Simplify the expression.

Please add an explanation if you understand how to do this.

Answer:

Hello,

Step-by-step explanation:

[tex]Let\ (u_n)\ the\ geometric\ progression.\\\\r\ is\ the\ common\ ratio.\\\\u_3=u_0*r^3\\u_6=u_0*r^6\\\\\dfrac{u_6}{u_3} =r^3=\dfrac{\frac{243}{16} }{\frac{9}{2} } =\dfrac{27}{8} =(\frac{3}{2} )^3\\\\\boxed{r=\dfrac{3}{2} }\\\\\\u_3=u_1*r^2 \Longrightarrow\ u_1=\dfrac{u_3}{r^2} =\dfrac{\frac{9}{2} }{(\frac{3}{2^2}) } =2\\\\\\u_7=u_6*\dfrac{3}{2} =\dfrac{729}{32}[/tex]

We know

Sum of two interior angles =exterior angle

[tex]\\ \sf\longmapsto 2x+x=3x[/tex]

[tex]\\ \sf\longmapsto 3x=3x[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Answer:

(a) [tex]P" = (-4,-3)[/tex]

(b) [tex](x,y) \to (4,-8)[/tex]

Step-by-step explanation:

Given

[tex]P = (4,3)[/tex]

Solving (a): Reflect across x and y-axis.

Reflection across x-axis has the following rules

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]P' = (4,-3)[/tex]

Reflection across y-axis has the following rules

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]P" = (-4,-3)[/tex]

Hence, the new point is: (-4,-3)

Solving (b): Rx . Do,2 (2,4)

[tex]R_x \to[/tex] reflect across the x-axis

Reflection across x-axis has the following rules

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex](2,4) = (2,-4)[/tex] ---- when P is reflected across the x-axis

[tex]D_{o,2} \to[/tex] dilate by a scale factor of 2

The rule is:

[tex](x,y) \to 2 * (x,y)[/tex]

So, we have

[tex](x,y) \to 2 * (2,-4)[/tex]

Open bracket

[tex](x,y) \to (4,-8)[/tex]

Answer:

14.17 kilograms

Step-by-step explanation:

Find what quantity of tomatoes was in each batch by dividing the total amount of tomatoes by the number of batches:

99.19/7

= 14.17

So, the factory put 14.17 kilograms of tomatoes in each batch.

Answer:

14.36 AND 9.89 ===> 14 or 10

Step-by-step explanation:

Y =  Ax2 Bx C

Enter coefficients here >>>  -4 97 -568

Standard Form: y = -4x²+97x-568    

-24.25 -12.125 147.015625 -588.0625 20.0625

Grouped  Form: No valid Grouping      

Graphing Form: y = -4(x-12.13)²+20.06    

Factored Form: PRIME    

Solution/X-Intercepts: 14.36 AND 9.89    

Discriminate =321 is positive, two real solutions    

VERTEX: (12.13,20.06)     Directrix: Y=20.13    

Answer:

Hello,

Answer D

Step-by-step explanation:

Each value of the graph, y=f(x) is multiplied by 2

Red graph has for eqution y=2*f(x) or y/2=f(x)

Answer:

288 cubic ft look at explanation, please give me a thanks if this answer helped!

Step-by-step explanation:

The volume of a pyramid is equal to to 1/3 bh

so first you would find the base which is the rectangle at the bottom

Base= 9 x 8= 72

height has already been given- 12

now your equation is 12 x 1/3 x 72

you can simplify 12 and 1/3 to 4

so now you would have 72 times 4

which is 288

Answer:

85/100

Step-by-step explanation:

0.85 from a decimal is equal to 85/100 in fractions

Answer:

15/4

Step-by-step explanation:

sin60 =z/15

z=15sin60 =(15√3)/2

cos30 =b/z

b = zcos30 = (15√3)/2 * √3/2 = 45/4

a = 15-b = 15-45/4 = 15/4

The value of a is 15/4

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

According to the given figure,

Here is a right triangle

Let, The hypotenuse = 15

perpendicular = z and base = 15 = a + b

⇒ sin60 = perpendicular/hypotenuse = z/15

⇒ z = 15sin60 = (15√3)/2

⇒ cos30 = base/hypotenuse = b/z

⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4

⇒ a + b = 15

Substitute the value of b in the above equation,

⇒ a = 15-b = 15-45/4 = 15/4

Hence, the value of a is 15/4.

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Step-by-step explanation:

Which correlation coefficient indicates the data set with the strongest linear correlation?

0.66

The correlation coefficient indicates the data set with the strongest linear correlation is -0.83

"It measures the strength of the relationship between two relative variables."

"When the rate of change is constant between two variables then it is said to be linear correlation."

For given example,

We have been given correlation coefficients.

We need to find the correlation coefficient that indicates the data set with the strongest linear correlation.

We know, the correlation coefficient lies between -1 to 1.

So, the strongest linear correlation is indicated by a correlation coefficient of -1 or 1.

From given correlation coefficients,

-0.83 is close to -1.

Therefore, the correlation coefficient indicates the data set with the strongest linear correlation is -0.83

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First check the characteristic solution. The characteristic equation to this DE is

r ² - r = r (r - 1) = 0

with roots r = 0 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(0x) + C₂ exp(1x)

y (char.) = C₁ + C₂ exp(x)

For the particular solution, we try the ansatz

y (part.) = (ax + b) exp(x)

but exp(x) is already accounted for in the second term of y (char.), so we multiply each term here by x :

y (part.) = (ax ² + bx) exp(x)

Differentiate this twice and substitute the derivatives into the DE.

y' (part.) = (2ax + b) exp(x) + (ax ² + bx) exp(x)

… = (ax ² + (2a + b)x + b) exp(x)

y'' (part.) = (2ax + 2a + b) exp(x) + (ax ² + (2a + b)x + b) exp(x)

… = (ax ² + (4a + b)x + 2a + 2b) exp(x)

(ax ² + (4a + b)x + 2a + 2b) exp(x) - (ax ² + (2a + b)x + b) exp(x)

= x exp(x)

The factor of exp(x) on both sides is never zero, so we can cancel them:

(ax ² + (4a + b)x + 2a + 2b) - (ax ² + (2a + b)x + b) = x

Collect all the terms on the left side to reduce it to

2ax + 2a + b = x

Matching coefficients gives the system

2a = 1

2a + b = 0

and solving this yields

a = 1/2, b = -1

Then the general solution to this DE is

y(x) = C₁ + C₂ exp(x) + (1/2 x ² - x) exp(x)

For the given initial conditions, we have

y (0) = C₁ + C₂ = 6

y' (0) = C₂ - 1 = 5

and solving for the constants here gives

C₁ = 0, C₂ = 6

so that the particular solution to the IVP is

y(x) = 6 exp(x) + (1/2 x ² - x) exp(x)

Answer:

4(2e - 3)(3e + 1)

Step-by-step explanation:

Given

24e² - 28e - 12 ← factor out 4 from each term

= 4(6e² - 7e - 3) ← factor the quadratic

Consider the factors of the product of the e² term and the constant term which sum to give the coefficient of the e- term.

product = 6 × - 3 = - 18 and sum = - 7

The factors are - 9 and + 2

Use these factors to split the e- term

6e² - 9e + 2e - 3 ( factor the first/second and third/fourth terms )

= 3e(2e - 3) + 1 (2e - 3) ← factor out (2e - 3) from each term

= (2e - 3)(3e + 1)

Then

24e² - 28e - 12 = 4(2e - 3)(3e + 1) ← in factored form

The volume of prism is,

⇒ V = 42.09 cubic units

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Base = 5.12

height = 4.11

Lenght = 4

Now, We can formulate;

The value of volume of prism is,

⇒ V = 1/2 (b x h) l

⇒ V = 1/2 (5.12 x 4.11) 4

⇒ V = 42.09 cubic units

Thus, The volume of prism is,

⇒ V = 42.09 cubic units

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The question is an illustration of a function using graphs. When a function is plotted on a graph, the x-axis represents the domain, while the y-axis represents the range of the function.

The domain and the range of the given function are:

Domain: [tex](-\infty,\infty)[/tex]

Range: [tex](3,\infty)[/tex]

From the question, we have the function to be:

[tex]g(x) = 3^x + 3[/tex]

First, we plot the graph of g(x)

To do this, we first generate values for x and g(x). The table is generated as follows:

[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]

[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]

[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]

[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]

[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]

In a tabular form, we have the following pair of values

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]

See attachment for graph

From the attached graph of g(x), we can observe that the curve stretches through the x-axis and there are no visible endpoints.

This means that the curve starts from - infinity to +infinity

Hence, the domain is: [tex](-\infty,\infty)[/tex]

Also, from the same graph, we can observe that the curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction.

This means that the curve of g(x) is greater than 3 on the y-axis.

Hence, the range is: [tex](3,\infty)[/tex]

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Answer:

5(n+4)

5n+20

Step-by-step explanation:

Let n be the number

5* (n+4)

Distribute

5n+20

ABC = $425

Load = 0

Total Cost = $425

Sales Price = $850

Sales price ÷ total cost = 850/425

= 2%

DEF = $600

Load = $375

Total Cost = $975

Sales Price = $1200

Sales Price ÷ Total cost = 1200/975

= 1% (Nearest 1%)

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Answer:

There is a   min     value of   376     located at (x,y) =   (9,7)  

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

Explanation:

Solve the second equation for y

x+y = 16

y = 16-x

Then plug it into the first equation

f(x,y) = 3x^2+4y^2 - xy

g(x) = 3x^2+4(16-x)^2 - x(16-x)

g(x) = 3x^2+4(256 - 32x + x^2) - 16x + x^2

g(x) = 3x^2+1024 - 128x + 4x^2 - 16x + x^2

g(x) = 8x^2-144x+1024

The positive leading coefficient 8 tells us we have a parabola that opens upward, and produces a minimum value (aka lowest point) at the vertex.

Let's compute the derivative and set it equal to zero to solve for x.

g(x) = 8x^2-144x+1024

g ' (x) = 16x-144

16x-144 = 0

16x = 144

x = 144/16

x = 9

The min value occurs when x = 9. Let's find its paired y value.

y = 16-x

y = 16-9

y = 7

The min value occurs at (x,y) = (9,7)

Lastly, let's find the actual min value of f(x,y).

f(x,y) = 3x^2+4y^2 - xy

f(9,7) = 3(9)^2+4(7)^2 - 9*7

f(9,7) = 376

The smallest f(x,y) value is 376.

OSEAMENTE no se la respuesta

Answer:

The molecules of the substances must be touching

FOR EXAMPLE, a metal spoon placed in a hot coffee mug shows the flow of heat from coffee to the spoon. and now we can conclude that a condition that must exist in order for conduction to occur between two substances is that the objects must be touching each other.

Answer:

The molecules of the substances must be touching.

A

Step-by-step explanation:

1) Seven less than twice a number, n, is 32.

ANS) B. 2n - 7 = 32

Answer:

1.

B. 2n - 7 = 32 is the right answer

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

D.) y = 2x + 2

Step-by-step explanation:

First, we need to find the slope.

Lets use the points (0, 2) and (-2, -2).

Using the formula for calculating slope, we get 2 as our slope.

Since the equation should be in slope-intercept form, we use this formula.

y = mx + b

We'll use our first point (0, 2) to substitute for x and y and use 2 to substitute for m (slope):

2 = 2(0) + b

2 x 0 = 0

2 = 0 + b

-0 = -0

= 2 = b

Now, substitute b for 2 for 2 for m.

= y = 2x + 2.

Hope this helps!

If there is something wrong, please let me know.

Answer:

17

Step-by-step explanation:

T4 = 4² + 1

T4 = 4² + 1 = 17

Yip yip that's all

Answer:

click in photo

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nxndjdbbdjf

lấy x=0 ta có y= -2 => A(0;-2)

lấy y=0 ta có x=2 => B(2;0)

nối 2 điểm A và B ta có đồ thị:

Answer:

x = -1.4 and x=2

Step-by-step explanation:

The solutions are where the graphs intersect

The graphs appear to intersect at x = -1.4 and x=2

Answer:

Its A

Step-by-step explanation:

The tangent of the given circle is FG hence the correct option will be an option (B).

The tangent of a circle is a line that intersects the circle at the periphery of the circle.

If you draw a line that goes through the center to the tangent touching point then it will give you a 90-degree angle.

Given the circle it's clear that the tangent is only FG hence it will be the correct option  

A circle can have an infinite number of tangents.

In other words, a straight line that only touches a circle twice is said to be tangent to it. The term point of intersection refers to this location

At the tangent line, the tangent to a circle is orthogonal to the radius.

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Answer:

A

Step-by-step explanation:

32 hundredths is 32/100

Side note

32/100 can be simplified to 8/25.

Answer:

# of cases: 11

Additional units: 2

Step-by-step explanation:

If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).

As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.

Answer:

95% confidence level should be used for a confidence​ interval.

The given confidence interval contains the value of 85 ​sec, so there is not sufficient evidence to support the claim that the mean is greater than 85 sec.

Step-by-step explanation:

0.05 significance level

1 - 0.05 = 0.95

0.95*100% = 95%

This means that a 95% confidence level should be used for a confidence​ interval.

Confidence interval is found to be −1.8 sec<μ<213.5 ​sec, what should we conclude about the​ claim?

Contains the value of 85 sec, thus there is not sufficient evidence to support the claim that the mean is greater than 85 sec.