Answers
Answer:
DC = 39
Step-by-step explanation:
From inspection of the diagram:
EA is tangent to both circlesDE is the radius of circle DCA is the radius of circle CThe tangent of a circle is always perpendicular to the radius, therefore:
DE ⊥ EA and CA ⊥ EA
As ∠DEB and ∠BAC are both 90°, then DE is parallel to CA.
Therefore, ∠DBE and ∠ABC are vertically opposite angles, and are therefore equal.
As triangles ΔBED and ΔBAC have two pairs of corresponding congruent angles, the triangles are similar.
Therefore:
[tex]\implies \sf \dfrac{DE}{CA}=\dfrac{EB}{BA}[/tex]
[tex]\implies \sf \dfrac{10}{5}=\dfrac{24}{BA}[/tex]
[tex]\implies \sf BA=12[/tex]
Using Pythagoras' Theorem for ΔBED to find DB:
[tex]\implies \sf DE^2+EB^2=DB^2[/tex]
[tex]\implies \sf 10^2+24^2=DB^2[/tex]
[tex]\implies \sf DB^2=676[/tex]
[tex]\implies \sf DB=\sqrt{676}[/tex]
[tex]\implies \sf DB=26[/tex]
Using Pythagoras' Theorem for ΔBAC to find BC:
[tex]\implies \sf CA^2+BA^2=BC^2[/tex]
[tex]\implies \sf 5^2+12^2=BC^2[/tex]
[tex]\implies \sf BC^2=169[/tex]
[tex]\implies \sf BC=\sqrt{169}[/tex]
[tex]\implies \sf BC=13[/tex]
Therefore, the distance between the center of the circles DC is:
[tex]\begin{aligned} \implies \sf DC & = \sf DB + BC\\& = \sf 26 + 13\\& = \sf 39\end{aligned}[/tex]
Use Pythagorean theorem
DB²=DE²+EB²DB²=10²+24²DB²=100+576DB²=676DB=26Now use proportion
DE/DB=AC/BC10/26=5/BC5/13=5/BCBC=13Now
DC=DB+BC=26+13=39
Related Questions
Simplify the given polynomial expressions as much as possible
(12a2 + 6a - 8) + (-22a2 + 12 - 15a)
Answers
Answer:
- 10a² + a + 4
Step-by-step explanation:
( 12a² + 6a - 8 ) + ( - 22a² + 12 - 5a )
= 12a² + 6a - 8 - 22a² + 12 - 5a
= 12a² - 22a² + 6a - 5a + 12 - 8
= - 10a² + a + 4
Answer:
Step-by-step explanation:
Remark
There is an isolated plus sign in the middle so removing the brackets is going to allow you to collect like terms quickly and immediately.
Solution
12a^2 + 6a - 8 - 22a^2+ 12 - 15a Group like terms together in pairs.
12a^2- 22a^2 + 6a - 15a - 8 + 12 Combine like terms.
Answer
-10a^2 - 9a + 4
Scott received a score of 91, 85, and 89 on three tests. What score must Scott get on the fourth test to have an overall average score of 90
Answers
Answer:
95
Step-by-step explanation:
So if you wanted to figure the average of the 3 tests, you would add 91+85+89 to get 265 & then divide by 3 tests to get an average of 88.
So that means for four tests, 91+85+89+4th test = answer that divided by 4 tests will equal 90. 90 x 4 = 360. Then 360 -265 (sum for 1st 3 tests) = 95
A shipping box has a width of 6 inches, a length of 10 inches, and a height of 7 inches. What is the volume of the shipping box?
Answers
Answer:
V = 420 in^3
Step-by-step explanation:
Formula
The volume of a 3 dimensional box is V = L * w * h
Givens
L = 10 in
w = 6 in
h = 7 in
V = ?
Solution
Substitute the givens into the formula
V = 10 * 6 * 7 Combine
V = 420 in^3
Please help me solve this as soon as possible!
Answers
66 ☁️
What is the area of a parallelogram with a base of 26 m and a height of 18 m?
Answers
Answer:
468 m²
Step-by-step explanation:
Given:
→ Base = 26 m
→ Height = 18 m
Formula:
[tex]\text{Area of parallelogram: Base} \times \text{Height}[/tex]
To determine the area of the parallelogram, we need to substitute the base and the height in the formula.
Substitute the measures in the formula:
[tex]\implies \text{Area of parallelogram: Base} \times \text{Height}[/tex]
[tex]\implies \text{Area of parallelogram} = 26 \times 18[/tex]
Evaluate the area of the parallelogram:
[tex]\implies \text{Area of parallelogram} = 26 \times 18[/tex]
[tex]\implies \text{Area of parallelogram}= \bold{468 \ \text{m}^{2}}[/tex]
Answer:
468 m²
Step-by-step explanation:
Given,
Base ( b ) = 26 m
Height ( h ) = 18 m
To find : The area of parallelogram
Formula : -
Area of parallelogram = bh
Area of paralleogram
= 26 x 18
= 468 m²
Therefore,
the area of the parallelogram is 468 m².
please find the area of the shaded region
Answers
Answer:
Step-by-step explanation:
Remark
The way to solve the shaded region is to find the area of the square first and subtract the area of the circle from it.
Area of the square
Area = s^2
s = 12
Area of the square = 12 * 12
Area of the square = 144 yd^2
Area of the circle = pi * r^2
r = d/2
d is actually the same as the side length of the square
r = 12/2
r = 6
pi = 3.14
Area of the circle = pi * 6^2
Area of the circle = 3.14 * 36
Area of the circle = 113.04
Area of the shaded region
Area of shaded region = area of the square - area of circle
Area of shaded region = 144 - 113.04
Answer: Area of the shaded region 30.96
The figure below represents a top view of Johns patio. What is the value of X?
Answers
Answer:
The value of x = 110°
Step-by-step explanation:
=> x° + 90° + 90° + 70° = 360 ° { sum of angles of a quadrilateral is 360 }
=> x + 250° = 360°
=> x = 360 - 250
=> x = 110°
What type of triangle is defined by the following set of side lengths
10, 9, 5
Question 3 options:
Acute
Obtuse
Right
Not a triangle
Answers
Answer:
the answer is acute according to this triangle calculator
What is the slope of the line that contains the points (-1, 2) and (3, 3)?
Answers
Answer:
[tex]\text Slope = \frac{1}{4}[/tex]
Step-by-step explanation:
the slope of the line that passes through the points
[tex]\large A\left( x_{1},y_{1}\right) \text{and} \ B\left( x_{2},y_{2}\right)[/tex]
[tex]\large \text{slope} =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
the slope of the line that contains the points (-1, 2) and (3, 3) is :
[tex]\Longrightarrow \text{slope} =\frac{3-2}{3-\left( -1\right) }= \frac{1}{4}[/tex]
Rasheed has tan pants, black pants, gray pants, and blue pants. He has a brown sweater and a white sweater. How many different ways can he wear a sweater and pants together
Answers
Answer:
Step-by-step explanation:
There are 4 different colors of pants.
There are 2 sweaters.
The total number of ways of making a particular pair of pants and a sweater = 4 * 2 = 8
Answer: there are 8 combinations of clothing
Chloe looked at the data below and said, "The median is 37." Which answer points out Chloe's
mistake?
38, 42, 51, 55, 37, 57, 34, 44, 56
A. Chloe should have added the numbers and divided by 9.
The median is 46.
B. Chloe did not make a mistake; the median is 37.
C. Chloe forgot to arrange the numbers in ascending order. The median is 44.
D. The median is the number which appears the most; there is no median.
Answers
Answer:
C. Chloe forgot to arrange the numbers in ascending order. The median is 44.
Step-by-step explanation:
We arrange the 9 numbers of the data from the least to the greatest
Then we spot the middle number (5th number) which is 44:
34 < 37 < 38 < 42 < 44 < 51 < 55 < 56 < 57
Multiply: (x−3)(x 4) simplify and write your answer in standard form. hint standard form: ax2 bx c
Answers
x^5-3x^4
both simplified and in standard form
The record low temperature in Fargo, ND is -37°F. The record high is 109°F. What is the difference in the record high and the record low temperatures?
Answers
Answer:
109 - -37 = 146
Step-by-step explanation:
Answer:
146
Step-by-step explanation:
Find the area of the shaded region. (Blue is the shaded region)
Answers
Answer:
135ft^2
Step-by-step explanation:
area of trapzoid= (a+b)/(2)×h
area of traingle= 1/2(b)(h)
area of the shaded region equals (a+b)/(2)×h-1/2(b)(h)
so
(8+18)/(2)×15-(1/2)(8)(15)
=135ft^2
33 pounds of dog food for $45 how much is it per pound
Answers
Answer:
1 pound = .73 dollars rounded.
Step-by-step explanation:
This is like a rate question. Speed is in miles / hour only the units for this question is pound / dollar.
pounds = 33
dollars = 45
1 pound is 33/45
1 pound = 0.73
The value of a company equipment is $25000 and decreases at a rate of 15% per year. What is the value of the equipment after 8 years.
Answers
Answer: $6812.3
Step-by-step explanation: Just solve decreasing 15% each year
Multiply (-x^2 + 2x + 4) (x-3)
Answers
Answer:
−x^3+5x^2-2x−12
Step-by-step explanation:
-x*3+2x*2+4x+3x*2-6x-12
-x*3+5x*2-2x-12
Which equation represents the Temperture, t, at hour h?
Answers
4 . 7 p - 10 p =
Answer please !! Wrong answer will get you reported !
Answers
-3p
Step by step explanation:
It’s basically a subtraction so 7-10=-3 and it’s the same as 7p-10p=-3p
Hey there!
4 * 7p - 10p
= 4(7p - 10p)
= 4(7p) + 4(-10p)
= 28p - 40p
= -12p
Therefore, your answer is: -12p
Good luck on your assignment & enjoy day!
~Amphitrite1040:)
3) Solve 5(x + 3) - 3x = 55 for x. Use mathematical properties to justify each step in the process.
Step 1
Step 2
Step 3
Step 4
Step 5
Answers
solution
5(x+3)-3x=55
5x+15-3x=555x-3x+15=552x+15=552x=55-152x=402x/2=40/2x=20due today need help pls
Answers
Answer:
I beleive that the systems of transformation are that
Figure JKLM to Figure J' K' L' M' is a Rotation
Figure J' K' L' M' to Figure J" K" L" M" is a Dilation
Step-by-step explanation:
Sonia will go on a 9-day vacation with his grandparents. He will take $57 of his
own money. His grandparents will give him another $78. Sonia will spend all
of the money and he will spend the same amount each day. How many dollars
will Sonia spend each day of the vacation?
Answers
Answer:
$15
Step-by-step explanation:
Sonia will take $57, and his grandparents will give another $78. 57 + 78 = 135. Sonia will have 135 dollars, but it is a 9 day vacation, so 135/9 = 15
Sonia will spend 15 dollars a day.
Do number 7 pleaseeee
Answers
Answer:
it says percentage increase so you do...
Step-by-step explanation:
106 divide by 100=1.06
then the answer multiply by 1.50=1.59
What is the solution of startroot x 12 endroot = x? x = –3 x = 4 x = –3 or x = 4 no solution
Answers
An equation is formed of two equal expressions. The solution of the equation √(x+12)=x is x=4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation √(x+12)=x can be done as,
[tex]\sqrt{x+12} = x\\\\\text{Square both the sides of the equation}\\\\x+12=x^2\\\\x^2-x-12=0\\\\x^2-4x+3x-12=0\\\\x(x-4)+3(x-4)=0\\\\(x-4)(x+3)=0[/tex]
Equate each of the factors with 0,
[tex](x-4)=0\\x=4\\\\(x+3)=0\\x=-3[/tex]
Now, if we substitute the value of x in the equation given, only the value of x as 4 will satisfy the equation.
Thus, the solution of the equation √(x+12)=x is x=4.
Learn more about Equation:
https://brainly.com/question/2263981
Pls help NEED BY 9:07
30 POINTS
Answers
a, Joseph got better gas mileage
Take gallon and
Divide by miles,
Pls answer and show me how u got answer
Answers
Answer:
B which is 2/4.
Step-by-step explanation:
Elin: worked for 2/4 + 1/4 = 3/4 of an hour on an assignment
Jocyln worked for 5/4 of an hour the same assignment
The difference in time is 5/4 - 3/4 = 2/4 or 1/2 hour.
Note: when you subtract fractions, the denominators must be the same. What you subtract is the numerators (top part of the fraction).
NEED DONE ASAP. what is 6x3
Answers
Answer:18
Step-by-step explanation: pretty much 6 plus 6 plus 6 you add six 3 times.
State if the three
numbers below can be
the measure of the sides
of a triangle.
3, 10, 7
Answers
These Numbers CAN make a Triangle.
3 + 7 = 10 and the third number is equal.
Therefore these measurement can make a triangle.
Hope this helps!!
Carlos says that 17.43 divided by 100 is the same as 174.3 times 0.01. Is he correct?
Answers
Answer:
that's not correct.
17.43/100= 0.1743
174.3×0.01=1.743
One angle of a triangle measures 20°the other two angles are in a ratio of 3:5. What are the measures of those two angles?
Answers
Answer:
180-20 = 160 = sum of the other two angles
3/(3+5) = 3/8 x 160 = 60 degrees
5/(3+5) = 5/8 x 160 = 100 degrees
or in radians the other two angles are pi/3 and 5pi/9
Step-by-step explanation:
THIS ANSWER IS CORRECT
BRAIN LESS ANSWER