Answers
Answer:
C = 70π cmA = 2,450 cm²Step-by-step explanation:
The perimeter of the given figure is equal to the circumference of whole circle.
The formula of a circumference of a circle:
[tex]C=\pi d[/tex]
d - diameter
We have d = 70 cm. Substitute:
[tex]C=70\pi\ cm[/tex]
The area of given figure is equal to the area of rectangle 70cm × 35cm.
(look at the picture).
The area of a rectangle:
[tex]A=(70)(35)=2,450\ cm^2[/tex]
The area of a circle is given by the formula A = πr², where π represents pi, and r the radius. The area can be left in terms of pi to avoid rounding errors, with the example of a circle with 1.2-meter radius having an area of approximately 4.5 m² when considering significant figures.
The area of a circle is expressed as A = πr², where π (pi) is approximately 3.14159265, and r is the radius of the circle. In terms of pi, this formula is often left in the form of πr² to retain the exact value without rounding. For example, if we have a circle with a radius of 1.2 meters, the area would be calculated as A = π(1.2 m)² = 4.5238934 m² using a calculator with eight-digit precision. However, since the radius is given with two significant figures, the appropriate representation of the area would be A=4.5 m².
It is important to note that when expressing the area in terms of pi, you may encounter different contexts such as finding the area of a semicircle using the definite integral that results in r²/2 for the semicircle's area, or understanding proportionalities in a circle divided into slices.
Related Questions
Hodaya is drawing a map of the trials in the canyon near her house. She knows that the distance from the first creek crossing to the second creek crossing is 1.8 miles. If every 3 inches on the map represents 0.75 of a mile, how far apart will the two creek crossing be on the map, to the nearest tenth of an inch.
Answers
Answer:
It would roughly be 7 inches and 1/5 of an inch.
I hope this answer helped you! If you have any further questions or concerns, feel free to ask! :)
Step-by-step explanation:
Two creek crossings are separated by distance A = 7.2 inches on the map.
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
The information is ,
Let's say the equation looks like this: A
Right now, A is valued at
The two stream crossings' separation is indicated on the map as A.
And on the chart, 3 inches equals 0.75 miles, therefore the distance between the two stream crossings is 1.8 miles.
hence, 3 / 0.75 inches Equals 1 mile.
In the map, 1 mile equals 4 inches after simplifying the calculation.
The two creek crossing's distance on the map is therefore equal to 1.8 x 4.
The two stream crossings will be separated by 7.2 inches on map A.
Hence, the distance on the map is 7.2 inches.
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Jayla buys and sales
Answers
Answer:
There is no question
Step-by-step explanation:
A line segment with endpoints (5,8) and (-6,8) is rotated around the origin 270 clockwise how long will the new segment be?
Answers
A rotation doesn't change the length of anything.
The length of the rotated line segment would be the same as the original line segment.
Because both Y values are the same, you just need to calculate the length of the X values.
5 to 0 = 5
0 to -6 = 6
Total length = 5 +6 = 11 units long.
Angle 1 and angle 2 are complementary the measure of angle 2 is 15 degrees less than twice the measure of angle 1 what is the measure of each angle plz help me
Answers
The measure of Angle 1 is 35 degrees and the measure of Angle 2 is 55 degrees.
Explanation:When two angles are complementary, their measures add up to 90 degrees. Let's define these two angles as follows: Angle 1 = x and Angle 2 = 2x - 15 (since it is 15 degrees less than twice the measure of Angle 1). You set up an equation based on the fact that the two angles add up to 90 degrees: x + 2x - 15 = 90. Solving this equation, you get 3x = 105, so x = 35. Thus, Angle 1 = 35° and Angle 2 = 2(35) - 15 = 55°.
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x+y=70
65x+15y=2400
solve by substitution
please show work very important thank you so much
Answers
The solution is
x = 27 and y = 43
Step-by-step explanation:See the image
Answer dis in a big hurry and will give brainliest!!!
Answers
Each square is 1/2 inch, so 4 squares is 2 inches.
The sum of three numbers is 83. The second number is 5 less than the first. The third number is 2 times the first. what are the numbers
Answers
Answer:
22, 17, and 44.
Step-by-step explanation:
So what you do is you will have three equations that we will put together.
1. x. The first number is x because they don't give us anything about it.
2. x-5. It says that the second number is 5 less than the first number.
3. 2x. It says that the third number is 2 times the first number.
x+x-5+2x=83.
4x-5=83.
4x=88.
x=22.
That is the first number. To find the second and third, you will plug 22 into the x.
2. 22-5=17.
3. 2(22)=44.
22, 17, 44 are your answers.
Final answer:
By setting up equations based on the information provided, we solved for x as the first number and then used it to determine the other two numbers. The three numbers are 22, 17, and 44.
Explanation:
The sum of three numbers is 83. This is the first equation we'll use to solve the problem. Let's denote the first number as x. According to the question, the second number is 5 less than the first, which gives us the second equation y = x - 5. For the third number, it is given as 2 times the first, hence the third equation is z = 2x.
Now, we'll combine all three equations to express the sum:
x + (x - 5) + 2x = 83
Simplifying, we combine like terms:
4x - 5 = 83
Adding 5 to both sides gives us:
4x = 88
Dividing by 4, we find the first number:
x = 22
Now we'll use x to find the other two numbers:
y = 22 - 5 = 17
z = 2 × 22 = 44
Therefore, the three numbers are 22, 17, and 44.
Three years ago, Sherman was twice as old as Clive. If Clive’s present age is c, which expression represents Sherman’s present age in terms of Clive’s age?
A.
2c − 3
B.
2c + 6
C.
2(c − 3)
D.
2c + 3
Answers
Sherman would still be double Clive's age (2c) and he would have aged 3 years (+3)
Would you use more centimeters or meters to measure the length of a car? Explain.
Answers
Answer:
Meters
Step-by-step explanation:
Because centimeters are to small to be a reasonable measurement for a car so you would have to use meters
Which expression does the fraction 3/8 represent?
1.8/3 2.3-8 3. 3/8 4. 3*8
Answers
Answer:
Im gonna guess and say it is answer 3.
Step-by-step explanation:
m∠A=(x+45)°,
mKE =(x+20)°,
mEW=(3x)° ,
Find: mKW.
Answers
Answer:
The measure of the arc KW is [tex]160\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<A=\frac{1}{2}(arc\ KE+arc\ EW)[/tex]
substitute the values and solve for x
[tex](x+45)\°=\frac{1}{2}(x+20+3x)\°[/tex]
[tex](2x+90)\°=(4x+20)\°[/tex]
[tex]4x-2x=90\°-20\°[/tex]
[tex]2x=70\°[/tex]
[tex]x=70\°/2=35\°[/tex]
Find the measure of the arc KW
[tex]arc\ KW=(arc\ KE+arc\ EW)=(4x+20)\°[/tex]
substitute the value of x
[tex]arc\ KW=4(35\°)+20\°=160\°[/tex]
Louis spins the spinner twice. Which probability are correct? Check all that apply
Answers
Answer:
Step-by-step explanation:
Only first one
P(both green) : [tex]\frac{1}{16}[/tex], P(both blue) : [tex]\frac{1}{4}[/tex], P(first orange and then blue) : [tex]\frac{1}{8}[/tex]
These probabilities are correct.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
According to the question
Louis spins the spinner twice.
Total number of favorable outcomes = {OB, OO, OB,OG, BB, BO, BB, BG, GG, GB, GO, GB, BB, BO, BB, BG} = 16
P(both green) :
Number of favorable outcomes = 1
P(both green) = [tex]\frac{1}{16}[/tex]
It is applicable.
P(both blue) :
Number of favorable outcomes = 4
P(both blue) = [tex]\frac{4}{16}[/tex] = [tex]\frac{1}{4}[/tex]
It is applicable.
P(first green and then blue) :
Number of favorable outcomes = 1
P(first green and then blue) = [tex]\frac{1}{16}[/tex]
P(first orange and then blue) :
Number of favorable outcomes = 2
P(first orange and then blue) = [tex]\frac{2}{16}=\frac{1}{8}[/tex]
It is applicable.
P(first orange and then green) :
Number of favorable outcomes = 1
P(first orange and then green) = [tex]\frac{1}{16}[/tex]
Hence,
P(both green) : [tex]\frac{1}{16}[/tex], P(both blue) : [tex]\frac{1}{4}[/tex], P(first orange and then blue) : [tex]\frac{1}{8}[/tex]
These probabilities are correct.
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I don’t know how to start it.
Answers
Answer:
36°
Step-by-step explanation:
∠A + ∠B + ∠C = 180°
∠A:∠B:∠C = 8:10:12 = 8x:10x:12x
8x + 10x + 12x = 180
20x = 180
x = 9
∠A = 8x = 8 × 9 = 72°
∠B = 10x = 10 × 9 = 90°
∠C = 12x = 12 × 9 = 108°
∠C - ∠A = 108 -72 = 36 °
The difference between the largest and the smallest angle is 36°.
(EASY) WILL MARK BRAINEST! Question: Write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph
(-9,-2) y=-4x+1
Answers
Answer:
y = -4x - 38
Step-by-step explanation:
Parallel lines are parallel because they never intersect. As such, they have the same slope. The slope of the line y = -4x + 1 is -4. Substitute m = -4 and the point (-9,-2) into the point slope form of a line.
[tex]y -y_1 = m(x-x_1)\\y --2 = -4(x --9)\\y + 2 = -4(x+9)\\[/tex]
Apply the distributive property to find the slope intercept form.
y + 2 = -4(x+9)
y + 2 = -4x - 36
y = -4x - 38
PLS HELP!!
A circle is centered at point (-7,-1) and passes through the point (8,7).
The radius of the circle is _____ units. The point (-15,___) lies on this circle.
Answers
Answer:
Part 1) The radius of the circle is [tex]17\ units[/tex]
Part 2) The points (15,14) and (-15,-16) lies on this circle
Step-by-step explanation:
Part 1
we know that
The distance between the center of the circle at point (-7,-1) and the point (8,7) is equal to the radius of the circle
so
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}[/tex]
[tex]r=\sqrt{(8)^{2}+(15)^{2}}[/tex]
[tex]r=\sqrt{289}}[/tex]
[tex]r=17\ units[/tex]
Part 2
we know that
If the point (-15,y) lies on the circle, then the ordered pair must be satisfy the equation of the circle
The equation of the circle is equal to
[tex](x+7)^{2}+(y+1)^{2}=17^{2}[/tex] -----> equation of the circle in center radius form
substitute the value of x=-15 in the equation and solve for y
[tex](-15+7)^{2}+(y+1)^{2}=289[/tex]
[tex]64+(y+1)^{2}=289[/tex]
[tex](y+1)^{2}=289-64[/tex]
[tex](y+1)^{2}=225[/tex]
[tex]y+1=(+/-)15[/tex]
[tex]y=-1(+/-)15[/tex]
so
[tex]y=14[/tex]
[tex]y=-16[/tex]
therefore
The points (15,14) and (-15,-16) lies on this circle
see the attached figure to better understand the problem
Answer:
Part 1) The radius of the circle is
Part 2) The points (15,14) and (-15,-16) lies on this circle
Step-by-step explanation:
The members of a track team ran laps around their school. They ran a total of 6 3/4, each lap was 7/8 miles long. How many laps did they run?
Answers
Answer:
[tex]7\frac{5}{7}\ laps[/tex]
Step-by-step explanation:
we know that
To find out how many laps they ran, divide the total distance by the distance of one lap
step 1
Convert the total distance from mixed number to an improper fraction
[tex]6\frac{3}{4}\ mi=\frac{6*4+3}{4}=\frac{27}{4}\ mi[/tex]
step 2
Find the number of laps
[tex]\frac{(27/4)}{(7/8)}=\frac{54}{7}\ laps[/tex]
step 3
Convert the number of laps to mixed number
[tex]\frac{54}{7}=\frac{49}{7}+\frac{5}{7}=7\frac{5}{7}\ laps[/tex]
Can anyone help me please?
Which expression can be used to find the area of a circle with a diameter of 30 cm?
a. π • 30
b. 2 • π • 15
c. π • 30^2
d. π • 15^2
Answers
Answer:
its b
Step-by-step explanation:
Answer:
2 × pi or (π) × 15 = 30 cm
Step-by-step explanation:
What is the product?
Answers
Answer:
So option B is the correct answer .
Step-by-step explanation:
Since it is the multiplication of 1 X 3 matrix to 3 X 3 order matrix,
so the resultant product should be 1 X 3 because when we multiply two matrices it is the condition that if A is of order p X q and B is of order q X r,
the product matrix (suppose C ) will be of order p X r.
so the product will be
= [-1*3+2*2+4*0 -1*6+2*4+4*6 -1*1+2*0+4*2]
= [ 1 26 7] .
I don’t get how the answer is one..
not sure how to factor/reduce what I was able to reduce to equal 1
Did I do something wrong
Answers
Answer:
see explanation
Step-by-step explanation:
Factorise the numerators on both fractions
a² + 10a + 25 = (a + 5)(a + 5) ← perfect square
a² - 25 = (a - 5 )(a + 5) ← difference of squares
To divide, leave the first fraction, change division to multiplication and turn the second fraction upside down.
Hence
= [tex]\frac{(a+5)(a+5)}{a+5}[/tex] × [tex]\frac{a-5}{(a-5)(a+5)}[/tex]
Cancel both the (a + 5) factors on the numerator/ denominators and the (a - 5) factor on the numerator/denominator, leaving
= 1 ← as required
-2x+15y=-24
2x+9y=24
Answers
Answer:
x = 12 and y = 0
Step-by-step explanation:
Use elimination by adding the equations together.
-2x + 15y =-24
2x + 9y = 24
---------------
24y = 0
y=0
Then substitute y = 0 into one equation to find x.
-2x + 15(0) = -24
-2x + 0 = -24
-2x = -24
x = 12
Answer: x = 12 y = 0
Step-by-step explanation:
What is the answer????
Answers
ANSWER
f(x) is an odd function.
EXPLANATION
The given function is symmetric with respect to the origin.
Hence it is an odd function.
We can also see from the graph that,
[tex]f(1) = 2[/tex]
and
[tex]f( - 1) = - 2[/tex]
This implies that,
[tex]f( - 1) = - f(1)[/tex]
Since
[tex]f( - x) = - f(x)[/tex]
the function is odd.
The correct answer is A.
Factor completely.
x2−8x+15
Do not include any spaces in your answer. Use parentheses to separate your factors. A sample answer might be (x+1)(x-4).
Question 5 options:
Answers
The answer is :
(x+5)(x+3)
The area of a circular trampoline is 112.07 square feet. What is the radius
Answers
Answer: The correct answer is B. 5.97 feet
Step-by-step explanation:
Formula⇒A=π r2
* Hopefully the work helps:) Mark me the brainliest;)!!!
Answer:
5.97 feet
Step-by-step explanation:
Set up your equation as 112.07 = Pi*r^2
To simplify, divide 112.07 by Pi or an approximation of it and then find the square root of your answer.
112.07 = Pi*r^2
112.07/Pi = r^2
(112.07/Pi)^0.5=r
Last week byron bought 5 containers of yogurt and spent 12.88 on other groceries this week Cassandra bought 3 containers if the same yogurt and spent 11.50 on the other groceries how much more money did byron spent than Cassandra?
Answers
Answer:1.33
Step-by-step explanation:
Byron spent $1.38 more than Cassandra on other groceries, as we subtracted Cassandra's spending ($11.50) from Byron's ($12.88) to determine the difference.
The question asks us to determine how much more money Byron spent compared to Cassandra on their grocery shopping. To find this out, we need to compare the total amount of money each person spent. We have the cost of other groceries for each person, but the cost of yogurt is not given. To solve this problem, we just need to compare the cost of other groceries since that is the only information provided.
Byron spent $12.88 on other groceries.
Cassandra spent $11.50 on other groceries.
To find out how much more Byron spent, we subtract Cassandra's total from Byron's total:
$12.88 - $11.50 = $1.38
Therefore, Byron spent $1.38 more than Cassandra on other groceries.
Mary has rehearsed her ballet solo for five and a half hours. A week from now, she wants to have rehearsed at least a total of nineteen and a half hours. If she rehearses for the same amount of time each day for the next 7 days, at least how many hours must she rehearse per day?
Answers
Answer:
2 hours per day
Step-by-step explanation:
19.5 - 5.5 = 14
14 / 7 = 2 hours per day
Mary needs to rehearse 2 hours per day for the next 7 days to meet her total rehearsal goal.
To calculate the total rehearsal time for Mary:
She has rehearsed for 5.5 hours.
She wants to rehearse a total of 19.5 hours.
Therefore, 19.5 - 5.5 = 14 hours
She needs to rehearse an additional 14 hours in the upcoming week.
To find out how many hours Mary must rehearse per day in the next 7 days:
14 / 7 = 2 hours/day
Your friend pulls out a huge home baked pizza from the oven and tells you the area is a=625(pi)cm2. What is the diameter of this pizza
Answers
Answer:
Diameter = 50 cm
Step-by-step explanation:
We are given that the area of a home bakes pizza is [tex] 6 2 5 \pi cm ^ 2[/tex].
Here, we are assuming that the pizza is circular and we know that the area of a circle is given by: [tex]\pi r^2[/tex]
So equating the given value to find the value of the diameter.
[tex]\pi r^2[/tex] [tex]=625\pi[/tex]
[tex]r^2=625[/tex]
[tex]r=\sqrt{625}[/tex]
[tex]r=25[/tex]
If the radius is 25 cm, then diameter = 25 × 2 = 50 cm
Answer:
The diameter of the pizza= 50 cm
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r is the radius of circle
It is given that, area of pizza is 625π cm²
A pizza is like a circle.
Find the radius of pizza
Area = πr²= 625π cm²
r² = 625π/π = 625
r = √625 = ±25
radius r = 25cm
To find the diameter of pizza
Diameter = 2r = 2 * 25 = 50 cm
find the product: (2/3)(5/3)(21)
Answers
Answer:
Here is the following answers I got.
Step-by-step explanation:
(70/3)
23.3333
23 1/3
2. The two figures are similar.
a) Write the similarity statement.
b) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
c) What is the scale factor? Explain.
Answers
Answer:
Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure.(the scale factor is greater than 1)
Part c) The scale factor is [tex]3[/tex]
Step-by-step explanation:
Part a) Write the similarity statement
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
substitute the values
[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45'}[/tex]
[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3'}[/tex] ----> is true
therefore
the figures are similar
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure. (the scale factor is greater than 1)
Part c) we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z------> the scale factor
x-----> corresponding side of the image
y------> corresponding side of the original figure
so
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=A'B'=27\ units[/tex]
[tex]y=AB=9\ units[/tex]
substitute
[tex]z=\frac{27}{9}=3[/tex]
The scale factor is greater than 1
therefore
Is an enlargement
Answer:(A) ab/a’b’=bc/b’c’=ac/a’c’ (B) Figure a’b’c’ is an enlargement because it increase it’s sides larger than 1. (C) So we have to divide to get the scale factor for both of these figures 18/6=3 then you found the scale factor 3.
Step-by-step explanation:
What is the approximate circumference of a circle with the diameter of 6
Answers
Circumference= [tex]2\pi r[/tex]
If the diameter is 6 the radius will be 3
[tex]2\pi (3)[/tex]
Circumference= 18.85
Hey there!
The formula for circumference is πd, where d is diameter.
We are given that the diameter is 6, so the circumference is 6π.
However, we are asked for the approximate circumference, not the exact.
So, let's use 3.14 as π and simplify.
6 x 3.14 = 18.84
The approximate circumference of a circle with the diameter of 6 is 18.84.
Hope this helps!
Someone help me please
Answers
Answer:
Look at the picture
Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\\text{Therefore}\\\\f(x)=b^x\to y=b^x\\\\\text{find}\ f^{-1}(x).\ \text{Exchange}\ x\ \text{and}\ y\ \text{and solve for}\ y:\\\\b^y=x\qquad\text{logarithm iwth base b of both sides}\\\\\log_bb^y=\log_b(x)\qquad\text{use}\ \log_ab^m=m\log_ab\\\\y\log_bb=\log_b(x)\qquad\text{use}\ \log_aa=1\\\\y=\log_b(x)\\\\f^{-1}(x)=\log_b(x)\to g(x)=f^{-1}(x)\\\\\text{Then:}\ f(a)=b\to g(b)=a[/tex]