Solve for y in this diagram. Justify your answer.

Answer:

24

Step-by-step explanation:

Proof of ray BC is the angle bisector of angle ABA' is given.

Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.

A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.

Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.

Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.

Therefore, <A'B'C' = <ABC

by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.

Therefore, the ray BC is the angle, bisector of angle ABA'.

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The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.

Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Given that the rectangular box is made from cardboard the thickness is x.

The length of the box will be,

L = 4.5 - 3x

The width of the box will be,

W = 4 - 2x

The thickness of the box is,

H = x

The volume of the box will be calculated as,

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 18 - 12x - 9x + 6x² ) x

V = 6x³ -21x² + 18x

For maximum volume differentiate the volume with respect to x and get the value of x,

dV / dx = d / dx (  6x³ -21x² + 18x ) = 0

d / dx (  6x³ -21x² + 18x ) = 0

18x² - 42x + 12 = 0

3x² - 7x + 6 = 0

Solve the above quadratic equation as,

x = [ -b ±√(b² - 4ac) ] / 2a

x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )

x = 1.17

The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,

V = 6x³ -21x² + 18x

V = 6(1.17)³ -21(1.17)² + 18(1.17)

V = 9.6 - 28.7 + 21.06

V = 1.96 cubic inches

The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.

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The proposition ststement is: the only prime number that is odd is 2.

The correct answer is an option (d)

In this question we have been given some statements.

we need to identify the proposition statement.

We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.

a) get me a glass of milkshake.

It is a commanding statement.

b) god bless you!

It is a type of optative statement.

c) what is the time now?

It is a question sentence.

d) the only odd prime number is 2.

It is a false proposition statement.

Therefore, option (d) is a proposition statement.

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The equations of inequalities are y < 4 and y > x.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The line of the graph is not solid. The lines of the graph is dotted. Thus the inequality sign will be less than or greater than.

One graph line is parallel to x-axis and it intersect y axis at (0,4).

The equation of the line that is parallel to x-axis and it intersect y axis at (0,a), then the equation of the line is y = a

The equation of the line parallel to x-axis is y = 4.

The equation of line that passes through origin is y = mx

The line passes through the point (1,1).

Putting x = 1 and y = 1 in y = mx:

1 = m

Therefore the equations of lines are y = x and y = 4

The inequality will be y < x or y > x for the line  y = x.

The inequality will be y < 4 or y > 4 for the line  y = 4.

(-2,0) is a point on the shaded area.

Putting x = -2 and  y = 0 in y > x

0 > -2 true.

The inequality is y > x

Putting x = -2 and  y = 0 in y < 4

0 < 4  true.

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Answer:

4th one

Step-by-step explanation:

Hope that helps.

The glide reflection that maps ABC to A'B'C' is given as follows:

The glide reflection is a combination of a reflection with a translation.

The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.

The midpoint of segment A'B' is given as follows:

The slope of this segment is given as follows:

m = (-6 - (-2))/(6 - 4) = -1.

Then the slope of the reflection line is of:

m = 1.

(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).

Then:

y = x + b.

When x = 5, y = -4, then the intercept b is calculated as follows:

-4 = 5 + b

b = -9.

Thus the reflection line is of:

y = x - 9.

Then the translation is given subtracting the coordinates of one of the vertices, as follows:

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The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.

What is a sphere?

The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.

Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.

The radius of a sphere is the half of its diameter.

The radius of the bottom ball is 3/2 feet =1.5 feet

The radius of the middle ball is 2/2 feet = 1 feet.

The radius of the top ball is 1/2 feet = 0.5 feet.

The volume of a sphere is 4/3 × ∏r³.

The volume of  bottom ball is  4/3 × ∏ × (1.5)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (1)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (0.5)³  cubic foot.

The total amount of snow is

4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³

=  4/3 × ∏ [1.5³  +1³  + 0.5³ ]

=  4/3 × ∏× 4.5

= 18.84

≈ 19 cubic foot

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The algebraic expression for "The room capacity does not exceed 250" is D. c≤250

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

It should be noted that "the room capacity does not exceed 250" simply means it should be less than or equal to 250. This will be c≤250.

In conclusion, the correct option is D.

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According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.

In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.

According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:

m ∠ x = 74°

x = 74°

Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.

The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.

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Answer:

Option 3:  the function that goes through the point (3, 5) is f(x-5)-1

Step-by-step explanation:

To find which function goes through the point (3, 5), we can substitute 3 for x and solve for the value of f(x).

For option 1, f(x-5)+1, we have:

f(3-5)+1 = f(-2)+1 = 6+1 = 7

For option 2, f(x+5)-1, we have:

f(3+5)-1 = f(8)-1 = ?

For option 3, f(x-5)-1, we have:

f(3-5)-1 = f(-2)-1 = 6-1 = 5

For option 4, f(x+5)+1, we have:

f(3+5)+1 = f(8)+1 = ?

Answer:

D

Step-by-step explanation:

when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.

f(x) = (x - 3)(x + 6)(x - 1)

we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :

-3 × +6 × -1 = +18

and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).

The value of a+b is 67.5+52.2=120.1 degree.

Which is the value of B?

The middle number, the one immediately following the x, is the b-value. A and C are also numerals, much as the letter B. These can all have any number. They all work together to show you how the quadratic function will be graphed. If you haven't used your y = mx + b equation in a while, dust it off and use the three values you were given for x, y, and m to solve for the b-value, which is the value of the y-intercept. The equation is then solved for the last variable: b, the y-value intercept's.

[tex]\begin{aligned}& 360-90=270 \\& 270-2=135 \\& 180-135=45 \\& \frac{45}{2}=22.5 \\& 90-22.5=67.5 \\& b=67.5^{\circ}\end{aligned}[/tex]

90 *67.8+a 110 =360

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question, we have to calculate the ratio by dividing a by b we will get the ratio as [tex]\frac{4}{3}[/tex].

Using the ratio formula, ratios can be represented as a fraction. The ratio formula for any two quantities says a and b, is a:b = a/b. Because a and b are individual amounts for two portions, the total quantity is given as (a + b).

Known Total Amount

Determine the total quantity to be produced.

Determine the total number of parts in the ratio.

Divide the total quantity made by the total number of parts to get the amount per part.

Calculate the amount of each ingredient by multiplying each component by the amount per part.

Given:

Here is the ratio of eggs to flour

Eggs(a)     0    2     4    6

Flour(b)     0   1.5   3    4.5

For the table look at the image.

as per the question, we have to calculate the ratio by dividing a by b we will get the ratios as [tex]\frac{4}{3}[/tex].

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The maximum width Casket that will fit in a standard vault is 28 inches.

Standard measurements may vary significantly depending on the manufacturer.

Caskets normally measure 84 inches long, 28 inches broad, and 23 inches tall. Both wood and metal caskets often have the same proportions. Caskets are intended to fit into normal burial sites, which are generally 30-inches wide and may accommodate ordinary caskets as well as enlarged caskets of 28-inch and 29-inch dimensions.

Casket inside dimensions vary significantly; the metal caskets are typically 78 or 79 inches long and 23 or 24 inches broad.

A typical size casket/coffin is enough for the most majority of individuals. Standard caskets can typically (but not always) fit people up to 6'5" and 350 pounds, but we strongly advise you to speak with your funeral director to determine the precise casket size you require.

The maximum width Casket that will fit in a standard vault is 28 inches.

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True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.

When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.

                   While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.

When there is no association in a correlational analysis, what happens?

The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.

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First, state the null and alternate hypothesis for the hypothesis test

H0:p=0.52

Ha:p≠0.52

z=pˆ−p/√p(1−p)/n

z= pˆ−p divided by the square root of p(1−p) divided by the sample (n)

z= 0.49^-0.52/ √0.52 ( 1- 0.52) / 340 = -2.24

z=-2.24

When using rejection regions, we reject the null hypothesis, H0, if:

z<−zα for a left-tailed test

z>zα for a right-tailed test

|z|>zα/2 for a two-tailed test

Thus the decision rule is: Reject the null hypothesis, H0, if |z|>2.33.

Since the absolute value of the z test statistic, 2.24, is less than the critical value, 2.33, we fail to reject the null hypothesis.

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Answer:

Step-by-step explanation:

You want to know the measure of angle 1 given that angle 2 is four times angle 1, and their sum is 95°.

The angle sum theorem tells you the whole is equal to the sum of the parts.

  ∠1 +∠2 = ∠WXZ

Using the given information, we can write ...

  ∠1 + (4×∠1) = 95°

  5×∠1 = 95° . . . . . . . . collect terms

  ∠1 = 19° . . . . . . . . . divide by 5

Then angle 2 is ...

  ∠2 = 4×∠1 = 4×19°

  ∠2 = 76°

6/7

Step-by-step explanation:

1 - x = 1/7

- x = 1/7 - 1

- x = 1/7 - 7/7

- x = -6/7

x = -(-6/7)

x = 6/7

thus,

1 - 6/7 = 1/7

The coordinates of C are (8/7, 10/7) if point A is (-4, -2) and point B is

(8, 6)

The section formula aids in finding a point's coordinates so that the line connecting two points can be divided in a ratio. This involves both internal and external activities. P (x, y) = (c, m, plus a, plus n, plus d, plus b, plus n). The Section formula is used to determine the ratio by which a line segment is divided by a point either internally or externally in coordinate geometry. It is used to identify a triangle's centroid, incenter, and excenter. Physics uses this technique to determine equilibrium points, the centers of mass of systems, and other things.

A(-4, -2), B(8, 6)

m:n=3:4

((3(8)+4(-4))/(3+4) , ((3(6)+4(-2))/(3+4))

=((24-16)/7, (18-8)/7)

=(8/7, 10/7)

Therefore, the coordinates of C are (8/7, 10/7)

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Answer: B

Step-by-step explanation:

Answer: The answer is D. 2 | 0.25

Step-by-step explanation:

I don't really have a good explanation, but I hope it helps!

In 3 hour  Mr. Reed can presents 15 presentations.  The division equation and a multiplication equation are 3 ÷ 1/5 =15 and 3 × 5 = 15 respectively.

What is an equation of division?

Mathematical equations involving the division operator are referred to as division equations. An equals sign appears in a division equation in its entirety. The division operator and the numbers that are being divided will both be on one side. The other side displays the result of the division.

The 3 large rectangles represent the 3 hours.

Each presentation is 1/5 hour so each rectangle is divided into 5 equal sections.

From the model you can write the division equation: 3 ÷ 1/5 =15

You can also write the multiplication equation: 3 × 5 = 15

Both equations show 15 projects are presented in 2 hours.

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Answer: C

Step-by-step explanation:

It should be 5 x 3, considering that rows come before the columns.

Answer:

Step-by-step explanation:

Answer: 2

Answer:2

Step-by-step explanation:

The true statements about the image of the parallelogram are,

The corresponding sides have different lengths.

The parallelograms are congruent.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A parallelogram in a coordinate plane is translated, rotated, and then reflected.

In the case of translation, rotation and reflection would only change its coordinate points, and the preimage and image will be congruent.

The coordinate points of the vertices would only change if given.

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Answer:

None of these

Step-by-step explanation:

[tex]\frac{1}{4}+\frac{1}{2} \cdot \frac{4}{7}=\frac{1}{4}+\frac{4}{14}=\frac{1}{4}+\frac{2}{7}=\frac{7+8}{28}=\frac{15}{28}[/tex]

A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

If the age is expressed as a ratio, such as p:q, then qx and px are taken into account as the age. If you assume that you are x years old now, then n times that number is (xn) years. If you're assuming that x is the current age, then 1/n of that number will equal (x/n) years.

calculation

Let's say there is an age difference of x and y,

in which case the answer to question 28 should be 2.03 years:

(x-y)*60/100.

A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

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The volume of the rectangular block in this problem is given as follows:

1300 cm³.

The block is a rectangular prism, hence it's volume is given by the multiplication of it's dimensions, as follows:

V = length x width x height.

The dimensions for this block are given as follows:

However, there is a small rectangular block that is removed from the prism, with the dimensions given as follows:

Hence the volume of the rectangular block can be calculated as follows:

V = 16 x 10² - 6 x 5 x 10 = 1300 cm³.

(total volume subtracted by the removed volume from the empty space at the middle).

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Answer:

Mabel will use scale factor of 20 to enlarge the design.

{ If you do need explanation, Please inform me.}