Birthday Party!
Sandy and her twin brother Jason are having a birthday party, but... they haven't yet decided how many candy bars to buy.
and they haven't yet decided how many people to invite!
They made a chart to
write down all the
possible combinations
of people and candy
bars so they could
figure out how many people to invite
and how many candy bars to buy.
Across the top is the number of
people they are thinking about
inviting. On the left is the number of
candy bars they are thinking about
buying.
Help them fill out the chart!
Put the number of candy bars that
each person will get in the cell. Look
for patterns as you work to help you
fill the chart out more quickly!
What patterns do you see in the
chart?
How many candy bars will they buy?
1
2
3
4
5
6
7
8
9
10
1
How many people will they invite?
3
5 6
7
8
2
4
5.7 Apprentice Birthday Party Student
Unless otherwise noted, SFUSD Math Core Curriculum is licensed under the Creative Commons Attribution 40 International License
9 10

The solution set of the equation x^2+3x-4=6 is {-5, 2}.

The answer of the given question are as follows :-

Para encontrar el conjunto de soluciones de la ecuación x^2+3x-4=6, debemos primero llevarla a su forma canónica. Restando 6 de ambos lados, obtenemos:

x^2+3x-10=0

Luego, podemos resolver esta ecuación utilizando la fórmula cuadrática:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

donde a = 1, b = 3, y c = -10.

Reemplazando estos valores, obtenemos:

x = (-3 ± sqrt(3^2 - 4(1)(-10))) / 2(1)

x = (-3 ± sqrt(49)) / 2

x = (-3 ± 7) / 2

x1 = 2

x2 = -5

Por lo tanto, el conjunto de soluciones de la ecuación x^2+3x-4=6 es {-5, 2}.

Translation in english :-

To find the solution set of the equation x^2+3x-4=6, we must first bring it to its standard form. Subtracting 6 from both sides, we get:

x^2+3x-10=0

Then, we can solve this equation using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 3, and c = -10.

Substituting these values, we get:

x = (-3 ± sqrt(3^2 - 4(1)(-10))) / 2(1)

x = (-3 ± sqrt(49)) / 2

x = (-3 ± 7) / 2

x1 = 2

x2 = -5

Therefore, the solution set of the equation x^2+3x-4=6 is {-5, 2}.

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Answer:

Step-by-step explation: Revised 8/15. F001. Surface area of a pond, acres = Length, ft x Width, ft. 43560. F002. Volume

The value of x, given the measurements of the other sides of the triangle, would be 8.

The side lengths of the triangle form a Pythagorean triple.

To determine if the side lengths form a Pythagorean triple, we need to apply the Pythagorean theorem.

Using the Pythagorean theorem, we get:

6^2 + x^2 = 10^2

36 + x^2 = 100

x^2 = 100 - 36

x^2 = 64

x = 8

To determine if the side lengths form a Pythagorean triple, we need to check if the Pythagorean theorem holds true. Plugging in the values, we get:

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

The theorem holds true so this is indeed a Pythagorean triple.

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The full question is:

Find the value of x. Then tell whether the side lengths form a Pythagorean triple.

10, 6​

Answer: To solve this problem, we can use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal, r is the interest rate as a decimal, and t is the time in years.

We are given that the interest rate is 1.95% = 0.0195, the time is 30 years, and the final amount in the account is $800. Let P be the principal we are trying to find.

First, we can use the formula to find the total interest earned over the 30-year period:

I = P * r * t

I = P * 0.0195 * 30

I = 0.585P

Next, we can use the fact that the final amount in the account is the sum of the principal and the interest:

800 = P + 0.585P

800 = 1.585P

P = 504.71

Therefore, the principal was $504.71 and the interest earned over the 30-year period was:

I = 0.585P

I = 0.585 * 504.71

I = 294.29

So the interest earned was $294.29.

Step-by-step explanation:

Answer: 260 ft^2

Step-by-step explanation:

Find the area of the triangle: 0.5*height*base = 0.5*10*20 = 100 ft^2

Find the area of the rectangle: 20*8 = 160 ft^2

Add them together: 160+100 = 260 ft^2

Answer:

81 is the answer

Step-by-step explanation:

87-6 range is highest and lowest number subtracted hope this helps:)

Problems:

Solve for x: 2x - 5 > 9x + 2

Solve for x: 3x + 2 < 7x - 5

Solve for x: 4x + 3 < 2x - 1

Solve for x: -2x - 4 > -8x + 3

Solve for x: 5x + 1 < 2x + 7

Answers:

x < -0.7

x > 1.75

x < -1

x < 0.875

x < 1.2

Answer:  

Example 1

Solve 3x − 5 ≤ 3 − x.

Solution

We start by adding both sides of the inequality by 5

3x – 5 + 5 ≤ 3 + 5 − x

3x ≤ 8 – x

Then add both sides by x.

3x + x ≤ 8 – x + x

4x ≤ 8

Finally, divide both sides of the inequality by 4 to get;

x ≤ 2

Example 2

Calculate the range of values of y, which satisfies the inequality: y − 4 < 2y + 5.

Solution

Add both sides of the inequality by 4.

y – 4 + 4 < 2y + 5 + 4

y < 2y + 9

Subtract both sides by 2y.

y – 2y < 2y – 2y + 9

Y < 9 Multiply both sides of the inequality by −1 and change the inequality symbol’s direction. y > − 9

Solving linear inequalities with subtraction

Let’s see a few examples below to understand this concept.

Example 3

Solve x + 8 > 5.

Solution

Isolate the variable x by subtracting 8 from both sides of the inequality.

x + 8 – 8 > 5 – 8 => x > −3

Therefore, x > −3.

Example 4

Solve 5x + 10 > 3x + 24.

Solution

Subtract 10 from both sides of the inequality.

5x + 10 – 10 > 3x + 24 – 10

5x > 3x + 14.

Now we subtract both sides of the inequality by 3x.

5x – 3x > 3x – 3x + 14

2x > 14

x > 7

Solving linear inequalities with multiplication

Let’s see a few examples below to understand this concept.

Example 5

Solve x/4 > 5

Solution:

Multiply both sides of an inequality by the denominator of the fraction

4(x/4) > 5 x 4

x > 20

Step-by-step explanation:

Hope this helps :3

The estimated value of cos(48) by using tangent line is found to be

0.99989.

A straight line which thus touches a function only once is called a tangent line.

The first step is to calculate y when x=π/4. We will receive that target coordinate point as a result.

The required coordinate point is ( π/ 4, √(2) / 2)

The derivative of such function y is then discovered.

y ' = -sin(x)

Input the derivative with the value of x. This corresponds to the tangent line's slope.

y' = -sin(π/4)

y' = - √(2) / 2

The slope plus coordinate point are now entered into the gradient intercept form of the formula to obtain b.

y = mx + b

√(2) / 2 = (-√(2) / 2)(π / 4) + b

√(2) / 2 = (-π√(2) / 8) + b

(√(2) / 2) + (π√(2) / 8) = b

[4√(2) + π√(2)] / 8 = b

[(4 + π)√(2)] / 8 = b

The tangent line comes out to be:

y = (-√(2) / 2)x + [(4 + π)√(2) / 8]

Now , for cos(48).

48° = π/180 * 48 radians

48° = 3.14/180 * 48  radians

48° = 0.01744*48 radians

48° = 0.83712 radians

So,  cos(48) =  cos(  0.83712 )

Using scientific calculator:

cos(48) =  cos(  0.83712 )  = 0.99989

Thus, the estimated value of cos(48) by using tangent line is found to be

0.99989.

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Answer: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that is only divisible by 1 and itself.

Step-by-step explanation:

For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and so on, are prime numbers because they can only be divided by 1 and themselves without any remainder.

However, 4 is not a prime number because it can be divided by 1, 2, and 4, and 6 is not a prime number because it can be divided by 1, 2, 3, and 6.

Answer:

A prime number is a number that can be multiplied by one and itself~
eg- 2,3,5,7,11
Let me know if this helps

The solution of the equation is x = 2. If we had multiplied both sides by a different number, such as 3 or -4.

What is solution of the equation ?

The solution of an equation is the value(s) of the variable(s) that make the equation a true statement. In other words, it is the value(s) that satisfy the equation.

For example, consider the equation 3x + 4 = 13. To find the solution, we need to determine the value of x that makes the equation true. the solution of the equation 3x + 4 = 13 is x = 3.

According to the question:
The first statement, "Both sides of an equation can be multiplied by the same number without changing the solution of the equation" is always true.

Example: Consider the equation 3x = 6. If we multiply both sides of this equation by 2, we get:

2 * 3x = 2 * 6

6x = 12

The solution of the equation is x = 2. If we had multiplied both sides by a different number, such as 3 or -4, we would still get the same solution.

The second statement, "A number can be added to both sides of an equation changing the solution of the equation" is sometimes true.

Example: Consider the equation 2x = 4. If we add 3 to both sides of the equation, we get:

2x + 3 = 4 + 3

2x + 3 = 7

The solution of the equation is x = 2.5. Adding 3 to both sides did not change the solution.

However, if we add a number that is equal to or related to the variable, the solution will change. For example, if we add x to both sides of the equation 2x = 4, we get:

2x + x = 4 + x

3x = 4 + x

The solution of the equation is x = 4/2 = 2, which is different from the previous solution of x = 2. Therefore, the statement "A number can be added to both sides of an equation changing the solution of the equation" is sometimes true, depending on the number being added.

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Answer:

(3, 0) and (5, 0)

Step-by-step explanation:

Parabola equation is
g(x) = x²- 8x + 15

x-intercepts are the x-values when y = 0

Solve for x at g(x)=

==> x² - 8x + 15 = 0

This is a quadratic equation which has two solutions

Factoring x² - 8x + 15 gives (x - 3)(x - 5) which makes the quadratic equation
(x - 3)(x - 5) = 0

==> x - 3 = 0 giving x = 3 as one solution and x - 5 = 0 giving x = 5 as the other solution

At both intercepts, y = 0

So the correct answer is
(3, 0) and (5, 0)

Answer:

8*7=56 + 8*3=24 = 80_squared

Step-by-step explanation:

The values of x that could make the triangle into different types of triangles are:

For a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the third side.

Right Triangle:

A triangle is a right triangle if it satisfies the Pythagorean theorem: a² + b² = c², where c is the longest side (hypotenuse).

6² + 8² = x²

36 + 64 = x²

100 = x²

x = 10

Acute Triangle:

A triangle is acute if the sum of the squares of the two shorter sides is greater than the square of the longest side. Since we already know that the right triangle has x = 10, we can choose a value for x that is less than 10 to form an acute triangle.

Let's take x = 9:

6² + 8² > 9²

36 + 64 > 81

100 > 81

Obtuse Triangle:

A triangle is obtuse if the sum of the squares of the two shorter sides is less than the square of the longest side. We can choose a value for x that is greater than 10 to form an obtuse triangle.

Let's take x = 11:

6² + 8² < 11²

36 + 64 < 121

100 < 121

The possible values of x for each triangle type are:

Right Triangle: x = 10

Acute Triangle: x = 9

Obtuse Triangle: x = 11

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Answer:

The surface area of the soup can is given by the formula:

SA = 2πr² + 2πrh

where r is the radius of the circular ends of the can, h is the height of the can, and π is approximately 3.14.

The radius of the can is half of the diameter, so r = 4.5 cm.

Therefore, the surface area of the can is:

SA = 2π(4.5)² + 2π(4.5)(11)

SA = 2π(20.25) + 2π(49.5)

SA = 40.5π + 99π

SA = 139.5π

Approximating π as 3.14, we get:

SA ≈ 139.5 × 3.14

SA ≈ 438.03 cm²

Therefore, at least 438.03 square centimeters of paint are needed to cover the can.

So, the answer is 438.03 cm2.

I Hope This Helps!

Answer:

0.375

Step-by-step explanation:

3/2 equals 1 and a half, and 1 and a half divided by 4 will get you 0.325

Answer:

4x - 2 = 3x + 1. Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member. 4(3) - 2 = 3(3) + 1.

The prοbability οf exactly 3 successes in 6 trials οf a binοmial experiment with a prοbability οf success οf 75% is 31.1%, rοunded tο the nearest tenth οf a percent.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο find the prοbability οf exactly 3 successes in 6 trials οf a binοmial experiment, we use the fοrmula:

The prοbability οf r successes in n trials is [tex]\rm _nC_r(p)^r(q)^{n-r[/tex], where p is the prοbability οf success οn a given trial and q = 1-p.

In this prοblem, n = 6, r = 3, p = q = 0.75

Sο, P(3 successes in 6 trials) = [tex]\rm _6C_3(0.75)^3(0.75)^3[/tex] =  0.13184 ≈ 13.2%

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Evaluating the linear equation in x = 19 we can see that the temperature was 5.76 degrees, so your answer is correct.

Here we have a linear equation that relates the wind temperature with the wind's velocity.

The linear equation is:

y = -0.36*x + 12.6

Where y is the temperature and x is the wind speed. We want to find the temperature when the speed is 19 miles per hour, to get it, just replace x by 19 in the linear equation above, then we will get:

y = -0.36*19 + 12.6

y = -6.84 + 12.6

y = 5.76

So your answer is correct.

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The area of the region in which the burro can graze will be 833 pi square feet.

Each interior vertex angle of a regular hexagon is (n - 2)·180°/n  =  (6 - 2)·180°o/6  =  120°

I'll break up the area into three sections.

There is one major section, going 150' along one side in a circular arc to 150' along the adjacent side.

Since the interior angle is 120°, the exterior angle will be 240°.

The area of this section will be:  (240°/360°)·pi·radius2  =  (2/3)·pi·1502  =  15,000 pi

Then, on each end, around the corner of the barn, the goat can go in a circular arc with radius = 50'.

This angle will be 60°, or one-sixth or a circle.

The area of each section will be (1/6)·pi·502  =  416 2/3 pi

Total area:  15,000 pi + 416 2/3 pi + 416 2/3 pi  =  833 1/3 pi square feet.

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Answer:

# rad u cant take 67 from it its going 35 mps

Step-by-step explanation:

Answer:

linear

Step-by-step explanation:

this is a linear function!

linear functions follow y = mx+b, where m is the slope and b is the y-intercept

let's write our y = mx+b equation

for each value that x increases, y increases by DOUBLE that amount. slope is y/x, so since y increases by 2 and x increases by 1, the slope is 2/1 which is 2.

the y-intercept is where the line passes the x axis, or when x is 0. in this table, it gives you your y-intercept, which is -6

your equation is y=2x+(-6); which simplified to y=2x-6

if you plug in the y and x values, you'll get the same thing. i hope this helped!

Answer:

slope intercept form= y=2x+2

point form= y+4=2*(x+3)

Step-by-step explanation:

Answer y = -2x -2 is your equation of the line crossing those points

Step by step

To find your equation of the line, use slope (-2) and the points (-3, 4) and point slope formula y- y1 = m (x - x1)

y - 4 = -2 ( x - -3)

Simplify

y - 4 = -2x -6

Add 4 to each side to isolate y

y -4 +4 = -2x -6 +4

Simplify

y = -2x -2 is your equation of the line crossing those points

Answer:

e

Step-by-step explanation:

The reduced price of the swimsuit is $28.05 being obtained by using the mark down  value and selling price of the product.

Explain Pricing?

A price technique that allows for discussion between the supplier and the buyer is flexible pricing. The supplier does not provide a fixed price while using this tactic. They decide on a price range in advance so that they can haggle with the customer. A vendor will have a minimum number they can take and a maximum number they may charge when using flexible pricing.

Using the formula M=S-N, where M is the mark down, S is the original selling price, and N is the reduced price, we can find the reduced price of each swimsuit as follows:

M = $17.90

S = $45.95

N = S - M

N = $45.95 - $17.90

N = $28.05

Therefore, the reduced price of each swimsuit is $28.05.

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Answer:

the possible answers are 80 and 140

Step-by-step explanation:

since one angle has a measure of 20 in isosceles triangle let this be vertex angle and other two as base angles then

in isosceles triangle base angles must be equal to each other so

x+x+20 = 180

2x+20 = 180

2x = 160

x=80

so the base angles are equal to 80

now if you suppose 20 as base angle then other base angle should also be 20 since it is an isosceles triangle and the vertex angle can be calculated as

20+20 + x = 180

x = 140

Answer:

190°

Step-by-step explanation:

56 = (1/2)(x - 78)

112 = x - 78

190 = x

x = 190

Answer: 190°

I'm a pretty sure that the answer is 190°, Hope this helps (:

This report highlights the impact of human activity on three different locations: New York City, the Amazon Rainforest, and the Sahara Desert. The measurements were taken 50 years ago, in the present day, and the predicted future development impact.

## New York City

Water pollution in parts per million (ppm) was measured in New York City. Fifty years ago, the water pollution was 625ppm, and presently, it has increased to 893ppm. The predicted future development impact is 843ppm. To decrease human impact on this location, it is recommended to create gardens on all of the rooftops. The plants will help absorb some of the pollutants and reduce runoff into waterways.

## Amazon Rainforest

CO2 levels in parts per million (ppm) were measured in the Amazon Rainforest. Fifty years ago, the CO2 levels were 318ppm, and presently, it has increased to 402ppm. The predicted future development impact is 378ppm. To decrease human impact on this location, it is recommended to limit the amount of timber that can be removed per year. The Amazon Rainforest is often referred to as the "lungs of the planet" due to its ability to absorb carbon dioxide and produce oxygen. By limiting deforestation, the amount of carbon dioxide released into the atmosphere will decrease, and the rainforest will continue to produce oxygen, benefiting both the local and global environment.

## Sahara Desert

The loss of land by erosion in meters was measured in the Sahara Desert. Fifty years ago, the erosion was 1.2 meters, and presently, it has increased to 3.5 meters. The predicted future development impact is 2.6 meters. To decrease human impact on this location, it is recommended to build better enclosures to decrease overgrazing by livestock. Overgrazing leads to soil compaction, which makes it difficult for vegetation to grow and prevents the soil from holding water. By implementing better enclosures, the livestock will be limited to a smaller area, allowing the vegetation to recover and hold the soil in place.

## Conclusion

In conclusion, all three locations experienced an increase in human impact over the years. By analyzing the data, the location that could benefit the most from decreasing human impact is the Amazon Rainforest. Limiting the amount of timber that can be removed per year will have a positive impact on this location. However, it is important to continue monitoring all three locations to ensure that the human impact is decreasing and not increasing.

## Recommendations for Local Communities

To decrease the local effects of human impact on the environment, two recommendations are:

1. Reduce the use of single-use plastics, such as straws and bags, to decrease pollution. Single-use plastics are a major source of pollution in our oceans, and by reducing our reliance on them, we can help reduce the amount of plastic that ends up in our waterways.

2. Plant more trees and vegetation to increase the amount of oxygen in the air. Trees and plants produce oxygen through photosynthesis, which helps clean the air we breathe. By planting more trees and vegetation in our communities, we can help reduce the amount of pollution in the air and create a healthier environment for ourselves and future generations.

## Recommendations for Global Governments

To decrease the global effects of human impact on the environment, two recommendations are:

1. Invest in renewable energy sources, such as solar and wind power, to decrease the use of fossil fuels. Fossil fuels are a major contributor to greenhouse gas emissions, which are responsible for climate change. By investing in renewable energy sources, we can decrease our reliance on fossil fuels and reduce our carbon footprint.

2. Implement policies to decrease deforestation and promote reforestation to decrease the loss of wildlife habitats and increase the amount of oxygen in the air. Deforestation is a major contributor to climate change, as it releases carbon dioxide into the atmosphere and reduces the amount of oxygen produced by trees. By implementing policies to decrease deforestation and promote reforestation, we can help mitigate the effects of climate change and create a healthier environment for all living beings.