Make b the subject of P = 1/2 a b² + c where b is positive. (3 marks)

Answer:

Step-by-step explanation:

Mark the two points (-1,7) and (1,-1) on the graph.  Then draw a straight line between them.  To determine the equation that goes through these two points, we can use the two given points to find the slope of the line.  The standard form of a straight line equation is

y = mx + b,

where m is the slope and y is the y-intercept (the value of y when x = 0).

Slope is also known as the "Rise"/"Run" - the change in y divided by the change in x.  We can use the two points to calculate this:

       Rise (-1-(7) = -8   Run = (1 - (-1) = 2

The slope is therefore (-8/2) or -4.  

y = -4x + b

We can find b by entering either of the two points in y = -4x + b and solve for b.  I'll use (1,-1) since I have my 1's multiplication table memorized

y = -4x + b

-1 = -4(1) + b

b = 3

The straight line equation that connects the two points is

  y = -4x + 3

You can graph this equation (e.g., on DESMOS) to see how it intersects the points.  [Attached]

The coordinates of the y intercept are (0,3).

The coordinate of the y-intercept of the line is (0, 3)

The equation of a line in slope-intercept form is expressed as y = mx + b.

where:

Given the coordinate points (-1, 7) and (1, -1).

Get the slope

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-7}{1-(-1)}\\ m=\frac{-8}{1+1}\\ m=\frac{-8}{2}\\ m=-4[/tex]

Get the y-intercept:

Recall that y = mx + b

Using the coordinate point (1, -1) and m = -4

-1 = -4(1) + b

-1 = -4 + b

b = -1 + 4

b = 3

The equation of the line is y = -4x + 3

The y-intercept occurs at the point where x = 0

y = -4(0) + 3

y = 0 + 3

y = 3

Hence the coordinate of the y-intercept of the line is (0, 3)

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Answer:

Assuming the question is:  3 + 1 16  [I see no "working below."

Step-by-step explanation:

3 + 1 16

48/16 + (16/16 + 1/16)  [Make all numbers into fractions using 16 as the denominator.  E.g. 48/16 = 3.

Add:  48/16 + (16/16 + 1/16)

  (48+16+1)/16

=63/16

[Also equal to 3 15/16]

Answer:

13/8

in decimal form it is 1.625

Step-by-step explanation:

Answer:

13/8 or 1 5/8

Step-by-step explanation:

Answer:

6x - 18

Step-by-step explanation:

2x - 6 + 4x - 12 = 6x - 18

First, distribute the 4 and then combine the like terms to get 6x - 18.

Answer:

x=-2

Step-by-step explanation: First we can multiply 4 times anything in the parenthesis to get rid of it.

(2x-6)+4(x-3)

(2x-6)+4x-12

Then we combine like terms.

(2x-6)+4x-12

6x-6-12

6x-18

Finally we divide both sides by 6.

6x-18

6x/6-18/6

x=-2

Answer:

[tex]gy78093 x^{2} 67[/tex]

Step-by-step explanation:

Answer:

[tex]<174\frac{4}{9}[/tex] hopes this helps :D

Step-by-step explanation:

The solution is s > 174 4/9

The inequality equation is s > 174 4/9 and it will take 174 4/9 seconds for the hot air balloon to reach below 215 feet

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is given by

Let the total altitude of the hot air balloon be = 1000 feet

Now , the hot air to reach below 215 feet , the hot air balloon should descend a total of = 1000 - 215 feet

So , the value of hot air balloon should descend = 785 feet

And ,

The rate at which the hot air balloon descends = 4 1/2 feet per seconds

So , the number of seconds s for the hot air balloon to reach an altitude more than 785 feet is given by the inequality equation A

where ( 4 1/2 ) x s > 785

On simplifying the equation , we get

( 4 1/2 )s > 785

( 9/2 ) s > 785

Multiply by 2 on both sides of the equation , we get

9s > 1570

Divide by 9 on both sides of the equation , we get

s > 174 4/9

Therefore , the value of A is s > 174 4/9

Hence ,

The inequality equation is s > 174 4/9 where s is the number of seconds

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Answer:

ok, but i can't even see nothing, though ;-;

Answer:

6hm-8h^2

Step-by-step explanation:

2h(3m-4h)

2h*3m=6hm

2h*4h=8h^2

=6hm-8h^2

Answer:

The first and third are functions.

Step-by-step explanation:

Functions must have only one y-value for an x-value.

here u go! sorry I didn't give an exact answer but i hope this works bc it did for me

Answer:

In My Opinion, A

Step-by-step explanation:

the measurements are obeying the rule of Pythagorean triplet.

Hence,

This rule also satisfies Pythagorean theorem.

So therefore,

The triangle is a right angled triangle.

I hope this helps

Answer:

x = 18

Step-by-step explanation:

10  − 3x = − 2 (x + 4)

=> 10  − 3x = -2x - 8

=> x = 18

Hoped this helped.

Answer:

x = 18

Step-by-step explanation:

10 - 3x= -2(x+4)

First, we solve inside the parentheses.

10 - 3x= -2x - 8

Like terms:

-3x + 2x= -10 - 8

-x/-1 = -18/-1

x = 18

Answer: 150 m, 5.305*10^-5 kW/m^2, No

Step-by-step explanation:

See attachment, hope this helps

Using the radiation intensity formula we will have to:

a) [tex]150 m[/tex]

b) [tex]5.305*10^{-5} kW/m^2[/tex]

c)No

From the data informed, we have:

[tex]h=150m\\P=40KW[/tex]

Using the given formula and performing some mathematical operations:

[tex]I=\frac{12Psin^2(\theta)}{32(\pi)r^2} \\I= \frac{12(40)(R/r)^2}{32(\pi)r^2} \\= \frac{15R^2}{r^2\pi } \\= \frac{15R^2}{(R^2+150^2)^2\pi} \\[/tex]

deriving the given equation, we will have:

[tex]=\frac{(R^2+150^2)^22R-R^2(2(R^2+150^2))2R}{(R^2+150^2)^2}[/tex]

So from this equation we have that the answer of the letter A corresponds:

[tex]R=150[/tex]

For letter B we will have to develop this equation:

[tex]I= 5.30X10^{-5}[/tex]

As for the letter C, when converting the value found, it should give 200 microwatts, which is false.

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Answer: They are 100 miles apart

Step-by-step explanation:

1 inch = 25 miles

4x25=100

Answer: 100 miles

Step-by-step explanation:

Since we have 25 miles per inch. and there are 4 inches, you would multiply 25 by 4 to get to your answer of 100 miles.

25x4=100

Answer:

The GCF of 3 and 9 is 3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

y 1 = StartFraction log x Over log 0.5 EndFraction, y 2 = StartFraction log 2 Over log 3 EndFraction + x

Answer:

Answer:

of what???????..???..

Answer:

Step-by-step explanation:

-1 to 0 is divided in four parts.

similarly 0 to 1 is divided in four parts

so each fraction on either side is 1/4 onthe right of 0 and -1/4 on the left of 0.

A is 2 parts on the right of 0,A=2×1/4=1/2=0.5

Bis 1 part left of 0,B=1×(-1/5)=-1/5=-0.2

Answer:

The answer is 4 hope this helps

Answer:

They would be equally caramelly, the ratio of oats:caramel is equal

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

You would have to turn 7 1/4 into a whole fraction.

Do,

7 * 4 = 28

28 + 1 = 29

Your new fraction would be,

29/4

Now you have to make them equal denominators with 1/8.

Lets see,

Now multiply 4 * 2 is 8.

So multiply 29 times 2.

Which is 58.

Your new fraction is,

58/8

So therefore you would have 58 pieces.

Answer:

9 dollars 70 cents

Step-by-step explanation:

20% of 48.50

Answer:

Whats the question

Step-by-step explanation:

Answer:

ll available yellow and red flowers at the two businesses

Population: all available flowers at the two businesses

Step-by-step explanation:

The sample and population should be sample represents all yellow and red flowers while the population represents all flowers.

The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.

An entire group from which a conclusion should be derived is referred to as a population. The sample, on the other hand, refers to the population from which the data is drawn.

So based on this, we can say that the sample represents all yellow and red flowers while the population represents all flowers.

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The special right triangle is the right triangle that have acute angle values

that simplify the process of finding its dimensions.

The correct values are;

1. The angle the ladder makes with the ground, is approximately 66.93°

2. The length of YZ is approximately 19.18 ft.

3. CB = 7 ft. and AB = 7·√3 ft.

Reasons:

1. The length of the ladder = 15 ft.

Height of the ladder above the ground, h = 13.8 ft.

Required:

The angle the ladder makes with the ground.

Solution:

The angle the ladder makes with the ground is given by the equation;

[tex]sin(\theta) = \dfrac{Length \ of \ the \ ladder}{Height\ of \ the \ ladder \ above the \ ground} = \dfrac{13.8}{15} = 0.92[/tex]

[tex]\theta = arcsin\left(0.92 \right) \approx 66.93^{\circ}[/tex]

2. The given parameters are;

XY = 11

∠Z = 35°

YZ = Required

In a right triangle, the side facing the acute angle is a leg of the triangle.

Therefore;

XY is the opposite side to ∠Z

[tex]sin(\angle Z) = \dfrac{XY}{YZ}[/tex]

Which gives;

[tex]sin(35^{\circ}) = \dfrac{11}{YZ}[/tex]

[tex]YZ= \dfrac{11}{sin(35^{\circ}) } \approx 19.18[/tex]

YZ ≈ 19.18 ft.

3. AC = 14 ft.

∠A = 30

Required:

The length of the other two sides

Solution:

Where by AC is the hypotenuse side, we have;

CB = AC × sin(∠A)

Therefore;

CB = 14 × sin(30°) = 7

CB = 7 ft.

AB =  AC × cos(∠A) = 14 × cos(30°) = 7·√3

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1. The angle the ladder makes with the ground, is approximately 66.93°

2. The length of YZ is approximately 19.18 ft.

3. CB = 7 ft. and AB = 7·√3 ft.

Answer:

$2160

Step-by-step explanation:

Since she moved out 3 months early, you would do 720x3, since she pays $720 every month. 3x720 = $2160

Answer: Yes

Step-by-step explanation:

You can find out by inputting your values

2y + 3x = 13

x = 5

y = - 1

2(- 1) + 3(5) = 13

- 2 + 15 = 13

13 = 13