Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. ASA Postulate

Answer:

(c) [tex]x = 0.6[/tex] and [tex]x = 0.7[/tex]

(d) [tex](x,y) = (0.67,2.33)[/tex]

Step-by-step explanation:

Given

See attachment

First, we complete the table

[tex]y = -x + 3[/tex]                                               [tex]y = 2x + 1[/tex]

[tex]y = -0.6 + 3 = 2.4[/tex]                                   [tex]y = 2 * 0.6 + 1 = 2.2[/tex]

[tex]y = -0.7 + 3 = 2.3[/tex]                                   [tex]y = 2 * 0.7 + 1 = 2.4[/tex]

[tex]y = -0.8 + 3 = 2.2[/tex]                                   [tex]y = 2 * 0.8 + 1 = 2.6[/tex]

[tex]y = -0.9 + 3 = 2.1[/tex]                                   [tex]y = 2 * 0.9 + 1 = 2.8[/tex]

So, we have:

[tex]\begin{array}{ccc}x & {y = -x + 3} & {y = 2x + 1} & {0.5} & {2.5} & {2} & {0.6} & {2.4} & {2.2} & {0.7}&{2.3} & {2.4} & {0.8}&{2.2} & {2.6} & {0.9}&{2.1} & {2.8} & {1}&{2} & {3} \ \end{array}[/tex]

Solving (c): Between which values is y

The values of y are for both equations are closest at:

[tex]x = 0.6[/tex] and [tex]x = 0.7[/tex]

Hence, the solution is between

[tex]x = 0.6[/tex] and [tex]x = 0.7[/tex]

Solving (d): Approximated value of the solution

We have:

[tex]y = -x + 3[/tex]

[tex]y = 2x + 1[/tex]

[tex]y=y[/tex]

So:

[tex]-x + 3 = 2x + 1[/tex]

Collect like terms

[tex]2x + x = 3 - 1[/tex]

[tex]3x= 2[/tex]

Divide both sides by 3

[tex]x = 0.67[/tex]

Substitute [tex]x = 0.67[/tex] in [tex]y = -x + 3[/tex]

[tex]y =-0.67 + 3[/tex]

[tex]y =2.33[/tex]

So, the solution is:

[tex](x,y) = (0.67,2.33)[/tex]

Answer:

The equation is x + 4 = 0.

Step-by-step explanation:

Point (-4 , 8)

A line parallel to the Y axis has slope is infinite.

The equation of line is

[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]

Answer: The answer that I got for z was 0.111575, which when you round it to the hundredths place would be 0.11

Answer:

Step-by-step explanation:

C. f(x) will be a very small negative number, approaching -∞

Answer:

The solution is defined in the attached file please find it.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

We need to evaluate :-

[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]

Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,

[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]

Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,

[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]

Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,

[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]

Hence the required answer is 6.

Answer:

[tex]2827.4 \dfrac{ft}{s}[/tex]

Step-by-step explanation:

[tex] A = \pi r^2 [/tex]

[tex] \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt} [/tex]

[tex] \dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s} [/tex]

[tex] \dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s} [/tex]

Answer:

The answer is "No, There are more than two possible outcomes on each trial of the experiment ".

Step-by-step explanation:

When various ice cream products are known. This might surpass 2 brands or more. Thus the number of different results varies considerably.

BINOMIAL DISTRIBUTION:

An investigation with a set set of individual tests, each only with two possible results.

Four conditions are met by the binomial experiment

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y  = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

Answer:

x = 16

Step-by-step explanation:

7(x + 2) = 6(x + 5)

First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.

7x + 14 = 6x + 30

Next, let's subtract "6x" from both sides of this equation!

x + 14 = 30

Now, we have to subtract "14" from both sides of the equation.

x = 16

Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.

7(16 + 2) = 6(16 + 5)

7(18) = 6(21)

126 = 126

Since our equations equal each other we know that our x-value is correct!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

A monomial in standard form is (essentially) the product of one or more factors: a constant coefficient and one factor for each variable in the expression.

Step-by-step explanation:

For example, in the monomial 4x2y3, the factors are 4, x2, and y3. First, the coefficient is 4. The next factor, x2, is the x-factor, whose degree is 2.

9514 1404 393

Answer:

  27/64

Step-by-step explanation:

The fraction being cubed is already in simplest form, so the cube is ...

  [tex]\left(\dfrac{3}{4}\right)^3=\dfrac{3^3}{4^3}=\boxed{\dfrac{27}{64}}[/tex]

Answer:

Here is your Answer

Step-by-step explanation:

27

Answer:

B. 1✓3 in.

Search It ok

I see the answer :)

Answer:

7 and 3 are two numbers that work

Step-by-step explanation:

7-3=4

7×3=21

Answer:

we need a picture...

Step-by-step explanation:

Answer:

1600 Rupees

Step-by-step explanation:

20 divided by 100 times 8000 will give you 1600 so the carpet costed him 1600

Answer:

The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.

The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2

Explanation:

Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.

The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.

I hope this helps!

Answer:

In LDR

In PDR

Exterior angle of a triangle is formed when one side of the triangle is extended .

Interior remote angles the angles in the triangle that do not lie on the extended side.

Answer:

[tex]15x - 5 + x = - 47 \\ 15 + x - 5 = - 47 \\ 16x - 5 = - 47 \\ 16x = - 47 \\ x = \frac{ -16x}{16} = \frac{ - 45}{16} \\ x = - \frac{21}{8} [/tex]

Answer:

j * .07 +j

Step-by-step explanation:

The tax on the jewelry is J* .07

Add the tax to the cost of the jewelry to get the total cost

j * .07 +j

Answer:

0.0306

Step-by-step explanation:

I don't know if there is any significance to both being drawn at the same time. I'm going to say there isn't.

The first draw gives

9/49

Their is no replacement. That's because both marbles are drawn together. The second draw is

8/48

P(both red) = 9/49 * 8 / 48 = 3/98 = 0.03061 which rounds to 0.0306

9514 1404 393

Answer:

  10

Step-by-step explanation:

The n-th triangular number is given by ...

  t(n) = n(n+1)/2

We went to find n when t(n) = 55.

  55 = n(n+1)/2

  110 = n(n+1)

Adding 1/4 completes the square.

  110.25 = (n +0.5)^2

  √110.25 = n+0.5 . . . . . we are interested in the positive value of n

  n = 10.5 -0.5 = 10

The triangular number that has 55 dots in its shape is the 10-th number.

__

Additional comment

Here, we have gone to the trouble to formally complete the square to find the value of n. You may realize that it isn't really necessary to go to that trouble.

A reasonable estimate of the value of n is possible by considering that the product n(n+1) is a little more than n², so the value of n will be a little less than √110 ≈ 10.49. The nearest integer is 10, which is the answer we're looking for.

Answer:

y = -1.5x - 1

Step-by-step explanation:

We can use the general equation of y = mx + c to form our linear equation as seen on this graph.

Choosing two points on the graph (I will choose 0,-1 and 2,-4) we can find the gradient, m, as the distance between these points

[tex]\frac{Rise}{Run} = \frac{(-1)-(-4)}{(0)-(2)} = \frac{3}{-2} =-1.5[/tex]

We can find the c value by seeing where the graph cuts through the y-axis

This point is -1

Therefore our equation is y = -1.5x - 1

Alternatively, you could write it as [tex]y= -\frac{3}{2} x - 1[/tex]

Answer:

y = -1.5x - 1

Answer:

519.99(.0825) = 42.899

519.99 + 42.899 = $562.89

Step-by-step explanation:

Answer:

the process capability index of the machine is 2.5

Option c) [More than 2 but less than or equal to 3] is the correct answer

Step-by-step explanation:

Given the data in the question;

process average ( x') = 12.000 ounces

standard deviation σ = 0.002 ounces

the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.

so

Upper specification Limit USL = 12.000 + 0.015 = 12.015 ounces

Lower specification Limit LSL = 12.000 - 0.015 = 11.985 ounces

the process capability index of the machine will be;

Cp = ( process average - Lower specification Limit ) /  3σ

so we substitute

Cp = ( 12 - 11.985 ) / ( 3 × 0.002 )

Cp = 0.015 / 0.006

Cp = 2.5

Therefore, the process capability index of the machine is 2.5

Option c) [More than 2 but less than or equal to 3] is the correct answer

Answer:

11/2

Step-by-step explanation:

[tex]\frac{\frac{3}{4} + \frac{5}{8} }{\frac{3}{4} - \frac{1}{2} }[/tex]

= 3/4 + 5/8 = 11/8 (take LCM)

3/4 - 1/2 = 1/4 (take LCM)

11/8 ÷ 1 /4

= 11/8 x 4

= 11/2

Answered by Gauthmath

Answer:

The dimensions of the rectangle are 8 by 7 centimeters.

Step-by-step explanation:

The length of a rectangle is 13 centimeters less than three times its width. In other words:

[tex]\ell = 3w-13[/tex]

Given that the area of the rectangle is 56 square centimeters, we want to determine its dimensions.

Recall that the area of a rectangle is given by:

[tex]A = w \ell[/tex]

Substitute in known values and equations:

[tex](56)=w(3w-13)[/tex]

Solve for w. Distribute:

[tex]3w^2-13w=56[/tex]

Isolate the equation:

[tex]3w^2-13w-56=0[/tex]

Factor. We want to find two numbers that multiply to 3(-56) = -168 and that add to -13.

-21 and 8 suffice. Hence:

[tex]3w^2 - 21w + 8w - 56 = 0 \\ \\ 3w(w-7) + 8(w-7) = 0 \\ \\ (3w+8)(w-7) = 0[/tex]

Zero Product Property:

[tex]3w+8=0\text{ or } w-7=0[/tex]

Solve for each case:

[tex]\displaystyle w = -\frac{8}{3} \text{ or } w=7[/tex]

Since the width cannot be negative, we can ignore the first solution.

Therefore, the width of the rectangle is seven centimeters.

Thus, the length will be:

[tex]\ell = 3(7) - 13 = 8[/tex]

Thus, the dimensions of the rectangle are 8 by 7 centimeters.