determine the area of the yellow sector

Answer:

C. [tex]x=20^{\circ}[/tex]

Step-by-step explanation:

Angle 6 and angle with measure 45° are vertical angles (opposite angles whan two lines intersect). By Vertical Angles Theorem, vertical angles are congruent, so

[tex]m\angle 6=45^{\circ}[/tex]

Angle 6 and angle with measure [tex]5x+35^{\circ}[/tex] are the same side interior angles when two parallel lines are cut by transversal. The same side interior angles add up to 180°, then

[tex]m\angle 6+5x+35^{\circ}=180^{\circ}\\ \\45^{\circ}+5x+35^{\circ}=180^{\circ}\\ \\5x=180^{\circ}-45^{\circ}-35^{\circ}\\ \\5x=100^{\circ}\\ \\x=20^{\circ}[/tex]  

Good evening ,

Answer:

domain: ]−∞,+∞[

range: ]−∞,4]

Step-by-step explanation:

Look at the photo below for more info.

:)

The domain of the function f(x) = -3(x-5)² +4 is all real numbers, written as (-∞, ∞). The range, or possible values of f(x), is (-∞, 4] since the parabola opens downwards and the maximum value is 4.

The function f(x) = -3(x-5)² +4 is a parabola that opens downwards. The domain of a function is the set of all values that x can take. For any parabolic function, the domain is always all real numbers, which we could write as (-∞, ∞).

The range of a function refers to the possible values of f(x). In this case, since the parabola opens downwards, the maximum value of f(x) is at the vertex of the function. This parabola's vertex is at (5,4), so its maximum, and thus the upper boundary of the range, is 4. The parabola continues downwards to negative infinity, so the range is (-∞, 4].

Therefore, the domain is (-∞, ∞), and the range is (-∞, 4].

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Answer:

  Car A: 40 mph

  Car B: 50 mph

Step-by-step explanation:

For the same travel time, the ratio of speeds is the same as the ratio of distances:

  (speed B)/(speed A) = 150/120 = 5/4

The difference in the (reduced) ratio units is 1, so 1 ratio unit corresponds to 10 mph. Multiplying the reduced ratio by 10 mph, we get ...

Speed B is 50 mph; speed A is 40 mph.

Rhonda must collect at least 240 stamps in order to reach her goal.

Step-by-step explanation:

Given,

Stamps Rhonda wants to collect = 575

Stamps already in collection = 335

Let,

d represents the number of stamps Rhonda needs to collect to achieve her goal.

Stamps to collect + Stamps already in collection ≥ 575

[tex]d+335\geq 575\\d\geq 575-335\\d\geq 240[/tex]

Rhonda must collect at least 240 stamps in order to reach her goal.

Keywords: inequality, addition

Learn more about inequalities at:

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Using [tex]a/b+c/b=(a+c)/b[/tex], we find that [tex]2/5+2/5=4/5[/tex].

Hope this helps.

The period will be the length for one cycle of the function.

answer: 10

Answer:

125

Step-by-step explanation:

Answer:

n=6

Step-by-step explanation:

4(n+2)=2(n+10)

4n+8=2n+20

4n-2n+8=20

2n+8=20

2n=20-8

2n=12

n=12/2

n=6

Answer:

There is 1.587 ounces of sodium chloride that he will need.

Since we have given that

Quantity of sodium chloride in grams = 45 grams

We need to find the number of ounces of sodium chloride.

As we know that

1 ounce = 28.35 gram

So, 1 gram =

So, 45 grams =

Hence, there is 1.587 ounces of sodium chloride that he will need.

Step-by-step explanation: Since we have given that

Quantity of sodium chloride in grams = 45 grams

We need to find the number of ounces of sodium chloride.

As we know that

1 ounce = 28.35 gram

So, 1 gram =

So, 45 grams =

Hence, there is 1.587 ounces of sodium chloride that he will need.

Answer:

The Probability of Alicia picking a red shirt is [tex]\frac{2}{9}[/tex].

Step-by-step explanation:

Given,

Number of White shirts = 4

Number of Red shirts = 2

Number of Blue shirts = 3

Solution,

Total number of shirts = Number of White shirts + Number of Red shirts + Number of Blue shirts = [tex]4+2+3=9[/tex]

[tex]P(E)=\frac{Total\ number\ of\ possible\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Therefore,

[tex]P(of\ red\ shirts)=\frac{2}{9}[/tex]

Hence The Probability of Alicia picking a red shirt is [tex]\frac{2}{9}[/tex].

Answer:

50m

Step-by-step explanation:

Information from the question:

The length is 15m

The width is 10m

Length is represented by "l"

Width is represented by "w"

The perimeter is the total of its side lengths. A rectangle has four sides that are two lengths and two widths.

Use the formula for perimeter:

P = 2(l + w)            Put in the length and width measurements

P = 2(15m + 10m)    Add inside the brackets

P = 2(25m)        Multiply

P = 50m           Answer

Therefore the perimeter of the rectangular swimming pool is 50 meters.

26:4

Hope this helps!

An equivalent ratio to 13:2 can be found by multiplying or dividing both terms of the ratio by the same number. For instance, when both terms are multiplied by 2, the equivalent ratio is 26:4 because the proportion remains unchanged.

To find a ratio equivalent to 13:2, you need to multiply or divide both terms of the ratio by the same number. For example, if you multiply both terms of the ratio 13:2 by 2, you would get 26:4 which is an equivalent ratio. This is because the relationship or proportion between the two terms remains the same.

Here's the step-by-step calculation:

So, the ratio that is equivalent to 13:2 is 26:4.

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The items are classified as M1, M2, or neither based on their liquidity and spendability. A line of credit and traveler's checks are neither M1 nor M2 as they are not actual money. Physical currency and money in a checking account are classified as M1, while money in a money market account is classified as M2.

M1 refers to the narrowest definition of the money supply, which includes only the most liquid forms of money that can be easily spent. M2 is a broader measure of the money supply and includes M1 as well as other less liquid forms of money. Neither refers to items that do not fit into either M1 or M2.

a. Your $5,000 line of credit on your Bank of America card is neither in M1 nor M2 as it is not actual money but a credit limit.

b. $50 dollars' worth of traveler's checks you have not used yet is neither in M1 nor M2 as they need to be exchanged for cash before they can be spent.

c. $1 in quarters in your pocket is in M1 as it is physical currency that can be spent.

d. $1200 in your checking account is in M1 as it is a liquid form of money that can be spent.

e. $2000 you have in a money market account is in M2 as it is a less liquid form of money that can be accessed but may have restrictions or penalties for withdrawal.

Answer:

Mutually exclusive,

[tex]P(\text{Lemon-lime or orange})=\frac{2}{3}[/tex]

Step-by-step explanation:

Please consider the complete question:

Determine if the scenario involves mutually exclusive or overlapping events. Then find the  probability.

A cooler contains twelve bottles of sports  drink: four lemon-lime flavored, four  orange flavored, and four fruit-punch  flavored. You randomly grab a bottle. It  is a lemon-lime or an orange.

Let us find probability of finding one lemon lime drink.

[tex]P(\text{Lemon-lime})=\frac{\text{Number of lemon lime drinks}}{\text{Total drinks}}[/tex]

[tex]P(\text{Lemon-lime})=\frac{4}{12}[/tex]

[tex]P(\text{Lemon-lime})=\frac{1}{3}[/tex]

Let us find probability of finding one orange drink.

[tex]P(\text{Orange})=\frac{\text{Number of orange drinks}}{\text{Total drinks}}[/tex]

[tex]P(\text{Orange})=\frac{4}{12}[/tex]

[tex]P(\text{Orange})=\frac{1}{3}[/tex]

Since probability of choosing a lemon lime doesn't effect probability of choosing orange drink, therefore, both events are mutually exclusive.

We know that probability of two mutually exclusive events is equal to the sum of both probabilities.

[tex]P(\text{Lemon-lime or orange})=P(\text{Lemon-lime})+P(\text{Orange})[/tex]

[tex]P(\text{Lemon-lime or orange})=\frac{1}{3}+\frac{1}{3}[/tex]

[tex]P(\text{Lemon-lime or orange})=\frac{1+1}{3}[/tex]

[tex]P(\text{Lemon-lime or orange})=\frac{2}{3}[/tex]

Therefore, the probability of choosing a lemon lime or orange is [tex]\frac{2}{3}[/tex].

Average rate of change is 0

Interpretation: The crop yield did not change from year 5 to year 15

Solution:

The function that models the yield is:

[tex]f(x) = -x^2 + 20x + 75[/tex]

The average rate of change of f(x) from x = a to x = b is given by the formula:

[tex]\text{ average rate of change }=\frac{f(b)-f(a)}{b-a}[/tex]

Find and interpret the average rate of change from year 5 to year 15

[tex]f(5) = -(5)^2 + 20(5) + 75\\\\f(5) = -25 + 100 + 75\\\\f(5) = 150[/tex]

[tex]f(15) = - (15)^2 + 20(15) + 75\\\\f(15) = -225 + 300 + 75\\\\f(15) = 150[/tex]

Thus average rate of change:

[tex]\text {average rate of change}=\frac{f(15)-f(5)}{15-5}[/tex]

[tex]\text {average rate of change}=\frac{150-150}{10}=0[/tex]

Thus Average rate of change is 0

Interpretation: The crop yield did not change from year 5 to year 15.

Final answer:

The average rate of change in wheat yield from year 5 to year 15 is 0 pounds per acre per year, symbolizing that there was no change in the crop yield between these years.

Explanation:

To find the average rate of change of the wheat yield from year 5 to year 15, we will apply the function f(x) = −x² + 20x + 75 to these years and then calculate the rate of change. First, we'll find the yield for year 5 and year 15:

Next, we'll calculate the average rate of change using these yields:

Average rate of change = (f(15) - f(5)) / (15 - 5) = (150 - 150) / (10) = 0

Therefore, the crop yield did not change from year 5 to year 15. The function indicates that at both year 5 and year 15, the farmer's land yielded 150 pounds per acre, so the average rate of change in yield over this period is 0 pounds per acre per year.

Answer: 108

Step-by-step explanation:

Answer:

Approx. 2

Step-by-step explanation:

round 3.8 to the nearest whole number, which is 4.

Divide 4 by 2.

3.8/2 is approx. 2.

(the exact answer would be 1.9)

To estimate the result of 3.8 divided by 2, you can round 3.8 to 4 which, when divided by 2, gives an estimate of 2. This method provides a result that is close to the actual answer of 1.9.

The question '3.8 divided by 2 estimated' is asking for an approximate result of dividing 3.8 by 2. To estimate this, you can round 3.8 to 4 because it is close to this even number which makes mental math easier. Now, divide 4 by 2 to get 2. Although this is an estimate, the actual calculation of 3.8 / 2 yields 1.9. So, our estimated answer is close to the actual result.

When performing division, estimation can be a useful tool, especially when dealing with decimals. Estimating can also help in checking the reasonableness of answers obtained via calculators, which can sometimes provide more precision than necessary. For example, when using significant figures in calculations, a calculator does not limit the precision of the result, but estimating can help a user decide how many decimal places to report.

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Answer:

[tex]y=\frac{11}{5}[/tex]

Step-by-step explanation:

Given expression

[tex]\frac{1}{3}(y-2)-\frac{5}{6}(y+1)=\frac{3}{4}(y-3)-2[/tex]

To solve for [tex]y[/tex] for the given expression.

Solution:

We multiply each term with the least common multiple of the denominators of the fraction in order to remove fractions.

The multiples of the denominators are:

3 = 3,6,9,12,15

6 = 6,12

4 = 4,8,12

The least common multiple = 12.

Multiplying each term with 12.

[tex]12.\frac{1}{3}(y-2)-12.\frac{5}{6}(y+1)=12.\frac{3}{4}(y-3)-2(12)[/tex]

[tex]4(y-2)-10(y+1)=9(y-3)-24[/tex]

Using distribution.

[tex]4y-8-10y-10=9y-27-24[/tex]

Simplifying.

[tex]-6y-18=9y-51[/tex]

Adding [tex]6y[/tex] both sides.

[tex]-6y+6y-18=9y+6y-51[/tex]

[tex]-18=15y-51[/tex]

Adding 51 both sides.

[tex]-18+51=15y-51+51[/tex]

[tex]33=15y[/tex]

Dividing both sides by 15.

[tex]\frac{33}{15}=\frac{15y}{15}[/tex]

[tex]\frac{33}{15}=y[/tex]

Simplifying fractions.

[tex]\frac{11}{5}=y[/tex]

∴ [tex]y=\frac{11}{5}[/tex]  (Answer)

Answer:

True

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

20 squared+21 sqaured= 29 squared

The expression for the total cost of bats and gloves is b*x + 5*y. To find the total cost when three bats are bought, you need to know the costs of a bat (x) and a glove (y), and substitute those into the expression.

Assume that the cost of a baseball bat is 'x' dollars and each glove costs 'y' dollars. The total cost can be calculated by making 'b' the number of bats and adding the cost of 5 gloves. Therefore, the expression representing the total cost is b*x + 5*y.

Now, if the coach bought 3 bats, and we're given the costs for a bat and a glove, we can substitute '3' for 'b', 'x' for the cost of a bat, and 'y' for the cost of a glove.

For example, if a bat is $50 (x=50) and a glove is $20 (y=20), the total cost would be: 3*50 + 5*20 = 250 dollars.

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Final answer:

The expression for total cost of baseball bats and gloves is 'b times the number of bats plus 5 times the cost of a glove', where 'b' represents the cost of a bat. In the bat and ball problem, if a bat costs $1 more than the ball and together they cost $1.10, the ball costs $0.05. For three bats, the total cost is $3.15.

Explanation:

The question posed is a classic algebra problem from mathematics often used to illustrate a common cognitive error. To write an expression for the total cost of the baseball bats and gloves, let the cost of each bat be represented by 'b' and assume each glove has a fixed cost 'g'. The expression is then b times the number of bats plus 5 times the cost of a glove. However, we require additional information regarding the cost of individual gloves to complete this expression.

Turning to the bat and ball problem, if a bat and ball together cost $1.10, and the bat costs $1 more than the ball, we can set up the following equations where 'x' is the cost of the ball:

x + (x + $1) = $1.10

2x + $1 = $1.10

2x = $1.10 - $1.00

2x = $0.10

x = $0.05

Thus, the ball costs $0.05 and the bat costs $1.05. Finding the cost of three bats, we simply multiply $1.05 by 3 to get $3.15.

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = [tex]a^2[/tex]

6 is subtracted from the square of a number = [tex]a^2 - 6[/tex]

5 times the number = [tex]5 \times a[/tex]

So we can frame a equation as:

6 is subtracted from the square of a number = 5 times the number

[tex]a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0[/tex]

Let us solve the above quadratic equation

For a quadratic equation [tex]ax^2 + bx + c = 0[/tex] where [tex]a \neq 0[/tex]

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Here in this problem,

[tex]a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6[/tex]

Substituting the values in above quadratic formula, we get

[tex]\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}[/tex]

We have two solutions for "a"

[tex]\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}[/tex]

We have asked negative solution. So a = -1

Thus the negative solution is -1

Answer:

Step-by-step explanation:

16) 4 * y/5

The value of y should be greater than 5

For example if y = 6, then 4* 6/5 = 24/5 = 4.8

If y= 10, then 4* 10/5 = 4 * 2 = 8

y > 5

17) 1 pound = 16 ounce

3020 pounds =3020 * 16 = 48320 ounces

Answer:

k=2

Step-by-step explanation:

We are given that two function f(x) and g(x)

[tex]g(x)=f(kx)[/tex]

From given graph

[tex]g(-2)=0[/tex]

[tex]f(-4)=0[/tex]

[tex]g(-2)=f(-4)[/tex]

By comparing we get

x=-2 and

[tex]kx=-4[/tex]

[tex]k(-2)=-4[/tex]

[tex]k=\frac{-4}{-2}=2[/tex]

Hence, the value of k=2

Based on information provided, the value of k is 2.

Here's why:

1. Understanding the problem: We are given two functions, f(x) and g(x), where g(x) is defined as f(k * x). The graph shows both functions, and we are asked to find the value of k.

2. Analyzing the graph: The graph shows two lines:

  - The red line represents f(x).

  - The blue line represents g(x).

3. Key observation: We are given that g(-2) = 0. This means the blue line intersects the x-axis at x = -2.

4. Relating g(x) to f(x): Since g(x) = f(k * x), we know that the blue line is obtained by horizontally stretching or compressing the red line by a factor of k.

5. Finding k: To make the blue line intersect the x-axis at x = -2, we need to stretch the red line to the left by a factor of 2. This means k = 2.

Therefore, based on the given information and the analysis of the graph, the value of k is 2.

Answer:

(2.5, 2 )

Step-by-step explanation:

Given the 2 equations

2x + 2y = 9 → (1)

2x - y = 3 → (2)

Rearrange (2) expressing y in terms of x

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (1)

2x + 2(2x - 3) = 9 ← distribute left side and simplify

2x + 4x - 6 = 9

6x - 6 = 9 ( add 6 to both sides )

6x = 15 ( divide both sides by 6 )

x = 2.5

Substitute x = 2.5 into (3) for corresponding value of y

y = 2(2.5) - 3 = 5 - 3 = 2

Solution is (2.5, 2 )

Solve this using the elimination process.

They're already lined up so just solve!

2x + 2x = 4x

2y+ (-y) = 3y

9 + 3 = 12

4x + (-1y) = 12

Now solve.

4x + -1 x y = 12

4x - y = 12

4x = 12 + y

x = 12 + y / 4

First, when a problem is lined up with the same vales/terms, you can use the elimination process while doing math.

Then, make your equation by adding and subtracting the same terms.

Therefore, you finally get your answer.

Keep in mind not all answers will be a full number.

Step-by-step explanation:

If you're asking for an equation, the equation would be: [tex]y=-4x-3[/tex]

(probably what you're looking for) if you're looking for what y equals, the answer is: 9

for equation:

1. write an equation with the information you have

[tex]y=-4x+b[/tex]

2. Plug in the values for x and y

[tex]-7=-4(1)+b[/tex] where b equals -3

so your equation would be [tex]y=-4x-3[/tex]

for what y equals:

1. since you've figured out the equation, plug in the value for x and solve for y

[tex]y=-4(-3)-3[/tex] which then gives you [tex]y=9[/tex]

Trevon have 692 paper clips after buying 500 more clips.

Step-by-step explanation:

Let,

Paper clips Caroline have = x

Paper clips Trevon have = y

According to given statement;

x = 5y   Eqn 1

After Trevon buys another 500 paper clips, he has 268 paper clips fewer than Caroline.

y + 500 = x - 268

y + 500 +268 = x

y + 768 = x     Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]y+768 = 5y\\768=5y-y\\768 = 4y\\4y=768[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{768}{4}\\y=192[/tex]

Number of paper clips Trevon has now = y+500 = 192+500 = 692

Trevon have 692 paper clips after buying 500 more clips.

Keywords: linear equation, substitution method

Learn more about substitution method at:

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To find out how many paper clips Trevon has now, we set up an algebraic equation and solve it to determine that Trevon originally had 192 paper clips. After buying an additional 500, he now has a total of 692 paper clips.

The student's question involves solving a basic algebra word problem where Caroline has 5 times as many paper clips as Trevon. When Trevon buys another 500 paper clips, he has 268 paper clips fewer than Caroline. To solve this, we can set up the equation to find the original number of paper clips Trevon had:

So, Trevon originally had 192 paper clips. After buying another 500, Trevon now has 192 + 500 = 692 paper clips.

Option C

The explicit formula for the arithmetic sequence is [tex]a_n = 9 - 6n[/tex]

Solution:

Given that the arithmetic sequence is:

3, -3, -9, -15, -21, ...

To find: Explicit formula for the arithmetic sequence

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

Where [tex]a_n[/tex] is nth term of sequence

n is the term's location

[tex]a_1[/tex] is the first term of sequence

d is the common difference between terms

In an arithmetic sequence, the difference between successive terms is constant. This means that we can move from any term to the next one by adding a constant value.

In the given sequence:

3, -3, -9, -15, -21, ...

[tex]a_1 = \text{ first term } = 3[/tex]

d = difference between any two terms in sequence

[tex]d = a_2 - a_1[/tex]

d = -3 - (3) = -6

Substituting the values in above formula,

[tex]a_n = 3 + (n - 1)(-6)\\\\a_n = 3 -6n + 6\\\\a_n = 9 - 6n[/tex]

Thus the explicit formula to find any term in sequence is found

To find the product for 2(2n + 3), use the distributive property to multiply 2 with each term inside the parentheses, resulting in 4n + 6.

The question asks to find the product for 2(2n + 3). To solve this, we need to use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this rule to the given expression, we multiply 2 with each term inside the parentheses.

First, multiply 2 by 2n to get 4n. Next, multiply 2 by 3 to get 6. Therefore, the expression simplifies to 4n + 6.

We have successfully used the distributive property to find that the product of 2(2n + 3) is 4n + 6.

Answer:

(0,-26)

Step-by-step explanation:

Write the equation of the line in the slope-intercept form:

1. The slope of the line is

[tex]\dfrac{-65-(-52)}{51-34}=-\dfrac{13}{17}[/tex]

2. The equation of the line is

[tex]y-(-52)=-\dfrac{13}{17}(x-34)\\ \\y+52=-\dfrac{13}{17}x+26\\ \\y=-\dfrac{13}{17}x-26[/tex]

Now, find the y-intercept, substitute x = 0:

[tex]y=-\dfrac{13}{17}\cdot 0-26\\ \\y=-26[/tex]