Which of the following shows the solution and graph to the inequality
2x + 1 ≤ 15?

After solving the quadratic equation, the roots are (x - 2) and (x + 7).

To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.

The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.

As per the given equation in the question,

x² + 5x - 14 = 0

b² - 4ac

5² - 4(1)(-14)

25 + 56 = 81

Use the equation,

-b ± \(\sqrt{b^2-4ac}/2a\)

Substitute the values,

(-5 + 9)/2 = 2 and,

(-5 - 9)/2 = -7

Therefore, the root will be (x - 2) and (x + 7).

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Answer:

3

Step-by-step explanation:

\(\sqrt{9}=\sqrt{3*3} = 3\)

The algebraic expression after combining the like terms is

c² - 6c + 4cx - 7x + 1 .

An algebraic expression is a combination of constants, variable and coefficients in such a way that they form several terms in the form of a multi-variable polynomial.

A simple algebraic expression is given by :

3x+4y+2xy-9.

This algebraic expression contains four separate terms where x and y are variables , 3 and 4 and 2 are coefficients and 9 is a constant.

The given algebraic expression is:

-6c+c²-6x+4cx-x+1

To combine all the like terms we separate the variables and the constants.

or, c² - 6c + 4cx - 6x - x + 1

or, c² - 6c + 4cx - 7x + 1

Hence the required simplified expression is given by  :

c² - 6c + 4cx - 7x + 1

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In this case, were a box plot to be plotted, the maximum age of the youngest 25% of passengers would be represented by the value 30.

It is to be noted that to determine the maximum age of the youngest 25% of passengers, we need to first find the median of the data set, which is the middle value when the data is sorted in ascending order.

The median of the data set {33, 45, 60, 15, 30, 36, 50, 62, 18, 19, 64, 75, 45} is 45.

Next, we need to find the first and third quartiles of the data set, which are the values that split the data into four equal groups.

To find the first quartile, we need to find the median of the data set after removing the top 25% of the data (the highest values).

The median of the data set {15, 18, 19, 30, 33, 36, 45, 45} is 30. This is the first quartile.

Note that to find the third quartile, we need to find the median of the data set after removing the bottom 25% of the data (the lowest values). The median of the data set {50, 60, 62, 64, 75} is 60. This is the third quartile.

Once we have the first and third quartiles, we can construct the box plot. The maximum age of the youngest 25% of passengers would be represented by the end of the box on the left side, which is the first quartile.

In this case, the maximum age of the youngest 25% of passengers would be represented by the value 30.

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The grams of zinc that the jar contains is 108.

It should be noted that ratio simply means the comparison of one thing with another thing.

In this case, the ratio of zinc to copper is 4 to 17 and a jar of the chemical contains 459 grams of copper.

Let the grams of zinc be x. This will be illustrated as:

4/17 = x/459

Cross multiply

17x = 4 × 459

x = (4 × 459) / 17

x = 108

It has 108 zinc.

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The inversion point of (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

To find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0, we need to follow these steps:

Step 1: Write the equation of the given circle in standard form by completing the square for x and y: (x - 2)² + (y - 3)² = 16.

Step 2: Find the radius of the circle by taking the square root of the constant term: r = √16 = 4.

Step 3: Find the distance between the given point (4, 5) and the center of the circle (2, 3) using the distance formula: d = √[(4 - 2)² + (5 - 3)²] = √8.

Step 4: Use the formula for inversion point to find the coordinates of the inversion point (x', y'): (x', y') = (h + r²/d² * (x - h), k + r²/d² * (y - k)), where (h, k) is the center of the circle and r is the radius.

Plugging in the values, we get: (x', y') = (2 + 4²/8 * (4 - 2), 3 + 4²/8 * (5 - 3)) = (6, 7).

Therefore, the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

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Answer:

yes

Step-by-step explanation:

Answer:

1. -13

2. 36

3. -2

4. -.5

5. -6x

6. -216cm

y is -2 is the answer for the question

Answer:

6x + 3y = 1

I hope this helps!

Answer:

A

Step-by-step explanation:

Hi I don't usually upload pictures but I was too lazy to type so I did it on paper. I had to get the numbers in the parenthesis out so I multiplied the + by everything in the parenthesis following the negative and positive multiplication rules. Then, I combined and subtracted like terms.

Hope this helps !!

-Ketifa

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Answer:

A=(-2,-2) B=(-2,-6) D=-5,-2 C=(-5,-6)

Step-by-step explanation:

Answer:

45 degree . my step-by-step solution is in this picture

Answer: 72 cm

Step-by-step explanation:

So since we know its length is 12 cm, that leaves us with finding the width. You could do that by adding the two length's together to get 24, then subtract that from the perimeter to get 12. The widths being added together must equal 12 and be the same, so we can divide by 2 to get 6 cm as the width. Then multiply 6 times 12 to get 72

Answer: A=72 cm²

Step-by-step explanation:

Let the width of the rectangle be x

Hence,  P=36 cm      l=12 cm

P=2(l+x)

P=2l+2x

P-2l=2x

Divide both parts of the equation by 2

Thus,

\(\displaystyle\\x=\frac{P-2l}{2} \\\\x=\frac{36-2(12)}{2}\\\\x=\frac{36-24}{2} \\\\x=\frac{12}{2} \\\\x=6 cm\\\\\)

Area A=l*x

A=12*6

A=72 cm²

Answer:

9/10

Step-by-step explanation:

Answer:

9:10

Step-by-step explanation:

27:30 = 9:10

BRAINLIEST PLEASE

Answer:

Hypothesis

Step-by-step explanation:

 a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.

hope this helps

The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

Given the diagram of the hanger which one side has 10 + 5x  and other side has 11.

To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.

Thus, the equation is 10 + 5x = 11.

Consider the equation 10 + 5x = 11

On subtracting 10 from each side gives,

5x = 1

Divide each side by 5 gives,

x = 1/5.

Hence,  the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

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Answer:

dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)

Step-by-step explanation:

x² / (x + y) = y² + 7

x² = (x + y) (y² + 7)

Take derivative of both sides with respect to x.  Use power rule, product rule, and chain rule.

2x = (x + y) (2y dy/dx) + (y² + 7) (1 + dy/dx)

Simplify.

2x = (2xy + 2y²) dy/dx + y² + y² dy/dx + 7 + 7 dy/dx

2x = (2xy + 3y² + 7) dy/dx + y² + 7

2x − y² − 7 = (2xy + 3y² + 7) dy/dx

dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)

The volume of the triangular prism will be 400 cubic feet.

Given that:

Width, W = 15 feet

Height, h = 8 feet

Base length, b = 6²/₃ feet

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The volume of the triangular prism is calculated as,

V = 1/2 · b · h · W

V = 0.5 · 6²/₃ · 8 · 15

V = 400 cubic feet

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The new price for the car when there's an increase of 6% is $35616.

Given that the dealership increased the price of a certain car by 6% and the original price was $33,600.

The new price will be:

= Original price + Increase in price

= $33600 + (6% × $33600)

= $33600 + $2016

= $35616

The new price is $35616.

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Answer:

F

E or C (depending on the actual angles - see below in the details)

Step-by-step explanation:

two triangles are congruent, when after some rotation or mirroring they can cover each other exactly.

that means they must both have the same angles and side lengths.

these are the possible conditions to determine that 2 triangles are congruent (without knowing ALL of the sides and angles) :

SSS (Side-Side-Side) - all 3 sides of triangle 1 are exactly of the same length as the 3 sides of triangle 2.

SAS (Side-Angle-Side) - 2 sides and one angle are the same

ASA (Angle-Side-Angle) - 2 angles and the side between these 2 angles are the same

AAS (Angle-Angle-Side) - 2 angles and any not-included side are the same

RHS (Right angle-Hypotenuse-Side) - both triangles are right-angled (one angle is 90 degrees), and the Hypotenuse (the side opposite to the 90 degree angle) and another side are the same.

so, now look at a).

we only know the angles. but we could use a zoom lens of a camera and make them bigger and smaller, while their angles remain actually the same.

therefore, we cannot say, if they are actually congruent (only if their side lengths are the same too).

but we can say that they could be congruent.

and therefore also none of the congruent conditions apply, because for all of them we always need at least one side length. and we don't have that.

now looking at b)

I am not sure I can read one of the given angles correctly.

case one: I read the angles in triangle 2 as 66 and 58 degrees. that would make the third angle

180 - 66 - 58 = 56

but triangle 1 has the angles of 68, 54 and

180 - 68 - 54 = 58

=> the three angles are not the same, so the triangles are definitely not congruent

case two: I could read the angles in triangle 2 also as 68 and 58. that would make the third angle

180 - 68 - 58 = 54

and the side connecting the 68 and 58 angles has the same length, so the ASA criteria are fulfilled, and the triangles are congruent. C

Option B: \(4+x+7x^6-3x^2\) represents a sixth-degree polynomial with a leading coefficient of seven and a constant term of four.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. A function that can be expressed as a polynomial is referred to as a polynomial function. A polynomial equation's definition can be used to derive the definition. A polynomial is typically denoted by P. (x). The degree of the variable in P(x) is its maximum power. The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large. Whole real numbers make up a polynomial function's domain (R).

Option B: \(4+x+7x^6-3x^2\) represents a sixth-degree polynomial with a leading coefficient of seven and a constant term of four.

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Answer:

45

Step-by-step explanation:

Because the ratio of seaguls to other birds is 1:1 you can expect half of the birds to be seaguls. Divide 90 by 2

Answer:

-12

Step-by-step explanation:

To evaluate the expression the known value of a = -8 can be substituted in so the equation becomes -8 - 4.

From there the subtraction can be completed which equals -12. This can be visually seen on a number line if you look at -8 and move left 4 spaces.

The total surface area of below figure is 77 inch²

Surface area is a measurement of the total area that the surface of an object occupies. It is typically expressed in square units, such as square meters or square feet. The surface area of an object can be determined by adding up the areas of all of its individual faces or surfaces.

For example, the surface area of a cube can be calculated by finding the area of each face (which is the length of one side squared) and then adding all of those areas together. The formula for the surface area of a cube is 6a², where "a" represents the length of one side.

For the given figure the surface area is the sum of two triangle and one rectangle is;

SA = SA₁ + SA₂ + SA₃

SA = \((\frac{1}{2}* 3 *4 )+ (\frac{1}{2}* 3 *4 ) + (13*5)\)

SA = 6 + 6 + 65

SA = 77 inch²

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Complete question-

The required solution of the given expression is -9.

A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.

Given:

The given expression is

-2-(+7)

According to given question we have

Number line is a line with 0 in the middle, and then increasing positive numbers to the right of the 0 and decreasing negative numbers to the left of the 0. The line is infinite in length and it's not possible to show the whole line, but we will illustrate where on the line 9 and -9 are located.

-2-(+7)

=-2-7

=-9

Therefore, the required solution of the given expression is -9.

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The possible number of green tiles in the rectangle can be found to be H. 24.

The number of green tiles and red tiles in the rectangle will need to be expressed as whole number alone.

This means that because the ratio of the green tiles to the red tiles is 3 : 4, number of green tiles should be divisible by 3.

The numbers given are:

= 10 / 3

= 3.33

16:

= 16 / 3

= 5.33

24:

= 24 / 3

= 8

Because 24 is divisible by 3, there must be 24 green tiles in the rectangle.

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An orthonormal basis for the -eigenspace of \(\pi\)2 is

B1=(V3=\(\left[\begin{array}{ccc}1/\sqrt{3}\\1\sqrt{3}\\1/\sqrt{3} \end{array}\right]\)

What is Spectral Theorem?

There exists an invertible matrix C such that C 1 M C C-1 MC C1MC is a diagonal matrix, according to the spectral theorem, which asserts that if M equals the transpose of M, then M is diagonalizable.

Concept of theorem

If A is a symmetric matrix, then eigenvectors of different eigenvalues are orthogonal

here if v3 is an eigenvectors for eigenvalues \(\pi\)2 of matrix A,then by spectral theorem we have

v1.v3=0

-2x+0y+2z=0 ------------(1)

and v2.v3=0

-2x+y+z=0 ------------(2)

To find v3 we have solve system

-2x+0y+2z=0

-2x+y+z=0

\(\left[\begin{array}{ccc}-2&0&-1\\-2&1&1\end{array}\right]\) \(\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\) = \(\left[\begin{array}{ccc}0\\0\\\end{array}\right]\)

Applying R1 = -1/2 X R1

               R2= R2+2 X R2 We get

\(\left[\begin{array}{ccc}1&0&-1\\0&1&-1\\\end{array}\right]\)\(\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\) = \(\left[\begin{array}{ccc}0\\0\\\end{array}\right]\)

x-z=0

y-z=0

put z=t

x=t

y=t

\(\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\)=\(\left[\begin{array}{ccc}t\\t\\t\end{array}\right]\)=t\(\left[\begin{array}{ccc}1\\1\\1\end{array}\right]\)

thus eigenvector for eigenvalue \(\pi\)2 is v3=\(\left[\begin{array}{ccc}1\\1\\1\end{array}\right]\)

and basis for eigenspace of \(\pi \\\)2 is B=\(\left[\begin{array}{ccc}1\\1\\1\end{array}\right]\)

Next we will convert v3 into a unit vector

for this v3=\(\sqrt{(1.1)+(1.1)+(1.1)}\) = \(\sqrt{v3.v3}\)

v3=\(\sqrt{3}\)

v3= v3/v3 =1/\(\sqrt{3}\) (1   1   1)

an orthonormal basis for the -eigenspace is B1 = V3=\(\left[\begin{array}{ccc}1/\sqrt{3} \\1/\sqrt{3} \\1/\sqrt{3} \end{array}\right]\)

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