Total score:
of 15 points
(Score for Question 1: of 5 points)
1. The diagram shown is two intersecting lines. The measure of 22 is 29
2
(a) What is the measure of 24? How do you know? Explain your answer in complete sentences.
(b) Suppose the measure of 3 can be represented by (3x - 8)*. What equation can be written to solve for the value of x?
(c) What is the value of x? Show all work.
Answer:
•(Score for Question 2: _ of 5 points)
2. Draw a right triangle with side lengths of 6, 8, and 10 units. For full credit, be sure to include appropriate labels and symbols where necessary. © Stride, Inc. All rights reserved. No reproduction without written consent of Stride, Inc.
Answer:
•Score for Question 3:
_ of 5 points)
3. At a park, a statue has a ring-shaped brick path around it. The outer edge of the brick path is a circle with a radius of 13 m. The inner edge of the brick path is a circle with a radius of 8 m.
Brick path
13 m
8 m
Statue
(a) Write and simplify an expression for the exact area of the brick path. Show all work.
(b) Find the approximate area of the brick path. Use 3.14 to approximate r. Show all work.
Answers
The measure of angle ∠4 is 29°, the equation is 3x = 159 and the value of x is 53
The right angle using the given lengths is attachedThe exact area is 105π square meters and the approximate area is 330 square metersThe two intersecting linesGiven that, we have
∠2 = 29°
(a)
Angles 2 and 4 are vertical angles
So, we have
∠4 = 29°
(b) and (c)
We have
∠3 = (3x - 8)°
Angles 3 and 4 are angles on a straight line
So, we have the equation to be
3x - 8 + 29 = 180
Solving for x, we have
3x = 159
Divide by 3
x = 53
This means that the equation is 3x = 159 and the value of x is 53
The right angle with the given lengthsIn this section, we have the following side lengths
Lengths = 6, 8 and 10
This means that
Side lengths = 6 and 8
Hypotenuse = 10
Next, we create the right angle using the given lengths of the legs and the hypotenuse
Calculating the area of the brick pathHere, we have
R = 13
r = 8
The exact area is calculated as
A = π(R² - r²)
So, we have
A = π(13² - 8²)
Evaluate
A = 105π
For the approximate area, we have
A = 105 * 22/7
A = 330
This means that the exact area of the brick path is 105π square meters and the approximate area is 330 square meters
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Related Questions
(x+3) (x-2) =2x
find the valűe of x
Answers
Step-by-step explanation:
[tex](x + 3)(x - 2) = 2x\\ {x}^{2} + x - 6= 2x \\ {x}^{2} - x - 6 = 0 \\ (x - 3)(x + 2) = 0 \\ x = 3 \: or \: x = - 2[/tex]
Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.
Answers
The Surface area of the composite figure is calculated as approximately: 234 sq. cm
How to Find the Surface Area of a Composite Figure?The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:
Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)
Area of base = area of square = 6 * 6 = 36 sq. cm.
Surface area of the square prism = 2a² + 4ah
a = 6 cm
h = 4 cm
Plug in the values:
Surface area of the square prism = 2(6²) + 4*6*4
= 72 + 96
= 168 sq. cm.
Surface area of the square pyramid = 2bs + b²
b = side length = 6 cm
s = slant height = √(8² + 3²) = 8.5 cm
Plug in the values:
Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.
Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm
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College Level Trigonometry Question!
Answers
The angle measures for this problem are given as follows:
θ = 150º and θ = 330º.
How to obtain the angle measure?The trigonometric expression for this problem is given as follows:
[tex]\theta = \arctan{\left(-\frac{\sqrt{3}}{3}\right)}[/tex]
The solution to the arctangent function is the angle which has the given tangent value.
The angle on the first quadrant with a tangent value of sqrt(3)/3 is given as follows:
θ = 30º.
The quadrants in which the tangent is negative are given as follows:
2nd and 4th.
Hence the equivalent angles are given as follows:
2nd quadrant: θ = 180 - 30 = 150º.4th quadrant: θ = 360 - 30 = 330º.More can be learned about arctangent at https://brainly.com/question/10061217
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A sample of a radioactive substance has an initial mass of 45.1 mg. This substance follows a continuous exponential decay model and has a half-life of 19
minutes.
(a)let t be the time (in minutes) since the start of the experiment, and
let y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ()e^()t
(b) How much will be present in 9 minutes?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
Answers
a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.
How to Write a formula relating y to t.(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.
To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.
Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:
19 = 0.693 / k
k = 0.693 / 19
So the formula relating y to t is:
y = 45.1 * e^(-0.693/19 * t)
(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):
y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg
So, there will be approximately 30.1 mg of the substance present after 9 minutes.
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prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
Answers
The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below
How to prove the given identityGiven the following equation
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
We start by simplifying the left-hand side of the equation:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]
Next, we have the following steps to simplify the expression
= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]
= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]
= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]
= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]
= -4(2p² + 1)/(p²-4) (p² - 1)
Hence, the given identity is proven.
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Drag-and-Drop Technology-Enhanced
An expression is shown.
14a +7+ 5b+ 2a + 10b
Move words into the columns to describe the parts of the expression. Not all words will be used, and each column should
have at least one word to describe it.
14a
sum
term
factor
7
5
product
quotient
coefficient
2a + 10b
Answers
The value of expression 14a +7+ 5b+ 2a + 10b will be 16a + 15b + 7
Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given the expression as;
14a +7+ 5b+ 2a + 10b
Combine like terms;
14a + 2a + 10b +7+ 5b
16a + 15b + 7
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A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet. In how many ways can this be done?
Answers
Total number of ways = (Number of ways to select appetizers) x (Number of ways to select main courses) x (Number of ways to select desserts)
Number of ways to select appetizers = C(5,4) = 5
Number of ways to select main courses = C(11,9) = 330
Number of ways to select desserts = C(4,3) = 4
Therefore, the total number of ways the customer can select 4 appetizers, 9 main courses, and 3 desserts is:
Total number of ways = 5 x 330 x 4 = 6,600
So, there are 6,600 ways the customer can select the items for the banquet.
There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.
Given that,
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.
We have to find how many ways can this be done.
We know that,
Number of appetizers offered = 5
Number of appetizers customer is to select = 4
Number of main courses offered = 11
Number of main courses customer is to select = 9
Number of desserts offered = 4
Number of desserts the customer is to select = 3
So,
To determine the number of ways this can be selected,
By using the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100
Therefore, There are 1100 many ways this can be done.
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what's equivalent to x^2-4x-l2
Answers
Answer:
Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:
(x - 6)(x + 2)
Step-by-step explanation:
This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:
(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12
For any positive values x and y, f(xy) = f(x) + f(y). f(1/2021) = 1.
Find f(2021).
I will give BRAINLIEST to correct answer.
Answers
f(1/2021 * 2021) = f(1/2021) + f(2021)
Simplifying the left-hand side gives us:
f(1) = f(1/2021) + f(2021)
Substituting f(1/2021) = 1, we have:
f(1) = 1 + f(2021)
Therefore,
f(2021) = f(1) - 1.
However, we don't know what f(1) is. One way to find it is to let x = y = 1. Then we have:
f(1) = f(1) + f(1),
which implies that f(1) = 0.
Therefore,
f(2021) = f(1) - 1 = -1.
So the answer is -1.
How many quarters do you need to add to 31/4 to get 41/2
Answers
Answer:
51/4 quarters
Step-by-step explanation:
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator for 4 and 2 is 4x2=8.
So we need to convert both fractions to have a denominator of 8:
31/4 = (31/4) x (2/2) = 62/8
41/2 = (41/2) x (4/4) = 164/8
Now we can add the fractions:
62/8 + x/4 = 164/8
Subtracting 62/8 from both sides:
x/4 = 102/8
Simplifying:
x = 51/4
Therefore, we need to add 51/4 quarters to 31/4 to get 41/2
Find mJKM
J= 3x
L=64
JKM=(5x+4)
Answers
The measure of angle JKM is 26°
What is exterior angle theorem?The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite angles in the triangle.
Also the sum of angle in a triangle is 180°
Therefore ;
3x+64 = 5x+4
collecting like terms
5x -3x = 64-4
2x = 60
x = 60/2
x = 30
since x = 30
value of the exterior angle = 5x+4
= 5×30+4
= 150+4 = 154
therefore angle JKM = 180-( 154)
= 26°
Therefore the measure of angle JKM is 26°
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On a scale drawing of a soccer field, 0.5 cm equals 8 m.
If the drawing has dimensions 6.5 cm X 3.25 cm, what is the actual length of the soccer field, in meters?
Answers
[tex]\sf Length\, of\,the\,field=\boxed{\sf 104(m)}}.[/tex]
Step-by-step explanation:1. Create a conversion factor.A conversion factor is just a fraction that contains an equivalence. We make the numerator be the unit we want to have as a result and the denominator is the current unit that we have.
The problem states that 0.5 cm equals 8 m, and we want to convert from cm to m, therefore, a conversion factor for this problem is:
[tex]\sf \dfrac{8(m)}{0.5(cm)}[/tex]
2. Use the conversion factor to convert each unit,To use the conversion factor, just multiply each measure by the fraction:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}[/tex]
Here the centimeters (cm) cancel out each other and the ending answer is expressed in meters:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 104(m)}.[/tex]
For the other measure:
[tex]\sf 3.25(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 52(m)}.[/tex]
So a soccer field, as you may already know, is always longer than it is wide, therefore, the greatest measure (104m) should be the length of the field.
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a2=25 i cant find the ancer to thiss
Answers
The value of the variable a in the equation is 5 from the calculation here.
How to determine the value?We need to square of a number is described as a number that when multiplied by itself give the original number.
Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.
From the information given, we have the equation;[tex]a^2[/tex]=25
find the square root of value of 25,
We have;25 = [tex]5^2[/tex]
Substitute the value, we get;[tex]a^2[/tex] = [tex]5^2[/tex]
Take out the similar factor, this is their exponents.
We then have;
a = 5
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Complete question;
Find the value of a in the equation;a² = 25
Suppose that $2000 is invested at a rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 6 years
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Answer:
$2,631.55
Step-by-step explanation:
To find the total amount in the account after 6 years, we can use the compound interest formula.
Compound Interest Formula[tex]\boxed{\sf A=P\left(1+\dfrac{r}{n}\right)^{nt}}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $2,000r = 4.6% = 0.046n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2000\left(1+\dfrac{0.046}{4}\right)^{4 \cdot 6}[/tex]
[tex]\implies \sf A=2000\left(1+0.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.3157739...\right)[/tex]
[tex]\implies \sf A=2631.54794...[/tex]
Therefore, the total amount after 6 years is $2,631.55 rounded to the nearest cent.
for each pair of lines determine whether they are parallel, perpendicular, or neither
Answers
Answer:
All lines are parallel.
Step-by-step explanation:
Get each equation in Slope-Intercept form:
1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]
2. No change
3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]
Notice:
a. All slopes are -4/3
b. All y-intercepts are different
I deposited #300.00 in a bank for
four years. If it earned simple
interest at the rate of 6% per annum,
how much interest did I get for the
four years?
Answers
Answer:
Simple interest= PRT/100
parameters
price =300
Rate=6%
Time=4years
300*6*4/100
7200/100
=72
can some one help me
Caleb is selecting cards from a set of 12 cards numbered 1-2-4-4-5-5-5-5-6-9-10-13.
What is the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection?
Answers
The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.
There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.
Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.
Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:
P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)
= (1/3) x (1/3)
= 1/9
Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.
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Can someone help me with this? I can't figure it out
Answers
In linear equation, 9 is the constant of variation k.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
given x varies inversely with y then
xy = k ← k is the constant of variation
to find k use the condition x = - 4 when y = - 9, hence
k = -4 × -9 = 36
x = 36/y
when x = 4 , then y = 36/4
x = 9
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A bag contains 19 blue, 28 purple, 21
red, and 29 orange balls. You pick
one ball at random. Find the
probability that it is purple or orange.
P(purple or orange) =
Simplify your answer completely.
Answers
Thus, the probability for the outcome of either purple or orange: P(purple or orange) = 57/97.
Explain about the term random selection:a choice that is made at random (entirely by chance, with no predictability). Every person in the population under study need to have an equal probability of getting chosen. Every person who is under investigation has an equal probability of being chosen at random for the sample.
Given bag with balls:
19 blue, 28 purple, 21 red, and 29 orange ballsTotal = 97 ballsprobability = favourable outcome / total outcome
P(purple) = 28/97
P(orange) = 29/97
Thus,
P(purple or orange) = 28/97 + 29/97
P(purple or orange) = 57/97
Thus, the probability for the outcome of either purple or orange ball : P(purple or orange) = 57/97.
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Solve the equation.
3/4x+3-2x = -1/4+1/2x+5
If necessary:
Combine Terms
Apply Properties:
Add Subtract
Multiply Divide
Answers
The solution of the equation is x = -1.
Given is an equation we need to solve it,
3x/4 + 3 - 2x = -1/4 + x/2 +5
Multiplying the equation by 4 both the sides,
3x + 12 - 8x = -1 + 2x + 20
Combining the like terms,
3x - 8x - 2x = 20 - 1 - 12
3x - 10x = 7
-7x = 7
x = -1
Hence the solution of the equation is x = -1.
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3⋅f(−4)−3⋅g(−2) = ?
Ayuda por favor
Answers
The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40
Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;
f( - 4 ) = 15
g( - 2 ) = 5
Substitute the given parameters into the expression to have:
3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5
= 45 - 5
= 40
Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40
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i need answer please
Answers
The surface area of the rectangular prism is 210 in²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The surface area of a rectangular prism is the sum of each area for the surface.
Hence:
Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²
The surface area of the prism is 210 in²
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Which linear equation is represented in the graph?
A. y = x – 1
B.y = 2x – 1
C. y = x + 1
D. y = 3x – 1
Answers
Find the distance from G to S.
Answers
Answer:
i think its b sorry if it's wrong
Step-by-step explanation:
help!!!
in the fridge below, m WXZ =72, abs m 1 is 6 degrees more than m 2. find m2
Answers
Step-by-step explanation:
m ∠WXY = 72°
m ∠ 1 = m ∠ 2 + 6°
m ∠WXY = m ∠ 1 + m ∠ 2
72° = (m ∠ 2 + 6°) + m ∠ 2
72° = 2 × (m ∠ 2) + 6°
2 (m ∠ 2) = 72° - 6°
2 (m ∠ 2) = 66°
(m ∠ 2) = 33°
#CMIIWWhich of the following is the graph of the quadratic function y = x² - 4x+4?
A. Graph C
B. Graph B
C. Graph D
D. Graph A
Answers
Answer:
The correct answer is C, Graph D.
x^2 - 4x + 4 = (x - 2)^2.
I would love some help please 18-20
Answers
18. C
(m / 2) - 6 = (m / 4) + 2
---Multiply everything by the LCM of the denominators
---LCM = 4
2m - 24 = m + 8
m - 24 = 8
m = 32
19. A
k / 12 = 25 / 100
---We can simplify 25/100
---We want to simplify enough to where the denominator of 25/100 is a multiple or factor of 12
k / 12 = 1 / 4
---4 x 3 = 12, 1 x 3 = 3
k = 3
20. A
9 / 5 = 3x / 100
---Cross multiply and solve algebraically
(5 * 3x) = (9 * 100)
15x = 900
x = 60
Hope this helps!
19.A
20.A
are the answers
How many different ways are there to arrange the letters in the word MISSISSIPPI?
Answers
Answer: 34,650 permutations
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
x=38.6
Step-by-step explanation:
x=b/cos(alpha)
x=30/cos(39⁰)
x=38.602
Find the slope of the tangent to f(x) = x^2 at the point (-2,4).
Answers
Answer:
f'(x) = 2x, so f'(-2) = 2(-2) = -4.
