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1 year ago

What is the solution to the system of equations graphed below?

Mathematics

2 answers:

MaRussiya [10]1 year ago

8 0

Answer:

The correct option is D.

Step-by-step explanation:

The given system of equations is

$y=-2x-3$ .... (1)

$y=3x+2$ .... (2)

The intersection point of both equation is the solution to the system of equations.

Substitute the value of y in equation (2) from equation (1).

$-2x-3=3x+2$

Isolate the like terms.

$-2x-3x=3+2$

$-5x=5$

Divide both sides by -5.

$x=-1$

The value of x is -1. Put this value in equation (1) to find the value of y.

$y=-2(-1)-3=2-3=-1$

The value of y is -1.

The solution to the system of equations is (-1,-1). Therefore the correct option is D.

RideAnS [48]1 year ago

7 0

D....................

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A customer purchased a total of 16 washcloths and towels. Each washcloth cost $10.50 and each towel cost $15.00. The customer sp

IgorC [24]

Answer:

Step-by-step explanation:

10.50 x 3 = 31.5

15 x 13 = 195

195 + 31.5 = 226.50

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1 year ago

A quadratic function has a line of symmetry at x = –3.5 and a zero at –9. What is the distance from the given zero to the line o

kap26 [50]

Given:

A quadratic function has a line of symmetry at x = –3.5 and a zero at –9.

To find:

The other zero.

Solution:

We know that, the line of symmetry divides the graph of quadratic function in two congruent parts. So, both zeroes are equidistant from the line of symmetry.

It means, line of symmetry passes through the mid point of both zeroes.

Let the other zero be x.

$-3.5=\dfrac{(-9)+x}{2}$

Multiply both sides by 2.

$-7=-9+x$

Add 9 on both sides.

$-7+9=-9+x+9$

$2=x$

Therefore, the other zero of the quadratic function is 2.

8 0

1 year ago

A triangular-shaped deck has one side that is 4 feet longer than the shortest side and a third side that is 4 feet shorter than

Inessa05 [86]

Answer:

The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.

Step-by-step explanation:

Assuming that the shortest side of this triangle has a length of "x" feet, then one side is "x + 4" feet and the third is "2*x - 4" feet. Since the perimeter of the deck is 80 feet, then the sum of the length of these sides should be equal to that.

$x + x + 4 + 2*x - 4 = 80\\4*x = 80\\x = \frac{80}{4} = 20 \text{ feet}\\$

The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.

8 0

2 years ago

What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFractio

aalyn [17]

Answer:

StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction

Step-by-step explanation:

Apparently you want to simplify ...

$\sqrt{\dfrac{72x^{16}}{50x^{36}}}$

The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

1/a^b = a^-b

(a^b)^c = a^(bc)

So the expression simplifies as ...

$\sqrt{\dfrac{72x^{16}}{50x^{36}}}=\sqrt{\dfrac{36}{25x^{36-16}}}=\sqrt{\dfrac{36}{25x^{20}}}\\\\\sqrt{\left(\dfrac{6}{5x^{10}}\right)^2}=\boxed{\dfrac{6}{5x^{10}}}$

9 0

1 year ago

Consider △RST and △RYX. If the triangles are similar, which must be true? A. RY/YS=RX/XT=XY/TS B.RY/RS=RX/RT=XY/TS C.RY/RS=RX/RT

trasher [3.6K]

Answer:

B.RY/RS=RX/RT=XY/TS

Step-by-step explanation:

If Triangles RST and RYX are similar, then the ratio of their corresponding sides is:

$\dfrac{RS}{RY}= \dfrac{ST}{YX}=\dfrac{RT}{RX}\\$This could also be written by switching the numerator and denominators as:\\\dfrac{RY}{RS}= \dfrac{XY}{TS}=\dfrac{RX}{RT}$

Out of the given options, Option B is true.

3 0

2 years ago