Darius correctly answered 51 questions on his Pre-Algebra 2 class. He received a score of 75%. How many questions were on the quiz?

Answer:

Step-by-step explanation:

The coordinates of N so that MN is 1/3 of MP are:

(0,7/4)

In geometry line segment is a part of a line that is bounded by two end points, and contains every point on the that is between end points.

Given, coordinates of M(-3,-2)

and coordinates of P(9,13)

so we have,

x₁ = -3

y₁ = -2

x₂ = 9

y₂ = 13

Also we know that MN is 1/3 of MP

⇒ MN/MP = 1/3 = mn

here, m= 1 and n=3

Let the coordinates of N be (x,y)

Therefore,

(x,y)  = (nx₁+mx₂)/(m+n) , (ny₁+my₂)/m+n

⇒ (x,y) = (3(-3)+1(9)/1+3) , (3(-2)+1(13)/1+3)

⇒ (x,y) = (-9+9/4) , (-6+13/4)

⇒ (x,y) = (0,7/4)

Thus the coordinates of N so that MN is 1/3 of MP is (0,7/4)

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The slope is 1/2 and the y-intercept is 3/4 in the equation  - [ (1/2)x - y ] = 3/4.

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We know that the equation for slope(m) and y - intercept(c) of a line is given by :

y = mx + c

Here given the equation - [ (1/2)x - y ] = 3/4, lets simplify

⇒ - [ (1/2)x - y ] = 3/4

⇒ -(1/2)x + y  = 3/4

⇒ y =  (1/2)x + 3/4

Hence, the slope is 1/2 and the y-intercept is 3/4 in the equation  - [ (1/2)x - y ] = 3/4

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Answer:

30 inches

Step-by-step explanation:

We know that the total length of the board is 90 inches and we know that the shorter piece is two times smaller than the other so we have two pieces divided into three sections 90 divided by three is 30 and since we realize that 30x2=60 and 60+30=90 it means the longer board is 60 inches and smaller one is 30 I hope this helps.

Answer:

7

Step-by-step explanation:

Hope this helps!!

Answer:

y = 2016 - 112x

Step-by-step explanation:

because he is paying 112 dollars each month for 18 months

y= 2016 -112x

for instance, he paid it for 6 months we would say

y = 2016 - 112(6)

y = 2016 - 672

y = 1334

so, y = 2016 - 112x

The amount of you swam is +15 feet and your friend swam is -6 feet.

Given that you move forward 15 feet and your friend is not a strong swimmer, so he moves back 6 feet.

The arithmetic operators means performing an addition, subtraction, multiplication, division, exponentiation, and modulus operations.

It is given that you move the forward that means you move in positive direction.

So, you move forward means you move +15 feet.

It is also given that your friend is not a strong swimmer, so he moves back that means he move in negative direction.

So, your friend moves backward means he move -6 feet.

Hence, you move forward 15 feet is +15 feet and your friend is not a strong swimmer, so he moves back 6 feet is -6 feet.

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Answer:

C. 5/12

Step-by-step explanation:

Let's solve your equation step-by-step.

3/5a= 1/4

Step 1: Multiply both sides by 5/3.

(5/3)*(3/5a)=(5/3)*(1/4)

a = 5/12

Answer:

3 option

Step-by-step explanation:

To find the missing side (c) you need to do a^2 and b^2

Formula a^2 + a^2 = c^2

Answer:

is it -180?

I don't remember most of this stuff!

sorry if its wrong

Step-by-step explanation:

Answer: 2 quarts of pure antifreeze are needed.

Step-by-step explanation:

The simplied form of the given fraction will be -3 11/40.

There is a fraction, containing numerator(upper value) and denominator(lower value).  When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1 an improper fraction is ≥ 1. A mixed fraction contains a sum of whole number and a proper fraction.

WE have been given an expression as;

−3/8+(−2 9/10)

Then first we will solve the mixed fraction;

−2 9/10 = -29/10

Now solve the fraction;

−3/8+-29/10

-131/40

In mixed number form:

-3 11/40

Hence, The simplied form of the given fraction will be -3 11/40.

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Answer:

[tex]10 { }^{ - 5} [/tex]

Step-by-step explanation:

that is the answer above

A rectangle as the only parallelogram that can be inscribed in a circle.

Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.

The only parallelogram that can be inscribed in a circle is a rectangle. Because every rectangle can be inscribed in a (unique circle), the important point is that the radius of the circle is R. (I think). One of the properties of a rectangle is that the diagonals bisect in the 'center,' which is also the center of the circumscribing circle.

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The sum of an infinite geometric series is twice its first term then the common ratio(r) be 1/2.

An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

Given: S = 2a₁

a₁ be the first term

r be the common ratio

Let the equation be S = a₁/1-r

2a₁ = a₁/1-r

substitute the values in the above equation, we get

2 = 1/1-r

2 - 2r = 1

2r = 1

The value of r = 1/2

Therefore, the common ratio(r) be 1/2.

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Answer:

C

Step-by-step explanation:

Just the spread of normally distributed data tells us nothing about the mean, mode or median, so answers A, B, and E are out of question.

The range is based on the difference between the highest and lowest elements. As there can be big outliers, we have no idea if D is true, although we expect distributions with bigger spread to generally exhibit bigger ranges.

We're left with answer C. Standard deviation is a measure of "how much the data can deviate from the mean". It's also one of the measures of spread. We expect data that's more spread out (higher spread) to have a higher standard deviation.

Answer:

112.5miles

Step-by-step explanation:

4hrs=8 half hours

And 1hr30min=3 half hours

If a car travels 300miles in 8 half hours with the mathematical expression of

300miles-8hh

Then for the 3 half hour we have

X-3hh

Comparing the two

300miles-8hh

Xmiles-3hh

By cross multiplying

8×X=3×300

8X=900

X=900/8

X=112.5miles

Answer:

650 Rupees

Step-by-step explanation:

Add all together

The simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]  is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5,  x≠ -1.

As given in the question,

Given expression is [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]

Simplify the given two rational expressions by factorizing them,

[tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{x^{2} +5x +x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{(x+5)(x+1)}\\\\= \frac{x^{2} -1-(x+3)}{(x+5)(x+1)}\\\\= \frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]

Restriction on the variables is given by  x≠ -5,  x≠ -1.

Therefore, the  simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]  is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5,  x≠ -1.

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Answer: The answer is 25/3.

Step-by-step explanation: 8 1/3 = 8 x 3 + 1/3 = 24 + 1    =   25/3

                                                      --------           -----------                                                      

                                                         3                    3

4 cups of pasta are used per cup of sauce.

Given,

Greta uses 3 cups of pasta for every 3/4 cup of sauce.

We need to find how much pasta she uses per cup of sauce.

Example:

12 apples = 2 basket ____(1)

For 5 baskets:

We need to make 2 baskets = 5 baskets.

We can divide by 2 and multiply 5 on both sides on (1).

5/2 x 12 apples = 5/2 x 2 baskets

30 apples = 5 baskets.

We have,

3 cups of pasta = 3/4 cup of sauce

We need to make 3/4 cup of sauce as 1 cup of sauce.

Multiply 4/3 on both sides.

4/3 x 3 cups of pasta = 4/3 x 3/4 cup of sauce

4 cups of pasta = 1 cup of sauce

Thus 4 cups of pasta are used per cup of sauce.

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A parabola with a vertical axis of symmetry is graphed at the end of the answer.

The equation of a quadratic function, of vertex (h,k), with a vertical axis of symmetry, is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The most simple example of this is the parabola y = x², which is graphed at the end of the answer.

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Answer:

0, -7 or Slope is Undefined

Step-by-step explanation:

y2 - y1 / x2 - x1

(x2 - y2) (x1 - y1)

Answer:

From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville

The slope of the given problem is 14

It is a problem of linear regression Line

y = a +by

where a = ∑Y - b ∑X / N  

and b = N ∑XY - (∑X×∑Y)/ ( N∑x²- (∑X)  

      Month(X) Temperature (y)  X²              XY

               1                   42                        1                  42

               2                  56                        4                 112

               3                  70                         9                210

               4                  84                        16               336

Total        10               252                     30               700

Number of observation (n) = 4

So, b = 4(700) - (10)(252) / ( 120 - 10²)

         = 2800-2520/20

        = 280/20

         = 14

b = 14

Now a=  252 - (14)10/ 4

          =112 /4

         = 28

So, The linear regression line is

         y= 28 + 14x

Slope = 14

The slope here is positive which means increase in period or moving forward in month is increasing the average temperature of the month.

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The measure of ∠C in ΔABC is 35°.

Angle Sum Property of a triangle states that sum of all the interior angle of a triangle is 180°.

In the given Question

∠B=90° , ∠A=∠C+20°...(1)

By angle sum property of triangle for ΔABC

we get

∠A+∠B+∠C=180°

Substituting the values of ∠B and ∠C from equation (1) we get

∠C+20°+90°+∠C=180°

2∠C+110°=180°

2∠C=180°-110°

2∠C=70°

∠C=35°

Therefore  , the value of ∠C in ΔABC is 35°.

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