In the adjoining parallelogram ABCD, A is joined to any point E on BC. AE and DC produced meet at E Prove that. area of ∆BEF = area of ∆ CDE​

Answers:  x = 1 and y = -1

Explanation:

Start where your teacher left off, which is -3y = 3.

We solve for y by dividing both sides by -3

That turns -3y = 3 into y = -1

Then we use this y value to find x

x - 5y = 6

x - 5(-1) = 6

x + 5 = 6

x = 6-5

x = 1

The solution is (x,y) = (1, -1)

Answer:

-1,1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Starting with the original equation:

[tex]\sqrt{1-3x} =x+3[/tex]

Squaring both sides to remove the root, and expanding the right side:

[tex]1-3x=(x+3)(x+3)[/tex]

Multiplying the right side:

[tex]1-3x=x^{2} +6x+9[/tex]

Combine like terms:

[tex]x^{2} +9x+8[/tex]

Factor:

(x+8)(x+1)

If x+8=0, then x= -8

If x+1=0, then x=-1

Answer:

Dilated pupils

Long periods of wakefulness

Loss of appetite

Overconfidence

Over-excitement

Paranoia

Runny nose or frequent sniffles

White powder around nostrils

Legal issues

Missing or being late to work

Financial problems

Mood swings

Irritability

Depression

Answer:

13

Step-by-step explanation:

Distance between points (1, 3) and (6, 15) is 13

Answer:

Last year sales increased by 200%. This year sales decreased by 50%.

Step-by-step explanation:

Answer:

Date                  Account Title                                              Debit             Credit

XX-XX-XXX      Sales returns and Allowances              Rs. 5,000

                        Accounts receivable - M Center                                   Rs. 5,000  

                         Inventory                                                Rs. 5,000

                         Cost of Goods sold                                                        Rs. 5,000

Answer:

12.

Step-by-step explanation:

6x10 = 60.

60 divided by 12 =5.

Answer:

12

Step-by-step explanation:

5x = 60

x  = 12

Answer:

No its doesn't satisfy the equation.

[tex]{ \bf{area = 2(l + w)}} \\ { \tt{48 = 2((x + 10) + (x - 3))}} \\ { \tt{24 = 2x + 7}} \\ 2x = 17 \\ x = 8.5 \\ \\ { \bf{in : \: {x}^{2} + 7x - 78 = 0 }} \\ x = 6 \: \: and \: \: - 13[/tex]

Answer:

88%

Step-by-step explanation:

to initial price (100%) was increased by 10% (resulting in 110% of the initial price).

then these 110% were decreased by 20%.

so, the final price is actually 80% of 110% of the initial price

20/100 = 1/5

80/100 = 4/5

so, the customer pays only 4/5 of the 110% price.

110 × 4/5 = 22 × 4 = 88%

so, the final price was 88% of the initial price

Answer:

f(-5) = 7

Step-by-step explanation:

f(-5) means find the y value when x = -5

y = 7 when x = -5

Answer:

The quotient is 10x+16

The remainder is 28x²+10x+22

Step-by-step explanation:

Solution,

                              ___________________________

x^3 - 3x^2 + x - 2 ]    10x^4 - 14x^3 -  10x^2 +  6x  -  10   [ 10x + 16

                                 10x^4 - 30x^3 + 10x^2 -  20x

                                              16x^3   -  20x^2 + 26x  - 10

                                              16x^3  -  48x^2 + 16 x   - 32

                                                            28x^2  +  10x  + 22

Answer:

The quotient is 10x+16

The remainder is 28x²+10x+22

Step-by-step explanation:

Answer:

Option A, $65,280

Step-by-step explanation:

The volume of the tank is,

12×20×15+40×(50-15)×12

= 3600+16800

=20400 cubic meters

For each cubic meter, it costs $3.20, so for 20400 cubic meters it'll cost,

20400×$3.20

= $65,280

Answered by GAUTHMATH

Answer:

0.50=1.7. They do not equal each other

Step-by-step explanation:

Thats what I got from this question

Given:

The x- intercepts of a parabola are (0,-6) and (0,4).

The parabola crosses the y- axis at -120.

Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).

To find:

Whether Lucas is correct or not.

Solution:

The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.

[tex]y=a(x+6)(x-4)[/tex]             ...(i)

The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).

[tex]-120=a(0+6)(0-4)[/tex]

[tex]-120=a(6)(-4)[/tex]

[tex]-120=-24a[/tex]

Divide both sides by -24.

[tex]\dfrac{-120}{-24}=a[/tex]

[tex]5=a[/tex]

Substituting [tex]a=5[/tex] in (i), we get

[tex]y=5(x+6)(x-4)[/tex]

[tex]y=5(x^2+6x-4x-24)[/tex]

[tex]y=5(x^2+2x-24)[/tex]

[tex]y=5x^2+10x-120[/tex]

So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].

The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:

[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].

[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]

[tex]-\dfrac{b}{2a}=-1[/tex]

Putting [tex]x=-1[/tex] in the equation of the parabola, we get

[tex]y=5(-1)^2+10(-1)-120[/tex]

[tex]y=5-10-120[/tex]

[tex]y=-125[/tex]

So, the vertex of the parabola is at point (-1,-125).

Therefore, Lucas is correct.

Answer:

4 cans of paint

Step-by-step explanation:

Take the area of the wall and divide by the area that the can of pain will cover

10.37 / 3.1

3.34516129 cans

We need to round up to make sure we buy enough cans of paint

4 cans of paint

We can take area as,

Area = A

The required formula is,

→ A of wall ÷ A that paint's can will cover

Then find the no. of cans of paint that are needed to paint the wall.

Now use the formula,

→ A of wall ÷ A that paint's can will cover

→ 10.37 ÷ 3.1

→ 3.34516129032

→ 4 cans (by nearest value)

Hence, we need 4 cans to paint the wall.

Answer:

Obviously B

Step-by-step explanation:

Answer:

[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex] would ensure that at least one real root exists for this equation when solving for [tex]x[/tex].

Step-by-step explanation:

Apply the Pythagorean identity [tex]1 - \sin^{2}(x) = \cos^{2}(x)[/tex] to replace the cosine this equation with sine:

[tex](1 - \sin^{2}(x)) - (m^2 - 3)\, \sin(x) + 2\, m^2 - 3 = 0[/tex].

Multiply both sides by [tex](-1)[/tex] to obtain:

[tex]-1 + \sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 3 = 0[/tex].

[tex]\sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 2 = 0[/tex].

If [tex]y = \sin(x)[/tex], then this equation would become a quadratic equation about [tex]y[/tex]:

[tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex].

However, [tex]-1 \le \sin(x) \le 1[/tex] for all real [tex]x[/tex].

Hence, the value of [tex]y[/tex] must be between [tex](-1)[/tex] and [tex]1[/tex] (inclusive) for the original equation to have a real root when solving for [tex]x[/tex].

Determinant of this quadratic equation about [tex]y[/tex]:

[tex]\begin{aligned} & b^{2} - 4\, a\, c \\ =\; & (m^{2} - 3)^{2} - 4 \cdot (-2\, m^{2} + 2) \\ =\; & m^{4} - 6\, m^{2} + 9 - (-8\, m^{2} + 8) \\ =\; & m^{4} - 6\, m^{2} + 9 + 8\, m^{2} - 8 \\ =\; & m^{4} + 2\, m^{2} + 1 \\ =\; &(m^2 + 1)^{2} \end{aligned}[/tex].

Hence, when solving for [tex]y[/tex], the roots of [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] in terms of [tex]m[/tex] would be:

[tex]\begin{aligned}y_1 &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) + \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) + (m^{2} + 1)}{2} = 2\end{aligned}[/tex].

[tex]\begin{aligned}y_2 &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) - \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) - (m^{2} + 1)}{2} \\ &= \frac{-2\, m^{2} + 2}{2} = -m^{2} + 1\end{aligned}[/tex].

Since [tex]y = \sin(x)[/tex], it is necessary that [tex]-1 \le y \le 1[/tex] for the original solution to have a real root when solved for [tex]x[/tex].

The first solution, [tex]y_1[/tex], does not meet the requirements. On the other hand, simplifying [tex]-1 \le y_2 \le 1[/tex], [tex]-1 \le -m^{2} + 1 \le 1[/tex] gives:

[tex]-2 \le -m^{2} \le 0[/tex].

[tex]0 \le m^{2} \le 2[/tex].

[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

In other words,  solving [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] for [tex]y[/tex] would give a real root between [tex]-1 \le y \le 1[/tex] if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

On the other hand, given that [tex]y = \sin(x)[/tex] for the [tex]x[/tex] in the original equation, solving that equation for [tex]x\![/tex] would give a real root if and only if [tex]-1 \le y \le 1[/tex].

Therefore, the original equation with [tex]x[/tex] as the unknown has a real root if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

Answer:

About Points

S = (x,y)        searched point (it will be in the third quadrant )

M = (-2,0)      Midpoint | SP |

P = (3,5)        one end of the segment | SP |

You have to draw Cartesian.

we set in a point M and P. We both points by a simple and we extend it for the third quarter of the system. Compass measure the distance from the point M to the point P. From the point M we set a compass point S. Figure attached. Received point S = ( -7 , -5 ) . It sought a point that calculate .

We use the information that | SM | = | MP |

Answer : S = (-7,-5)

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad \underline{Q}(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+3}{2}~~,~~\cfrac{y+3}{2} \right)=\stackrel{M}{(-2,0)}\implies \begin{cases} \cfrac{x+3}{2}=-2\\[1em] x+3=-4\\ \boxed{x = -7}\\[-0.5em] \hrulefill\\ \cfrac{y+3}{2}=0\\[1em] y+3=0\\ \boxed{y=-3} \end{cases}[/tex]

Answer:

Given: DB = 7.2 cm, AE = 1.8 cm and EC = 5.4 cm and DE || BC.

DB

AD

=

AC

AE

[by basic proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same.

7.2

AD

=

5.4

1.8

AD=

5.4

7.2×1.8

AD=

10

24

⟹AD=2.4cm

13% of 11900 films are action films =1547 films.

Answer:

[tex]{ \tt{ = \frac{13}{100} \times 11900 }} \\ = 1547 \: action \: films[/tex]

Answer:

not a factorable number i think

Step-by-step explanation:

Answer:

5!= 120

13!= 6227020800

12!/6!= 665280

10!/7! 3!= 120

5(4!)= 120

Step-by-step explanation:

Answer:

x² + y² = 85

Step-by-step explanation:

Using the expansion

(x - y)² = x² + y² - 2xy , then

x² + y² - 2xy = (x - y)² ( add 2xy to both sides )

x² + y² = (x - y)² + 2xy ← substitute given values

          = 9² + 2(2)

          = 81 + 4

          = 85

Answer:

The correct answers are:

The variable p is the independent variable.

The number of hours spent reading causes a change in the number of pages read.

The variable p is the dependent variable.

Step-by-step explanation: Hope this helps :)))

These two statements are correct and applicable

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."

"A dependent variable is the variable that changes as a result of the independent variable manipulation."

"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"

We have,

Kelvin read 35 pages per hour

According to the question,

Number of hours increasing, number of pages also increasing

∵ The table data shows linear graph

We can clearly say that from a line graph definition,

These two are correct and applicable to Kelvin's situation

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

Learn more about Line graph and variable here

https://brainly.com/question/20106471

https://brainly.com/question/20291071

#SPJ2

Answer:

1 = Input G

2 = Input F

3 = Input H

Step-by-step explanation:

Answer:

∠3 = 142°

Step-by-step explanation:

L // M

∠2 = 38°    {Corresponding angles are congruent}

∠2 + ∠3 = 180   {Linear pair}

38 + ∠3 = 180

       ∠3 = 180 - 38

∠3 = 142°

the answer is 142 degrees, get 180 degrees from a straight lines and subtract the acute angle from 180 to get the answer, 180-38

Answer:

441 miles

Step-by-step explanation:

Rate of the Car: 819/13 = 63mph

Miles Driven in 7 Hours: 63*7 = 441 miles

Answer:

441 miles

Step-by-step explanation:

* means multiply

819/13 = x/7

13 * x = 819 * 7

13x = 5733

x = 5733 ÷ 13

x = 441