A recent survey of
300 juniors and seniors in physics in a certain high school had the following results: 160 males, 80 junior females, 130 seniors. Draw a vent diagram and label the data.

To solve the linear system by graphing, convert the equations to slope-intercept form, plot the lines, and find the point of intersection.

To solve the given linear system by graphing, we need to graph both equations on the same coordinate plane and find the point of intersection.

Step 1: Convert both equations into slope-intercept form, y = mx + b.

Step 2: Plot the y-intercepts (b values) of both equations and use the slopes (m values) to draw the lines.

Step 3: The point where the lines intersect is the solution to the system of equations. In this case, the solution is x = 6 and y = 0.

Use Pythagorean Theorem (a² + b² = c²) to find the lengths of the sides. You can also use the distance formula.

6² + 14² = d²

36 + 196 = d²

232 = d²

15.23 ≅ d

2² + 5² = d²

4 + 25 = d²

29 = d²

5.39 ≅ d

Next, use the Perimeter formula:

P = 2L + 2w

  = 2(15.23) + 2(5.39)

  = 30.46 + 10.78

  = 41.24

For #6, Use the Area formula:

A = L x w

  = 5.39 x 41.24

  = 222.28

7x+9

5x+2x= 7x

5+4=9

7x + 9 is the result when combining like terms.

Answer:

7x+9

Step-by-step explanation:

Add the numbers

5x + 4 + 2x + 5

5x+9+2x

Combine like terms

5x+9+2x

7x+9

Solution:

7x+9

9)

[tex]\frac{24z^{5}y^{4}}{3z^{-2}y^{5}} = \frac{24}{3}*\frac{z^{5}}{z^{-2}}*\frac{y^{4}}{y^{5}} = \frac{8}{1} *\frac{z^{5+2}}{1}*\frac{1}{y^{5-4}} = \frac{8z^{7} }{y}[/tex]

11)

(a²b)³ = a²⁽³⁾b¹⁽³⁾ = a⁶b³

12)

The exponent tells you how many places to move the decimal. The positive/negative sign tells you which direction to move the decimal (negative is left, positive is right).

8.4 x 10⁻⁵ move the decimal 5 places to the left   =  0.000084

Positive, 72 minus negative 9 is the same thing as 72+9, which equals 81. So the answer is positive

Answer:

y=-0.7

Step-by-step explanation:

−(7y+0.6)=3.6−y

-7y+-0.6=3.6−y

-6y+-0.6=3.6

-6y=4.2

y=-0.7

[tex]3x^2+4y^2\\\\\text{Put the values of x=2, y=1 and z=-3 to the expression:}\\\\3(2^2)+4(1^2)=3(4)+4(1)=12+4=16[/tex]

Substituting the provided values of x and y into the equation 3x^2 +4y^2 gives a final result of 16.

The question is asking for the value of the mathematical expression 3x^2 +4y^2 when x is 2 and y is 1. To find this, we substitute the values of x and y into the expression.

Therefore, the value of 3x^2 +4y^2 when x=2 and y=1 is 16.

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To solve the equation x²−12x=−6, Lamar should first move the constant to the other side and complete the square, leading to x = 6 ±√30. This equation, which is a type of quadratic or second-order polynomial, may have two solutions, a typical characteristic of such equations.

The equation presented is x²−12x=−6. To solve this equation by completing the square, we first move the constant term to the other side, which leads to x² - 12x = -6, or x² - 12x + 36 = -6 + 36. We added 36 on both sides because (12/2)² = 36, which is a step in completing the square for the equation. Thus, we have (x-6)² = 30. Now, solve for x: x - 6 = ±√30, so x = 6 ±√30.

This method, known as completing the square, is a typical approach to solving quadratic equations. The general quadratic equation ax²+bx+c = 0 can also be solved using the quadratic formula -b ± √(b² - 4ac) / 2a. With both methods, remember that a quadratic equation will usually have two solutions, as it is a second-order polynomial.

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3 4/5 = 4l

A = l^2

Divide 3 4/5 by 4.

l = 0.95

0.95^2 = 0.9025

The area of the square is 0.9025 meters.

To find the area of a square with a perimeter of 3 4/5 meters, we first convert the perimeter to an improper fraction, divide by 4 to find the length of one side, and then square this length to get the area, resulting in 361/400 square meters.

The question is asking us to find the area of a square when the perimeter is given as 3 4/5 meters. First, we convert the mixed number to an improper fraction which is (3 × 5 + 4)/5 = 19/5 meters. Since the perimeter of a square is the sum of all its sides (P = 4a), we can find the length of one side (a) by dividing the perimeter by 4.

a = P / 4 = (19/5) / 4 = 19/20 meters.

Now that we have the length of a side, we can find the area by squaring this length:

Area = a · a = (19/20) · (19/20) = 361/400 square meters.

Therefore, the area of the square is 361/400 square meters.

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Answer:

192.5 acres.

Step-by-step explanation:

Total area of farm the farmer had = 420 acre.

Of these he did not plant full but only 7/12th of the total acres.

Planted area with corn = 7/12(420) = 245  acres

Of these 245 acres, 3/14th was affected by crop and the remaining part would be healthy

crop affected by disease = 3/14 (245) = 52.5 acres

Hence healthy corns = area planted for corn-diseased part of area

=245-52.5

= 192.5 acres

$60

$45 is 75% of the original price. 75/3 is 25, so divide 45/3=15. $15 is 1/4 of the original price. 15*4=60

The original price of the pair of shoes is $60.

To find the original price of a pair of shoes, we can use the given information that the sale price is $45 after a 25% discount.

Let's assume the original price of the shoes is "x" dollars.

The discount of 25% means that the sale price is equal to 75% (100% - 25%) of the original price.

Mathematically, we can express this as:

Sale price = Original price * (Discount percentage in decimal form)

$45 = x * (0.75)

To find the original price (x), we divide both sides of the equation by 0.75:

$45 / 0.75 = x

x = $60

Therefore, the original price of the pair of shoes is $60.

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For every 7 animals, you have 5 dogs to 2 cats. So divide 98 by 7 and you get 14 groups of 7.

Multiple 14 times 5 dogs and you get 70

Multiple 14 times 2 cats and you get 28

70 + 28 = 98.

Answer:

150

Step-by-step explanation:

50 lunches each day.

3 days in total that 50 lunches were severed.

50 x 3 = 150

50 + 50 + 50 = 150

First we know that,

3x+15=5x-65 because of vertical angle thr.

y=y because of reflex property

there are 360 degrees in a circle so..

3x+15+5x-65+2y=360

3x+15=5x-65

x=40

so each 2 of the angles are...(40*3+15)=135

Then your new equation is

135+135+2y=360

2y=90

y=45

Hope this helps :)

Hanna walks a total of 3 1/6 miles before and after school.

To find how many miles Hanna walks before and after school, we can add the distances she walks to school and to work.

Distance to school = 1 2/3 miles

Distance to work = 1 1/2 miles

To find the total distance Hanna walks before and after school, add the two distances:

Total distance = 1 2/3 + 1 1/2

To add these fractions, we need to convert them to have a common denominator, which is 6:

1 2/3 = (3/3 + 2/3) = 5/3

1 1/2 = (3/2)

Now, we can add the fractions:

Total distance = 5/3 + 3/2

To add these fractions, we need to have a common denominator, which is 6:

Total distance = (5/3) * (2/2) + (3/2) * (3/3)

Total distance = 10/6 + 9/6

Now, add the fractions:

Total distance = 19/6

We can simplify this fraction:

Total distance = 3 1/6 miles

So, Hanna walks a total of 3 1/6 miles before and after school.

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Answer:

c

Step-by-step explanation:

Answer:

Domain is -3

Step-by-step explanation:

Given that coordinate of a graph is (-3, -2)

We have to find out the domain.

We know that if A and B are two sets, a mapping from A to B is the subset of cartesian product AxB.

Domain is the set of values of A which have images in B.

Use the above definition.

We have A = {-3,...} and B = {-2,....}

The mapping is from -3 to -2

Hence domain is -3

Area = 9π cm².

Decimal approximation ⇒ 28.26 cm².

Work is provided in the image attached.

The volume of any prisma no matter wich one side it have got the following formula:

V=Ab*h where Ab is the base area and h is called height.

From our data we know the volume (6k^2-13K+5) and we know the base area (2k-1). Inserting this data in the general formula we got:

6k^2-13K+5=(2k-1)*h, solving for our unknown variable the height h

h=6k^2-13K+5/2k-1

factoring numerator :

h=(3k-5)(2k-1)/2k-1 simplifying

h=3k-5

The answer is 3k-5

Remark

The Volume = B * h

V = 6k^2 - 13k + 5

B = 2k - 1

h = ??

The volume will factor into (2k - 1)(3k - 5)

You can tell that one of the factors is 2k - 1 because that is the given amount for the base. You need only find the other factor. 3k is needed to multiply 2k to 6k^2.

- 1 needs - 5 to get the answer to 5

So the other factor is 3k - 5

Solution

V/b = h

(6k^2 - 13k + 5)/(2k - 1)

(3k - 5)(2k - 1) / (2k - 1)   The (2k - 1)s Cancel out

Answer

B = 3k - 5 Second one down.

So she pays 6 lb of chicken for $39 then $39/6 = $6.30 is the price per pound.

11lb + 6lb = 17lb total of  chicken then multiply it by the price per pound

17($6.50) = $110.50

Final answer:

Stacey will pay $71.50 for 11 more pounds of chicken.

Explanation:

To figure out how much Stacey will pay for 11 more pounds of chicken, we can use the given information that she bought 6 pounds of chicken for $39.

Therefore, Stacey will pay $71.50 for 11 more pounds of chicken.

Y=.25x+176.10 Y is the monthly cost and B would be the cost of the insurance every month. X is the amount of miles driven since the .25 stays constant but the amount of miles you drive in a month is different every month, Hence, needs to be a variable that can be adjusted,

A - The value of b, $176.10, represents the fixed costs like insurance and car payments, which remain constant regardless of the number of miles driven. B - It serves as the baseline monthly cost for driving the car.

(a) To model the monthly cost of driving the car (y) in terms of the number of miles driven (x), you can use the equation y = mx + b, where:

y represents the monthly cost of driving the car.

x represents the number of miles driven.

m represents the cost per mile for gasoline, oil, and routine maintenance, which is $0.25 in this case.

b represents the fixed costs, including insurance and car payments, which are $176.10 per month.

So, the values for m and b in this scenario are:

m = 0.25 (the cost per mile)

b = 176.10 (the fixed monthly costs)

Therefore, the equation to model the monthly cost of driving the car is:

y = 0.25x + 176.10

(b) The value of b, which is 176.10 in this equation, represents the fixed costs associated with driving the car. In this case, it includes the monthly insurance and car payment expenses. These are costs that do not depend on how many miles you drive.

Instead, they remain constant every month. So, b represents the baseline or starting point for the monthly cost of driving the car. Even if you were to drive zero miles in a month, you would still have to pay these fixed costs.

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Step 1. Take out the constants

3/9 y^2y^4

Step 2. Simplify 3/9 to 1/3

1/3 y^2y^4

Step 3. Simplify

y^2y^4/3

Step 4. Use the Product Rule

y^2 + 4/3

Step 5. Simplify 2 + 4 to 6

y^6/3

ANSWER

The line that is parallel to [tex]y=4x-6[/tex] through [tex](12,10)[/tex] is  [tex]y=2x-14[/tex].

EXPLANATION

The equation that is parallel to the line [tex]y=4x-6[/tex] has a slope that is equal to the slope of this line.

By comparing this equation to the general slope intercept form,

[tex]y=mx+c[/tex],this line has slope [tex]m=2[/tex].

Hence the line parallel to this line also has slope [tex]m=2[/tex].

Let [tex]y=mx+b[/tex] be the equation of the line parallel to the line

[tex]y=4x-6[/tex]

We can substitute [tex]m=2[/tex] to obtain;

[tex]y=2x+b[/tex]

If the line passes through the point [tex](12,10)[/tex],then this point must satisfy its equation.

We substitute [tex]x=12[/tex] and [tex]y=10[/tex] to obtain;

[tex]10=2(12)+b[/tex]

We this equation for [tex]b[/tex].

[tex]\Rightarrow 10=24+b[/tex]

[tex]\Rightarrow 10-24=b[/tex]

[tex]\Rightarrow -14=b[/tex]

We substitute this value of  [tex]b=-14[/tex] in to [tex]y=2x+b[/tex] to get;

[tex]y=2x+-14[/tex].

Hence the equation of the line that is parallel to [tex]y=4x-6[/tex] through [tex](12,10)[/tex] is  [tex]y=2x-14[/tex].