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AlexFokin [52]
4 years ago
8

Without drawing the graphs, find the points of intersection of the lines: a 7x+4y=23 and 8x–10y=19

Mathematics
1 answer:
emmainna [20.7K]4 years ago
8 0

Answer:

(3,0.5)

Step-by-step explanation:

The given system has equations:

7x + 4y = 23 \\ 8x - 10y = 19

Let us multiply the second equation by 4 and the first equation by 10.

70x + 40y = 230 \\ 32x - 40y = 76

We add both new equations to get:

102x = 306 \\ x =  \frac{306}{102}  = 3

Put x=3 into the first equation and solve for y.

7(3) + 4y = 23 \\ 21 + 4y = 23 \\ 4y = 23 - 21 \\ 4y = 2 \\  y =  \frac{1}{2}

The point of intersection is the solution to the system of equation which is (3,0.5)

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Find the length of side x simplest radical form with a rational denominator
Nuetrik [128]

Answer:

The length of x in the simplest radical form with a rational denominator will be:      

  •       x=\frac{5\sqrt{3}}{2}

Step-by-step explanation:

Given

hypotenuse = 5

angle Ф = 60°

To determine

x = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

Ф = 60°

adjacent of 60° = x

hypotenuse = 5

so substituting Ф = 60°, adjacent = x and hypotenuse = 5 in the equation

cos Ф = adjacent / hypotenuse

so

cos\:60^{\circ }\:=\:\frac{x}{5}

       \frac{\sqrt{3}}{2}=\frac{x}{5}

switch sides

         \frac{x}{5}=\frac{\sqrt{3}}{2}

Multiply both sides by 5

         \frac{5x}{5}=\frac{5\sqrt{3}}{2}

Simplify

         x=\frac{5\sqrt{3}}{2}

Therefore, the length of x in the simplest radical form with a rational denominator will be:      

  •       x=\frac{5\sqrt{3}}{2}
5 0
3 years ago
|-1 1/5| and |-3/5| from least to greatest
ZanzabumX [31]

Answer:

3/5 then 11/5

Step-by-step explanation:

These symbols "I  I" represent absolute values.

11/5 equals to 2 1/5

3/5 is less than 2 1/5

4 0
4 years ago
What is the leading coefficient of this polynomial when written in standard form?<br><br> 1-2x+5x^4
Goshia [24]

Answer:

5!!

Step-by-step explanation:

When writing the polynomial in standard form, we have:

5X⁴ - 2X + 1

The leading coefficient is 5, since it's part of the term with the highest degree.

6 0
3 years ago
Giving brainless &lt;33
ipn [44]

Answer: 87 percent

Step-by-step explanation:

Pls give brainliest (:

8 0
3 years ago
PLEASE HELP ASAP! What is the r-value of the following data, to three decimal places?
Kobotan [32]
A) Find the Sum of the X values: 4 +5+8+9+13 = 39

B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56

C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355

D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858

E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339

N = number of sets = 5

Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8

Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) = 
SQRT(355-39^2/5) x SQRT(858-56^2/5) =
SQRT(50.8) x SQRT(230.8) =
7.1274 x 15.1921 =
108.2803

r = -97.8 / 108.2803

r = -0.903

 Answer is A

5 0
4 years ago
Read 2 more answers
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