Points Y and Z are points of tangency. Find the value of a.

Points Y And Z Are Points Of Tangency. Find The Value Of A.

Answers

Answer 1

Answer:

a = 2

Step-by-step explanation:

If Y and Z are points of tangency, then |XY| = |XZ|.

We have

[tex]|XY|=9a^2-30\\|XZ|=3a[/tex]

Domain

[tex]a>0[/tex]

Substitute

[tex]9a^2-30=3a\qquad|\text{subtract}\ 3a\ \text{from both sides}\\\\9a^2-3a-30=0\qquad|\text{divide both sides by 3}\\\\3a^2-a-10=0\\\\3a^2-6a+5a-10=0\\\\3a(a-2)+5(a-2)=0\\\\(a-2)(3a+5)=0\iff a-2=0\ \vee\ 3a+5=0\\\\a-2=0\qquad|\text{add 2 to both sides}\\a=2\\\\3a+5=0\qquad|\text{subtract 5 from both sides}\\3a=-5\qquad|\text{divide both sides by 3}\\a=-\dfrac{5}{3}<0[/tex]


Related Questions

I NEED HELP WITH THESE PLEASE
2.) What about the next shape in this pattern? Write a conjecture that describes the pattern.
The red square is the next shape.
3) write a conjecture that describes the pattern below.
3,9,27,81
4) write a conjecture that describes this pattern.

Answers

Answer:

000, 001,010,011 (the next one would be 100,101....)

Step-by-step explanation:

That's the binary system

The answers are 1) The next shape will be  red square, 2) The next number will be 243 and 4) The pattern will be red,blue,blue.

What is conjecture?

A conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof.

1) According to given pattern, the next shape will be a shape a red square.

2) The given numbers are multiplied by 3 in every next term, 3, 3*3 = 9, 9*3 = 27 and 27*3 = 81 so, next number will be 81*3 = 243.

3) The 4th one is a pattern of binary system:

000, 001,010,011

Therefore, the next one would be 100,101.... That means red, blue, blue.

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please help i will mark branliest!

Answers

Answer:

The answer is A. 33 square inches

Step-by-step explanation:

Since the area of the Bisawi is a half total base multiplied in the height

[tex]area = \frac{1}{2} (8 + 3) \times 6 \\ = 33[/tex]

Solve -3x is less than or equal to 9 by adding 3x to each side of the inequality first. Then solve the resulting inequality.

Answers

Answer:

Step-by-step explanation:

-3x<9

+3x to ech side

0<9+3x

-9<3x

-3<x

or x>-3

[Help Asap, Will Mark Brainliest] Question is in the image.

Answers

Answer:

y = 30

z = 115

Step-by-step explanation:

z° + 65° = 180°

(Exterior Angles on the same side of transversal)

z° = 180° - 65°

z° = 115°

z = 115

(5y - 85)° + z° = 180°

(Linear pair angles)

(5y - 85)° + 115° = 180°

(5y - 85)° = 180° - 115°

(5y - 85)° = 65°

5y - 85 = 65

5y = 65 + 85

5y = 150

y = 150/5

y = 30

Tim wants to ride his bike for 25 miles or less on some mountain bike trails.
The table shows the distances of three different trails he can ride on.

Trail Distance
Black Bear
7
1
2
miles
Eagle Ridge
10
1
4
miles
Doe Run
8
3
4
miles


Select all combinations of trails that Tim can ride for 25 miles or less.

A.
Doe Run 3 times

B.
Eagle Ridge 2 times

C.
Black Bear 2 times and Eagle Ridge 1 time

D.
Black Bear 1 time and Doe Run 2 times

E.
Eagle Ridge 1 time and Doe Run 1 time

Answers

Answer:

Eagle Ridge 2 Times

Black Bear 1 time and Doe Run 2 Times

Eagle Ridge 1 time and Doe Run 1 time

B,D,E

Step-by-step explanation:

Took a test 100%

help please
Suleika has six cards numbered 1 to 6.

1 1

2

3

4

5

(a) She takes one card at random, records the number and replaces the card,

(i) Write down the probability that the number is 5 or 6.

6

[1]

(ii) Suleika does this 300 times.

Find how many times she expects the number 5 or 6.​

Answers

math is so hard.......

PLEASE HELP ILL MARK AS BRAINLIEST IF CORRECT
Beth travels at an average speed of 30 mph for 20 miles.
Without stopping, Beth then travels 70 miles in 1.5 hours.
Find her average speed for the entire journey to 2 dp.

Answers

Answer:

41.54 mph

Step-by-step explanation:

you need to find the total distanceand total time to find the average speed

use distance/time = speed equation

time = 1.5 hours + 40 mins = 2 hours 10 mins

distance= 20 + 70 = 90 miles

90/130 mins x 60 = 41.54 mph

what is the circumference of a circle that’s 9cm

Answers

Answer:

C=2πr hope this helps!! and have a great day!!!

Step-by-step explanation:

Answer:

I can't give you the answer to this because you didn't specify whether or not 9 was the radius or the diameter. could you comment back and ill give you an answer for this?

Step-by-step explanation:

Help !! Asap!! Please

Answers

Answer:

4

Step-by-step explanation:

so 8*6=48, so we know that (4*6)+(_*6) should equal 48.

4*6=24

subtract 24 by 48 and we get 24.

now you probably know that it equals 4, but to be sure, divide 24 by 6, and you'll get 4.

Answer:

From top to bottom:

1st box: 4

2nd box: 24

3rd box: 48

Step-by-step explanation:

So, based on my knowledge, you are learning the Distributive probability. So, what the Distributive property does is it basically allows to distribute the one of the numbers in the multiplication problem. In this problem, we can see that the 8 is being distributed into two groups of 4 to make (4 * 6) + (4 * 6). Then, we solve the things in the two parenthesis, making 24 + 24. Now, all we have to do is add 24 + 24, making 48.

Help me quick please!​

Answers

Answer:

-3 and 1

Step-by-step explanation:

Zeros of a function are usually the points the graph touches on the x axis.

two partners divide a profit of $2,000 so that's a difference between the two amounts is half of their average. what is the ratio of the larger to the smaller amount?

Answers

Answer:

5/3

Step-by-step explanation:

The partners have a total profit of $2000. Since there are only 2 partners, then the average profit each one makes is $2000/2 = $1000.

The difference between the 2 amounts is half of the average, so it is $1000/2 = $500.

One amount is x.

The other amount is x + 500

The sum is 2000

x + x + 500 = 2000

2x + 500 = 2000

2x = 1500

x = 750

x + 500 = 750 + 500 = 1250

The partners had profit of $1250 and $750.

The ratio is 1250/750 = 125/75 = 5/3

Answer: 5/3

The ratio of the larger to the smaller amount will be 5 : 3

What are ratios?

A ratio says how much of one thing there is compared to another thing. We can write the ratio as -

x : y

{x/y} = k

x = ky

[k] is called the scale factor.

Given is that two partners divide a profit of $2,000 so that's a difference between the two amounts is half of their average.

Assume that the amount with partner [1] is $[x] and with partner [2] is $[y]

. So, we can write according to the question as -

x + y = 2000      ......Eq [1]

x - y = {1/2 x (x + y)/2}     ......Eq [2]

Now -

x - y = {1/2 x (2000/2)}

x - y = {1/2 x 1000}

x - y = 500

x = 500 + y

So, we can write the equation [1] as -

x + y = 2000

500 + y + y = 2000

2y = 1500

y = 750

So, [x] will be equivalent to -

x = 2000 - 750

x = 1250

The ratio of the larger to the smaller amount will be -

x/y = 1250/750 = 250/150 = 50/30 = 5/3

Therefore, the ratio of the larger to the smaller amount will be 5 : 3.

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what number lies halfway between 16 and 38​

Answers

Answer:

27

Step-by-step explanation:

The number that lies halfway between 16 and 38 is 27.

What is the number system?

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

We have to determine the number that lies halfway between 16 and 38.

This is calculated by finding the average (or mean) of the two numbers. To do this, add the numbers together (16 + 38) and divide by 2.

⇒ 54/2

The result is 27.

Thus, the number that lies halfway between 16 and 38 is 27.

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A train is traveling at 30 miles per hour.

How long will it take the train to travel 180 miles?
FREE BRAINLIEST!!!

Answers

Answer:

Six hours

Step-by-step explanation:

Answer:

6 Hours

Step-by-step explanation:

If the train travels at 30mph for 6 hours it will have traveled 180 miles.

30 • 6 = 180

I hope this helps

PLEASE HELP ME IM DOING A TEST :Write in point-slope form an equation of the line that passes through the point (5, 9) with slope 7. ____

Answers

Answer:

y-9+7(x-5)

Step-by-step explanation:

y - x1 = m ( x - y1 )

Y1 = 9

x1 = 5

m=slope (in this case 7)

Answer:

[7x-y-26=0]

Step-by-step explanation:

point slope form =

y-y1=m(x-x1)

=

y-9=7(x-5)

=

[7x-y-26=0]

you may want the y-9=7(x-5) as your answer

second part of this is for vertex form

/////// vertex form ///////Use formula y=mx+b where m is slope

y is equal to 9

x is equal to 5

b=?

m=7

9=7*5+b ---> b=  -26

////////////////

HELP I NEED HELP ASAP

A. A student’s math grade decreases approximately 3 points for every 10 minutes of watching television.

B. A student watches approximately 3 minutes less television for every 10 points gained in their math grade.

C. A student watches approximately 3 minutes more television for every 10 points gained in their math grade.

D. A student’s math grade increases approximately 3 points every 10 minutes of watching television.

Answers

Answer:

B. A student watches approximately 3 minutes less television for every 10 points gained in their math grade.

what is 4,390.44 + 8.399, and show work pls

Answers

Answer:

4,398.839

Step-by-step explanation:

4,390.440 + 8.399=x

.000+.009=.009

.04+.09=.13

.4+.3=.7

.009+.13+.7=0.839

---------------------------

4390+8=4398

----------------------------

4398+0.839=4398.839

Henry is trapped at the roof top of a burning building, which is 24 feet high. In order to rescue him, his father, Diego, must find a ladder which will be used to cross the river, which is 7 ft wide, and go up directly to the top of the building. Help Diego to find the appropriate length of ladder from the other side of the river to the top of the building.​

Answers

Answer:

168

Step-by-step explanation:

so what you are going first is 24 times 7 which is

Help please!! Thanks a lot I’m advance

Answers

The answer is the 4th option.

Triangle ABC has vertices A(-5, 2), B(0,4), and C(3,3). Determine the coordinates of the C'' after a translation 2 units right and 4 units down followed by a reflection over the y-axis.

Answers

It is b since those coordinates reflect equally

HELP ASAP RN PLEASE!!

200 people got an email 37 people clicked on it how do you get 18.5%

Answers

Answer:

37/200

Step-by-step explanation:

Event/Sample Space = .185 = 18.5%

Answer:

Step-by-step explanation:

If 37 people out of 200 people opened an e-mail, you can write it as 37/200.

The number above the bar is the numerator: 37

The number below the bar is the denominator: 200

Divide the numerator by the denominator to get fraction's value:

Val = 37 ÷ 200

Val = 0.185

To calculate the percent value:

0.185 =  (Calculate fraction's value.)

0.185 × 100/100 =  

(0.185 × 100)/100 =  (Multiply that number by 100.)

18.5/100 =

18.5%;  (Add the percent sign % to it.)

So that's how you get 18.5%

DOES THIS SET OF ORDERED PAIRS
REPRESENT A FUNCTION?
{(2,4),(2,5), (2,6), (2,7) }

Answers

Answer:
No, this set of ordered pairs does not represent a function.

Explanation:
Functions have one y-value for a given x-value.

Ordered pairs are written (x, y).

In this set, when x=2, it has four y-values (4, 5, 6 and 7), so it cannot be a function.

Answer:

No

Step-by-step explanation:

No, this set of ordered pairs does not represent a function because functions  a relation in which each input has only one output.  

The ratio of plates to cups is 10:14. If
there are 7 cups, how many plates
are there?

Answers

Answer:

Step-by-step explanation:

p:c=10:14

p/c=10/14

p/7=10/14

p=7(10)/14

p=5

Answer:

5 plates

Step-by-step explanation:

First, make two fraction bars, one with the ratio 10/14 the other with the top blank and 7 on the bottom. Next, find how much to multiply 7 by to get 14. Use the number you get to divide 10 by. Then you should get 5. Hope this helped!

Translate each algebraic expression to a verbal phrase

1. x-7
2. y+9
3. 6m /8
4. 3y+5 =20
5. 2(x+8)= 23

Answers

Answer:

1.  A number decreased by seven.

2. A number increased by nine.

3. The product of six and a number, divided by eight.

4. The product of three and a number increased by five is equal to twenty.

5. The product of two and a number increased by eight is equal to twenty-three.

Step-by-step explanation:

1.   x-7

A number decreased by seven.

2. y+9

A number increased by nine.

3. 6m/8

The product of six and a number, divided by eight.

4. 3y+5 =20

The product of three and a number increased by five is equal to twenty.

5. 2(x+8)= 23

The product of two and a number increased by eight is equal to twenty-three.

The translation of each given algebraic expression to a verbal phrase has been provided.

1) We have; x - 7

This means that; a number x decreases by 7.

2) y + 9; This means that; a number y increases by 9.

3) 6m/8; This can be expressed as;

The product of six times a number m is divided by 8.

4) 3y + 5 = 20; This can be expressed as;

The sum of five and three times a number x is equal to 20.

5) 2(x + 8) = 23;

The product of 2 and the addition of a number x and 8 is equal to 23

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Tell whether -2 is a solution of the
inequality 6g – 14 > - 21

Answers

Answer:

3(4g + 6) = 2(6g + 9)

Distribute 3 and 2 inside their respective parentheses.

12g + 18 = 12g + 18

Step-by-step explanation:

(2g+3)(5g^2-6)

        or  (5g^2-6)(2g+3)

halla los valores de "x y "y" en cada caso, y todos los ángulos de las figuras​

Answers

Answer:

Step-by-step explanation:

dbbx

Write an equation for the nth term of each geometric sequence. (show work)
1. 1, 4, 16, ...
2. 1, 1/2, 1/4, ...
3. 7, -14, 28, ...

Answers

1) 4n

The arithmetic sequence is going up in 4’s (1 x 4 = 4, 4 x 4 = 16)
Therefore the answer is just 4n

2) 0.5n (1/2n)
The arithmetic sequence is going up in 0.5’s (1 x 0.5 = 1/2, 1/2 x 0.5 = 1/4)
Therefore the answer is just 0.5n or if you need it in a fraction it is (1/2n)

3) -7n
The arithmetic sequence is going up in -7’s (7 x -7 = -14, -14 x -7 = 28)
Therefore the answer is just -7n

please help! will give brainliest

Answers

Answer:

yes, the point (-1, 5) is in the solution set

Step-by-step explanation:

y ≥ 2x + 3

Is 5 ≥ 2(-1) + 3?  Yes

y + x > 0

Is 5 + (-1) > 0?  Yes

Answer:

Yes the Point (-1,5) is in the solution set.

Step-by-step explanation:

Well you have to sub in the x and the y.

In the first equation

5 >= 2(-1) +3 = 5>= 1 So this one is true and in the set.

The second one

5+-1>0 = 4>0. So this one is also true.

Sorry if im wrong. Hope this helps!

Please give me Branliest!

I need help with geometry

Answers

okayyy:))))))))))))))))))

Find the missing side of this right
triangle.
17
X
15
x=

Answers

Answer:

We can fine x by using the pythagoras formula

a²+b² = c²

Which C is X

And

a= 17

b= 15

So

a² + b² = c²

(17)² + (15)² = c²

289 + 225 = c²

514 = c²

√514 = c

22.67 = c

So basically X is (22.671)

The missing side of the given right angled triangle is 8 units.

In the given right angled triangle, the hypotenuse side is 17 units, base is 15 units and the height is x units.

By using Pythagoras theorem, we get

17²=15²+x²

289=225+x²

x²=289-225

x²=64

x=√64

x=8 units.

Therefore, the missing side of the given right angled triangle is 8 units.

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3) Consider a triangle with side lengths 5 and 13. What are the possibilities for the third side if the
triangle is right

Answers

Answer:

find the square of both numbers

13²=169

5²=25

minus the square

169-25 to get 144

find the square root of 144

✓144=12 the third side is 12

I think you already got the answer so im just gonna do this for points
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