters and the number of green counters that were in the bag originally.
Answer:
Total number of green counters = 9
Total number of red counters = 12
Step-by-step explanation:
Recall that probability is given by
P = number of desired events/total number of events
The probability that the counter is green is 3/7
P(green) = 3/7 = 3x/7x
Where 3x is the number of green counters
7x is the total number of counters
So then red counters are
red counters = 7x - 3x = 4x
4x is the number of red counters
P(green) = 3/7 = 3x/3x + 4x
The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. The probability that the counter is green is 6/13
So after addition of 3 green and 2 red new counters,
P(green) = 6/13 = (3x + 3)/(3x + 4x + 3 + 2)
Now solve for x
6/13 = (3x + 3)/(3x + 4x + 3 + 2)
6/13 = (3x + 3)/(7x + 5)
6(7x + 5) = 13(3x + 3)
42x + 30 = 39x + 39
42x - 39x = 39 - 30
3x = 9
x = 9/3
x = 3
So total number of green counters are
green counters = 3x = 3*3 = 9
So total number of red counters are
red counters = 4x = 4*3 = 12
Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.
Answer:
y=3/4 x+2
Step-by-step explanation:
y=mx+b
take two points from graph
(0,2) and (4,5)
find b when x=0 then y=b=2
find m : y2-y1/x2-x1=5-2/4-0
m=3/4
y=3/4 x +2
Please can someone help!
Answer:
51 mph
Step-by-step explanation:
→ The first thing we need is a formula which links speed, distance and time so,
Speed = Distance ÷ Time
Speed = mph
Distance = metres/miles
Time = hours
→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that the car travels at an average speed of 45 mph for 40 minutes, we can rearrange the formula to work out the distance so,
Speed = Distance ÷ Time
→ Rearrange to get distance as subject
Distance = Speed × Time
→ Substitute in the values
Distance = 45 × 40
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
40 ÷ 60 = 0.666666667
→ Substitute in the time value multiplied by the speed
Distance = 45 × 0.666666667 = 30
⇒ 30 metres/miles is overall distance for the first part of the journey
→ Now we have to work out the distance for the second part of the journey. State the distance formula.
Distance = Speed × Time
→ Substitute in the values into the distance formula
Distance = 60 × 25
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
25 ÷ 60 = 0.416666667
→ Substitute in the time value multiplied by the speed
Distance = 60 × 0.416666667 = 25
⇒ 25 metres/miles is overall distance for the second part of the journey
→ Now we have to add the distance of both the journeys together
25 + 30 = 55
→ Then we add the times of the journey together
40 minutes + 25 minutes = 65 minutes
→ Convert 65 minutes into hours
65 ÷ 60 = 1.08333 hours
→ Substitute both values into the speed = distance ÷ time formula
Speed = 55 ÷ 1.08333 = 50.76923077
→ The question says to round it to the nearest whole number so,
50.76923077 = 51 mph
Question 11 PLEASE HELP find the slope of the line that passes through the points (6,2) and (8,8)
Answer:
Slope would equal 3.
slope= (y2-y1)/(x2-x1)
Plug in you get (8-2)/8-6)
Simplify (6)/(2)=3
Step-by-step explanation:
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
Answer:
0.723 seconds
Step-by-step explanation:
Let h = 0
0 = -16t² + 6t + 4
Let’s solve by completing the square.
Subtract 4 from both sides.
-4 = -16t² + 6t
Since the coefficient of -16t² is -16, divide both sides by -16.
1/4 = t² - 3/8t
The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.
Then we need to add (b/2)² = 9/256 to both sides to complete the square.
Add 9/256 to both sides.
73/256 = t² - 3/8t + 9/256
Factor right side.
73/255 = (t-3/16)²
Take the square root on both sides.
±√(73/255) = t-3/16
Add 3/16 to both sides.
3/16 ± √(73/255) = t
The answer has to be positive, not negative.
0.72254626884 = t
0.723 ≈ t
Answer:
Rounding to the nearest hundredth, it is 0.72
Dale is following this recipe to make shortbread fingers. Dale uses 75 g of butter. How many shortbread fingers does he make? Recipe: Makes 20 fingers 125 g butter 55 g sugar 180 g flour
Answer:
For 75 g butter ≈ 27 fingers
Step-by-step explanation:
Using unitary method
For 20 fingers = 55 g butter
For 1 g butter = 20/55 fingers
=> For 1 g butter = 4/11 fingers (Simplified form)
Multiplying both sides by 75
=> for 75 g butter = [tex]\frac{4}{11} * 75 {fingers}[/tex]
=> For 75 g butter ≈ 27 fingers ( approximately )
A square is inscribed in a circle of diameter 12 millimeters. What is the area of the shaded region? A square is inscribed in a circle with a diameter of 12 StartRoot 2 EndRoot millimeters. Everything outside of the square is shaded. Recall that in a 45 – 45 – 90 triangle, if the legs each measure x units, then the hypotenuse measures x units. (72π – 144) mm2 (72π – 72) mm2 (288π – 288) mm2 (288π – 144) mm2
Answer: A. (72π - 144) mm²
Step-by-step explanation:
[tex]A_{shaded}=A_{circle}-A_{square}\\\\\\A_{circle}=\pi \cdot r^2\\.\qquad \ =\pi \bigg(\dfrac{12\sqrt2}{2}\bigg)^2\\\\.\qquad \ =\pi (6\sqrt2)^2\\.\qquad \ =72\pi\\\\\\A_{square}=side^2\\.\qquad \quad =\dfrac{12\sqrt2}{\sqrt2}^2\\\\.\qquad \quad =12^2\\\\.\qquad \quad =144\\\\\\\large\boxed{A_{shaded}=72\pi-144}[/tex]
The area of shaded region is (72π – 144) square millimeters.
To understand more, check below explanation.
Area of shaded region:It is given that,
The diameter of circle is [tex]12\sqrt{2}[/tex] millimeters.
Since, radius = diameter/2
So that, radius of circle[tex]=12\sqrt{2}/2=6\sqrt{2}[/tex]
now, we have to find area of circle,
[tex]Area=\pi *r^{2} \\\\Area=\pi *(6\sqrt{2} )^{2} \\\\[/tex]
Area = 72π square millimeters
The side of inscribed square[tex]=12\sqrt{2} /\sqrt{2}[/tex] = 12mm
Since, area of square= (side)^2
Area of square= 12 * 12 = 144 square millimeters
To find the area of shaded region, subtract area of square from area of circle.
Area of shaded region = area of circle - area of square
Area of shaded region = (72π – 144) square millimeters.
Learn more about the area of circle here:
https://brainly.com/question/14068861
A delivery company estimates that it will take 4 minutes for their drone to fly 7 km how long will it take the drone to fly 21 km
Answer: 12 minutes
Step-by-step explanation:
7 km ........ 4 minutes
21 km ...... ?
21/7 x 4= 12 minutes
Answer: 12 minutes.
Step-by-step explanation:
It is easy to put the numbers into a ratio form to work it out. So-
4 minutes for 7 km = 4 : 7
Then ? minutes for 21 km = ? : 21
You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.
Therefore your answer is 12 minutes.
Use the first four terms of the binomial theorem to approximate 2.2^7
Answer:
248.96 which is approximately 249
Step-by-step explanation:
2.2^7
The coefficients are;
1,7,21,35,35,21,7,1
So the terms we want to use are 1,7,21 and 35
We can write 2.2 as 2+ 0.2
So the approximations are;
1(2)^7(0.2)^0 + 7(2)^6(0.2) + 21(2)^5(0.2)^2 + 35(2)^4(0.2)^3
= 128 + 89.6 + 26.88 + 4.48 = 248.96
Solve for x 7 x − 4 = 6 Give your answer as an improper fraction in its simplest form.
Answer:
10\7
Step-by-step explanation:
7x-4=6
7x=6+4
7x=10
7x\7=10\7
x=10\7
Answer:-13/3
Step-by-step explanation:
the function g(x)=-5x-6
Answer:
D. the slope of f(x) is greater than the slope of g(x)
Step-by-step explanation:
slope of f(x) =rise/run
=y2 -y1 / x2 -x1
slope of f(x)= -1-2/1-0= -3
g(x)= -5x-6
slope of g(x)= -5
-3>-5
D. the slope og f(x) is greater than the slope of g(x)
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
Answer:
The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)
Step-by-step explanation:
Notice that when we start with the function [tex]f(x)=x^3[/tex], and then transform it into the function: [tex]g(x)=(x-4)^3-7[/tex]
what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).
Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).
then the point (0, 0) after the translation becomes: (4, -7)
Answer:4, -7
Step-by-step explanation:
please help me! Bethany incorrectly simplified the following expression: (4 x 10^11) (3 x 10^-14) + 0.000005 Which of Bethany’s steps show an error based solely on her previous step? Choose all that apply: A. Step one: (4 x 10^11) (3 x 10^-14) + (5 x 10^-5) B. Step two: (12 x 10^-3) + (5 x 10^-5) C. Step three: (120 x 10^-4) + (5 x 10^-5) D. Step four: (120 x 10^-4) + (50 x 10^-4) E. Step five: 170 x 10^-8 F. Step six: 1.7 x 10^-6
Answer:
Below.
Step-by-step explanation:
Step 1: it is 5 x 10^-6 not 5 x 10^-5.
Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.
Answer: yes that is correct explanation:
Four whole numbers are rounded to the nearest 10 The sum of the four rounded numbers is 90 What is the maximum possible sum of the original four numbers
Answer:
110
Step-by-step explanation:
example:
rounded 20+20+20+30 = 90
original 25+25+25+35 = 110
Find an equation for the nth term of the sequence. -3, -12, -48, -192, ... (1 point)
a = -3
common ratio(r) = -12/(-3) = 4
nth term = a.r^(n-1)
= -3.(4)^(n-1)
The circumference of a circular field is 285.74 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
yards
x
?
Answer:
The diameter is 91.
Step-by-step explanation:
The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91
Answer:
91 yards
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c=π * d
We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.
285.74= 3.14 *d
We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14
285.74/3.14= 3.14*d/3.14
285.74/3.14=d
Divide
91=d
d= 91 yards
The diameter of the field is 91 yards.
Find the area of the composite figure in square mm. Round your
answer to the nearest square milimeter. (Enter only a number as
your answer.)
Answer:
521
Step-by-step explanation:
Composite figure.
Draw a straight down from C to line segment AB. This forms a triangle.
Now, the area of this figure=
Area of semicircle+area of rectangle+ area of triangle.
Rectangle area formula = l times w
Length - 20
Width =14
14 times 20 = 280
Area of rectangle = 280
Semicircle area = area of circle/2
Area of circle = π[tex]r^2[/tex]
Diameter =20= 2r
r=10
π[tex]r^2[/tex]= π 10^2 =100π
100 times 3.14 =314
314/2 = 157
Area of semicircle = 157
Area of triangle= bh/2
Triangle's base= 32-20=12
Triangles height = 14
14 times 12 = 168
168/2 = 84
Area of triangle: 84
Area of semicircle+area of rectangle+ area of triangle.
157+280+84 =521
D. Is no solution please help
Answer:
B
Step-by-step explanation:
I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.
Answer:
B
Step-by-step explanation:
It is too blurry BTW but B is correct
The number 5600 is first decreased by 15 % . The value obtained is next increased by 10 % . Find the final number.
Answer:
5236
Step-by-step explanation:
the original number is equal to 100%
Therefore 5600=100% how about 85 %(which is what is left after decreasing 15%)
85×5600÷100=4760
the new original is(100%)=4760
4760=100% how about 110%(which is what you'll have after adding 10%)
4760×110÷100=5236
Complete the following equivalent fractions. 18/54 = ?/3
Answer:
1
Step-by-step explanation:
do 18 times 3
then do 54 divided by 54
to find the following number
hope this helps
Is 19⁄18 an improper fraction or a mixed number?
Answer:
Improper fraction.
Step-by-step explanation:
19/18 is an improper fraction. If it were a mixed number, you would have an integer followed by a fraction, like 1 and 1/18.
Hope this helps!
Answer:
It would be an improper fraction.
A mixed number would be 1 whole, while the other part is a fraction.
[tex]1\frac{1}{18}[/tex]
A improper fraction is when the numerator is greater than the denominator, such as
[tex]\frac{19}{18}[/tex]
Hope this helps
Answer by
~[tex]Fishylikeswater[/tex]~
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?
Explanation:
Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC/AX = AB 6. division property of equality
7. AC/AX = AB/AY 7. division property of equality
8. Corresponding sides are proportional 8. Definition of proportional
9. △ABC ~ △AYX 9. SAS similarity theorem
_____
The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.
Answer:
I think its A. ∠A ≅ ∠A; reflexive property
Step-by-step explanation:
What is the slope of the line that passes through the points (-3,2) and (6, -9)?
Answer:
-11/9 is the slope
Step-by-step explanation:
Use the formula and u will find this is the answer, hope this helped!
Y2 - Y1 / X2 - X1
(-9 - 2) / (6 - (-3))
<!> Brainliest is appreciated!
Answer:
-11/9
Step-by-step explanation:
In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:
[tex]\frac{-9-2}{6-(-3)}[/tex]
The negatives cancel out and become postive, so the denominator will then read to be 6+3:
[tex]\frac{-9-2}{6+3}[/tex]
[tex]-\frac{11}{9}[/tex]
Miss Smith bought 60 notebooks and 72 pencils to make identical packages with some notebooks and some pencils for her students. She used everything she bought, and every student got a package. What is the largest number of packages she can make? How many notebooks and pencils would be in each package?
Answer: 12 packages with 5 notebooks and 6 pencils in each package.
Step-by-step explanation:
The greatest common factor of 60 and 72 is 12. Thus divide both numbers(60 and 72) by 12 to get 5 and 6. Thus, Miss Smith made 12 packages with 5 notebooks and 6 pencils in each package.
Answer:
12 packages with 5 notebooks and 6 pencils in each package.
Step-by-step explanation:
Proofs are used to show that a mathematical statement is true. The most common form of mathematical statements are if-then statements. Give an example of a true mathematical statement and a false mathematical statement in if-then form. For the false statement, include a counterexample showing that the statement isn't true.
Answer:
See explanation
Step-by-step explanation:
True Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{xy}=ab[/tex]
False Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{x+y}=a+b[/tex]
To show using a counterexample that the statement isn't true.
[tex]\text{Let x}=16\\\text{Let y}=9\\\sqrt{16}=4\\\sqrt{9}=3\\\sqrt{16+9}=\sqrt{25}=5\\a+b=3+4=7\\5\neq 7[/tex]
Therefore, the mathematical statement is false.
What is the solution to this equation?
4x + 2(x + 6) = 36
O A. x = 7
B. x = 5
O c. x = 4
D. x = 8
Simplifying
4x + 2(x + 6) = 36
Reorder the terms:
4x + 2(6 + x) = 36
4x + (6 * 2 + x * 2) = 36
4x + (12 + 2x) = 36
Reorder the terms:
12 + 4x + 2x = 36
Combine like terms: 4x + 2x = 6x
12 + 6x = 36
Solving
12 + 6x = 36
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 6x = 36 + -12
Combine like terms: 12 + -12 = 0
0 + 6x = 36 + -12
6x = 36 + -12
Combine like terms: 36 + -12 = 24
6x = 24
Divide each side by '6'.
x = 4
Simplifying
x = 4
Which pair of quantities is LEAST likely to be directly proportional?
1. Hours worked and money earned
2. Distance and time when speed is constant
3. Area and side length of a square
4. Total cost and the number of hats purchased
Answer:
A
Step-by-step explanation:
Hours worked, probably because of commission or bonuses (the other ones seem to be proportional)
please solve and verify your answer 6j+7=21−j2
Answer:
j=1.75
Step-by-step explanation:
6j=21-2j-7
6j=14-2j
6j+2j=14
8j=14
[tex]\frac{8j}{8} = \frac{14}{8}[/tex]
j=1.75
Rewrite 4 − 5 using the additive inverse and display the new expression on a number line. (5 points) 4 + 5 An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 4 − (−5) An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 5 − 4 An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 and ends at 5. Another arrow begins at 5 and ends at 1. 4 + (−5) An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Answer: 4 + (−5)
An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Step-by-step explanation: The arrow from 0 running to 4 is the graph of how the point on the line is a positive 4: Four added to 0
The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5
4 + (-5) = -1 is the additive inverse of 4-5= -1
The descriptions of the number lines are well done, but difficult to sort out.
Answer:
4 + (−5)
Step-by-step explanation:
it is got it correct