The length of PC is 3.
What is tangent- secant theory?If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Given: BA = 5, AP = 4 and DP = 12.
PB= BA+AP= 9
Using tangent- secant theory
PA*PB= PC*PD
4*9= PC* 12
36= 12PC
PC= 36/12
PC= 3
Hence, length of PC is 3.
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Claudia is making a candle by pouring melted wax into a mold in the shape of a cylinder. The radius of the cylinder’s base is 4 cm, and the height of the cylinder is 9 cm. To get the wax for the candle, Claudia melts cubes of wax that are each 3 cm by 3 cm by 3 cm. How many of the wax cubes will Claudia need to purchase to make the candle? (Note that Claudia is not able to purchase partial cubes). Show all your work.
The formula of a cylinder is 2πr (r+h)
2π4 (4+9)
8π (13)
25.13 (13)
326.73
Cubes: area = a^3
3x3x3 = 27
326.73 / 27 = 12.1
Claudia would need to buy 13 wax cubes to fil the candle.
hope this helps k12 students :)
Write cos 32° in terms of sine.
cos 32° = sin
[tex]\cos32^{\circ} \\\\=\sin(90-32)^\circ~~~~~~~~~~~~~~;[\cos \theta = \sin(90- \theta)]\\\\=\sin 58^{\circ}[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
3 1/2
Step-by-step explanation:
the letter j is HALFway between four and three so it is 3 1/2
Sarah drives at a speed of 70 miles per hour.
How long will it take to drive 385 miles?
Answer:
5.5 Hours
or
5 Hours 30 Minutes
Step-by-step explanation:
Dirving speed = 70 mphDistance = 385 milesTo find: Time Formula relating speed, distance and time is given as: [tex]Time =\frac{Distance}{Speed}[/tex][tex]\implies Time =\frac{385}{70}[/tex][tex] \implies Time = 5.5\: hours [/tex][tex]\implies \red{\boxed{\bold{Time = 5\: hours\: 30\: minutes}}}[/tex]Solve the following equations:
[tex]1.\sqrt{5x+4}-1=2x[/tex]
[tex]1) \ 3\sqrt{x-1 }+11=2x[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 1. \ \sqrt{5x+4} -1=2x \end{gathered}$}[/tex]
The root of the equation is solved first. Afterwards, both members of the equality are squared, the powers are developed and it is solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{5x+4}=2x+1 \Longrightarrow 5x+4=(2x+1)^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 0=4x^2 +4x+1-5x-4 =4x^2-x-3 \\ &= 4\left(x^2-\dfrac{1}{4}-\dfrac{3}{4} \right)\\ &=4\left(x-1\right)\left( x+\dfrac{3}{4}\right) \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x_1=1 \qquad x_2=-\dfrac{3}{4} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2. \ 3\sqrt{x-1}+11=2x \end{gathered}$}[/tex]
The root of the equation is cleared. Then, both sides of the equality are squared, the powers are developed and it is solved by the general formula.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 3\sqrt{x-1}=2x-11 \Longrightarrow 9(x-1)=(2x-11)^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 0=4x^2 -44x+121 -9x+9 =4x^2-53x+130 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x_{1,2}=\dfrac{53\pm \sqrt{(-53)^2-4(4)(130)}}{2(4)}=\dfrac{53\pm \sqrt{2809-2080}}{8}\\ &=\dfrac{53\pm \sqrt{729}}{8} = \dfrac{53\pm 27}{8}; \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} \ \ \ \ \ \ x_{1}=\dfrac{53+ 27}{8} \qquad &\ \ \ \ \ x_2=\dfrac{53 - 27}{8}\\ x_1=\dfrac{80}{8} \qquad &\ \ x_2=\dfrac{26}{8}\ \ \ \\ x_1=10 \qquad &x_2=\dfrac{13}{4} \end{matrix} \end{gathered}$}[/tex]
find the cost of 10 pens at x pence each
Answer:
D. x + 10 pence
Step-by-step explanation:
Since the pen costs 10 pence more than the ruler, we need to add 10 to x.
Maria makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answer: p = 9h
Step-by-step explanation:
If she makes 9 dollars of every hour of work, this will be a linear equation. We will write it as the following:
p = 9h
Answer:
9h/p
Step-by-step explanation:
9 x # of hours = total pay
$9 is the dollars for each hour, so you multiply that by how many hours Maria works. You will get the total pay.
Help me this pls as soon as possible this is due today!!!
Answer:
you can find the given attachment
On March 1st Kendra’s checking account had a balance of $325.31. She wrote a check for $24.85, withdrew $40 from the ATM, and deposited $15. What was Kendra’s balance after these transactions?
Answer:
275.46
Step-by-step explanation:
She has $325.31
she writes a check for $24.85
she withdrew $40
and deposited $15
so do 325.31-24.85-40+15
and that equals
275.46
Lessons are 55 mins long, a history lesson ends at 3:30 pm at what time does the lesson start
Answer:
2:35 pm
If an hour is 60 minutes, what we know is that 30 minutes is half. However, we must subtract 55 from 30 (In time)
To make this easier, subtract 55 by actual 30, and split 55 into 2 parts, the result of subtraction, and the other value, 30
[tex]55-30=25[/tex]
Now, subtract.
[tex]3:30 - 30 = 3:00[/tex]
[tex]3:00-25=35[/tex]
If this is the case, the lesson must have started at 2:35 pm
1. Given O B and marked angle measure.
Find MZADC and find the measure of AC
с
135°
D
B
А
Step-by-step explanation:
angle ADC = angle ABC / 2
= 135/2 = 67.5°
AC = 2r * sin (62.5)
AC = 1.84r
r is the radius of circle
A tank contained 1.5 litres more water than a pail. Swee Leng transferred 300 millilitre of water from the pail to the tank. Now the tank contains 4 times as much water as the pail. How many litres of water were there in the tank at first?
Answer:
i think so 4.32 L
Find the surface area of the rectangular prism
Answer:
126 mi²
Step-by-step explanation:
Surface Area of a Rectangular Prism :
SA = 2(bh + lh + lb)SA = 2(3 × 5 + 6 × 5 + 6 × 3)SA = 2(15 + 30 + 18)SA = 2(63)SA = 126 mi²The third term in a sequence is 11.
The term-to-term rule is "take away 4".
Write an expression, in terms of n, for the nth term of the sequence.
Answer:
Nth term = 19 - 4(n-1)
Step-by-step explanation:
First term be A
Nth term = A - 4(n-1)
3rd term = 11 = A - 4*2 = A - 8
A = 19
Nth term = 19 - 4(n-1)
Alguien me ayuda? Who can help me?
Is for my litte brother
es para mi hermano pequeño
The solving of the fractions simply shows that the value of 1 2/3 + 3 1/2 is 5 1/6.
How to solve the fraction?The first fraction give is:
= 1 2/3 + 3 1/2
= 1 4/6 + 3 3/6
= 4 7/6
= 4 + 1 1/6
= 5 1/6
Also 3/4 - 5/7 will be:
= 3/4 - 5/7
= 21/28 - 20/28
= 1/8
It should be noted that when solving fractions, it's important to have a common denominator.
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Unit test
Problem
Here are two different samples drawn from two different populations:
Two dot plots show the distributions of two samples. For each sample, the number line has a scale from 0 to 100 in increments of 10. For sample A, n = 11. The distribution is right skewed between 70 and 100, with outliers at 0 and 10. For sample B, n = 14. The distribution is right skewed between 0 and 100.
Which sample satisfies the normal condition for constructing a ttt interval?
Using the Central Limit Theorem, it is found that none of the samples satisfy the normal condition.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as at least one of these following conditions is respected.
The underlying distribution is normal.The sample size is greater than 30.In this problem, the underlying distributions are skewed, and both sample sizes are less than 30, hence none of the samples satisfy the normal condition.
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Answer:
N/A
Step-by-step explanation:
4x + 90 find the value of x
Answer:
x = -22.5
Step-by-step explanation:
Assuming 4x + 90 = 0
4x + 90 = 0
4x = -90
-90/4 = -22.5
Find two numbers whose difference is 30 and whose product is a minimum.
Answer:60-30 I guess
Step-by-step explanation:n60-30=30
Let A = -4k+ 3 and B = 3k +17. If A = B, then what is the value of k?
Answer:
k=-2
Step-by-step explanation:
Using substitution to find what you're missing, (in this case k) is when you plug each letter into the other equation:
-4k+3=3k+17
So now solve for k:
subtract 3 from both sides...
-4k=3k+14
subtract 3k from both sides to combine with -4k...
-7k=14
divide -7 from both sides...
k=-2
Solve 10(0j + 4j + 40)
Hey there!
10(0j + 4j + 40)
DISTRIBUTE 10 WITHIN the PARENTHESES
= 10(0j) + 10(4j) + 10(40)
= 0j + 40j + 400
COMBINE the LIKE TERMS
= (0j + 40j) + (400)
= 0j + 40j + 400
= 40j + 400
Therefore, the answer should be:
40j + 400
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
[tex]\boxed{40j + 400}[/tex]
Step-by-step explanation:
Given expression:
[tex]10(0j + 4j + 40)[/tex]
Since the expression inside the parentheses can be simplified, it is suggested to simplify the expression, inside the parentheses, first.
[tex]\implies10[j(0 + 4) + 40][/tex]
[tex]\implies 10[4j + 40][/tex]
Now, simplify the distributive property.
The distributive property can be simplified by multiplying the term outside the parentheses with all the terms inside the parentheses.
[tex]\implies 10[4j + 40][/tex]
[tex]\implies [4j \times 10] + [40 \times 10][/tex]
[tex]\implies \boxed{40j + 400}[/tex]
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141,690 to the nearest 10 dollars
Answer:
$ 141 690 .
Step-by-step explanation:
It is already rounded to the nearest 10 dollars
Please help me with this math problem!! Will give brainliest!! :)
Answer:
A. 17
B. 16
Step-by-step explanation:
F(5)
5 > 2 so you plug the 5 into 3x+2
F(-2)
-5 < -2 < 2 so you plug the -2 into (x-2)^2
⚠ANSWER FOR THE 5TH GRADERS⚠
Answer:
vitamins - organic compound
minerals - inorganic compounds
Step-by-step explanation:
Answer:
1. minerals = B inorganic elements
2. Vitamins = A organic compound
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation x+y=3. Fully simplify your answer
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]x + y =3\implies y=-x+3\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+3 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1}\implies 1}}[/tex]
The graph from the US Department of Agriculture shows the growth of farmers markets in the United States. What was the first year that th enumber of farmers markets increased to over 3000?
2001
2002
2000
2003
Answer:
Its was 2002 since that is the first heightest bar pass 3000
PLEASE HELP ME.......
The equation first, third, fifth and seventh are equivalent to the fifth, second, fourth and eighth equation.
How to find the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
Equivalent expression can be found out by simplifying the given equation.
First equation given as,
[tex]\left(-14+\dfrac{3}{2}b\right)-\left(1+\dfrac{8}{2}b\right)[/tex]
Simplify it further,
[tex]\left(-14+\dfrac{3}{2}b\right)-\left(1+\dfrac{8}{2}b\right)\\-14+\dfrac{3}{2}b-(1+4b)\\-14+\dfrac{3}{2}b-1-4b\\-15-\dfrac{5}{2}b[/tex]
Third equation in the problem given as,
[tex]\left(5+2b\right)+\left(2b+\dfrac{3}{2}\right)\\5+2b+2b+\dfrac{3}{2}\\4b+\dfrac{13}{2}[/tex]
Simplify it further,
[tex]\left(-14+\dfrac{3}{2}b\right)-\left(1+\dfrac{8}{2}b\right)\\-14+\dfrac{3}{2}b-(1+4b)\\-14+\dfrac{3}{2}b-1-4b\\-15-\dfrac{5}{2}b[/tex]
Similarly, the fifth and seventh equation are simplified and equivalent to the fourth and eight respectively.
Thus, the equation first, third, fifth and seventh are equivalent to the fifth, second, fourth and eighth equation.
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What is the value of "a" in the following quadratic? (Make sure the equation is in
standard form: ax² + bx+c=0)
x^2 + 28 = -11x
Answer: a= - [tex]\frac{b}{x}[/tex]- [tex]\frac{c}{x2}[/tex]
Step-by-step explanation:
1. Move all terms not containing [tex]\alpha[/tex] to the right side of the equation.
[tex]\alpha[/tex][tex]x^{2}[/tex]=-bx-c
2. Divide each term in [tex]\alpha x^{2}[/tex]=-bx-c by [tex]x^{2}[/tex] and simplify.
a= - [tex]\frac{b}{x}[/tex] - [tex]\frac{c}{x^{2} }[/tex]
Example a) Name the vertex of the angle. b) Name the sides of the angle. c) Give three ways to name the angle. d) Classify the angle.
Answer:
OBtuse <
Step-by-step explanation:
The given two-way table shows the number of passengers, by type, on the Ferris wheel at an amusement part for its first two runs on a Sunday morning.
First Run
Second Run Total
Children 122 146 268
Adults 183 219 402
Total 305 365 670
Based on the data in the table, what is the value of P(Adult|Second run) rounded to the nearest thousandth?
The two-way table is an illustration of probability, and the value of P(Adult|Second run) is 0.600
How to determine the probability?The probability to calculate is given as: P(Adult|Second run)
This means:
The probability that an Adult is selected given that the adult runs the second run
The formula to solve this is:
P(Adult|Second run) = n(Adult and Second run)/n(Second run)
From the table, we have:
n(Adult and Second run) = 219
n(Second run) = 365
So, we have:
P(Adult|Second run) = 219/365
Evaluate
P(Adult|Second run) = 0.600
Hence, the value of P(Adult|Second run) is 0.600
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Answer:
The value of P rounded to the nearest thousandth would be 0.6
Hope this helped!
Please help me with this it's algebra WILL GIVE BRAINLIEST and 5 points
Answer: y-2 > 1/4(x-4)
Step-by-step explanation:
use slope formula y2-y1/x2-x1 so 2-0/4-(-4) = 1/4
slope int form is y-y1 = m(x-x1)
plug in one point
y-2 = 1/4(x-4)
insert (0,0)
you find y-2 > 1/4(x-4)