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3 years ago

Find the value of x in each case. Give reasons to justify your solutions! D ∈ AC

Mathematics

1 answer:

postnew [5]3 years ago

7 0

Answer:

x = 25 degrees.

Step-by-step explanation:

By the external angle of a triangle theorem x + <C = 50

But x = <C ( alternate angles).

Therefore 2x = 50

x = 25.

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Factor the trinomial 10x^2+11X-6

yan [13]

Answer:

Not factorable with rationable numbers

Step-by-step explanation:

You cannot factor this expression with rationable numbers.

6 0

3 years ago

Read 2 more answers

What is the radius of circle c

Oxana [17]

Answer:

radius = 13

Step-by-step explanation:

Look at the attached picture below. We can calculate radius with the help of the Pythagorean theorem. But first we have to find out the values of the two legs.

First let's find the shorter leg.

Equidistant Chords Theorem

Two chords are congruent if they are equidistant from the center.

Chords in the picture are congruent and that means that the distance from the center to each of them is the same!

Let's calculate the distance. But to get the distance we have to find x first.

Since the distances are the same:

$x + 3 = 2x + 1\\2 = x$

Therefore:

$\text{distance (short leg)} = 2x + 1 = 2\cdot2 + 1 = 5$

Let's focus on the longer leg. Since part of the radius is perpendicular to the chord, it actually bisects the chord! That means that the long leg is going to be a half of the length of the chord.

Therefore:

$\text{long leg} = \frac{\text{chord}}{2} = \frac{24}{2} = 12$

All that is left is the Pythagorean Theorem in the right triangle.

Pythagorean Theorem

$\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2$

Hypotenuse in our case is the radius.

$\text{radius}^2 = 5^2 + 12^2\\\text{radius}^2 = 25 + 144\\\text{radius}^2 = 169\\\text{radius} = 13$

7 0

2 years ago

Samuel charged me d dollars to fix my broken heater. He

juin [17]

Answer:

$15 per hour

Step-by-step explanation:

Since he charged $65 for the parts, and the total charge was $110, that's $110-$65 which is $45, the total hours was 3, so $45 divided by 3, and that equals $15.

3 0

3 years ago

What is the Y-intercept of (y-3)=1/3(x+4)

Debora [2.8K]

Answer: 0,13/3

Step-by-step explanation: Hope this helps - Lily ^_^

3 0

3 years ago

Find the equation of a line through (3, 1) and perpendicular to 10x + 3y = 5

Illusion [34]

Answer:

y = (3/10)x + 1/10

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. First, we need to rearrange the given equation to determine the slope of the original line.

10x + 3y = 5 <----- Original equation

3y = -10x + 5 <----- Subtract 10x from both sides

y = (-10/3)x + 5 <----- Divide both sides by 3

Now, we can tell that the slope of the original line is m = -10/3. The perpendicular line should have an opposite-signed, reciprocal slope to that of the original. Therefore, the new slope is m = 3/10.

We can find the value of "b" by plugging the new slope and values from the Point (3, 1) into slope-intercept form.

m = 3/10

x = 3

y = 1

y = mx + b <----- Slope-intercept form

1 = (3/10)(3) + b <----- Insert values

1 = 9/10 + b <----- Multiply 3/10 and 3

10/10 = 9/10 + b <----- Create common denominators

1/10 = b <----- Subtract 9/10 from both sides

Now that we know the values for "m" and "b", we can construct the equation of the perpendicular line.

y = (3/10)x + 1/10

3 0

2 years ago