Answers
Tangents from an external point to a circle's circumference are equal.
So
WZ = WX
WZ = 5a + 12
WX = 7a + 5
7a + 5 = 5a + 12 Subtract 5 from both sides.
7a = 5a + 12 - 5
7a = 5a + 7 Subtract 5a from both sides.
7a - 5a = 7
2a = 7 Divide by 2
a = 7/2
a = 3.5
Related Questions
Find the diameter of a circle whose equation is x2+(y−2)2=100x2+(y−2)2=100.
400
20
10
100
Answers
Take the square root of 100
sqrt(r^2) = sqrt(100)
r = 10
But you want the diameter.
d = 2 * r
d = 20
B answer.
Divide 2y2 + 8 by 2y + 4. Which expression represents the quotient and remainder?
Answers
Final answer:
To divide 2y² + 8 by 2y + 4, use long division to find the quotient and remainder.
Explanation:
To divide 2y² + 8 by 2y + 4, we can use long division. Here are the steps:
Divide the first term of the dividend by the first term of the divisor, which gives us y.
Multiply the entire divisor by y to get 2y² + 4y.
Subtract 2y² + 4y from the dividend 2y² + 8 to get 4.
Next, divide 4 by 2y + 4, which gives us 2.
Finally, we have a remainder of 0.
Therefore, the quotient is y + 2 and the remainder is 0.
katy buys ‘x’ cakes.
Gugu buys 3 times as many cakes as katy.
Deanna buys 2 more cakes than Katy.
Each cake costs 85p
The total of the cakes is £52.70
How many cakes did each girl buy?
Answers
Katy bought 12 cakes
Gugu bought 36 cakes
Deanna bought 14 cakes
Explanation:
We are given that:
Katy bought x cakes
Gugu bought 3 times as many as Katy. This means that Gugu bought 3x cakes
Deanna bought 2 cakes more than Katy. This means that Deanna bought x+2 cakes
Total number of cakes bought = x + 3x + x + 2 = 5x + 2 cakes
We know that the price of each cake is 85 p = £0.85 and that the total amount paid is £52.7
This means that:
(5x+2)(0.85) = 52.7
4.25x + 1.7 = 52.7
4.25x = 52.7 - 1.7
4.25x = 51
x = 51 / 4.25
x = 12
Now, we will get the number of cakes that each bought as follows:
Katy bought x cakes = 12 cakes
Gugu bought 3x cakes = 3(12) = 36 cakes
Deanna bought x+2 cakes = 12 + 2 = 14 cakes
Hope this helps :)
Answer:
Katy bought 12 cakes
Gugu bought 36 cakes
Deanna bought 14 cakes
Step-by-step explanation:
3(−4x) + 3(5) = 12
−12x + 15 = 12
−12x + 15 − 15 = 12 − 15
−12x = −3
x =
Answers
Answer: 1/4
don't forget to rate and thank plz.
WILL VOTE BRAINIEST IF CORRECT(must be next few minutes): The formula for the area of circle A is Area=πr2 . Sector CAB is a fraction of circle A. In degrees, the fraction is θ/360∘ . In radians, the fraction is _____. Inserting this fraction into the formula for the area of a circle, and then simplifying, results in the formula _____.
(image attached)
choices: 2pi0, 0pi, 0/2pi, area=0r^2, area= 2pi0r^2, area= 0/2r^2
Answers
The fraction of the sector of a circle in radians is (θπ/180). Substituting this fraction into the formula for the area of a circle, and simplifying, results in the formula for the area of the sector being A = (θπ/360) * r^2.
Explanation:In a circle, the angle in degrees is often converted to radians for calculations. A full circle is equivalent to 360 degrees or 2π radians. Therefore, if the sector angle is θ degrees, then in radians, the equivalent is (θ/360) * 2π = θπ/180.
Inserting this into the formula for the area of a circle, which is A = πr2, the area A of the sector becomes a fraction of the full circle's area, which is calculated as follows: (θ/360) * A = (θ/360) * πr2 = (θπ/180) * r2. Simplifying this results in the formula A = (θπ/360) * r2.
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For a sector in a circle, the fraction is θ/2π in radians. After substituting this into the formula for circle's area, we get the area of sector as Area = (θr²)/2.
Explanation:The fraction in radians for a sector in a circle is θ/2π, because there are 2π radians in a whole circle. As the formula for the area of circle A is Area=πr², when we insert this fraction, which represents the proportion of the circle that Sector CAB occupies, we get the formula for the area of a sector: Area= (θ/2π) * πr². This simplifies to Area= (θr²)/2, as the π's cancel out. This formula says that the area of a sector is proportionate to its central angle and the square of the radius of the circle.
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Cindy and Giovanni plan to make spaghetti sauce. Cindy needs 4 3/4 pounds of tomatoes for her recipe. Giovanni needs 5 /34 pounds of tomatoes for his recipe. If they make both recipes, how many pounds of tomatoes do they need?
Answers
Answer:
[tex]10\frac{1}{2}\text{ pounds}[/tex]
Step-by-step explanation:
Given,
For a recipe,
Cindy needs tomatoes = [tex]4\frac{3}{4}[/tex] pounds,
While, Giovanni needs tomatoes = [tex]5\frac{3}{4}[/tex] pounds,
If they make both recipes,
Then, total tomatoes they need = [tex]4\frac{3}{4}+5\frac{3}{4}[/tex]
[tex]=\frac{19}{4}+\frac{23}{4}[/tex]
[tex]=\frac{42}{4}[/tex]
[tex]=10\frac{2}{4}[/tex]
[tex]=10\frac{1}{2}\text{ pounds}[/tex]
How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?
A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h
Answers
New volume=(old volume)×(4×2/9×2/9)
simplifying the above we get:
New volume=(old volume)×16/81
Thus the new volume is 16/81 times the old volume
old volume=πr²h
Hence:
Answer:16/81πr²h
A company spent 32% of its annual budget developing a new machine. What fraction of the company's budget was spent developing the new machine?
Answers
We have been given that the company spent 32% of its annual budget developing a new machine.
Let us convert the percentage to fraction.
[tex]32 \%=\frac{32}{100} \\ \\ 32 \%=\frac{4\times 8}{4\times 25}\\ \\ \text{Cancel 4 from numerator and denominator}\\ \\ 32 \%=\frac{8}{25}[/tex]
Thus, when we convert 32% to fraction that will be equal to 8/25.
Hence, [tex]\frac{8}{25}[/tex] company's budget was spent developing the new machine.
The volume of a right triangular prism is 72 cubic feet. The height of the prism is 9 feet. The triangular base is an isosceles right triangle.
Answers
Answer:
Step-by-step explanation:
What is the area of the triangular base? 8 square feet
What is the length of edge DF? 4 feet
Answer:
What is the area of the triangular base?
8 square feet
What is the length of edge DF?
4 feet
Step-by-step explanation:
just did the quiz on EDG
Which expression is equivalent to x3 – 7x – 6?
Answers
The function is f(x) = (x + 2)(x + 1)(x - 3)
Answer is D.
It takes 60 pounds of seed to completely plant a 10-acre field. How many acres can be planted per pound of seed
Answers
You divide the amount of space planted by the weight of seeds it took
10 / 60 = 0.6
It takes 0.6 pounds of seeds to plant 1 acre of land
Hope this helps!
Multiply. 0.35 × 0.003 =
Answers
Answer:
0.00105
Step-by-step explanation:
Sharon wants to know the difference between the average amount she stacked and the average amount Diane stacked. Which operation would she use to find the difference?
Answers
Hope this helped :D
What is true about side AB and side AD?
Answers
HELP ME PLEASE I DONT UNDERSTAND THIS PROBLEM!!!!! Worth 20PT
a ball is thrown with a slingshot at a velocity of 100 ft/sec at an angle 21 above the ground from a height of 5ft approximately how long does it take for the ball to hit the ground? acceleration due to gravity is 32 ft/s^2
Answers
We use the equation h(t)=-1/2gt²+v₀t+h₀ to set this up. g is the acceleration due to gravity, v₀ is the initial velocity and h₀ is the initial height:
h(t) = -1/2(32)t² + 100t + 5
h(t) = -16t² + 100t + 5
We will use the quadratic formula to solve this:
[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\=\frac{-100\pm\sqrt{100^2-4(-16)(5)}}{2(-16)} \\ \\=\frac{-100\pm\sqrt{10000--320}}{-32} \\ \\=\frac{-100\pm\sqrt{10320}}{-32} \\ \\=\frac{-100\pm101.59}{-32} \\ \\=\frac{-100+101.59}{-32}\text{ or }\frac{-100-101.59}{-32} \\ \\=\frac{1.59}{-32}\text{ or }\frac{-201.59}{-32} \\ \\=-0.05\text{ or }6.3[/tex]
Since a negative amount of time makes no sense, the answer is 6.3.
Answer:
D) 2.37 seconds
Step-by-step explanation:
Took the test and got it wrong.
please help me figure out this probability problem!!!
Answers
The probability that the first ball is red: [tex]P(R)=\dfrac{10}{16}=\dfrac{5}{8}[/tex]
The probability that the second ball is black: [tex]P(B)=\dfrac{1}{15}[/tex]
Together:[tex]P(R)\cdot P(B)=\dfrac{5}{8}\cdot\dfrac{1}{15}=\dfrac{1}{24}[/tex]
So your answers are....
First ball being red: 5/8
Second ball being black: 1/16
Hoped this helped. Have a nice day!
For which angle is secant undefined?
30°
45°
180°
270°
Answers
The secant is undefined at angle values that represent 1/4 and 3/4 of a full circle. At these angles, the triangle geometrically vanishes into a simple line segment on the Y axis. The value of the triangle's adjacent side is zero and division by zero is undefined.
Answer:
the answer is 180 degrees
Step-by-step explanation:
i used my head and my google maths
The lateral area of a cone is 555 \pi cm^2 and the radius is 15.1 what is the slant height?
Answers
[LA]=pi*r*l
where
LA is the lateral area of the cone
r is the radius
l is the slant height
l=LA/(pi*r)
r=15.1 cm
LA=555*pi cm²
l=(555*pi)/(pi*15.1)----> l=36.75 cm
the answer is
the slant height is 36.75 cm
solve the equation
3x-3= -18
Answers
3x-3=-18
+3 +3 Remember: What you do to one side, you have to do to the other.
3x = -15
Now divide by the coefficient (the number in front of x).
(3x)/3 = (-15)/3
x = -5
The solution of the equation 3x-3= -18 is -5.
The algebraic expressions which are separated by an equal symbol in between them and with the same value is called is an equation
Example = 5x + 5 = 12
here, x is a variable and 5 and 12 are constants.
Given equation;
3x-3= -18
To find the value of x add 3 to both side, we get
3x = -18 +3
we get
3x = -15
divide both side by 3 we get
[tex]x = \dfrac{-15}{3}[/tex]
Convert in into the lowest form we get,
x = -5
The solution of the equation 3x-3= -18 is -5
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What is the 12th term of the sequence? 3, −9, 27, −81, 243, ...
531441
−531441
177147
−177147
Answers
There are 2 ways you can find this.
A. You can find this by starting with 3, and multiply -3 then multiply -3 to each product after that 11 times. Or...
B. Simply find 3 to the 12th power. Then add a negative since each even term (term 2, 4, 6, etc) are negative.
I hope this helps!
How many times larger is 4 x 1016 than 5 x 108?
Answers
5 × 108 = 540
4,064 ÷ 540 = 7.5
Answer = 7.5
~Aamira~
Hope this helped☺☺
Solve the equation using square roots. 3x2 – 27 = 0
Answers
The answers are x = 3 and x = -3.
[tex]3 {x}^{2} - 27 = 0[/tex]
Add 27.
[tex]3 {x}^{2} = 27[/tex]
Divide by 3.
[tex] {x}^{2} = 9[/tex]
Take the root and the negative root.
[tex]x = \sqrt{9} = 3 \: \: or \: \: x = - \sqrt{9} = - 3[/tex]
Therefore, the answers are x = 3 and x = -3.
~ Hope this helps you!
The value of X are x = 3 and x = -3. using square root.
What is square root?A square root can be regarded as a factor of a number in the sense that when that number is multiplied by itself, it gives the original number.
3x²– 27 = 0
⇒3x²= 27
⇒x²= 27/3
⇒x² = 9
⇒x = sqrt(9)
⇒ x =±3
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Seven of the 10 children at art camp make an average of 8 paintings. The remaining children make an average of 12 paintings. What is the average number of paintings made by children at the art camp? Enter your answer in the box.
Answers
I WILL GIVE BRAINLIEST The area of the surface of the trampoline (square) is equal to twice its perimeter. Find the dimensions. length= 4x ft., width= (x+6) ft.
FACTORING POLYNOMIALS/SOLVE THE EQUATION BY FACTORING HOMEWORK
Answers
length=4x ft, width=(x+6) ft
the perimeter will be:
P=2(L+W)
P=2(4x+(x+6))
P=2(4x+x+6)
P=2(5x+6)
P=(10x+12)
Area of the rectangle is:
A=4x(x+6)
A=4x²+24x
but:
2P=A
thus
2(10x+12)=4x²+24x
20x+24=4x²+24x
thus
4x²+4x-24=0
x²+x-6=0
x²-2x+3x-6=0
x(x-2)+3(x-2)=0
(x-2)(x+3)=0
thus the answer is:
x=-3 or x=2
thus
length=4x=4*2=8 ft
width=(x+6)=(2+6)=8 ft
What value of c makes the trinomial below a perfect square x2 + 7x + c?
Answers
x² + 7x + c
Group terms that contain the same variable
(x² + 7x )+ c
Complete the square. Remember to balance the equation
(x² + 7x+3.5² )+ c-3.5²
Rewrite as perfect squares
(x+3.5)²+ c-3.5²so
c-3.5² must be zero
c-3.5²=0------- c=3.5²------> c=12.25
the answer is
the value of c must be 12.25
Answer:49/4
Step-by-step explanation:
Algebra question ( Matrices and Determinants ) 20 points
Answers
A. -30
The determinant of B = -18*1 -3*4 = -18-12 = -30
Haley sings for $1,000 an hour. Her rate increases by 50% after midnight. If she sings one
night from 8:30 pm until 1:00 am, how much should she be paid?
a) $4500 b) $5000 c) $5500 d) $6000
Answers
A 3 inch wide border is wrapped around a rectangular prism. the length of the rectangular prism is 8 inches longer than its width. the surface area covered by the border is 383 square inches. what is the width of the rectangular prism? answer in units of inches.
Answers
How can you prove a triangle is a right triangle? select one:a. use the distance formula to see if at least two sides are congruent.b. use the slope formula to see if any sides are perpendicular.c. use the distance formula to see if all three sides are congruent.d. use the slope formula to see if any sides are parallel?
Answers
__________________
Help me please & thank ya
Answers
Hope this helps.