The circumference of a circle is found using the formula,
[tex]C=2\pi r[/tex]Where
C is the circumference
r is the radius
A circle has radius 12 cm, so its circumference is
[tex]\begin{gathered} C_1=2\pi r \\ C_1=2\pi(12) \\ C_1=24\pi \end{gathered}[/tex]When the radius (12 cm) is increased by a factor of 7, we mean the radius is 7 times the original, so, the new radius is
[tex]7\times12=84[/tex]So, the circumference of this circle will be >>>>
[tex]\begin{gathered} C_2=2\pi r \\ C_2=2\pi(84) \\ C_2=168\pi \end{gathered}[/tex]To find how many times larger this circumference is of the previous one, we divide,
[tex]\frac{C_2}{C_1}=\frac{168\pi}{24\pi}=7_{}[/tex]Answer7(b)Using the circumference formula, we can find the circumference of this circle,
[tex]\begin{gathered} C=2\pi r \\ C=2\pi(3) \\ C=6\pi \end{gathered}[/tex]The original circle had a circumference of 24π
The question basically asks "how many times is the circumference of this circle compared to the circumference of the original circle?"
Of couse, it will be less than 1 since this circle is smaller than the original one.
So,
[tex]\begin{gathered} \frac{6\pi}{24\pi} \\ =\frac{1}{4} \end{gathered}[/tex]So, the scale factor is 1/4, or 0.25
Answer0.25What is the measure of the base of the rectangle if the area of the triangle is 28 ft?
Answer:
14 ft
Step-by-step explanation:
The base of the rectangle and triangle is same.
Triangle area formula:
A = bh/2GivenA = 28 ft²,h = 4 ft.Find bSubstitute the values:
28 = 4b/228 = 2bb = 28/2b = 14 ftAnswer is 14 ft.
Explanation.Triangle Area Use Formula.
A = bh/2A = 28 ft2
H = 4 ft
B Value.
28 = 4b/2
28 = (4/2)b
28 = 2b
b = 28/2
b = 14
_____________________
Class: Middle School
Lesson: Triangle
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
What is the unit rate per bottle if a pack of 25 bottles of juice sells for $5
Answer:
Each bottle cost $0.20. That is the unit rate
Step-by-step explanation:
[tex]\frac{5.00}{25}[/tex]
Divide. Round your answer to the nearest tenth.
160 divided by 0.749 =
. La cuarta parte de un número, disminuida en 17,
es igual a 4. Calcula la mitad de dicho número.
Resolviendo una ecuación lineal veremos que el número es 76, y la mitad de ese número es 38.
¿Como calcular la mitad del número?Definamos la variable "x" como el número de la ecuación.
Tenemos la oración matematica:
"La cuarta parte de un número, disminuida en 17, es igual a 4"
Esto se puede escribir como la ecuacion:
(1/4)*x - 17 = 4
Esto es una ecuación lineal que puede ser resuelta para x.
(1/4)*x - 17 = 4
(1/4)*x = 4 + 17 = 19
x = 4*19 = 76
Entonces la mitad del número es:
x/2 = 76/2 = 38
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how do you know that the slope of every horizontal line is zero
Let:
[tex]\begin{gathered} P1=(x1,y1) \\ P2=(x2,y2) \end{gathered}[/tex]If the line is horizontal, then:
[tex]y1=y2[/tex]The slope is given by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ since\colon \\ y1=y2 \\ m=\frac{y1-y1}{x2-x1}=\frac{0}{x2-x1} \end{gathered}[/tex]Zero over any quantity is always zero, so:
[tex]m=\frac{0}{x2-x1}=0[/tex]What is 2/3−3 5/6
Help please.
Answer:
Step-by-step explanation:
First you want to make the denominator the first multiple of both numbers so: 2/3 -3 5/6 = 2/6 - 3 5/6
Next you want to multiply the numerator by the amount of times you had to multiply the denominator so: 4/6 - 3 5/6
Then subtract the answer: 3 1/6
2. The area of the base of the cone is 64π cm2 and the altitude is 6 cm. Calculate the cone: (a) the length of the constituent;(b) the area of the lateral area of the cone; c) the volume.
Answer: We have to calculate the (i) volume and (ii) the surface area of the cone:
[tex]\begin{gathered} A=\pi r^2+\pi rl\rightarrow(1) \\ \\ V=\pi r^2\frac{h}{3}\rightarrow(2) \end{gathered}[/tex]The formula (1) is for the lateral surface of the cone and the formula (2) is for the volume of the cone, the unknowns are determined as follows:
[tex]\begin{gathered} r=\sqrt{\frac{64\pi}{\pi}}=8cm \\ \\ r=8cm \\ \\ l=\sqrt{r^2+h^2}=\sqrt{(8cm)^2+(6cm)^2} \\ \\ l=\sqrt{100}=10 \\ \\ l=10 \end{gathered}[/tex]Therefore the volume and the lateral surface area is calculated as follows:
[tex]\begin{gathered} \begin{equation*} A=\pi r^2+\pi rl \end{equation*} \\ \\ A=\pi(8)^2+\pi(8)(10) \\ \\ A=144\pi cm^2\Rightarrow(x) \\ \\ \begin{equation*} V=\pi r^2\frac{h}{3} \end{equation*} \\ \\ V=\pi(8cm)^2\frac{6cm}{3} \\ \\ V=128\pi cm^3\Rightarrow(y) \end{gathered}[/tex]Therefore x and y are the answers.
in the figure below m
The value of x is 15
Here, we want to get value of x
From the question, we have that AC = AD
This means that what we have is an isosceles triangle
Mathematically, the bases of an isosceles triangle have same angle
For triangle ACD; the measure of angle D and the measure of angle C is same
That means the value of x is 15 too
Hello, I need help with this precalculus homework question, please?HW Q9
Solution
- The question would like us to determine the difference expression that corresponds to the following logarithm
[tex]\log_a(\frac{M}{N})[/tex]- In order to solve this question, we should apply the Law of Logarithm which states that:
[tex]\log A-\log B=\log(\frac{A}{B})[/tex]- Applying this law, we have:
[tex]\begin{gathered} \text{ Let A from the formula be M and Let B from the formula be N from the question} \\ Note\text{ that }a\text{ in the question is represented by 10 from the formula. The base 10 in logarithm is usually not } \\ \text{ indicated} \\ \\ \log_a(\frac{M}{N})=\log_aM-\log_aN \end{gathered}[/tex]Final Answer
The answer to the question is
[tex]\operatorname{\log}_{a}(\frac{M}{N})=\operatorname{\log}_{a}M-\operatorname{\log}_{a}N[/tex]If the length is 100 yards and the width is 55 yards, how many yards is the perimeter?
Answer:
perimeter = 310 yards
Step-by-step explanation:
If the length is 100 yards and the width is 55 yards, how many yards is the perimeter?
p = 2l + 2w
perimeter = 2(100) + 2(55)
perimeter = 200 + 110
perimeter = 310 yards
f(x) = x2What is f(x) + f(x) + f(x)?DONE
If we have the function
[tex]f(x)=x^2[/tex]Then
[tex]\begin{gathered} f(x)+f(x)+f(x)=x^2+x^2+x^2 \\ =3x^2 \end{gathered}[/tex]This also can be written in the form
[tex]f(x)+f(x)+f(x)=3f(x)=3x^2[/tex]We see that both answer are the same, like it should be.
PLEASE HELP!!!
In ΔJKL, m∠J = 78° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
168°
102°
57°
12°
The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168° so option (A) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠J + m∠L + m∠K = 180°
m∠K = 180° - 78° - 90°
m∠K = 12°.
The exterior angle of k = 180- 12 = 168°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168°".
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Find the slope of each line.
Given any line, to find the slope of the line, follow the procedure below:
First, pick any two points (x1,y1) and (x2,y2) on the line.
Then, substitute the points into the formula for slope below:
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]You can use this method to find the slope of any given line.
Carolyn leases a new Hyundai Elantra by paying $2400 up front and $167 a month over three years. The lease also stipulates he will be charged $0.12 per mile forevery mile over 36,000. If she puts 39,087 miles on the car, what will be the total cost of the lease?Round your answer to the nearest cent hundredth) but do not include a Sin your response
we have that
3 years=3(12)=36 months
so
$2,400+$167(36)=$8,412
and
39,087-36,000=3,087 miles
so
$0.12*(3,087)=$370.44
therefore
The total cost is
$8,412+$370.44=$8,782.44
the answer is $8,782.44The perimeter of the triangle and the perimeter of the square are equal. Create and solve an equation to find the value of x.
Answer: 16
Step-by-step explanation:
The perimeter of the triangle is [tex]2x+2x+x-8=5x-8[/tex].
The perimeter of the square is [tex]4(x+2)=4x+8[/tex].
Setting the perimeters equal to each other,
[tex]5x-8=4x+8\\\\x-8=8\\\\x=16[/tex]
Jonah picked 287 cherry tomatoes from his garden in May and 339 in June.
How many cherry tomatoes did Jonah pick in all?
The estimate by rounding to the nearest hundred. Then solve.
Answer:
600
Step-by-step explanation:
the total is 626 but round it to the nearest hundred is 600 because the rule 5 or more go up one more 4 or less stay at rest
Write the set in set-builder notation.
1) The set of all calculus books
The set-builder form is { x | x is a calculus book}.
A set is a collection of quantities based on a specific criteria. A set can be expressed in two forms.
We usually use the form {a, b, c,....} in which we include each element of the set separated with a comma in between. This form of set notation is called the roster form.
Another set notation is the set-builder form. This form is more concise and precise and easily understandable also. In this form, all the elements are included in the set which has a same property. That is, here we don't write each and every element separately in the set but just emphasize the property of the elements which are included in the set.
We are asked to write the set of all calculus books in set-builder form.
The set-builder form for 'The set of all calculus books' is { x | x is a calculus book}.
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Please help??????????
Answer:
Equation: 2x +2x +x -8= 4(x +2)
x= 16
Step-by-step explanation:
The perimeter is the total length of the sides of a particular shape or figure.
Given that the triangle and square have an equal perimeter,
Perimeter of triangle= perimeter of square
Since a square has 4 equal sides,
2x +2x +x -8= 4(x +2)
Let's solve the above equation.
Simplify and expand:
5x -8= 4x +8
Move x terms to the left of the equation, constants to the right.
5x -4x= 8 +8
x= 16
Thus, the value of x is 16.
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Answer:
x = 16
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
As the sides of a square are equal in length, the perimeter of a square is four times the length of one side.
[tex]\begin{aligned}\implies \textsf{Perimeter of the square}&=4(x+2)\\& = 4x+8\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Perimeter of the triangle}&=2x+2x+(x-8)\\&=4x+x-8\\&=5x-8\end{aligned}[/tex]
If the perimeter of the triangle and the perimeter of the square are equal then:
[tex]\begin{aligned}\implies\textsf{Perimeter of the triangle}&=\textsf{Perimeter of the square}\\5x-8&=4x+8\\5x-8-4x&=4x+8-4x\\x-8&=8\\x-8+8&=8+8\\x&=16\end{aligned}[/tex]
Therefore, the value of x is 16.
The function C(x) = 150 + 3.3x models the cost for a company to produce x units of a product. The function R(x) = 15x models the revenue the company earns if they sell x units of the product. Which function, P(x), models the profit the company earns if they sell x units of the product? (Profit = Revenue - Cost) O P(x) = 18.3x - 150 O P(x) = 11.7x - 150 OPlx) = 150 - 11.7x O P(x) = 18.3x + 150
Answer: We need to find the expression p(x) for profit.
[tex]\begin{gathered} \text{profit = revenue -cost} \\ \therefore\rightarrow \\ P(x)=R(x)-C(x) \\ P(x)=15x-(150+3.3x)=15x-150-3.3x=18.3x-150 \\ \therefore\rightarrow \\ P\mleft(x\mright)=18.3x-150 \\ \end{gathered}[/tex]Therefore the first option represents the profit of the company.
the figure above represents a closed cylindrical tank of height 15m.the radius of the Cross-section is 7m. Calculate a) the curved surface area of the tank. b) the volume of the tank. use π=22/7
Answer:
a) The curved surface area is;
[tex]660\text{ }m^2[/tex]b) The volume of the cylindrical tank is;
[tex]2310\text{ }m^3[/tex]Explanation:
Given that the cylindrical tank has height 15m and radius 7m.
[tex]\begin{gathered} h=15\text{ m} \\ r=7\text{ m} \\ \pi=\frac{22}{7} \end{gathered}[/tex]The curved surface area of a cylinder can be calculated using the formula;
[tex]A=2\pi rh[/tex]substituting the given values;
[tex]\begin{gathered} A=2\times\frac{22}{7}\times7\times15 \\ A=660m^2 \end{gathered}[/tex]Therefore, the curved surface area is;
[tex]660\text{ }m^2[/tex]The volume of the cylindrical tank can be calculated using the formula;
[tex]V=\pi r^2h[/tex]Substituting the given values;
[tex]\begin{gathered} V=\frac{22}{7}\times7^2\times15 \\ V=2310m^3 \end{gathered}[/tex]Therefore, the volume of the cylindrical tank is;
[tex]2310\text{ }m^3[/tex]Eric can choose Plan A or Plan B for his long distance charges. For each plan, cost (in dollars) depends on minutes used (per month) as shown below.
(a) Plan B, 8
At 150 minutes, Plan B costs $20 and Plan A costs $12.(b) 250, Plan A
The costs are the same when the graphs intersect.Before 250 minutes, the graph for Plan A is lower than the graph of Plan B, meaning the graph of Plan A will cost less.answer pls :DD
3x - 6 =42
Write 0.00128 in scientific notation
Given:
[tex]0.00128[/tex]To write it in scientific notation:
It can be written as,
[tex]\begin{gathered} 0.00128=\frac{1.28}{1000} \\ =\frac{1.28}{10^3} \\ =1.28\times10^{-3} \end{gathered}[/tex]Hence, the scientific notation is,
[tex]1.28\times10^{-3}[/tex]The amount of cereal in a box is normally distributed with a mean of 24 oz. and a standarddeviation of 0.62 oz. If 7,500 boxes of cereal are packaged in one day, approximately how many boxeswould contain less than 22.9 oz.?
Given data:
The given mean is m=24.
The given standard devaition is s=0.62.
The given vallue is x=22.9.
The expression for the value of z is,
[tex]\begin{gathered} P(x<22.9)=P(z<\frac{x-m}{s}) \\ =P(z<\frac{22.9-24}{0.62}) \\ =P(z<-1.774) \end{gathered}[/tex]Refer the standard z-table.
[tex]P(x<22.9)=0.03836[/tex]The number of box required are,
[tex]\begin{gathered} N=7,500\times0.03836 \\ =287.7 \\ \approx288 \end{gathered}[/tex]Thus, the number of boxes are 288.
Paul sold 162 cups of lemonade in 5 hours. About how many cups of lemonade did she sell each hour?
The number of cups of lemonade sold in each hour is 32.4.
The number of cups of lemonade in each hour is the rate of selling. The rate of selling will be calculated by the formula : number of cups ÷ time.
Keep the values in formula to find the number of cups of lemonade sold each hour
Number of cups of lemonade sold each hour = 162 ÷ 5
Performing division to find the number of cups sold each hour
Number of cups of lemonade sold each hour = 32.4
Thus, each hour, 32.4 cups of lemonade are sold.
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A custormer spends $240 at Kal's on a shopping trip The customer hands the cashier a 25% off coupon. How much should the customor pay for their purchase? Enter your answer in the field below. Thero is a sciontific calculator avalable at tho top of the screen, if you need it.
Let's begin by listing out the information given to us:
Amount spent = $240
discount = 25%
[tex]\begin{gathered} Pay=Amountspent-(AmountSpent\cdot discount)_{} \\ P=240-(240\cdot\frac{25}{100})=240-60 \\ P=180 \end{gathered}[/tex]Therefore, the customer paid $180 for his purchase
Evaluate the finite geometric series. 3 + 4.5 + 6.75 + … + 34.171875
First determine the common ratio between consecutive terms.
4.5/3 = 9/6 = 3/2
6.75/4.5 = 27/18 = 3/2
and so on. The [tex]n[/tex]-th term in the sequence is given by
[tex]a_n = 3 \cdot \left(\dfrac32\right)^{n-1}[/tex]
Solve for [tex]n[/tex] that gives the last term to find how many terms are in the sum.
[tex]n = 1 + \log_{3/2}\left(\dfrac{a_n}3\right)[/tex]
Plug in the last term.
[tex]n = 1 + \log_{3/2} \left(\dfrac{34.171875}3\right) = 1 + 6 = 7[/tex]
Then the sum of the first 7 terms of this sequence is
[tex]\displaystyle \sum_{n=1}^7 3 \cdot \left(\frac32\right)^{n-1} = 3\cdot\frac{1 - \left(\frac32\right)^7}{1-\frac32} = \boxed{\frac{6177}{44}} = 96.515625[/tex]
where we use the formula
[tex]\displaystyle \sum_{n=1}^k r^{n-1} = \frac{1-r^n}{1-r}[/tex]
Put the rational numbers in order from least to greatest. -4.2, -4 1/2, -4, 0, 4
Let's express the mixed fraction in decimal.
[tex]-4\frac{1}{2}=-4.5[/tex]Then, from least to greatest, the numbers are
[tex]-4.5,-4.2,-4,0,4[/tex]What strategy would be the best to solve this problem?To get into shape, Miles ran for 1 minute on Monday, 3 minutes on Tuesday, 6 minutes on Wednesday, and 10 minutes on Thursday. If he continues, how many minutes will Miles run on Sunday?A. guess, check and reviseB. work backwardsC. use a formulaD. look for patterns
As we can see from the given data, that, it gives some informtaion about, an on going process, that is almost in rythm.
[tex]\begin{gathered} 1\text{ minute:Monday} \\ 3\text{minute: Tuesday} \\ 6\text{minute: Wednesday} \\ 10\text{ minutes: Thursday} \end{gathered}[/tex]So, from that we can see that, Mile had increased the running time in a particular pattern, at first he had increased the time by 2, then by 3, then by 4, and so on.
So to find the running time for sunday, we can solve this problem by analysing this pattern.
Therefore the answer is (D): looking for patterns.
This is 2.Dotty and Lionel are making a graph comparing a car's age with its gasmileage. Dotty says the graph should show discrete points because the car'sage is stated in whole numbers of years. Lionel says they should make acontinuous line because age increases gradually, like time. Which student doyou agree with and why?
Lionel should be the correct answer.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Dotty and Lionel are making a graph comparing a car's age with its gas mileage.
Dotty says the graph should show discrete points because the car sage is started in whole numbers of years.
Lionel says they should make a continuous line because age increases gradually, like time.
Now,
Clearly, The Lionel is correct because when we talk about the age, that means time and Time is continuous , never stopping or slowing down for anyone.
Thus, Lionel should be the correct answer.
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