For which values of A, B, and C will Ax + By = C be a horizontal line through the point (4, -9)?

Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.

To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.

Now, total distance in race

8/18 + 16/18

= (8+16)/18

= 24/18

= 4/3

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

Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

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The given triangle is a right angled triangle having the follwoing sides;

Hypotenuse = x (longest side)

Opposite = 14 (side facing the given acute angle)

Theta = 15 degrees

Using the SOH trigonometry identity;

sin 15 = opposite/hypotenuse

sin15 = 14/x

x = 14/sin15

x = 14/0.2588

x = 54.09

x is approximately equal to 54.1. Option B is coorect

The number and type of roots of each quadratic function are:

The type of roots of a quadratic function is given by the value of the discriminant, which is the value under the square root of the quadratic formula.

The types of roots of a quadratic equation are;

The roots or solution to the quadratic equation, a·x² + b·x + c = 0, are given by the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}[/tex]

Where:

b² - 4·a·c is known as the discriminant of the quadratic equation.

The type of root of a quadratic equation is given by the discriminant, b² - 4·a·c, as follows:

The given functions are:

Comparing the above equation to the, general form of a quadratic equation, f(x) = a·x² + b·x + c, we have;

a = 1, b = -9, and c = 21

The discriminant is therefore, (-9)² - 4 × 1 × 21 = -3 < 0

The quadratic equation therefore, has complex roots.

The quadratic equation, f(x) = x² + 16·x - 64 has a discriminant given as follows;

The discriminant is: 16² - 4 × 1 × (-64) = 512 > 0, therefore, the quadratic equation two real roots, given by the equation;

[tex]x = \dfrac{-16\pm \sqrt{16^2 - 4\times 1 \times 64} }{2\times 1}= \dfrac{-16\pm \sqrt{512} }{2}= \dfrac{-16\pm 16\cdot \sqrt{2} }{2}[/tex]

x = -8 + 8·√2 or x = -8 - 8·√2

The value of the discriminant is 10² - 4 × (-4) × 84 = 1444 > 0, therefore, the equation has two real and distinct roots, given by the equation;[tex]x = \dfrac{-10\pm \sqrt{1444} }{2\times (-4)}= \dfrac{-10\pm 38 }{-8}[/tex]

[tex]x = \dfrac{28 }{-8}= -3.5[/tex] and [tex]x = \dfrac{-48 }{-8}= 6[/tex]

The discriminant of the above quadratic equation is; 0² - 4 × 3 ×24 = -288 < 0

Therefore, the quadratic equation, f(x) = 3·x² + 24, has no real roots or complex roots

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Table A shows a proportional relationship

What is proportional relationship?

When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.

In the figure we are given 2 tables

We plot both the curve on the graph we get

Table A shows a linear relationship where are Table b Does not shows a proportional relationship

Hence Table A shows a proportional relationship

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Answer:

Step-by-step explanation:

In these linear expressions one is equivalent which is  3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.

Alternatively pluging; we will see that none of the exponents can be greater than 1.

2x - 3(1.3x - 2.5) = 5.9x + 7.5

2x -3.9x + 7.5 = 5.9 + 7.5

-1.9x + 7.5 ≠  5.9 + 7.5

thus linear expression is not equivalent.

3- 2( - 2.6x + 2.1) = 5.2x - 1.2

3 + 5.2x -  4.2 = 5.2x - 1.2

5.2x - 1.2 = 5.2x - 1.2

thus, linear expression is equivalent.

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The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²

Missing data from the problem:

radius of the barrel = 0.4 meters

height of the barrel = 1.2 meters

The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:

A = 2. πr² + 2. πr.h

Where:

r = radius

h = height

Plug the parameters into the formula:

A = 2. π(0.4)² + 2. π(0.4).(1.2)

A = 13 m²

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We are given that the length of a rectangle is 3 inches greater than the width.

Let us draw a rectangle and label the width and length.

Part A:

Let the width of the rectangle is x inches.

Then the length of the rectangle is (x + 3) inches.

Now recall that the area of a rectangle is given by

Where L is the length and W is the width of the rectangle.

Therefore, the above polynomial represents the area of the rectangle.

Part B:

We are given that the width is 4 inches.

Substitute the width (x = 4) into the equation of the area that we found in part A.

Therefore, the area of the rectangle is 28 square inches.

Since the translation is 8 units right and 4 units down, we have to add 8 to the x coordinate and subtract 4 to the y coordinate.

R=(-2,1)

R' = (-2+8,1-4)= (6,-3)

R' = (6,-3)

Answer:

b= -1, -6

Step-by-step explanation:

divide by common factor

then use x=- b+- sqrt b^2-4ac/2a

separate the equations and solve them

Answer:

Brainliest Answer?

( 7 / 8 ) seconds

( 77 / 4 ) feet

Step-by-step explanation:

The question is a bit confusing but I will do it both ways. I will assume that you made a mistake copying over the function because the graph s( t ) is linear. Linear functions have a maximum value of infinity because it is an odd-degree polynomial.

Assume that s( t ) = - 16t² + 28t + 7;

The equation forms an upside-down parabola which means it has a maximum value.

Complete the square to get the axis of symmetry and the maximum value of the parabola or use my very cool formula. The variables h and k represent the axis and max respectively.

ax² + bx + c = a( x - h )² + k;

ax² + bx + c = a( x - ( - b / 2a ) )² + c - ( b² / 4a );

ax² + bx + c;

Take a as a factor.

a( x² + ( b / a )x + ( c / a ) );

Add and subtract the square of ( 1 / 2 ) of ( b / a ). This is called completing the square because it forms a perfect square trinomial.

a( x² + ( b / a )x + ( b / 2a )²  - ( b / 2a )² + ( c / a ) );

Factorise the trinomial.

a( ( x + ( b / 2a ) )² - ( b / 2a )² + ( c / a ) );

Use the distributive property of multiplication.

a( x + ( b / 2a )² + a( ( c / a ) - ( b / 2a )² );

a( x + ( b / 2a )² +  a( ( c / a ) - ( b² / 4a² ) );

Simplify the fractions.

a( x + ( b / 2a )² + c - ( b² / 4a );

Substitute the values.

- 16( t - ( - 28 / 2( - 16 ) )² + 7 - ( ( 28 )² / 4( - 16 ) );

Time is the x-axis so we need to solve for the axis of symmetry.

h = ( - 28 / 2( - 16 ) );

h = ( - 28 / - 32 );

Simplify the fraction.

h = ( 7 / 8 );

Maximum height is the parabola's y of the vertex.

k = 7 - ( ( 28 )² / 4( - 16 ) );

k = 7 - ( ( 28 )( 28 ) / - 64 );

k = 7 - ( 784 / - 64 );

k = 7 - ( - 49 / 4 );

k = ( 28 / 4 ) + ( 49 / 4 );

k =  77 / 4;

Answer:

y = - 2x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 7 ) into the partial equation

- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1

y = - 2x - 1 ← equation of line

The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%

The percentage of adult females have pulse rates below 90 bpm - 89.97%

a)

X ~  N ( µ = 74 , σ = 12.5 )

P ( 49 < X < 86.5 )

Standardizing the  value

Z = ( X - µ ) / σ

Z = ( 49 - 74 ) / 12.5

Z = -2

Z = ( 86.5 - 74 ) / 12.5

Z = 1

P ( -2 < Z < 1 )

P ( 49 < X < 86.5 )  =  P ( Z < 1 ) - P ( Z < -2 )

P ( 49 < X < 86.5 )  = 0.8413 - 0.0228

P ( 49 < X < 86.5 )  = 0.8186  ≈  81.86%

b)

X ~ N ( µ = 74 , σ = 12.5 )

P ( X < 90 )

Standardizing the value

Z = ( X - µ  ) / σ

Z = ( 90 - 74 ) / 12.5

Z = 1.28

P (  ( X - µ ) / σ )  < ( 90 - 74 ) / 12.5 )

P ( X < 90 ) =  P ( Z < 1.28 )

P ( X < 90 ) = 0.8997  ≈  89.97%

The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).

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The length of XY=19.894 cm when the angle XYZ=90° and angle YZX=61° and the length of hypotenuse=17.4 cm. Using the property of trigonometry, a=b.sinα/sinβ.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Here,

a=b.sinα/sinβ

=17.4·sin(90°)/sin(61°)

=19.89436 cm

≈19.9 cm

When the hypotenuse is 17.4 cm long and the angles XYZ and YZX are 90° and 61°, respectively, the length of XY is 19.894 cm. Using the trigonometric formula a=b.sinα/sinβ.

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Answer:

See below

Step-by-step explanation:

From 5 to 10 mugs is 5 mugs  

   These cost  110 - 67.50 = 42.50

        So each mug costs 42.50 / 5 = 8.50 each  

              With a 'base cost' of 25 dollars

   (Base cost might be artwork, design, order processing, shipping or whatever.....but this amount is added to each order)

(As a check    20 mugs would be   25 + 20 (8.50) = 195   <====yep

150 mugs will then be 25   +  150 ( 8.50) = 1300 dollars

Answer:

y = [tex]\frac{3x -6}{5}[/tex]

Step-by-step explanation:

3x - 5y = 6 ( subtract 3x from both sides )

- 5y = - 3x + 6 ( multiply through by - 1 )

5y = 3x - 6 ( divide both sides by 5 )

y = [tex]\frac{3x-6}{5}[/tex]

Answer:

y=.25x+6

Step-by-step explanation:

Answer:

15/8 for exact form

1.875 for decimal form

And

1 and 7/8 for mixed number form

hope this helps you!

(also already in the simplest form :)

Answer: the radius of a cylinder is 4 cm

Step-by-step explanation:

[tex]S_{ts}=352\ cm\ \ \ \ H=10\ cm\ \ \ \ \ r=?[/tex]

The total surface area:

[tex]\displaystyle\\ S_{ts}= 2\pi r^2+2\pi rH\\\\S_{ts}=2\pi (r^2+rH)\\\\352=2\pi (r^2+10r)\\\\[/tex]

Divide both parts of the equation by 2π:

[tex]\displaystyle\\56=r^2+10r\\\\56-56=r^2+10r-56\\\\0=r^2+10r-56\\\\Thus,\\\\ r^2+10r-56=0\\\\D=(-10)^2-4(1)(-56)\\\\D=100+224\\\\D=324\\\\\sqrt{D}=\sqrt{324} \\\\\sqrt{D}=18\\\\ r=\frac{-10б18}{2(1)} \\\\r=-14\notin\ (r > 0)\\\\r=4\ cm[/tex]

Answer:

r ≈ 4 cm

Step-by-step explanation:

Total Surface Area of a cylinder

A = Base Area x 2 + Lateral Surface Area

A = 2(πr²) + 2πrh

where r = radius of base and h = height of cylinder

Solving for r we get

[tex]\displaystyle r = \dfrac{1}{2} \sqrt{h^2 + 2 \dfrac{A}{\pi} }-\dfrac{h}{2}\\\\[/tex]

Given h = 10 cm and A = 325 we get

[tex]\displaystyle r = \dfrac{1}{2} \sqrt{10^2 + 2 \dfrac{352}{\pi} }-\dfrac{10}{2}\\\\\\[/tex]

[tex]\sqrt{10^2 + 2 \dfrac{352}{\pi} } =\sqrt{100+\dfrac{704}{\pi }}\\\\= \sqrt{100 + 224.09}\\\\\\[/tex]

= [tex]\sqrt{324.09}[/tex]

= 18.0025

1/2 x 18.0025 ≈ 9

So r ≈  9 - 10/2 = 9 -5 = 4

r ≈ 4 cm

Given:

Product of two numbers is 1.

The one number is 5/2.

Let the another number be x.

Answer: Option a) is correct. the other number is 2/5.

Concept; Probability

Step1: The total number of tokens is

let the probability of blue be P(B) and the probability of red be P(R)

The probability that the first is Blue is

The probability the second is white without replacement is

Hence the combined probability of Blue and Red is

Therefore the probability that the first is blue and the second is white is 4/15

Answer:

Mexico to the United States in 1947

Step-by-step explanation:

Answer:

Step-by-step explanation:

she would have to use 3/4 of the ingrediants to the 400g of minced beef.

tomato sauce would be 600g

stock would be 225g

and red wine would be 225g

The quantity of chopped tomatoes is 600 g, of stock is 225 ml, and of red wine is 225 ml if Julie only has 300 g of minced beef.

The ratio is the comparison of two quantities to determine how frequently one quantity obtains the other. It can be shown as a fraction between two numbers.

Quantity of minced beef = 400 g

Quantity of chopped tomatoes = 800 g

Quantity of stock = 300 ml

Quantity of  red wine = 300 ml

Taking ratios of all the quantities, we get:

minced beef: chopped tomatoes:stock: red wine

= 400:800:300:300

= 100:200:75:75 ( Dividing by 4, as a common factor)

Multiplying the above ratio by three to make the quantity of minced beef 300 g

= 300:600:225:225

Thus, the quantity of chopped tomatoes is 600 g, the quantity of stock is 225 ml, and the quantity of red wine is 225 ml if Julie only has 300 g of minced beef.

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Therefore let us input the values to find the volume of the cone

The answer should be A.

Answer:golden hour by JVKE

Step-by-step explanation:

Answer: 50%

Step-by-step explanation:

The error percent of the fish tank is 50%

Error percent:

Error percent means the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. It is also known as the percent error is the relative error multiplied by 100.

The formula to calculate the error percent is

δ = |vA - vE|/vA x 100

δ  = percent error

vA = actual value observed

vE = expected value

Given,

Raul estimated that a fish tank contained 20 gallons of water. He later  found that the fish tank had a 40-gallon capacity.

Here we need to calculate the error percent.

According to the error percent formula,

In this question

The estimated value = 20 gallons

Actual value = 40 gallons.

Now, we have to apply the values on the formula, then we get,

P% = (40 - 20)/40 x 100

P% = 20/40  x 100

P% = 1/2 x 100

P% = 0.5 x 100

P% = 50.

Therefore, the error percent is 50%.

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Using concept of Linear equation in two variables, we got 23 is  denomination count of 5$ bills and 21 is denomination count of 20$ bills.

Linear equations are used to solve equation in which two variables are connected with each other via some specific methods.

The linear equations in two variables are the equations in which each one of the two variables are of the highest exponent order of the 1 and have one, none, or may be infinitely many solutions. The standard form of a two-variable linear equation is given by ax + by + c = 0 where x and y are the two variables. The solutions can also be written in form of ordered pairs like (x, y).

It is given that 5$ bills are 2 more than 20$ bills,

so let suppose 20$ bills denomination count is x,

then 5$ bills denomination count=x+2;

It is also given that 535$ worth is summation of 5$ bills and 20$ bills

Therefore,[5×(x+2)+(20×x)]=535

On solving for x, we get x=21

Therfore,20$ bills denomination count is 21,and 5$ bills denomination count is 23.

Hence,5$ bills denomination count is 23 and 20$ bills denomination count is 21

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If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute

Referring to the attached picture, the two triangles in a cone are similar. Hence,

r/h = 48/24

or

r = 2h.

The volume of the liquid is given by:

V = 1/3 . πr²h

Substitute r = 2h,

V = 1/3 . π(2h)²h = 4/3 . πh³

Take the derivative with respect to t

dV/dt = 4/3 .  3πh² . dh/dt

dV/dt = 4 .  πh² . dh/dt

Substitute dV/dt = -40 and h = 10

-40 = 4 .  π(10)² . dh/dt

dh/dt = - 0.0318 in./minute

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Answer:0.0008994

Step-by-step explanation:

Answer:

x = 7 , ∠ A = 36°

Step-by-step explanation:

since ∠ ADB ≅ ∠ CBD ( alternate angles )

and ∠ ABD ≅ ∠ CDB ( alternate angles )

then ABCD is a parallelogram

the opposite angles of a parallelogram are congruent , so

∠ C = ∠ A , that is

8x - 20 = 3x + 15 ( subtract 3x from both sides )

5x - 20 = 15 ( add 20 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Then

∠ A = 3x + 15 = 3(7) + 15 = 21 + 15 = 36°

Answer: x = 7 and m∠A = 36

Step-by-step explanation:

Here ∠ADB ≅ ∠CBD and ∠ABD ≅ ∠CDB

This configuration is found when a quadrilateral has two parallel sides which have a diagonal as their transversal. Thus the figure is of parallelogram. In a parallelogram, opposite angles are equal. Thus m∠A = m∠C

⇒3x +15 = 8x - 20

⇒3x + 15 - 3x = 8x - 3x -20

⇒5x = 20 + 15

⇒x = 7

Now m∠A = (3X7) +15 = 36