Answers
In the first circle, x is the radius and also the hypotenuse of a right triangle with legs measuring 9 and 12. So by the Pythagorean theorem,
x² = 9² + 12² = 225 = 15² ⇒ x = 15
In the second circle, the chords AB and CD have the same length, and each of AP, BP, CP, and DP are radii of the circle and also have the same length. This means ∆ABP and ∆CDP are congruent, so the two labeled angles are also congruent, so x = 54.
Related Questions
Triangle ABC is congruent to triangle DEF. Angle B is a right angle, and m∠C = 34°. What is m∠D?
56°
34°
64°
46°
Answers
Answer: 56°
Step-by-step explanation:
Can anyone solve number 20?
Answers
Answer:
X=80
Step-by-step explanation:
Angle OAB=50(Properties of isosceles traingle)
X+50+50=180(sum of the interior angles of the traingle)
X=180-100
X=80
Answer this volume based Question. I will make uh brainliest + 50 points
Answers
Answer:
[tex]\huge{\purple {r= 2\times\sqrt[3]3}}[/tex]
[tex]\huge 2\times \sqrt [3]3 = 2.88[/tex]
Step-by-step explanation:
For solid iron sphere:radius (r) = 2 cm (Given)Formula for [tex]V_{sphere} [/tex] is given as:[tex]V_{sphere} =\frac{4}{3}\pi r^3[/tex][tex]\implies V_{sphere} =\frac{4}{3}\pi (2)^3[/tex][tex]\implies V_{sphere} =\frac{32}{3}\pi \:cm^3[/tex]For cone:r : h = 3 : 4 (Given)Let r = 3x & h = 4xFormula for [tex]V_{cone} [/tex] is given as:[tex]V_{cone} =\frac{1}{3}\pi r^2h[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (36x^3)[/tex][tex]\implies V_{cone} =12\pi x^3\: cm^3[/tex]It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume[tex]\implies V_{cone} = V_{sphere}[/tex][tex]\implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}[/tex][tex]\implies 12x^3= \frac{32}{3}[/tex][tex]\implies x^3= \frac{32}{36}[/tex][tex]\implies x^3= \frac{8}{9}[/tex][tex]\implies x= \sqrt[3]{\frac{8}{3^2}}[/tex][tex]\implies x={\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\because r = 3x [/tex][tex]\implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\implies r=3\times 2(3)^{-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{1-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{\frac{1}{3}}[/tex][tex]\implies \huge{\purple {r= 2\times\sqrt[3]3}}[/tex]Assuming log on both sides, we find:[tex]log r = log (2\times \sqrt [3]3)[/tex][tex]log r = log (2\times 3^{\frac{1}{3}})[/tex][tex]log r = log 2+ log 3^{\frac{1}{3}}[/tex][tex]log r = log 2+ \frac{1}{3}log 3[/tex][tex]log r = 0.4600704139[/tex]Taking antilog on both sides, we find:[tex]antilog(log r )= antilog(0.4600704139)[/tex][tex]\implies r = 2.8844991406[/tex][tex]\implies \huge \red{r = 2.88\: cm}[/tex][tex]\implies 2\times \sqrt [3]3 = 2.88[/tex]A local couple is deciding to invest their lifetime savings of $68,000.00 into a Fijian business. They are considering two businesses. Business A, in the food and beverage (FNB) industry, provides an annual cash income of about $8,000 for 10 years. Business B, in the clothing and textiles industry, provides an annual cash income of $7,500 for 11 years commensurate with their level of investment. If the couple on the other hand decide to leave their lifetime savings into a fixed deposit at their current bank, which is a large international bank, they would get about 1.5 percent per annum. The economy is currently in the expansionary phase of the business cycle. However, it is forecasted that a severe global downturn is expected in 1 years’ time and the resulting recession will last about 1 year thereafter. During the recession, it is expected that cash flows in the FNB industry will fall by 40 percent per annum. In the clothing and textiles industry, it is expected that cash flows will fall by about 35 percent per annum. The general elections are expected to be held in 4 years’ time. Policy changes around taxation could be expected but at present are uncertain.
Required:
i. Calculate the present value of the cash inflows of both alternatives and compare it against the investment required. Clearly show which investment is preferred
ii. Identify and discuss the key risks faced by the couple in each scenario
iii. Against the type of risks involved, please discuss which investment would you choose
Answers
The best investment option for this couple is the Food and Beverage industry because it is the one that gives them the highest profits within 11 years compared to the other alternatives.
How to calculate the profit of the couple in each investment alternative?To calculate the pair's gain in each alternative we must perform the following mathematical operations:
Food and beverage (FNB) industry
$8,000 × 10 years = $80,000$8,000 ÷ 100 = $80$80 × 40% = $3,200$80,000 - $3,200 = $76,800$76,800 + $8,000 = $84,800Clothing and textiles industry
$7,500 × 11 years = $82,500$7,500 ÷ 100 = $75$75 × 35% = $2,625$82,500 - $2,625 = $79,875Current Bank
$68,000 ÷ 100 = $680$680 × 1.5% = $1,020$1,020 × 11 = $11,200$68,000 + $11,200 = $79,220Based on the foregoing, it can be inferred that the best investment option for the couple is the Food and Beverage (FNB) industry because it is the one that leaves the highest profits despite the decrease in profits during the second year.
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Audrey is running for student council president. she estmates her chances of winning to be 1/5 chance. Which likelihood describes aubrey's estimated chances of winning?
A. Impossible
B. Unlikely
C. likely
D. Certain
Answers
Answer:
B. Unlikely
Step-by-step explanation:
Generally speaking, a probability of 0.11 to 0.40 is unlikely. 1/5 is 0.2, which falls in this range.
x²+8x-16 by factorising method
what is the ans pls I need it fast ASAP
Answers
Answer:
this cannot be factored since nothing shares factorable groups/values
Step-by-step explanation:
hope this helps:)
What is the length of a side of an equilateral triangle inscribed in a circle with a radius of 10 cm?
Answers
Answer:
a = √3 * r
a = √3 * 10
a = 10√3 cm
Step-by-step explanation:
simplify. 5ab/15a+10a²
Answers
A triangle has a base of 4 m and a height of 3 m.
What is the area of the triangle?
Enter your answer in the box.
m²
Answers
Answer:
Area of the triangle is 6
Step-by-step explanation:
The formula for the area of a triangle is the base x height / 2. This means we can just plug in the variables and solve
A = b x h/2
A= 4 x 3/2
A= 12/2
A= 6
Answer: 6
Step-by-step explanation:
solve the equation 1/x+3/x=16
Answers
[tex] \frac{1}{x} + \frac{3}{x} = 16 \\ [/tex]
[tex] \frac{4}{x} = 16 \\ [/tex]
[tex]16x = 4[/tex]
[tex]x = \frac{4}{16} \\ [/tex]
[tex]x = \frac{1}{4} \\ [/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{1}{x} + \frac{3}{x} = 16} \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{4}{x } = 16 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ x = 16 \times 4 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \implies \orange{\underline{\boxed{\large\frak \pink{x = 64 }}}} \\ \end{gathered}[/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Stan pays a 10% deposit to put a pool table on lay-by.
If the pool table costs $1590, how much does he have left to pay?
Answers
Answer:
$1431
Step-by-step explanation:
If Stan pays a 10% deposit, he pays $159. 10% of $1590 is simply 0.1 * 1590 = 159. Assuming this is the only amount he pays, he then simply needs to pay the full price minus $159. We can find this by simply subtracting 159 from 1590 to get 1431. Stan still needs to pay $1431.
If h(x)=(0,-9),(5,2)(8,-3),(10,11) which set of ordered pairs represents the inverse of h(x)
Answers
Set of ordered pairs is {(-9,0),(2,5)(-3,8),(11,10)
What is ordered pair?
An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
Given:
h(x)=(0,-9),(5,2)(8,-3),(10,11)
The inverse of anything interchange the position of variables or numbers or etc.
In ordered set the inverse will be x- coordinate become y- coordinate and y- coordinate become x- axis.
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please help will mark Brainliest!!
Answers
Answer:
number 2
Step-by-step explanation:
im not that sure but i think it's that one
Can someone please just check my answers over to make sure I got them right. Thank you so much!
Let me know if you need a close up on any of the pictures!
Answers
Answer: they are all correct congrats!
Step-by-step explanation:
Linda asked the students of her class their hockey scores and recorded the scores in the table shown below:
Hockey Scores
Score Number of Students
0 2
1 1
2 3
3 6
4 2
5 3
6 2
Based on the table, what is the mean hockey score?
2.7
2.9
3.2
5.2
Answers
Answer:
C) 3.2
Step-by-step explanation:
[tex]\text{Mean}=\frac{2(0)+1(1)+3(2)+6(3)+2(4)+3(5)+2(6)}{19}\approx3.2[/tex]
Answer:
2.7
Step-by-step explanation:
the hockey score is 2.7
PLEASE HELP ME
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level a.
n=11, a = 0.01
A r=+0.735
B r=+0.602
C r= 0.765
D r= 0.735
Answers
The reason for why the answer is not “A” is due to the fact that we’re finding all of the possible r values, we are not a evaluating r to see whether or not it is significant.
What is the volume of this box? Cardboard box A. 15 cm3 B. 96 cm3 C. 120 cm3 D. 148 cm3
Answers
use a formula to find the surface area of the cylinder use 3.14 for pi
Answers
Answer:
376.8 cm²
Step-by-step explanation:
Given:
Radius of circular base: 4 cmHeight of cylinder: 11 cmSurface area = 2πrh + 2πr²
[Where "r" and "h" represents the radius and the height respectively]
Let's substitute the height and the radius in the formula and simplify it.
[tex]\implies 2\pi rh + 2\pi ^{2}[/tex]
[tex]\implies 2\pi (4)(11) + 2\pi (4)^{2}[/tex]
[tex]\implies 2\pi (44) + 2\pi (16)[/tex]
[tex]\implies 88\pi + 32\pi[/tex]
We can factor π out of the expression. Therefore, we get:
[tex]\implies 88\pi + 32\pi[/tex]
[tex]\implies \pi (88 + 32)[/tex]
Now, simplify the expression inside the parentheses.
[tex]\implies \pi (88 + 32)[/tex]
[tex]\implies \pi (120)[/tex]
The value of π, we are given, is 3.14. When substituted, we get:
[tex]\implies \pi (120)[/tex]
[tex]\implies 3.14(120) = 31.4(12) = \boxed{376.8 \ \text{cm}^{2} }[/tex]
Therefore, the surface area of the cylinder is 376.8 cm².
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What are the coordinates of the focus of the parabola?
y=−0.25x2+6
Answers
Translate to an equation and solve the following. The quotient of k and 22 is -66. What is k
Answers
Answer:
Below.
Step-by-step explanation:
k / 22 = -66
k = 22*-66
= -1452.
On his third math quiz of the semester, Cooper answered 28 questions correctly and got 7 wrong. What is the ratio of the number of questions he got right on the quiz to the total number of questions?
Answers
Step-by-step explanation:
Given that Cooper answered 28 questions correctly and 7 incorrect answers, If the total number of questions is x,
let total number of questions be X,therefore X = 28+7
= 35
ratio of right answered questions to the total questions, R isR =
[tex] \frac{28}{35} [/tex]
=
[tex] \frac{4}{5} [/tex]
therefore, the ratio is 4:5
4x+3y=6
-4x+2y=14
Solve the system of equations.
A. x= 1/2, y=3
B. x=3, y =1/2
C. x=4, y = -3/2
D. x=-3/2, y = 4
Answers
Answer:
D
Step-by-step explanation:
4x + 3y = 6
-4x + 2y = 14
0 + 5y / 5 = 20/ 5 = 4 = y
4x + 3(4) = 6
4x + 12 - 12 = 6 - 12
4x / 4 = -6 / 4 = -3 / 2 =x
What is the median of the data represented by the box plot?
Answers
Answer: 20
Step-by-step explanation:
Box plots give us the median just by looking at them. See attached.
A quarterback is standing on the football field preparing to throw a pass. His receiver is standing 20 yards down the field and 15 yards to the quarterback’s left. The quarterback throws the ball at a velocity of 60 mph towards the receiver at an upward angle of 30° (see the following figure). Write the initial velocity vector of the ball ⃑ , in component form.
Answers
Answer:
I did the work and uploaded the answer as a picture for you
I hope it was helpful!!
Step-by-step explanation:
A plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labor. If the total bill was $190, how many hours did the plumber spend fixing the sink?
Answers
The plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the plumber spend x hours to fixing the sink.
Then we can frame a linear equation in one variable:
55 + 45x = 190
45x = 135
x = 3 hours
Thus, the plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.
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1: solve the following pair of equations simultaneously using the method stated.
a) 2x-3y = 5 and 3x+4y = 6 (elimination method)
b) 4x-y = 9 and 3xy = -6 (substitution method)
c) y=x^2 - 2x and y = 2x -3 (substitution method)
Answers
Answer:
Your answers are below ↓
Step-by-step explanation:
Given ↓
A) 2x-3y = 5 and 3x+4y = 6 ( The method this has to be solved in is the elimination method. )
Now using these,
(1)×3 - (2)×2 = 6x + 9y - 6x - 8y = 15 - 12
therefore,
y = 3
putting the value of y in eqn. (1)
2x + 6 = 5
therefore,
x = -1/2
B) y=x^2 - 2x and y = 2x -3 ( The method this has to be solved in is the substitution method. )
Reduce the greatest common factor on both sides of the equation:
[tex]\left \{ {{4x-y=9} \atop {xy=-2}} \right.[/tex]
Rearrange like terms to the same side of the equation:
[tex]\left \{ {{-y=9-4x} \atop {xy=-2}} \right.[/tex]
Divide both sides of the equation by the coefficient of the variable:
[tex]\left \{ {{y=-9+4x} \atop {xy=-2}} \right.[/tex]
Substitute the unknown quantity into the elimination:
[tex]x(-9+4x)=-2[/tex]
Apply Multiplication Distribution Law:
[tex]-9x+4x^2=-2[/tex]
Reorder the equation:
[tex]4x^2-9x=-2[/tex]
Divide the equation by the coefficient of the quadratic term:
[tex]\frac{1}{4}(4x^2)+\frac{1}{4}(-9x)=\frac{1}{4}*(-2)\\[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}=-\frac{1}{2}[/tex]
Add one term in order to complete the square:
[tex]x^2-\frac{9x}{4}+(\frac{9}{4}*\frac{1}{2})^2=-\frac{1}{2}+(\frac{9}{4}*\frac{1}{2})^2[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}+(\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Factor the expression using [tex]a^2$\pm$2ab+b^2=(a$\pm$b)^2[/tex]:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Simplify using exponent rule with the same exponent rule: [tex](ab)^n=a^n*b^n[/tex]
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +\frac{9^2}{8^2}[/tex]
Calculate the power:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2}+\frac{81}{64}[/tex]
Find common denominator and write the numerators above the denominator:
[tex](x-\frac{9}{8} )^2=\frac{-32+81}{64}[/tex]
Calculate the first two terms:
[tex](x-\frac{9}{8} )^2=\frac{49}{64}[/tex]
Rewrite as a system of equations:
[tex]x-\frac{9}{8} =\sqrt{\frac{49}{64} }[/tex] or [tex]x-\frac{9}{8} =-\sqrt{\frac{49}{64} }[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=\frac{\sqrt{49} }{\sqrt{64} } +\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over the common denominator:
[tex]x=\frac{7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{16}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=2[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=-\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{a} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=-\frac{\sqrt{49} }{\sqrt{64} }+\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=-\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=-\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over common denominator:
[tex]x=\frac{-7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{2}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=\frac{1}{4}[/tex]
Find the union of solutions:
[tex]x=2[/tex] or [tex]x=\frac{1}{4}[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*2[/tex]
Calculate the first two terms:
[tex]y=-9+8[/tex]
Calculate the first two terms:
[tex]y=-1[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*\frac{1}{4 }[/tex]
Reduce the expression to the lowest term:
[tex]y=-9+1[/tex]
Calculate the first two terms:
[tex]y=-8[/tex]
Write the solution set of equations:
[tex]\left \{ {{x=2} \atop {y=-1}} \right.[/tex] or [tex]\left \{ {{x=\frac{1}{4} } \atop {y=-8}} \right.[/tex] -------> Answer
C) y=x^2 - 2x and y = 2x -3 ( This method this has to be solved in is the substitution method. )
Step 1: We start off by Isolating y in y = 2x - 3
y=2x-3 ----------> ( Simplify )
y+(-y)=2x-3+(-y) ---- > ( Add (-y)on both sides)
0=-3+2x-y
y/1 = 2x-3/1 --------> (Divide through by 1)
y = 2x - 3
We substitute the resulting values of y = 2x - 3 and y = x^2 - 2x
(2 * x - 3) = x^2 - 2x ⇒ 2x -3 = x^2 - 2x ----> ↓
(Substituting 2x - 3 for y in y = x^2 -2x )
Next: Solve (2x - 3 = x^2 - 2x) for x using the quadratic formular method
2x - 3 = x^2 - 2x
x = -b±b^2-4ac/2a Step 1: We use the quadratic formula with ↓
a = -1,b=4,c= - 3
x = -4±(4)^2-4(-1)(-3)/2(-1) Step 2: Substitute the values into the Quadratic Formular
x = -4± 4/ - 2 x = 1 or x = 3 Step 3: Simplify the Expression & Separate Roots
x = 1 or x = 3 ------- ANSWER
Substitute 1 in for x in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (1) - 3 (Substituting)
y = -1 (Simplify)
Substitute 3 for in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (3) - 3 (Substituting)
y = 3 (Simplify)
Therefore, the final solutions for y = x^2 -2x; y = 2x - 3 are
x₁ = 1, y₁ = -1
x₂ = 3, y₂ = 3
Please help me. I don’t understand at all.
Answers
Answer:
Option 2
Step-by-step explanation:
Evaluating the options :
Option 1
2 |x - 5| - 4 < -82 |x - 5| < -4|x - 5| < -2Empty set as modulus cannot be less than 0Option 2
|2x - 1| - 7 < -6|2x - 1| < 1x < 1There is a solution set other than empty setOption 2 is the right answer.
Which is in slope intercept form? Any fractions must be in simplest form.
A. 4y = -6x + 8
B. y = -6/4x+8/4
C. y = -3/2x+2
D. 6x + 4y = 8
Answers
Answer:
B and C are both in slope-intercept-form.
Step-by-step explanation:
Slope Intercept Form is --> y = mx + b, where m is the slope, and b is the y-intercept.
Both B and C have a slope (-6/4 for B, -3/2 for C) and both have a y-intercept (8/4 or 2).
I hope this helps. Please mark me brainliest!
I really need a help, help help helppp Helpppppp please
Answers
Answer:
I am clueless. Take care though.
Step-by-step explanation:
simply an surds
√75+ √48 -2√675
Answers
The simplification of √75+ √48 -2√675 is -21√3.
What is a surd?Surds are irrational numbers.
To simplify the surd in the question above, we use the addition and subtraction of surds.
Addition and subtraction of surdsTwo or more surds can be added or subtracted if they are in the same basic form.
E.g
a√b+c√b = (a+c)√ba√b-c√b = (a-c)√bUsing the above example,
Given:
√75+√48-2√675Express the surds to the same basic form
5√3+4√3-(2×15)√35√3+4√3-30√39√3-30√3 = -21√3Hence, the simplification of √75+ √48 -2√675 is -21√3.
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