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2 years ago

What is the answer for question 1 and how

Mathematics

2 answers:

Evgesh-ka [11]2 years ago

8 0

CAB= 180-42= 138/2= 69° as base angles of an isosceles triangle are equal
CAO= 90 as radius meets the tangent at 90°
OAB = 90-68= 21°
AOB= 180-(21+21)
=180-42= 138°
a²= b²+c²-2bcCosA
AB²= 7²+7²-2x7x7Cos138
AB²= 170.8281929
AB= √170.8281929
AB= 13.07012597cm
Or 13.1 to 3sf

quester [9]2 years ago

4 0

Step-by-step explanation:

ABC is an isoceles triangle (both legs are equally long). and AB is its baseline.

OC is now a median for ABC splitting the angle at C and AB in half.

so, we have 2 right-angled triangles : OAC and OBC.

the half-angles at C are 42/2 = 21°.

the angles at A and B are 90°.

and the half-angles at O are 180 - 90 - 21 = 69°.

remember that the sum of all angles in a triangle must always be 180°.

AB are the heights of both of these triangles.

the single height is sin(69)×7 = 6.535062985... cm

and so,

AB = 2× height = 13.07012597... cm.

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Write a linear equation based on given information. Through (5,-5) and (4,0)

Katena32 [7]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope of the line

b: It is the cut point with the y axis

We have the following points:

$(x_ {1}, y_ {1}) :( 5, -5)\\(x_ {2}, y_ {2}) :( 4,0)$

We find the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0 - (- 5)} {4-5} = \frac {5} {- 1} = - 5$

Thus, the equation is of the form:

$y = -5x + b$

We substitute a point and find b:

$0 = -5 (4) + b\\0 = -20 + b\\b = 20$

Finally, the equation is:

$y = -5x + 20$

Answer:

$y = -5x + 20$

6 0

3 years ago

Suppose that Upper X has a discrete uniform distribution f left-parenthesis x right-parenthesis equals StartLayout left-brace1st

emmasim [6.3K]

Answer:

the probability that the sample mean is greater than 2.1 but less than 2.4 is 0.2444

Step-by-step explanation:

Given the data in the question;

x f(x) xp(x) x²p(x)

1 1/3 0.33333 0.33333

2 1/3 0.66667 1.33333

3 1/3 1.00000 3.0000

∑ 2.0000 4.6667

∑(xp(x)) = 2

∑(x²p(x)) = 4.6667

Variance σ² = ∑(x²) - ∑(x)² = 4.6667 - (2)² = 4.6667 - 4 = 0.6667

standard deviation σ = √variance = √0.6667 = 0.8165

Now since, n = 33 which is greater than 30, we can use normal approximation

for normal distribution z score ( x-μ)/σ

mean μ = 2

standard deviation = 0.817

sample size n = 33

standard of error σₓ = σ/√n = 0.817/√33 = 0.1422

so probability will be;

p( 2.1 < X < 2.4 ) = p(( 2.1-2)/0.1422) < x"-μ/σₓ < p(( 2.4-2)/0.1422)

= 0.70 < Z < 2.81

= 1 - ( 0.703 < Z < 2.812 )

FROM Z-SC0RE TABLE

= 1 - ( 0.25804 + 0.49752 )

= 1 - 0.75556

p( 2.1 < X < 2.4 ) = 0.2444

Therefore, the probability that the sample mean is greater than 2.1 but less than 2.4 is 0.2444

7 0

3 years ago

Find the equation of the line through (6,4) and (-3,-8)

alexdok [17]

Answer:

y = 4/3x - 4

Step-by-step explanation:

to find the equation of a line with 2 points, we use the slope formula which is:

$\frac{y_2-y_1}{x_2-x_1}$

we will use (6,4) as $x_1[tex] and [tex]y_1$ and we will use (-3,-8) as $x_2[tex] and [tex]y_2$ . we plug this into the slope formula:

$\frac{-8-4}{-3-6}$

-8 - 4 = -12

-3 - 6 = -9

the slope is $\frac{-12}{-9}$

but we can simplify this further by dividing the fraction by -3

-12 / -3 = 4

-9 / -3 = 3

the simplified version of the slope is $\frac{4}{3}$

we can write this in slope-intercept form which is y =mx + b, with b being the y intercept and m being the slope

y = 4/3x + b <--- we need to solve for <em>b</em> in order to find the y intercept, so substitute x & y for a point on the line, we can use any point we are given, but for this example i will use (6,4)

4 = 4/3(6) + b < multiply 4/3 x 6

4 = 8 + b < subtract 8 from both sides

-4 = b

our y intercept would be (0,-4)

the equation looks like the following:

y = 4/3x - 4, which is our answer

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3 years ago

Can someone tell me what the answer for this problem is? (and how you are able to get that answer)

exis [7]

$\bf y=\cfrac{1}{2}(x-7)(x-7)$

now, if you set y to 0, so you can solve for "x", you'll notice, you'll get 7 twice, you can see it from (x-7) twice there, it has that root twice.

so, when x = 7, y = 0, that's the x-intercept, or so-called a solution or zeros.

now, it happens twice though, so, that simply means, the root of 7 has a multiplicity of 2 and is an even multiplicity, and even number, and when that happens, the graph doesn't really cross the x-axis, it simply bounces off of it.

so the graph goes down down, gets to 7, bounces back up, well, it made a U-turn, that's the vertex, at 7,0 as well.

to find the y-intercept, simply set x = 0, let's do so

$\bf y=\cfrac{1}{2}(x-7)(x-7)\implies y=\cfrac{1}{2}(0-7)(0-7)\implies y=\cfrac{1}{2}(-7)(-7)
\\\\\\
y=\cfrac{49}{2}\implies y=24.5$

so is at 0, 24.5

the stretch will be the coefficient in front of the function, in this case is 1/2, is stretches in relation to the y-axis by twice as much.

7 0

3 years ago

Please help me and make sure to show your work

irina1246 [14]

Answer: C 20

Explanation: Plug in 2 for k.

2^2 - (2-10) + 4(2) = 20

4 0

3 years ago

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