There is a mound of g pounds of gravel in a quarry. Throughout the day, 200 pounds of gravel is added to the mound. Two orders of 700 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.

According to law of cosines the length of RQ can be written as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

Given the length PR is 6 , the length of RQ is p, the length of PQ is 8 and the angle RPQ is 39 degrees.

A length of the triangle can be written as according to law of cosines if sides are given and one angle is [tex]a^{2} =b^{2} +c^{2} -2bccos(A)[/tex]

We have to just put the values in the above equation.

as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

p is the side opposite to angle given , the length of other sides are 6 and 8 and angle is 39 degrees.

Hence the side can be written as according to law of cosines if the angle is 39 degrees is  as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

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Answer: OPTION B

Step-by-step explanation:

edge22

The complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

The complete question is in the attachment

The given parameters are:

The vertex is represented as (h, k ± a).

So, we have:

h = -5

k + a = 14

k - a = -2

Add the last two equations

2k = 12

Divide by 2

k = 6

Substitute k = 6 in k + a = 14

6 + a = 14

Solve for a

a = 8

The ellipse equation is represented as:

[tex]\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1[/tex]

So, we have:

[tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

The ellipse passes through the point (0,6).

So, we have:

[tex]\frac{(0 + 5)^2}{b^2} + \frac{(6 - 6)^2}{8^2} = 1[/tex]

This gives

[tex]\frac{5^2}{b^2} + \frac{0}{8^2} = 1[/tex]

Evaluate the quotient

[tex]\frac{5^2}{b^2} = 1[/tex]

Cross multiply

[tex]b^2 = 5^2[/tex]

Take the square root of both sides

b = 5

Substitute b = 5 in [tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

[tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

Hence, the complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

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The amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

Gertrude has a life insurance policy that will pay her family $97,000 per year.

If interest rates are at 1.4% when the insurance company has to pay

r = 1.4%

or

r = 0.014

The amount of the lump sum that the insurance company must put into a bank account:

= 97,000/0.014

= 6928571.429 ≈ $6,928,571.43

Thus, the amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.

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To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

Use the distributive property to distribute 3x into the term (x + 6):

[tex]3x(x+6)=-10[/tex]

[tex]3x^2+18x=-10[/tex]

To create a quadratic equation, add 10 to both sides of the equation:

[tex]3x^2+18x+10=-10+10[/tex]

[tex]3x^2+18x+10=0[/tex]

The quadratic formula is defined as:

[tex]\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

Set up the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}[/tex]

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}[/tex]

Simplify the radicand:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}[/tex]

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

[tex]\sqrt{4\times51}[/tex]

Then, using the Product Property of Square Roots, break this into two radicands:

[tex]\sqrt{4} \times \sqrt{51}[/tex]

Since 4 is a perfect square, it can be evaluated:

[tex]2 \times \sqrt{51}[/tex]

To simplify further for easier reading, remove the multiplication symbol:

[tex]2\sqrt{51}[/tex]

Then, substitute for the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}[/tex]

This gives us a combined root, which we should separate to make things easier on ourselves.

Separate the roots at the plus-minus symbol:

[tex]\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}[/tex]

[tex]\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}[/tex]

Then, simplify the numerator of the roots by factoring 2 out:

[tex]\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}[/tex]

[tex]\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}[/tex]

Then, simplify the fraction by reducing 2/6 to 1/3:

[tex]\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}[/tex]

[tex]\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}[/tex]

The final answer to this problem is:

[tex]\displaystyle x=\frac{-9 + \sqrt{51}}{3}[/tex]

[tex]\displaystyle x=\frac{-9 - \sqrt{51}}{3}[/tex]

Answer:

Step-by-step explanation:

Open the brackets

3 x 2x = 6x

3x -3 = -9

4 x 2x= 8x

4 x 4= 16

6x - 9 = 8x + 16

Move same to same side

-16 -9 = 8x - 6x

-25 = 2x

x -25/2

x = -12.5

Answer:

Step-by-step explanation:

3*(2x - 3) = 4*(2x + 4)​

6x - 9 = 8x + 16

6x - 8x = 16 + 9

-2x = 25

x = -25/2 or -12.5

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

check

3 * (2 * (-12.5) - 3) = 4 * (2 * (-12.5) + 4)

3 * (25 - 3) = 4 * (12.5 + 4)

3 * 22 = 4 * 16.5

66 = 66

the answer is good

Answer:

y = 4(x+6)(x-2)

Step-by-step explanation:

y = 4x² + 16x - 48, factor out the 4

y = 4(x² + 4x - 12), find factors of 12

Factors of 12:

1*12, 2*6, 3*4; find a pair that sums to 4x or 4

6-2 = 4, since 12 is a negative number, a number in the factor must be negative, in this case, making 2 negative, would make 6-2 = 4

y = 4(x+6)(x-2)

[tex]\mathsf {2(10 + 2) = 3(y + 3)}[/tex]

[tex]\mathsf {24 = 3y + 9}[/tex]

[tex]\mathsf {3y = 15}[/tex]

[tex]\textsf {y = 5}[/tex]

[tex]\textsf {The value of y will be 5. }[/tex]

Answer:

The volume of the pyramid with a base area of s² and the heights iss

The formula for calculating the volume of a square based pyramid is expressed as:

Volume = 1/3* Base area* Height

Since it is a square-based pyramid, the base area is calculated as:

Base Area = s ^ 2

If the height of the pyramid is equal to of the length of a side on the base, hence h = s

Substituting the base area and the height into the formula for the volume, this will give;

V = BH / 3

V = (s ^ 2 * s)/3

V = (s ^ 3)/3

V = 1/3 * s ^ 3

Hence the volume of the pyramid with a base area of s ^ 2 and the height s is 1/3 * s ^ 3

Answer:

The total money we have to pay is $69.

Step-by-step explanation:

MARKUP is the amount added to the cost price.

MARKUP formula = 100*profit / cost

Cost of the item = $60.00

put the value in the formula

15 = 100*profit/60

profit = 60 × 15 ÷ 100 = 9

the total money  is  cost + profit

which is 60 + 9 = $69.

So the total money we have to pay is $69.

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Answer:

C

Step-by-step explanation:

HOPE THAT HELPSBDNQBDB

Answer:

9=0

Step-by-step explanation:

9=0

The roots of x in the equation -10x² + 12x - 9 = 0 are:

x = (3/5) + (3/5)√(6)i

x = (3/5) - (3/5)√(6)i

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

To find the roots of x in the equation -10x² + 12x - 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).

In this case, a = -10, b = 12, and c = -9. Substituting these values into the quadratic formula, we get:

x = (-12 ± √(12² - 4(-10)(-9))) / 2(-10)

x = (-12 ± √(144 - 360)) / (-20)

x = (-12 ± √(-216)) / (-20)

Substituting this into the expression for x, we get:

x = (-12 ± 6√(6)i) / (-20)

Simplifying the expression further, we get:

x = (3/5) ± (3/5)√(6)i

Therefore, the roots of x in the equation -10x² + 12x - 9 = 0 are:

x = (3/5) + (3/5)√(6)i

x = (3/5) - (3/5)√(6)i

These roots are complex conjugates of each other.

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Substitute 5 in the place of X

[tex]f(x) = \frac{1}{8} \times 4 ^{x} \\ f(5) = \frac{1}{8} \times 4 ^{5} \\ f(5) = \frac{1}{8} \times 1024 \\ f(5) = 0.125 \times 1024 \\ f(5) = 128[/tex]

The asnwer is D

PLEASE GIVE BRAINLIEST

Step-by-step explanation:

1) the equation of the line represented is

y=0.5x+3 (slope-interception form), the slope is 0.5, the intercept is 3.

x-2y+6=0 (common form);

2) x-intersection is at -6, y-intersection is at 3.

Answer:

cp = rs 400

loss = 10%

Then SP = 400 - 10% of 400

= 400 - 40

= 360

Therefore SP = Rs. 360

Answer:

37.5

Step-by-step explanation:

37.5×144/100=54 the number is 37.5

The possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

(k - 1)x² + (4k)x + k -3 = 0

Here,

a = k - 1

b = 4k

c = k - 3

As we know for distinct real roots:

D > 0

[tex]\rm {b^2-4ac}} > 0[/tex]

(4k)² - 4(k-1)(k-3) > 0

[tex]\rm 16k^2-4\left(k-1\right)\left(k-3\right) > 0[/tex]

[tex]\rm 12k^2+16k-12 > 0[/tex]

[tex]\rm 3k^2+4k-3 > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2-\dfrac{13}{3} > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{3}[/tex]

[tex]\rm \left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{9}[/tex]

[tex]\rm k < \dfrac{-\sqrt{13}-2}{3}\quad \mathrm{or}\quad \:k > \dfrac{\sqrt{13}-2}{3}[/tex]

or

[tex]\rm k < -1.868 \quad \mathrm{or}\quad \:k > 0.535[/tex]

Thus, the possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

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Parallel lines are those on a plane that do not intersect while perpendicular lines are those that intersect at an angle of 90°.

Parallel lines will never intersect with each other and will maintain the same distance from each other for as long as they are on the same plane.

Perpendicular lines on the other hand will intersect each other and will do so at a 90° angle. An example of such a line is the steps on a ladder which intersect the beam at a 90° angle.

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Answer:

f(2) =  18

Step-by-step explanation:

Put '2' into the equation where 'x' is to get :

f(2)  =  2 (2^2) + 5 (sqrt(2+2)

        =  8        + 5 (2)   =  18

Answer:

- 7x + 5y= (-11) -------(1)

-4x + 3y,= (-7) ----------(2)

Multiplying eq 1 with 3 and eq 2 with 5

3( -7x + 5y) = 3(-11)

5(- 4x + 3y) = 5(-7)

-21x + 15y = (-33)

-20x + 15y,= (-35)

Subtracting both the eq.

-x = 2

x = (-2)

Putting this value in eq. 1

- 7x + 5y= (-11)

-7(-2)+ 5y= (-11)

14 + 5y = (-11)

5y = (-11) - 14

5y= (-25)

y = (-5)

Answer:

237 grams

50 * 4

= 200

4 weight of 50 g

1 weight of 20g

1 weight of 10g

7 weight of 1g

Answer: (0, 1, 3)

Step-by-step explanation:

If we multiply both sides of the equation [tex]4x-2y=-2[/tex] by 7, we get [tex]28x-14y=-14[/tex].

If we multiply both sides of the equation [tex]9x-7y=-7[/tex] by 2, we get [tex]18x-14y=-14[/tex].

Subtracting the equation [tex]28x-14y=-14[/tex] from the equation [tex]18x-14y=-14[/tex], we get that [tex]-10x=0 \longrightarrow x=0[/tex].

This means that [tex]4(0)-2y=-2 \longrightarrow y=1[/tex]

And thus, [tex]4(0)-2(1)-z=-5 \longrightarrow -2-z=-5 \longrightarrow z=3[/tex].

So, the solution is (0, 1, 3).

The time taken by a group of 8 people working half the rate of the first group is 7.5 hours.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

A Group of 5 people can do a piece of work in 6hrs.

5 people, at a rate of 1, and the time taken is 6 hours

Work done is 30

8 people, at a rate of 1/2, and the time taken is x hours

8(1/2)x = 30

x = 60/8 = 7.5 hours

Thus, the time taken by a group of 8 people working half the rate of the first group is 7.5 hours.

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En una tienda se fabrican

La cantidad de mesas de 3 patas que tiene para la venta la tienda que las

fabrica es: 47

¿Qué es un sistema de ecuaciones?

Es un arreglo de ecuaciones que se caracteriza por tener el mismo número de incógnitas que de ecuaciones.

Existen diferentes métodos para su resolución:

Sustitución: se despeja de una ecuación una variable, quedando en función de otra para luego sustituirla en otra ecuación y así obtener

Igualación: se despeja la misma variable en dos de las ecuaciones y se igualan los resultados.

Eliminación: se resta o suman dos ecuaciones para que quede un resultado en función una variable y así despejarla.

Gráfico: se grafican las rectas y el punto de intersección es la solución del sistema.

¿Cuántas mesas de 3 patas se tienen para vender?

Definir;

x: mesas de 3 patas

y: mesas de 4 patas

Ecuaciones

x + y = 89

5x + y = 277

Aplicar método de eliminación;

Restar 1 - 2;

x + y = 89

-5x - y = -277

-4x + 0 = -188

Despejar x;

x = 188/4

x = 47

Sustituir;

47 + y = 89

Despejar y;

y = 89 - 47

y = 42

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Answer: the fourth one

Step-by-step explanation:

Answer:

D.) 8x¹²y³

Step-by-step explanation:

When an expression is raised to a power, you have to raise everything in the expression to the power when simplifying. This includes the coefficients and variables. When a variable already raised to a power is raised to another power, the powers are multiplied.

Therefore,

2³ = 8

(x⁴)³ = x⁴*³ = x¹²

(y)³ = y³

Combined, the final answer is 8x¹²y³.

[tex]x^2-10x=30x\\x^2-40x=0\\x(x-40)=0\\x=0 \vee x=40[/tex]

The length of CD will be option C. 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

AB/ED = AC/EC = BC/CD

AC/EC = BC/CD

18/6 = (12 - x)/x

Simplifying the expression,

We get

18x = 6(12 - x)

Multiplicating the terms in right hand side,

18x = 72 - 6x

Solving 6x on both sides,

we get

18x + 6x = 72 - 6x + 6x

24x = 72

Dividing both the sides by 24, we get

24x/24 = 72/24

x = 3

Hence, the length of CD is 3.

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Answer:

the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

Answer:

4/10, 6/15, 8/20, etc.

Step-by-step explanation:

I hope you got some idea

Answer:

It's most likely he was charged a late fee