Solve the following problems: Given: ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° Find: Area of ∆AFD
Answers
We have the triangle 30° - 60° - 90°.
The sides are in proportion: 2 : √3 : 1
(look at the picture).
[tex]2a=14[/tex] divide both sides by 2
[tex]a=7[/tex]
[tex]a\sqrt3=7\sqrt3[/tex]
The area of a trinagle AFD:
[tex]A_{\Delta}=\dfrac{1}{2}(7)(7\sqrt3)=\boxed{\dfrac{49\sqrt3}{2}}[/tex]
Related Questions
if you know 72=9×8,then _is_times as many as_
Answers
Answer:
72 is 8 times as many as 9
Step-by-step explanation:
72 is the product of 8 groups of nine
72 is 9 times as many as 8 is the answer that completes the statement.
To solve the equation 72 = q × 8, we need to find the value of q.
By dividing both sides by 8, we get:
72/8 = q × 8/8
q = 72/8
q = 9.
This means that 72 is 9 times greater than 8 and to correctly complete the statement, we write: 72 is 9 times as many as 8.
what is equivalent to the expression 4 / -3 to the square root of 64
Answers
[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\dfrac{4}{-3\sqrt{64}}=\dfrac{\not4^1}{-3(\not8_2)}=-\dfrac{1}{6}[/tex]
Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while checking account B has monthly fee of $14 and a per-check fee of $0.12. She want to know how many checks she would need to write per month for the accounts to charge the same amount in fees.
Part 1: If x represents the number of checks Cecily writes per month, what expression represents the monthly fee in dollars charged by checking account A?
Part 2: What equation can be set up to solve for the number of checks Cecily would need to write per month for the accounts to charge the same in fees?
Answers
Answer:
Total charge per month = $ 16 + (0.08) * x
equation for having same charge
0.08 x - 0.12 y = 8
Step-by-step explanation:
Part 1:
Monthly fee = $ 16
Per check fee = $ 0.08
Checks signed in month = x
Total Charge monthly = Monthly fee + Checks fee
Putting the values
Total charge per month = 16 + (0.08) * x ...........(i)
Part 2: Let she signs y checks for account B
Monthly fee of B = $ 14
per check fee = @ 0.12
Total Charge = monthly fee + checks fee
= $ 14 + y *(0.12) ..................(ii)
For having same value in the bank then equation (i) and (ii) shuld be equal to each other
i.e.
16 + 0.08x = 24 + 0.12y
0.08 x - 0.12 y = 24-16
0.08 x - 0.12 y = 8
this will be the equation
Taylor saw an American alligator at a zoo that measures 12 11/12 feet long the record length of an American alligator is 19 1/6 feet long how much longer is the record alligator than the American alligator Taylor saw?
Answers
To find out how much longer the record alligator is than the one Taylor saw, we subtract the length of the alligator Taylor saw from the record length. The record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.
Explanation:To find out how much longer the record alligator is than the one Taylor saw, we need to subtract the length of the alligator Taylor saw from the record length.
To do this, we need to convert the mixed numbers to improper fractions. 12 11/12 is equal to 155/12 and 19 1/6 is equal to 115/6.
Subtracting 155/12 from 115/6 gives us (115/6) - (155/12) = (230/12) - (155/12) = 75/12 = 6 3/4.
Therefore, the record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.
answer please as best as you can
Answers
The volume of a larger cone:
[tex]V_l=\dfrac{1}{3}\pi\cdot4.5^2\cdot(3+6)=\dfrac{1}{\not3_1}\pi\cdot20.25\cdot\not9^3=(20.25)(3)\pi=60.25\pi\ cm^3[/tex]
The volume of a smaller cone:
[tex]V_s=\dfrac{1}{3}\pi\cdot3^2\cdot6=\dfrac{1}{\not3_1}\pi\cdot\not3^1\cdot3\cdot6=18\pi\ cm^3[/tex]
The volume of the frustum:
[tex]V=V_l-V_s\\\\V=60.25\pi-18\pi=42.75\pi\ cm^3[/tex]
Answer: 42.75π cm³.I am a number between 80 and 100 my ones digit is two less than my tens digit I am a prime number what number am I
Answers
The number you are looking for is 89.
Explanation:The number you are looking for is 89.
Here is how we can find it:
Since the number is between 80 and 100, we know it must have a tens digit of 8. The ones digit is two less than the tens digit, so it would be 6. Now we have the number 86, but we need to check if it is a prime number. A prime number is a number that is only divisible by 1 and itself. We can check if 86 is divisible by any number less than itself.Since we can divide 86 by 2 and get 43, it is not a prime number.Therefore, we have to keep increasing the ones digit by 1 until we find a prime number.The next number is 87, but it is divisible by both 3 and 29. Finally, we arrive at 89, which is only divisible by 1 and itself, making it a prime number.Learn more about Prime numbers here:https://brainly.com/question/35915729
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Lee bought a couch for $600. He made equal payments of 10% of the total cost. How much was each payment?
$6
$10
$60
$100
Answers
Answer:
$60
Step-by-step explanation:
Each payment was 10% of $600.
You need to find what 10% of $600 is.
To find a percent of a number, multiply the percent by the number. Change the percent to a decimal by moving the decimal point of the percent two places to the left.
10% of $600 =
= 10% * $600
= 0.10 * $600
= $60
Answer:
60
Step-by-step explanation:
600 * .10= 60
the sides of a triangle are 12,15, and 20. if the shortest side of a familiar triangle is 3, what is the longest side of the triangle?
Answers
Answer: Let x=length of the longest side of the smaller triangle.
x/20=3/12
x=60/12
x=5
Final answer:
To find the longest side of the similar triangle, multiply the longest side of the original triangle (20) by the scale factor, which is the ratio of the shortest sides (3/12 = 0.25). This results in a longest side of 5 units for the similar triangle.
Explanation:
The question pertains to finding the longest side of a similar triangle given that the shortest side is 3 and the original triangle has sides 12, 15, and 20. To find the answer, we need to calculate the scale factor between the similar triangles. The scale factor is obtained by dividing the shortest side of the new triangle (3) by the shortest side of the original triangle (12), which is ¼ or 0.25.
We then multiply the longest side of the original triangle (20) by the scale factor (0.25) to get the longest side of the similar triangle. Calculating, 20 * 0.25 = 5. Therefore, the longest side of the triangle with the shortest side 3 is 5 units long.
Functions and graphs
Answers
Answer:
f(x) = -8 x + 34
Step-by-step explanation:
First, normalize the equation 8y = x-16 into y = ... form (divide by 8):
y = 1/8 x - 2
So the slope of this line is 1/8. The slope of a perpendicular line is the negative reciprocal, which means you swap numerator and denominator and add a minus sign. So the slope of our line is -8 and our function will look like f(x) = -8x + b
Now all we have to do is find b such that f(x) goes through (5,-6).
So f(5) = -8*5 + b = -6, and solve it for b:
-40 + b = -6 =>
b = 34.
So f(x) = -8x + 34
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}.\\\\\text{We have}\ 8y=x-16\qquad\text{divide both sides by 8}\\\\y=\dfrac{1}{8}x-2\to m_1=\dfrac{1}{8}.\\\\\text{Let}\ y=mx+b.\ \text{It's perpendicular to given line. Therefore}\ m=-\dfrac{1}{\frac{1}{8}}=-8.\\\\y=-8x+b.\\\\\text{The line passes through point (5, -6)}.\ \text{Put the coordinates of the point}\\\text{to the equation of a line:}[/tex]
[tex]-6=-8(5)+b\\-6=-40+b\qquad\text{add 40 to both sides}\\34=b\to b=34\\\\Answer:\ \boxed{f(x)=-8x+34}[/tex]
You will be Brainiest Answered if answered.
Thanx
Answers
Answer:
9R30
Step-by-step explanation:
9
36)354
324
30
use the elimination method to solve the system of equations. Choose the correct ordered pair.
2y=x+2
x-3y=-5
Answers
The concept of solving a problem by elimination is to solve for one variable, by getting rid of the other.
Let's solve [2y = x + 2, x - 3y = -5] in terms of y.
Start by transforming the second equation into one of the same form as the first (y = x + c).
x-3y = -5
x = -5 + 3y
3y = x+5
Now we have two equations that are in the same form:
3y = x+5
2y = x+2
To solve in terms of y, we need to get rid of x -- so subtract the first equation from the second equation - this will yield the following:
y = 3 [[ 3y - 2y = y, x - x = 0, 5 - 2 = 3 ]]
Now take this information and solve for x:
2(3) = x+2
6 = x+2
x = 4
Now we have the solution, just make it a coordinate point:
(4, 3)
Answer:
Apex Answer (4,3)
Step-by-step explanation:
Just did the apex quiz yall add me julius_rob
What is the algebraic expression of 4n+3=11
Answers
Answer:
n=2
Step-by-step explanation:
I am assuming that you want to solve this algebraic equation
4n+3 =11
Subtract 3 from both sides
4n+3-3=11-3
4n =8
Divide each side by 4
4n/4 = 8/4
n =2
solve the system by substitution 2x+y=10 x-3y=-2 state whether the system had one solution infinite solutions or no solution
Answers
Answer:
System has only one solution. x= 4 and y = 2.
Step-by-step explanation:
We have given two equations :
2x + y = 10 ----------(1)
x - 3y = -2 ----------(2)
From equation (2), we can write:
x - 3y = -2
or x = -2 + 3y , substitute this in equation (1).
We get, 2x + y = 10
2*(-2 + 3y) + y = 10
-4 + 6y + y = 10
7y = 10 + 4
y = 14/7 = 2
And x = -2 + 3*2 = -2 + 6 = 4
Hence we get x= 4 and y = 2. System has only one solution
The system of equations 2x+y=10 and x-3y=-2 has one solution, which is found by solving for y in terms of x using the first equation, substituting into the second equation, and solving for x, then solving for y. The solution is (4, 2).
To solve the system by substitution, we can express one variable in terms of the other using one of the equations and then substitute this into the second equation. Starting with the system:
2x + y = 10
x - 3y = -2
We can solve the first equation for y:
y = 10 - 2x
Next, we substitute this expression for y into the second equation:
x - 3(10 - 2x) = -2
Solving this equation for x:
x - 30 + 6x = -2
7x = 28
x = 4
Now we substitute x = 4 back into the equation y = 10 - 2x to find y:
y = 10 - 2(4)
y = 2
So the one solution to the system is (4, 2).
Since we found a unique solution, the system of equations has exactly one solution and is therefore consistent and independent.
That u have to find the distance between the pair of points
Answers
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (1, 3) and (3, 1). Substitute:
[tex]d=\sqrt{(3-1)^2+(1-3)^2}=\sqrt{2^2+(-2)^2}=\sqrt{4+4}=\sqrt8\approx2.8[/tex]
Answer: C. 2.8Someone please help me solve this
Answers
Answer:
First, you have to get all of the variables on one side of the equation.
x15 on both sides
8 + a = 15+15a/6
x6 on both sides
48 + 6a=15+15a
Subtract 15 on both sides and Subtract 6a on both sides
33=11a
a=3
Step-by-step explanation:
isabell is mixing red paint with blue paint to make purple paint.she adds 3/10 of a fluid ounce of red to 11/15 of a fluid ounce of blue to make 1 1/30 fluid ounces of blue to make 1 1/30 of purple.how many fluid ounces of red will she need to make 3 fluid ounces of purple paint
Answers
Answer:
We will need 27/31 of an ounce of red
Step-by-step explanation:
3 /10 red + 11 /15 blue makes 1 1/30 purple
Get a common denominator of 30
3/10 * 3/3 = 9/30 red
11/15 *2/2 = 22/ 30 blue
1 1/30 = 31/30 purple
So the ratio of red to purple is
9/30
-------- = 9/ 31
31/30
Keeping this ratio, we want 3 ounces purple
9 red x red
-------- = --------------
31 purple 3 purple
Using cross products,
9*3 = 31 *x
27 = 31x
Divide each side by 31
27/31 = x
We will need 27/31 of an ounce of red
Della by tree seedling that was 2 1/4 feet tall during the first year it grew 1 1/6 ft after two years it was 5 ft tall how much did the seedling grow during the second year
Answers
Answer:
[tex]\frac{19}{12}[/tex] feet
Step-by-step explanation:
First, we need to find the height after one year:
2.25 + 1 1/6 = [tex]\frac{41}{12}[/tex]
Now to find the amount in the second year, we can subtract the above amount from 5:
5 - [tex]\frac{41}{12}[/tex] = [tex]\frac{19}{12}[/tex]
So in the second year it grew [tex]\frac{19}{12}[/tex] feet
Hope this helps!
Caleb has 1/3 of a watermelon. He cuts it into 4 equal pieces. What fraction of the watermelon is each piece
Answers
Answer:
1/12 of the watermelon in each piece
Step-by-step explanation:
We must divide 1/3 by 4.1/3 divided by 4 is also 1/3 x 1/4.The final answer is 1/12.
I hope this helped!
Answer:
The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Caleb has [tex]\frac{1}{3}[/tex] of a watermelon. To know what fraction each portion of watermelon represents after cutting it into 4 equal parts, just divide the portion that Caleb owns ([tex]\frac{1}{3}[/tex]) by the amount of sliced portions (4):
[tex]\frac{\frac{1}{3} }{4}[/tex]
Given that 4 can also be represented by the fraction [tex]\frac{4}{1}[/tex], then:
[tex]\frac{\frac{1}{3} }{\frac{4}{1} }[/tex]
To divide two fractions, the SECOND FRACTION must be reversed, that is, change the denominator to the numerator and change the numerator to the denominator. Then, the two fractions are multiplied.
[tex]\frac{\frac{1}{3} }{\frac{4}{1} } =\frac{1}{3} *\frac{1}{4} =\frac{1}{12}[/tex]
The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]
Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies. Nonmembers pay $3 for new release movies. Write a system of linear equations that represents this situation
Answers
Answer:
The system of linear equations are
y = 15 + 2x
y = 3x
Step-by-step explanation:
Let us assume that the number of new release movies be x.
Let us assume that the total cost be y.
As given
Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies.
Than the equation becomes
y = 15 + 2x
As given
Nonmembers pay $3 for new release movies.
y = 3x
Therefore the system of linear equations are
y = 15 + 2x
y = 3x
Simplify the expression left parenthesis (3/5)2
Answers
Answer:
9/25
Step-by-step explanation:
The answer is 9/25
What is the coefficient of q in the sum of these two expressions? (23q – 34) and (–16q – r) NEED HELPPP
Answers
The coefficient of q in the sum of (23q - 34) and (-16q - r) is 7.
Explanation:In mathematics, a coefficient is a numerical factor or constant that multiplies a variable or term in an algebraic expression. It determines the scale or magnitude of the term and is often used in equations, polynomials, and linear expressions.
The sum of the two expressions is (23q - 34) + (-16q - r).
To find the coefficient of q in this sum, we need to combine the like terms.
Combining the q terms, we have 23q - 16q = 7q.
Therefore, the coefficient of q in the sum of the two expressions is 7.
You had 15 text messages, deleted 2 then got 5 more, you responded to 4,
and whats your total? a, b, or c?
A. 12
B. 14
C. 18
Answers
Answer: The answer is C
Step-by-step explanation: 15 - 2 = 13 13+5=18
Hope this helps :)
Dr. Peterson works about 178 hours each month. Which of the following is the best estimate of the number of hours she works in a year?
Answers
Answer:
Option B.
Step-by-step explanation:
Dr. Peterson works about 178 hours each month.
There are 12 months in one year.
So Dr. Peterson works in a year = 178 × 12 = 2,136 hours
We will go through all the options to find which is the closest to the answer.
Option A : 200 × 20 = 4,000 hours
Option B : 180 × 10 = 1,800 hours
Option C : 100 × 12 = 1,200 hours
Option D : 100 × 10 = 1,000 hours
Therefore, Option B is the best estimate of the number of the hours she works in a year.
325 Students and adult Will be riding the buses .Each buses hold 48 people.how many buses are needed .
Answers
7 busses
Answer:
7 buses are needed.
Step-by-step explanation:
There are 325 students and adults.
Each bus holds 48 people.
The number of buses needed = [tex]\frac{325}{48}[/tex] = 6.770833333
Since we cant have 0.770833333 buses, we accept that only 7 buses are needed here and that;
325 - (48 × 6) = 37 people will not fill the last bus.
double d, then divide 9 by the result
Answers
Divide 9 by the result (2d): 9/2d
Answer: 9/2d (with 2d in the Denominator)
Perform the indicated operation. 4/11÷ 4/9
Answers
The answer you are looking for is 9/11.
When dividing fractions, you multiply the first value by the inverse of the second value. The inverse is found by simply flipping the numbers of the last fraction. So, the inverse is 9/4. Then, multiply 4/11 and 9/4 to get 36/44. 36/44 simplified (divided by 4/4) is 9/11. Thus making 9/11 the answer.
I hope this helps.
Answer:
9/11
Step-by-step explanation:
What is y=-2/3x written in standard form?
Answers
Answer:2x−3y=6
Step-by-step explanation:Standard form: Ax + By = C
Just take 2/3x to the other side.
So the answer would be
−23x+y=−2
In standard form
x
can't be negative and A, B and C need to be an integers (whole numbers)
(I multiplied the whole equation by -3)
2x−3y=6
So the final answer would be: 2x−3y=6
Triangles △ABC and △DEF are similar. Find the angles of these triangles if
m∠A=100°, m∠B=30°.
Answers
Answer:
angle A and angle D equals 100 degrees, angle B and angle E equals 30 degrees, and angle C and angle F equal 50 degrees.
Step-by-step explanation:
a triangle has to equal 180 degrees, and since they are similar, it should equal the same. Hope this helped you. :))
The angles of triangles △ABC and △DEF, which are similar, are 100°, 30°, and 50°. This is calculated using the properties of similar geometry and the fact that the sum of all angles in a triangle equals 180°.
In Triangle Similarity, the corresponding angles are equal due to the property of similarity in geometry.
Since we know that △ABC and △DEF are similar and we have m∠A=100° and m∠B=30°, we can determine that angles A and B in triangle △DEF are also 100° and 30°, respectively.
The third angle in both triangles can be calculated using the property that the sum of all angles in a triangle equals 180°.
Hence, in △DEF and △ABC we can calculate the measure of the third angle by 180° - (100°+30°) = 50°.
So for triangles △ABC and △DEF, the angles are 100°, 30° and 50° respectively.
Learn more about Triangle Similarity here:
https://brainly.com/question/14926756
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What is the vertex form of the quadratic y = 3x^2 + 18x - 4?
Answers
Answer:
y = 3(x + 3)² - 31
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h. k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
take out a common factor of 3 from the first 2 terms
y = 3(x² + 6x) - 4
add/subtract ( half the coefficient of the x-term)² to x² + 6x
y = 3(x² + 2(3)x + 9 - 9 ) - 4
y = 3(x + 3)² - 27 - 4
y = 3(x + 3)² - 31 ← in vertex form
What is the surface area, in square inches, of a sphere with a diameter of 8 in.? and round to the nearest whole number. Enter only the number.
Answers
Answer:
SA = 201 in^2
Step-by-step explanation:
The formula for surface area of a sphere is
SA = 4pi r^2
We know that the diameter is 8
To find the radius we cut the diameter in half.
r = d/2
r = 8/2 =4
Substitute in what we know.
SA = 4 *pi *4^2
= 4*pi*16
= 64*pi
Letting pi = 3.14
= 200.96 in^2
We want to round to the nearest whole number
SA = 201 in^2