A textbook store sold a combined total of 447 biology and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of biology textbooks sold. How many textbooks of each type were sold?

Answer:

x = 8

y = 36

Step-by-step explanation:

The triangle shown in the image is an isosceles triangle.

We can find the value of x using the above mentioned information:

∠B = ∠A

5x = 40 divide both sides by 5

x = 8

The sum of interior angles in a triangle is equal to 180°.

Since ∠B and ∠C are both 40°:

40 + 40 + 3y - 8 = 180 add/subtract like terms

72 + 3y = 180 subtract 73 from both sides

3y = 108 divide both sides by 3

y = 36

Answer:

perimeter is 6 times as long as the width

Step-by-step explanation:

let width be w then length l = 2w

perimeter (P) of a rectangle is calculated as

P = 2(l + w )

  = 2(2w + w)

 = 2(3w)

 = 6w

Perimeter is 6 times as long as the width

The width of the rectangle is (1/6) times long as the perimeter of the rectangle.

The area of a rectangle is given by -

A{R} = Length x Breadth

A{R} = L x B

Given is the length of a rectangle is twice its width.

Assume the width of the rectangle be [x] units. Then, the length will be [2x] units. For the width of the rectangle to be as long as the perimeter of the rectangle -

{P} = 2{L + B} = 2{x + 2x} = 6x

Now -

{w} = x

So, we can write that -

{P} = 6{w}

{w} = {1/6}{P}

Therefore, the width of the rectangle is (1/6) times long as the perimeter of the rectangle.

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Answer:

You're welcome. :)

Step-by-step explanation:

Hope you're able to understand it.

In given expression constant term is 4, degree of expression is 2, coefficient of second term is 5 and at x=-1 value of expression is 6.

The highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial.

The degree denotes the polynomial's highest exponential power.

A term in an equation with a fixed value that is unaffected by variations in the variable.

A constant is typically represented as c to reflect a fixed value when written as a variable.

The usage of the word "variable" in this terminology may be perplexing, but all it really implies is that c is a variable that may stand in for any fixed value.

Given: p(x)=7x²+5x+4

(a) Constant term is coefficient of [tex]x^{0}[/tex].

So constant term in given equation is 4.

(b) Degree of expression is highest power of x in the expression. For our expression we have two as our highest power.

So, degree of expression is 2.

(c) Coefficient of second term is 5.

(d) On substituting value of x as -1, we get

7× (-1)² +5(-1) +4 = 7-5+4 = 6

So, value of expression at x=-1 is 6.

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Answer:

Step-by-step explanation:

-3.45

From the given 2D graph:

1. It took 20 minutes for Alec to get to his first friend's house.

2. Alec stayed for 40 minutes at his first friend's house.

3. It took 10 minutes for Alec to ride his bike from his first friend's house to his second friend's house.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

4. Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.

5. In part E of the graph Alec is riding his bike toward his home.

6. In part A of the graph Alec is traveling the fastest.

7. Alec was away from his house for 115 minutes.

1. From the given graph we can observe that part A of the graph is the time taken by Alec to reach his first friend's house which is 20 minutes.

2. From the given graph we can observe that part B of the graph is the time that Alec stayed at his first friend's house.

3.  From the given graph we can observe that part C of the graph is the time that Alec took to ride his bike from his first friend's house to his second friend's house.

4. Alec stayed at his first friend's home for 40 minutes, and he stayed at his second friend's home for 30 minutes, therefore Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.

5. In part E of the graph Alec is riding his bike toward his home.

6. In part A of the graph Alec is traveling the fastest.

7. Alec was away from his house for part(A+B+C+D+E)=20+40+10+30+15=115 minutes.

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The vertex of the graph for the given equation is (-1, -8).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).

Its geometrical aspect is the slope of the tangent at a given point.

The given equation is y = 2x² + 4x - 6.

The vertex is a point at the graph where the slope becomes zero. It can be found by equating the differentiation of the equation to zero as below,

y = 2x² + 4x - 6

=> y' = 4x + 4 = 0

=> x = -1

At x = -1 the value of y can be found as,

y = 2 × -1² + 4 × -1 - 6

  = 2 - 4 - 6

  = -8

Thus, the vertex is given as (-1, -8) which is only valid for option (b).

Hence, the key points to be used by sandy to draw the graph are x-intercept (1, 0), y-intercept (-3, 0) and vertex (-1, -8).

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Answer:

I think its these:

(0,3)

(1,4)

(2,5)

Step-by-step explanation:

The equation in point slope form will be -

y - 2 = 2(x - 3).

The general equation of a straight line is -

Other possible equations of lines are -

We have some equations of line as given in the question.

The point slope form is -

(y - y₁) = m(x - x₁)  

The points are -

(3, 2) and (5, 6)

So -

m = (6 - 2)/(5 - 3)

m = 4/2

m = 2

Equation will be -

y - 2 = 2(x - 3)

Therefore, the equation in point slope form will be -

y - 2 = 2(x - 3)

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The equation that represents the model is 6x + 3 = 27, the solution of the equation is x = 4

Total number of pack of eraser = 6

Number of eraser in one pack = x

Number of erasers in 6 pack = 6x

Add 3 more erasers

Total number of erasers = 6x + 3

Total number of erasers = 27

Then the equation that represents the model will be

6x + 3 = 27

Solve the equation

6x = 27 - 3

Subtract the numbers

6x = 24

x = 24/6

Divide the numbers

x = 4

Therefore, the equation is 6x + 3 = 27, and the solution of the equation x = 4

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1) 18 Quarts of Sparkling water needs to be mixed with 9 quarts grape juice.

2) 15/2 Quarts of grape juice is required for 15/4 quarts of sparkling water.

3) The Quantity of grape juice and sparkling water in 100 quarts of punch are 33 1/3 quarts and 66 2/3 quarts respectively.

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I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:pt 1). Oliver is correct

pt 2). The volumes are the same

yw

They took 1.53 hrs long before they are 1000 nautical miles apart.

What is the distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Here, we have

A plane leaves Charlotte at 9:00 AM and flies north at 400 knots. At the same time, another plane flies south from Charlotte at 250 knots

The speeds are added when going in opposite directions = 400 + 250knots =  650 knots

We apply here distance formula,

Distance = rate × time

t = d/r

= 1000/650 hours

= 1.53 hours

Hence, they took 1.53 hrs long before they are 1000 nautical miles apart.

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Answer:

-10x = -51 + 5

-10x = -46

x=-46/-10

x=46/10

x=4.6

Answer:

x=23/5

Step-by-step explanation:

-10x-5=-51

-10x=-51+5

-10x=-46

10x=46

x=46/10

x=23/5

Answer: 28.3 calories

Step-by-step explanation:

From 12 oz down to 2 oz, we divided by 6

So take 170 divided by 6 = 28.33 cal; ground up will be 28.3 cal

Answer:

8x ≤ 53 - 10

8x ≤ 43

x ≤ 43/8

X is smaller or equal to 43/8 (5.375)

Answer:

81/2 is answer.......2/3× 81/ 2 = 27

Answer:

x=40.5

Step-by-step explanation:

2/3x=27

x3.    x3

2x=81

/2 /2

x=40.5

hopes this helps please mark brainliest

Answer:

The answer is 6, I am going to give you a explanation just in case you need one.

Step-by-step explanation:

We are going to refer seed packets as SP just to make it more simple. And flowers F this is just to make it easier on ourselves.

Ok since we know that in order to plant 9 F we need 3 SP.

If we do the equation correctly we should get

3 SP × ? = 9

In order to do this there is two ways I am going with the easier one we just have to add 3 to 3 until we get 9 ok so 3 + 3 = 6 so lets add more 3's 6 + 3 = 9 great so this means 3 + 3 + 3 = 9. Now if  you noticed he had three three's which means our equation now is

3 SP × 3 = 9

Now that we are done with the first part it should just get easier from here.

We know that each SP has 3 F to grow and each SP has 9 F to grow we just have to do 9 + 9 which gives us 18.

Therefore the answer is 2 SP needed to plant 18 flowers.

Hope this helped :)

To make 26 gallons of the shade of green paint, 13 gallons of blue paint is needed.To make 26 gallons of the shade of green paint, 20.8 gallons of yellow paint is needed.

Finding the product of two or more integers is done mathematically through the action of multiplication. It entails adding a number, known as the , known as the multiplier. For instance, adding three to itself four times produces the result of multiplying three by four, which is twelve. In other ways, repeated addition may be expressed using the abbreviation "multiplication." It is frequently used to calculate the overall worth of a set of paint, such as the cost of numerous products in a shopping cart. Finding the area of a rectangle or the volume of a cube are two more more difficult mathematical procedures that employ it.

How to solve?

To make 26 gallons of the shade of green paint, 1/2 * 26 = 13 gallons of blue paint is needed.

To make 26 gallons of the shade of green paint, 4/5 * 26 = 20.8 gallons of yellow paint is needed.

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45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.

Two or more expressions with an Equal sign is called as Equation.

Given,

Salad 'n Scoops is a food truck that sells salads for $4 and scoops of ice cream for $2

On a hot July day, they had 118 customers and earned $326.

Let x be the number of scoops of ice cream sold and y be the number of salads sold that day.

From the given information

4x+2y=$326...(1)

x+y=118

x=118-y..(2)

Substitute 2 in 1

4(118-y)+2y=326

472-4y+2y=326

472-2y=326

Subtract 472 on both sides

-2y=-146

Divide both sides by 2

y=73

Plug in y value in equation 2'

x+y=118

x+73=118

x=118-73

x=45

Hence, 45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.

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The slope of a line parallel to the line 8x - 6y = -24 is 4/3.

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of the line.

8x - 6y = -24

First, rewrite in slope-intercept form.

8x - 6y = -24

Solve for y

8x + 24 = 6y

6y = 8x + 24

y = (8/6)x + 24/6

y = (4/3) + 4

Now, from the slope-intercept form;

y = mx + b

Where m is the slope

Slope of the line y = (4/3) + 4 will be

m = 4/3

All line parallel to the line y = (4/3) + 4 must have the same slope.

Hence, the slope of a parallel line to the line y = (4/3) + 4 will be;

m_parallel = 4/3

Therefore, the slope of the parallel line is 4/3.

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In 2011 we can predict there will be only 1.13 million VHS movie rentals.

A regression equation is utilized in details to figure out what relationship, if any, exists between sets of information. For instance, assuming that you measure a kid's level consistently you could find that they develop around 3 inches a year. That pattern (growing three inches a year) can be displayed with a regression equation.

The remarkable relapse condition is the dramatic capability that best fits the arrangement of information and it is given in the structure:

y = a · bˣ

where:

a = beginning worth of the model

b = remarkable develop or rot

x = time elapsed all along

For our situation,

y = 9.92 · (0.8208)ˣ

where:

a = 9.92

b = 0.8208

Since 0 < b < 1 we have an outstanding rot, affirming that the quantity of VHS is diminishing with time.

We can then utilize this condition to gather the quantity of VHS motion pictures in 2011.

As something first, compute how long all along (2000) would pass:

x = 2011 - 2000 = 11

Presently, substitute this worth in the situation:

y = 9.92 · (0.8208)¹¹

  = 1.13

Thus, number of vhs movies in 2011 is 1.13 million.

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The equation that represents the situation will be y = 1.5x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the y-intercept of the line is zero. Then the equation is given as,

y = mx

The line is passing through (6, 9), then we have

9 = 6m

m = 9 / 6

m = 1.5

Then the equation that represents the situation will be y = 1.5x.

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21.8 cm  is length of rectangle .

What is the name of the rectangle shape?

A rectangle may also be referred to as an equiangular quadrilateral. This is so because a rectangle is a quadrilateral (4-sided form) with parallel sides that are equal to one another and corners with 90o angles on each side.

             An equiangular quadrilateral is another name for a rectangle shape because all of the angles are 90 degrees.

L=5+6W

156 = 2L + 2w

2(5+6W) + 2W = 156

10+ 12W +2W =50

   14W = 40

    W = 40/14

      W = 2.8 CM

W =5 cm

L= 5+6( 2.8 ) = 21.8 cm

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Answer:

Step-by-step explanation:

7y = -3x + 7

y = -3/7x + 1

Answer: I think its 10%

Step-by-step explanation: I hope that helps

Answer:

x = 2

Step-by-step explanation:

X is the vertical edge

x=2

Answer: x = 2

Step-by-step explanation:

The slope of a vertical line is undefined, so the equation of a vertical line is x = a

In this problem, the only choice that represents a vertical line is x = 2 (where a = 2)

The equation of the line tangent to the graph of g at the point where x = 1 y + 10x + 44 =0.

What is line tangent?

A line that touches a curve at one point is said to be tangent. A point of tangency is the location where a curve and a line intersect. Y = mx + b is the slope-intercept formula for a line, where m is the line's slope. The straight line that "just touches" the curve at a particular location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

Given g(x)=f(2x)

Differentiate it on both side with respect to x.

[tex]\begin{aligned}& \frac{d g(x)}{d x}=2 * \frac{d f(2 x)}{d x} \\& \frac{d g(-1)}{d x}=2 * \frac{d f(-8)}{d x}=-5^* 2=-10\end{aligned}[/tex]

Slope =-10

Here x coordinate = -4

g(-4)=f(-8)=-4 = y coordinate

Thus point of tangency on function g is (-4,-4)

Thus equation of tangent is

y + 4= -10(x+4)

y + 10x + 44 =0

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Answer:

  y = 8x -11

Step-by-step explanation:

You want the equation of the line tangent to g(x) = f(2x-6) at x=1, where f is a differentiable function with f(1) = 2, f(-4) = -3, f'(1) = 3, f'(-4) = 4.

The equation of the tangent line at x=1 can be written ...

  y = g'(1)(x -1) +g(1)

The necessary function values are ...

  g(1) = f(2·1 -6) = f(-4) = -3

and

  g'(x) = f'(2x -6)·(2x -6)' = 2f'(2x -6)

  g'(1) = 2f'(2·1 -6) = 2f'(-4) = 8

Then the equation of the line is ...

  y = 8(x -1) +(-3) = 8x -8 -3

  y = 8x -11 . . . . . . tangent to g(x) at x=1

__

Additional comment

The minimum polynomial function f(x) that can have the desired values and derivatives is a cubic. The attached graph shows g(x) and the tangent at x=1 using that cubic for f(x).