Solve the system of equations algebraically.

4x-3y = 8
5x-4y = 5

a. (16,21)

b. many solutions

c. No solution

d.(17,20)

Answer:

5/2 13/6 80/21

Step-by-step explanation:

the reciprocal is just flipping the fraction over, if they asked you to simplify its

4 1/2, 2 1/6, and 3 4/5  

The sequence of Transformation that could take figure 1 to figure 2 is; Translate by direct Line segment AD.

In the given graph, we can notice that figure 1 is exactly the same as figure two just that they are at different coordinates.

Now, to map figure 1 to figure two, what needs to be done is called translation. This is because In translation transformation, all the points in the object are moved in a straight line in the same direction.

Thus, the correct answer will be to translate by directed line segment AD.

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The quadrilateral that matches the characteristics is a square.

A quadrilateral is a 2 dimensional figure with 4 sides. Example of quadrilaterals are rectangle, rhombuses, square, parallelograms and many more.

Therefore, the quadrilateral that matches the characteristics is a square.

Properties of a square

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Answer: Both diagonals bisect each other.

The correct expansion of (4x-2)(2x² + 3) is 4x 2x² + 4x 3+ (-2) 2x² + (-2) 3.

The correct option is (C).

An expression is a set of terms combined using the operations +, – , x or ,/.

Given expression: (4x-2)(2x² + 3)

= 4x (2x² + 3) -2 (2x² + 3)

= 4x* 2x² + 4x * 3- 2* 2x² - 2*3

= 4x* 2x² + 4x *3+ (-2) *2x² + (-2)* 3

Hence, the correct expansion is 4x 2x² + 4x 3+ (-2) 2x² + (-2) 3.

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Answer:

5

Step-by-step explanation:

2 negatives will make a positive so 3-(-2) is equal to 3+2 and the answer is 5.

hope it helps

Answer:

Answer:

=5^(-4)*5^(-3)

=5^(-7)

=1/5^(7)

Step-by-step explanation:

i took the denominator and multiplied it to the numerator

when powers of the same base are multiplying we add the exponents, so I added the -3 to -4 and got -7 which gives me 5^(-7) which is 1/5^(7)

If the linear equation with one variable is x / 4 + 2 = –2. Then the value of x will be negative 16.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The equation is given below.

x / 4 + 2 = –2

Solving for x, we have

x / 4 + 2 = –2

     x / 4 = – 2 – 2

     x / 4 = – 4

          x = – 4 × 4

          x = – 16

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The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. The correct options are A, B, and, C.

The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. In other words, it is the point at which the internal angle bisectors of the triangle intersect.

The properties that are true about the incenter of a triangle are:

A. The incenter is equidistant from each side of the triangle.

B. The incenter of a triangle is always inside it.

C. The incenter is where all of the bisectors of the angles of the triangle meet.

Hence, the correct options are A, B, and, C.

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Answer:

1 - 135

2 - 45

3 - 45

4 - 135

5 - 135

6 - 45

7 - 45

8 - 135

Work Shown:

[tex]_{n} C _{r} = \frac{n!}{r!(n-r)!}\\\\_{25} C _{3} = \frac{25!}{3!*(25-3)!}\\\\_{25} C _{3} = \frac{25!}{3!*22!}\\\\_{25} C _{3} = \frac{25*24*23*22!}{3!*22!}\\\\ _{25} C _{3} = \frac{25*24*23}{3!}\\\\ _{25} C _{3} = \frac{25*24*23}{3*2*1}\\\\ _{25} C _{3} = \frac{13800}{6}\\\\ _{25} C _{3} = 2300\\\\[/tex]

6 / 2 =  3

Every 3 feet of shadow would be 1 foot of height of the tower.

171 feet/ 3 = 57

Answer: The tower is 57 feet tall.

The theorem that verifies that the two right angled triangles are similar is HA.

Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.

Analysis:

From the diagrams KL = OQ ( hypotenuse)

∠L is equal to ∠Q which are acute.

so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.

In conclusion, the HA theorem verifies that the two triangles are similar.

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The length of PC  is 6

Sure hope this helps you :D

Answer:

D

Step-by-step explanation:

the angle bisector divides the opposite side into segments that are proportional to the other 2 sides.

note that BP = 16 - PC , then

[tex]\frac{BP}{PC}[/tex] = [tex]\frac{AB}{AC}[/tex] ( substitute values )

[tex]\frac{16-PC}{PC}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex] ( cross- multiply )

4 PC = 5(16 - PC) ← distribute parenthesis

4 PC = 80 - 5 PC ( add 5 PC to both sides )

9 PC = 80 ( divide both sides by 9 )

PC = 8.888... ≈ 9 ( to the nearest whole number )

Answer:

Yes because 2(3) + 3 equals 9

Step-by-step explanation:

He correctly substituted x=3 into the equation and y=9. When working out both sides, he saw that both sides were equal to each other, so (3,9) is a solution!

Answer

720π cm²

Step-by-step explanation:

Surface area of cylinder

A=2πr(s+r)

for r=12cm, s=18cm

A= 2π×12(12+18)

=24π×30

=720π

Answer:

[tex]11x - 4[/tex]

[tex]11x {}^{1 - 1} [/tex]

[tex]11x {}^{0} [/tex]

[tex]11 \times 1[/tex]

[tex]x = 11[/tex]

After 15 seconds rocket reaches to maximum height is 225 units.

Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.

Here, the given equation of height

            h(t) = -t² + 30t

             y = -t² + 30t

Now, on differentiating both side with respect to t, we get

        dy/dt = -2t + 30

put dy/dt = 0, we get

       0 = -2t + 30

        2t = 30

        t = 15

Now, at t = 15 sec. rocket reach at its maximum height.

maximum height at t = 15 sec is

     h(15) = -(15)² + 30(15)

     h(15) = -225 + 450

    h(15) = 225

Thus, after 15 seconds rocket reaches to maximum height is 225 units.

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The time taken for the person to get to school based on the equation will be 7 minutes.

From the information given, the equation is given as:

g(x) = x⁴ - 3x² + 4x - 5

Then, we'll put 2 as x. This will be:

= 2⁴ + 3(2)² + 4(2) - 5

= 16 - 12 + 8 - 5

= 7

Therefore, the time taken for the person to get to school based on the equation will be 7 minutes.

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Answer:  Choice A

f(x) = (x + 2)^2 - 11

=========================================================

Work Shown:

y = x^2 + 4x - 7

y+7 = x^2 + 4x

y+7+4 = x^2 + 4x + 4

y+11 = x^2 + 4x + 4

y+11 = (x + 2)^2

y = (x + 2)^2 - 11

f(x) = (x + 2)^2 - 11

In the third step, I added 4 to both sides to complete the square for the x^2+4x portion. Notice that (x+2)^2 = x^2+4x+4. So I added 4 to fill in the missing piece needed to complete the square.

Put another way the '4' added to both sides is because we first divided the x coefficient 4 in half to get 4/2 = 2. Then you square it to get 2^2 = 4.

--------------------

Alternative Method (optional)

y = x^2 + 4x - 7 is in the form of y = ax^2+bx+c

where: a = 1, b = 4, c = -7

Plug those a,b values into the formula below

h = -b/(2a)

h = -4/(2(1))

h = -2

This is the x coordinate of the vertex.

Use it to find the y coordinate of the vertex.

y = x^2 + 4x - 7

y = (-2)^2 + 4(-2) - 7

y = -11

The vertex is located at (h,k) = (-2,-11)

We have the template y = a(x-h)^2 + k update to y = (x + 2)^2 - 11 after plugging in a = 1, h = -2, and k = -11.

Hi Student!

Looking at this problem, it's fairly simple and just asks us to determine whether x = 1 is a solution to the expression that was provided.  The first step that we must take to solving this is to plug in the value 1 for each of the places that we have x.  Then we simplify and look at the final expression and if it evaluates to true than x = 1 is a solution to the expression.

Plug in the values

Simplify both sides

Looking at the final expression that is shown, we can see that it states that 4 is greater than or equal to 4 which evaluates to true since 4 is equal to 4.  Therefore, x = 1 would be considered a solution of the expression that was provided in this problem.

Answer:

Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.

For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.

Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.

Draw squares on each of these sides.These squares have areas p²,b² and h².

For any right angled triangle with sides of length p,b and h;

[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]

[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]

From (i); p²=h²-b²

[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]

Similarly,

[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]

Step-by-step explanation:

[tex] \blue{ \frak{seolle_{aphr.odite} }}[/tex]

The relation that describes the graph {(-1, 3), (-2, 1), (-3, -3), (-4, -5)}

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of given graph:

Hence, the relation is {(-1, 3), (-2, 1), (-3, -3), (-4, 5)}.

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Proving that Triangle CDA is congruent to triangle CDB below:

Congruent triangles can be defined as triangles that have the same size and shape.

A congruent triangle, corresponding angles are equal also the corresponding sides are equal.

In conclusion, the proof that Triangle CDA is congruent to triangle CDB is given above

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Answer:

3x^2-5x+8 is the answers for the question

Step-by-step explanation:

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Answer:

62 degree

Step-by-step explanation:

A triangle has 180 degree

180 - (43 + 75) = 62