Answer:
12^2x = 7^4 = 2401
7^2=12^x
We know that a^x * a^x = a^(x+x) or a^2x
Multiply each side by 12^x
7^2 * 12^x=12^x * 12^x
7^2 * 12^x = 12^(x+x)
Replace 12^x with 7^2 on the left hand side since they are equal
7^2 * 7^2 = 12^ (2x)
7^(2+2) = 12^(2x)
7^4 = 12^2x
2401 = 12^2x
Step-by-step explanation:
Help me , it is 50 point
Answer:
a) 52.0 cm
b) 62.8 cm
c) 114.8 cm
Conversion:
120° = 2π/3 radians
(a) Find Length of chord PR;
⇒ 2(radius)sin(θ/2)
⇒ 2(30)sin((2π/3)/2)
⇒ 2(30)sin((2(3.142)/3)/2)
⇒ 30√3
⇒ 52.0 cm
(b) Find Length of arc PQR;
⇒ radius(θ)
⇒ 30(2π/3)
⇒ 30(2(3.142)/3)
⇒ 62.8 cm
(c) The perimeter of shaded region;
⇒ Length of chord + Length of arc
⇒ 62.84 + 51.965
⇒ 114.8 cm
Answer:
(a) 52.0 cm
(b) 62.8 cm
(c) 115 cm
Step-by-step explanation:
Part (a)
[tex]\textsf{Chord length}=2r \sin \left(\dfrac{\theta}{2}\right)[/tex]
where:
r = radius[tex]\theta[/tex] = central angle (measured in degrees)Given:
r = 30 cm[tex]\theta[/tex] = 120°chord = PRSubstitute the given values into the formula:
[tex]\begin{aligned}\implies PR & =2(30)\sin \left(\dfrac{120^{\circ}}{2}\right)\\\\& = 30\sqrt{3}\\\\ & = 52.0\:\sf cm\:(3\:sf)\end{aligned}[/tex]
Part (b)
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad[/tex]
where:
r = radius[tex]\theta[/tex] = central angle (measured in degrees)Given:
r = 30 cm[tex]\theta[/tex] = 120°arc = PQR[tex]\pi[/tex] = 3.142Substitute the given values into the formula:
[tex]\begin{aligned}\implies PQR & =2 (3.142)(30)\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \quad\\\\ & = \dfrac{1571}{25}\\\\ & = 62.8 \sf \:\:cm \:(3 \:sf)\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}\textsf{Perimeter of shaded portion} & = \textsf{chord length} + \textsf{arc length}\\\\ & = 30\sqrt{3}+\dfrac{1571}{25}\\\\ & = 114.80152...\\\\ & = 115\:\: \sf cm\:(3\:sf)\end{aligned}[/tex]
PLEASE HELP!!
Identify an obtuse angle and give its measure.
Answer:
Angle HEF
105*
Step-by-step explanation:
Find all sets of four consecutive even integers whose sum is between 155 and 165
Answer:
36 38 40 42
and
38 40 42 44.
Step-by-step explanation:
160 / 4 = 40 so the numbers are close to 40.
38 + 40 + 42 + 44 = 164
36 + 38 + 40 + 42 = 156.
please solve quickly
Answer:
75.36
hope this helps :)
Can someone please answer this by today
Please help me find the area of compound shapes?!?!
Answer:
[tex]27cm^{2}[/tex]
Step-by-step explanation:
Area of compound shapes = Area of shape A + Area of shape B
Area of this shape = (L x B) + (L x B)
= (5 x 3) + (6 x 2)
= 15 + 12
= [tex]27cm^{2}[/tex]
Answer:
A = 27 cm²
Step-by-step explanation:
the figure consists of 2 rectangles
the one on the right with dimensions 2 cm by 6 cm and
the one on the left with dimensions 5 cm by 3 cm
the total area (A) is then calculated as
A = (2 × 6) + (5 × 3) = 12 + 15 = 27 cm²
Pls help!
Simplify sin θ/√1-sin^2 θ
A) tan Θ
B) tan^2 Θ
C) 1
D) -1
Answer:
hope this will help you ( ◜‿◝ )♡
Step-by-step explanation:
[tex] \frac{ \sin(theta) }{ \sqrt{1 - \sin {}^{2} ( theta) } } \\ \frac{ \sin(theta) }{ \cos(theta) } \\ \tan(theta) [/tex]
Susie is thinking about changing her auto insurance policy at fret-no-more auto insurance. her current policy includes the following options: $50/100,000 limit for bodily injury, $25,000 limit for property damage, $250 deductible for collision, and $50 deductible for comprehensive. which of the following changes would increase susie’s limits the most without increasing her monthly premium by more than $5.00? fret-no-more auto insurance type of insurance coverage coverage limits annual premiums bodily injury $25/50,000 $21.35 $50/100,000 $32.78 $100/300,000 $42.10 property damage $25,000 $115.50 $50,000 $142.44 $100,000 $193.78 collision $100 deductible $490.25 $250 deductible $343.33 $500 deductible $248.08 comprehensive $50 deductible $105.79 $100 deductible $88.23 a. increase coverage on bodily injury to $100/300,000. b. increase coverage on property damage to $50,000. c. increase coverage on bodily injury to $100/300,000 and on property damage to $50,000. d. increase coverage on bodily injury to $100/300,000 and on property damage to $100,000.
The change that would increase Susie’s limits is C. increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.
What is an insurance?It should be noted that an insurance simply means a form of risk reduction that is taken regarding an asset.
In this case, the change that would increase Susie’s limits is to increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.
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Please help! Will give Brainliest!!!!!!!!!!!!
Answer:
for the first answer the second option is correct and 8 will go in the box and for the second question the second option is correct and 40 will go in the box.
Find the measures of the missing angles. The triangle is not drawn to scale.
108°
A=
B= 31
Answer:
B=41
Step-by-step explanation:
Triangle = 180 degrees.
108+31=139
180-139=41\
B = 41 degrees
Hey guys! Sorry to bother but I need help with these. 5th grade math, will give brainliest! (If you see multiple questions by me that look the same, they are all different.)
Answer:
Question seven is 14, Question 8 is 16
Step-by-step explanation:
hoped this helped
A rectangular courtyard has a length of 16 m and a width of 10 m. Find the perimeter of the rectangle defined by this courtyard. In other words, what is the length of the fence required to encompass the courtyard?
Answer:
26^2 meters
Step-by-step explanation:
l + b
16 + 10
= 26m×2
Image for last question look at my last
Answer:
Part A: 12.5 cm
Part B: 0.8 km
Step-by-step explanation:
Map scale problems can be solved with proportions.
Part A
5 cm / 2 km = x cm / 5 km
5/2 = x/5
2x = 25
x = 12.5
Answer: 12.5 cm
Part B
5 cm / 2 km = 2 cm / x km
5/2 = 2/x
5x = 4
x = 4/5
x = 0.8
Answer: 0.8 km
The volume of a cone is 108 pi cubic inches. Its height is 4 inches. What is the radius of the cone? Round the answer to the nearest tenth if necessary. 5. 2 in. 9 in. 34. 7 in. 81 in.
Answer:
im gonna say it would be around 9 inches, because the actual answer, a decimal, isnt an option so the closest would be around 9 in.
Examine the tree diagram. What is the theoretical probability of spinning AT LEAST one blue out of two spins?
Answer:
5/9.
Step-by-step explanation:
Theoretical probability = number of outcomes with1 or 2 blues
-------------------------------------------------------
number of all possible outcomes
= 5/9
What is the solution to the following equation?
-3+x=-8
A. X-11
OB. x=-11
OC. x=5
D. x=-5
Answer:
x = -5
Step-by-step explanation:
-3+x = -8
Add 3 to each side to isolate x
-3+x+3 = -8+3
x = -5
In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio. What is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election?
0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio
We need to find the probability of that the democratic candidate wins both Michigan and Ohio in the next presidential election
As 6 wons from Michigan out of 10, so it 6/10
4 wons from Ohio out of 10, so it 4/10
The probability is 6/10/×4/10
24/100=0.24
In the next year also democratic candidate wons then the probabiltiy will be same 0.24
Hence 0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election
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Which of the following is the shape of a cross-section of the figure shown
below?
A. Rectangle
B. Square
C. Prism
D. Pentagon
Answer:rectangle
Step-by-step explanation:
what’s the area and perimeter for this problem?
Answer:
area: 1.9×0.75÷2
0.7125
perimeter: 2+0.75+2.25
5
Evaluate the function 2/3t , when t = 30.
Question 2 options:
10
15
20
25
Answer:
20
Step-by-step explanation:
2/3(30)
=20
For a certain population of penguins, the distribution of weight is approximately normal with mean 15.1 kilograms (kg) and standard deviation 2.2 kg. Approximately what percent of the penguins from the population have a weight between 13.0 kg and 16.5 kg
Using the normal distribution, it is found that 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 15.1, \sigma = 2.2[/tex].
The proportion of penguins from the population have a weight between 13.0 kg and 16.5 kg is the p-value of Z when X = 16.5 subtracted by the p-value of Z when X = 13.
X = 16.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16.5 - 15.1}{2.2}[/tex]
Z = 0.64
Z = 0.64 has a p-value of 0.7389.
X = 13:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13 - 15.1}{2.2}[/tex]
Z = -0.95
Z = -0.95 has a p-value of 0.1711.
0.7389 - 0.1711 = 0.5678.
0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
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( multiplying matrixes please help) Find the product of the following two
matrices.
[tex]\left[\begin{array}{cc}1&3\\0&-2& \end{array}\right] \begin{bmatrix} 3& 1&-1& 0 \\ -1& 0&3&-1\end{bmatrix}\\\\\\=\begin{bmatrix} 3-3& 1+0&-1+9&0-3\\ 0+2&0-0&0-6&0+2\end{bmatrix}\\\\\\=\begin{bmatrix} 0&1&8&-3\\2&0&-6&2\end{bmatrix}[/tex]
AYO HELP ME OUT ASAP :(
Answer:
122.7 cm³
Step-by-step explanation:
Volume of composite figure:Square pyramid:
a = 4 cm ; h = 4 cm
[tex]\boxed{\text{Volume of square pyramid = $\dfrac{1}{3}$*base area * height}}[/tex]
[tex]\sf = \dfrac{1}{3}*a^{2}*h\\\\ =\dfrac{1}{3}*4*4*4\\\\ = 21.3 \ cm^3[/tex]
Rectangular prism:
l = 6 cm ; w = 6 cm ; h = 4 cm
[tex]\boxed{\text{Volume of rectangular prism = l*w*h}}[/tex]
= 6 * 6 * 4
= 144 cm³
Volume of composite figure = volume of rectangular prism - volume of pyramid= 144 - 21.3
= 122.7 cm³
There are 15 boys in school base ball team , they represent 5% of grace Christian school , In all how many are there in school
Answer:
300
Step-by-step explanation:
[tex]5\% \: of \: x = 15 \\ x = 1500 \div 5 = 300[/tex]
Kelly used the vertical line test to determine whether or not the curve that she
had been given is a function. After conducting the vertical line test, Kelly
determined that the curve is a function. Which of the following choices
represents the result of Kelly's vertical line test?
A. All vertical lines intersected the curve at exactly 2 points.
B. One vertical line intersected the curve at exactly 2 points.
C. One vertical line intersected the curve at exactly 1 point, while
another vertical line intersected the curve at exactly 2 points.
OD. All vertical lines intersected the curve at exactly 1 point.
All vertical lines intersected the curve at exactly 1 point.
===========================================================
Explanation:
If there is a case when a single vertical line crosses 2 or more points on the curve, then it will not be a function. In this situation, it is said that the curve fails the vertical line test.
Passing the vertical line test means that every vertical line passes through exactly one point on the curve. Each x input leads to exactly one output. If such a situation happens, then we have a function.
Since Kelly concluded that the curve is a function, this means the curve passed the vertical line test, and it points us to choice D as the answer.
I will gove you 100 points
To find side given angle and two sides:
a² = b² + c² − 2bc cos(A)
Here given:
a = AC cmb = 10 cmc = 7 cmangle A = 120°Solve for AC (a):
a² = (10)² + (7)² − 2(10)(7) cos(120)a² = 219a = √219a = 14.7986 cma = 14.8 cmAnswer:
AC = 14.8 cm (1 dp)
Step-by-step explanation:
Cosine rule
[tex]\sf b^2=a^2+c^2-2ac \cos B[/tex]
(where a, b and c are the sides, and B is the angle opposite side b)
Given:
a = 10 cmc = 7 cmB = 120°b = ACSubstituting the given values into the formula and solving for b:
[tex]\implies \sf AC^2=10^2+7^2-2(10)(7) \cos 120^{\circ}[/tex]
[tex]\implies \sf AC^2=100+49+70[/tex]
[tex]\implies \sf AC^2=219[/tex]
[tex]\implies \sf AC=\pm\sqrt{219}[/tex]
As length is positive,
[tex]\implies \sf AC=\sqrt{219}\:cm[/tex]
[tex]\implies \sf AC=14.8\:cm\:(1\:dp)[/tex]
The art club raised \$248$248dollar sign, 248 through fundraisers. Then they spent \$206$206dollar sign, 206 to set up an art show. They raised another \$316$316dollar sign, 316 at the art show. How much money did the art club have after the show
Considering the amount they raised and the amount they spent, it is found that the art club had $358 after the show.
How to find the net amount of the art club?The net amount is found by the subtraction of the amount raised by the amount spent.
In this problem:
The amount raised, in dollars, is of 248 + 316 = 564.The amount spent is of $206.Then:
A = 564 - 206 = $358.
The art club had $358 after the show.
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Evaluate the expression for the given value.
Answer:
a² = 16
Step-by-step explanation:
substitute a = 4 into the expression
a² = 4² = 4 × 4 = 16
Answer:
16
Step-by-step explanation:
Rob is travelling at a constant speed in a car. He travels 105km in 1 hour and 30 minutes. The speed limit is 80km/h. Is Rob travelling within the speed limit? Show how you decide.
Answer:
Yes.
Step-by-step explanation:
Let's first convert his speed to km/h.
[tex]\frac{105km}{1.5h} = 70\frac{km}{h}[/tex] > [tex]80\frac{km}{h}[/tex]. Therefore, Rob is traveling within the speed limit.
Find the value of X.
Answer:
x=4
Step-by-step explanation:
We know that in a parallelogram opposite sides are equal
Hence on equating we get,
[tex]6x - 20 = 4[/tex]
[tex]6x = 4 + 20[/tex]
[tex]6x = 24[/tex]
[tex]x = 4[/tex]
