The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.

The method that will be used in solving for x in the expression 5x + 6x = 22 is simplifying using addition and division operation

solving the equation gives x to be equal to 2

The expression given 5x + 6x = 22 is a linear function having one unknown variable and the solution is sought by using the relevant mathematical operations

Applying addition operation in solving for x

5x + 6x = 22

11x = 22

Applying division operation in solving for x

11x = 22

x = 2

hence, the solution of the the expression is x = 2

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The position of the sprinter is equal to the value of definite integral of the given velocity function v(t). The position at t = 4, 7, and 9 is 8, 8, 0.

The velocity is the first derivative of the position function. The position function is given in the attached picture.

s'(t) = v(t)

The position at time t is therefore equal to the definite integral from t = 0 to time t.

Since the graph is linear, the evaluation of each definite integral is equal to the area of triangles underneath the lines.

∫₀⁴ v(t) dt = (1/2) x 2 x 6 = 6

∫₄⁷  v(t) dt = (1/2) x 1 x 8 - (1/2) x 2 x 4  = 0.

∫₇⁹  v(t) dt = 2 x (-4) = -8

The position at t = 0 is s(0) = 2

Hence,

s(4) = s(0) + ∫₀⁴ v(t) dt  = 2 + 6 = 8

s(7) = s(0) +  ∫₀⁴ v(t) dt + ∫₄⁷  v(t) dt = 2 + 6 + 0 = 8

s(9) = s(0) +  ∫₀⁴ v(t) dt + ∫₄⁷  v(t) dt  + ∫₇⁹  v(t) dt = 2 + 6 + 0 - 8 = 0

The graph in your question was missing. Most likely it was like on the attached picture.

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What the area of the pre-image should be multiplied by to obtain the area of the image rectangle is; 4

The scale factor in the dilation of a mathematical object is one that determines how much larger or smaller the image will be when compared to the original image.

Now, the formula for area of a rectangle is;

A = LW

Where;

L is length

W is width

If the rectangle is dilated by a scale factor of 1/2, then it means that;

New length = ¹/₂L

New Width = ¹/₂W

New Area = ¹/₂L * ¹/₂W

= ¹/₄LW

Thus, to get the pre image are, we have;

Area of pre-image = 4 * Area of new image

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When she comes back to the lab the next morning at 8:00AM, the number of bacteria that will there be is 2000.

From the information, the biologist is researching a newly-discovered species of bacteria. At 8:00AM when she arrives at the lab, she puts a population of 600 bacteria into a favorable growth medium.

She measures the sample again before she goes home at 4:00PM and notes that the population is now 1300 bacteria. The difference in the population will be:

= 1300 - 600

= 700

When she comes back to the lab the next morning at 8:00AM, the number of bacteria that will there be will be:

= 1300 + 700

= 2000

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F(x) = 2x³ - x² + 5x − 3 is the polynomial that is in standard form. Thus, option D is correct.

Algebraic expressions called polynomials can include exponents that are multiplied, divided, or added. Different types of polynomials exist. specifically, monomial, binomial, and trinomial. A polynomial with only one term is referred to as a monomial. A polynomial with two unlike terms is referred to as a binomial. An algebraic expression with three terms is known as a trinomial.

Monomials - The term "monomial" refers to algebraic expressions with a single term. In other words, it is an expression that includes any number of similar terms. Hence the name "Bi"nomial," binomials are algebraic expressions with two unlike terms. Trinomials - Trinomials are algebraic expressions with three dissimilar terms, hence the name "Tri"nomial.

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120 tacos were sold that day. I have attached the work down below.

On solving the provide question, we got to know that volume of cube is  and volume of cuboid is , so volume cube is greater.

We are aware that a rectangle has four corners and is a two-dimensional form. Think of the form as a collection of parallel rectangles. The resultant form is known as a cube. Take a look at the following three-dimensional cube. Height, Width, and Length

The volume of the cube = [tex]a^3[/tex]

Where a is the length of the side = 7cm

volume of cube =                  

[tex]7*7*7[/tex]We are aware that a rectangle is a two-dimensional shape with four corners. Consider the shape to be a set of parallel rectangles. The resulting shape is referred to as a cube. Look at the following cubic object in three dimensions. Length, Width, and Height

volume of the cuboid = l*b*h =

[tex]7*8*4 = 224 cm^2[/tex]

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The number of children that attend the fair on the day tha 350 were present in the fair is 200

The number of children in the fair is obtained by solve a simultaneous equation generated as follows

let x be the number if children be x and the number of adults be y. such that

x + y = 350

and from  the cost we  have

$3y + $2x = 900

the two equations are

x + y = 350

3y + 2x = 900

solving simultaneously with a calculator

x = 200 and y = 150

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For the given expression, the correct answer is C, 7x².√2x⁴.6√2x¹² = 84x¹⁰.

Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

A variable is a letter, like x, y, or z, that stands in for an arbitrary number. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.

Given,

the expression is 7x².√2x⁴.6√2x¹²,

Solving the under root,

⇒ 7x².√2x².6√2x⁶

⇒ 7x² . √2 x². 6. √2 . x⁶     [√2 × √2 = 2]

⇒ 7 × 6 × 2 × x¹⁰ = 84 x¹⁰

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The table with values in the equivalent ratio is completed as

1 : 1/2

4 : 2

6 : 3

1/2 : 1/4

When we compare ratios, equivalent ratios are the ones that don't change. In order to determine whether or not different ratios are equivalent, we compare them side by side. An example makes it clear that the ratios 1:2 and 2:4 are equivalent. With the aid of division and multiplication, we can determine the two equivalent ratios.

In order to create a ratio that is equal to one that is already given, we must multiply or divide the given ratio's two terms by a non-zero number.

1 cup of flour = 1/2 cup of water

4 cups of flour = 1/2 × 4

                       = 2 cups of water

1/2 cup of flour = 1/2 × 1/2

                          = 1/4 cups of water

2 cups of water = 4 cups of flour

1 cup of water = 4/2

                          = 2  cups of flour

3 cups of water = 2 × 3

                           = 6 cups of flour

Thus, the table with values in the equivalent ratio is completed as 1 : 1/2, 4 : 2, 6 : 3 and 1/2 : 1/4.

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The resulting quadratic equation is x^2 - x - 7 = 0.

The x-values for which f(x) < 1 can be determined by solving the inequality f(x) < 1.

Since f(x) is not given in the question, we must first define it. Let's assume f(x) = x^2 - 2x + 1.

The resulting equation is (x - 1)^2 < 0.

The function f(x) is defined as f(x) = x^2 - x - 6.

From here, the equation can be solved for x using the quadratic formula, which gives us x = [7 + sqrt(73)]/2 and x = [7 - sqrt(73)]/2.

Therefore, the x-values for which f(x) < 1 can be expressed in interval notation as (-∞, [7 - sqrt(73)]/2) U ([7 + sqrt(73)]/2, ∞).

(-∞, -3/2] ∪ [-3/4, 1)

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Answer:

11.  TS = 123.8 cm

12.  SW = 108.8 cm

13.  m∠SVU = 123°

14.  m∠STU = 123°

15.  US = 217.6 cm

16.  m∠TUV = 57°

Step-by-step explanation:

Properties of a Parallelogram:

11.  Opposite sides are equal in length:

12. Diagonals bisect each other (divide into 2 equal parts):

13. Adjacent angles are supplementary (sum to 180°):

     ⇒ m∠SVU + m∠TSV = 180°

     ⇒ m∠SVU + 57° = 180°

     ⇒ m∠SVU = 123°

14. Opposite angles are equal:

15. Diagonals bisect each other (divide into 2 equal parts):

     ⇒ US = 2 × UW

     ⇒ US = 2 × 108.8

     ⇒ US = 217.6 cm

16. Opposite angles are equal:

On solving the provided question, we can say that vertices D(1, 4), E(5, 5), F(4, 1) and G(0, 0),  area of rhombus = S*S = 5*5 = 25 cm sq.

A rhombus is an equal-sided quadrilateral in Euclidean plane geometry. The term "equilateral triangle" also refers to a quadrilateral whose sides are of the same length. A parallelogram has a unique variation known as a rhombus. In a rhombus, the opposite sides and angles are parallel and equal. A rhombus's diagonal is split in half by a right angle, and each of its sides is the same length. Rhombic diamonds and diamonds are other names for rhombuses. The length of every side is the same. Diagonals are equal in a rhombus. At a 90° angle, parallel lines split in half. 180 degrees is the sum of adjacent angles.

here,

vertices D(1, 4), E(5, 5), F(4, 1) and G(0, 0)

so area of rhombus = S*S = 5*5 = 25 cm sq.

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Answer:

581.3

Step-by-step explanation:

The equation of this parallel line using point slope is  y = 4x - 31.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis may be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given that the equation of a line is y = 4x - 2.

Here, we observe that the slope m = 4

Parallel lines have the same slope. So, the slope of the new line is:

m = 4

Given that points (x1, y1) = (5, -11) are also in the new parallel line.

Using the Point-Slope form we can write:

y - y1 = m (x - x1)

Substitute the value of x and y coordinates in the above equation:

y - (-11) = 4 (x - 5)

y + 11 = 4x - 20

y = 4x - 20 -11

y = 4x - 31

Hence, the equation of this parallel line using point slope is  y = 4x - 31.

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Noah's ambition was $90, and he raised $54 toward that total, or 60% of his fundraising target, in order to benefit the animal sanctuary.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.

given

60% x what= $54

Then, by converting 60% to a decimal, we can turn it into a useful number: 0.6. We will substitute x for what because we also need to make "what" simpler to use:

0.6x=54

Get x by itself next, which is referred to as isolating the variable. To accomplish this, divide both sides by 0.6, which is referred to as employing inverse operations.

You must obtain x=90.

Noah's ambition was $90, and he raised $54 toward that total, or 60% of his fundraising target, in order to benefit the animal sanctuary.

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Step-by-step explanation:

[tex] - 1 > - 2(x - 4) - 5(4x - 7) \\ - 1 > - 2x + 8 - 20x + 35 \\ - 1 > - 2x - 20x + 8 + 35 \\ - 1 > - 22x + 43 \\ 22x > 43 + 1 \\ 22x > 44 \\ \frac{22x}{22} > \frac{44}{22} \\ x > 2[/tex]

The correct answer is 75001+9< 75100.The 75010 is less than 75100.Because we can count to prove it.

The greater than and less than symbols are generally used to represent the inequality expressions. The symbol used to represent greater than is “>” and less than is “<”. If one value is larger than the other value we use greater than. Similarly,if we want to represent one value that is less than the other value we use less than.

Many teachers use the Alligator Method analogy to teach greater than and less than. They will draw an Alligator mouth on the greater than and less than signs.We can say the alligator is going to want to eat more.

Now

75001+9= 75010

This will seventy five thousand and ten

75100 = seventy five thousand and one hundred

So,  75001+9 <75100

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Answer:

[tex]\displaystyle x=\frac{1\pm\sqrt{5}i}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle 2x^2=2x-3\\2x^2-2x+3=0\\\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(3)}}{2(2)}\\\\x=\frac{2\pm\sqrt{4-24}}{4}\\ \\x=\frac{2\pm\sqrt{-20}}{4}\\ \\x=\frac{2\pm2\sqrt{5}i}{4}\\\\x=\frac{1\pm\sqrt{5}i}{2}[/tex]

The probability that Jay fails the final exam and passed the remedial exam is P(fail the final and passed the remedial) = 0.32.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

After giving the final exam, the professor found that many of his students failed the test, so he decided to give a remedial exam.

The probability that a student passes the final exam is 0.6. Given that a student fails the final exam, the probability that the student passes the remedial exam is 0.8.

We are given the following probabilities:

P(passes the final exam) = 0.6

P(fail the final exam = (1 - 0.6) = 0.4

P(passes through the remedial | failed the final) = 0.8

We have to find P(fail the final and passed the remedial).

P(fail the final and passed the remedial) = P(passes the remedial | failed the final)*P(failed the final)

P(fail the final and passed the remedial) = 0.8 x 0.4

P(fail the final and passed the remedial) = 0.32

Hence, the probability that Jay fails the final exam and passed the remedial exam is P(fail the final and passed the remedial) = 0.32.

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The Pythagorean theorem states that the square of a right-angled triangle's hypotenuse is equal to the sum of the squares of its other two sides.

You can demonstrate the congruence of two right triangles using the Hypotenuse-Leg (HL) Triangle Congruence Theorem, which is a particular instance. A right triangle is congruent with another right triangle if its hypotenuse and one of its legs are congruent with its hypotenuse and one of its legs.

The hypotenuse (longest side) square in a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem (base and perpendicular).

The right triangles are said to be congruent if their respective hypotenuses and legs are congruent with one another, according to the hypotenuse-leg (HL) theorem. By the HL theorem, these triangles are congruent.

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Answer:

9) 11.18 feet

10) 6.14 inches

Step-by-step explanation:

The first problem sets up a situation with a right triangle. See image. Two sides are given, so you can use Pythagorean Theorem to find the last side. See image.

The second problem also sets up a right triangle. But here only one side length is given and one angle, so you use trigonometry. Sine is the ratio of the opposite side/hypotenuse. Use sine to find the missing length. See image.

I rounded these answers to the nearest hundredth (two decimal places) Check directions if they should be rounded more or less.

Answer: 9/4 (This a fraction)

Step-by-step explanation:

We do Keep. Switch. Flip aka KSF

we keep 3/4 and change the sign multiplication and flip 1/3 to 3/1

3/4 x 3/1 = 9/4

Note: I tried my best, don't hate me if it's wrong.

The value of y in the table would be greater than the value on the graph, when x = 11 by: B. 110.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

For the table, an equation which represent its data points is given by:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 270 = (360 - 270)/(4 - 3)(x - 3)

y = 90(x - 3) + 270

y = 90x - 270 + 270

y = 90x.

When x = 11, the value of y is given by:

y = 90(11)

y = 990.

For the graph, an equation which represent its data points is given by:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 160 = (320 - 160)/(4 - 2)(x - 2)

y = 80(x - 2) + 160

y = 80x - 160 + 160

y = 80x.

When x = 11, the value of y is given by:

y = 80(11)

y = 880

Next, we would determine the difference:

Difference = 990 - 880

Difference = 110.

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Answer: the third one

y=2^x-1

Step-by-step explanation:

Answer: The correct answer is choice A. 5.4

Step-by-step explanation:

I hope this helps! :D

Frank is going to plant d vegetable seeds in one garden, and 3d + 6 vegetable seeds in another. So Frank is going to plant 4d + 6 vegetable seeds in total.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebra is used to solve problems and to describe patterns and relationships between variables. It is a powerful tool for modeling and understanding many types of real-world situations.

In algebra, letters or other symbols are used to represent numbers or quantities that are not known. These symbols can be manipulated using mathematical operations, such as addition, subtraction, multiplication, and division. Equations and inequalities involving these symbols can be solved to find the values of the unknowns. Algebraic equations can also be graphed to visualize the relationship between the variables.

To find the total number of vegetable seeds Frank is going to plant, we can add the number of seeds he is planting in each garden:

d + (3d + 6) = d + 3d + 6 = 4d + 6

So Frank is going to plant 4d + 6 vegetable seeds in total.

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From the following set of points, 26 is a trapezoid but not a isosceles trapezoid while 27 is not a trapezoid at all.

A closed, four-sided trapezoid in two dimensions has a perimeter and an area. Two of the sides are considered the bases of the trapezoid because they are parallel to one another.

The non-parallel sides of a trapezoid are referred to as its legs or lateral sides. The altitude is that distance between two parallel sides that is shortest. The area of a trapezoid can be easily calculated because the opposite sides are parallel to one another.

If the given points make an isosceles trapezoid then AB and CD must be equal and BC and AD must not be equal

Lets solve

26. AB =  [tex]\sqrt{(-4-(-4))^2+(-1-6)^2}[/tex]  = 7

CD =  [tex]\sqrt{(2-(2))^2+ (6-(-4))^2}[/tex] = 10

BC = [tex]\sqrt{(-4-2)^2+ (6-6)^2}[/tex] = 6

AD = [tex]\sqrt{(-4-2)^2+ (-1-(-4))^2}[/tex] = 3√5

Thus, this not an isosceles trapezoid.

27. AB =  [tex]\sqrt{(-5-2)^2+(2-6)^2}[/tex]  = 8.06

CD =  [tex]\sqrt{(-1-2)^2+ (6-1)^2}[/tex] = 5.83

BC = [tex]\sqrt{(-5-(-1))^2+ (6-6)^2}[/tex] = 6

AD = [tex]\sqrt{(2-(-5))^2+ (-1-2)^2}[/tex] = 3√5

None of the side make an trapezoid and it is not a isosceles trapezoid

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