Which equation represents a line that passes through the two points in the
table?

For the triangle ABC, if B or C is an obtuse angle, then a = b cos C + c cos B  according to the law of sines and the addition formula.

For a triangle ABC with angles ∠A, ∠B, and ∠C and with sides a, b, and c

Thus, we can write,

sinA/a = sinB/b = sinC/c

or

a/sinA = b/sinB = c/sinC

It is given that in a ΔABC,

The ∠B or ∠C is an obtuse angle.

So, ∠A = 180° - (B + C)

⇒ sin A = sin (180° - (B + C))

⇒ sin A = sin (B + C) (since we know that sin(180° - θ) = sinθ)

From the addition formula,

sin (B + C) = sin B cos C + sin C cos B

⇒ sin A = sin (B + C)

⇒ sin A = sin B cos C + sin C cos B

From the law of sines,

a/sinA = b/sinB = c/sinC = K

⇒ aK =sin A, bK = sin B, cK = sin C

On substituting,

⇒ sin A = sin B cos C + sin C cos B

⇒ aK = bK cos C + cK cos B

⇒ K(a) = K(b cos C + c cos B)

∴ a = b cos C + c cos B

Hence it is proved.

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Answer:

12 yd^2 (c)

Step-by-step explanation:

A=1/2bh

= 1/2 x 8 x 3

=12 yd^2

Hope it helps!!!

Answer: 12 yd^2

Step-by-step explanation:

Area=[tex](1/2) *base*height\\[/tex]

here

base= 8yd

height =3 yd

putting values

area=(1/2)*(8)*(3)

area=12 yd^2

By applying Pythagorean's theorem, the missing side of this right-angled triangle is: A. 7√3 inches.

By critically observing the triangle shown in the image attached below, we can logically deduce that it is a right-angled triangle. Thus, we would find the missing side by applying Pythagorean's theorem:

z² = x² + y²

Also, the sides of this right-angled triangle are:

Substituting the given parameters into the formula, we have;

14² = x² + 7²

196 = x² + 49

x² = 196 - 49

x² = 147

x = √147

x = √49 × √3

x = 7√3 inches.

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Answer:

A.)  7√3 in

Step-by-step explanation:

I got it correct on founders edtell

The equation of the perpendicular line as required is; y = 2x -3.

Since the line in discuss is perpendicular to the given line whose slope is; -1/2. It therefore follows that the slope of the line to be determined is;

m = -1/(-1/2) = 2.

The equation of the required line can therefore be written as;

2 = (y-7)/(x-2)

2x -4 = y -7

Hence, y = 2x -3 is the equation of the line.

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Answer: 9

Step-by-step explanation:

 Given:

n², n = 3

  Plug-in:

(3)²

  Square 3:

3 * 3 = 9, so (3)² = 9

  Simplify:

9

Answer:

0

Step-by-step explanation:

First, lets solve what's in the parentheses.

(6-2) = 4

(3-3) = 0

(3-6) = -3

Now, we put that into the equation.

4*0*-3

We get 0

Answer:

f(x)=x²-3x-10

Step-by-step explanation:

\begin{gathered}f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\end{gathered}

f(x)=x

2

−3x−10

tofindxinterceptorzerosubstitutef(x)=0

0=x

2

−3x−10

x

2

−3x−10=0

x

2

+2x−5x−10=0

x(x+2)−5x−10=0

x(x+2)−5(x+2)=0

(x+2).(x−5)=0

x+2=0

x−5=0

x=−2

x=5

therefore the zeros of the equation are x₁=-2,x₂=5

AB = AC, they are equivalent. Since an isosceles triangle has the congruent angle property, mB = mC cannot be shown until AB=AC.

Generally, Isosceles triangles are those that have two sides that are equal in length and two angles that are also equal in size.

Hence The sides and angles theorem for triangles., and the side AB is equal to the other side AC,

In conclusion, Assuming that the base angles, mB, and mC, are of equal measure, the triangle sides and angles theorem states that segment AC is larger than AB. The bigger angle of a triangle is always opposite to the longer side, according to the theorem.

AB is congruent to AC cannot be proven unless AB=AC then,

m<B = m<C because the isosceles triangle has the congruent angle property

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Answer:

AB = AC

Triangle parts relationship theorem

side AB is congruent to side AC

angle B is congruent to angle c

Step-by-step explanation:

Answer:

ok this is pretty simple we just have to look at the chart

8 like hot dog

10 like salad

10-8=2

Hope This Helps!!!

Answer:B.2

Step-by-step explanation:

Answer:

The 3rd-grade teacher should say that the school systems and ways of teaching get updated each year.

Step-by-step explanation:

Children's parent's schools would have probably taught different techniques and ways of learning a topic. As years go by, more efficient ways of learning that topic are presented and selected.

If the parent would like the child to learn that way, they may teach them at home, but the school has decided on a system for at-school learning that seems to have worked the best.

Hopefully, that should answer the parent's questions!

Answer:

29893

Step-by-step explanation:

167 x 179

Step-by-step explanation:

sin if -7.2 = -0.79 approximately -0.8

Hope you understand and hope this helps.

Good luck ✅.

Answer:

x = 3y + 4

Step-by-step explanation:

add 4 to both sides

simplify

Answer: J

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

[tex]\frac{3x-9}{x+8}=\frac{45}{30}=\frac{3}{2}\\\\2(3x-9)=3(x+8)\\\\6x-18=3x+24\\\\3x-18=24\\\\3x=42\\\\x=14\\\\\implies YX=14+8=22[/tex]

The amount of money in the account if compounded quarterly at 6% after 9 years is $22,217

A = P(1 + r/n)^nt

= 13,000(1 + 0.06/4)^4×9

= 13,000(1 + 0.015)^36

= 13,000(1.015)^36

= 13000(1.709)

= $22,217

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The number of terms in the expression given is; 2.

It follows from the task content that the expression given is; (3x^2-3)(3x^2+3).

It therefore follows the converse of law regarding difference of two squares that the expression given can be rewritten as;

= 9x⁴ -9

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Answer:

Step-by-step explanation:

For there to be no solution, the graphs must never intersect.

An equation is formed of two equal expressions. The graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of a pair of equations is the point at which the graph of the two functions intersects each other. The number of times the two graphs intersect is the number of solutions to the pair of equations.

Since there are only two graphs where the graphs do not intersect.

Thus, the graphs that indicate that the equation has no solution are the first graph from the top row and the last graph from the second row.

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El resultado de esta división es 0.010

Para solucionar la operación matemática debemos realizar los siguientes pasos:

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Answer:

x-7y

Step-by-step explanation:

7x-9y-6x+2y

Combine like terms

7x -6x    -9y +2y

x       -7y

x-7y

Answer:

x -7y

Step-by-step explanation:

7x - 9y - 6x + 2y

Rearrange so like terms are together (these are terms that are similar such as 5b and 7b; 7 and 1)

7x - 6x - 9y + 2y

Group into brackets one-by-one and solve

(7x-6x) -9y + 2y

x -9y + 2y

x (-9y + 2y)

x -7y

Note that 1x, 1b, 1z etc are simply written as their variable eg x, b and z

The correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.

The degree of a polynomial is the highest power of the variable in the expression.

In the expression 5x + 3x⁴ - 7x³ + 10, there are 4 terms, and the term 3x⁴ involves the highest power = 4.

Therefore, the degree of the polynomial is 4.

Hence, we can say that the correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.

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Answer:

The unknown length = 12 units.

Step-by-step explanation:

The small and large triangles are similar because of the parallel lines.

So

6 / (6+4) = x / 20

10x = 120

x = 12.

Select a random sample of 35 unmarried and 15 married subjects

A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried.

To achieve stratified random sampling in a sample of 50 subjects, the researcher will:

Select a random sample of 35 unmarried and 15 married subjects.

hence, Select a random sample of 35 unmarried and 15 married subjects.

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Answer:

81/4

Step-by-step explanation:

By the Pythagorean theorem, the length of the altitude drawn from the hypotenuse is

[tex] \sqrt{65} [/tex]

This means that by the geometric mean theorem, that out of the two segments the hypotenuse is split into, the one with unknown length has length 65/4.

Thus, x = 65/4 + 4 = 81/4.

The distance between  (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]

The point is given as:

(x, y, z) = (-4,3,-6)

The origin is

(x, y, z) = (0,0,0)

The distance between the point and the origin is calculated as:

[tex]d = \sqrt{x^2 + y^2 + z^2[/tex]

So, we have:

[tex]d = \sqrt{(-4)^2 + (3)^2 + (-6)^2[/tex]

Evaluate

[tex]d = \sqrt{61[/tex]

Hence, the distance between  (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]

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Answer: x = 80°

Step-by-step explanation:

Hi,

Since the angle is bisected, that means it is split in half and that both sides equal each other.
Therefore,

50 = 1/2x + 10

subtract 10 from both sides

40 = 1/2x

divide 40 by 1/2

x = 80°

Hope this helped :)

Graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is

Which graph shows a system of equations with a solution at (2,-1)?

The graph is in the picture, please refer to the attached picture.

As we can see in the graph there are two graphs of a function shown.

The first one is a parabola and the second one is a linear graph.

From the graph, the intersection point of the two groups is at (2, -1)

The intersection point is shown in graph fourth.

Thus, graph fourth shows a system of equations with a solution at (2, -1) option fourth is correct.

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Answer:

Graph 4

Step-by-step explanation:

The percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.

The standard deviation of a data set is defined as how the data is dispersed in relation to the mean.

From the question,

The raw time given (X) = 14.4 sec

The mean value(m) = 18sec

The standard deviation(d) = 1.2 sec

Using the formula,

z = X - m/ d

z= 14.4- 18/1.2

z = -3.6/1.2

z= -3

Using a Z table to find the percentage equivalent of P(x<14.4) is 0.0013499 which is approximately = 0.15%.

Therefore, the percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.

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All the points which are at the distance of PQ from the center of the circle will be located on the circle.

A circle is a closed shape created by following a moving point on a plane while maintaining a constant distance from another point.

According to the given question, the circle named A has it's center at the point P and has a point Q on the circumference of the circle, so any point at the distance of PQ from the center of the circle will lie on the circumference of the circle.

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Answer:

Points S, T, and W

Hope this helps!

Step-by-step explanation: