Which expression is equivalent to −3(2x − 8) + 4x?
A -2x - 8
B -2x + 24
C -10x - 8
D -10x + 24

The present ages of the teachers are 25 and 29 years old.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that sum of the present ages of two teachers is 54 years. If the age of one teacher is 4 years more than the other, then;

Let the ages of teachers are x and y

x + y = 54

x = 4 + y

So, 4 + y + y = 54

4 + 2y = 54

y = 25

x = 29

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Answer:

yes, but not less than zero.

Step-by-step explanation:

The absolute value is only greater than or equal to zero.

[tex] | - x| \geqslant 0[/tex]

where x is real number

Answer:

  see attached for a graph

  a. BA≅BC (the compass told me so)

  c. AD≅CD

Step-by-step explanation:

You want a graph of ∆ABC, with A(4, 7), B(0, 0), and C(8, 1). You want to identify the congruent sides, construct an angle bisector, and comment on how it divides the opposite side.

The graph of the points, and the construction of the angle bisector are shown in the attachment.

Since you have your compass available for construction, you can use set it to the measure of one side and compare that to the other two sides. It does not take long to identify AB ≅ BC. (A compass setting shows they are the same length.)

As you know, an angle bisector is constructed by first identifying two points on the sides of the angle that are the same distance from the vertex of the angle. Then two intersecting arcs are drawn with the same radius using those points as their centers. The vertex and the intersection of the arcs defines the ray that is the angle bisector. This is shown in the attachment.

You can count grid squares (or use the compass) to determine that AD and CD are the same length: D is the midpoint of AC.

This reinforces your knowledge that the angle bisector of the a.pex angle of an isosceles triangle is also an altitude and a median.

Plug in t = 0, in the given equation to get d=32-5t² = 32

Plug in t = 0.5, in the given equation to get d= 30.75

Plug in t = 1 , in the given equation to get d= 27

Plug in t = 1.5, in the given equation to get d= 20.75

Plug in t = 2 , in the given equation to get d= 12

Below is the completed table and the data on the coordinate plane.

The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. Vertices (also known as nodes or points) make up a graph in this sense, which are connected by edges (also called links or lines).

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics of study in discrete mathematics is graphs.

In physical, biological, social, and information systems, graphs can be used to model a wide variety of linkages and processes. Graphs can be used to represent a variety of real-world issues.

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Answer:

Untuk mencari nilai x dari persamaan 4x+7x+141+85+x+27=360, pertama-tama kita harus menyederhanakan persamaan tersebut dengan menambahkan semua x yang ada di sisi kiri persamaan.

4x+7x+x = 12x

Selanjutnya, kita harus mengurangi semua bilangan yang ada di sisi kiri persamaan dari kedua sisi persamaan:

360 = 12x + 141 + 85 + 27

Setelah itu, kita harus mengurangi semua bilangan yang ada di sisi kanan persamaan dari kedua sisi persamaan:

360 - 253 = 12x

107 = 12x

Akhirnya, kita harus membagi 107 dengan 12 untuk mencari nilai x:

x = 8.9167

Jadi, nilai x dari persamaan tersebut adalah 8.9167.

It's worth noting that some steps are not needed to be done and the equation can be simplified by doing some operations at once like : (4x+7x+x+141+85+27=360) => (12x+253=360) => (12x=107) => (x=8.9167)

The four types of data in excel are text type, number type, logical and error type.

Excel data types are the four different kinds of values in Microsoft Excel. The four types of data are text, number, logical and error.

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Answer: 4xy²(5-y)

Step-by-step explanation:

To factorize, we must take out common multiples in both parts of the equation. Think of 20xy² and -4xy³ as two completely separate parts. Now, we need to see which parts of the equation are found in both. For instance, 4 can go into both, an x can go into both, and y² can go into both. Now, we simply factor.

Bring the similarities out to the front: 4xy²()

Now, use division to find what would be inside the parenthesis: 5 - y

Now, combine these two parts: 4xy²(5-y)

To check your work, you can simply multiply the outside of the parenthesis by the inside, and you should get the same as what you started with. Hope this helps!

The width of the parallelogram can be any value greater than or equal to 14 feet.

What is parallelogram ?

A parallelogram is a four-sided polygon with opposite sides that are parallel. It has opposite angles that are equal and opposite sides that are equal in length. A special cases of parallelograms are rectangles, which have four right angles, and squares, which have four right angles and all sides are equal in length.

P = 2l + 2w >= 40

where P is the perimeter, l is the length and w is the width.

Substituting the given value for the length, we get ,

2(6) + 2w >= 40

Simplifying and solving for w ,

12 + 2w >= 40

2w >= 28

w >= 14

Therefore, the width of the parallelogram can be any value greater than or equal to 14 feet.

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A total of 96 pots can be made in one eight-hour day.

The result of two numbers being multiplied is known as the product. The multiplier is the number of such equal groups, and the multiplicand is the number of items in each group. In this instance, the multiplicand is, the multiplier is, and the product is 6.

Speed of coffee machine = 12 pots of coffee per hour.

Amount received after selling each pot of coffee = $10

For finding the total pots of coffee made by the coffee machine in 8 Hr, we will simply multiply the total number of hours which is 8 Hr to the efficiency of the machine which is 12 pots per hour.

So, the total pot made by the machine will be 12*8 = 96 pots

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When you divide a number by 1/2, it is the same as multiplying the number by 2. Therefore, the result of the division is two times the original number.

Let's say we have a number, X.

When you divide X by 1/2, you can rewrite the equation as:

X ÷ 1/2 = X × 2

Thus, the result of the division is two times the original number, X.

Let's say we have a number, X. When you divide X by 1/2, you are essentially multiplying X by 2. This means that the result of the division is two times the original number. In other words, if you divide X by 1/2, the answer will be 2X. To put it another way, if you take any number, X, and divide it by 1/2, the result will be two times the original number. This is because 1/2 is the same as multiplying the number by 2. For example, if you divide 10 by 1/2, the result will be 20, since 10 multiplied by 2 is 20. Similarly, if you divide 25 by 1/2, the result will be 50, since 25 multiplied by 2 is 50. In conclusion, when you divide any number, X, by 1/2, the result will always be two times the original number.

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As a result, the solution is shaped like a circle ( -5 , 7 ). The second half of the text has a 6 mm diameter. Three and four are FALSE. There are ten miles between points A and B.

The construction of a circle is the outcome of following a thinking object in a plane and keeping a fixed distance from a particular location. A Greek word kirkos, which means hoop or ring, is the source of the English word circle.

Here,

Typically, a circle's equation is,

( x - h )² + ( y - k ) ( y - k )

x² = r²

( y - k ) ( y - k ) = r²

6² = r²

where the radius of the ring is and the center's coordinates are (h, k).

Part 1.

We arrive to using the formula for the common circle.

The circumference of a circle's coordinate is ( -5 , 7 )

As a result, the second choice is the best.

Part 2.

We arrive to using the formula for the common circle.

The circle's diameter is six.

The initial choice is therefore the best.

Part 3.

We arrive to using the equation again for common circle.

Circle circumference coordinate: ( 2 , 3 )

False as a result.

The axis coordinates of the circle are: ( 2 , 3 )

False, then.

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The manager of a garden shop wants to make a mixture that contains 74% rye grass. The weight of the 60% mixture used in this composition is 30 lb.

Percentage is used to denote a fraction of a hundred.

Suppose q represents the weight of the mix that contains 60% rye grass, then the weight of rye grass in this mix is:

w1 = 60% q = 0.6 q

Mix 2: 70 lb grass seed that contains 80% rye grass. The weight of rye grass in the second mix is:

w1 = 80% x 70 = 56 lb

The final mixture has 74% rye grass. Total weight of rye grass in the final mixture:

weight of rye grass = w1 + w2

                                = 0.6 q + 56

Total weight of the final mixture = (q + 70) lb

74% = 0.74 = (0.6 q + 56) / (q + 70)

0.6 q + 56 = 0.74 (q + 70)

0.74 q - 0.6 q = 56 - 0.74 x 70

0.14 q = 4.2

q = 4.2/0.14 = 30

Hence, the weight of 60% mixture is 30 lb.

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A. Johnny's biweekly gross pay is $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay is $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $37.63.

D. Johnny's new annual salary with a 14.5% raise is $71,179.93.

A. Johnny's biweekly gross pay is $62,285.50 / 24

= $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay, which is $2,595.23 * 6.2% = $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $2,595.23 * 1.45% = $37.63.

D. Johnny's new annual salary with a 14.5% raise is $62,285.50 * 1.145 = $71,179.93.

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Answer:The graph of x = -4 is a vertical line located 4 units to the left of the y-axis.

The domain of x = -4 is the set of all real numbers, since any real number can be plugged into x = -4 and the equation will be true. This is because x = -4 is a vertical line and not a function, it cuts the y-axis at one point, so it doesn't matter what value you put on x it will always be -4.

The range of x = -4 is a single point on the y-axis, y = -4.

Step-by-step explanation:

The original expression [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex] was rationalized by multiplying both numerator and denominator by [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex], and then dividing numerator and denominator by [tex]$\sqrt[3]{4}$[/tex].

[tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}} = \frac{\sqrt[3]{8}}{4}$[/tex]

Minimum possible value of [tex]$ab = 32$[/tex]

[tex]= \frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{4}$[/tex]

We start with the given expression, [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex], which is in the form [tex]$\frac{p}{qr}$[/tex]. To rationalize the denominator, we need to multiply both numerator and denominator by qr (which is [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex] in this case). This gives us[tex]$\frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$[/tex]. We can simplify this expression further by dividing both numerator and denominator by [tex]$\sqrt[3]{4}$[/tex], giving us [tex]$\frac{\sqrt[3]{8}}{\sqrt[3]{2} \sqrt[3]{4}}$[/tex]. Finally, we can simplify the denominator further by multiplying both numerator and denominator by [tex]$\sqrt[3]{2}$[/tex], giving us the final result of [tex]$\frac{\sqrt[3]{8}}{4}$[/tex]. The minimum possible value of ab is 32.

The original expression [tex]$\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$[/tex] was rationalized by multiplying both numerator and denominator by [tex]$\sqrt[3]{4} \sqrt[3]{2}$[/tex], and then dividing numerator and denominator by [tex]$\sqrt[3]{4}$[/tex]. The final result was[tex]$\frac{\sqrt[3]{8}}{4}$[/tex], and the minimum possible value of ab was 32.

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The given condition can be modeled by the compound inequality:

x < -3 or x > 3.

We want to find an inequality that describes the next condition:

"All real numbers X with an absolute value of greater than three"

So our variable will be X, and the absolute value of X is written as:

|X|

We want to have an absolute value larger than 3, so we can write the inequality:

|X| > 3.

The absolute value part can be separated into two, such that we will get two inequalities:

x > 3

x < -3

So the inequality that illustrates the given condition is the compound inequality:

x < -3 or x > 3.

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Answer: Well you have to see on the number that is close to the decimal point

Step-by-step explanation:

0.2438

0.4485

0.8641

3.2527

17.9926

The equation of the best-fit model is given as follows:

y = 5.33x + 67.78.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

The points for this problem are given as follows:

(10, 120), (15, 150), and (25, 200).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 5.33x + 67.78.

Meaning that the correct option is given by the first option.

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462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

given that

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) If the set has n elements, the number of k-combinations, denoted as nck

there are 5 hats

there are 11 people

now , we need to distribute all five hats among all eleven people so that no one gets more than one hat = 11 [tex]C_{5}[/tex]

= [tex]\frac{11!}{5!(11-5)!}[/tex]

=462 combinations

462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

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Answer: II Only

Step-by-step explanation:

Let's see.

The given inequality is -2<=-8-x

Therefore, we can add 8 to both sides and get

6<=-x

Now we need to multiply -1 to both sides to get

x<=-6, which means that x is less than or equal to -6.

Now the only choice that satisfies this inequality is -6.

So II only is the answer.

The angle measure of triangle DEF in order of smallest to largest is m∠E = 36.03°, m∠F = 70.72° and m∠D = 73.25°.

The answer is: m∠E < m∠F < m∠D

The angle of a triangle can be found given its 3 sides using the cosine rule.

The formula is: cos(C) = (a² + b² -c²) / 2ab  

where c is the length of the side opposite angle C, a and b are the lengths of the other two sides, and cos(C) is the cosine of angle C.

DE = f = 69 miles, EF = d = 70 miles and DF = e = 43 miles

cos (F) = (d² + e² -f²) / 2de  

cos (F) = (70² + 43² -69²) / (2*70*43)

cos (F) = 71/215

F = cos⁻¹(71/215)

F = 70.72°

cos (E) = (d² + f² -e²) / 2df

cos (E) = (70² + 69² -43²) / (2*70*69)

cos (E) = 93/115

E = cos⁻¹(93/115)

E = 36.03°

DE = f = 69 miles, EF = d = 70 miles and DF = e = 43 miles

cos (D) = (e² + f² - d²) / 2ef

cos (D) = (43² + 69² - 70²) / (2*43*69)

cos (D) = 285/989

D = cos⁻¹(285/989)

D = 73.25°

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The break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

What is average ?

The average is a measure of central tendency that is calculated by adding a set of values together and dividing the sum by the number of values. It is also known as the arithmetic mean. It is a way to represent a typical value of a dataset.

The break-even point is the point at which the cost of the products equals the revenue from the sales of the products. To find the break-even point, we need to set the cost function (C(x) = 550 + 3.00x) equal to the revenue function (R(x) = 5.50x) and solve for x.

C(x) = 550 + 3.00x = R(x) = 5.50x

3.00x = 5.50x - 550

0.50x = 550

x = 1100

So the break-even point is 1100 products sold. This means that if the store can sell 1100 products, it will be able to cover its costs and make a profit.

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Answer:

34.5 square units.

Step-by-step explanation:

We can construct a 7 x 7 square around the polygon. Then, we measure the two right triangles that together, along with the polygon, make up the 7x7 square. The total measure of the two triangles is 15/2+7=14.5. Now we subtract that from the area of the square to get the area of the polygon. 49-14.5=34.5, so 34.5 square units is the answer.

$156.78 is the total cost of material for the bunny costumes.

Given a specified quantity of goods produced, a cost function is a mathematical formula that may be used to determine the overall cost of production. 

Given that,

Total required bunny costumes = 6

Total faux fur requirements for each bunny costume =  2.6 square yards

Cost of faux fur = $10.05 per square yard

The costume budget for the bunny costumes = $200

The total cost of material for the bunny costumes = 2.6 *10.05 *6 = $156.78.

Thus, $156.78 is the total cost of material for the bunny costumes.

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The measure of the largest angle in wxyz is 4 times the measure of angle w, plus double that measure, plus 3 degrees.

Angle w: x = 4w

Angle y: y = 2x = 8w

Angle z: z = y + 3 = 8w + 3

The largest angle in wxyz is z = 8w + 3.

In a convex quadrilateral wxyz, the degree measure of angle x is four times that of angle w. This means that the measure of angle x is four times the measure of angle w. The measure of angle y is double that of angle x. This means that the measure of angle y is twice the measure of angle x, or eight times the measure of angle w. Lastly, the measure of angle z is 3 degrees larger than that of angle y. This means that the measure of angle z is eight times the measure of angle w plus three degrees. Therefore, the measure of the largest angle in wxyz is 8w + 3.

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The study method used to evaluate mother-child attachment is best described as option A: experimental.

Children who refuse food by acting negatively or in opposition seem to be a common theme in feeding interactions between depressed mothers and their kids. The purpose of this study was to examine parenting behaviours in the setting of feeding in moms who were suffering from serious depression from an attachment theory perspective. The easiest way to sum up the research design used to assess mother-child attachment is option A: experimental.

The idea of sensitive responsiveness was developed by attachment theory to measure a mother's capacity to empathetically recognise and respond to her child's signals. Their attitudes and behaviours when providing care may be badly impacted by this distress, which may be pervasive.

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