The equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
What is defined as the even integers?An even integer is one that is divisible by two, i.e. a multiple of two.For eg:- 2,4,6,... and −2,−4,−6,.... are divided by twoAs a result, the integers 2,4,6,... and −2,−4,−6,.... are all even integersThus, the integer of a form 2k is a even integer, in which k is an integer.For the given data in question.
Let the first even integer be 'x'.
Second even integer will be 'x + 2'.
Thirst even integer will be 'x + 4'.
The sum is 72
x + x + 2 + x + 4 = 72
Simplifying;
3x + 6 = 72
Divide whole equation by 3.
x + 2 = 24
Thus, the equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
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There are 9 athletes at a track meet. How many different ways can they finish first'orsecond?
For the first place, we have 9 different options from the athletes, then for the second place, we would only have 8 different options, therefore, there are 9x8=72 ways they can finish first or second
Challenge: The price of Stock A at 9 A.M. was $14.76. Since then, the price has been increasing at the rate of $0.09 each hour. At noon the price of Stock B was $15.26. It begins to decrease at the rate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
In one hour, the prices of the two stocks will be the same.
The price of stock A at 9 a.m. was $14.76.The rate of increase in the price of stock A per hour is $0.09.The price of stock B at 12 p.m. was $15.26.The rate of decrease in the price of stock B per hour is $0.14.Let the number of hours after which the prices of the two stocks become the same be "x".We also need to consider that the price of stock A is given at 9 a.m., whereas the price of stock B is given at 12 p.m.14.76 + (3+x)*0.09 = 15.26 - (x)*0.1414.76 + 0.27 + 0.09x = 15.26 - 0.14x0.23x = 0.23x = 1Thus, the number of hours after which the prices of the two stocks become the same is one hour.To learn more about rate, visit :
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Which is the equation of a circle that is centered at the origin?O (– 1)2 + (y – 1)2 = 4O2? + (y - 1)2 = 2O 2 + y2 = 7Ox+y=8
Standard equation of circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex][tex]\begin{gathered} \text{If centered at the origin:} \\ (h,\text{ k) = (0, 0)} \\ h\text{ = 0, k = 0} \end{gathered}[/tex][tex]\begin{gathered} \text{The equation of circle becomes:} \\ (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}[/tex]comparing the above equation with the options given:
[tex]\begin{gathered} x^2+y^2=7\text{ has the form} \\ x^2+y^2=r^2,wherer^2\text{= }7 \end{gathered}[/tex][tex]x^2+y^2\text{ = 7 (option C)}[/tex]Can you find the area of a square using the given side lengths:
Answer
• d) 0.01 m²
,• e) 12.25cm²
Explanation
The area of a square (A) is given by:
[tex]A=s^2[/tex]where s represents the side length.
• d) ,s = 0.1 ,m
Replacing the data we get:
[tex]A=(0.1)^2[/tex]Simplifying:
[tex]A=0.01m^2[/tex]• e) ,s = 3.5cm
Replacing the data we get:
[tex]A=(3.5)^2=12.25cm^2[/tex]A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches. Which equation models this? A. 2w + 3 = 96 B. w + 2m + 3 = 96 C. 2(w) + 2(w + 3) = 96 D. 2(w) + 2(2w + 3) = 96
ANSWER
EXPLANATION
Let the length of the rectangle be L.
Let the width of the rectangle be w.
The length of the rectangle is 3 more than twice the width.
This means that:
L = 3 + (2 * w)
L = 2w + 3
The perimeter of a rectangle is given as:
P = 2w + 2L
The perimeter of the rectangle is 96 inches. This means that:
96 = 2L + 2w
Recall that: L = 2w + 3
=> 96 = 2(w) + 2(2w + 3)
=> 2(w) + 2(2w + 3) = 96
Museum entrance tickets cost $25. Then each special exhibit a person wishes to visit costs an additional $4. Write an expression that represents the cost to enter the museum and visit any number of special exhibits. Then find the cost for a person to enter and visit three exhibits.
ANSWER
T = 4x + 25;
T = $37
EXPLANATION
Let the number of special exhibits to be visited be x.
The cost of the musuem entrance ticket is $25 and each special exhibit costs an additional $4.
This means that the cost of cisiting x additional exhibits is:
4 * x = $4x
Therefore, the total cost to enter the musuem and visit any number of special exhibits is:
T = 4x + 25
That is the expression that represents the total cost.
If a person wants to visit three exhibits, it means that:
x = 3
Therefore, the total cost, T, is:
T = 4(3) + 25
T = 12 + 25
T = $37
That is the total cost to enter and visit three exhibits.
PLEASE HURRY
What is an equivalent expression for −12(8a − 7b) + 8(4x + 3y)?
Answer:
-96a + 84b + 32x + 24y
Step-by-step explanation:
if you simplify an answer then it is equivilent to the beggining equation
hope this helped:)
hwlp
The length of a rectangle is 6 feet more than twice the width. If the perimeter is 132 feet, find the dimensions.
Find the area of the circle pictured above. Round your answer to the nearest tenth in^2
Area of the circle is 28.3 in^2
Here, we want to find the area of the circle
Mathematically, the area is;
[tex]\begin{gathered} \text{Area of circle = }\pi\text{ }\times r^2 \\ But\text{ r = }\frac{d}{2} \\ \\ Area\text{ of circle = }\frac{\pi\text{ }\times d^2}{4} \\ \\ from\text{ the question, d = 6 inches} \\ \pi\text{ = }\frac{22}{7} \\ \\ \\ \text{Area of circle = }\frac{\frac{22}{7\text{ }}\text{ }\times6^2}{4} \\ \\ \text{Area of circle = }\frac{22\text{ }\times\text{ 36}}{28} \\ \\ \text{Area of circle = 28.2857} \\ \\ \text{Area of circle = 28.3 in\textasciicircum{}2} \end{gathered}[/tex]Metric area unit conversion with decimal valuesA rectangular field is 0.35 kilometers long and 0.2 kilometerswide. What is the area of the field in square meters? Do notround your answer.mX 5 ?Conversion facts for length1000 millimeters (mm) = 1 meter (m)100 centimeters (cm) = 1 meter (m)10 decimeters (dm) = 1 meter (m)1 decameter (dam) = 10 meters (m)1 hectometer (hm) = 100 meters (m)1 kilometer (km) = 1000 meters (m) I need help with this math problem.
Given that
The length of the rectangular field is 0.35 km and the width is 0.2 km. And we have to find the area of this field.
Explanation -
The formula for the area of the rectangle is
[tex]Area=length\times breadth[/tex]On substituting the values we have
[tex]\begin{gathered} Area=0.35\times0.2\text{ km}^2 \\ Area=0.07\text{ km}^2 \end{gathered}[/tex]Since the conversions are given as
[tex]\begin{gathered} 1\text{ km = 1000 m}^{\text{ }}=10^3\text{ m} \\ 1\text{ km}^2=10^6\text{ m} \end{gathered}[/tex]So the required answer in sq meters will be
[tex]\begin{gathered} Area=0.07\times10^6\text{ m}^2 \\ Area=7\times10^4\text{ m}^2=70000\text{ m}^2 \end{gathered}[/tex]So the final answer is 70000 sq meters.The next model of a sports car will cost 13.8% more than the current model. The current model costs $56,000. How much will the price increase in dollars? What will be the price of the next model?
Current model is $56,000
New model is 13.8% more expensive
13.8% of 56,000 = 56000*13.8/100 = 772800/100 = 7728
Nex model price = 56000+7728 = 63728
Answers:
The price increase in dollars is $7,728
The price of the next model is $63,728
351,528.094 in word form
Three hundred fifty-one thousand five hundred twenty-seven and ninety-four thousandths
Latoya opened a savings account and made an intial deposit. After the intial deposit, she added money into the account each week she added the same amount each week with out any withdrawals after the forth week she had $450 by the ninth week she had $825 what was latoya's intial deposit?
She made an initial deposit that we will call "D", as it is one of the unknowns.
We know that she made a weekly deposit (lets call this amount "w").
After 4 weeks she had $450 in the account balance and this is the sum of the initial deposit and 4 weekly deposits, so we can write:
[tex]D+4w=450[/tex]At the ninth week she had $825, that correspond to the initial deposit and 9 weekly deposits. This can be written as:
[tex]D+9w=825[/tex]We have a system of linear equations that we will solve by elimination: we will substract the first equation from the second and then find w.
[tex]\begin{gathered} (D+9w)-(D+4w)=825-450 \\ 5w=375 \\ w=\frac{375}{5} \\ w=75 \end{gathered}[/tex]Now that we know "w", we can calculate D with any of the two equations:
[tex]\begin{gathered} D+4w=450 \\ D+4\cdot75=450 \\ D+300=450 \\ D=450-300 \\ D=150 \end{gathered}[/tex]Answer: the initial deposit was $150.
In the figure below, circle 1 is a unit circle. Circle 2 has a diameter that is one and half times longer than that of circle 1, and circle 3 has a diameter that is twice as long as that of circle 1. If angle Z is equal to 2 radians, what is the length of the arc between points I and J?
The length of an arc is given by:
[tex]s=r\timesθ[/tex]where r is the radius and θ is the measure of the angle in radians.
To find the radius:
radius in circle 1 = 1 (unit circle)
radius in circle 3 = 2 x 1 = 2.
Hence:
[tex]s=2\times2=4[/tex]ANSWER
the length of the arc between points I and J is 4
Find the probability.When a single card is drawn from an ordinary 52-card deck, find the probability of getting a heart.A) 1/13B) 1/4C) 1/26D) 1/52
The probability of getting a red 7 would be; 1/26
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given that the total number of cards is 52.
WE are asked to find the he probability of getting a red 7
Since there are 2 red 7 cards in the deck of cards.
So, the number of favourable outcomes would be 2.
n (E) = 2
The probability
P(E) = n (E) /n (S)
Therefore, the probability of getting a red 7 will be;
P(E) = n (E) /n (S)
P(E) = 2/52
P(E) = 1/26
Hence, The probability of getting a red 7 would be; 1/26
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The formula used to convert degrees Celsius to degrees Fahrenheit is
F = C +32.
Convert 77°F to degrees Celsius. Solve the formula for C, and then use it to
convert the temperature.
Which is the correct formula and conversion?
77°F is equivalent to 45°C as per the given equation.
The correct formula for conversion is,°F = (°C × 9/5) + 32, and 77°F is equivalent to 25°C
This is a problem with the temperature conversion. We can solve this problem by following a few steps.
F = C +32 as per the question and the temperature is given as 77°. We have to convert this temperature to degrees Celsius. We can write C as (F-32).
Hence the formula for C can be written as C = F - 32
Now we can find convert the temperature,
C = F - 32
Or, C = 77 - 32 [ subtracting 32 from both sides ]
Or, C = 45
Here we can conclude that 77°F is equivalent to 45°C as per the question.
The correct formula for conversion is,
°F = (°C × 9/5) + 32
Or, 77 = (C × 9/5) + 32
Or, (C × 9/5) = 77 - 32 [ subtracting 32 from both sides ]
Or, (C × 9/5) = 45 [ multiplying both side with 5/9 ]
Or, C = (45×5) / 9 = 25
According to the correct conversion equation, 77°F is equivalent to 25°C
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if tommy has 34 has apples and she puts them in 3 baskets whats the anwser and with the reminder if it has one
If a number is added to the number of 5/6 and twice as much is added to the denominator, the result is 3/5, find the number
Answer:
[tex]x=7[/tex]Step-by-step explanation:
We have the number:
[tex]\frac{5}{6}[/tex]If a number is added to the numerator and twice as much is added to the denominator and the result is 3/5, we can create the following equation:
[tex]\frac{5+x}{6+2x}=\frac{3}{5}[/tex]Solve for x, using cross multiplication:
[tex]\begin{gathered} 5(5+x)=3(6+2x) \\ 25+5x=18+6x \\ -x=-7 \\ x=7 \end{gathered}[/tex]What is the rest of the pattern.
3, 6, 10, 15, _, _, _.
Answer:
3, 6, 10, 15, 21, 28, 36.
Step-by-step explanation:
3 (+3),
6 (+4),
10 (+5),
15 (+6),
21 (+7),
28 (+8),
36
Answer:
If my theory is right the next 3 numbers are 21,28,36
Step-by-step explanation:
Looking at the beginning you see that 3 goes to 6 which is a hop of 3
Then next is 6 to 10 which is a hop of 4
Then next is 10 to 15 which is a hop of 5
So I think it’s going in a chronological number order
So I say the next hops will be 6,7,8
solve for g: g - 0.6 < 3.172. ,part c: in one paragraph explain ur work in parts a and b
Explanation
[tex]g-0.6\leq3.172[/tex]
Step 1
To solve the inequality means to find a range, or ranges, of values that an unknown g can take and still satisfy the inequality.
so
[tex]\begin{gathered} g-0.6\leq3.172 \\ \text{add 0.6 in both sides} \\ g-0.6+0.6\leq3.172+0.6 \\ g\leq3.772 \end{gathered}[/tex]it means the solution is the set of values equal or smaller than 3.772,so
Part A:
[tex]g\leq3.772[/tex]Step 2
Part B:the graph of the inequality looks like a marked line in the number line, from3.772 to negative infinite, as the symbol is smaller or equal, the number3.772 is part of the set , so we use a filled circle
Step 3
in step 1 we used the addition property of inequality to isolate x, then in step 2 we draw the set solution .
I hope this helps you
The circumference of a circle is 67 inches. What is the area in
terms of π ?
The surface area of a cube is 42 in2. What is the volume of the cube?
Answer:
7√7 in or 18.52 in=======================
Let the side of the cube be a.
Then its surface area is:
S = 6a²Find the side of the cube:
42 = 6a²a² = 7a = √7Find the volume of the cube:
V = a³ = (√7)³ = 7√7 ≈ 18.52 inWrite the equation for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).
Given the figure of the functions f(x) and g(x)
The graph of the function is the shown lines
The equation of f(x):
As shown the line of f(x) passes through the points: (-2, 0) and (0, -1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{0-(-2)}=\frac{-1}{2}[/tex]The y-intercept = -1
so, the equation of f(x) =
[tex]f(x)=-\frac{1}{2}x-1[/tex]The equation of g(x):
As shown the line of g(x) passes through the points: (-2, 0) and (0, 1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-(-2)}=\frac{1}{2}[/tex]The y-intercept = 1
So, the equation of g(x) will be:
[tex]g(x)=\frac{1}{2}x+1[/tex]Identify the reflection that transforms the graph of f(x) to the graph of g(x).
As shown, the functions are symmetric around the x-axis
And as we can see for the same value of x: g(x) = -f(x)
So, the type of transformation is: Reflection over the x-axis
The ratio of boys to girls in Janice's classroom is 3:5, and there are a total of 32 students in the class. Using completesentences, explain how you could draw a tape diagram to represent this situation. In your answer, draw a diagramand make sure to include what quantity each bar represents.
Teh ratio of boys to girls in JAnice's classroom is 3:5
Total number of students 32
Let the ratio constant is K
So,
The equation will be
3K + 5K=32
8K=32
K=32/8
K=4
So,
the boys will be
4 + 4 + 4 =3K =12
The number of girls will be :
4 + 4 + 4 + 4 + 4 = 5K =20
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
The given function for the sales of [tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex], gives the tax rate that maximizes government revenue as t = 343/512
What is a government tax rate?The tax rate is the percentage of an amount that is paid to the government as tax.
The given function is presented as follows;
[tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex]
Where;
t = The tax rate on imported shoes
S = The total sales
Taking the total sales as contributing to the government revenue, R(t), we have;
Revenue = R(t)
Which gives;
[tex]R(t) = t \times (7 - 6 \cdot {t}^{ \frac{1}{3} }) [/tex]
At the maximum total sales, we have;
[tex] \frac{dR(t)}{dt} = \frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 0 [/tex]
[tex]\frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 7- 8 \cdot \sqrt[3]{t} = 0[/tex]
Which gives;
At maximum revenue, t = (7/8)³
t ≈ 0.669921875
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Which of the following ordered pairs represent a direct variation. Find the missing value. 1. (32, 80) and (x, 100) x = _____ 2. (-28,-7) and (20, y) y = _____
When having an ordered pair, we say they are in direct variation if the quotient:
[tex]\frac{y}{x}[/tex]is constant. For case 1 we have:
[tex]\frac{80}{32}=\frac{100}{x}[/tex]we can solve for "x" by multiplying by "x" on both sides:
[tex]\frac{x80}{32}=100[/tex]Now we multiply by 32/80 on both sides:
[tex]x=\frac{100\times32}{80}[/tex]Solving the operations we get:
[tex]x=40[/tex]For case 2 we have:
[tex]-\frac{7}{-28}=\frac{y}{20}[/tex]Now we solve for "y" by multiplying by 20 on both sides:
[tex]\frac{-7\times20}{-28}=y[/tex]Solving the operations:
[tex]y=5[/tex]LOOK AT THE PICTURE BELOW. Find an approximation for [tex] \sqrt{18} [/tex]
ANSWER:
[tex]\sqrt[]{18}=4.25[/tex]STEP-BY-STEP EXPLANATION:
We have to calculate the square root of 18, to locate it on the graph, like this:
[tex]\sqrt[]{18}=4.2426\cong4.25[/tex]Use the graph to answer the following questions.how much does the cost of cheese and crease for each ounce Milan buys? What is the slope of the line?
The graph given is a linear graph,
so that means that the cost of cheese is linearly related to the weight of cheese bought.
The increase in the cost of cheese increase for each ounce Milan buys is, therefore, the slope of the graph;
to find the slope of the graph, we use any two points on the line; i'll be using (4,96) and (2,48)
[tex]\text{slope}=\frac{96-48}{4-2}=\frac{48}{2}=24[/tex]This means that the cost of cheese increases by 24 cents for each ounce Milan buys.
Y varies inversely with the square of x. When x=4, then y=3. Find y when x=2
Answer:
y = 6
Step-by-step explanation:
y= [tex]\frac{1}{x}[/tex]
3 = [tex]\frac{1}{4}[/tex]k Solve for k by multiplying both sides by 4
12 = k
y = [tex]\frac{1}{2}[/tex](12)
y = [tex]\frac{12}{2}[/tex]
y= 6
1-9.b.C.GROWING, GROWING, GROWING, PART ONECopy the tile pattern shown below onto graph paper.Figure 2Figure 3Figure 4Draw the 1st, 5th, and 6th figures on your paper.How is the pattern changing?What would the 100th figure look like? How many tiles would it have?How can you justify your prediction?
Answer:
Explanation:
a) To draw the 1st , 5th and 6th figures, we need to know the count of squares
For the first figure, we would have 3 squares
The fifth figure would have 35 squares
The sixth figure will have 48 squares
The way to get this is to add 2 to the odd number difference between the last two terms
b) Here, we want to know how the pattern is changing
From the information provided, the first pattern has 8 squares, the second has
15 squares while the last has 24 squares
We can have a formula as follows:
[tex][/tex]