Answers
=======================================================
Work Shown:
We use the intersecting chords theorem
(AH)*(HG) = (FH)*(HB)
(x-2)*(x+7) = (2x-1)*(4)
x*(x+7) - 2(x+7) = 4(2x-1)
x^2+7x - 2x - 14 = 8x - 4
x^2 + 7x - 2x - 14 - 8x + 4 = 0
x^2 - 3x - 10 = 0
(x - 5)(x + 2) = 0
x-5 = 0 or x+2 = 0
x = 5 or x = -2
If x = -2, then AH = x-2 = -2-2 = -4, but having a negative segment length is not possible. Lengths must be positive. So we ignore x = -2
If x = 5, then we find the following lengths
AH = x-2 = 5-2 = 3HG = x+7 = 5+7 = 12FH = 2x-1 = 2*5-1 = 9Then note how AH*HG = 3*12 = 36 while FH*HB = 9*4 = 36. This confirms that (AH)*(HG) = (FH)*(HB) is a true equation and confirms we have the correct x value.
Related Questions
$6,000 at 6%
for 8 years
What is the amount of interest earned
Answers
Answer:
13,243
Step-by-step explanation:
hope this helps
i am bad at math
Jorge has some dimes and quarters. He has 10 more dimes than quarters and the collection of coins is worth $2.40. How many dimes and quarters does Jorge have?
Answers
Answer:
14 dimes and 4 quarters
Step-by-step explanation:
x= number of dimes
y=number of quarters
x-10=y
0.10x+0.25y=2.40
substitute for y
0.10x+0.25(x-10)=2.40
0.35x-2.50=2.40
0.35x=4.90
x=14
y=4
Solve for x in the triangle,round your answer to the nearest tenth
Answers
cos (49)= x/27
27 * cos(49) = x
27 * 0.656 = x
x = 17.7
What is OB'?
1.5 units
3 units
4.5 units
6 units
Answers
Answer: it's b on edge
Step-by-step explanation:
Can someone help me please
Answers
1, 2, 3 have the same solution
May Nilbin Be With You
When a teacher counted her students in groups of 4, there were two students left over. When she counted them in groups of 5, she had 1 student left over. If 15 of her students were girls and she had more girls than boys, how many students did she have?
Answers
Number of students in class = x students
X is two more than a multiple of 4
So x is an even number because multiples of 4 are even & adding 2 would mean it’s still equal
X is 1 more than a multiple of 5. We know x is an even number. It has to be a multiple of 5 ending in 5 not 0
5 + 1 = 6
All multiples of 4 ending in 6 are 16, 36, 56...
Since there are 15 girls and there are less boys than girls
16 - 15 = 1
Therefore there’s 16 students
Can You please help me
Answers
9514 1404 393
Answer:
S > 2
Step-by-step explanation:
In this context, "over" means "greater than." The problem statement tells you the weight (S) is greater than 2 kilograms:
S > 2
How many ways are there to add three positive even numbers to get a sum of 20? Solve this
problem by making a systematic list, then state your solution.
Help!!!!! can you show your work too thanks
Answers
Answer:
no entender veri mucho......aaaa
Steve manages a skate park and he has been analyzing the attendance data. Steve finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 5x. Steve also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by f(x) = −x + 6. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents. (10 points)
Answers
Answer:
(1, 5)Step-by-step explanation:
Both of the graphs include infinite number of points.
The solution is the common point that belongs to both of the graphs, the intersection point.
We can see it is the point (1, 5)
This is the point when the temperature change is positive 1 degree. At this point number of visitors is equal to number of those leaving the part early.
Recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length. The length of a rectangle is 2 times the width. If the area is 392 square feet, then what is the length of the rectangle, in feet?
Answers
Answer:
7.7
Step-by-step explanation:
I did it on edu!
You can use the fact that area of a rectangle is its length times its width.
The length of the given rectangle is 28 feet.
What is the area of a rectangle?Area of a rectangle is its length times its width.
If a rectangle has length x units and width y units, then we have:
[tex]Area = x \times y \: \rm unit^2[/tex]
How to calculate the values of items which are not known?Most of the times, you will get some other facts or information by which the unknown values of those items can be known. For simple daily life cases, we can use variables, which are nothing but just placeholders for those unknown values. We can then operate on those variables assuming them to be actual values, thus, getting near to their original values.
Using above method for getting the length of the rectangleLet the length of the given rectangle be x units, and let its width be y
Then as it is given that
Length of the rectangle = 2 times width of the rectangle
or
[tex]x = 2 \times y[/tex]
We have area= 392 square feet
Since area = length times width, thus, we have
[tex]Area = x \times y\\392 = 2 \times y \times y\\\\\dfrac{392}{2} = y^2\\\\y^2 = 186\\\\\text{\:(Taking positive root on both the sides since y is width, a non negative quantity)}\\\\y = \sqrt{196} = 14[/tex]
Thus, the width of the rectangle is 14 feet
And thus, the length of the rectangle = double of width = 28 feet.
Thus,
The length of the given rectangle is 28 feet.
Learn more about area of rectangle here:
https://brainly.com/question/349091
Verify that f and g are inverses functions using composition , show your steps
Answers
Answer:
See explanations below
Step-by-step explanation:
Given the functions
f(x) = 12x - 12
g(x) = x/12 - 1
To show they are inverses, we, must show that f(g(x)) = g(f(x))
f(g(x)) = f(x/12 - 1)
Replace x with x/12 - 1 into f(x)
f(g(x)) =12((x-12)/12) - 11
f(g(x)) = x-1 - 1
f(g(x)) =x - 2
Similarly for g(f(x))
g(f(x)) = g(12x-12)
g(f(x)) =(12x-12)/12 - 1
12(x-1)/12 - 1
x-1 - 1
x - 2
Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other
PLEASE HELP! Which of the following expressions are equivalent to (x+y) - (-z)?
A) (x+y)-z
B)x+(y+z)
C) none of the above
Answers
Answer:
c
Step-by-step explanation:
none of them equal (x+y)-(-z)
What is 22.5% written as a fraction in simplest form?
Answers
Answer:
9/40
Step-by-step explanation:
Write down the percent divided by 100 like this:22.5/100
Multiply both top and bottom by 10 for every number after the decimal point:As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,(22.5*10)(100*10)= 225/1000
Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(225,1000) = 25.225 ÷ 25/ 1000÷25 = 9/40
please help i’m so confused, it’s geometry!
Answers
Answer:
The correct answer is (-1,-3)
Step-by-step explanation:
its right i think lol
How tall would the lighthouse be?...
Answers
Answer:
122.6 m
Step-by-step explanation:
Shadow cast by the man = 3.1 m
Height of the man = 1.9 m
Shadow cast by the lighthouse = 200 m
Height of the lighthouse = x
If two shapes are similar, the ratio of their corresponding sides would be equal.
Therefore,
x/1.9 = 200/3.1
Multiply both sides by 1.9
x = (200*1.9)/3.1
x = 122.6 m (nearest tenth)
The lighthouse is 122.6 m tall
60° 2x + 149 degrees
Answers
Answer:
x = 23
Step-by-step explanation:
60°=x+14
60+14=84=X
Help I don’t know the answer
Answers
Answer:
the last one
Step-by-step explanation:
the input cannot be negative
Find the slope of the line that passes through the two points.
Answers
Answer:
slope is 5
Step-by-step explanation:
use formula (y2-y1)/(x2-x1) to find the slope
(2-(-3))/(6-5)
= 5/1
=5
if you want the equation to the graph here:
y=mx+b
2=5(2)+b
2=10+b
b=-8
equation: y=5x-8
What is the area of the arrow shown
Answers
Answer:
Step-by-step explanation:
a b c d
Find the missing side. Round to the nearest HUNDRETH.
*
10 points
X
240
12
5.34
6.98
O
12.42
5.25
Answers
Answer:
A. 5.34
Step-by-step explanation:
Reference angle = 24°
Opposite = x
Adjacent = 12
Thus, applying trigonometric ratio, we have:
tan (24) = x/12
Multiply both besides by 12
12*tan (24) = x
x = 5.34 (nearest hundredth)
Help please being timed and I don’t get it...?
Answers
Answer:
i got you.
whats up
Step-by-step explanation:
If p:q=2/3:3 and p:r=3/4:1/2, calculate the ratio p:q:r
Answers
p/q = 2/9 = 6/27
p:r = ¾:½
p/r = 3/2 = 6/4
p:q:r = 6:27:4
Zara want to purches a new shirt for $19.98 and a pair of sneakers for $64.95.She only has $73.17 saved.How much more money dose she need to purchase the new shirt and the sneakers.
A. 158.10
B. 11.76
C. 84.93
D. 11.84
Answers
B. 11.76
19.98 + 64.95 = 84.93
84.93-73.17=11.76
B) is Your answer
11.76
Step-by-step explanation:
[tex]19.98 + 64.93 = 84.93[/tex]
[tex]84.93 - 73.17 = 11.76[/tex]
is Your perfect answer
11.3
Example 3: A person randomly selects one of the four envelopes
shown below. Each envelope contains a check that the person gets
to keep. However, before the person can select the envelope, he or
she must pay $7 to play. Determine the person's expectation for the
following:
Answers
Answer:
Mathematical expectation is to get %280%2B3%2B7%2B22%29%2F4 = 32%2F4 = 8 dollars from the envelopes.
Statistically, it is loosing game.Step-by-step explanation:
Review the work showing the first few steps in writing a partial fraction decomposition.
StartFraction 2 x squared + 15 x + 19 Over (x + 4) cubed EndFraction = StartFraction A Over x + 4 EndFraction + StartFraction B Over (x + 4) squared + StartFraction C Over (x + 4) cubed EndFraction
2x2 + 15x + 19 = A(x + 4)2 + B(x + 4) + C
2x2 + 15x + 19 = Ax2 + 8Ax + 16A + Bx + 4B + C
Which system of equations can be used to determine the values of A, B, and C?
Answers
Answer:
[tex]A = 2[/tex]
[tex]B = -1[/tex]
[tex]C = -9[/tex]
Step-by-step explanation:
Given
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
Required
Find A, B and C
Rearrange the expression
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + Bx + 16A + 4B + C[/tex]
To do this, we simply compare the expressions on both sides of the equation.
So, we have:
[tex]Ax\² = 2x\²[/tex] --- (1)
[tex]8Ax + Bx = 15x[/tex] --- (2)
[tex]16A + 4B + C = 19[/tex] --- (3)
Divide both sides by x² in (1)
[tex]Ax\² = 2x\²[/tex]
[tex]A = 2[/tex]
Divide both sides by x in (2)
[tex]8Ax + Bx = 15x[/tex]
[tex]8A + B = 15[/tex]
Substitute 2 for A.
[tex]8*2 + B = 15[/tex]
[tex]16+ B = 15[/tex]
Make B the subject
[tex]B = 15 - 16[/tex]
[tex]B = -1[/tex]
Substitute 2 for A and -1 for B in (3)
[tex]16A + 4B + C = 19[/tex]
[tex]16*2 + 4*-1 + C = 19[/tex]
[tex]32 - 4 + C = 19[/tex]
[tex]28 + C = 19[/tex]
Make C the subject
[tex]C = 19 - 28[/tex]
[tex]C = -9[/tex]
Answer:
it D
Step-by-step explanation:
I just used elimination like a small brain
like so
when a = 1, b = 0, c = 3, d = -3
x^3 + 8x – 3 = Ax^3 + 5Ax + Bx^2 + 5B + Cx + D
You have a problem. You are running out of M&Ms (the candy). Originally, you had 200 small pieces. Last week, you got a little excited and ate 151 pieces of your original amount in one week (7 days). You are determined to last the remaining M&Ms for exactly one more week. If you eat the same amount every day, how many pieces will you be able to eat each day?
Create an equation to show how you would find the number of M&M pieces you could now have each day.
What is the answer to your equation in part 1? What steps did you take to solve your equation?
Please explain how you know your equation is correct.
Answers
Answer:
49 = 7m
m = 7
Step-by-step explanation:
200 - 151 = 49
There are 49 M&M's left
m = M&M's per day
7(7) = 49
Answer:
49 ÷ 7 = 7
Step-by-step explanation:
200 - 151 is 49 so 7 beacuase 49 divided by 7 is 7
the square of a number plus three times the number is 70. find the numbers.
Answers
Answer:
Step-by-step explanation:
The equation for that is
[tex]x^2+3x=70[/tex]
If we subtract over the 70, we have a quadratic that we can factor to solve for the values of x that will make that equation true.
[tex]x^2+3x-70=0[/tex]
Now we need the factors of 70 that will either add or subtract to give us the linear term of 3. The factors of 70 that will work are 10 and 7. 10 times 7 is 70, and 10 - 7 = 3:
[tex]x^2+10x-7x-70=0[/tex] and now we will factor by grouping:
[tex](x^2+10x)-(7x-70)=0[/tex] and factor out what's common:
[tex]x(x+10)-7(x+10)=0[/tex]
The factor (x + 10) is common, so we will now factor that out:
[tex](x+10)(x-7)=0[/tex]
By the Zero Product Property, either x + 10 = 0 or x - 7 = 0, so x = -10 or 7
Those are the 2 numbers that will work.
[tex](-10)^2+3(-10)=70[/tex] simplifies to
100 - 30 which does in fact equal 70. OR
[tex](7)^2+3(7)=70[/tex] which simplifies to
49 + 21 which also equals 70.
So you're done!
The values of the unknown number is 7 or - 10
The given expression from words to algebra;
let the unknown number = n
the square of the number = n²
three times the number = 3n
n² + 3n = 70
To find:
the values of nThe values of n is calculated as follows;
[tex]n^2 + 3n = 70\\\\n^2 + 3n - 70 = 0\\\\factorize \ the \ equation;\\\\n^2 + 10n - 7n - 70 = 0\\\\n(n + 10) - 7(n + 10) = 0\\\\(n-7)(n+ 10) = 0\\\\n = 7 \ or \ - 10[/tex]
Thus, the values of the unknown number is 7 or - 10
Learn more here: https://brainly.com/question/16889590
Which students reads the faster rate in your final answer include all necessary calculations
Answers
Answer:
Connie
Step-by-step explanation:
Determine the reading rate of the three students each. The student with the highest number of pages per minute is the fastest student (i.e. reads more words per minute).
✔️Stew's Reading Rate:
2650 ÷ 10 = 265 words per minute
✔️Connie's Reading Rate:
From the graph, it shows that 200 words are read in 1 minute.
So we have, 200 words per minute.
✔️Felicia = 260 words per minute
Therefore, we can conclude that Connie is the fastest because Connie reads more words per minute, which is 265 words per minute. Connie reads at a faster rate.
find the value of x for the following equation 4(6x -9.5) = 46
Answers
Step-by-step explanation:
step 1. 24x - 38 = 46 (distributive property)
step 2. 24x = 84 (add 38 to both sides)
step 3. x = 84/24 = 21/6 = 7/2 (divide by 24 and simplify).
The sum of two numbers is 23. The sum of the smaller and 2 times the larger is 36. Find the numbers.
Answer
How to enter your answer
larger number:
smaller number:
Answers
10+13x2=36