The function of the area of the forest in terms of time is A(t) = π(2t + 1)²
How to determine the area function?The given parameters are
Radius function, r(t) = 2t + 1
From the question, we understand that:
The pattern is circular
The area of a circle is
A = πr²
Express as a function
A(r) = πr²
Substitute r(t) = 2t + 1
A(t) = π(2t + 1)²
Hence, the area function in terms of time is A(t) = π(2t + 1)²
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Mr. Michael’s class sold fruit cups for $1.55 each and Mr. Lee’s class sold bottles of sports drink for $1.09 each. Together, the classes sold 97 items and earned $120.45 for their school.
Question 1
Let x represent the number of fruit cups sold and let y represent the number of bottles of sports drinks sold.
Write and solve a system of equations that models the problem.
Enter your answers in the boxes to correctly complete each equation.
Question 1
Let x represent the number of fruit cups sold and let y represent the number of bottles of sports drinks sold.
Write and solve a system of equations that models the problem.
Enter your answers in the boxes to correctly complete each equation.
= 120.45
= 97
Question 2
How much money did Mr. Michael's class earn?
Enter your answer in the box.
$
Question 3
How much money did Mr. Lee's class earn?
Enter your answer in the box.
$
Answer:
Question 1:
x + y = 97
$1.55x + $1.09y = $120.45
Question 2:
32
Question 3:
65
Step-by-step explanation:
phew, way to long to explain why. A brainliest would be nice :)
Translate the sentence into an equation
Nine times the sum of a number and 7 is equal to 5
Use the variable y for the unknown number
Which mapping diagram is not a function?
Mapping diagram (D) is not a function.
What is a function?A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. Four broad categories can be used to classify different types of functions. Dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.So, an option which is not a function:
According to the given image, we can easily point out that option (D) is not a function.As the f(x) has two mirror images g(x) which is not possible, and hence option (D) is not a function.Therefore, mapping diagram (D) is not a function.
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Which graph represents the solution set of the system of inequalities?
The correct graph that represents the solution set of the system of inequalities is in Option(b).
What is Inequality in mathematics?Inequality is a statement of an order relationship (greater than, greater than, or equal to, less than, or less than or equal to) between two integers or algebraic expressions in mathematics.
The given system of inequalities are,
y < -3x - 2
y ≤ x - 2
We have to select the graph that represents the solution set of the system of inequalities.
y < -3x - 2
Let, y = -3x - 2
Now, plot the graph of the line y = -3x - 2 with a Dotted line ( as < is a strict inequality).
y ≤ x - 2
Let, y = x - 2
Now, plot the graph of the line y = x - 2 on the graph.
The area between the two lines of inequalities on the graph represent the solution set.
Upon comparison with the graphs in the options, the correct graph is present in Option(b).
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building a is 881 ft tall and contains 66 stories. building b contains 103 stories. if the two buildings have the same number of feet per floor approximately the height of building b. what is the approximate height of building b?
Answer:
approximately 1,375 feet
Step-by-step explanation:
Set up and solve this proportion:
[tex] \frac{881}{66} = \frac{h}{103} [/tex]
[tex]66h = 90743[/tex]
[tex]h = 1375[/tex]
So the height of building b is about 1,375 feet.
A Sony LCD TV has a selling price of $925 and a 62% markup on selling price. What is the dollar markup and what is the cost?
Answer
Selling price = $ 925
Mark percentage = 62%
[tex]\begin{gathered} \text{Let's x represent Cost price i.e C. P=x} \\ \text{Selling price =C P +profit} \\ Profit\text{ =}\frac{\text{62x}}{100} \\ \\ S\text{. P =x+}\frac{\text{62x}}{100} \\ S\text{. P=x+0.62x} \\ S\mathrm{}P=1.62x \\ \therefore1.62x=925 \\ \end{gathered}[/tex][tex]\begin{gathered} \therefore1.62x=925 \\ \text{Divide both sides by 1.62} \\ \therefore\frac{1.62x}{1.62}=\frac{925}{1.62} \\ \\ x=570.99 \end{gathered}[/tex]The cost price is 570.
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Given expression is (a+b)^8 and we need to find the 5th term of this series.
Explanation -
The general binomial expression is given as
[tex](x+y)^n=^nC_0x^ny^0+^nC_1x^{n-1}y^1+^nC_2x^{n-2}y^2+............upto\text{ x}^0[/tex]So the given expression can be written as
[tex](a+b)^8=^8C_0a^8b^0+^8C_1a^7y^1+^8C_2a^6b^2+^8C_3a^5b^3+^8C_4a^4b^4+...[/tex]So the 5th term will be
[tex]\begin{gathered} 5th\text{ term = }^8C_4a^4b^4 \\ The\text{ general comb}\imaginaryI\text{nat}\imaginaryI\text{on formula }\imaginaryI\text{s = }^nC_r=\frac{n!}{(n-r)!r!} \end{gathered}[/tex]Then we have
[tex]\begin{gathered} 5th\text{ term = }\frac{8!}{(8-4)!4!}a^4b^4 \\ 5th\text{ term = }\frac{8\times7\times6\times5}{4!}a^4b^4 \\ 5th\text{ term = }\frac{8\times7\times6\times5}{4\times3\times2\times1}a^4b^4=2\times7\times5\times a^4b^4=70a^4b^4=70(ab)^4 \end{gathered}[/tex]So the final answer is 70(ab)^4can u pls help me with this question
Answer:
Explanation:
eight of the bush when it was first planted int he garden = 12cm
After 2 weeks, its height = 120% of Height when it was planted.
[tex]=120\%\text{ of 12cm}[/tex]We solve for the result.
[tex]\begin{gathered} =\frac{120}{100}\times12 \\ =1.2\times12 \\ =14.4\operatorname{cm} \end{gathered}[/tex]The bush was 14.4cm tall after two weeks.
Which is greater? -7/10 or -0.66?
Answer:
-7/10
Step-by-step explanation:
First, we obviously need to convert 0.66 into a fraction. Since -7/10 cannot be changed, we need to change AND simplify -0.66.
-0.66 is equal to -66/100, but we can still simplify this. We can divide the numerator and denominator by 2.
66 divided by 2 is 33.
100 divided by 2 is 50.
-33/50 CANNOT be simplified anymore.
So -7/10 _ -33/50. Which is greater?
-7/10 is closer to 0 on the number line. -33/50 isnt.
So -7/10 is the answer.
-7/10 > -0.66
QUESTION 3After surgery a patient was put on a restricted diet. In the first 2 days after surgery the patient was only allowed to consume•800 Cal/day. In the following 3 days the patient was allowed to consume 1100 Cal/day. In the final 4 days at the hospital thepatient was allowed to consume 1500 Cal/day.a) What was the average energy per day consumed? Round answer to the one if necessary.b) What is the unit symbol for the answer?
Given the patient consumption rate on his diet:
[tex]\begin{gathered} 1-2\text{days}=\text{ 800 Cal/day} \\ 2-3\text{days}=1100\text{ Cal/day} \\ 3\text{ -4days=1500 Cal/day} \end{gathered}[/tex](a) Average energy per day consumed will be since the number of days = 4
[tex]\begin{gathered} =\frac{800+1100+1500}{4} \\ =\frac{3400}{4} \\ =850\text{ Cal} \end{gathered}[/tex]The average energy per day consumed = 850 Cal(b) The unit symbol for the answer = calorie
A designer builds a model of a bicycle. The finished model is exactly the same shape as the original, but smaller. The scale factor is 2:7. (a) Find the ratio of the height of the model to the height of the original. (b) Find the ratio of the surface area of the model to the surface area of the original. (c) Find the ratio of the volume of the model to the volume of the original. Write these ratios in the format m:n.
Given
Scale Factor of 2:7
When the scale factor is a:b
Recall the following
[tex]\begin{gathered} \text{The ratio of the sides is} \\ a:b \\ \; \\ \text{The ratio of the area is} \\ a^2:b^2 \\ \; \\ \text{The ratio of the volume is} \\ a^3:b^3 \end{gathered}[/tex]Given that the ratio is is 2:7 then we have the following
[tex]\begin{gathered} \text{The ratio of the height of the model to the height of the original is} \\ 2:7 \\ \; \\ \text{The ratio of the surface area of the model to the surface area of the original is} \\ 2^2:7^2\Longrightarrow4:49 \\ \; \\ \text{The ratio of the volume of the model to the volume of the original is} \\ 2^3:7^3\Longrightarrow8:343 \end{gathered}[/tex][tex]undefined[/tex]
i am needing help with this
Side BC is opposite to angle BAC, in the picture.
Answer: Angle BAC - first option
PLEASE HELP!!! PLEASE HURRY!!!
Answer:
C.
Step-by-step explanation:
as M is right over the middle of LN, this is an isoceles triangle (both legs are equally long).
so, we need to calculate only one leg and then double it fit both legs.
we get e.g. LM via Pythagoras.
LM is the Hypotenuse of the right-angled triangle with half of LN and the height to M being the legs.
so,
LM² = height² + (LN/2)² = 3² + 6² = 9 + 36 = 45
LM = sqrt(45) = 6.708203932... units
the perimeter is the sum of all 3 sides :
LN + LM + MN = LN + 2×LM = 12 + 2×sqrt(45) =
= 25.41640786... units
round 286 to the nearest ten with explanations
Answer:290
Step-by-step explanation:
first look at the ones place it is greater than 4 so round up
286 to the nearest tenth is 290.
What is a place value?Place value, which is related to a digit's location in a number, is the amount that each digit is worth.
Given:
The number is 286.
The digit in tenth place is 6.
And the number 6 is greater than the number 4.
And 6 > 4.
So, the number will round off to the nearest tenth.
6 becomes zero.
And the number left to 6 will increase by 1.
That means 8 + 1 = 9.
So,
286 to the nearest tenth is 290.
Therefore, 290 is the nearest ten of the required number.
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After a 70% reduction, you purchase a new clothes dryer on sale for $204. What was the original price of the
clothes dryer?
Answer:$346.8
Step-by-step explanation:
1. X - 70% = 204
Want to get the value of X
2. X + 70% = 204 + 70%
= X = 204 x 1.7
= X = $346.8
Answer:
Original Price = $680
Step-by-step explanation:
Think about what a 70% reduction in price means.
If the original price of an item is $100 then a 70% reduction would mean that it costs 70% less from the original price. This means you would be paying only 30% of the original price
Let the original price be $P
Then the price you pay after 70% reduction is 30% of P
= P x 30/100
= P x 0.3 (30% = 30/100 = 0.3)
= 0.3P
We are given that this sale price = $204
--> 0.3P = 204
Dividing both sides by 0.3 gives us the value for P
0.3P/0/3 = 204/0.3
P = 204/0.3 = 680
So
Original Price = $680
We can double check our computations as follows
If original price = 680, then a reduction of 70% would be a discount of
0.7 x 680 = 476
Price after discount = Original Price - Discount
= 680 - 476 = 204
So our results are consistent
what is a possible value for the missing term of the geometric sequence? 43____2107
Answer:
150
Step-by-step explanation:
Moving waves can be described either as a function of time or as a function of
a. amplitude.
b. frequency.
c. speed.
d. position.
Moving waves can be described either as a function of time or as a function of position
What is a wave?A wave is a dynamic disturbance of one or more quantities that propagates in physics, mathematics, and related sciences. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.
In a medium, a wave is a disturbance or variation that gradually transfers energy from one point to another. It can be an elastic deformation or a change in pressure, electric or magnetic strength, electric potential, or temperature.
It should be noted that it can be a function of the position as well as the time.
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what is the measure of a
Answer:
Measure of Angle A is 100°
Step-by-step explanation:
The sum of interior angles of a polygon is given by the formula :
(n-2)×180 (where n is the number of sides)
n = 6
(6-2)×180 =
4 × 180 = 720
So :
A + B + C + D + E + F = 720
Substitute values given in diagram (angle d is 90 as the little square indicates a right angle) (Calling angle a as x) :
x + 135 + 115 + 90 + 110 + 170 = 720
Simplify :
x + 620 = 720
Subtract 620 from both sides :
x = 720 - 620
x = 100
Measure of Angle A is 100°
Hope this helped and have a good day
Elena is traveling to visit her grandparents who live 125 miles away.
a. Elena stops for lunch 2/3 of the way. How far has Elena traveled?
b. Elena enters the city where her grandmother lives after 110 miles. Is she more or less than 9/10 of the way there?
PLS PLS PLS HELPP
a . After stopping for lunch Elena has travelled 50 miles.
b . She is less than 9 / 10 to her grand mother's location after travelling for 110 miles.
How to find the number of miles she travelled?She is traveling to visit her grandparents who live 125 miles away.
a.
She stops for lunch 2/3 of the way.
The distance she has travelled after she stopped for lunch can be calculated as follows:
distance in miles = 2 / 5 × 125
distance in miles = 2 × 25
distance in miles = 50 miles
b.
She enters the city where her grandmother lives after 110 miles.
Hence,
9 / 10 × 125 = 1125 / 10 = 112.5 miles
Therefore, she is less than 9 / 10 of her way there.
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The cross section (with units in inches) of a parabolic spotlight can be modeled by the equation x=1/20y^2
How far is the bulb from the vertex of the cross section?
The bulb is 5 inches far from the vertex of the cross section.
What is cross section of a parabola?A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the conic figure.
The standard equation for a parabola is typically expressed as y² = 4ax if the directrix is parallel to the y-axis, and y² = 4ax if the parabola is in the negative quadrants. The conventional equation of a parabola is x² = 4ax if the parabola is sideways, or if the directrix is parallel to the x-axis. If the parabola is in the negative quadrants, the equation is x² = 4ax.
Given, The equation x = 1/20y² can be used to model the cross section of a parabolic spotlight (with units in inches).
We must determine the distance between the bulb and the cross section's vertex.
Equation x = 1/20y² is alternatively denoted by the expression y² = 20x.
Now, comparing the equation to the parabola's conventional form, y²=4ax
So, 4a=20
a=5
Consequently, a=5 represents the distance from the cross section's vertex to the bulb.
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EASY POINTS - CORRECT ANSWER = BRAINLIEST
The animals at a safari park include gorillas, buffalo and wallabies. There are 24 more buffalo than there are gorillas. There are 7 times as many wallabies as there are gorillas. There are the same number of buffalo as there are wallabies. How many gorillas are there at the safari park?
Answer:
Step-by-step explanation:
The first thing you need to do, is find the total amount of gorillas.
to do this, you are going to use the equation:
24 + g = 7g
Both sides are equal, since the wallabies and the buffalo are equal. This makes the equation true.
you subtract g from 7g, and you should get:
24= 6g
Divide by six:
4 = g
That is the # of gorillas.
Now, if you add 24 + 4
You get the # of buffalo.
Which is: 28
Since the buffalo and wallabies are the same, the # of wallabies is also 28.
if you want to check, multiply 4x7 to get the amount of wallabies.
Pls help need asap!thx
Answer:
(0,7]
Step-by-step explanation:
It is an open circle at 0 and a closed circle at 7.
help meeeeee plssss with steps
Answer:
p = 18, q = 0
Step-by-step explanation:
The expression on the left side of the equation is
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}[/tex]
Multiply the denominators to get a common denominator:
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$}[/tex]
= [tex]\left(\sqrt{5}\right)^2-2^2[/tex] ∵ (a + b)(a - b) = a² - b²
[tex]=5-4\\\\= 1[/tex]
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}\\\\[/tex]
[tex]=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}+2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)} + \dfrac{\left(\sqrt{5} - 2\right)\left(\sqrt{5} - 2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}[/tex]
Since denominator
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$} = 1,[/tex]
the expression becomes
[tex]=\left(\sqrt{5}+2\right)^2 + \left(\sqrt{5}-2\right)^2\\\\= 5 + 4\sqrt{5} + 4 + 5 - 4\sqrt{5} + 4\\\\[/tex]
[tex]= 10 + 8 = 18[/tex]
Therefore
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} = p + q\sqrt{5}$}\\\\\\= > \large \text{$ 18 = p + q\sqrt{5}$}[/tex]
Now [tex]\sqrt{5}[/tex] is an irrational number and p = rational so since there is no [tex]\sqrt{5}[/tex] term on the left side, q = 0 and p = 18
write an expression that can be used to find the value of x in the diagram below
since the angles are opposite by the vertex, we have that the expression to find the value of x is:
[tex]4x-1=55[/tex]and if we solve it, we obtain:
[tex]4x=54[/tex][tex]x=13.5[/tex]Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
3 answers for this problem.
CORRECT ANSWERS ONLY
If the second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. The number of phone calls did she receive each evening is: 30, 80, 20.
Number of phones receivedLet x , y, z represents the 1st , 2nd, and 3rd evenings respectively
X + Y + Z = 130
Y = 4Z
X = z+10
Substituting the second and third equations into the first:
z+10 + 4z + z = 130
Combine like terms
6z + 10 = 130
Subtract 10 from both sides
6z +10 -10 = 130 -10
6z =130 -10
6z =120
Divide both side by 6z
z = 120/6
z = 20
Solving for y
y = 4z
y = 4×20
y = 80
Solving for x
x = z+10
x = 20 +10
x = 30
Check:
x + y + z =130
30 +80 + 20 =130
Therefore they each received 30 phones, 80 phones and 20 phones.
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Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.
The surface area and volume of the solid are 104 in² and 60 in³
How to determine the volumeIt is important to note that the figure takes the shape of a cuboid.
The formula for determining the surface area of a cuboid is expressed as;
SA = 2lw + 2lh + 2hw
Where;
SA is the surface areal is the length of the cuboidw is the width of the cuboidh is the height of the cuboidNow, let's substitute the values into the formula, we have;
Surface area = 2(5× 2) + 2(5 ×6) + 2(6 × 2)
expand the bracket
Surface area = 2(10) + 2(30) +2 (12)
Surface area = 104 in²
The formula for volume is given as;
Volume = l × w × h
Volume = 5 × 2 × 6
Volume = 60 in³
Thus, the values are 104 in² and 60 in³
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a department store buys 300 shirts at a cost of 3600 and sells them at a selling price of $20 each find the percent markup
We have the following:
To find the percent markup, we must calculate the profits, knowing that there are 300 shirts and they sell them for a total of $ 20
[tex]300\cdot20=6000[/tex]Now we subtract from what was initially spent and then divide by that same amount and multiplying by 100 we will know the percent markup
[tex]\frac{6000-3600}{3600}\cdot100=66.67\cong67[/tex]Which means that the percent markup is 67%
A person from Switzerland consumes about 9.1 kilograms of chocolate per
year. A person from the United States consumes about 4.7 kilograms of
chocolate per year. How many times as much chocolate will a Swiss
person consume in one year than someone from the United States? Round
your final answer to the nearest tenths
Answer:
switzerland was the leading country in chocolate consumption per capita in 2017, with citizens eating nearly nine kilos of the sweet stuff in that year. World renowned for the chocolate they produce, it seems the Swiss themselves can’t get enough of the candy. Germany, the country’s neighbor, is equally addicted, importing the largest share of Swiss chocolate of all countries in the world.
Step-by-step explanation:
Answer: a swede would consume 1.9 times as much chocolate as an American.
Step-by-step explanation: 9.1 / 4.7 = 1.93617021. round to the nearest tenth = 1.9.
1.93617021 times 4.7 equals 9.1
Help me with this question within 1-5 minutes please
Answer:
[tex]-12w + x[/tex]
Step-by-step explanation:
question:
[tex]-3w - 3x - 7w + 4x - 2w[/tex]
first you add all the 'w' together.
(-3)+(-7)+(-2) = -10+(-2)=-12
so, [tex]-12w - 3x + 4x[/tex]
second you add all the 'x' together
(-3)+(4) = 1
so, [tex]-12w+1x[/tex]
then simplify:
[tex]-12w + x[/tex] <--answer
hope this helps!
I need answer on this graphing va substitution.Problem 7 I tried to solve it but not sure that’s correct
Given the system of equations:
[tex]\begin{gathered} 2x+9y=27 \\ x-3y=-24 \end{gathered}[/tex]To solve it by substitution, follow the steps below.
Step 1: Solve one linear equation for x in terms of y.
Let's choose the second equation. To solve it for x, add 3y to each side of the equations.
[tex]\begin{gathered} x-3y=-24 \\ x-3y+3y=-24+3y \\ x=-24+3y \end{gathered}[/tex]Step 2: Substitute the expression found for x in the first equation.
[tex]\begin{gathered} 2x+9y=27 \\ 2\cdot(-24+3y)+9y=27 \\ -48+6y+9y=27 \\ -48+15y=27 \end{gathered}[/tex]Step 3: Isolate y in the equation found in step 2.
To do it, first, add 48 to both sides.
[tex]\begin{gathered} -48+15y=27 \\ -48+15y+48=27+48 \\ 15y=75 \end{gathered}[/tex]Then, divide both sides by 15.
[tex]\begin{gathered} \frac{15y}{15}=\frac{75}{15} \\ y=5 \end{gathered}[/tex]Step 4: Substitute y by 5 in the relation found in step 1 to find x.
[tex]\begin{gathered} x=-24+3y \\ x=-24+3\cdot5 \\ x=-24+15 \\ x=-9 \end{gathered}[/tex]Answer:
x = -9
y = 5
or (-9, 5)
Also, you can graph the lines by choosing two points from each equation, according to the picture below.