what is the slope intercept form of the linear equation 4x + 2y = 24
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Answer:

B 8/21

Step-by-step explanation:

Answer:

Option 4 - [tex]y-8=-(x+3)[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line that passes through point (–3, 8) is [tex]y =-x+ 6[/tex].

The general form of slope intercept is [tex]y=mx+c[/tex]

where, m is the slope and c is the y-intercept.

On comparing,

m=-1 and c=6

The point slope form of the equation of a straight line is

[tex]y-y_1=m(x-x_1)[/tex]

Point is [tex](x_1,y_1)=(-3,8)[/tex]

Substitute the values,

[tex]y-8=-1(x-(-3))[/tex]

[tex]y-8=-(x+3)[/tex]

The point-slope form of the equation for this line is [tex]y-8=-(x+3)[/tex]

Therefore, Option 4 is correct.

Answer:

Length= 30 feet, breadth = 55 feet.

Step-by-step explanation:

Length of building in blue print= 3 inches

Breadth of building in blue print= 5.5 inches

It is given that 1 inch on the blue print is equivalent to 10 feet in actual building

We have to convert the dimensions

So Length of building in blue print in feet= 3 inches= 3×10=30 feet

Breadth of building in blue print in feet= 5.5 inches= 5.5×10= 55 feet

Hence the correct answer is Length= 30 feet, breadth = 55 feet.

The diameter of Virus B, which is 15 times larger than Virus A, is 3.9 • 10^-6 millimeters.

Virus A possesses a minute diameter, measuring at 2.6 x 10^(-7) millimeters. When comparing it to Virus B, which is 15 times larger, you simply multiply Virus A's diameter by 15. Therefore, Virus B boasts a diameter of (2.6 x 10^(-7) mm) x 15, resulting in 3.9 x 10^(-6) millimeters. This means that Virus B is significantly larger than Virus A. This mathematical relationship highlights the scale and size differences between these two viruses, emphasizing the substantial increase in diameter when transitioning from Virus A to Virus B, due to the multiplication factor of 15.

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we know that

Yousef typed a [tex]36[/tex]-word paragraph in [tex]2/3[/tex] minute

so

by proportion  

Find  the number of words typed in one minute

[tex]\frac{36}{(2/3)} \frac{words}{minutes} =\frac{x}{1} \frac{words}{minute}\\ \\x=36*\frac{3}{2}\\ \\x= 54\ words[/tex]

therefore

the answer is

Yousef typing speed, in words per minute is equal to

[tex]54\frac{words}{minute}[/tex]

The typing speed of Yousuf in words per minutes is [tex]54\;\rm words\;per\;minute[/tex].

Yousuf typed 36 words in  [tex]\dfrac{2}{3}\;\rm minutes[/tex].

By Unitary method, calculate the speed of typing by Yousuf as-

[tex]\dfrac{2}{3} \;\rm minutes \rightarrow 36\;\rm words\\1\;\rm minute \rightarrow \dfrac{36}{(\frac{2}{3})}\;\rm words\\1\;\rm minute \rightarrow \dfrac{36\times 3}{2}\;\rm words\\1\;\rm minute \rightarrow 54\;\rm words[/tex]

Hence, the typing speed of Yousuf in words per minutes is [tex]54\;\rm words\;per\;minute[/tex].

Learn more about unitary method here:

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Answer:

360 feet

Explanation:

There are 10 hash marks between 0 and 300; this means that each hash mark is 300/10 = 30 feet.

Miranda's location is 5 hash marks below 0; this puts her at 5(30) = 150 feet below 0, or -150.

Blake's location is 7 hash marks above 0; this puts him at 7(30) = 210 feet above 0, or 210.

This means they are 210--150 = 210+150 = 360 feet.

To find the distance between Miranda and Blake on a number line, you sum the absolute values of the distances each has traveled from the starting point O, regardless of direction.

If Miranda walks due west and Blake walks due east from the same starting point O (represented as 0 on the number line), then the distance between Miranda and Blake is the sum of their absolute distances from the starting point. For example, if Miranda walks 2 feet west and Blake walks 3 feet east, the distance between them on the number line would be 2 (west) + 3 (east) = 5 feet.

Here, we're using the concept of absolute value where negative values represent westbound distances, and positive values represent eastbound distances.  Unlike calculating displacement, where direction mattered, calculating the distance between two points doesn't require you to consider direction. The magnitude of distance traveled in opposite directions from the same starting point is simply added together.

So, applying these principles of number lines and absolute values, to get the distance between Miranda and Blake, you add the distance each has traveled from the starting point O, regardless of their directions.

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Decimals B, C, and D can be converted into rational numbers as they have repeating patterns.

A nonterminating decimal can be converted into a rational number if it is a repeating decimal. Among the given options, decimals B, C, and D can be converted into rational numbers because they have repeating patterns.

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Answer:

all real numbers from 10 to 30, inclusive

Step-by-step explanation:

The practical domain of function is , Roscoe can ride his bike only from 10 miles to 30 miles.

Domain of function is defined as the set of input values for which the function is defined i.e.  the set of its possible inputs,

The amount of time it takes for Roscoe to ride his bike m miles is represented by a function.

                       [tex]t(m) = m/10.5[/tex]

Where m represent, number of miles he can ride.

Above function is defined for every value of m . But in question it is mention that Roscoe rides his bike at least 10 miles but not more than 30 miles.

Therefore, Domain of function is from 10 miles to 30 miles.

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Final answer:

To calculate the number of unopened bottles after some have been opened, subtract the number of opened bottles (b) from the total number brought to the picnic (8), resulting in the expression 8 - b.

Explanation:

The expression to determine the number of unopened bottles of water at the end of the picnic, when Nora took 8 bottles and a certain number of bottles were opened, would be 8 - b. Here, the variable b represents the number of bottles that were opened, and since we start with 8 bottles, we subtract the number that were opened (b) from the total number of bottles (8) to get the number that remain unopened.

Answer:

she needs 1 [tex]\frac{1}{3}[/tex]   cup  of strawberries

Step-by-step explanation:

To find the number of cups needed, we will simply solve using proportion

From the question, Jade picked  1 cup of strawberries for 3/4 of a cake

and we are asked to find the number of cups needed for a whole cake

Let x be the number of cups needed for the whole cake

[tex]\frac{3}{4} cake[/tex]       =      1 cup of strawberries

1 cake     =       x

Cross multiply

[tex]\frac{3}{4}[/tex]   ×  x     =    1  ×    1

[tex]\frac{3x}{4}[/tex]    =   1

cross multiply

3x =4

To get the value of x, we simply divide both-side of the equation by 3

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

(On the left-hand side of the equation, 3 will cancel out 3 leaving us with x and on the right-hand side of the equation 4 will be divided by 3 which will give us 1 [tex]\frac{1}{3}[/tex] )

x =  1 [tex]\frac{1}{3}[/tex]

Therefore  1 [tex]\frac{1}{3}[/tex]  cup of strawberries is needed for the whole cake.