Algebra Find the value of each variable using the given chord, secant, and tangent lengths. If the answer is not
a whole number, round to the nearest tenth.
Answers
Answer:
15. [tex] x = 15 [/tex]
17. [tex] c = 13.2 [/tex]
19. [tex] x = 25.8 [/tex]; [tex] y = 12.4 [/tex]
Step-by-step explanation:
15. [tex] 20*6 = 8*x [/tex] (intersecting chord theorem)
Solve for x
[tex] 120 = 8x [/tex]
Divide both sides by 8
[tex] 15 = x [/tex]
[tex] x = 15 [/tex]
17. [tex] (11 + 20)*11 = (13 + c)*13 [/tex] (two secants intersecting theorem)
Solve for c
[tex] 31*11 = 169 + 13c [/tex]
[tex] 341 = 169 + 13c [/tex]
Subtract 169 from each side
[tex] 341 - 169 = 169 + 13c - 169 [/tex]
[tex] 172 = 13c [/tex]
Divide both sides by 13
[tex] \frac{172}{13} = \frac{13c}{13} [/tex]
[tex] 13.2 = c [/tex] (nearest tenth)
19. [tex] (x + 5)*5 = (15 + 7)*7 [/tex] (two secants intersecting theorem)
Solve for x
[tex] 5x + 25 = 22*7 [/tex]
[tex] 5x + 25 = 154 [/tex]
Subtract 25 from each side
[tex] 5x + 25 - 25 = 154 - 25 [/tex]
[tex] 5x = 129 [/tex]
Divide both sides by 5
[tex] \frac{5x}{5} = \frac{129}{5} [/tex]
[tex] x = 25.8 [/tex] (nearest tenth)
[tex] y^2 = 7*(15 + 7) [/tex] (tangent and secant theorem)
Solve for y
[tex] y^2 = 7*22 [/tex]
[tex] y^2 = 154 [/tex]
Take the Square root of both sides
[tex] \sqrt{y^2} = \sqrt{154} [/tex]
[tex] y = \sqrt{154} [/tex]
[tex] y = 12.4 [/tex] (nearest tenth)
Related Questions
Find the area of the triangle 8 cm 15 cm
Answers
Answer:
60 cm squared
Step-by-step explanation:
area of a triangle is [tex]\frac{bh}{2}[/tex]
base and height are interchangable; 8 cm and 15 cm
[tex]\frac{8(15)}{2}[/tex]
[tex]\frac{120}{2}[/tex]
60
(45x-7)4x=57 solve this and ill make out with you
Answers
Answer:
After solving [tex](45x-7)4x=57[/tex] we get [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]
Step-by-step explanation:
We need to solve the equation: [tex](45x-7)4x=57[/tex]
Solving:
[tex](45x-7)4x=57[/tex]
Multiply 4x with terms inside the bracket
[tex]180x^2-28x=57[/tex]
[tex]180x^2-28x-57=0[/tex]
We need to solve above equation to find value of x
Using quadratic formula for finding value of x: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=180, b=-28 and c=-57
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-28)\pm\sqrt{(-28)^2-4(180)(-57)}}{2(180)}\\x=\frac{28\pm\sqrt{784+41040}}{360}\\x=\frac{28\pm\sqrt{41824}}{360}\\x=\frac{28\pm204.51}{360}\\x=\frac{28+204.51}{360} \ or \ x=\frac{28-204.51}{360}\\x=0.645 \ or \ x = -0.490[/tex]
Values of x are [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]
So, After solving [tex](45x-7)4x=57[/tex] we get [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]
Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(6, 0) and line x = −6.
Answers
The equation of the graph is [tex]x = \frac 1{24}y^2[/tex]
How to determine the equation?Generally, a point is represented as:
(x,y)
The line x = -6 means that:
(-6, y)
So, we calculate the distance between (x,y) and (-6, y) as follows:
[tex]d = \sqrt{(x + 6)^2 + (y - y)^2}[/tex]
This gives
[tex]d = \sqrt{(x + 6)^2 }[/tex]
Next, we calculate the distance between (6,0) and (x, y) as follows:
[tex]d = \sqrt{(x - 6)^2 + (y - 0)^2}[/tex]
This gives
[tex]d = \sqrt{(x - 6)^2 + y^2}[/tex]
Equate both distance expressions
[tex]\sqrt{(x + 6)^2} = \sqrt{(x - 6)^2 + y^2}[/tex]
Square both sides
[tex](x + 6)^2 = (x - 6)^2 + y^2[/tex]
Expand
[tex]x^2 + 12x + 36 = x^2 - 12x + 36 + y^2[/tex]
Evaluate the like terms
[tex]12x = - 12x + y^2[/tex]
Add 12x to both sides
[tex]y^2 = 24x[/tex]
Make x the subject.
[tex]x = \frac 1{24}y^2[/tex]
Hence, the equation of the graph is [tex]x = \frac 1{24}y^2[/tex]
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Faith spent $78 at Fashion Warehouse. She bought 2 shirts that each cost $17.50 and a pair of shoes. How much did she spend for shoes?
Answers Choices
A. 34.00
B. 60.50
C. 43.00
D. 113.00
Answers
Answer:
C. 43.00
Step-by-step explanation:
If we add up the amount she paid for shirts we would get 35, then we subtract 78 by 35 to get our answer.
what is the correct evaluation of 3x-x+2,when x is equal to -4?
14
-6
6
-14
Answers
Answer:
The answer is -6.
Step-by-step explanation:
You have to substitute x = -4 into the expressions :
3x - x + 2
= 3(-4) - (-4) + 2
= -12 + 4 + 2
= -6
1 point
The weights of laboratory cockroaches follow a Normal distribution with
mean 80 grams and standard deviation 2 grams. Use the figure from above.
About what percent of the cockroaches have weights less than 78 grams?
16%
none of these
32%
34%
O 2.5%
Answers
Answer:
16% of the cockroaches have weights less than 78 grams.
Option A is correct.
Step-by-step explanation:
Mean = 80 g
Standard Deviation = 2
We need to find percent of the cockroaches have weights less than 78 grams so, x=78
First we will find z using formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Putting values of x, mean and Standard Deviation to find z
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{78-80}{2}\\z=-1[/tex]
We need to find P(z<-1)
Looking in the normal distribution table
[tex]P(z<-1)=0.15866\\P(z<-1)\approx 0.16\\Converting \ into \ percentage\\P(z<-1)=16\%[/tex]
So, 16% of the cockroaches have weights less than 78 grams.
Option A is correct.
I am kind of stuck on this question could someone explain and answer this question I would really appreciate it :)
Answers
Answer:
First one
Step-by-step explanation:
Supplementary angles basically means which angles added together equals 180 degrees, 180 degrees is also a straight line.
So the answer would be the first one because both the angles added together is 180.
Geometry: Express the area of each figure as a monomial. I need help with this, anyone?
Answers
Answer:
answer 28ab³ I think maybe
The area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].
Here,
The formula to calculate the area of a right-angled triangle is:
Area = (1/2) * base * height
In this case, the right-angled triangle has a height of [tex]6ab^3[/tex] and a base of [tex]4a^2b[/tex].
Now, let's substitute these values into the formula:
Area = [tex](1/2) * 4a^2b * 6ab^3[/tex]
Now, simplify the expression:
Area = [tex]2 * a^2b * 6ab^3[/tex]
To find the monomial representation, multiply the coefficients and add the exponents of like terms:
Area = [tex]12a^{(2+1)}b^{(1+3)[/tex]
Finally, simplify the exponents:
Area = [tex]12a^3b^4[/tex]
So, the area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].
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How would you describe the relationship between the real zero(s) and x-intercept(s) of the function
f(x) =
3x(x - 1)
x2(x+3)(x + 1)
When you set the function equal to zero, the solution is x = 1; therefore, the graph has an x-intercept of (1,0).
O When you set the function equal to zero, the solutions are x = 0 or x = 1; therefore, the graph has x-intercepts at
(0, 0) and (1,0).
O When you substitute x = 0 into the function, there is no solution, therefore, the graph will not have any X-
intercepts.
Since there are asymptotes at x = -3, x = -1, and x = 0, the graph has no x-intercepts and therefore, no real
zeros.
Answers
The description of the relationship between the real zero(s) and x-intercept(s) of the function should be option A.
Relationship between the real zero(s) and x-intercept(s) of the function:Since it is given that
f(x) = 3x(x - 1)
x2(x+3)(x + 1)
Also, the function should be set out and equivalent to zero when x = 1
and, the graph should have an x-intercept of (1,0).
Therefore, the option A is correct.
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Answer:
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
Step-by-step explanation:
A car and a truck leave the same intersection, the truck heading north at 60 mph and the car heading west at 55 mph. At what rate is the distance between the car and the truck changing when the car and the truck are 30 miles and 40 miles from the intersection, respectively?
Answers
Answer: -81
Step-by-step explanation:
Let x = the car moving towards west = 30
Let y = truck moving towards north = 40
dx/dt = -55
dy/dt = -60
We the use Pythagoras theorem to solve further where,
s² = x² + y²
s² = 30² + 40²
s² = 900 + 1600
s² = 2500
s =✓2500
s = 50
We then differentiate with respect to t, then we will have:
s² = x² + y²
2s ds/dt = 2x ds/dt + 2y dy/dt
50 ds/dt = (30 × -55) + (40 × -60)
50 ds/dt = -1650 - 2400
50 ds/dt = - 4050
ds/dt = -4050/50
ds/dt = -81
The table shows the highest and lowest golf scores for your cousin and your friend over the summer. Find the ranges of golf scores for your cousin and your friend. Who has the greater range of scores?
highest +6, +3
lowest -2, -3
Answers
Answer:
Cousin has a greater range of score.
Step-by-step explanation:
Range = Highest No. - Lowest No.
Range of cousin's score = +6 - (-2)
= +6+2 = 8
Range of friend's score = -2 - (-3)
= -2 + 3 = 1
Cousin has a greater range of score.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807Give the values of the coefficients [a], [b], and [c] regarding the product in the form of ax^2+bx+c. Use "0" if the term isn't present.
Answers
==================================================
Explanation:
Expand out the expression using the FOIL rule
(x+7)(x-7)
x^2 - 7x + 7x - 49
1x^2 + 0x - 49
We see that a = 1, b = 0, c = -49
-------------
Another way to expand is to do the following
(x+7)(x-7)
y(x-7) .... let y = x+7
xy - 7y .... distribute
x( y ) - 7( y )
x( x+7 ) - 7( x + 7 ) ... replace y with x+7
x^2 + 7x - 7x - 49 .... distribute
1x^2 + 0x - 49
We get the same result.
-------------
Lastly, a shortcut can be used as yet another method to expand.
The shortcut is the difference of squares rule
(a + b)(a - b) = a^2 - b^2
In this case, a = x and b = 7, so,
(a + b)(a - b) = a^2 - b^2
(x + 7)(x - 7) = x^2 - 7^2
(x + 7)(x - 7) = x^2 - 49
(x + 7)(x - 7) = 1x^2 + 0x - 49
Who is the most powerful undertale character
Answers
Answer:
Asriel Dreemurr
Step-by-step explanation:
Answer:
clearly the gay robot
hes my favorite <3
4x <64 what is the answer
Answers
Answer:
x < 16
Step-by-step explanation:
4x < 64
To solve for x, we simply divide by 4 on both sides. This results us with:
x < 16
#teamtrees #WAP (Water And Plant)
4x <64
Divide both sides by 4:
x < 16
The number of passengers in the bus double every minute. The bus was full of
passengers at 7.45am. When was it one quarter full?
Answers
Answer:
7:43 am.
Step-by-step explanation:
it was 1/2 full one minute ago then another 1/2 = 1/4 full 2 minutes ago.
Knowing how the bus fills, we want to find the time where the bus is one-quarter full.
The bus is one-quarter full at 7:43 am.
We know that at 7:45 am the bus is full. Let's say that the full bus has N people inside.
Each minute the population doubles, so if we go backwards, each minute the population is divided by 2.
One minute before, the bus must have half of the above population, meaning that at 7:44 am, the bus has N/2 people.
Another minuter before the people inside is halved again, then at 7:43 am we will have (N/2)/2 = N/4 people.
And if N is the people in a full bus, then N/4 represents the buss a quarter full.
Then we can answer the question as:
The bus is one-quarter full at 7:43 am.
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Geometry please help
Answers
You can use the alternate interior angles theorem to put XVW as 52 degrees and then add 52 and 60 up and subtract from 180 since every triangle has 180 degrees
solve 1,000x10 hint: use a strategy
Answers
Answer:
10000
Step-by-step explanation:
Answer:
10,000
Step-by-step explanation:
You just take the 0's and then you mutiply 1x1 and the answer you add the cero's you left the one from the number 10 and allso the ones from 1000
15. Harold learned that 6 out of 10 students at his school live within two miles of the school. If 240 students attend Grade 6 at his school, about how many of these students should Harold expect to live within two miles of the school? A 24 ® 40 © 144, 180
Answers
Answer:
144
Step-by-step explanation:
Write a equation(or whatever it is called)
6/10=x/240Cross multiply, 1440=10xDivide, 144=xCheck your work:
6/10=144/240Cross multiply, 1440=1440
Four students took an exam. The
fraction of the total possible points that each
received is given. Which student had the highest
score? If students receive a whole number of
points on every exam item, can the exam be
worth a total of 80 points? Explain.
Answers
Answer:
what are the fractions
What is the area of the shaded triangle inside the square? Round your answer to the nearest square inch.
A triangle has a base of 16 inches and a height of 16 inches.
_____ in²
Answers
Answer:
I believe the answer is the triangle has an area of 256 inches. I may be wrong though.
Step-by-step explanation:
Answer:
128 in² but only type 128 to complete the answer
Step-by-step explanation:
4. Victoria fills a 15-gallon pool. She has a 2-liter
bucket she uses to fill the pool. If 1 gallon is
approximately 3.79 liters, what is the
maximum number of full buckets Victoria can
pour into the pool without it overflowing?
A. 56 buckets
B. 57 buckets
C. 28 buckets
D. 29 buckets
Answers
Because when you multiply dkdjended
what is the solution to this equation: 5x to the 2 power - 36x - 81 = ?
Answers
Answer:
5x² - 36x - 81
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Combining Like TermsStandard Form: ax² + bx + c = 0Step-by-step explanation:
Step 1: Define expression
5x² - 36x - 81
Step 2: Simplify
We cannot simplify the expression down further.
Which direction am I going if I drive from Washington DC to Dallas texas
Answers
Answer:
north
Step-by-step explanation:
What is B^y=x in logarithmic form?
Answers
Answer:
The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logb x is read, “y equals log to the base b of x,” or more simply, “y equals log base b of x.” As with exponential functions, b > 0 and b ≠ 1
Step-by-step explanation:
ttygytex x so r5f3ygthttg
which rational number is negative?
Answers
Answer:
-1/6, 2/-7, 30/11, 13/-19 and -15/23 are negative rationals
What is the x-coordinate of point B? Write a decimal coordinate.
(brainliest ) Edge 2020
Answers
Find the dimensions of a rectangle with area 729000 m2 whose perimeter is as small as possible. (Give your answers in increasing order, to the nearest meter.)
Answers
Step-by-step explanation:
Area of a rectangle = Length * Width
A = LW
729000 = LW .... 1
Perimeter of a rectangle P = 2L+2W
P = 2L+2W
From 1;
W = 729000/L
P = 2L + 2(729000/L)
P = 2L + 1458000/L
To minimize the perimeter, dP/dL = 0
dP/dL = 2 - 1458000/L²
2 - 1458000/L² = 0
2L² - 1458000 = 0
2L² = 1458000
L² = 729000
L = √729000
Length = 853.8m
W = A/L
Width = 729000/853.8
Width = 853.8
Hence the dimension to the nearest meter is 854m by 854m
Do you guys know this?
Answers
Answer:
3
Step-by-step explanation:
You solve the inner first, then move to the outer.
Let's look at g(3) first. It is stated in the problem that g(3) = 2.
We then use this value for f(x). It is stated in the problem that f(2) = 3.
The answer is 3.
(Ill give brainliest if u help!)
Which equation has a value less than 54,811?
A) 54,811 x 2 = ________
B) 54,811 x one and two fourths = ________
C) 54,811 x 1 = ________
D) 54,811 x two fourths = ________
Answers
Answer:
Answer is D
Step-by-step explanation:
Answer:
The answer would be D.
Step-by-step explanation:
Please help I need these quickly. Please answer sensibly! I will give brainliest to the correct answer.
Answers
Answer:
n+n= 2n
[tex](3n) ^{2} = 9n ^{2} [/tex]
5(n+2)=5n+10
2(n+1)=2n+1
[tex]n \div 4 = \frac{n}{4} [/tex]
[tex]n(n - 2 = n{2} - 2n[/tex]