Evaluate each logarithm. log₅ 25

The value of x is 280

From the information given, we have that;

It is important to note that, the angle subtended by an arc at the center is twice the angle subtended at the circumference.

Example;

If AOB  is the angle at the circumference and ACB is the angle at the center

Then, we have that;

Angle AOB = 2 × Angle ACB

2(140) = x

expand the bracket

x = 280

Thus, the value of x is 280

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Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.

If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).

Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.

c^2 = a^2 + b^2

where c is the total displacement from the starting point to the end point

a is the distance he walks up north

b is the distance he walks to the west

c^2 = 100^2 + 100^2

c^2 = 10,000 + 10,000

c^2 = 20,000

c = 141.42 meters

Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.

100 meters + 100 meters - 141.42 meters = 53.58 meters

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Option D) is correct option that is the function ,  (f + g)(x) = x – 7

Note that if we have been given two functions which are f(x) and g(x) then their addition will be given as

            (f + g)(x) = f(x) + g(x)             (1)

We have been given the equation as

f(x) = -3x - 5     and g(x) = 4x – 2

putting the required value in equation (1) we get

            (f + g)(x) = (-3x-5) + (4x-2)

            (f + g)(x) = -3x – 5 + 4x – 2

            (f + g)(x) = x – 7

Thus option D) is the correct option that is the function,  (f + g)(x) = x – 7

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The image of the point (3,4)(3,4) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin is (-3,4).

A point's reflection

The mirror's "reflection" of the specified point P causes it to appear at an equal distance away on the other side of the line. To view this, move the point P. According to tradition, the "image" of point P is the reflection of point P across the line, which is designated by the term P' (pronounced "P prime").

As the rotation is counterclockwise around the origin,

the coordinates of the image will be - (-3,4)

The graph is attached at the end of the solution.

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Answer:

-4, 3

Step-by-step explanation:

The situation given that can be represented by a graph with a y-intercept of -8 is A. Hal bought $8 worth of supplies, then sold x buttons for $3 each. His profit is y dollars.

The y-intercept is a figure in the linear equation that shows the original number of units before the value of x either started to increase or to decrease and therefore cause a change in x.

The situation where Hal bought $8 worth of supplies would be represented by the y-intercept of -8 because the $8 that Hal bought represents his total profit before he sells anything. That total profit is -8 because Hal has spent -$8 but has not sold anything.

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Based on the table of the number of species in the United States, the probability that a randomly selected endangered species is a bird is 17.1%

The probability that a randomly selected mammal is endangered is 81.4%.

The probability that when an endangered species is selected randomly, it is a bird can be found as:

= Number of endangered birds / Number of endangered species

= 80 / (70 + 80 + 318)

= 17.1%

The probability that should a randomly selected mammal be picked, the mammal is endangered is:
= Number of endangered mammals / Number of mammals

= 70 / (70 + 16)

= 81.4%

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The total amount raised is the same for both Roxy and Randy if they sell 50 Plates.

Let the number of plate = 'p'

Roxy :

Selling price of plates = $5.00

Raised = $175

Total plates sold = 5.00p

Total amount raised = 5.00p + 175  ...eq.(1)

Randy :

Selling price of plates = $3.50

Raised = $250

Total plates sold = 3.50p

Total amount raised = 3.50p + 250  ...eq.(2)

Now we will equate the eq.(1) and eq.(2) to find the same amount raised by both Roxy and Randy ,

5.00p + 175 = 3.50p + 250

5.00p - 3.50p =250 - 175

              1.5p = 75

                   p = 75/1.5

                   p = 50

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Answer:

3

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

5-2*3+4   First multiply.

5-6+4 Now do addition or subtraction what comes first, from left to right.

-1+4 =

3

Answer: C

Step-by-step explanation:

180° = 96° + 8y + 12

180° = angles on a straight line

180 - 96 - 12 = 8y

8y = 180 - 96 - 12

8y = 72

y = 72 / 8

y = 9

Answer:

x=8

Step-by-step explanation:

multiply both sides of the equation by 8

combine like terms

divide both sides of the equation by -5

Solution of polynomial 4/2a = 5/a +6 is , [tex]a=-\frac{1}{2}[/tex]

In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as monomials, quadratic equation, cubic equation, linear equation of one degree, two degree and more  which has non  negative number as their powers all are part of polynomial equation and can be taken as types of the polynomial equations.

Some examples of polynomial equation are :

According to question,

[tex]\frac{4}{2a} = \frac{5}{a} +6\\\\= > \frac{2}{a} = \frac{5}{a} +6\\\\= > 5 + 6a =2\\ \\= > 6a = -3\\\\= > a = -\frac{3}{6} =-\frac{1}{2}[/tex]

Thus a = -1/2

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For the given equation, the value of d = 30

To solve linear equations, utilize the steps that are provided below. Remove parenthesis from either side of the equation and combine similar phrases to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.

Divide both sides of the equation by the coefficient of variable: d-12 = 10÷ 5/9

Divide a fraction by multiplying its reciprocal: d 9 -12=10 x 9/5

Write as a single fraction: d-12 = (10 x 9) / 5

Calculate the product or quotient: d-12= 90 / 5

Reduce fraction to the lowest term by canceling the greatest common factor: d-12 = 18

Rearrange unknown terms to the left side of the equation: d=18+12

Calculate the sum or difference: d=30

Answer: d=30

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Hence , the diameter of the trunk of the tree is 2.54 × 10⁻¹ m which is option (B) .

Let the diameter of stem of a flower be " x"  and diameter of the trunk of a tree be " y " .

According to the question  "The diameter of the trunk of a tree is 40 times greater than the stem of the flower " which can be represented by

y = 40 x       .....(1)

It is given that stem of a flower has a diameter of 6.35 × 10⁻³ meters.

Putting x = 6.35 × 10⁻³ in equation (1) , we get

 y = 40 × 6.35 × 10⁻³

 y = 254 × 10⁻³

 y = 2.54 × 10⁻¹ m

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The length of BD is 4.29

BF is the radius of circle and CE is the chord. BF perpendicularly bisects the chord into two equal halves. Thus, we can say that -

CD = 1/2CE

Keep the values in equation to find the value of CD

CD = 1/2×13.5

CD = 6.75

Now, taking BCD as right angled triangle, we can say -

BC is hypotenuse, CD is base and BD is perpendicular. Using Pythagoras theorem to find the length of BD.

BC² = CD² + BD²

8² = 6.75²  + BD²

BD² = 64 - 45.5625

BD² = 18.4375

BD = √ 18.4375

BD = 4.29

Hence, the length of BD is 4.29

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The complete question is attached in the image below.

4 lines of symmetry are there in the pattern.

What are an example and a pattern?

The square's two diagonals are symmetry lines.

Additionally, symmetry lines are formed by connecting the midpoints of the opposing sides. Consequently, there are four lines of symmetry overall.

4 lines of symmetry are there in the pattern.

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The diameter is the length of the line passing through the center and touching two points on the circle's edge.

In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.

The diameter is defined as the length of a line passing through the center and touching two points on the circle's rim.

A circle's diameter extends from one side to the other, with its midpoint in the center. Divide the radius of the circle by two to get the diameter.

A circle's diameter divides the shape in half. The radius of a circle is half the length of its diameter (or, conversely, the diameter of a circle is twice the length of its radius).

The complete question is:

Identify each

b. a diameter

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Answer:

-2

Step-by-step explanation:

Slope = rise/run

[tex]\mathrm{Slope} = \frac{y_2-y_1}{x_2-x_1}\\m=\frac{1-5}{4-2}\\1 - 5 = -4\\4 - 2 = 2\\=\frac{-4}{2}\\ =-2[/tex]

Answer:

-2.6

Step-by-step explanation:

The domain of the function is {x | 2 ≤ x ≤ 9}

The domain of the function is the set of input values of the graph

The given parameters are

A linear function begins with closed circle at (2,0) and ends with a closed circle at (9,7)

This is represented as

(x, y) = Closed (2, 0)

(x, y) = Closed (9, 7)

Remove the y values to determine the domain

x = Closed 2

x = Closed 9

The closed statement represents the inequality ≤

So, we have

2 ≤ x ≤ 9

Hence, the domain of the function is {x | 2 ≤ x ≤ 9}

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Answer:

B. {x | 2 ≤ x ≤ 9}

Step-by-step explanation:

The length of the fence around the triangular land is equal to 180 meters.

The perimeter of a figure is the sum of the side lengths of the figure. Triangles have three sides and we need to determine the perimeter of the triangular land. If we know that l₁ = 55 meters, l₂ = 60 meters and l₃ = 65 meters, then the perimeter of the figure is:

p = l₁ + l₂ + l₃

p = 55 m + 60 m + 65 m

p = 180 m

The length of the fence around the triangular land is equal to 180 meters.

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Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.

An acute angle triangle (also known as an acute-angled triangle) is a triangle with all of its interior angles being acute angles. Remember that an acute angle is one that is less than 90°.

A triangle with three acute angles is known as an acute triangle. An obtuse triangle has one obtuse angle and two acute angles. Because the angles of a triangle in Euclidean geometry must sum to 180°, no Euclidean triangle can have more than one obtuse angle.

Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.

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The properties in each step is:

Step 1 and 2: distributive property

Step 3: addition property of equality

Step 4: division property of equality

Given the equation, x + 0.06x - 1.50 = 3.80, we can solve for x using the steps with the following appropriate properties shown below:

Step 1:

(1 + 0.06)x - 1.50 = 3.80 (distributive property)

Step 2:

1.06x - 1.50 = 3.80 (distributive property)

Step 3: Add 1.50 to both sides of the equation

1.06x = 5.30 (addition property of equality)

Step 4: Divide both sides by 1.06

x = 5.00 (division property of equality)

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Answer:

  D

Step-by-step explanation:

You want to find the number line that shows the solution to -4 -(-6).

The first number in the "sum" is -4, so the first arrow on the number line should go from 0 to -4. (All choices show that.)

The second number is -6. Addition of -6 would create an arrow from -4 going 6 units to the left. Subtraction works in the opposite direction, so the subtraction of -6 will show as an arrow from -4 extending 6 units to the right. Only answer choice D shows this.

__

Additional comment

You know the solution is -4 -(-6) = -4 +6 = +2, so the graph showing the solution will have an arrow ending at +2. This eliminates all answer choices except the correct one.

<95141404393>

Answer: god please help the world

Step-by-step explanation: we are struggling

Answer: -6/7p+1/7

Step-by-step explanation: thank god I'm smart lol... I'm a big brain!!!

It should be noted that the distance of

Bellevue from the office be located will be 13.85 miles.

It should be noted that based on the information, the handyman company serves customers from two cities 60 miles apart, Jonesville and Bellevue and the vompany would like to position a new office between the two cities using weighted averages based on the typical number of calls received from each city.

From the information, Jonesville has a weight of 3 and Bellevue has a weight of 5, the distance of

Bellevue from the office be located will be:

= (0 × 5 + 60 × 4) / (5 × 8)

= 180 / 13

= 13.85

The office should be 13.85 miles from Bellevue.

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The ΔXYZ is an Right Angled triangle.

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

Distance Formula is used to calculate distance between two points A(a,b) and B(c,d)

denoted by [tex]d=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex]

In the given question , first calculate the length of each side of the triangle.

given X(3,1),Y(3,7),Z(11,1)

using distance formula

XY=[tex]\sqrt{(3-3)^{2} +(7-1)^{2} } =\sqrt{36} =6[/tex]

YZ=[tex]\sqrt{(11-3)^{2} +(1-7)^{2} } =\sqrt{8^{2}+(-6)^{2} } =\sqrt{64+36}= \sqrt{100} =10[/tex]

XZ=[tex]\sqrt{(11-3)^{2}+(1-1)^{2} } =\sqrt{8^{2} } =\sqrt{64} =8[/tex]

The longest side is 10 and other two sides are 8,6.

by using Pythagoras Theorem

[tex]hypotnuse^{2} =base^{2} +perpendicular^{2}[/tex]

[tex]YZ^{2} =XY^{2} +XZ^{2} \\ \\ 10^{2} =8^{2} +6^{2} \\ \\ 100=64+36\\ \\ 100=100[/tex]

Since Pythagoras Theorem is satisfied It is a right  angled triangle.

Therefore ,  The ΔXYZ is an Right Angled triangle.

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Answer:

you should use subtraction to solve this problem

Antonio spent 1/2 hours longer at soccer practice then baseball practice

Step-by-step explanation:

9/10-2/5

9/10-4/10

=

5/10 or 1/2

The simplified expression for (6-5 / 4-2) is 1/2 .

The given expression is,

6-5 / 4-2

First we need to solve the numerator which is (6-5) and on simplifying the numerator we can write,

Numerator = ( 6 - 5 ) = 1                         equation 1

Similarly, now we can proceed to solve the denominator which is (4 - 2) and on simplifying the denominator we write,

Denominator  = (4 - 2) =2                       equation 2

Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression (6-5 / 4-2) as,

(Numerator / Denominator) = (6-5 / 4-2) = 1/2

The simplified expression for (6-5 / 4-2) is 1/2 .

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Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

16 + 18 > 26

18 + 26 > 16

26 + 16 > 18

Hence, these set of numbers can be the measures of the sides of a triangle.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if [tex]a^{2} + b^{2} < c^{2}[/tex]

obtuse if  [tex]a^{2} + b^{2} > c^{2}[/tex]

right if  [tex]a^{2} + b^{2} = c^{2}[/tex]

∴The longest side is 26.

Hence, a = 16, b = 18 and c = 26;

Consider [tex]a^{2} + b^{2[/tex]  :

= [tex]16^{2} + 18^{2}[/tex]

= 580.

Now consider [tex]c^{2}[/tex] :

= [tex]26^{2}[/tex]

= 676.

Thus, [tex]a^{2} + b^{2} < c^{2}[/tex].

Hence, the triangle is acute.

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