Answers
Answer:
36[tex]\sqrt{3}[/tex] + 72
Step-by-step explanation:
The length of the rectangle = diameter of 2 circles = 4 × 3 = 12 mm
The width of the rectangle = 2 radii + distance d between radii ( lower to upper )
Using the right triangle formed by joining the 3 centres with legs 3 and d and hypotenuse 6
Using Pythagoras' identity, then
d² + 3² = 6²
d² + 9 = 36 ( subtract 9 from both sides )
d² = 27 ( take the square root of both sides )
d = [tex]\sqrt{27}[/tex] = 3[tex]\sqrt{3}[/tex]
Thus width of rectangle = 3 + 3[tex]\sqrt{3}[/tex] + 3 = 6 + 3[tex]\sqrt{3}[/tex]
Hence
area = length × width
= 12 × (6 + 3[tex]\sqrt{3}[/tex] ) = 36[tex]\sqrt{3}[/tex] + 72 mm ²
36 [tex]\sqrt{3}[/tex]+ 72
The length of the rectangle = diameter of 2 circles = 4 × 3 = 12 mm
The width of the rectangle = 2 radii + distance d between radii ( lower to upper )
Using the right triangle formed by joining the 3 centres with legs 3 and d and hypotenuse 6
Using Pythagoras' identity, then
d² + 3² = 6²
d² + 9 = 36 ( subtract 9 from both sides )
d² = 27 ( take the square root of both sides )
d = = 3
Thus width of rectangle = 3 + 3 + 3 = 6 + 3
Hence
area = length × width
= 12 × (6 + 3 ) = 36 + 72 mm ²
Related Questions
PLZ HELP Find the value of x that makes ΔXYZ~PQR
Answers
Answer:
x = 8
Step-by-step explanation:
[tex] \triangle XYZ \sim\triangle PQR... (GIVEN) \\
\therefore \frac{XY}{PQ} = \frac{YZ}{QR}.. (csst) \\
\therefore \frac{20}{30}= \frac{x+6}{21}\\
\therefore \frac{2}{3}= \frac{x+6}{21}\\
\therefore \frac{2\times 21}{3}= {x+6}\\
\therefore 14= {x+6}\\
\therefore 14-6= {x}\\
\therefore 8= {x}\\
\huge \orange{\boxed {\therefore x = 8}} [/tex]
What is the equation of the line that passes through the points (−2, 1) and (1, 10)?
Answers
Answer:
Slope-Intercept form: y=3x+7
Standard form: 3x-y=-7
Point-slope form: y-1=3(x+2)
Step-by-step explanation:
Slope-Intercept form:
First, find the slope, using the formula: [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Our x₁ and y₁ will be the point (-2,1) and our x₂ and y₂ wwill be the point (1,10).
So let's write those in our equation to find slope:
[tex]m=\frac{10-1}{1-(-2)}=\frac{9}{3}=3[/tex]
Therefore, our slope is 3.
Now let's write our linear equation with what we have already in slope-intercept form:
y=3x+b
Well, we still need to find the y-intercept, or "b".
Plug in one of your points for the x and y values of the equation. We'll use the point (-2,1)
[tex]y=3x+b\\1=3(-2)+b\\1=-6+b\\1+6=-6+6+b\\7=b[/tex]
This means our y-intercept is 7. Now we can write our equation in slope-intercept form completely:
y=3x+7
Standard form:
Now, let's find this equation is standard form.
Take your equation in slope-intercept form and write it out again:
[tex]y=3x+7[/tex]
Now, standard form of a linear equation is ax+by=c, so subtract 3x from both sides:
[tex]y-3x=3x-3x+7\\-3x+y=7[/tex]
The "a" coefficient in standard form cannot be negative, so divide the entire equation by -1:
[tex]\frac{-3x+y}{-1}=\frac{7}{-1}\\3x-y=-7[/tex]
Therefore, your equation in standad form is:
3x-y=-7
Point-Slope form:
The formula for point-slope form is y-y₁=m(x-x₁). We already know that our x₁ and y₁ is the point (-2,1) and we know that our slope, m, is 3, so we just have to plug then in where the fit in the equation.
x₁ is -2 and y₁ is 1 and m is 3, so:
y-1=3(x-(-2)) or y-1=3(x+2)
That means our equation in point-slope form is:
y-1=3(x+2)
find the distance between points P(3, 4) and Q(4, -6) If necessary round to the nearest hundredth.
Answers
Answer:
10.05 units
Step-by-step explanation:
We can find the distance between these points using the distance formula. The distance formula is:
[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
We know that x1 is 3, x2 is 4, y1 is 4, and y2 is -6, so we can substitute inside the equation.
[tex]\sqrt{(4 - 3)^2 + (-6 - 4)^2} \\\\\sqrt{1^2 + -10^2} \\\\\sqrt{1 + 100} \\\\\sqrt{101} \\\\\approx10.05[/tex]
Hope this helped!
Find the value of m. A. 32 B. 50 C. 63 D. 74
Answers
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Two straight edges of a pizza slice meet at an angle of 30°. If the pizza has a radius of 12
inches, what is the area of the slice and how long is its crust? Show how you got your answer step-by-step.
Answers
Answer:
area of the slice: A = 12π in² ≈ 37.7 in² lenght of its crust: L = 24π in ≈ 6.28 inStep-by-step explanation:
R = 12 in
360°:30° = 12
so the area of the slice is ¹/₁₂ of whole pizza
A = ¹/₁₂•πR² = ¹/₁₂•π•12•12 = 12π in² ≈ 37.7 in²
Crust is the perimeter of pizza so crust of the slice is ¹/₁₂ of the perimeter:
L = ¹/₁₂•2πR = ¹/₁₂•2π•12 = 2π in ≈ 6.28 in
We run a linear regression and the slope estimate is 0.5 with estimated standard error of 0.2. What is the largest value of b for which we would NOT reject the null hypothesis that β1=b ? (assume normal approximation to t distribution, and that we are using the 5% significance level for a two-sided test; need two significant digits of accuracy)
Answers
Answer:
0.9
Step-by-step explanation:
Y = B0 + B1X
B1 is the slope an from the question the slope estimate is 0.5
S.E= standard error at 0.2
At 5percent Level of significance, the z value for the test is equal to 1.96
We are required to find out the largest value of b for which the null hypothesis would be accepted.
0.5 + 1.96 x 0.2
= 0.892
Approximately 0.9
HELP ME!!! Why is it possible to isolate the variable, x, in the equation 2x = 20 by using either the division property of equality or the multiplication property of equality?
Answers
Answer: Because division is the inverse of multiplication.
Step-by-step explanation:
By multiplying the equation 2x=20 by 1/2 you will be able to eliminate the x variable,
For example,
1/2 * 2x = 20*1/2
x= 10
The same way if you divide both sides of the equation 2x=20 by 2 you will be able to to eliminate the x variable.
For example
2x = 20 Divide both sides by 2
x= 10
As you can see 2 is the division inverse of 1/2.
6. Tori and Terry spend the day at the mall. At the end of the ey, se two added up their
purchases and found they spent a total of $107.50, Tori spent $10.00 more fean Tery, Witte
guation that can be used to find how much each girl spent
Answers
Answer:
y + (y+10) = 107.50
Step-by-step explanation:
Let y represent Terry's purchases. Then Tori's purchases are (y+10). The sum of their purchases is given by the equation ...
y + (y+10) = 107.50
_____
Then y = 48.75 represents Terry's spending, while y+10 = 58.75 represents Tori's spending.
|4x + 8| + 12= 4 I subtracted 12 by 4 and got -8. Would I still solve the equation or would it be no solution?
Answers
Answer:
no solution
Step-by-step explanation:
|4x + 8| + 12= 4
Subtract 12
|4x + 8| = -8
An absolute value must be non negative
Since ours is negative, there is no solution
The population of a city is 1,880,000 what is the value of each of the two 8s in this number how are the two values related
Answers
Answer:
The value of the 8 in the front is 800,000 and the value of the second is 80,000. The front value is ten times as big as the second value.
Step-by-step explanation:
Intersecting lines are _____ coplanar. Sometimes Never Always
Answers
Answer:
Always
Step-by-step explanation:
Coplanar lines are lines that intersect making intersecting lines always coplanar.
Christine is typing at a rate of 75 words per
minute. Paula is typing at twice Christine's
speed. If together they need to transcribe a 2000
word paper which of the following expressions
would illustrate the time in minutes, x, it would
take for them to do so.
A) 150
2000X
75
150
B)
+
= 2000
C) 150 + 75 =
2000
2000
D) x =
(150+75)
Answers
Answer:
X = 2000 / (75 + 150)
Step-by-step explanation:
Given the following :
Christine's typing rate = 75 words per minute
Paula's speed = 2 times Christine's speed
If 2000 words needs to be transcribed. The time taken in minute 'x' will be :
From the relation :
Time = distance / speed
Distance here is the number of words in the document
Christine's speed = 75 words per minute
Paula's speed = 150 words per minute
Combined speed per minute = 150 + 75 = 225 words per minute
Time taken (x) = 2000 / 225
X = 2000 / (75 + 150)
Joan is filling a 2-liter soda bottle with different colors of sand to make an art project for her class. She has 1,000 milliliters of
red sand, 35 centiliters of blue sand, and 2,5 deciliters of yellow sand in the bottle, but it is not full yet. How many liters of
purple sand will she need to use to have the bottle completely full?
Answers
Answer:
0.4 l of purple sand
Step-by-step explanation:
Volume to be filled in:
2 liter = 2000 mlRed sand
1000 mlBlue sand
35 centiliters = 35*10 ml = 350 mlYellow sand
2.5 deciliters = 2.5*100 ml = 250 mlTotal volume filled:
1000 + 350 + 250 = 1600 mlPurple sand needed:
2000 - 1600 = 400 ml = 0.4 lAnswer is 0.4 l of purple sand required
A hubcap has a radius of 14 centimeters. What is the area of the hubcap?asap pls
Answers
Answer:
The area of the hubcap is 196π or 615.7521601
Step-by-step explanation:
You can use A=πr² to find the area of a circle. So that would mean that A equals 14². 14²=196. If the answer is in π form, then the answer is 196π. If not then its 196·π. 196·π=615.7521601
Hope that helps!
Answer:
The area of the hubcap is about 615.44 cm²
Step-by-step explanation:
A = πr²
Use the formula.
A = π(14)²
Substitute. Use 14 for r.
A ≈ 3.14 × 14²
Substitute. Use 3.14 for π.
A ≈ 3.14 × 196 Evaluate the power.
A ≈ 615.44 Multiply.
What is the measure in degrees of angle EDF?
Answers
Answer:
20 degrees.
Step-by-step explanation:
Since these triangles are similar, they will have congruent angles.
Since BAC is corrosponding to EDF, they will have the same angle measurment.
BAC = 20, so EDF = 20
Answer:
EDF = 20
Step-by-step explanation:
If the triangles are similar, the angle measurements have to be equal
<A = <D
<B = <E
<C = <F
Since BAC = 20, <A = 20 that means D = 20
EDF = 20
Enter the mixed number as an improper fraction. 1 5/6 =
Answers
Answer:
11/6
Step-by-step explanation:
To find the improper fraction
Take the denominator times the whole number
6*1 = 6
Add the numerator
6+5 =11
Put this over the denominator
11/6
Answer:
[tex]\frac{11}{6}[/tex]
Step-by-step explanation:
What is 1 5/6 as an improper fraction?
If you wanna make 1 5/6 as a improper fraction, you must take the 5 from 1 5/6 and add it 6.
[tex]6+5=11[/tex]
[tex]\frac{11}{}[/tex]
Since the denominator is 6, you will put it down.
[tex]\frac{11}{6}[/tex]
So now you got your answer!
Hope this Helps!
Evaluate 9/g+2h+5
when g=3 and h=6
Answers
Answer:
20
Step-by-step explanation:
[tex] \frac{9}{g} + 2h + 5 \\ = \frac{9}{3} + 2 \times 6 + 5 \\ = 3 + 12 + 5 \\ = 20[/tex]
What is the equation of the circle with center (–2, 5) that passes through the point (–3, 8)?
Answers
Is the third
Go to my profile and go to the question where it says “what is the simplified expression.....” and please answer I need help!!
Answers
Answer:
Noun. (plural simplified expressions) (mathematics) an expression that has been condensed and shortened, so that all the like terms have been combined.
Step-by-step explanation:
you are welcome!
Answer:
i answered all of them!
Step-by-step explanation:
HELP!!!
Which of the following data sets is illustrated by this stem and leaf plot?
Answers
Answer:
it will be A. good buddy
Step-by-step explanation:
The data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123. The correct option is B.
What is a stemplot?A stem-and-leaf display, also known as a stem-and-leaf plot, is a technique used to visualize the shape of distribution by displaying data in a graphical fashion, similar to a histogram.
The data represented by the different rows of stem-and-leaf display is,
First row → 25, 26, 27
Second row → 53, 58
Third row → 62, 67, 69
Fourth Row → 96, 96
Fifth Row → 123
Hence, the data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123.
Learn more about Stemplot here:
https://brainly.com/question/9125085
#SPJ2
Name a point on the point
Answers
Answer:
B
Step-by-step explanation:
the question is asking to name any point, B is a point that falls on the graph
A scuba diver started her dive at 2{:}42 \text { p.M.}2:42 p.M.2, colon, 42, start text, space, p, point, m, point, end text and finished diving at 3{:}17 \text { p.M.}3:17 p.M.3, colon, 17, start text, space, p, point, m, point, end text How long did the dive last?
Answers
Answer:
35 minutes
Step-by-step explanation:
From 2:42 to 3:00, there are 18 minutes and from 3:00 to 3:17, there are 17 minutes so the answer is 18 + 17 = 35 minutes.
Find the mistake made in the steps to solve the equation below.
61 - 1 = -21 + 9
81 - 1 = 9
80 = 10
1. Addition property of
equality
2. Addition property of equality
3. Division property of equality
to
I
CHA
4. Simplification
OA. The justification for step 2 is incorrect and should be the subtraction property of equality.
OB. Step 3 is incorrect and should be r = 100
OC. Step 2 is incorrect and should be r = 8.
OD. The justification for step 3 is incorrect and should be the multiplication property of equality,
Answers
Answer:
A
Step-by-step explanation:
A
The mistake made in the justification for step 2 is incorrect and should be the subtraction property of equality. which is the correct answer would be an option (A).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question
6x - 1 = -2x + 9
Addition property of equality
8x - 1 = 9
Subtraction property of equality
8x = 10
Division property of equality
x = 10/8
Simplification
x = 5/4
Thus, the mistake made in the justification for step 2 is incorrect and should be the subtraction property of equality.
Hence, the correct answer would be option (A).
Learn more about the equation here:
brainly.com/question/13947055
#SPJ5
Which expression is equivalent to (StartFraction 125 squared Over 125 Superscript four-thirds Baseline EndFraction? StartFraction 1 Over 25 EndFraction One-tenth 10 25
Answers
Answer:
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Step-by-step explanation:
Given
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Required
Find an equivalent expression
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Apply the following law of indices;
[tex]\frac{a^m}{a^n} a^{m-n}[/tex]
The expression becomes
[tex]125^{2-\frac{4}{3}}[/tex]
Solve the exponents
[tex]125^{\frac{6-4}{3}}[/tex]
[tex]125^{\frac{2}{3}}[/tex]
Express 125 as 5³
[tex]5^{3^*\frac{2}{3}}[/tex]
Solve the exponents
[tex]5^2[/tex]
[tex]25[/tex]
Hence;
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Answer:
d
Step-by-step explanation:
i just took it! edgen
f(x) = 7x − 13. Find f−1(x)
Answers
Explanation:
Inverse of f(x) = 7x - 13
f-1(x) = (x + 13)/7
solve 3(5y+2)–y=2(y–3)
Answers
Answer:
y= -1
Step-by-step Explanation:
3(5y +2)-y=2(y-3)
Distribute- 15y +6-y=2y -6
Combine variables- 15y-2y-y=-6-6
Add everything together- 12y= -12
Divide- y= -1
Answer:
y = -1
Step-by-step explanation:
Step 1. Expand the brackets.
3(5y + 2) - y = 2(y - 3)
(3 x 5y) + (3 x 2) - y = (2 x y) - (2 x 3)
15y + 6 - y = 2y - 6
Step 2. Simplify the expanded brackets (not always necessary but is in this case).
15y + 6 - y = 15y - y + 6 = 14y + 6
So
14y + 6 = 2y - 6
Step 3. Solve the equation.
14y + 6 = 2y - 6
+ 6 to both sides
14y + 12 = 2y
- 14y from both sides
12 = -12y
÷ 12 on both sides
1 = -y
flip the negative
-1 = y
Step 3. Write your answer.
y = -1
Help me please. I don't understand.
Answers
Answer:
what is it
Step-by-step explanation:
Simplify the expression: (5 - 4i) (6 - 2i).
Answers
Answer:
22 - 34i
Step-by-step explanation:
note that i² = - 1
Given
(5 - 4i)(6 - 2i) ← expand factors using FOIL
= 30 - 10i - 24i + 8i²
= 30 - 10i - 24i - 8 ← collect like terms
22 - 34i
Answer:
22 - 34i
Step-by-step explanation:
Q2) If z is directly proportional to x and z = 12 when x = 3, find the value of x when z = 18.
Answers
Answer:
4.5
Step-by-step explanation:
→ Set up the direct proportion equation
z = kx
→ Substitute in the values
12 = 3k
→ Divide both sides by 3 to isolate k
4 = k
→ Substitute the value of k back into the original direct proportion equation
z = 4x
→ Substitute the value of z in
18 = 4x
→ Divide both sides by 4 to isolate x
4.5 = x
Answer:
4.5
Step-by-step explanation:
(a+3) (a-3)find the products
Answers
Answer:
a^2-9
Step-by-step explanation: