-3x+4y=2
-6x+6y=-3
solve by substitution method and explain steps please

The solution of the given quadratic equation is -2 ± √6.

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Solution of a quadratic equation ax² + b x + c = 0 can be found by,

x = [-b ± \(\sqrt{b^2-4ac}\)] / 2a, where \(b^2-4ac\) is called discriminant.

Given quadratic equation is x² + 4x - 2 = 0.

Discriminant = 4² - (4 × 1 × -2) = 16 + 8 = 24

x = [-4 ± √24] / 2

  = [-4 ± 2√6] / 2

  = -2 ± √6

Hence the solution of the given quadratic equation is -2 ± √6.

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The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

90

Step-by-step explanation:

Just multiply what the variables equal to

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}} }: \)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Solution}}} : \)

Plug the values of x , y & z in the given expression and then multiply !

⇾ \( \tt{2 \times ( - 5) \times ( - 9)}\)

⇾ \( \tt{( - 10) \times ( - 9)}\)

⇾ \( \tt{90}\)

\( \red{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \underline{ \tt{ 90}}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

The length of u to the nearest centimeter is about 30 cm.

We are given that;'

s = 730 cm, t = 270 cm and U=125°.

Now,

The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:

c2=a2+b2−2abcosC

To find c = u. Plugging in the values, we get:

u2=7302+2702−2×730×270×cos125°

Using a calculator, we get:

u2≈912.9

Taking the square root of both sides, we get:

u≈30.21

Rounding to the nearest centimeter, we get:

u≈30cm

Therefore, by the law of cosine the answer will be 30 cm.

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Answer:

see below

Step-by-step explanation:

D miles / M miles per gallon  = gallons used

Answer:

0.41

Step-by-step explanation:

p (A) = 0.2

P (B) =?

P (A or B) = 0.61

but P (A or B) = P (A) + P (B)

therefore P(B) = P (A or B) - P(B)

= 0.61 - 0.2

= 0.41

Answer:

n > p + 1 + 7k

Step-by-step explanation:

21k - 3n + 9 > 3p + 12

21k - 3n > 3p + 12 - 9

3n > 3p + 3

3n > 3p + 3 + 21k

n > (3p + 3 + 21k)/3

n > p + 1 + 7k

Answer:

what?

Step-by-step explanation:

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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Answer:

2.4

Step-by-step explanation:

If you replace m with 7, the expression is now 7-4.6.

7-4.6=2.4

The value of the expression is 2.4.

-hope it helps

Answer:

987 cm²

Step-by-step explanation:

We are given a figure which consists of the a triangle, a rectangle, and a semicircle.

To find the area of the figure, calculate the area of each shape that makes up the figure as follows:

=>Area of triangle: ½(a*b)

Leg a = 20cm

Leg b = 49-34 = 15cm

Area = ½(20*15) = 300/2

Area = 150 cm²

==>Area of rectangle: L*W

L = 34cm

W = 20cm

Area = 34*20 = 680cm²

==>Area of semicircle: ½πr²

r = ½ of 20cm = 10cm

Area = ½*3.14*10² = ½*3.14*100

Area = 314/2

Area = 157cm²

Area of the figure = 150+680+157 = 987 cm²

The country's area is 117% of Iowa's area, indicating that the country's area is 17% more than Iowa's area.

To find the percentage that represents the country's area in comparison to Iowa's area, we need to calculate the ratio of the country's area to Iowa's area and then express it as a percentage.

Let's assume that the area of Iowa is represented by x. According to the given information, the area of the country is 17% more than the area of Iowa. Therefore, the area of the country can be calculated as 1.17x (x + 17% of x).

To find the percentage of the country's area in comparison to Iowa's, we need to divide the area of the country by the area of Iowa and multiply the result by 100:

[(1.17x) / x] * 100

Simplifying this expression, we get:

(1.17 * 100) = 117

The country's area is 117% of Iowa's area.

The country's area is 117% of Iowa's area, indicating that the country's area is 17% more than Iowa's area.

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Answer:

Step-by-step explanation:

the "answer" below is why the brainly community, most of it atleast is shi

percent change = (new value - original value)/original value

= (16,700-12,500)/12,500

= 4,200/12500

= 0.336 * 100%

= 33.6% increase

12 : 16

divide by 4

3 : 4

that's it

The scale factor of for the given scaled reproduction of figure {P} to figure {Q} is 7/10.

A scale factor is used to dilate a given two - dimensional figure proportionally in a way such that the figures remain similar after the dilation but not congruent.

Given is figure {Q} is a scaled reproduction of figure {P}.

Since figure Q is a scaled reproduction of figure P, we can write the ratio of their corresponding sides as constant. So, we can write, the scale factor as -

K = 14/20

K = 7/10

Therefore, the scale factor of for the given scaled reproduction of figure {P} to figure {Q} is 7/10.

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{QUESTION IN ENGLISH -

Figure Q is a scaled reproduction of Figure P. What is the number by which the measurement of Figure Q must be multiplied to obtain Figure P?

Figure P

20cm

Figure Q

14cm

Answer:

she got: $117.25

Step-by-step explanation:

Total money she got after selling:

            \(8*5.75+10*6.25+5*\frac{2.5}{2} +2*\frac{1}{3} * 3.75\)

                    $117.25

Answer:

113.5 i hope its right

Step-by-step explanation:

plz give brainliest

Answer:

2x-5 if u want u can substitute any other variables and constant

Answer:

Well, if you are doubling a number with a product that can be decreased by 4 to go back to your original number, the answer to your question is 8.

Step-by-step explanation:

(4)(2 : double) = 8

8 - 4 = 4 (original number)

Answer: 10 minutes

Step-by-step explanation: the red line (company a) and the blue line (company b) intersect at the same point one time, at the $20 for 10 minutes point on the graph

Answer:

20$

Step-by-step explanation:

the lines Intersect on the 20

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

2.5

Step-by-step explanation:

First, you want to identify the slopes and y-int.

Equation 1 = y = -2x + 2

Slope = -2

y-int. = 2 or (0,2)

Equationt 2 =  y = 2x + 3

Slope = 2

Y-int.  = 3 or (0,3)

To graph, first plot the y-intercepts. Then do the slopes.

Slope = -2

Down 2 over 1 (to the right)

Slope = 2

Up 2 over 1 (to the right)

Then just connect the dots in a line!

The segment bisector of line segment XY is line n.

The length of the line segment XY is 6 units.

A line segment is a section of a line with two endpoints. A line segment, unlike a line, has a fixed length.

As per the given diagram in the question.

It is clear that the line segment XY is being divided by another line named n.

Thus,

The two segment of the line segment XY must be equal.

XM = MY

Substitute the values from the diagram;

5x + 8 = 9x + 12

Simplifying;

4x = -4

x = -1

Put the values in each segment;

XM = 5x + 8

XM = 5(-1) + 8

XM = 3 units.

Put the value in MY

MY = 9x + 12

MY = 9(-1) + 12

MY = 3 units.

As, it is clear from above values that the both segment are equal of 3 units each.

XY = XM + MY

XY = 3 + 3 = 6

Therefore, the value of XY is 6 units.

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