All categories

3 years ago

X + 4y = 23 -2x + 3y = -2

Mathematics

1 answer:

astraxan [27]3 years ago

6 0

Answer:

(x, y) = (7, 4)

Step-by-step explanation:

I find a graphing calculator to give a solution quickly and easily.

(x, y) = (7, 4)

Here, we can solve the first equation for x, then substitute into the second.

x = 23 -4y

-2(23 -4y) +3y = -2 . . . . . substitute for x

-46 +8y +3y = -2 . . . . . eliminate parentheses

11y = 44 . . . . . . . . . . . collect terms

y = 4 . . . . . . . . . . . . divide by the coefficient of y

x = 23 -4·4 = 7 . . . . use the expression for x to find x

(x, y) = (7, 4)

You might be interested in

What is the general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12)?

ki77a [65]

The general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12) is x²-4x+7.

<h3>What is the vertex form of a quadratic equation?</h3>

Vertex form of the quadratic equation is used to find the coordinate of vertex points at which it crosses its symmetry.

The standard equation of the vertex form of quadratic is given as,

$y=a(x-h)^2+k$

Here, (h, k) is the vertex point.

The vertex of quadratic at (2, 3) and passing through the point (5, 12). Put the value of vertex point in the above equation,

$y=a(x-2)^2+3$

As the quadratic passes through the point (5, 12). Thus, put the value of this point,

$12=a(5-2)^2+3\\12-3=a(3)^2\\9=a\times9\\a=\dfrac{9}{9}\\a=1$

Put the value of <em>a</em> in the above expression,

$y=1(x-2)^2+3\\y=(x-2)^2+3\\y=x^2-4x+4+3\\y=x^2-4x+7$

Thus, the general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12) is x²-4x+7.

Learn more about the vertex form here;

brainly.com/question/17987697

#SPJ1

4 0

3 years ago

11/40ths simplified in fractions

777dan777 [17]

11/40 is a fraction, and it is already in the simplest form. This is because they don't have any common factors, which means we can't use the GCF, greatest common factor, to divide each number. So 11/40 is already in simplest form.

So, 11/40ths is already in simplest form.

Hope I helped ya!! xD<span />

5 0

4 years ago

Read 2 more answers

Given: angle Q is congruent to angle T and line QR is congruent to line TR

Ainat [17]

3. <u>Two angles and included side (ASA congruence theorem)</u>.

<u>Reason:</u> This is because, it is given that angle Q is congruent to angle T and line QR is congruent to line TR. Also, we proved in step 2 that $\angle PRQ\cong\angle SRT$ . Thus, we have two angles and the side included as congruent and thus, the two triangles are congruent.

4. <u>CSCT (Corresponding Sides of a Congruent Triangle)</u>

<u>Reason:</u> PR and SR are the corresponding sides of the congruent triangles $\Delta PRQ$ and $\Delta SRT$ , therefore, by the CSCT these corresponding sides have to be congruent.

3 0

4 years ago

Adult tickets to space amusement parkcost x dollars. Children's tickets cost y dollars. The henson family bought 3 aduly and 1 c

vesna_86 [32]

Answer:

3x + 1y = $163

2x + 3y =$174

Step-by-step explanation:

Adult tickets to space amusement park cost x dollars children’s tickets cost y dollars.

Henson family bought 3 adults and 1 child's tickets for $163

x + y = 163

3x + 1y = 163

The Garcia family bought 2 adults and 3 child’s ticket for $174.

x + y = $174

2x + 3y = $174

Therefore the equations representing both families cost are

Henson family

3x + 1y = $163

Garcia family

2x + 3y = $174

3 0

4 years ago

50 people were asked if they speak French or German or Spanish. Of these people, 31 speak French, 2 speak French, German and Spa

deff fn [24]

The probability that they both only speak Spanish is P = 0.005

<h3>How to find the probability?</h3>

There are 50 people.

We know that:

31 of these speak French.
2 speak French, German, and Spanish.
4 speak French and Spanish.
7 speak German and Spanish.
8 speak any of the lenguages.
10 speak german (and also other lenguages).

Then, the number that speaks only Spanish is:

50 - (31 + 10 + 8 - 3) = 4

(this is, the total number of people minus the ones that speak the other (or neither) lenguages, the "-3" appears there because 3 of the ones that speak German also speak French)

Then the probability that the first randomly selected person speaks Spanish is equal to the quotient between the number that speaks Spanish and the total number:

p = 4/50

For the next person we compute the probability in the same way, but this time there are 3 people that talk Spanish and 49 people in total:

q = 3/49

The joint probability is the product of the two individual ones:

P = (4/50)*(3/49) = 0.005

If you want to learn more about probability:

brainly.com/question/25870256

#SPJ1

4 0

2 years ago