Determine the number of solutions to the system of linear equations shown on the graph.

coordinate plane with one line that passes through the points negative 1 comma 4 and 0 comma 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 3

One solution at (1, −2)
One solution at (−2, 1)
Infinitely many solutions
No solution

Different triangles with the same areas include:

Right angle triangle: base = 6, height = 4

Acute triangle: base = 8, height = 3

Obtuse triangle: base = 16, height = 1.5

To create a right angle triangle, an acute triangle, and an obtuse triangle that all have the same area, we can use the following dimensions:

Right triangle: base = 6, height = 4

Acute triangle: base = 8, height = 3

Obtuse triangle: base = 16, height = 1.5

We can calculate the area of each triangle using the formula A = 1/2 (base x height):

Right triangle: A = 1/2 (6 x 4) = 12

Acute triangle: A = 1/2 (8 x 3) = 12

Obtuse triangle: A = 1/2 (16 x 1.5) = 12

Therefore, we can see that all three triangles have the same area, which is 12 square units. We know this because they all have the same base-to-height ratios, which means they have the same "steepness" or "slope". This means that the area of each triangle is proportional to its base and height, and since they all have the same ratio of base to height, they will all have the same area.

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Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

We must first divide the value by the whole sum, and then multiply the result by 100 to get the percentage.

Let's use algebra to solve the problem.

If 19,700 employees represent 22.9% of the company's total number of employees, we can write:

0.229 = 19,700 / Total number of employees

To find the total number of employees, we can isolate the variable on one side of the equation:

Total number of employees = 19,700 / 0.229

Using a calculator, we get:

Total number of employees = 86,026.2

Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

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Answer: 3

Step-by-step explanation: try to solve for a by itself by multiplying it on both sides that give you 3 = 1*a. that simply just means that a is equal to 3, so you substitute three to the a variable that will give 3/3 that's equal to 1.

The grocer should use 15 pounds of almonds and 25 pounds of cashews to create a 40 pound mixture that will sell for $12.50 per pound.

To create a 40 pound mixture of almonds and cashews that will sell for $12.50 per pound, the grocer should use a combination of both almonds and cashews that will give him the desired price. We can use a system of equations to solve for the amount of each ingredient the grocer should use. Let x be the amount of almonds and y be the amount of cashews.

Solving for x in the first equation gives us: x = 40 - y

Substituting this value of x into the second equation gives us: 10(40 - y) + 14y = 12.50(40)

Simplifying and solving for y gives us: 4y = 100 -> y = 25

Substituting this value of y back into the first equation gives us: x + 25 = 40 -> x = 15

Therefore, the grocer should use 15 pounds of almonds and 25 pounds of cashews to create a 40 pound mixture that will sell for $12.50 per pound.

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The value of x will be 6° according to the remaining angles values in the diagram.

What is a Triangle?

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

How are the sum of triangles calculated in a triangle?

In a triangle, the total interior angles are supplementary. In other words, the sum of a triangle's inner angle measurements is 180°. Hence, we can write the triangle sum theorem's formula as A + B + C = 180° for the triangle ABC.

Now according to the question

                          => 40+110+8x-18=180 (Theorem)

                          => 150+8x-18=180

                          => 8x=180-150+18

                          => 8x=48

                          => x=6°

The  value of x will be : 6°

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The solution to the equation is z = 15.

To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.

On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:

2(2z) - 2(3) = 4z - 6

On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:

3(z) + 3(3) = 3z + 9

Now we can rewrite the equation as:

4z - 6 = 3z + 9

Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:

4z - 3z = 9 + 6

Simplifying gives us:

z = 15

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The roommate is wrong. The scaled desk should be 1 1/3 inches high, as per Olaf's initial scaling of 1 inch representing 30 inches of actual length in the room. The other dimensions of the scaled desk would be 12 inches long and 6 2/3 inches wide.

When Olaf decided to let 1 inch represent 30 inches of actual length in the room, he created a scale factor of 1:30. This means that for every inch in the scale model, there are 30 inches in the actual room. Using this scale factor, the scaled desk height should be 40/30 = 4/3 inches. Therefore, the roommate's suggestion of 10 inches high is incorrect.

To find the other dimensions of the scaled desk, we need to apply the same scale factor of 1:30. The scaled length would be 36/30 = 12 inches, and the scaled width would be 20/30 = 2/3 inches. However, it's easier to work with whole numbers, so we can multiply both dimensions by 10 to get 120 inches long and 6 2/3 inches wide, which is equivalent to 12 inches long and 2/3 inches wide in the scaled model.

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Answer:

(-3, -4)

Step-by-step explanation:

Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (−x,−y). Ari's error was that she rotated "N" by 90 degrees instead of 180 degrees, as the rule for a 90 degree rotation is (-y, x). Therefore, the correct coordinated for N' can only be (-3,-4)

Answer:

  (364.0, 236.4)

Step-by-step explanation:

You want the vector 434∠33° written as an ordered pair.

The "ordered pair" representation of a vector can take different forms. we're not sure the form your curriculum materials are asking for, so we'll show it a couple of ways.

(magnitude; direction) = (434; 33°) or maybe (434, 33)

(x, y) = 434·(cos(33°), sin(33°) ≈ (364.0, 236.4)

__

Additional comment

We like the form used in the problem statement above (434∠33°) for vectors expressed in polar form. For vectors expressed in rectangular form, many calculators work nicely with a complex number representation (364 +236.4i).

The ordered pair using a semicolon (;) separator is written that way to distinguish it from the (x, y) ordered pair. That form is used by some geometry software. A calculator may use [434, 33] or [364, 236.4] (for example), leaving it up to the user to remember what the pair represents.

Some authors use a combination of complex and polar representations like this:

  A(cos(B) +i·sin(B)) = A·cis(B)

In this, the "cis" is a reminder of the "cosine + i·sine" complex number representation. It is also a longer way to write A∠B.

The second attachment shows our preferred calculator using our preferred vector notations. YMMV

→ Be sure your calculator is in "degrees" mode.

a)91.44 m

b)51.18 in

c)372.85 W

d)2383186.955 Pa

e)10000 ????????/m3

f)0.4667 T????/ℎ

g)41840 J

300 ft = m

1 ft = 0.3048 m, so 300 ft = 300 * 0.3048 m = 91.44 m



130 cm = in

1 in = 2.54 cm, so 130 cm = 130/2.54 in = 51.18 in



0.5hp = W

1 hp = 745.7 W, so 0.5 hp = 0.5 * 745.7 W = 372.85 W



350psi = Pa

1 psi = 6894.757 Pa, so 350 psi = 350 * 6894.757 Pa = 2383186.955 Pa



10 ????????/????????3 = ????????/m3

1 ????????/????????3 = 1000 ????????/m3, so 10 ????????/????????3 = 10 * 1000 ????????/m3 = 10000 ????????/m3



350 W = ????T????/ℎ

1 W = 0.00134 T????/ℎ, so 350 W = 350 * 0.00134 T????/ℎ = 0.4667 T????/ℎ



10,000 cal = ????

1 cal = 4.184 J, so 10,000 cal = 10,000 * 4.184 J = 41840 J

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Answer:

A

Step-by-step explanation:

trust

The solutions for the equation 6x²-11x-7=0 are x = -1/2 and x = 7/3

It is important to note that quadratic equations are defined as equations having the highest degree of x as 2.

From the information given, we have that the quadratic equation is given as;

6x²-11x-7=0

Now, multiply the coefficient of x squared with the constant value, then find the pair factors of the product that adds up to given the coefficient of x = -11

We have;

6x² - 14x + 3x - 7 =0

Group the expression in pairs

(6x² - 14x) + (3x - 7) = 0

Factor the expressions

2x(3x - 7) + 1(3x - 7) = 0

Then, we have;

(2x + 1) and (3x - 7) = 0

x = -1/2

x = 7/3

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We can use the properties of logarithms to evaluate each expression. The properties of logarithms include:

1) loga (xy) = loga (x) + loga (y)

2) loga (x/z) = loga (x) - loga (z)

3) loga (x^p) = p loga (x)

4) loga (square root x) = (1/2) loga (x)

Using these properties, we can evaluate each expression as follows:

(a) loga (xy) = loga (x) + loga (y) = 3.1 + 5.8 = 8.9

(b) loga (x/z) = loga (x) - loga (z) = 3.1 - 1.1 = 2

(c) loga (y^7) = 7 loga (y) = 7 * 5.8 = 40.6

(d) loga (square root y) = (1/2) loga (y) = (1/2) * 5.8 = 2.9

Therefore, the answers are:

(a) loga (xy) = 8.9

(b) loga (x/z) = 2

(c) loga (y^7) = 40.6

(d) loga (square root y) = 2.9

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The baker makes a total of 140 muffins on Monday.

The baker makes 18 blueberry muffins on Tuesday.

What are percentages?

Percentages are a way of expressing a fraction or proportion out of 100. The term "percent" literally means "per hundred." Percentages are commonly used in many areas of everyday life, including finance, science, and statistics.

To express a number as a percentage, it is multiplied by 100. For example, 0.75 is equivalent to 75 percent, since 0.75 x 100 = 75. Similarly, 50 percent is equivalent to 0.5 or 1/2.

Percentages are commonly used to express changes and comparisons. For example, if a product's price increases from $100 to $120, this represents a 20 percent increase in price. If a person scored 80 out of 100 on a test, this represents an 80 percent score.

Percentages are also used to calculate percentages of a total. For example, if a person earned $40,000 out of a total company income of $500,000, their income represents 8 percent of the total income. Similarly, if a person wants to calculate a 20 percent tip on a $50 meal, they would calculate 20 percent of $50, which is $10.

In summary, percentages are a way of expressing a fraction or proportion out of 100, and are commonly used to express changes, comparisons, and percentages of a total in everyday life.

A. Let's assume the total number of muffins the baker makes on Monday to be x.

According to the problem, the number of blueberry muffins that the baker makes is 30% of the total number of muffins.

So, 30% of x is equal to 42:

0.30x = 42

To solve for x, we can divide both sides by 0.30:

x = 140

Therefore, the baker makes a total of 140 muffins on Monday.

B. Let b be the number of blueberry muffins the baker makes on Tuesday.

According to the problem, the number of blueberry muffins is still 30% of the total number of muffins. So, we can set up the equation:

0.30(60) = b

Simplifying the left side:

18 = b

Therefore, the baker makes 18 blueberry muffins on Tuesday.

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The function that describes the height of the rocket in terms of time t is h(t) = -16t² + 236t + 128

The maximum height is 962.125 feet.

The rocket reaches its maximum height at 14.75 seconds.

The rocket will hit the ground after 14.88 seconds.

a) The function that describes the height of the rocket in terms of time t is given by:
h(t) = -16t² + 236t + 128

b) To determine the time at which the rocket reaches its maximum height, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:
t = -b/2a = -236/(2*-16) = 7.375 seconds

The maximum height is then found by plugging this value of t back into the function:
h(7.375) = -16(7.375)² + 236(7.375) + 128 = 962.125 feet

c) To find the time interval during which the rocket is more than 845 feet above ground level, we need to solve the inequality:
-16t² + 236t + 128 > 845

Rearranging and factoring gives:
-16t² + 236t - 717 < 0
(4t - 59)(-4t + 12) < 0

The solutions to this inequality are t = 59/4 and t = 12/4. Therefore, the rocket will be more than 845 feet above ground level for the time interval 12/4 < t < 59/4, or 3 < t < 14.75 seconds.

d) To find when the rocket will hit the ground, we need to solve the equation:
-16t² + 236t + 128 = 0

Using the quadratic formula gives:
t = (-236 ± √(236² - 4(-16)(128)))/(2(-16))
t = (-236 ± 244.28)/(-32)

The two solutions are t = 14.88 seconds and t = -0.51 seconds. Since time cannot be negative, the rocket will hit the ground after 14.88 seconds.

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The following o-fields are equal to each other because they both represent the Borel sigma field on the real line:
i. B= o({(-20,x); r < R})
ii. B2 = o({(-0,2); 2 € R})

Note that the Borel sigma field on the real line is the smallest sigma field containing all the open intervals on the real line. This means that any set that can be constructed from countable unions, intersections, and complements of open intervals is in the Borel sigma field.

In the first o-field, B= o({(-20,x); r < R}), the set {(-20,x); r < R} is an open interval on the real line, so it is in the Borel sigma field. Similarly, in the second o-field, B2 = o({(-0,2); 2 € R}), the set {(-0,2); 2 € R} is also an open interval on the real line, so it is also in the Borel sigma field.

Since both o-fields contain sets that are in the Borel sigma field, they are both equal to the Borel sigma field on the real line. Therefore, B= o({(-20,x); r < R}) = B2 = o({(-0,2); 2 € R}).

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Mrs. Andretti is right, of course. In the equation 15x + 250, x stands for the fabric's overall expense.

An expression in mathematics is a collection of numbers, variables, and operations that can be evaluated to create a value, including addition, subtraction, multiplication, and division. Expressions can be straightforward—like 3 + 4 or 5x—or complex—involving numerous factors and operations. From basic arithmetic to intricate functions and equations, a broad range of mathematical concepts can be represented by expressions.

given

The fabric's overall cost is indicated by the value x.

No, x stands for the drapes' total expense.

No, x is the overall number of yards of fabric used.

Mrs. Andretti is right, of course. In the equation 15x + 250, x stands for the fabric's overall expense.

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X = 7 & -7/2

First, use the distributive property to simplify the equation:

2 - 5/(x+7) = -7/(x-3)(x+7)

2(x-3)(x+7) - 5(x-3) = -7(x+7)

2x2 + 7x - 6x - 15 = -7x - 49

2x2 -13x - 49 = 0

This equation can be solved by factoring the binomial:

2x2 -13x - 49 = 0

2x(x-7) - 7(x-7) = 0

(2x-7)(x-7) = 0

Therefore, the solution for x is x = 7 and x = -7/2.

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The probability when analyst performed a two-tailed test for the given one tailed probability is equal to 0.2.

Mean = 500

Standard deviation = 100

Number of applicants in art college = 100

Mean of the art college = 510

t-statistic = 1.70

One tailed probability = 0.4

Analyst performed a two-tailed test,

⇒ Probability value = 2(one-tailed probability value)

In a two-tailed test, deviations from the mean in both directions.

Probability of observing values are both higher and lower than the mean.

⇒ Probability for two-tailed test = Probability value for one-tailed test / 2

⇒Probability for two-tailed test = 0.4 / 2

⇒Probability for two-tailed test = 0.2

Therefore, the probability for a two-tailed test is equal to 0.2.

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Answer: Third answer option, [tex]\sqrt{3} *\sqrt{12}[/tex]

Step-by-step explanation:

     Both 3 and 9 are not irrational numbers, so the first option is incorrect.

     The [tex]\sqrt{3}[/tex] is irrational, but 0 is not, so the second option is also incorrect.

     The [tex]\sqrt{3}[/tex] and [tex]\sqrt{12}[/tex] are both irrational. Let us see if they result in a rational number when multiplied together;

                 [tex]\sqrt{3} *\sqrt{12} =\sqrt{3*12} =\sqrt{36} =6[/tex]

      They do, so this answer option is correct.

The lines are parallel , based on their. So the C option  is correct.

What is slope formula?

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

Line f has a slope of -2 and line g has a slope of -8/4. To determine the relationship between the lines based on their slopes, we can compare their slopes.

If two lines have the same slope, they are parallel. If two lines have slopes that are negative reciprocals of each other, they are perpendicular (and intersect to form right angles). Otherwise, the lines are neither parallel nor perpendicular and will intersect at some point.

The slope of line g can be simplified to -2, which is the same as the slope of line f. Therefore, the lines f and g have the same slope and are parallel (option C).

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Answer:

To find the percentage of the money collected from entry fees over the 3 days that was collected on Day 2, we need to first find the total amount collected for all three days.

Total amount collected = $750 + $400 + $300 = $1450

Then, we need to find what fraction of the total was collected on Day 2:

Amount collected on Day 2 = $400

Fraction of total collected on Day 2 = $400 / $1450

Finally, we convert the fraction to a percentage:

Fraction of total collected on Day 2 = $400 / $1450 = 0.2759

Percentage of total collected on Day 2 = 0.2759 x 100% = 27.59%

Therefore, approximately 27.59% of the money collected from entry fees over the 3 days was collected on Day 2.

Answer:

The math coach has delivered 4 boxes of books, so the number of boxes she still needs to deliver is b. Each box contains 15 books, so the total number of books she still needs to deliver is 15b. She has 495 books to deliver in total. Therefore, we can write the equation:

15b = 495 - 4(15)

Simplifying the right-hand side:

15b = 495 - 60

15b = 435

Dividing both sides by 15:

b = 29

So the math coach still needs to deliver 29 boxes of books.

1:1.618 (the golden ratio).

To construct a golden spiral that involves a golden rectangle with length 4 meters, first draw a 4 meter long line. Divide it into two segments, such that the longer segment has a ratio of 1:1.618 (the golden ratio) to the shorter segment.

Draw a right angle at the end of the shorter segment. This creates a square that has a side length of 4 meters. Draw an arc centered at the intersection of the two line segments with a radius equal to the shorter segment and connect the ends of the arc. This creates a golden rectangle with a length of 4 meters.

Draw a quarter circle at each corner of the golden rectangle and connect the endpoints. This creates a spiral, and it is a golden spiral if the ratio of the lengths of the two line segments is 1:1.618 (the golden ratio).

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a)0.1587 (or 15.87%)

b)0.6827 (or 68.27%)

c)0.0228 (or 2.28%)

1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).

2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).

3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).

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Answer:

60

Step-by-step explanation:

24 + 36 = 60

You can use the Gold Digger for the distributive property! * Factor as if you want to find the Greatest Common Factor.

The measure that is considered an outlier is the data-set is a measure of 29.5.

The interquartile range is calculated as the difference between the third quartile and the first quartile.

The values that are outliers are given as follows:

The quartiles for this problem are given as follows:

Q1 = 17, Q3 = 22.

Hence the IQR is of:

IQR = 22 - 17

IQR = 5.

Meaning that the outliers are given as follows:

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