The graph of a linear function passess through the points (3, 19) and (5, 23). Write an equation for the function. Show your work

Answer:

(3, - 2 )

Step-by-step explanation:

Given the 2 equations

4x - 2y = 16 → (1)

y = - 5x + 13 → (2)

Substitute y = - 5x + 13 into (1)

4x - 2(- 5x + 13) = 16 ← distribute and simplify left side

4x + 10x - 26 = 16

14x - 26 = 16 ( add 26 to both sides )

14x = 42 ( divide both sides by 14 )

x = 3

Substitute x = 3 into (2) for corresponding value of y

y = - 5(3) + 13 = - 15 + 13 = - 2

solution is (3, - 2 )

[tex]7.8 \times {10}^{ - 7} [/tex]

Answer:

1) The equation for the of the ball in y = a·(x - h)² + k is;

y = -16·(x - 5)² + 25

2) The height of the dock, d =  -375 feet below the water level

Step-by-step explanation:

1) The question is with regards to quadratic function representing projectile motion

The given parameters are;

The height the ball reaches 4 seconds after Sarah kicked the ball = 9 feet

The time the ball hits the water = 6 seconds after reaching the 9 feet height

The form of the quadratic equation representing the motion is given as follows;

y = a·(x - h)² + k = a·x² - 2·a·h·x + a·h² + k

Let 'x' represent the time of motion of the ball, and let 'a', represent the acceleration due to gravity, we have;

The equation for the ball, y = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

h = The horizontal component of the vertex coordinate = 0

Therefore, we have;

When x = 0, y = d

d = -16·(0 - h)² + k =  -16·h² + k

d = -16·h² + k  

When x = 4, y = 9 - d

9 - d = -16(4 - h)² + k = -16(4 - h)² + k

When x = 2, y = d

d = -16(2 - h)² + k

When x = 6, y = 9

9 = -16(6 - 5)² + k

When x = 8, y = d

d = -16(8 - h)² + k

-16(8 - h)² - (-16(2 - h)²) = 0

h = 5

From 9 - d = -16(4 - h)² + k = -16(4 - 4)² + k

d = 9 - k

9 = -16(6 - h)² + k

k = 9 + 16(6 - 5)² = 25

d = 9 - k = 9 - 25 = -16

Therefore, h = 5, k = 25

The equation for the of the ball in y = a·(x - h)² + k is therefore;

y = -16·(x - 5)² + 25

2) When x = 0, y = d, ∴ d = -16(0 - 5)² + 25 = -375 feet below the water

The height of the dock, d =  -375 feet below the water level

Answer:

34cm

Step-by-step explanation:

bc i konow

Answer:

no, a right angle is 90 degrees. it isn't.

Step-by-step explanation:

the bottom left angle should look like this:  L, which it doesn't.

Answer:

Plus 4 miles every 2 hours

Hours= +2

Miles= +4

Answer:

Answer 1: $6,289

Answer 2: $198

Step-by-step explanation:

1-

a(10)=10,000(1+.05)^10

=16,288.95  =16,288-10,000=$6,289

2-

A(t)=pe^rt=a(10)=10,000e^(.05)(10)=16,487-10,000=6487

6487-6289=$198

[tex]v =\dfrac{d}{t}[/tex]

[tex]5 = \dfrac{22}{t}[/tex]

[tex]t = \dfrac{5}{22}[/tex]

She will take [tex]\dfrac{5}{22}[/tex] hours or 13 minutes and 38 secs.

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Answer:

Step-by-step explanation:

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The answer is C because it matches the other graph from Desmos.

( -1.333,0 ) ( 0,-2 )

( Picture Below )

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Hope this helps! <3

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The graph of the equation y = -(3/2)x -2 is C.

Slope of a line is defined as the change in the value of y-coordinate with respect to the value of the x-coordinate. It is usually denoted by 'm'.

Slope can also be defined as the tangent of the angle that the line is making with the X-axis.

The equation of a line in slope-intercept form is y = mx + c, where m is the slope and c is the y-intercept.

For  y = -(3/2)x -2, m = -3/2 and c = -2

Here slope is negative, so the line will be directing downwards from left to right.

So we eliminate graph B.

y-intercept is the y-coordinate of the point where the line touches with the X-axis. The x-coordinate at that point will be zero.

So we got the a point on the line ( 0, -2 )

Since graph A does not pass through this point, it is also eliminated.

Now we find x-intercept which is the x-coordinate of the point where the line touches with the X-axis. The y-coordinate will be zero there.

So, 0 = -(3/2)x -2

⇒ 2 = -(3/2)x

⇒ x = -4/3

⇒ x = -1.333

So the line touches ( -1.333, 0).

Hence, graph C is the one which satisfies the equation  y = -(3/2)x -2.

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Answer:

a = [tex]\frac{9}{4}[/tex] , b = - 2

Step-by-step explanation:

Given the 2 equations

9 = ab² → (1)

- 72 = a[tex]b^{5}[/tex] → (2)

Divide (2) by (1)

[tex]\frac{-72}{9}[/tex] = [tex]\frac{ab^5}{ab^2}[/tex]

- 8 = b³ ( take the cube root of both sides )

[tex]\sqrt[3]{-8}[/tex] = b , that is

b = - 2

Substitute b = - 2 into (1) and solve for a

9 = a(- 2)² = 4a ( divide both sides by 4 )

[tex]\frac{9}{4}[/tex] = a

Step-by-step explanation:

3x is answer because emily = 2X , mike = x

X + 2x

= 3x

The first one is correct you take the slope and multiple it by x and then add or subtract your y intercept depending on whether it is positive or negative. In this case it's positive so it would by -3/7x+9

Answer:

x = 7

Step-by-step explanation:

Given

5x - 1 - 2x = 20, that is

3x - 1 = 20 ( add 1 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Step-by-step explanation:

5x-1-2x=20

3x-1=20

3x=20+1

3x=21

3x/3=21/3

x=7

-------- hope it helped

Answer:

The change of rate of the situation is 5.

Step-by-step explanation:

Given f(n) = 2 + 5n. The rate of change is still the same as the slope of the equation. We know that the equation of a line is given as:

f(x) = y = mx + c where m is the slope. In our given equation, f(n) = 2 + 5n = 5n + 2, we see that m = 5 which is our slope.

Therefore, the change of rate of the situation is 5.

Answer: In fraction form it will be 1/160

Step-by-step explanation: Hope this helps :)

Answer:

[tex]\displaystyle m\angle RTU=73^\circ[/tex]

Step-by-step explanation:

Interior Angle of a Circle

An interior angle of a circle is formed at the intersection of two lines that intersect inside a circle.

Lines AC and BD of the figure attached below intersect forming arcs p and q. The measure of the interior angle x  is:

[tex]\displaystyle x=\frac{p+q}{2}[/tex]

The question includes the drawing of a circle with lines US and RV intersecting at point T. The measure of the interior angle RTU is:

[tex]\displaystyle m\angle RTU=\frac{68^\circ+78^\circ}{2}[/tex]

[tex]\displaystyle m\angle RTU=\frac{146^\circ}{2}[/tex]

[tex]\boxed{\displaystyle m\angle RTU=73^\circ}[/tex]

Answer: (I REDID THIS ANSWER)

$128

Step-by-step explanation:

20% off of $16,000 = $3,200

20% off of $3,200 = $640

20% off of $640 = $128

Answer= $128

Answer:

Both a and b

Step-by-step explanation:

The height of the cylinder is 8cm

The formula for calculating the volume of the cylinder is expressed as;

[tex]V = \pi r^2 h[/tex]

r is the radius

h is the height

Substitute the given parameters into the formula:

[tex]V = \pi r^2 h\\72 \pi = \pi \times 3^2h\\72 = 9h\\h=\frac{72}{9}\\h = 8cm[/tex]

Hence the height of the cylinder is 8cm

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Answers

I got answer 16.9

Step-by-step explanation:

1. Let's first look at triangle XYC. We know angle Y is 90 degrees because it has the symbol. and it is given that Angle X 45 degrees. Using the triangle interior angle theoreom, a triangle has 180 degrees so Angle C is 45 degrees. Know let find the sides, First we can deduce XY is 5 cm because of the triangle midsegment theorem XY is half of BC so since we know BC is 10  that means XY is 5.  Then applying 45-45-90 triangle rules, XY=5, YC=5 and XC=[tex]5\sqrt{2}[/tex].

2.Now let look at the triangle XBC. Let find one  missing angles. In the triangle . A  angle bisector  XC bisects XY and BC  . Using that information Angle C of XYC = Angle C of XBC. So angle C=45 degrees. Knowing looking at the main triangle ABC  Angle A=30, Angle C= 45+45=90 and Angle B=60 by interior triangle theorem. So going back to Angle X so angle x is 75 degrees due to interior triangle theorm. Also since Y=90 degrees it forms a linear pair to triangle AXY so Y=90 for AXY

Now let apply 30-60-90 triangle rules to AXY. XY =5, AY=[tex]5\sqrt{3}[/tex] and AX=10.  

Finally. Apply 30-60-90 triangle rules to ABC. AC=[tex]5\sqrt{3}[/tex] +5 BC=10 and AB should turrn out to be 16.9.

This may not be right,but good luck:)

Answer:

Mark borrowed> (Subtracting) 125 dollars, so he will have negative 125 because he took it away. He gives back> (Addition) 30 dollars.

-125+30= -95. So, he owes 95 dollars.

(Easy way)

I hope this helped :))

Answer:

72

Step-by-step explanation:

(pls mark me brainliest if u can)

Sam's "bearing" is simply the direction in which he's moving, which is the angle made with due East.

From point A to point B, his bearing is 335°, and from point B to C, his bearing is 45°. In both cases, the angle is made with due East from the second point. See the sketch for a rough approximation of this. Note that it is not to scale.

To get it into scale, you have to compute the distances traveled along each bearing.

• Moving at 6 km/h for 20 min = 1/3 h would cover a distance of

(6 km/h) • (1/3 h) = 2 km

• Moving at 10 km/h for 15 min = 1/4 h would mean a distance of

(10 km/h) • (1/4 h) = 2.5 km

In your sketch, 1 cm should represent 500 m = 0.5 km, so the arrow from A to B should have a length of 4 cm, while the arrow from B to C should have a length of 5 cm.

By answering the above question, we may state that by equation Once more, we can observe that the two conjugates' product is an integer.

Using the equals notation (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of three mathematical expressions by a mathematical assertion.

The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are inscribed on opposite sides of a letter. Most of the time, the symbol and the particular software match. e.g., 2x - 4 = 2 is an example.

An integer is always obtained when a radical expression is multiplied by its conjugate since the product has the form[tex]a^2 -b^2[/tex], where a and b are rational numbers. This is so that we may obtain the difference of the squares of the two terms within the radical when we multiply the two conjugates.

Consider the radical expression [tex]\sqrt3 - \sqrt2[/tex] and its conjugate,  [tex]\sqrt3 - \sqrt2[/tex] , to understand this. These two expressions can be multiplied as follows:

[tex]\sqrt{\sqrt3 - \sqrt2\\[/tex]

[tex]\sqrt{(\sqrt3 - \sqrt2) ((\sqrt(3 + \sqrt(2)))} = 3 - \sqrt(2 ) = 1$$[/tex]

As a result, we can observe that the two conjugates' product is an integer.

The radical phrase [tex]\sqrt5 - \sqrt3[/tex] and its conjugate, [tex]\sqrt5 +\sqrt3[/tex] , serve as another illustration.

[tex](\sqrt5 -\sqrt3)[/tex]

[tex](\sqrt(5) + \sqrt(3)) = \sqrt(5) \times \sqrt(5) + \sqrt(5) \times \sqrt(3) - \sqrt(3) \times \sqrt(3)[/tex]

[tex](\sqrt5 - \sqrt3)( \sqrt 5+ \sqrt3) = 5 - 3 = 2[/tex]

Once more, we can observe that the two conjugates' product is an integer.

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Answer:

q= -3

Step-by-step explanation: