Which equation represents the line that passes through the point (-2.4, -7.1) and has a slope of -5.3

Answer:

A

Step-by-step explanation:

y = - 2x + 5 → (1)

y = x² + 3x + 9 → (2)

substitute y = x² + 3x + 9 into (1)

x² + 3x + 9 = - 2x + 5 ( subtract - 2x + 5 from both sides )

x² + 5x + 4 = 0 ← in standard form

(x + 1)(x + 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 4 = 0 ⇒ x = - 4

substitute these values into (1) for corresponding values of y

x = - 1 : y = - 2(- 1) + 5 = 2 + 5 = 7 ⇒ (- 1, 7 )

x = - 4 : y = - 2(- 4) + 5 = 8 + 5 = 13 ⇒ (- 4, 13 )

[tex]\textsf {21 cm}[/tex]

[tex]\textsf {If it is correct to the nearest centimeter, then the least side length}\\\textsf {would be 8 - 1 = 7 cm. }[/tex]

[tex]\textsf {Then, the least possible perimeter would be :}[/tex]

[tex]\mathsf {7 \times 3}[/tex]

[tex]\textsf {21 cm}[/tex]

Answer:

Slope =  - 1

Step-by-step explanation:

The equation is in form [tex]y=mx+c[/tex], [tex]m[/tex] s the slope and [tex]c[/tex]  is the intercept on [tex]y[/tex] axis.

Hence, in [tex]y=-x+3[/tex] , slope is -1  and intercept on [tex]y[/tex] axis is 3.

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

A polynomial is a mathematical expression consisting of variables , constants and mathematical operators.

The standard form of a polynomial is

[tex]\rm a_1x^n +a_2x^{n-1}+............+a_0[/tex]

The only equation that is in its standard form or in other words

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

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The value of h is -1.5 if the graph shows the function f(x)= |x-h| + K or f(x) = |x + 1.5| - 3.5.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

f(x) = |x - h| + k is shown in the graph.

The above function is a transformation of a parent function:

F(x) = |x|

After applying transformation we get:

f(x) = |x + 1.5| - 3.5

On comparing:

h = -1.5

k = -3.5

Thus, the value of h is -1.5 if the graph shows the function f(x)= |x-h| + K or f(x) = |x + 1.5| - 3.5.

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Considering the given histogram, the mean of the data-set is closest to:

B. 5.

An histogram is a graph that shows the number of times each element of x was observed.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Hence, considering the histogram, the mean is given by:

M = (1x1 + 2x2 + 3x3 + 4x1 + 5x1 + 6x2 + 7x3 + 8x1 + 9x1)/(1 + 2 + 3 + 1 + 1 + 2 + 3 + 1 + 1) = 4.87.

Which is closest to 5, hence option B is correct.

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The fields in which Trigonometry is well applied and their explanations are as explained below.

The three fields that trigonometry is useful are as described below;

1) In construction;

Trigonometry is useful in Construction field because it can be used in measurement of walls parallel and perpendicular; Installing ceramic tiles; Roof inclination; the height of the building, the width length e.t.c. It is also useful in finding roof slopes, ground surfaces, sun shading and light angles.

2) In marine biology;

Marine biologists utilize trigonometry to establish measurements. For instance, when trying to find out the manner in which light levels at different depths affect the ability of algae to photosynthesize. Trigonometry is used in finding the distance between celestial bodies. Marine biologists also use it to create mathematical models to measure and understand sea animals and their behavior.

3) In criminology:

In criminology, trigonometry is useful in calculating a projectile’s trajectory in order to estimate the possible cause of a collision in a car accident or the manner in which an object fall down or in which angle a bullet was shot etc.

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Answer:

(i) x-intercepts: (2, 0), (6, 0)

(ii) vertex : (4, -4)

Explanation:

y = x² - 8x + 12

To find x intercepts, [set y = 0]

x-intercepts: (2, 0), (6, 0)

To find vertex:

x = -b/2a

  = -(-8)/2(1)

  = 4

y = x² - 8x + 12

  = 4² - 8(4) + 12

  = -4

Vertex : (4, -4)

Solve the equation for y=0

X inetercepts (2,0) and (6,0)

Vertex :-

x coordinate

Y coordinate

Verted at (4,-4)

Answer:

-12x²-25x+13

Step-by-step explanation:

First open parenthesis.

(3 − 13x − 7x²) − (5x² + 12x − 10)

3 − 13x − 7x² − 5x² - 12x + 10

Now combine like terms.

3 − 13x − 7x² − 5x² - 12x + 10=13-25x-12x²

Now put into standard form, exponents greatest to least.

-12x²-25x+13

Hope this helps!

If not, I am sorry.

Answer:-12x²-25x+13

Step-by-step explanation:

There are 5 students who are 65 inches or taller. Option C is correct.

Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.

The term "height" is frequently used to describe someone's or something's height.

The height of the student in the Spanish class in the data set;

65, 63, 67, 59, 73, 60, 68, 61, 64, 60, 69

Student's heights are 65 inches or taller from the data set are;

65,67,73,68,69

There are 5 students who are 65 inches or taller.

Hence, option C is correct.

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The age of Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.

An equation is a statement that contains algebraic expressions equated by an equal sign with constants or other variables.

Let the age of Kwaku is x

Let the age of Esi is y

From the given data

The age of Kojo is 2y

y = x +5

Sum of their age = 47

2y = 2x +10

therefore the equation formed is

x + y +2y = 47

x + x+5 + 2x +10 = 47

4x +15 = 47

4x = 32

x = 8

y = 13

2y = 26

Therefore Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.

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Answer:

the cost price is Rs. 4500 and the sale price is Rs. 5040.

Step-by-step explanation:

Let the cost price of the compute be Rs. x.

The profit earned is, Rs. 540.

The profit percentage is, 12%.

The formula to compute profit is:

Profit = SP - CP

\begin{gathered}540=x[1+\frac{12}{100}]-x\\540=1.12x-x\\540=0.12x\\x=\frac{540}{0.12}\\x=4500\end{gathered}540=x[1+10012]−x540=1.12x−x540=0.12xx=0.12540x=4500

Compute the selling price as follows:

SP = CP + profit

     = 4500 + 540

     = 5040

Thus, the cost price is Rs. 4500 and the sale price is Rs. 5040.

Answer:

All answers are correct.

Step-by-step explanation:

A. 1.84 is between 1.74 and 1.84.

B. 1.84 < 1.85. Lower values go to the left.

C. 1.84 > 1.83. Higher values go to the right.

D. 1.84 is between 1.0 and 2.0.

The simplified radical for the given equation is 2√3.

The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].

Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.

To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:

[tex]\frac{3}{x} =\frac{x}{4}[/tex]

⇒x×x=3×4

⇒x²=12

⇒x=±√12

From this, we can see that the solutions for the equation are the positive and negative roots of 12.

By simplifying the radical, we get √12 = √(2² x 3) = 2√3

Therefore, the simplified radical for the given equation is 2√3.

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Answer: (2,9)

Step-by-step explanation:

It lies in the region that is shaded both red and blue (representing the fact that it satisfies both inequalities).

Answer:

25 minutes

150 gallons

Step-by-step explanation:

Definition of variables

Let t = time in minutes

Let V = volume in gallons

Create two equations with the given information:

Pool A

⇒ V = 300 - 6t

Pool B

⇒ V = 400 - 10t

To find after how many minutes the two pools will have the same amount of water, substitute the equation for pool A into the equation for pool B and solve for t:

⇒ 300 - 6t = 400 - 10t

⇒ 300 - 6t + 10t = 400 - 10t + 10t

⇒ 300 + 4t = 400

⇒ 300 + 4t - 300 = 400 - 300

⇒ 4t = 100

⇒ 4t ÷ 4 = 100 ÷ 4

⇒ t = 25

Therefore, the two pools will have the same amount of water after 25 minutes.

To find how much water will be in the pools at that time, substitute the found value of t into one of the equations and solve for V:

⇒ V = 400 - 10t

⇒ V = 400 - 10(25)

⇒ V = 400 - 250

⇒ V = 150

Therefore, the amount of water in the pools at the time when they have the same amount of water is 150 gallons.

If time be x and volume be y

The equations are

Equate and solve

Now

Answer: B

Step-by-step explanation:

[tex]P(x) Q(x)=R(x) \implies Q(x)=\frac{R(x)}{P(x)}\\\\Q(x)=\frac{2x^{3}+2x^{2}+3x+3}{x+1}={2x^{2}(x+1)+3(x+1)}{x+1}=\boxed{2x^{2}+3}[/tex]

Answer:

x=3.5

Step-by-step explanation:

x × 2 = 7

   ÷2     ÷2

    x=3.5

Step-by-step explanation:

[tex]z - 6 < 3 \\ z < 3 + 6 \\ z < 9[/tex]

Hope it helps

Z – 6 < 3

Z < 3 + 6

Z < 9

The boat's travel from when it was first noticed until it stopped is 554.89 ft.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

tan14.86 = 200/AC

AC = 753.772 ft

In the right-angle triangle DBC:

tan45.16 = 200/CB

CB = 198.886 ft

AB = AC - CB

AB =  753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

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Answer: [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

perpendicular = opposite recipricol

-3 = [tex]\frac{1}{3}[/tex]

switch the sign and flip it (3/1 => 1/3)

The figure is given in the below diagram.

The steps of constructing a square inside a circle are as follows:

Start from the middle O of the provided circle.

Finding the center of a circle's approach can be used to create the center of the circle's center point is not known.

1. Draw a circle and label point A. This will turn into one of the square's vertices.

2. Create point C by drawing a diameter line from point A through the center and back out to the outside of the circle.

3. Set the width of the compass to a little bit more than the distance to O.

4. Sketch an arc above and under O.

5. Repeat by moving the compass to C.

6. To create the new points B and D, draw a line across the intersection of the arc pairs that is long enough to touch the circle at both the top and bottom.

This diameter is perpendicular to the first AC.

7. Draw a line connecting each pair of points A, B, C, and D.

Done. The circle is circled by the square ABCD.

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Answer:

2 1/4

Step-by-step explanation:

Half of 4 is 2 and half of 1/2 is 1/4 so half of 4 1/2 is 2 1/4

I assume you meant r(x) = |x-2| -1.

Answer:

if a line is parallel they have the same slope

so the slope is 5

Hope This Helps!!!

Answer: 8

Step-by-step explanation:

We know that scale factor = (image)/(preimage).

Substituting in what we have,

[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]

Answer:

Step-by-step explanation:

We know that r's't' was formed by a scale factor of 5.

This means rst was multiplied by 5 to create r's't'.

Dividing the sides of r's't' by 5 will give us the sides of the

pre-image.  If r's' = 40 - dividing 40 by 5 = 8.

So rs is 8.

The central tendency of the given data will be 22.79.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

There are 3 ways in which we can express the centre of the data given: (1) mean or average, (2) mode, (3) median

For the mean, we sum up all the given and divide them by the number of data

mean = 433 / 19 = 22.79

For the mode, we just determine which among the given data appears more frequently and in this given that is 23.

For the median, we arrange the numbers from highest to lowest and determine which number will appear in the centre. Since there are 19 data, we need to find which among them will appear to be the 10th. That is also 23.

So, the value that would best describe the central tendency is 23. Since the values to the left of 23 are more scattered than those to its right, the distribution exhibits negative.

Therefore central tendency of the given data will be 22.79.

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