12m ² - 4mn-5n².solve the quadratic equation​

Answer:

x = -11

Step-by-step explanation:

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

[tex]3x + 12 - 2x = 1[/tex]

[tex]12 + x = 1[/tex]

[tex]x = - 11[/tex]

Answer:

Step-by-step explanation:

The quadratic function in vertex form is  f(x) = -(x + 5)^2 - 23

To find the quadratic function in standard form, we first need to determine the factors of the quadratic equation that corresponds to the given x-intercepts. Since the x-intercepts are at x = -12 and x = 2, we can write the quadratic equation in factored form as:

f(x) = a(x + 12)(x - 2)

where a is a constant that we need to determine.

To find the value of a, we can use the given minimum y-value of -49. Since the vertex of a quadratic function occurs at the axis of symmetry, which is the midpoint of the x-intercepts, we can find the x-coordinate of the vertex by taking the average of the x-intercepts:

x-coordinate of vertex = (-12 + 2)/2 = -5

Substituting this value of x into the factored form of the quadratic function, we get:

f(-5) = a(-5 + 12)(-5 - 2) = 49a

Since the minimum y-value is -49, we have:

f(-5) = 49a = -49

Solving for a, we get:

a = -1

Substituting this value of a into the factored form of the quadratic equation, we get:

f(x) = -(x + 12)(x - 2)

Expanding this equation, we get the quadratic function in standard form:

f(x) = -x^2 - 10x - 24

To find the quadratic function in vertex form, we can complete the square on the standard form of the equation:

f(x) = -x^2 - 10x - 24

f(x) = -(x^2 + 10x) - 24

f(x) = -(x^2 + 10x + 25) + 1 - 24

f(x) = -(x + 5)^2 - 23

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Answer: y=1/6x

Step-by-step explanation:

1. Identify the type of graph (linear)

2. the linear line equation is y=mx+b

3. find the slope, in this case, 1/6

a. to find the slope follow the equation (y1-y2)/(x1-x2)

b. plug in the x and y of two different points ex: (0,0) and (18,3)

4. plug into the equation the slope and a set of points - 3=18(1/6) +b

5. solve for b (0)

6. plug b and the slope into the original equation

7. y=1/6x

8. Done :)

bearing in mind that the sum of all interior angles in a polygon is

180(n - 2)    n = number of sides in the polygon

a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.

[tex]\bold{120+140+160+130+125+140+165+160+140+v=1440}[/tex]

[tex]\bold{1275+v=1440 \implies v=1440-1275 \implies v=165}[/tex]

Answer:

g(x) = -5tan(x) - 3

Step-by-step explanation:

the parent tangent function would be g(x) = tan(x)

- reflection over the x-axis is going to make it negative

- horizontal stretch by a factor of 5 is going to multiply it by 5

- vertical shift down 3 units will subtract 3

so together, this would be the equation g(x) = -5tan(x) - 3.

Lauren assumed that the Roof Truss Diagram is an accurate representation of the actual roof design that will be used on the shed. She used the given measurements, such as the length of the bottom chord, and the angles in the diagram to calculate the pitch of the roof. If the diagram was not accurate, her calculations would not have been useful in determining the pitch of the actual roof. Therefore, Lauren had to make the assumption that the diagram was a reliable representation of the shed's roof design.

The logical assumption that Darin make about the Roof Truss Diagram is that the rise is 4.6 ft and the run is 9 feet.

A logical assumption is simply an idea that can be inferred, or identified, in a text without the writer stating it in an obvious way. One simple example may be the logical assumption that if you do not turn in your homework, your teacher will be disappointed in you.

Here, we have,

Based on the information provided, it appears that Darin assumed that the Roof Truss Diagram is symmetrical, meaning that both sides of the roof have the same dimensions and angles. This assumption is supported by his calculation that the pitch of both sides of the roof is close to 1/2.

Rise will be:

= 9 × tan 27°

= 9 × 0.5095

= 4.6 feet.

Run will be 9ft

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Answer:

11 adults

Step-by-step explanation:

First, set up a system of equations:

Let x = number of children and y = number of adults

There is a total of 16 people, so x+y = 16. This is your first equation.

Each child ticket costs $6, so 6x = cost of children's tickets based on the number of children present (x)

Each adult ticket costs $9, so 9y = cost of adult's tickets based on the number of adults present (y)

The total cost of tickets is $129, so 6x+9y = 129. This is your second equation.

Your system of equations is now this:

x +   y = 16

6x + 9y = 129

You can solve this system using the method of elimination, where we will eliminate the variable x (number of children), since we are focused on y (number of adults).

Multiply the top equation by -6. This will give the following equation:

-6x - 6y = -96

You can now solve the system of equations by placing the new equation under the second equation like this:

6x + 9y = 129

-6x - 6y = -96

Now, add the two equations together.

6x + (-6x) = 0

9y + (-6y) = 3y

129 + (-96) = 33

After doing this, you get the following equation:

3y = 33

As you can see, the variable x has been eliminated, and you are left with y.

Solve the equation for y:

3y = 33

y = 33/3 = 11

y = 11 adults

Answer: Problem 3:

The triangles are not similar. They have different angles.

Problem 4:

The triangles are similar by SSS~. A valid similarity statement is:

Triangle ABC ~ Triangle DEF.

Step-by-step explanation:

So the acute angle of the rhombus is 90 degrees, and the obtuse angle is twice as large, or 180 degrees.

The Pythagorean theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's start by finding the length of one half of the longer diagonal. We can use the shorter diagonal (which we know is 10 cm) and the side length (which we know is 13 cm) to form a right triangle. The hypotenuse of this triangle is half of the longer diagonal, so we can solve for it using the Pythagorean theorem:

[tex]a^2+b^2 = c^2 \\(13/2)^2 + 10^2 = c^2\\169/4+100 =c^2 \\ 269/4= c^2 \\c = \sqrt{(269)}/2\\[/tex]

Therefore, the length of one half of the longer diagonal is sqrt(269)/2 cm. To find the full length of the longer diagonal, we just need to double this value:

longer diagonal = [tex]2 \times \sqrt{(269)}/2 = \sqrt{(269)}cm[/tex]

Now, we can use the fact that the sum of the angles in a rhombus is 360 degrees to solve for x:

2x + 2x = 360

4x = 360

x = 90

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Answer: 10

Step-by-step explanation: you look at x=1 and go over to x=3 and do rise over run

The stem-and-leaf plot that correctly graphs the data set {15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5} is given as follows:

0| 0 5

1| 1 5 5 5

2| 0 0 0 0 3 6

3| 1 4 9 9

Key 1|1 = 11

A stem and leaf plot is a type of data visualization that displays numerical data in a way that shows the distribution of the data while also preserving the individual data points. It is particularly useful for small to medium-sized data sets.

In a stem and leaf plot, the digits in each data point are split into two parts: the stem and the leaf. The stem is usually the leftmost digits of the number, while the leaf is the rightmost digit. The stems are listed in a column from top to bottom, and each leaf is listed next to its corresponding stem. The resulting plot looks like a table with two columns, where the first column shows the stems and the second column shows the leaves.

For example, as the team scored 20 points four times, we have the following observation:

2| 0 0 0 0

(one leaf of zero for each time, with the stem of 2).

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The measure of angle 4 is 45.6( nearest degree)

Two angles are complementary when the sum of the two angles is 90°. For example if x and y are complementary, then x+y = 90°.

Example of complementary angles are 50 and 40 , 30 and 60 , 25 and 65 e.t.c

Since angle 3 and angle 4 are complementary, therefore, 5x -15 + 3x+10 = 90

5x -15 + 3x+10 = 90

collect like terms

5x+3x -15 +10 = 90

8x -5 = 90

8x = 95

x = 95/8

x = 11.875

Therefore the measure of angle 4 is

3( 11.875) + 10

= 35.625 + 10

= 45.6 (nearest degree)

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The point on the image of figure 2 corresponds to point I from Figure 1 is Q, as figure 2 is the image of the figure one after reflection about its origin.

When a figure is constructed around a single point known as the figure's centre, or point of reflection, the result is a point reflection.

From the two given figures: the figure 2 is the image of the figure one after reflection about its origin.

Thus, the point on the image of figure 2 corresponds to point I from Figure 1 is Q.

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Complete question :

Figure 1 and figure 2 below are congruent. Which points corresponds to point I.

The figure is attached.

When Sarah and Gavyn win money, they divide it in a 5:3 ratio.If  Sarah gets £14 more than Gavyn, Gavyn gets £21.

Let's call the amount of money that Sarah and Gavyn win "x".

According to the problem, they share the money in the ratio 5:3, which means that Sarah gets 5 parts and Gavyn gets 3 parts.

Let's call the amount of money that Gavyn gets "y". Then, we know that:

Sarah gets £14 more than Gavyn, which means that Sarah's share is y + £14.

We can set up an equation to represent the fact that the ratio of their shares is 5:3:

5/3 = (y + £14)/y

To solve for y, we can cross-multiply:

5y = 3(y + £14)

5y = 3y + £42

2y = £42

y = £21

Therefore, Gavyn gets £21.

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Value of angle C in the cyclic quadrilateral is 62°

A cyclic quadrilateral is a quadrilateral that can be circumscribed by a circle such that all four vertices of the quadrilateral lie on the circle.

Some properties of cyclic quadrilaterals include:

In the given diagram

∠B=3x°

∠D=x+20°

For cyclic quadrilateral opposite angle sum is 180°

∠B+∠D=180°

3x°+x°+20°=180°

4x+20=180°

x=160/4

x=40°

∠A+∠C=180°

C=180-2x+38

C=180-2*40-38

C=62°

Hence, Value of angle C in the cyclic quadrilateral is 62°

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Answer:

NO

Step-by-step explanation:

It is a parabola, you can tell cuz of the x^2

:)

Answer:

The inequality that describes the problem is given as follows:

x ≤ 75.

How to obtain the inequality?

To describe the inequality in this problem, we need to obtain the upper bound of the total amount that Ted and his friends are expected to spend.

To obtain the upper bound of the total amount, the relevant information is given as follows:

Ted and his friends decided to split the bill evenly among the 5 of them.

Ted figured that each person will pay no more than $15.

Hence the upper bound of the total amount is calculated as follows:

5 x $15 = $75.

The upper bound of $75 means that in total, they are expected to pay at most $75, hence the inequality that describes this problem is given as follows:

x ≤ 75.

The area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.

The area of the new deck is 64% of the area of the original deck.

What is a triangle?

A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane. It is one of the basic shapes in geometry and is characterized by its three sides, three angles, and three vertices.

Part A:

The original deck has a base of 15 feet and a height of 6 feet. To create a 4:5 scaled version of the deck, we can multiply the base and height by the scale factor of 4/5:

New base = 15 * 4/5 = 12 feet

New height = 6 * 4/5 = 4.8 feet

Therefore, the dimensions of the new deck are 12 feet for the base and 4.8 feet for the height.

Part B:

The area of the original deck can be calculated using the formula for the area of a triangle:

Area of original deck = 1/2 * base * height = 1/2 * 15 * 6 = 45 square feet

The area of the new deck can be calculated in the same way, using the new dimensions:

Area of new deck = 1/2 * new base * new height = 1/2 * 12 * 4.8 = 28.8 square feet

Therefore, the area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.

Part C:

The ratio of the areas can be calculated by dividing the area of the new deck by the area of the original deck:

Area ratio = Area of new deck / Area of original deck = 28.8 / 45 = 0.64

The scale factor is 4/5, which is equal to 0.8. Therefore, we can compare the ratio of the areas to the scale factor to see if they are equivalent:

Area ratio / Scale factor = 0.64 / 0.8 = 0.8

Since the result is equal to the scale factor, we can conclude that the ratio of the areas and the scale factor are equivalent. This means that the area of the new deck is 64% of the area of the original deck.

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Step-by-step explanation:

The three angles of the triangles are equal ...use  A-A-A theorem

Answer:

The mean, median and mode are exactly the same.

Step-by-step explanation:

I ( g o o g l e d ) ur answer and gave u it

The characteristics of a normal distribution are  Symmetric, Unimodal,  Bell-Shaped,  Mean and Median are equal.

A. Symmetric: True. A normal distribution is symmetric, meaning the left and right halves of the distribution are mirror images of each other.

B. Unimodal: True. A normal distribution is unimodal, meaning it has a single peak.

C. Bimodal: False. A normal distribution is not bimodal; it has only one mode (peak).

D. Bell-Shaped: True. A normal distribution is bell-shaped, meaning it forms a symmetric, bell-like curve.

E. Mean and Median are equal: True. In a normal distribution, the mean and median are equal, and they both coincide with the highest point of the curve.

F. The Peak is on the left: False. The peak of a normal distribution is at the center; it is not necessarily on the left.

G. 64% of the data falls within 1 standard deviation of the mean: False. In a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, not 64%.

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Answer: [tex]\frac{1}{3}[/tex] yds²

Step-by-step explanation:

    To find the area, we will multiply 2/3 by 2/4. When multiplying fractions, you multiply straight across.

[tex]\displaystyle \frac{2}{4} *\frac{2}{3} =\frac{2*2}{4*3} =\frac{4}{12} =\frac{1}{3}[/tex]

    We can also use the model, see attached.

Answer:

A histogram would be the most appropriate graphical representation for the given data because it shows the distribution of the data and helps identify patterns or trends.

Answer:  I think the answer is bar chart, but it could also be Box plot

Step-by-step explanation:

All I know is that it is either one of those 2 options, it is NOT the others.

.........................

Hello and greetings ririleyyyii

The discriminant of 6y² - 9y + 1 = 0 equals 57.

6y² - 9y + 1 = 0

We identify the coefficients a, b and c of the quadratic equation.

The coefficients of a quadratic equation are the numbers that multiply the variables together with the independent term.

ax² + bx + c = 0

So the coefficients are: a = 6, b = -9, c = 1.

We evaluate the discriminant by substituting a, b and c inside the expression b² - 4ac.

The exercise remains: (-9)² - 4 × 6 × 1

                                      (-9)² - 4 × 6

                                      81 - 4 × 6 = 24, so 81 - 24 = 57

The discriminant of 6y² - 9y + 1 = 0 equals 57.

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Answer:

When the bases are the same, we can combine the exponents. Therefore, we can rewrite the equation as:

4^-2x * 4^x = 4^(-2x+x) = 4^(-x) = 64

To solve for x, we need to isolate x on one side of the equation. We can rewrite 64 as a power of 4:

4^3 = 4^(-x)

Now we can equate the exponents:

3 = -x

Therefore, x = -3.

To check the solution, we can substitute x = -3 back into the original equation:

4^-2(-3) * 4^(-3) = 4^6 * 4^(-3) = 4^3 = 64

So x = -3 is indeed a solution to the equation.

Warren Braxton paid $2,700.30 for his homeowner insurance policy.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages: (Value/Total value) * 100

Given that, Warren Braxton purchased homeowner insurance for 70%.

Thus,

0.7 x $495,000 = $346,500.

Now, the premium is:

Premium = ($346,500 / 100) x $0.78 = $2,700.30

Hence, Warren Braxton paid $2,700.30 for his homeowner insurance policy.

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The standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.

The standard deviation of the average cholesterol levels will be given by the standard error of the mean, which is calculated as

standard error of the mean = standard deviation / sqrt(sample size)

In this case, the sample size is 4, so we have

standard error of the mean = 30 / sqrt(4) = 15

Therefore, if we take many samples of 4 fourteen-year-old boys and average their cholesterol levels, the standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.

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Answer:

b

Step-by-step explanation:

By addressing the posed question, we can get the following conclusion: Volume equation of six tennis balls = 6 179.59 1077.54 cm

In mathematics, an equations is a promise that two expressions are equivalent. Two sides that are divided by the algebraic symbol (=) make up an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is indeed the goal of equation solving. Equations can include one or more parts and be simple or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. A line is utilized in many different areas of mathematics, such as algebra, calculus, and geometry. We can calculate the volume of the container and the volume of one tennis ball, and then check if the volume of six tennis balls is less than or equal to the volume of the container.

Volume of container = πr2h

Volume of container = π[tex](3.5)^2[/tex](40) ≈ 1540.48 cm

Volume of one tennis ball = 4/3 π[tex]r^3[/tex]

Volume of one tennis ball = 4/3 π[tex](3.5)^3[/tex] ≈ 179.59 cm

Volume of six tennis balls = 6 × volume of one tennis ball

Volume of six tennis balls = 6 × 179.59 ≈ 1077.54 cm

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