How do you Simplify a4 x a5

Answer:

x=-5, x=1

Step-by-step explanation:

y=x-8/x^2+4x-5

[tex]y=\frac{x-8}{x^2+4x-5}[/tex]

When denominator becomes 0 in a rational function then there will be a break in the graph

To find any points of discontinuity for the rational function , we set the denominator =0 and solve for x

x^2 + 4x -5 =0

Now we factor x^2 +4x -5

product is -5  and sum = 4

5 * (-1) = -5

5 +(-1) = 4

(x+5)(x-1) =0

set each factor =0 and  solve for x

x+5=0 , so x= -5

x-1=0 , so x= 1

x=-5, x=1 are the points of discontinuity for the rational function

Answer:

x=-5 , X=1

Step-by-step explanation:

we are given

m∠BCD =67

and  m∠BDC=60

we know that

m∠ABC is exterior angle

m∠BCD  and  m∠BDC are interior angles

exterior angle is sum of interior angles

so, we can write it as

m∠ABC=m∠BCD+m∠BDC

now, we can plug values

and we get

m∠ABC=60+67

m∠ABC=127

so, option-4.........Answer

Answer:

8x+2

fx= 8x+2

Step-by-step explanation:

Answer: x= -4, 4

Step-by-step explanation:

Answer:

Adjacent angles whose exterior sides are opposite rays are "supplementary"

Step-by-step explanation: Theorem 3-2 states this fact

Answer:

4.6

Step-by-step explanation:

Answer:  The art club president need to buy 14 bottles of paint for the project.

Step-by-step explanation:  Given that each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles.

We are to find the number of bottles of paint that the art club president need to buy for the project.

We will be using the unitary method to solve the given problem.

Number of bottles filled by 8 ounces of paint = 1.

So, the number of bottles filled by 1 ounce of paint is

[tex]\dfrac{1}{8}.[/tex]

So, the number of bottles filled by 4 ounces of paint will be

[tex]\dfrac{1}{8}\times4=\dfrac{1}{2}.[/tex]

Now, number of bottles of paint needed by 1 student [tex]=\dfrac{1}{2}.[/tex]

Therefore, the number of bottles of paint needed by 14 students will be

[tex]\dfrac{1}{2}\times14=7.[/tex]

Thus, the art club president need to buy 14 bottles of paint for the project.

Answer:

y=x^2-6x+13

Step-by-step explanation:

The second equation, representing the total cost of both apples as 0.75d + 1.25g = 21.

Given is that Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples.

Assume that the number of Delicious apples are (d) and Golden Delicious are (g) apples.

We can write the second equation as -

0.75d + 1.25g = 21

and the first equation as -

d + g = 22

Therefore, the second equation, representing the total cost of both apples as 0.75d + 1.25g = 21.

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If y varies directly as x, the expression that can used to determine the value of y when x is 11 is y = 18/5 × 11 .

The equation that can be used to represent direct variation is:

y= kx

Where:

k = y/x

k = 18/5

y = 18/5 × 11

To learn more about direct variation, please check: https://brainly.com/question/4838941

Quadrilateral ABCD undergoes a series of transformations to become A’’B’’C’’D’’.

The first transformation is a reflection over the y-axis.

The coordinate of C’ would be (-6,3) in this case.

If the image is rotated counter clock wise around the point A then it will result in the final image which is presented in the attached figure.

Hope this helps ..!!

Thank you :)

The correct answer is option c) 624.99

To find the sum of the first eight terms of the series: (-500) + (-100) + (-20) + (-4) + (-0.8) +..., we first need to recognize that this is a geometric series where each term is a constant multiple of the previous term.

The first term (a) is -500, and the common ratio (r) can be found as follows: [tex]r = \frac{-100}{\ 500} = \frac{1}{5} \ or\ 0.2.[/tex]

Geometric Series Sum Formula

The sum ([tex]S_n[/tex]) of the first n terms of a geometric series is given by the formula:

[tex]S_n = a * \frac{1-r^n}{1-r}[/tex]

Here, a = -500, r = 0.2, and n = 8.

The sum of the first eight terms of the series, rounded to two decimal places, is -624.99.

The complete question is:

What is the sum of the first eight terms of the series?

(−500)+(−100)+(−20)+(−4)+(−0.8)+...

Round the answer to two decimal places if necessary.

a) −996.09

b) −625

c) −624.99

d) −623

Final answer:

To produce an irrational number by multiplying by 1/5, the other number must be irrational, such as √2.

Explanation:

The student is asking which number, when multiplied by 1/5, produces an irrational number. To produce an irrational number by multiplication, the other number must itself be irrational. Because rational numbers multiplied by rational numbers yield rational results. A classic example of an irrational number is √2, which, when multiplied by 1/5, gives 1/5√2 or √2/5, both of which are irrational.

It should be noted that a triangle is a polygon with three edges and three vertices.

A triangle is a simple closed curve or a polygon that is formed by three line segments.

It should be noted that triangles have 180°.  In this case, looking at the attached figure, it can be deduced that the addition of the angles equals 180.

Learn more about triangles on:

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Answer:

B

Step-by-step explanation:

The only thing that you can factor out of B is 6, while the others are not in simplest form. Answer C can still factor out 2 and answer choice D can still factor out a. Answer choice can still be factored further using difference of squares.

The area of triangle RST is also 20 20 square inches

Triangles having equal side lengths and equal corresponding angles measures are called congruent triangles.

Given that, triangle RST is congruent to triangle WXY, the area of triangle WXY is 20 square inches,

We are asked to find the area of triangle RST,

Since, triangles RST and WXY are congruent, therefore, they will have congruent sides and angles,

That means, they will have equal area also,

ar (Δ RST) = ar (Δ WXY)

Therefore,

ar (Δ RST) = 20 square inches

Hence, the area of triangle RST is also 20 20 square inches

Learn more about congruent triangles, click;

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Answer:

[tex]h(3)=122ft[/tex]

Step-by-step explanation:

The problem gives you everything, basically you only have to replace the given value, which is t=3 into the equation:

[tex]h(t)=-16t^2+79t+29[/tex]

But, let's do a deeper analysis. This a projectile motion problem. For this kind of problems there are some fundamental equation. For example, we need to find the vertical displacement of the rocket. So the equation for the vertical displacement in projectile motion is given by:

[tex]h_f-h_o=v_ot-\frac{1}{2}gt^2[/tex]  (1)

Where:

[tex]h_f=Final\hspace{3}height\\h_o=Initial\hspace{3}height\\t=Time\\v_o=Initial\hspace{3}velocity\\g=Gravitational\hspace{3}acceleration[/tex]

Isolating  [tex]h_f[/tex] and rearranging the equation (1) we get:

[tex]h_f=-\frac{1}{2}gt^2+v_ot+h_o[/tex]

Looks familiar? It has exactly the same form of the equation given by the problem. As you can see, if you replace the values of the speed and the initial position given by the problem, we got the same equation. Besides gravitational acceleration is a constant and its value is approximately 32ft/s^2, dividing it by 2, we get 16. Having this in mind, let's resolve the problem:

[tex]h(3)=-16(3)^2+79(3)+29=-144+237+29=266-144=122ft[/tex]