Graph the solution to this inequality on the number line.

−3x<4.2

Answer: Our arc length calculator can calculate the length of an arc of a circle

Step-by-step explanation:

Multiply the radius by the central angle to get the arc length.

Angle ∠ABC is bisected into two congruent angles by the bisector.

ΔABD and ΔCBD are equivalent, and by CPCTC, ∠ABD ≅ ∠CBD results;

• BD bisects ∠ABC.

Reasons:

The following is a presentation of the two column proof;

Statement

1. D is the midway of AC So AB ≅ BC.

2. AD ≅ DC

3. BD is Reflexive property of congruency

ΔABD ≅ ΔCBD , Side-Side-Side, Congruency Postulate

∠ABD = ∠CBD                              Definition of congruency

∠ABC = ∠ABD + ∠CBD                 Angle addition postulate

is bisects ∠ABC                     Definition of angle bisector

5. ∠ABD congruent to BD (Reasons 4; The SSS congruency postulate asserts that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Congruent Parts of Congruent Triangles are Congruent, or CPCTC, is the acronym for reason number five.

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The line equation for Carmen's donation plan is y + 2x ≤ 460.

Please refer to the attached graph below for the corresponding region.

From the case, we know that:

City youth fund = x

Educational growth foundation = y

Educational growth foundation = 2 city youth fund

Total budget = $460

Based on the case, we know that:

y = 2x --> the slope of the line constraint should be 2

Then, the line equation for this condition should be:

y + 2x ≤ $460

To construct the graph, we need to find the point constraint first.

(y= 0)

(0) + 2x = 460

x = 230 --> (230, 0)

(x = 0)

y + 2(0) = 460

y = 460 --> (0, 460)

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The steps to draw the absolute value graph is explained below.

The term graph is known as  a mathematical representation of a network and it describes the relationship between lines and points

Here we have to define the steps to be performed to plot the graph for the absolute value function.

As we all know that every absolute value graph will make a “V”-shaped figure.

And the graph consists of two pieces that is one with a negative slope and one with a positive slope.

Here we have the the point of their intersection is called the vertex.

Here we also know that the absolute value graph is symmetrical, which means it can be folded in half on its line of symmetry.

in order to plot the graph for the absolute value function then we have to plot two lines for the positive and negative cases that meet at the expression's zero.

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Answer:

22

Step-by-step explanation:

The ratio of length of one side of CEFGH and length of one side of SUVWX  is, 5/4. So Option A is correct

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

We have two pentagons,

CEFGH and SUVWX

length of CE = 5

length of SU = 4

Ratio of CE and SU,

Ratio =  CE/ SU

         =  5/4

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Opportunity cost increases along the production possibility frontier because of the principle of diminishing returns.

Diminishing returns refer to the fact that as we allocate more resources to the production of one good, the marginal productivity of those resources decreases. In other words, as we produce more of one good, it becomes increasingly difficult and costly to produce additional units of that good.

As we move along the PPF, we are producing more and more of one good and less and less of the other. The resources that were previously used to produce the other good are now being used to produce more of the first good. As we move along the PPF, we are sacrificing more and more of the second good in order to produce additional units of the first good, and this is reflected in the opportunity cost. The opportunity cost of producing one good increases as we move along the PPF.

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The perimeter of the card is 32 centimeters. Perimeter of a square is given by 4x, where x is the length of each side of the square.

Perimeter of a square is given by 4x, where x is the length of each side of the square.

In this case, x=4.

Therefore, the perimeter of the card is 4x = 4(4) = 32.

The perimeter of a square is determined by multiplying the length of each side by 4. In this case, the length of each side of the square tank you card is x=4. Therefore, the perimeter of the card can be calculated by multiplying 4 with 4 which is equal to 32 centimeters. This means that the perimeter of the tank you card when x=4 is 32 centimeters.

Perimeter of a square is given by 4x, where x is the length of each side of the square.

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I'm sorry that you don't understand this question but sadly I am unable to help since I don't understand this question and what is going on.

Composite figure has an area of 10.5 + 7.25π square units. (Correct choice: D)

Composite figure are the result of combining two or more geometric figures. In this case we find a composite figure that is a combination of a semicircle and a right triangle, whose area formulas are described below:

Right triangle

A = 0.5 · w · l

Semicircle

A = (π / 8) · D²

Where:

First, determine the diameter of semicircle by Pythagorean theorem:

D = √(7² + 3²)

D = √58

Second, determine the area of the right triangle:

A = 0.5 · 7 · 3

A = 10.5

Third, calculate the area of semicircle:

A' = (π / 8) · (√58)²

A' = 7.25π

Fourth, find the area of composite figure:

A'' = A + A'

A'' = 10.5 + 7.25π

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The combination of entrees and desserts that the restaurant serve will be:

A. The restaurant could serve 40 entrees and 25 deserts.

E. The restaurant could serve 64 entrees and 40 deserts.

The word problem in mathematics refers to a question that is written as a sentence which requires an individual to use his or her mathematics knowledge.

In this case, the local restaurant serves 8 entrees for every 5 desserts.

In this case it should be noted that:

40 / 25 = 8 / 5

64 / 40 = 8 / 5

The correct options are A and E.

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The triangle ΔABR and ΔRCA are congruent with each other. Then Line A R bisects Angle ∠BAC.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Line segment AB is-congruent-to line segment BC Line segment B C is congruent to line segment AC.

AB = BC = AC

In triangles  ΔABR and ΔRCA, we have

AB = AC               (Given)

∠RBA = ∠RCA     (Opposite sides have equal angle)

AR = AR               (Common sides)

The triangle ΔABR and ΔRCA are congruent with each other. Then Line A R bisects Angle ∠BAC.

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When solving a linear equation with x on both sides, you can have one, none, or infinite solutions.

What is the linear equation?

A linear equation is an equation that represents a straight line when graphed. It is an equation that can be written in the form of ax + b = 0, where a and b are constants and x is a variable.

When solving a linear equation with x on both sides, you can have one, none, or infinite solutions. This is option C. Linear equations can have one solution, when the equation has a unique value of x that makes the equation true. It can have no solutions when the equation is contradictory, meaning that no value of x can make the equation true. It can also have infinite solutions, when any value of x makes the equation true, typically represented by the equation being an identity.

Hence, When solving a linear equation with x on both sides, you can have one, none, or infinite solutions.

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The location of the vertices of the image of the rectangle WXYZ, following the dilation and reflection transformations are;

a. (-7, 5), (-4, 5), (-4, 3), (-7, 3)

b. (7, 5), (4, 5), (4, 3), (7, 3)

A dilation transformation involves the scaling of the dimensions of of the pre-image to get the dimensions of the image.

The points on the rectangle WXYZ are;

W(-7, 2), X(5, 2), Y(5, -6), and Z(-7, -6)

The scale factor of the dilation = 1/4

The center of dilation = (-7, 6)

The steps to perform the calculation of the dilation are as follows;

The coordinates of the rectangle following a translation rule of (7, -6) are;

W(-7, 2) ⇒ T₍₇, ₋₆₎ ⇒ W'(0, -4)

X(5, 2) ⇒ T₍₇, ₋₆₎ ⇒ X'(12, -4)

Y(5, -6)  ⇒ T₍₇, ₋₆₎ ⇒ Y'(12, -12)

Z(-7, -6) ⇒ T₍₇, ₋₆₎ ⇒ Z'(0, -12)

Dilating the image W'X'Y'Z' by a scale factor of 1/4, centered at the origin, we get;

W'(0, -4) ⇒ [tex]D_{1/4}[/tex]  ⇒ W''(0, -1)

X'(12, -4), ⇒ [tex]D_{1/4}[/tex]  ⇒ X''(3, -1)

Y'(12, -12)  ⇒ [tex]D_{1/4}[/tex]  ⇒ Y''(3. -3)

Z'(0, -12)    ⇒ [tex]D_{1/4}[/tex]  ⇒ Z''(0, -3)

Translating the above points, using the rule, (-7, 6), we get;

W''(0, -1)  ⇒ T₍₋₇, ₆₎  ⇒ W'''(-7, 5)

X''(3, -1)  ⇒ T₍₋₇, ₆₎  ⇒ X'''(-4, 5)

Y''(3. -3)  ⇒ T₍₋₇, ₆₎  ⇒ Y'''(-4, 3)

Z''(0, -3)  ⇒ T₍₋₇, ₆₎  ⇒ Z'''(-7, 3)

The coordinates of the rectangle WXYZ following the dilation by a scale factor of 1/4 with the center of dilation at (-7, 6) are;

b. The image following the reflection of a point (x, y), over the y-axis is (-x, y)

The coordinates of the image after a reflection across the y-axis are;

W'''(-7, 5) ⇒ [tex]R_{y-axis}[/tex] ⇒ W''''(7, 5) = R(7, 5)

X'''(-4, 5) ⇒ [tex]R_{y-axis}[/tex] ⇒ X''''(4, 5) = S(4, 5)

Y'''(-4, 3) ⇒ [tex]R_{y-axis}[/tex] ⇒ Y''''(4, 3) = T(4, 3)

Z'''(-7, 3)⇒ [tex]R_{y-axis}[/tex] ⇒ Z''''(7, 3) = U(7, 3)

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If the recipe needs 1/4 cup of brown sugar, that would be one batch.

2/4 = 2 batches

3/4 = 3 batches

So if there is one cup that would equal 4 bathes of yummy cookies.

The domain of the function y = √(x - 5) is x >= 5, that is [5, ∞).

The domain of the function y = sqrt(x - 5) is the set of all input values (x-values) for which the function is defined.

In this case, the square root function is defined for all non-negative values of x - 5. If x-5 is negative, it would result in an imaginary number, which is not defined. However, since x - 5 cannot be negative, x must be greater than or equal to 5. Therefore, the domain of the function y = √(x - 5) is x >= 5.

--The question is incomplete, answering to the question below--

"What is the domain of the function y = sqrt(x - 5)?"

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The perimeter of Equilateral Triangle is 14.547 m.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

The altitude of an equilateral triangle is 4.2 meters long.

let x is the measure of the side of the equilateral.

Using Pythagoras theorem

x = √(4.2)(4.2) + (x/2)(x/2) )

x = √( 4.2)² + (x²/4) )

x² = 17.64 + x²/4

3x²/4 = 17.64

x² = 17.64 (4)/3

x² = 23.52

x= 4.849

So, the perimeter of Equilateral Triangle

= 3 x side

= 3 (4.849)

=  14.547 m

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Now that we additionally know the point (3, -1) through which the new line should pass, we may express a line using the point-slope form: y = - 5 / 3 x + 4.

5x + 3y = 6

3y = -5x + 6

y = -5/3x + 6 / 3

y = - 5 / 3x + 2

y - y0 = m(x - x0)

y - (-1) = -5 / 3 (x - 3)

y + 1 = -5 / 3 x + 5

y = - 5 / 3 + 4.

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No triangle can be drawn having angles of 45°, 60° and 85°. This is because the sum of the angles of a triangle must equal 180°, and 45° + 60° + 85° = 190°.

No triangle can be drawn having angles of 45°, 60° and 85°. This is because the sum of the angles of a triangle must equal 180°, and 45° + 60° + 85° = 190°. A triangle is a three-sided polygon, with each side connected to the other two in a closed shape. All angles in a triangle must add up to 180° for the shape to be complete. If the angles in a triangle do not add up to 180°, then it is not a triangle, and cannot exist. Therefore, it is not possible to draw a triangle with angles of 45°, 60° and 85°, as the sum of these angles is 190°, which is greater than the 180° required.

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Answer:

-1 43/56

Step-by-step explanation:

Answer:

-99/56

Step-by-step explanation: i used my calc

On solving for {π}, we get that → π = (4ir/P).

Given is the statement as -

r equals the square root of P over 4 times pi times l.

We can write the statement as -

r = √(P/4πi)

√(P/4πi) = r

(P/4πi) = ± r

π(P/4i) = ± r

π = ± (4ir/P)

{π} is a non - negative value. We can write -

π = (4ir/P)

Therefore, on solving for {π}, we get that → π = (4ir/P).

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Answer: We can set up an equation to represent the total cost for both florists:

Cost for Flowers Florist = 2x + 10

Cost for Fub's Roses = 1x + 19

where x is the number of roses David buys.

To find out the number of roses David would have to buy for both florists to charge him the same amount, we set the two equations equal to each other and solve for x:

2x + 10 = 1x + 19

x = 9

So David would have to buy 9 roses for both florists to charge him the same amount.

Step-by-step explanation:

No, a triangle cannot have 2 obtuse angles as the sum of the angles of a triangle is 180.

An angle is a space shared by two rays that are joined at the same vertex. We can find different types of angles according to their amplitude.

If the amplitude is larger than 90º (90 degrees) and less than 180º (180 degrees) that tells us that it is an obtuse angle.

An obtuse angle is also defined as an angle that is formed when a ray rotates between 90º and 180º around a point.

Visually, this angle is more than a quarter of a circle but less than half of a circle. So, if we divide a circle into four parts, an obtuse angle will always occupy between 1/4 and 1/2 of a circle.

Thus, a triangle cannot have 2 obtuse angles as the sum of the angles of a triangle is 180.

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A hole occurs when there is a duplicate factor on the numerator or denominator. This is not the case here, so there are no gaps.

The denominator of f(x) cannot be zero because f(x) would become undefined. The values that x cannot be are obtained by equating the denominator to zero and solving.

To solve 5x² + 2x + 1 = 0

This does not factor, so verify the discriminant.

Here, a = 5, b = 2, and c = 1.

b² - 4ac = 4 - 20

= -16

Because the discriminant is 0, there are no real roots, and thus no vertical asymptotes.

Horizontal asymptotes can be found as

[tex]\lim_{x \to \infty}[/tex] , f(x) -> c

Divide the terms on the numerator/denominator by the highest power of x, x².

f(x) = (3x² /x² )/((5x²/x² )+(2x/x²) +(1/x²))

     = 3/ 5 + 2/x + 1/x²

Since x -> ±∞. f(x) -> 3/5 + 0 + 0

= y = 3/5

When there is a duplicate factor on the numerator/denominator, a hole occurs. This is not the case in this case, so there are no holes.

(3x2)/(5x2+2x+1) [-10, 10, -5, 5] graph

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(A) Approximately 65.85% of the survey respondents did not like either hamburgers or burritos.

(B) Approximately 26.36% of the students who like hamburgers also like burritos.

(C) The association between liking burritos and not liking hamburgers has the strongest association of its two factors.

Part A:

To find the percentage, we divide the number of respondents who do not like either by the total number of respondents and then multiply by 100:

[tex]\dfrac{135} { 205} \times 100 = 65.85\%[/tex]

Part B:

To find the percentage, we divide the number of respondents who like both by the total number of respondents who like hamburgers and then multiply by 100:

[tex]\dfrac{29} { 110} \times 100 = 26.36\%[/tex]

Part C: .

By examining the table, we can determine that the strongest association of its two factors is between the respondents who like burritos and do not like hamburgers, and the respondents who do not like burritos and do not like hamburgers.

The conditional relative frequency for respondents who like burritos and do not like hamburgers is:

[tex]\dfrac{41} { 110} \times 100 = 37.27\%[/tex]

The conditional relative frequency for respondents who do not like burritos and do not like hamburgers is:

[tex]\dfrac{54} { 205} \times 100 = 26.34\%[/tex]

Comparing these two conditional relative frequencies, we can see that the association between liking burritos and not liking hamburgers has a stronger association compared to not liking burritos and not liking hamburgers.

Therefore, the association between liking burritos and not liking hamburgers has the strongest association of its two factors.

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Answer:

7ft and 9ft need to be replaced

Step-by-step explanation:

in the image its clear that the length for 9ft seems too short and the length for 7ft seems too long so they have switched places

Answer:

Step-by-step explanation:

thats hard

The formula for the distance:

the distance (d) between two points x1, x2 is d = x2 - x1, where x2 > x1

We know that the distance is nothing but the length between 2 points.

It is measured in units of length.

For example, the distance between x = 5 and x = 8 on the x-axis of the is given by 8 - 5 = 3 units.

If we know the coordinates of the points then the distance between two poinnts is given by the distance formula.

For points p1, p2 with coordinates p1 = (x1, y1) and p2 = (x2, y2)

Using distance formula the distance (d) between points p1 and p2 is:

[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

The distance formula is an appliation of Pythagoras theorem.

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