Answers
9² + 12² = (x+9)²
We use x+9 because the unknown segment x would combine with the radius, 9, to give that side of the triangle (the hypotenuse).
81 + 144 = (x+9)(x+9) ---- remember that squared means multiplied by itself
225 = (x+9)(x+9)
Multiply the right hand side:
225 = x² + 9x + 9x + 81
225 = x² + 18x + 81
Subtract 225 from both sides:
225 - 225 = x² + 18x + 81 - 225
0 = x² + 18x - 144
Use the Quadratic Formula to solve:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\x=\frac{-18 \pm \sqrt{18^2-4(1)(-144)}}{2(1)} \\ \\x=\frac{-18 \pm \sqrt{324--576}}{2} \\ \\x=\frac{-18 \pm \sqrt{324+576}}{2} = \frac{-18 \pm \sqrt{900}}{2}[/tex]
This gives us
[tex]x=\frac{-18 \pm 30}{2} = \frac{-18+30}{2} \text{ or } \frac{-18-30}{2}[/tex]
Since -18 - 30 = -48, and a negative number doesn't make sense in this situation, we have
x = (-18+30)/2 = 12/2 = 6.
The value of x cannot be negative, hence the value of x would make rq tangent to Circle P at point Q is 6
From the given circle geometry, since the line PQ is perpendicular to QR, hence the triangle PQR is a right-angle triangle.Given the following from the geometry;
Adjacent side = QR = 12Opposite side = PQ = 9Hypotenuse side = PR = 9 + xUsing the pythagoras theorem;
[tex]c^2=a^2+b^2\\(9+x)^2=9^2+12^2\\81+18x+x^2=81+144\\x^2+18x+81-225=0\\x^2+18x-144=0\\[/tex]
Factorize the result to have;
[tex]x^2+24x-6x-144=0\\x(x+24)-6(x+24)=0\\(x-6)(x+24) =0\\x=6 \ and \ -24\\[/tex]
Since the value of x cannot be negative, hence the value of x would make rq tangent to Circle P at point Q is 6
Learn more on circle geometry here: https://brainly.com/question/22077295
Related Questions
How does a reflection affect the properties of a two-dimensional figure ?
Answers
Please tell me if I’m correct I hope this help you
Therefore in two-dimensional figure reflection show mirror image of flipped
A reflection affect the properties of a two-dimensional figure.
What is the reflection?A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
In two dimensional figure reflection affects
and it is it gets mirrored or flipped.
Therefore in two-dimensional figure reflection show mirror image of flipped.
To learm more about the reflection in two dimensional figure visit:
https://brainly.com/question/1211190
If you work for an hourly wage, your gross pay is a function of the number of hours that you work. If you earn $8 per hour, complete the following table:
Number of Hours
0
3
5
7
10
12
Gross Pay
If you were to plot the ordered pairs on a set of axes, in which quadrant would the domain and range of the function lie?
a.
8, 16, 24, 32, 40, 48; Quadrant I
b.
0, 24, 40, 56, 80, 96; Quadrant II
c.
8, 16, 24, 32, 40, 48; Quadrant II
d.
0, 24, 40, 56, 80, 96; Quadrant I
Answers
where
[tex]f(x)[/tex] is your gross pay.
[tex]x[/tex] is the number of hours that you worked.
To complete the table, we just need to evaluate the function at the given hours; in other words, we are going to replace [tex]x[/tex] with the number of hours in our linear function:
[tex]y=8(0)=0[/tex]
[tex]y=8(3)=24[/tex]
[tex]y=8(5)=40[/tex]
[tex]y=8(7)=56[/tex]
[tex]y=8(10)=80[/tex]
[tex]y=8(12)=96[/tex]
We can conclude that yous should fill your table as follows:
Number of Hours
0
3
5
7
10
12
Gross Pay
0
24
40
56
80
96
2. Remember that the domain of a function are the set of the x-values of the function; the range of a function are the set of y-values of the function. From our previous point, we can infer that the ordered pairs of the function are: (0,0), (3,24), (5,40), (7,56), (10,80), and (12,96). The y-values and hence the range of the function are: 0, 24, 40, 56, 80, 96. Remember that in the quadrant I both the x-coordinates and the y-coordinates are positive. Since all the coordinates of our points are positive, we can conclude that the correct answer is:
d. 0, 24, 40, 56, 80, 96; Quadrant I
Answer:
D is the answer
Step-by-step explanation:
yw :)
I need desperate help
Answers
How many sides does a regular polygon have if each exterior angle has a measure of 15 degrees? (Show work!!)
Answers
because the total amount of the exterior angles of a polygon is 360.
so if each exterior angle has a measure of 15:
[tex]360 \div 15 = 24[/tex]
Sum or product of a nonzero rational number and an irrational number is always_____
A. rational,
B. irrational,
C. a repeating decimal,
D. a fraction
Answers
The medicine capsule shown consists of a cylinder with a hemisphere at each end. The total length of the capsule is 15 millimeters. The diameter is 5 millimeters. Which choice is the best approximation of the total surface are of the capsule? Usa 3.14 to approximate pi.
Answers
Answer 236 square millimeters
YOUR WELCOME
MARK BE BRAINIEST
Greg is running a marathon while running he should drink 22 ounces of water per hour if he runs for 4 hours how much water should he drink
Answers
To determine how much water Greg should drink during his 4-hour marathon run, multiply the hourly water intake (22 ounces) by the number of hours (4), resulting in a total of 88 ounces of water.
The student asks about the amount of water Greg should drink while running a marathon for 4 hours, given that he should drink 22 ounces of water per hour. To calculate this, we simply multiply the amount of water he should drink per hour by the number of hours he will be running.
Multiply the amount of water needed per hour (22 ounces) by the total hours running (4 hours).
22 ounces/hour × 4 hours = 88 ounces.
Therefore, Greg should drink 88 ounces of water during his 4-hour marathon run.
In the diagram below, AC is perpendicular to BD. Find X.
Answers
6x = 90 + 15
6x = 105
x = 105/6
x = 17.5
Answer: The correct option is
(D) 17.5.
Step-by-step explanation: Given that in the diagram shown, AC is perpendicular to BD, where
[tex]m\angle BEC=(6x-15)^\circ,\\\\m\angle AED=(3y+12)^\circ.[/tex]
We are to find the value of x.
Since AC is perpendicular to BD and they are intersecting each other at the point E.
So, all the four angles made by this intersection are right angles.
That is, angle BEC is also a right angle.
Therefore, we get
[tex]m\angle BEC=90^circ\\\\\Rightarrow (6x-15)^\circ=90^\circ\\\\\Rightarrow 6x-15=90\\\\\Rightarrow 6x=105\\\\\Rightarrow x=\dfrac{105}{6}\\\\\Rightarrow x=17.5.[/tex]
Thus, the required value of x is 17.5.
Option (D) is CORRECT.
Write the slope-intercept form of an equation of the line that passes through (2,-4) and (0,6)
Answers
In order to write the slope-intercept form, we have to have slope, and the y intercepts, just as it says in the name. In order to find slope with two points, we use our formula:
y2-y1/x2-x1 =
6-(-4)/0-2 = 6+4/-2 =
10/-2 = -5
Now that we know our slope is negative five, we can use one of those poins to model our slope intercept form, y= mx+b, using our slope, to solve for b, our y intercepts. We'll use (0,6).
We have:
6 = -2(0) + b
6 = 0 + b
6 = b
Now, since we have the slope and y intercept, we can write the equation:
y = -2x + 6
Hope this helps!
we know that
the equation of the line in the slope-intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope of the line
b is the y-intercept of the line
Let
[tex]A(2,-4)\\B(0,6)[/tex]
Step [tex]1[/tex]
Find the slope of the line AB
the slope between two pints is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
substitute the values
[tex]mAB=\frac{(6+4)}{(0-2)}[/tex]
[tex]mAB=\frac{(10)}{(-2)}[/tex]
[tex]mAB=-5[/tex]
with the slope m and the point B find the value of b
[tex]B(0,6)[/tex]
[tex]6=-5*0+b[/tex]
[tex]b=6[/tex]
Find the equation of the line
[tex]y=mx+b[/tex]
[tex]y=-5x+6[/tex]
therefore
the answer is
[tex]y=-5x+6[/tex]
A biologist wants to estimate the median width of over 200 oak trees in a forest. Ten trees were selected at random, and their widths, in centimeters, were recorded. 63, 59, 12, 43, 71, 35, 28, 52, 47, 26 What is the estimated median width of all oak trees in the forest? Enter your answer in the box.
Answers
Answer:
45
Step-by-step explanation:
The estimated median width of all oak trees in the forest is 45 centimeters.
How to calculate the median width?
To estimate the median width of all oak trees in the forest, we can use the sample of ten trees that were selected at random.
First, we need to order the sample from smallest to largest:
12, 26, 28, 35, 43, 47, 52, 59, 63, 71
The median is the middle value in the ordered list. In this case, there are ten numbers in the list, so the median is the average of the fifth and sixth numbers:
median = (43 + 47) / 2 = 45
Therefore, the estimated median width of all oak trees in the forest is 45 centimeters.
Learn more about the median here:
https://brainly.com/question/17390781
#SPJ6
The gear ratio describes the ratio of one gear's diameter to another gear in the same chain. The gear ratio between two specific gears is 3 to 2. If the diameter of the larger gear is 18 cm, what is the diameter of the smaller gear?
A. 24 cm B. 18 cm
C. 12 cm D. 6 cm
Answers
Matt has a quiz every 6th day of class, and Meg has a quiz every 3rd day of class. When will they have a quiz on the same day?
Answers
Every other quiz for Meg will be with Matt, and their first one together will be on the 6th day of class.
Hope this helps!
The correct answer is:
The 6th day.
Explanation:
To solve this, we find the least common multiple (LCM) of 3 and 6. We find the prime factorization of each number:
3 = 3×1
6 = 2×3
We multiply the common factor, 3, by the uncommon factors, 2 and 1:
3×2×1 = 6
The LCM is 6; this means they will both have a quiz on the 6th day.
What is these answer
Answers
.. A = (1/2)bh
Filling in the given values, you get
.. A = (1/2)*22*9
.. A = 99
The rabbit population in a certain area is 500% of last year's population. There are 900 rabbits this year. How many were there last year?
Answers
Hope this helps
Answer:
180
Step-by-step explanation:
we got the same qustion and i just got this wrong
Rewrite the given expression in the form 2^u where u is a constant or an algebraic expression.
1/2^5 = ? (Put the answer in exponential notation.)
Answers
To rewrite 1/2^5 in exponential notation, remember that 1/2^5 is the same as 2^-5. Therefore, 1/2^5 = 2^-5.
Rewrite the given expression in the form 2u where u is a constant or an algebraic expression.
To rewrite 1/25 in exponential notation, we need to understand that 1/25 is the same as (2-1)5. Using the property of exponents, we can rewrite this as 2-5, where -5 is the new exponent.
Therefore, 1/25 = 2-5, where u = -5.
Leslie need 48 ounces of charcoal. How many pounds should she buy?
Answers
48÷16=3
3 pounds
The 48 ounces of charcoal will be equal to 2.5 pounds
What is ounces?The ounce is the name of several different units of mass, weight or volume and is derived almost unchanged from the uncia.
We have 48 ounces of charcoal.
We know the conversion that:
[tex]\rm 1 \ Ounce= 0.0625\ Pounds[/tex]
[tex]\rm 48\ ounce=48\times 0.0625\time \ Pounds=2.5\ pounds[/tex]
So the 48 ounces of charcoal will be equal to 2.5 pounds.
To know more about Ounces follow
https://brainly.com/question/3945391
#SPJ2
A cylinder has a radius of 4 feet and a height of 3 feet. What is the volume of the cylinder to the nearest tenth 3. Use 3.14 to approximate π
Answers
We must use a certain formula to find the volume of a cylinder. The formula is:
V = pi × r^2 × h
Pi = Approximately 3.14
Radius = 4 ft
Height = 3 ft
Use the formula to solve for the volume of this cylinder.
Substitute:
V = 3.14 × 4^2 × h
V = 50.24 × 3
V = 150.72
Round to the nearest tenth.
ANSWER:
The volume of the cylinder, to the nearest tenth, is 150.72 cubic feet.
**Volume is ALWAYS cubed, so put a small 3 just above the end of "feet" to indicate that it is cubed.
Answer:
70Pi ft2
Step-by-step explanation:
ed2020
a cylinder is 8 inches high. The circumference of the base 6pi inches. Find the volume
Answers
There has to be a variable to the number because this equations contains 2 factors and not 3.
Volume is measured W x H x L
How do you calculate the volume of a cone when given the height and diameter? Describe the steps used to solve.
Answers
First find the radius by taking half the diameter. Use the radius to find the base area by using the formula for the area of a circle. Find the product of the base area and height, and then take one-third of the product.
Answer:
Step-by-step explanation:
First find the radius by taking half the diameter. Use the radius to find the base area by using the formula for the area of a circle. Find the product of the base area and height, and then take one-third of the product.
A box is in the shape of a right rectangular prism. The base of the box has an area of 15 square inches. The height of the box is 12 inches. What is the volume in cubic inches, of the box
Answers
If RS//MN ,then the value of a is
Answers
a = 74 because angle TRS and angle TMN are corresponding angles
The 40 and 34 degree angles add to 40+34 = 74 which makes up angle TMN
TRS and TMN are corresponding angles because they are on the top side of the horizontal line RS and MN respectively; also they are on the right hand side of the transversal line TM. In short, the two angles are in the upper-right corner of each intersection. That's why they are corresponding.
how can you tell if radicals are like radicals
Answers
And there ya have it!
Happy studying.
~Brooke❤️
Answer and step-by-step explanation:
Like radicals have the same root (square root, cubed root, etc.) and the same expression under the radical sign.
In order to determine if two radicals are like, simplify both and then check both the root and the expression under the radical sign.
Alicia cashed her paycheck and used half her earnings to take three friends to dinner. She spent $42.15 on dinner and she brought home more than $20.00. Write an inequality to represent the situation, using x to represent the amount of Alicia's paycheck.
Answers
+ $42.15 + $42.15
x > $62.15
A teacher would like to estimate the percentage of her students who play chess. Which method should the teacher use to select the sample?
A select every other student in her classes until she has selected a total of 30 students
B select all students who are currently in the chess club
C use a computer to randomly select 30 student IDs from all her students
D use a computer to randomly select 30 student IDs from all students
Answers
I have this same question And the answer is C. Did you get your answer already
Answer:
the answer is C.
Step-by-step explanation:
since shes trying to find HER students D is wrong and since she needs a random amout of kids it doesnt make sense to choose a and since shes trying to find the percentage of her kids that play chess it would make sense to choose ppl who are already in the chess club.
the expression (x+a)(x+b) cannot be written as
Answers
The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.
What is the distributive property?The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
Using distributive property, we get
x(x+b)+a(x+b)
= x²+bx+ax+ab
= x²+x(a+b)+ab
The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.
Learn more about the distributive property here:
https://brainly.com/question/5637942.
#SPJ2
"Your question is incomplete, probably the complete question/missing part is:"
The expression (x+a)(x+b) can not be written as
a) a(x+b) + x(x+b)
b) x² + (a+b)x + ab
c) x² + abx + ab
d) x(x+a) + b (x+a)
lugos and paschal each wrote an equation for the line that passes through (-3,2) and (6,8) lugos says the equation is y=2/3x+4 and paschal says the equation is 2x-3y=-12. who is correct? why do you say so?
Answers
Step 1
find an equation for the line that passes through A (-3,2) and B (6,8)
m=(y2-y1)/(x2-x1)=(8-2)/(6+3)=6/9=2/3
y=mx+b
with point (6,8)
8=(2/3)*(6)+b-------------> 8=4+b------------> b=4
y=(2/3)x+4
the answer is
Lugo's equation is the correct one
Please help me!!! Zoom in on picture to read the other 2 questions. 1 questions if on 2 parts of the collage.
Ferris wheel is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the coordinates of the first car after a rotation of 270° about the origin?
Answers
Answer:
1. option A is correct i.e., [tex]\(90^{\circ}[/tex].
2. option B is correct.
3. the coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).
Step-by-step explanation:
1. The angle of rotation is [tex]\(90^{\circ}[/tex].
To calculate the angle of rotation we can use a protractor and measure the angle between two corresponding angles, using point C as a center.
2. Given: ΔPRS with coordinates P(-3,2), R(2,5) and S(0,0) is rotated through an angle of 270°, the new image will be as follows;
The formula for rotation through 270° is: (x,y) → (y,-x)
hence our image will be at point:
P(-3,2)→P'(2,3)
R(2,5)→R'(5,-2)
S(0,0)→S'(0,0)
from the above, the approximate image will be option B.
3. Given: Ferris wheel is drawn on a coordinate plane at the point P(30,0). The coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).
Because the formula for rotation through 270° is: (x,y) → (y,-x).
So, point P(30,0)→P'(0,-30).
Your school is 20 blocks east and 12 blocks south of your house. The mall is 10 blocks north and 7 blocks west of your house. You plan on going to the mall right after school. Find the distance between your school and the mall assuming there is a road directly connecting the school and the mall. One block is 0.1 mile. Round your answer to the nearest tenth of a mile.
East=X, West=-X, North=Y, South=-Y
Answers
Answer:3.623 miles
Step-by-step explanation:
Given
School is 20 blocks east and 12 blocks south
and mall is 10 blocks north and 7 block west.
There is a road directly connecting the school and the mall.
So distance between school and the mall is
[tex]=\sqrt{(20+12)^2+(10+7)^2}[/tex]
[tex]=\sqrt{32^2+17^2}[/tex]
[tex]=\sqrt{1024+289}[/tex]
=36.23 blocks
And 1 block is 0.1 mile so 36.23 blocks is 3.623 miles
Which expression best estimates
Answers
6 3/4 - 1 2/3
We can convert the fractions to decimals, and if the decimals are bigger than .5, we can round up to the nearest whole number.
3/4= .75 <== we can round up to the nearest whole number
6.75= 7
2/3= .66666 <=== we would also round this up to the nearest whole number
1.66666= 2
7-2 <=== estimated expression
I hope this helps!
~kaikers
7-2 is the correct answer because 6 3/4 can be rounded to 7 and 1 2/3 can be rounded to 2
The formula to find the perimeter of a regular polygon is P = n × s. This means that you multiply the number of sides times the length of each side. Which polygon will have the greatest perimeter? A. a hexagon with each side 3 cm B. a square with each side 5 cm C. a triangle with each side 7 cm D. a pentagon with each side 4 cm