Guys, can you please help me write an expression for shaded circle and please expand and simplify for me, guys, please? :)
Answers
Answer:
[tex]\sf Shaded \: Area=14 \pi r+49 \pi[/tex]
Step-by-step explanation:
Area of a circle
[tex]\sf A=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
To find the area of the shaded area, subtract the area of the unshaded circle from the larger circle.
Area of the larger circle
[tex]\implies \sf A=\pi (r+7)^2[/tex]
Area of the smaller (unshaded) circle
[tex]\implies \sf A=\pi r^2[/tex]
Therefore, the area of the shaded area is:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
Expand and simplify the expression:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
[tex]\implies \sf A=\pi (r^2+14r+49)-\pi r^2[/tex]
[tex]\implies \sf A=\pi r^2 +14 \pi r +49 \pi -\pi r^2[/tex]
[tex]\implies \sf A=14 \pi r+49 \pi[/tex]
OUTER CIRCLE AREA
π(r+7)²Inner circle area
πr²Area of shaded one
π(r+7)²-πr²π(r²+14r+49-r²)π(14r+49)14πr+49πRelated Questions
In order to create a system of equations that has the same solution as the system
x+y=4
2x+y = 7
complete three steps.
1
Step 1: Multiply the equation x + y = 4 by _[blank A]__.
Step 2: Add the equations 2x + y = 7 and _[blank B]_.
Step 3: Write the new system of equations as _[blank C]__.
Match each blank with the system or statement that correctly fills in that blank.
Answers
#Step1
Multiply by -2It will result -2x-2y=-8
#2
-2x-2y=-8#3
add
-y=-1y=1Find x
x+1=4x=3The scatter plot shows the height of an alfalfa plant over a period of time. Click on the table that best matches the data in the scatter plot.
Answers
Based on the information provided, the table that best matches the data in the scatter plot is shown below.
What is a scatter plot?A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided, the table that best matches the data in the scatter plot is given by:
Data 1 2 4 5.5 6.3
Height (cm) 1 2 3 4 5
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Based on the table below, determine the exponential function being used. Use x as your variable. Then, evaluate this expression for x=7.
Input (x) Output
0 1
1 5
2 25
3 125
4 625
Answers
The exponential function is used. Use x as your variable common ratio.
This is pretty obviously
If it wasn't obvious we can find the common ratio r by dividing successive values:
5/1=5
25/5=5
125/25=5
625/125=5
What is the common ratio?
The common ratio is the number you multiply or divide by at each stage of the sequence. You can find it by dividing two consecutive pairs of terms.
That's the common ratio. We multiply by the first term, but the first term is one, so that has no effect.
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In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is .
If the coordinates of point A are (0,6), the area of rectangle ABEF is square units, and the area of rectangle ACDF is square units.
The perimeter of rectangle BCDE is units.
Answers
Area of the rectangle is 96.05 sq.units , The ratio of the areas is 2/3 , Area of rectangle ABEF is 64.03 sq.units.
The complete question is
In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is(a)_____ . If the coordinates of point A are (0,6), the area of rectangle ABEF is(b)____ square units, and the area of rectangle ACDF is(c)____ square units. The perimeter of rectangle BCDE is(d)____ units.
What is a Rectangle ?A rectangle is a polygon with four sides and for angles and four vertices , Its opposite sides are parallel and equal.
The area of rectangle ACDF is square units. = ?
The perimeter of rectangle BCDE is units. = ?
[tex]\rm d = \sqrt{ (y_2 -y_1 )^2 + (x_2 -x_1)^2}\\\\\rm d = \sqrt{ (2 - 6 )^2 + (5 - 0)^2}[/tex]
d = 9.605
the length of [tex]\rm EF[/tex]
[tex]\rm FE[/tex] = 10 units.
and [tex]\rm FD[/tex] = 15 units
Area of a Rectangle [tex]\rm ACDF[/tex] is given by
Length x width
10 * 9.605
Area of the rectangle is 96.05 sq.units
Perimeter of a rectangle is = 2( length + breadth)
ED = FD-FE = 15- 10 = 5 units
Therefore
Perimeter = 2 ( 5 + √41 )
Perimeter = 22.81 units
Area of rectangle ABEF is 64.03 sq.units
The ratio of the areas
= 64.03/96.05
= 0.666667
= 2/3
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A. 21.50
B. 32.25
C. 30.15
D. 20.75
Answers
Answer:
B
Step-by-step explanation:
Similar to the one you asked earlier.
Given from the table
1 Gallon of gas = $2.15
15 gallons of gas = $2.15 x 15
= $32.25 (B)
1. What is the number of possible outcomes of picking one letter at a time from the word ANGELES CITY?
2. What is the probability of drawing E?
3. What is the probability of drawing a vowel?
4. What is the probability of drawing a consonant?
5. What is the probability of drawing P?
Answers
Answer:
4
Step-by-step explanation:
5
how many sets of 5 students can be selected out of 30 students?
Answers
Answer:
142 506
Step-by-step explanation:
here the order does not matter
Then
we the number of sets is equal to the number of combinations.
Using the formula :
the number of sets is 30C5
[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]
[tex]=142506[/tex]
There are 142506 ways in which 5 students can be selected out of 30 students.
How can a certain number of individuals be selected using a combination?The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.
By using the formula:
[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]
where;
n = total number of individual in the set = 30r = number of chosing individuals to be selected = 5[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]
[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]
[tex]\mathbf{^nC_r = 142506}[/tex]
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What is the length of DE?
A A
12
DXE
A. 6
B. 8
C. 5
D. 7
Answers
Answer:
A
Step-by-step explanation:
these two triangles are similar
therefore corresping sides are proportionate
12/8=9/x
12x=72
x=72/12=6
Answer:
the answer is 6
Step-by-step explanation:
i hope this is helpful
15 trucks can carry 26,850 kg weight. Find the weight carried by one truck.
Answers
[tex] \huge\underline{\underline{\boxed{\color{blueviolet}{ANSWER}}}}[/tex]
★ 15 trucks can carry 26,850 kg weight
★ We've to find the weight carried by one truck
[tex]\huge \pink {\overline{ \quad \quad \quad \quad \quad \quad \quad\quad \quad}}[/tex]
[tex] \sf{Number \: of \: trucks = 15 }[/tex]
[tex] \sf{Weight \: carried \: by \: one \: truck = \frac{26,850Kg}{15} }[/tex]
[tex] \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 1790Kg[/tex]
Therefore , the weight carried by one truck is 1790 kg
what is the correct arangement of 3-6x-2x^2+3x-6x^2+2
Answers
Answer:
-8x²-3x+5
Step-by-step explanation:
First, add like terms.
3-6x-2x²+3x-6x²+2=
= 5-3x-8x²
Put it in standard form. To put in standard form, put the exponent from greatest to least.
-8x²-3x+5.
Hope this helps!
If not, I am sorry.
The area of a square is given by and the perimeter is given by , where s is the side length of the square.
If the side length of a square is 4 inches, its area is
square inches and its perimeter is
inches.
Answers
The area of the square is 16 square inches and its perimeter is 16 inches.
What is Area of square ?
A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.
The area of a square is given by the formula:
A = s²
where A is the area and s is the length of a side.
If the side length of the square is 4 inches, the area can be calculated as:
A = 4² = 16 square inches.
The perimeter of a square is given by the formula:
P = 4s
where P is the perimeter and s is the length of a side.
If the side length of the square is 4 inches, the perimeter can be calculated as:
P = 4 x 4 = 16 inches.
Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.
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Circle Q is shown. Line segments P Q and R Q are radii. The length of R Q is 6. Angle P Q R is 45 degrees. Sector P Q R is shaded.
Which statements are true about circle Q? Select three options.
The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.
The area of the shaded sector is 4 units2.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.
The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.
Answers
The statements that are true about circle Q are:
The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.The area of the shaded sector depends on the length of the radius.The area of the shaded sector depends on the area of the circle.How to explain the circle?The measure of the central angle is 45°. The measure of the entire circle is 360°. This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8
To find the area of the shaded sector, this will be:
A = πr² = π(6²) = 36π
1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units. This is not 4 square units.
The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.
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Answer:
1,3,4
Step-by-step explanation:
Jamie is walking her neighbors’ dog while they are away. She is keeping track of the total number of blocks she walks over time.
A 2-column table with 3 rows. Column 1 is labeled Minutes with entries 6, 14, 20. Column 2 is labeled Blocks with entries 3, 7, 10.
Does the table represent a proportional relationship?
Yes, because both columns are written in ascending order.
Yes, because the values in the second column are less than the values in the first column.
Yes, because the ratios are equivalent between each pair of values.
No, because the values in the table do not increase by the same amount in each row.
Answers
Answer:
Yes, the relation is proportional because the ratios are equivalent between each pair of values
Step-by-step explanation:
Proportional relationships are relationships with equal ratios.
Entries in the respective columns are:
column 1 (Minutes) column 2 (Blocks) Ratios
6 3 1/2
14 7 1/2
20 10 1/2
As the ratio of Blocks and Minutes is same for every row,
the given table represent a proportional relationship.
hence, option c is correct.
Yes, because the ratios are equivalent between each pair of values.
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Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)
A (-3,6) B (-1, 3) Find the gradient of the line
Answers
Step-by-step explanation:
please mark me as brainlest
13 7in 7in 7in volume and surface area pyramid
Answers
The Volume and Surface Area of Prism is 294 in² and 114.33 in³.
What is pyramid?A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.
Surface rea of rectangular prism,
= 2( lb +bh +lh)
= 2 ( 7*7 + 7*7+ 7*7)
= 2 ( 49+49+49)
= 2*3*49
= 294 in²
Now, Volume,
= bhl/3
= 7*7*7/3
= 114.33 in³
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لیا
Use the drawing tools to form the correct answer on the graph.
Graph the line that represents this equation:
y + 2 = (x+2)
Drawing Tools
Select
Point
Line
P
K
Click on a fool to begin drawing.
17
-10
-8
-6
-4
4
10-
8
06000
Undo
Resef
Answers
The graph is plotted and attached in the attachment. The given equation is a linear equation with the intercept 0.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as y = mx + c.
Given equation;
y + 2 = (x+2)
Rearrange the equation;
y + 2 = x+ 2
y=x
The standard equation for the straight line is;
y = mx + c
Where c is the intercept and m is the slope
After comparing the given equation with the standard equation we get;
m = 1
c =0
Hence,the graph is plotted and attached in the attachment.
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Kaye bought 7 mangoes for $49, 4 apples for $24, and 3 oranges for $15. Which fruit is very cheap in price?
Answers
Answer:
oranges
Step-by-step explanation:
Answer: The oranges.
Step-by-step explanation: I'll set up my work below.
Mangoes: $[tex]49/7=7[/tex] =$7 per mango
Apples: $[tex]24/4=6[/tex]=$6 per apple
Oranges: $[tex]15/3=5[/tex]=$5 per orange
Given this, the cheapest fruit is the orange.
I hope this helps!! Pls mark brainliest :)
Suppose y varies directly as x, and y = 27 when x = 3. Find y when x = 4.
Answers
the initial statement is y ∝ x
to convert to an equation multiply by k the constant of variation
[tex]y = kx[/tex]
to find k use the given condition
[tex]y = 27 \\ \\ when \\ \\ x = 3[/tex]
[tex]y = kx \\ \\ k = \frac{y}{x} = \frac{27}{3} = 9[/tex]
equation is y = 9x
when x = 4 then
[tex]y = 9 \times 4 = 36.[/tex]
Answer:
y = 36
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 27 when x = 3 , then
27 = 3k ( divide both sides by 3 )
9 = k
y = 9x ← equation of variation
when x = 4 , then
y = 9 × 4 = 36
Tanya planted seedlings in her garden over the weekend. The instructions that came with the seedlings stated that they need to be planted 0.2 meters apart. Tanya has a measuring tape that has values in centimeters. Help Tanya convert meters to centimeters.
Determine the ratio to use: .
Tanya should plant the saplings 20 centimeters apart.
1 meter is equal to 100 centimeters.
Multiply the given value by the ratio: .
i think they're supposed to be in order i cant figure it out, please help ToT!!
Answers
One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
As we know;-
1 meter is 100 cm so 0.2 meters will be calculated as:-
1 meter = 100 cm
0.2 meter = 0.2 x 100 = 20 centimeters.
Therefore One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.
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The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the phone is used each month. Minutes 500 750 1,000 1,250 1,500 Total Monthly Cost (in dollars) $62 $77 $92 $107 $122Choose the correct linear model that represents the total monthly cost as a function of time. A y = 0.06 x + 500, B y = 16 x + 32,C y = 62 x + 16, D y = 0.06 x + 32 .
Answers
Answer:
ytyt
Step-by-step explanation:
tyt5667
What is The Value Of X
Answers
Answer:
X = 92 degrees
Step-by-step explanation:
the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88
180-88= 92 so X = 92
What is the length of the line?
Choose 1 answer: A. 7 B. The square root of 10 C. Square root of 29 D.Square root of 21
Answers
Answer:
C
Step-by-step explanation:
= The square root of (5^2+2^2)= The square root of 29 ---> C
For what value of x is line m parallel to line n?
Answers
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
Here, we can use an angle rule.
We see that angles [tex](8x+50)[/tex]° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.
This means we can use the rule:
Corresponding angles are equal.
This means that:
[tex]8x + 50 = 130[/tex]
We can now use this equation we have formed to solve for [tex]x[/tex]:
[tex]8x + 50 = 130\\8x = 80\\x = 10[/tex]
Therefore, our final answer is [tex]x=10[/tex].
Multiply (5z + 6)(2z + 1)(2z - 1)
Pls help and explain WELL ty
Answers
Answer:
[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]
Step-by-step explanation:
Given expression:= (5z + 6)(2z + 1)(2x - 1)
Using formula (a + b)(a - b) = a² - b²= (5z + 6)[(2z)² - (1)²]
= (5z + 6)(4z² - 1)
Distributing
= 5z (4z² - 1) + 6(4z² - 1)
= 20z³ - 5z + 24z² - 6
Arrange
= 20z³ + 24z² - 5z - 6
[tex]\rule[225]{225}{2}[/tex]
Analyze the diagram below and complete the instructions that follow.
/
Find the value of x.
A.
4
B.
5
C.
6
D.
9
Please select the best answer from the choices provided
A
B
C
D
Answers
The value of x will be 4 , Option A is the answer.
What is a Right Angled Triangle ?A triangle that has one angle as 90 degree is called a Right angled Triangle.
In a right angled triangle
the length of the sides can be determined using Pythagoras Theorem
The length of the side is given in the image attached as
x-2 , x , √20
Hypotenuse ² = Perpendicular² + Base²
(√20)² = x² + (x-2)²
20 = x² + x² +4 -4x
2x²-4x -16 = 0
x² -2x -8 = 0
x² - 4x +2x -8 = 0
x (x-4) +2(x-4) = 0
(x+2)(x-4) = 0
x = -2 , 4
The value of x will be 4 .
Therefore Option A is the answer.
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The length of an arc of a circle is 26/9 pi
centimeters and the measure of the corresponding central angle is 65 degrees. What is the length of the circle's radius?
Answers
The radius will be equal to 7.55 centimeters.
What is the length of arc of the circle?The arc length is the curved length on the circumference of a circle suspended by a small angle.
The radius will be calculated as follows:-
r = [tex]\dfrac{Arc}{Angle}[/tex]
r = [tex]\dfrac{\dfrac{26\pi}{9}}{\dfrac{69\times \pi}{180}}[/tex]
r = [tex]\dfrac{9.07}{1.20}[/tex]
r = 7.55 centimeters
Therefore the radius will be equal to 7.55 centimeters.
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what can this be classified as?
Answers
Answer:
D. None of the Above
Step-by-step explanation:
They don't relate whatsoever
A five-digit integer will be chosen at random from all possible positive five-digit integers. What is the probability that the number's units digit will be less than 5
Answers
The probability that the number's units digit will be less than 5 is 0.5 that it is equal to 1/2.
Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
There are 10 possible digits, 0, 1, 2, ... 9 that make up the 5-digit number made up of integral values.
There are 5 digits that are less than 5 which are 0, 1, 2, 3, and 4 so the probability will be found by taking only those nubers which have unit's place less than 5,
By probability formula , Probability= no. of favourable outcomes/total no. of outcomes
So probability will be found that will be equal to 5/10, or 1/2
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You buy 2 shirts and 1 pair of pants for $34. Your friend buys 3 shirts and 3 pairs of pants for $69. What is the price of 1 shirt and 1 pair of pants
Answers
You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?
First let’s define a shirt as X and pants as Y!
In the first scenario, the equation will be 3X + Y =$32
In the second scenario, the equation will be 2X + 3Y = $40
Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!
3X + Y= $32—> subtract 3X on both sides of the equation
-3X. - 3X
Net result: Y= 32- 3X
Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable
2X + 3(32-3X) = $40
2X + 96 - 9X = $40 —> simplify the equation
-7X + 96 = $40 —> substrate 96 from both sides
-7X = -56 —> divide both sides by -7
X= 8
Now reinsert 8= X into 3X + Y = $32
3(8) + Y = $32
24+ Y = $32 —> substract 24 from both sides
y = 8
ANSWER: X= 8, Y= 8
I’m not good at math PLEASE HELP
Answers
Explanation: for every x value given, plug it into the equation for the “x” variable. Then solve the equation. Make sure to remember that when simplifying “4-x” if x is larger than 4 you will get a negative number.