A book seller gains 30% on the cost price by selling a book for $130.Calculate the cost price of the book.​

Answer:

V = (2,-32)

Step-by-step explanation:

Hello!

The vertex of a quadratic lies on the Axis of Symmetry (AOS). The axis of symmetry is exactly in the middle of the roots of the Quadratic. We can solve for the AOS by finding the average of the two roots.

The two roots of the quadratic are 6 and -2.

The Axis of symmetry of the quadratic is 2.

Since the vertex lies on the AOS, we know the x-value of the vertex. We can solve for the y-value by plugging in the value of the AOS in the equation.

Find the Vertex

The Vertex of the quadratic is at (2,-32).

Answer:

the point of intersection is (-1 , -2)

Step-by-step explanation:

[tex]\begin{cases}x-y=1&(1)\\ 3x-y=-1&(2)\end{cases}[/tex]

(2) - (1) ⇒ (3x - y) - (x - y) = (-1) - 1

⇒ 3x - y - x + y = -2

⇒ 3x - x  = -2

⇒ 2x  = -2

⇒ x  = -1

……………………………

Now ,we can determine the value of y

by substituting x by its value -1 in the first equation (1) :

(1) x - y = 1 ⇒-1 - y = 1 ⇒ -y = 2 ⇒ y = -2

========================

Conclusion:

x = -1

y = -2

Then ,the point of intersection of the graphs is (-1 , -2)

Hello !

[tex]\begin{cases} x - y &=1 \\ 3x-y &= - 1 \end{cases} \\\Leftrightarrow \begin{cases} x =y + 1 \\ 3x-y = - 1 \: \: \: \: \: (a)\end{cases} [/tex]

We replace x by y+1 in (a) :

[tex]3(y + 1) - y = - 1 \\ 3y + 3 - y = - 1 \\ 2y = - 4 \\ y = \frac{ - 4}{2} = - 2[/tex]

Now we replace x by -1 in the first equation.

[tex]x + 2 = 1 \\ x = -1[/tex]

The point of intersection is (-1;-2).

Have a nice day

The expressions formed are,

Formation of expressions in 1, 2 and 3:

In 1, twelve times f is, 12f

Taking away 5, it becomes (12f-5)

In 2, sum of k and 6 is, (k+6)

One-half of the above quantity is, (k+6)/2

In 3, sum of 5 with x is, (x+5)

Now, x squared minus the above expression indicates (x²-x+5)

Formation of expressions in 4 and 5:

In 4, product of a and b, is ab and 3 times c is 3c

Sum of the expressions evaluated in the previous statement = ab+3c

In 5, 24 times the product of x and y is, 24xy

Adding, g in the above computed expression, we get, 24xy+g

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Answer:

(5, -3)

Step-by-step explanation:

So the center of the two points, or a line can be defined using the equation: [tex]midpoint=(\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})[/tex]. So using the two points you gave, you simply plug the values in to get

[tex]midpoint=(\frac{3+7}{2}, \frac{-1+(-5)}{2})\\[/tex]

Add numerators:

[tex]midpoint=(\frac{10}{2}, \frac{-6}{2})[/tex]

Simplify fraction:

[tex]midpoint=(5, -3)[/tex]

The sum of the geometric sequence is 31/3

The sequence is given as:

1/3, 2/3, 4/3, 8/3, 16/3

The sum of the sequence is;

Sum = 1/3+ 2/3+ 4/3+ 8/3+ 16/3

Evaluate

Sum = 31/3

Hence, the sum of the geometric sequence is 31/3

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The construction is the construction of the Perpendicular bisector.

The steps for the construction of perpendicular bisectors are as follows:

Open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.

Call the two points where these two arcs meet X and Y. Draw the line between X and Y.

So, the point where this line meets the line segment; M is called the mid point and the line XY is the perpendicular bisector of the line AB.

The figure is a construction of perpendicular bisector.

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The number of stuffed bears with Su=153181

Total number of bears Erin has=555555

The number of bears Erin took out=777

Remaining number of bears with Erin=555555-777

                                                                 =554778

Now, these remaining stuffed bears are to be divided equally among 333 sisters.

So, each sister gets [tex]\frac{554778}{333}[/tex]=[tex]1666[/tex] stuffed bears.

To find the number of stuffed bears Su has, find the sum of her share of stuffed bears and the number of stuffed bears she already had.

Number of stuffed bears Su already has=151515

Total number of bears she has at present=151515+1666

                                                                     =153181

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Answer:

29u

Step-by-step explanation:

a = (V-U)/t = (1.2u-u)/10 = 0.02u

D1: V₀t+0.5at² = (u)(10)+(0.5)(0.02u)+(10)(10) = 11u

D2: (V)(t) = (1.2u)(15) = 18u

D = D1 + D2 = 29u

For first half

We need acceleration first

So distance traveled (Apply second equation of kinematics

For second half

No acceleration

Distance=Speed×Time

Total distance

Th equation that can be used to determine when they would have saved the same amount is 0.3(10 + 4h) = 0.25(6h).

The equation that can be used to determine the amount saved by Fernando is:

total amount saved = percentage saved x (amount charged to drive to the appointment + total amount earned)

0.3( $10 + $4h)

The equation that can be used to determine the amount saved by Brenna is:

percentage saved x total amount earned

0.25h

When they save the amount amount, the two above equations would be equal:  0.3(10 + 4h) = 0.25(6h).

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Triangle ABC is congruent to triangle CDE using the side - angle - side congruence theorem. The sink hole is 52.2 ft and the Perimeter of ABC is 172.2 ft

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

In the image shown:

AC = CE, BC = ED and they have the same angle (opposite angles are congruent).

Hence:

Triangle ABC is congruent to triangle CDE using the side - angle - side congruence theorem.

AB = DE = 52.2 ft

Perimeter of ABC = AB + BC + AC = 50 + 70 + 52.2 = 172.2 ft

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The amount the first charity got is $10.

The amount the second charity got is $20.

The first step is to determine the amount raised by the second fifth grade class: 1.5 x $12 = $18

The total amount raised by the two classes : $18 + $12 = 30

Let x represent the amount gotten by the first charity

Amount gotten by the second charity : 2x

2x + x = $30

3x = $30

x = $30 / 3

x = $10

Amount gotten by the second charity : 2(10) = $20

Two fifth grade classes raised money for their local animal shelters. there are 20 students in class a each student raised $12. there are 26 students in class b each student in class b raised 1.5 times as much as each student in class a. The money raised went to two charity. One charity received two times as much as the other. How much money did each charity receive? Show your work and explain your answer.

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The smallest positive integer that has a square root that is greater than 10 is 101

Let the integer be represented by n

The square root is greater than 10.

So, we have:

[tex]\sqrt n > 10[/tex]

Square both sides

n > 100

The above means that the integer is greater than 100.

The smallest integer greater than 100 is 101

Hence, the smallest positive integer that has a square root that is greater than 10 is 101

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Answer:

∠ C = 26°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

∠ A + ∠ B + ∠ C = 180°

120° + 34° + ∠ C = 180°

154° + ∠ C = 180° ( subtract 154° from both sides )

∠ C = 26°

y = 2x² - 16x - 32 is the quadratic function of function passes through the points (-2,0), (4,0), and (0,-32).

y=ax²+bx+c is called as Quadratic function

y=ax²+bx+c

The three points are (-2,0), (4,0), and (0,-32)

Let,

(-2,0) in equation

0=a(-2)²+b(-2)+c

0=-2b+c...(1)

(4,0)

0=a(4)²+b(4)+c

0=16a+4b+c..(2)

(0,-32)

-32=a(0)²+b(0)+c

c=-32...(3)

Hence put c value in (1)

0=-2b-32

2b=-32

b=-16

Now put b and c value in 2

0=16(a)+4(-16)+32

0=16a-64+32

0=16a-32

a=2

Hence y = 2x² - 16x - 32 is the quadratic function of function passes through the points (-2,0), (4,0), and (0,-32).

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Using proportions, it is found that between stops the driver averages 57.75 miles.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In 1,386 miles, the driver had 24 stops, hence the number of miles per stop is found as follows:

1386/24 = 57.75 miles.

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Answer:

0.995 centigram

Step-by-step explanation:

divide the mass value by 10

(a) The relation is a function because each value of x maps onto only one value of y.

(b) Domain is [tex](-\infty, 3][/tex], range is [tex][-1, \infty)[/tex].

The solutions to the given system of equations are x = 4 and y = -9

From the question, we are to determine the solutions to the given system of equations

The given system of equations are

-8x-4y=4  --------- (1)

-5x-y=-11   --------- (2)

Multiply equation (2) by 4

4 ×[-5x-y=-11 ]

-20x -4y = -44  -------- (3)

Now, subtract equation (3) from equation (1)

-8x -4y = 4  --------- (1)

-(-20x -4y = -44)  -------- (3)

12x = 48

x = 48/12

x = 4

Substitute the value of x into equation (2)

-5x -y = -11

-5(4) -y = -11

-20 -y = -11

-y = -11 + 20

-y = 9

∴ y = -9

Hence, the solutions to the given system of equations are x = 4 and y = -9

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Answer:

a) 5.7%

b) 45.8%

c) 6.4%

d) 47.6%

Step-by-step explanation:

remember, we find percentage as:

specific / total

(ex. if we have 2 dogs and 2 cats, and we want to find what percentage of total animals are dogs, we divide 2/4 to get 0.5, or 50%)

percentage of female students who prefer sci-fi

here, we know we have 106 female students (total: 106)

and we have 6 of those students who prefer sci-fi (specific: 6)

6 / 106 = 0.05660..

which we can round to: 0.0566

So, the first percentage is 5.66%

(5.7%)

percentage of students who prefer comedies that are male

we have 118 students who prefer comedies (total: 118)

and 54 of those students that are male (specific: 54)

54 / 118 = 0.4576...

which we can round to 0.4576

So, the second percentage is 45.76%

(45.8%)

percentage of male students who prefer dramas

we have 94 male students (total: 94)

and 6 who prefer dramas (specific: 6)

6 / 94 = 0.0638298...

which we can round to 0.0638

So, the third percentage is 6.38%

(6.4%)

percentage of students who prefer action movies that are female

we have 42 students who prefer action movies (total: 42)

and 20 of those who are female (specific: 20)

20 / 42 = 0.47619..

which we can round to 0.4762

So, the fourth percentage is 47.62%

(47.6%)

hope this helps! have a lovely day :)

Both distributions are bell-shaped and symmetric but where the peak falls on the number line is determined by the mean.

The given statement is false.

A bell curve is a graph depicting the ordinary distribution, which has a shape harking back to a bell. The top of the curve suggests the mean, mode, and median of the records accrued.

The everyday distribution is a bell-fashioned and symmetrical distribution this is used to calculate the opportunity. in the everyday distribution, the mathematics means, mode, and median are usually the same, and the normal distribution is likewise called the Gaussian distribution.

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Answer:

find the graph where y is 3 less than x in value

Step-by-step explanation:

the answer explains it if you showed us the graphs we would be able to answer it for you

The confidence interval for the true mean height of the PBL above the Great Basin Desert is (651.48,748.52) and there is any sufficient evidence that the true mean is different from 700 m .

Given Heights in meters: 673,664,906,956,751,752,654,610,816,667,690,657,920,741,646,682,715,618 and confidence level of 95%.

We have to show the evidence that the true mean height is different from 700 m.

We have to first make hypothesis.

[tex]H_{0}:[/tex]μ=700

[tex]H_{1}[/tex]:μ≠700

We have to first find the population standard deviation.

σ=[tex]\sqrt{(x-x bar)^{2}/n-1 }[/tex]

=[tex]\sqrt{187375.1/17}[/tex]

=104.98

Z=(X-μ)/σ

=(700-728.78)/104.98      (μ=728.78 is calculated in figure)

=-0.2741

p value of -0.2741 =0.39358

0.39358

0.39358<0.90

so we reject the null hypothesis.

Which means that the true mean is different from 700m.

Confidence level=X±z*s/[tex]\sqrt{n}[/tex]

Upper level=700 +1.96*104.98/[tex]\sqrt{18}[/tex]

=700+48.52

=748.52.

Lower level=700-1.96*104.98[tex]\sqrt{18}[/tex]

=700-48.52

=651.48

Hence the confidence interval is (651.48,748.52).

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The inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality are expressions not separated by an equal sign. Given the inequality expression below;

–3(2x – 5) < 5(2 – x)

Expand

-6x  + 15 < 10 - 5x

Collect the like terms

-6x + 5x < 10 - 15

-x < -5

x > 5

Hence the correct representations of the inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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Rate is the distance between the cars increasing two hours later is 52 miles/hr

Let x(t) be distance of first car from starting point at time t

Let y(t) be distance of second car from starting point at time t

Let s(t) be distance between the two cars at time t. We need to evaluate ds/dt at time t = 2.

We know x2(t) + y2(t) = s2(t). Therefore 2x * dx/dt + 2y * dy/dt = 2s * ds/dt. The 2s cancel.

At t=2 hours, x = 96 miles. and y = 40 miles.

We will need the distance between the cars at t=2:

s(2) = √x(2)2 + y(2)2 = √96 2 + 40 2 = √10816 = 104.

Now fill in x * dx/dt + y * dy/dt = s * ds/dt at time t = 3 and solve for ds/dt:

96 * 48 + 40 * 20 = 104 * ds/dt

ds/dt = 5408/104 = 52 miles/hr

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The correct option is (D)

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

the complete question is attached below

As, per the data given we can say that

the variation of quantity is 2.

So, the equation can be

y=2x

This equation defined by part (4) of the question.

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It has been proven that the trigonometric Identity (1 - secA + tanA)/(1 + secA + TanA) is equal to; (secA + tanA - 1)/(secA + tanA + 1)

We want to prove that;

(1 - secA + tanA)/(1 + secA + TanA) = (secA + tanA - 1)/(secA + tanA + 1)

We know from trigonometric identities that;

(secA)² – (tanA)² = 1   ----(1)

Also, from algebra we know that;

a² - b² = (a + b)(a - b)

The numerator of LHS of the original given Identity is:

1 - sec A - tan A

Using equation 1, we can say that;

(secA)² – (tanA)² - (sec A + tan A)

⇒ (sec A + tan A)(sec A - tan A) - (sec A - tan A)

This can be factorized to get;

(sec A - tan A)(sec A + tan A - 1)

Similarly, the denominator can be expressed as;

(sec A - tan A)(sec A + tan A + 1)

Thus, combining the numerator and denominator together gives us:

[(sec A - tan A)(sec A + tan A - 1)]/[(sec A - tan A)(sec A + tan A + 1)]

⇒ (secA + tanA - 1)/(secA + tanA + 1)

That expression is equal to the Right hand side and as such the Trigonometric Identity is proved.

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