What is the value of the logarithm below? (Round your answer to two decimal
places.)
log₂7
A. 0.58
B. 2.11
C. 0.85
D. 2.81

The expression given in the task content can be evaluated and simplified to be equal to; sin²(x).

It follows from the task content that the result of the product given is to be determined.

Hence, the multiplication is as follows;

1 -cos(x) +cos(x) -cos²(x).

1 -cos²(x).

However, since sin²(x) + cos2(x) = 1; it therefore follows that;

1 -cos²(x) = sin²(x)

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Answer:

Step-by-step explanation:

1). 7x - 2y = 5 , A = 7 , B = 2 , C = 5

2). 4x - y = 1 , A = 4 , B = - 1 , C = 1

3). 5x - 2y = 3 , A = 5 , B = - 2 , C = 3

4). 4x - 3y = 3 , A = 4 , B = - 3 , C = 3

5). 2x + y = 15 , A = 2 , B = 1 , C = 15

Answer:

19.6ft (nearest tenth)

Step-by-step explanation:

Please refer to the attached photo for better understanding.

Given Length of Wire = BC = 22ft

Given Distance from Grounded Wire to Base of Pole = AC = 10ft

Length of Pole = AB

We can use Pythagoras' Theorem to find Length of Pole, AB.

By Pythagoras' Theorem,

[tex]c^{2} =a^{2} +b^{2} \\BC^{2} =AB^{2} + AC^{2} \\22^{2} =AB^{2} +10^{2} \\484=AB^{2} +100\\AB^{2} =484-100\\AB=\sqrt{384} ft\\=19.6ft (nearest tenth)[/tex]

True, a circle can be circumscribed about the quadrilateral described in the task content.

It follows from the task content that quadrilateral in discuss has angles; 95, 80, 85 and 100.

By convention, it follows that circles can be circumscribed about only cyclic quadrilaterals in which case their opposite angles are supplementary. Hence, since opposite angles of the quadrilateral are supplementary (i.e amount to 180). Then, True, the circle can be circumscribed about the quadrilateral.

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Answer:

Step-by-step explanation:

[tex]if A+B=45\\tan(A+B)=tan(45)\\\dfrac{tanA+tanB}{1-tanA.tanB}=1\\ \implies tanA+tanB=1-tanA.tanB\\\frac{1}{cotA}+\frac{1}{cotB}=1-\frac{1}{cotA}\frac{1}{cotB}, \{tanX=\dfrac{1}{cotX} \}\\ cotA+cotB=cotA.cotB-1\\cotA.cotB-cotA-cotB=1.[/tex]

The linear are said to be parallel.

Collinear points are the points that lie on the same straight line or in a single line.

Given:

slope= 3

If two non co-linear segments with a slope of 3 in a coordinate plane, which means that the two line segments are parallel to each.

So, the same slope symbolise the  concept of parallel line in same plane.

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The only wrong spot would be box 1 because the graph is not decreasing over the longest interval.

In the first graph, we see that the y-intercept which is the point where the curve crosses the y-axis is at y = -1. However, the interval for which it is decreasing is from x = -1 to x = 0.5.

For the second table, we see that the y-intercept is -1 and that as values of x keeps increasing, g(x) becomes more negative. Thus, it is decreasing on the longest interval.

For the third function which is;

h(x) = 3 + 4x³

The y-intercept is 3.

However, the higher the value of x, the greater the function.

Thus, the only wrong spot would be box 1 because the graph is not decreasing over the longest interval.

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Answer:

B. Yes, she used systematic random sampling

Explanation :

Systematic random sampling is method of sampling use in term of finding the the percent of a given population to find the final sample.

The solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.

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 complete question is:

Solve for x and y:

2/x+3/y=9/xy; and 4/x+9/y=21/xy   x ≠ 0, y ≠ 0

We have two equations:

2/x+3/y=9/xy;

4/x+9/y=21/xy

Solving substitution method:

[tex]\rm \dfrac{4}{\dfrac{9-2y}{3}}+\dfrac{9}{y}=\dfrac{21}{\dfrac{9-2y}{3}y}[/tex]

y = 3

x = 1

Thus, the solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.

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The proportion that could be used to find the value of x is 3/x= x/11

The complete question is added as an attachment

From the attachment, the common side length between both right triangles is x

While the other sides are adjacent sides.

This means that the proportion is:

3/x= x/11

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The solutions to this triangle are:

Using the law of cosine we would have

a²=b²+c²-2bc cos A

a² =100+49-2(10)(7)cos 52

This would give us

=149 -140 x (0.6157)

=62.82

We take the square root of 62.82 =

7.93 or 7.9

We have to use the sine law to find the other side

7.9/sin 52=10.057

10.06=7/sin C

such that

sin C = sin(0.6958)

=44.1°

10.06=10/sin B

cross multiply

sin B=10/10.06

= sin⁻¹0.9940

Then B = 83.7°

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The equation for the trend line in the scatter plot will be Y= 5x-1. Option B is correct.

In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.

When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.

The graphs are attached in the attachment.

The equation for the trend line in the scatter plot will be Y= 5x-1.

Hence, option B is correct.

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Answer:

Choice A

Step-by-step explanation:

[tex] \rm \: a {}^{2} \{ \cdot \: \cfrac{1}{a {}^{ \frac{2}{3} } \ } \}[/tex]

Applying Distributive property;

Choice A is accurate.

Step-by-step explanation:

sinA=sinA

sin2A

(sinA)2

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of GF is 254 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Since a centroid of a triangle divides the median into a ratio of 2:1. Therefore, the ratio of AG: DG is,

AG / DG = 2/1

(19x+14)/(9x+20) = 2/1

19x + 14 = 18x + 40

19x - 18x = 40 - 14

x = 26

Assuming the triangle is an equilateral triangle, therefore, the length of GF will be,

GF = DG = 9x+20

GF = DG = 9(26) + 20

GF = 254 units

Hence, the length of GF is 254 units.

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Answer:  26 units

Step-by-step explanation:   Trust Me!!!  

The answer is correct on Edge. I just got it right!

Answer:

x = -4.5

Step-by-step explanation:

Solving the equation :

[tex]\left\vert -4+\frac{5}{2} \right\vert -\left( -x\right) =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-8}{2} +\frac{5}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-8+5}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-3}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \frac{3}{2} +x =-3[/tex]

[tex]\Longleftrightarrow x =-3-\frac{3}{2}[/tex]

[tex]\Longleftrightarrow x =-\frac{6}{2} -\frac{3}{2}[/tex]

[tex]\Longleftrightarrow x = -(\frac{6}{2} +\frac{3}{2} )[/tex]

[tex]\Longleftrightarrow x =-\frac{9}{2}[/tex]

[tex]\Longleftrightarrow x =-4.5[/tex]

[tex]x \geqslant - 3 \: \: \: \: \: \: x < 3[/tex]

Answer:

The answer is D intersection

Remember that AND indicates an intersection and OR indicates a union.

Step-by-step explanation:

Solve each inequality and then find the intersection.

Inequality Form: −3≤ x<3

Interval Notation:[−3,3)

Answer: C / d=1

Step-by-step explanation:

Just did it

Answer: C

Step-by-step explanation: Just took the quiz

The value of <RQZ has been calculated as 21 from the solution we have below.

We have

< PZQ= <PQZ

PQR - PRQ = 42

Let < PZQ = y⁰

PQZ = y⁰

Let PRQ = x⁰

< PQR = x + 42⁰

< QpZ + y + y = 180⁰

such that

QPZ + 2y = 180⁰

<QPZ = 180⁰ - 2y

<(QPZ + PQR + PRQ) = 180

Adding these equations, we would have

180 - 2y + x + 42 + x = 180⁰

180 would cancel out

We have

2x - 2y + 42 = 0

x- y +21 = 0

We have to add 21 to both sides of the equation

x- y + 42 = 21

(x + 42) - y = 21

(x + 42) = <PQR and y = < PQZ

Hence 21 = <RQZ

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Answer:

16a^2b^2

Step-by-step explanation:

An exponent that is over a whole entire fraction can be split up and put separately onto the numerator (top number) and denominator (bottom number) See image.

Then you can get rid of a negative exponent (make it positive) by moving the whole term across the fraction bar. The top moves to the bottom and the bottom moves to the top. See image.

In the term (4ab)^2, the exponent 2 can be passed out to the 4 and the a and the b. See image.

Answer: D

Step-by-step explanation:

The trinomial represented by the algebraic tiles is x^2  + 4x + 3

On the horizontal axis, we have:

1 row under the big square.

This represents x + 1

On the vertical axis, we have:

3 columns beside the big square.

This represents x + 3

So, we have:

(x + 1) * (x + 3)

Expand

(x + 1) * (x + 3) = x^2  + x + 3x + 3

Evaluate

(x + 1) * (x + 3) = x^2  + 4x + 3

Hence, the trinomial represented by the algebraic tiles is x^2  + 4x + 3

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Answer:

f(-3) =8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer

f(x) has the same meaning as y. So you could rewrite the question as "What value of x gives y a value of 8"

The graph tells you that x = - 3 when y = 8.

f(-3) = 8

The least possible value of the expression is 2020

The expression is given as:

[tex](x + 4)(x + 5) + \frac{10^6}{x(x + 9)}[/tex]

Next, we plot the expression on a graph (see attachment)

From the attached graph, the minimum value of the expression is 2020 under the domain of x > 0

Hence, the least possible value of the expression is 2020

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Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Dilation does not preserve the size of a figure, it only preserves the shape and angle.

Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′

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In the beginning, they have 50 and 180 cows respectively.

The two farmers bought  a total of 230 cows .

A year later the first farmer had 10% more cows than in the beginning.

Therefore,

let

x = number of cow he has initially.

A year later the percentage increase = 0.1x

whereas the second had 20% increase. Therefore,

let

y = number of cow he has initially.

A year later percentage increase = 0.2y

Hence,

x + y = 230

1.1x + 1.2y = 263

1.1x + 1.1y = 253

1.1x + 1.2y = 263

0.2y = 10

y = 10 / 0.2

y = 50

x = 230 - 50

x = 180

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The equivalent expression of a + 5 is -(-a - 5)

The expression is given as:

a + 5

Multiply by 1

1 * (a + 5)

Express 1 as -1 * -1

-1 * -1 * (a + 5)

Open the bracket

-1 * (-a - 5)

This gives

-(-a - 5)

Hence, the equivalent expression of a + 5 is -(-a - 5)

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The image of the figure under reflections in line m and then line t is shown below.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the square DEFG will be given in the figure.

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Answer:

a1

Step-by-step explanation:

Just add the numerators if both fractions to get: a + 1 = a1

Answer:

a+1

Step-by-step explanation:

Well if you have the same denominator, which in this case you do, it's equal to b, you can simply add the numerators. This gives you the expression [tex]\frac{a+1}{b}[/tex] so the numerator is a+1

No, we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

Given mean of 15.5 minutes , standard deviation of 1.7 minutes, sample size of 90 and sample mean of 15.4 minutes.

We can do the following study for conclusion:

Firstly the null hypothesis is

[tex]H_{0}: x=15.5[/tex]

The alternate hypothesis is

[tex]H_{1}: x < 15.5[/tex]

since the value is less than this is a one tailed test.

Z=x bar-x/d/[tex]\sqrt{n}[/tex]

where x is sample mean and d is standard deviation.

Z=15.4-15.5/1.7/[tex]\sqrt{90}[/tex]

=-0.1/1.7/9.4868

=-0.560

Critical value of Z at 0.1 level of significance

Z=-1.28

We fails to reject the null hypothesis since -0.560>-1,28

Hence we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

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Question is incomplete. It should include:

mean of 15.5 minutes ,

standard deviation of 1.7 minutes,

sample size of 90

and sample mean of 15.4 minutes.