12.2 Apples and Oranges
At the corner produce market, apples cost $1 each and oranges cost $2 each.
1. Find the cost of:
a. 6 apples and 3 oranges
b. 4 apples and 4 oranges
c. 5 apples and 4 oranges
d. 8 apples and 2 oranges
Unit 3: Linear Relationships
Lesson 12: Solutions to Linear Equations
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Georgia  takes 24 minutes to clean the espresso machine by herself.

The correct answer is an option D.

The equation for the situation is:

[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8}[/tex]

here, x is the number of minutes it takes Georgia to clean the machine by herself.

We need to find the value of x.

Consider the equation,

[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8} \\\\\frac{(x -12)+x}{x(x-12)}=\frac{1}{8}\\\\\frac{x -12+x}{x^2-12x}=\frac{1}{8}[/tex]

(2x - 12) × 8 = x² - 12x

16x - 96 =  x² - 12x

x² - 12x -16x + 96 = 0

x² - 28x + 96 = 0

x²-24x-4x+96 = 0

(x - 24)(x - 4) = 0

x = 24 or x = 4

If x = 4, then x - 12 would be negative which is not possible.

Thus, it takes 24 minutes for Georgia.

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Find the complete question below.

The amount of money in Lucia's account after 5 years will be $1,105.5.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,

A = $600 × (1 + 0.13)⁵

A = $600 × (1.13)⁵

A = $600 × 1.84

A = $1,105.5

The amount of money in Lucia's account after 5 years will be $1,105.5.

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If Barry has 120 stamps and Bob has 3/5 as many stamps as Barry, you can set up the proportion:

3/5 = x/120

Where x is the number of stamps Bob has. To solve for x, you can cross-multiply:

3 * 120 = 5 * x

Simplifying:

360 = 5x

x = 72

So, Bob has 72 stamps. To find out how many more stamps Barry has than Bob, you can subtract the number of stamps Bob has from the number of stamps Barry has:

120 - 72 = 48

Barry has 48 more stamps than Bob.

Answer: 72

Multiply 120 by 3/5 to get Bob's amount of stamps.

JKLM is a parallelogram with four sides and four angles, meaning its measure of angle K is equal to the measure of angle M.

A parallelogram is a quadrilateral having four equal-length sides and opposing sides that are parallel. It is a two-dimensional form with two pairs of parallel sides and equal angles on all sides.

JKLM has four sides and four angles if it is a parallelogram. Because it is a parallelogram, the opposite sides of the figure will be parallel, as will the opposite angles. This signifies that the angle K measure is equal to the angle M measure. As a result, if the measure of angle M is known, the measure of angle K may be calculated.

For example, if angle M is 70 degrees, then angle K is also 70 degrees. In general, if the measure of angle M is x, the measure of angle K must be x as well.

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The Healthy People 2030 initiative goals of reducing obesity and promoting a healthy lifestyle.

One change that should be made in school cafeterias is to reduce the number of protein choices. This can be done by decreasing the amount of red meat, poultry, and fish in the cafeteria by at least 50%. The number of vegetarian and vegan options should also be increased. This would reduce the amount of saturated fat and cholesterol that students are consuming and help them to make healthier food choices. It would also help to reduce the environmental impact of the cafeteria by reducing the amount of animal products being consumed. This change would help schools to meet the Healthy People 2030 initiative goals of reducing obesity and promoting a healthy lifestyle.

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The estimated weight of three containers weighing 1. 656 kg each =  5 kg

Let w represents the weight of each contaoner.

Here, each container weighs 1.656 kg

⇒ w = 1.656 kg

Here, the weight of all containers are the same.

To determine the estimated weight of three containers we us the Unitary method.

We simply multiply the given weight by the number of containers.

Let W be the estimated weight of three containers.

Using Unitary method,

W = 3 × w

W = 3 × 1.656

W = 4.968

W ≈ 5 kg

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Answer:

Step-by-step explanation:

I DON'T KNOW

Answer:

Step-by-step explanation:

ok so with triangle sum theorem the equation we use for this is n-2•180 (n equals number of sides, for 3*180 is 540, 540-all non variable numbers leave us with 165, divide 165 by 13 and that’s your answer, if anything round. Please lmk if this is wrong

Answer: x = 13

Step-by-step explanation:

       To solve, we will isolate the variable.

Given:

3x − 2 = 37

Add 2 to both sides equation:

3x = 39

Divide both sides of the equation by 3"

x = 13

As, a = -49 is a negative number, so there is no real root for the integer.

What is square root?

A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root.

The expression is given as - a = -49

The value for n is n = 2

Find the nth root value for the expression a.

Since a = -49 is a negative number there is no real square root for the number.

If it would have been a = 49, then there would have been one real square root.

n=2 which generates √49.

This gives the value as 7.

Therefore, there are no roots for -49.

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a) The approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 59.2 and 434.2 is of 99.7%.

b) The approximate percentage of women with platelet counts between 184.2 and 309.2 is of 68%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

Hence the percentages are given as follows:

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Answer:

see below.

Step-by-step explanation:

1. g(x) = 2^(x-5) +3

2. g(x)= 1/3 * 2^x

3. f(x) was vertically stretched by 3.  K value is 3.  The Y intercept became augmented by 3 folds.

4. k value = 5, the curve basically got "lifted" up by 5 units.

Answer:

1 = 18

Step-by-step explanation:

The amount for each berry are 5.60 and 1.60 respectively.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

Given that, Jeffrey wants to make jam. He needs a combination of raspberries and blackberries totaling six pounds. Blueberries cost $1.00 per pound, and raspberries cost $2.00 per pound. If Jeffrey can afford $11.60,

We will set a system of linear equations, to solve this,

Establishing the equation,

Let the amount of raspberries be x and that of blueberries be y,

x + y = 6

y = 6-x...(i)

2x + y = 11.60

y = 11.60 - 2x...(ii)

Equating eq(i) and eq(ii)

6-x = 11.60 -2x

x = 5.60

Put x = 5.60 in eq(i)

y = 6-5.60

y = 1.60

Hence, the amount for each berry are 5.60 and 1.60 respectively.

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      Statement                                                Given

1. X is the midpoint of VY              1. Given

2. WV ║ YZ                                     2. Given

3. VX = XY                                       3. X is midpoint

4. ∠WXY = ∠YXZ                            4. Corresponding Angle Theorem

5. ∠WVX = ∠XYZ                            5. Vertical Angle Theorem

6. △YXZ = △VWZ                           6. AA Similarity

7. WV ≅ YZ                                      7. Prove

We know that WV ║ YZ, X is the midpoint of VY.

If X is the midpoint of VY. So VX = XY

The corresponding angles in the two regions of intersection are congruent when a line intersects two parallel lines.

From the Corresponding Angle Theorem

∠WXY = ∠YXZ

When two straight lines cross, the Vertical Angle Theorem states that they create two sets of linear pairings with congruent angles.

From the Vertical Angle Theorem

∠WVX = ∠XYZ

According to the AA similarity theorem, two triangles are similar if two of their triangles' triangles are congruent with two of their other triangles' angles.

By AA Similarity

△YXZ = △VWZ

Hence, WV ≅ YZ

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The complete question is given below:

Answer:

y =  [tex]\frac{1}{3}[/tex]x + 6

Step-by-step explanation:

The equation we currently have right now is y = -3x+2. Since we know that the line equation is y = mx + b, let's take out m to find the slope of a perpendicular line. M will be -3.

To convert a regular slope to a perpendicular one, we have to:

- reciprocal/flip it (this means that if m = 3, the perpendicular will be [tex]\frac{1}{3}[/tex])

- swap the signs (this will mean that if a number is positive, then it will become negative)

Therefore, if m = -3, the perpendicular slope will be [tex]\frac{1}{3}[/tex] (we flipped and changed signs)

Now, we are also given that this line passes through the point (6,8), so we can use this formula: [tex]y - y1 = m(x-x1)[/tex]

What do we know right now?

- y1 = 8 (from (6,8))

- x1 = 6 (from (6,8))

- m =  [tex]\frac{1}{3}[/tex]

Let's plug in what we know:

y - 8 =  [tex]\frac{1}{3}[/tex](x - 6)

y =  [tex]\frac{1}{3}[/tex](x-6) + 8

y =  [tex]\frac{1}{3}[/tex]x - 2 + 8

y =  [tex]\frac{1}{3}[/tex]x + 6

Answer:

Rectangles

Squares

A square is a special type of rectangle. All squares are rectangles, but not all rectangles are squares. In a square, all four sides are equal in length (congruent), making it a special case of a rectangle where all angles are right angles and all four sides have the same length. In contrast, a rectangle can have sides of different lengths.

The scale factor of the dilation is equal to: B. 5.

In Geometry, a scale factor simply refers to the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object based on a specific scale factor with respect to the origin is given by this mathematical expression:

(x, y)      →    (SFx, SFy)

Where:

Scale factor = 15/3 = -25/-5

Scale factor = 5.

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The required solution to the given radical expression √45 is 3√5.

Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.

The radical expression is given in the question

√45

As per the given question, the required solution would be as:

√45 = √(3 × 3 × 5)

√45 = 3√5

Thus, the solution to the given expression is 3√5.

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The lines, y = -1 and x = 1 are perpendicular lines.

If two lines are perpendicular to each other, it means they form right angle at the point of intersection, and also, they have slopes that are negative reciprocals to each other.

Also, vertical and horizontal lines are perpendicular to each other because horizontal line has a slope that is zero while vertical line has an undefined slope.

y = -1 is a horizontal line, while x = 1 is a vertical line. Therefore, we can concluded that, they are perpendicular to each other.

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The meaning of the y-intercept is that Nora paid her plumber an initial fee of $50.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this equation is 50 and it represents the initial fee being charged by the plumber.

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The explicit equation for this arithmetic sequence is: aₙ =  9 + (n-1)(-8).

An arithmetic series is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d,... The basic distinction of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

The formula for an arithmetic sequence is given as an=a1+(n1)d, where an a n is a broad term, a1 a 1 is the initial term, and d is the huge distinction. This is done in order to locate the general phrase in the list.

The general form of the explicit equation for an arithmetic sequence is:

an = a1 + (n-1)d

Given that the first term is 9 and the second term is 1,

d = a2 - a1 = 1 - 9 = -8

So the explicit equation for this arithmetic sequence is:

aₙ = 9 + (n-1)(-8)

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the probability that it will complete the textural transformation

is 0.90334.

Let A be the event that a leaf completes the color transformation and B be the event that a leaf completes the textural transformation.

n(A) = 243 +  26 = 269

n(B) = 243 +  13  = 256

n (A∩ B)  = 243

n(S) = 243 +26+13+18 = 300

Finding the Probability of the event that the leaf completes the color transformation by using the Probability of an event formula

P(A)= 269 / 300

     =  0.89667

p(A∩ B) = 243/300

          =  0.81

By using the conditional probability of a leaf completing textural transformation given a leaf completing color transformation

P(B/A) = p(A∩ B) / P(A)

          = 0.81/0.89667

          = 0.90334

The conditional probability of a leaf completing textural transformation given a leaf completing color transformation is 0.90334

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The complete question is :

The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type of transformation completed:

(a) ) If a leaf completes the color transformation, what is the probability that it will complete the textural transformation?

The y-intercept of the linear function 11x - 10y = 2 is given as follows:

y = -1/5.

The function for this problem is defined as follows:

11x - 10y = 2.

The y-intercept of a function is given by the value assumed by y when x assumes a value of 0.

Considering it's concept, the y-intercept of the function in this problem is obtained as follows:

-10y = 2

10y = -2

y = -2/10

y = -1/5.

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The rate of change of the function is: 2.

The y-intercept/initial value is: 3.

The rate of change is also the slope of a function, which is calculated as, m = change in y / change in x.

Given the points, (0, 3) and (2, 7):

Rate of change/slope (m) = (7 - 3) / (2 - 0)

m = 4/2

m = 2

To find the initial value/y-intercept (b), substitute m = 2 and (x, y) = (0, 3) into y = mx + b:

3 = 2(0) + b

3 = 0 + b

3 = b

b = 3

y-intercept = 3.

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In quadrilateral ABCD, m∠C = 70°.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

Given:

ABCD is a quadrilateral.

m∠A =80°, m∠B = 100° and m∠D = 110°.

The sum of all the interior angles is 360°.

m∠A + m∠B + m∠C + m∠D = 360°.

80 + 100 + 110 + m∠C = 360

m∠C = 360 - 290

m∠C = 70°

Therefore, m∠C = 70°

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Step-by-step explanation:

In a quadrilateral, the sum of the measures of the angles is 360 degrees. Therefore, if we know the measures of three of the angles in a quadrilateral, we can use this information to find the measure of the fourth angle.

In this case, we know that:

m(<A) = 80 degrees

m(<B) = 100 degrees

m(<D) = 110 degrees

So, to find m(<C), we can use the equation:

m(<A) + m(<B) + m(<C) + m(<D) = 360

Substituting in the known values, we get:

80 + 100 + m(<C) + 110 = 360

Solving for m(<C), we get:

m(<C) = 360 - (80 + 100 + 110) = 360 - 290 = 70 degrees

So the measure of angle C is 70 degrees.

The insect's length as seen via a microscope is found to be 56 millimeters.

For the stated question:

Then,

body length (under microscope) = 7*8 millimeters

body length (under microscope) = 56 millimeters

Thus, the insect's length as seen via a microscope is found to be 56 millimeters.

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Answer: d

Step-by-step explanation:

put some clothes on