Need help with this math question

to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]

Answer:

Step-by-step explanation:

V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight

The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.

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The number of socks for Hailey will be 163.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The number of Haley's socks will be calculated as=

Socks = 777 x 21/100

Socks = 777 x 0.21

Socks = 163

Therefore the number of socks for Hailey will be 163.

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Answer:9

Step-by-step explanation:

Use the pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]

We know both a and c, so it becomes

[tex]4^{2}+b^{2}=\sqrt{97}^{2}[/tex]=

16+b^2=97=

97-16=b^2=

81=b^2=

9=b

Answer:

[tex]13\frac{1}{3} \pi[/tex]

Step-by-step explanation:

First, find the area of the small circle whose radius is 3cm.

[tex]A = \pi r^{2} \\A = \pi (3^{2})\\A = \pi (9)\\A = 9\pi \\[/tex]

Next, find the area of the large circle. First, you need to find the radius of the large circle by adding the 3 and 4.

Radius of large circle.

3 + 4 = 7 cm

Area of large circle:

[tex]A = \pi r^{2} \\A = \pi (7^{2})\\A = \pi (49)\\A = 49\pi \\\\[/tex]

Now subtract the area of the small circle from the large circle since the shaded area doesn't include the small circle.

[tex]49\pi -9\pi =40\pi[/tex]

Finally find the shaded area. To do this first find what degree of the circle is shade by dividing 120 by 360.

120/360 = 1/3

Now multiply the area by 1/3, or you can divide it by 3

[tex]\frac{40\pi }{3} =13\frac{1}{3} \pi[/tex]

Answer:

yes they do

Step-by-step explanation:

they share a ray

Answer: The value of x is 3.5

Explanation:

Equation:

y = 2x - 7

When the equation's Line intersects the x-axis, the value of y shall be always 0

Insert y = 0, to find x intercept

⇒ 0 = 2x - 7

⇒ 2x - 7 = 0

⇒ 2x = 7

⇒ x = 3.5

So coordinates: (x, y) → (3.5, 0)

The expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.

It is defined as the combination of constants and variables with mathematical operators.

We have:

Sheryl makes $7 per a pair of earrings, e, and $13 per necklace, n, she sells.

Let's suppose the total income of Sherly is T:

Then,

T = 7e + 13n

Here e is the number of earrings she sells and n is the number of necklace she sells.

T is the total income and the expression T = 7e + 13n represents the total income of Sherly.

Thus, the expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.

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It makes that every time we flip a fair the probability of flipping tails is 50%.

Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. If it is equally likely and unlikely that the event would happen, it would have a probability of 0.5

Probability of flipping tails = number of tails / number of sides

1/2 = 0.5 = 50%

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Answer:

2/9

Step-by-step explanation:

8/12 you pick an office worker

4/12 chance you pick a manager

8/12 multiplied by 4/12 is 32/144

We can simplify this to 16/72

We can simplify this to 8/36

We can simplify this to 4/18

We can simplify this to 2/9

Step-by-step explanation:

1) x+6 =4

x. =4-6

x. =-2

2) x-(-4) =-6

x+ 4. =-6

x. =-6-4

x. =-10

3)2(x-1)=-200

2x-2 =-200

2x. = -200+2

2x. = -198

x. = -198/2

x. = -99

4)2x+(-3) =-23

2x-3. =-23

2x. =-23+3

2x. =-20

x. =-20/2

x. = -10

Answer:

[tex](6x-5)(x^2+2)[/tex]

Step-by-step explanation:

[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]

Answer: y - 17 = -2(x-7)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

   = 9+17/-6-7

   = 26/-13

   = -2

y1 = -17

x1 = 7

y - 17 = -2(x-7)

The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

The general equation of a straight line is-

y = mx + c

where, m is the gradient and is given by y₂ - y₁/x₂ - x₁

and, c is the value where the line cuts y-axis.

Now it is given that the line passes through points (−6,9) and (7,−17)

Therefore we have,

x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17

So, the slope m of the line is given as,

m = (y₂ - y₁)/(x₂ - x₁)

Put the values,

m = (-17 - 9)/(7 - (-6))

m = -26/7+6

m = -26/13

m = -2

Thus, the equation parallel to the line will be given as:

y - y₁ =  m(x - x₁)

y - 9 =  -2{x - (-6)}

y - 9 =  -2(x + 6)

y =  -2x - 12 + 9

y =  -2x - 3

Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

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Answer:

tanD =4/7

Step-by-step explanation:

tanD = P/B

Where P=4 and B=7

So;

tanD=4/7

Using a dot plot, it is found that the number of dots of each point are given as follows:

The dot plot shows the number of times each measure appears in the data-set.

In this problem, one measure has a value of 1/8, hence:

The value [tex]\frac{1}{8}[/tex] will have one dot above it.

Two measures have a value of 1/4, hence:

The value [tex]\frac{1}{4}[/tex] will have two dots above it.

Three measures have a value of 3/8, hence:

The value [tex]\frac{3}{8}[/tex] will have three dots above it.

Five measures have a value of 1/2, hence:

The value [tex]\frac{1}{2}[/tex] will have five dots above it.

Two measures have a value of 5/8, hence:

The value [tex]\frac{5}{8}[/tex] will have two dots above it.

Three measures have a value of 3/4, hence:

The value [tex]\frac{3}{4}[/tex] will have three dots above it.

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Answer:

1 2 3 5 2 3

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

The 3 angles add up to 180 degrees as they are in a triangle.

So 10x - 33 + 4x - 19 + 100 - 2x = 180

12x = 180 + 33 + 19 - 100

12x = 132

x = 11.

So the 3 angles are

10(11) - 33 = 110 - 33 = 77 degrees

4(11) - 19  =  25 degrees

100 - 2(11) = 78 degrees

The expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.

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.

We have a demand function:

q=0. 6(3800-p²)

Differentiate with respect to p:

[tex]\rm \dfrac{dq}{dp} = -1.2p[/tex]

We know the elasticity:

[tex]\rm E(p) = \dfrac{dq}{dp}\times\dfrac{p}{q}[/tex]

[tex]\rm E(p) =-1.2p \times\dfrac{p}{0.6(3800-p^2)}[/tex]

[tex]\rm E(p) = -\dfrac{2p^2}{(3800-p^2)}[/tex]

Here the data for p and q are not given, but we can find any value using the above expression by putting the known data.

Thus, the expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.

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610

Step-by-step explanation:

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

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

We have three linear equations in three variables:

x - y - z = 0 ..(1)

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

x - y + z = -2 ..(3)

From the equation (1):

[tex]\rm x=y+z[/tex]

Plug this value in the equation (2) and (3):

[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

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Answer:

Area of Circle  = 346.5 cm².

Area of square = 272.25 cm ² .

Step-by-step explanation:

So , 2πR = 66

2 × 22 / 7 × R = 66

R comes out is 21/2 cm .

Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2

= 693 / 2 = 346.5 cm².

If bent into the shape of a square ;

4 a = 66

a = 33/2 . ( Side of a square )

Area of square = a ² = 33×33/4 = 1089/4

= 272.25 cm ² .

The Correct match up is:

The first proof of complex numbers was done by an Italian mathematicians known to be Girolamo Cardano and Raphael Bombelli.

The person who illustrated geometry of iterations is Gaston Maurice Julia.

Benoit Mandelbrot is known to have discover fractal geometry. Rene Descartes is known to be famous for making a connection between geometry and algebra.

Therefore, from the above, you can see that the only correct matchup is Leonhard Euler - developed geometry of curved surfaces

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Answer :

proof of complex functions --- > Maryam Mirzakhani

illustrated geometry of iterations --- > Benoit Mandelbrot

developed geometry of curved surfaces --- > Leonhard Euler

In the 15th century, Rene Descartes developed the field of analytical geometry by using functions to describe lines and curves in a coordinate plane. In the 18th century, Leonhard Euler extended geometric analysis to curved surfaces. in the late 20th century, Benoit Mandelbrot used computers to illustrate the geometry of iterations (fractals). In 2014, Maryam Mirzakhani received the Fields Medal for her work on geometric proofs involving complex functions.

Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.

Looing at ΔOAB and ΔOEF

It is clear that

OB = OF (O is the midpoint)

∠OBA = ∠OFE = 90°

Therefore

∠AOB = ∠EOF (Vertically Opposite Angles)

⇒ ΔOAB ≅ ΔOEF and

∠ A ≅ ∠E.

QED

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Answer:

No

Step-by-step explanation:

Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled. A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute.

Answer:

false

Step-by-step explanation:

Answer:

7.5 m = 0.0075 km (Correct)

0.31 = 310 mm (Correct)

46 m = 4,600 cm (Correct)

457 mm =4.57 cm (Incorrect)

0.6 km = 6,000 m (Incorrect)

Step-by-step explanation:

Tell me if something is wrong.

The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).

A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.

The three sides of the triangle will be calculated by applying the Pythagorean theorem:-

The sum of the square sides will be equal to the square of the third side.

For sides  (6,6√3, 12)

12² = 6² + (6√3)²

144 = 36 + (36 x 3)

144 = 36 + 108

144 = 144

Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).

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(x+8/3)²+y²=1

(x+8/3)²+y²+0²+2×0y=1

(x+8/3)²+(y+0)²=(V1)²

->center: C(8/3,0)

-> radius: V1

The correct true statement is the swimmer comes back up 9 seconds after the timer was started.

The maximum height of a function is the  point where the velocity the body is zero.

Given the function that represent the height of the swimmer as  h(t)=t^2−12t+27

If the velocity of the function is zero, hence;

h'(t) = 2t - 12

0 = 2t - 12

2t = 12

t = 6secs

Substitute t = 6 into the function as shown:

h(6) = 6^2−12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.

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The data values that are outliers are 4 and 56.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier distorts the mean and median of the dataset.

In this data, 4 is smaller than the average of the data set and 56 is larger than the average numbers. They are the outliers.

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