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Nata [24]
2 years ago
11

PLEASE HELP ME ITS TIMED!!

Mathematics
2 answers:
Sindrei [870]2 years ago
6 0

Answer:

x=40°

Step-by-step explanation:

(x-5)+(x+15)=90°

2x+10=90

2x=80

x=40°

atroni [7]2 years ago
5 0

Answer: x= 40⁰

Step-by-step explanation:

x+15+x-5=90

          2x= 90-10

             x= 80/2

             x= 40⁰

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How to graph -x+y=-6 , 3x+5y=2
Grace [21]
Solve for y for both
6 0
3 years ago
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0
3 years ago
PLEASE PLEASE HELP PLEASE
kogti [31]

Answer:

r = 6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

PR² = PQ² + QR² , substitute values

(r + 4)² = r² + 8²

r² + 8r + 16 = r² + 64 ( subtract r² from both sides )

8r + 16 = 64 ( subtract 16 from both sides )

8r = 48 ( divide both sides by 8 )

r = 6

3 0
2 years ago
A man 50 years old has 8 sons born of equal intervals. The sum of the ages of the father and sons is 186. What is the age of the
Rudiy27
<span>let x be the interval, then: 186 = 50 + 3 + (3+x) + (3+2x) + (3+3x) + (3+4x) + (3+5x) + (3+6x) + (3+7x) 186 = 74 + 28x x = 4 Eldest son age = 3+7x = 3+28 = 31.</span>
8 0
3 years ago
Calculus question....does anyone know how to solve this?
iogann1982 [59]
h(x)=(f\circ g)(x)
\sqrt{x+5}=\sqrt{g(x)+2}
x+5=g(x)+2
g(x)=x+3

Just to check this is correct:

(f\circ g)(x)=f(g(x))=f(x+3)=\sqrt{(x+3)+2}=\sqrt{x+5}=h(x)
6 0
3 years ago
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