If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation.

2x – 3y = –29
x + 4y = 13

2(4y + 13) – 3y = –29

2(–4y + 13) – 3y = –29

2x – 3(4y + 13) = –29

2x – 3(–4y + 13) = –29 ...?

Answer: The area of the face is 15 sq. in.

Step-by-step explanation:  We are given to find the area of the yellow-coloured face in the figure.

The area of the coloured face is equal to the area of one face of a cube of side 4 in MINUS the area of one face of a cube of side 1 inch.

The area of one face of a cube of side 4 in is given by

[tex]A=\textup{area of a square of side length 4 in.}=4\times 4=16\textup{ sq. in.}[/tex]

and the area one face of a cube of side 1 in is given by

[tex]a=\textup{area of a square of side length 1 in.}=1\times 1=1\textup{ sq. in.}[/tex]

Therefore, the area of the coloured face will be

[tex]Area=A-a=16-1=15\textup{ sq. in.}[/tex]

Thus, the area of the face is 15 sq. in.

The area of the face which is indicated in the figure is 15 in².

Use the concept of quadrilateral defined as:

Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

For big cube:

length of sides = 4 in

Area of one face = 4x4 in²

Area of one face = 16 in²

For small cube:

length of sides = 1 in

Area of one face = 1x1 in²

Area of one face = 1 in²

Since we can see that

The area of one face of a small cube coincides with the face of the big cube.

Therefore,

We have to remove the area of one face of the small cube from the big cube,

So, the area of the face indicated in the figure is,

(16 - 1) in² = 15 in²

Hence,

The area of the required face is 15 in²

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The given statement translates to the inequality x - 5 ≥ 9.

To do this, we first need to interpret ‘a number’ as a variable, which we can call x. ‘Five less than a number’ means we subtract five from our variable, expressed as x - 5. ‘At least nine’ indicates that the value should be greater than or equal to nine, which in inequality form is ( ≥ 9 ). Therefore, the complete inequality that represents the given statement is x - 5 ≥ 9.

Answer:

15%

Step-by-step explanation:

Answer:

[tex](x^{2} + 5)(3x^{2} - 2)[/tex]

Step-by-step explanation:

The polynomial is first correctly stated as follows

[tex]3x^{4} - 2x^{2} + 15x^{2} - 10[/tex]

This is rearranged, grouped and solved as follows:

[tex]3x^{4} + 15x^{2} - 2x^{2} - 10[/tex]

[tex](3x^{4} + 15x^{2}) - (2x^{2} + 10)[/tex]

[tex]3x^{2} (x^{2} + 5) - 2(x^{2} + 5)[/tex]

Factorizing the common factors [tex](x^{2} + 5)[/tex], we have the product of the factored form of the polynomial as follows:

[tex](x^{2} + 5)(3x^{2} - 2)[/tex]

That is the third option in the question if rewritten in the correct form.

The amount of interest earned is $5,400

From the question,

We are to calculate the simple interest earned

Interest can be calculated by using the simple interest formula

I = PRT

Where I is the interest

P is the principal

R is the rate

T is the time

From the question

P = $12,000

R = 15%

T = 3 years

∴ Interest,

I = $12000 × 15% × 3

I = $12000 × 0.15 × 3

∴ I = $5400

Hence, the amount of interest earned is $5,400

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Answer:

The answer is Edge. A segment that is formed by the intersection of two faces is called an EDGE.

Step-by-step explanation:

A segment that is formed by the intersection of two faces is called an EDGE.

An edge is defined as a type of line segment, that joins two vertices in a polygon, polyhedron etc. In a  polytope, an edge is a line segment between faces.

The probability that exactly one girl and two boys will receive awards is 75%.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that there are:-

6 girls

4 boys

Probability of 1 girl being chosen: 1/6

Probability of 1 boy being chosen: 1/4

Probability of another boy being chosen: 1/3

1/6 = 0.17 x 100% = 17%

1/4 = 0.25 x 100% = 25%

1/3 = 0.33 x 100% = 33%

17% + 25% + 33% = 75%

Therefore the probability that exactly one girl and two boys will receive awards is 75%.

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commutative for addition

Answer:

commutative - addition

associative - addition

Step-by-step explanation:

Answer:

f(x)= 3x + 10 and g(x)= 2x - 4

(f+g)(x)= 3x + 10 + 2x - 4

3x + 2x + 6

5x + 6

b and c

Answer:

C. (f + g)(x) = 5x + 6.

Step-by-step explanation:

test approved

The two points which shows the object traveling at the greatest speed is D. between points A and B because that slope is the steepest

How does this section show the greatest speed ?

The segment between points A and B has the steepest slope, indicating a rapid change in distance over a short period, which implies a higher speed.

This makes sense given the concept of the physics of motion, where a steeper slope on a distance-time graph represents a higher velocity or speed.

Between points C and D has the second greatest speed because it shows that as time went, distance was covered unlike between points B and C.

Answer:

They would be Equal

Step-by-step explanation:

if we split a rectangle into two triangles it would be the same triangle just flipped!

The circumference of the circle with a diameter of inch is 3.14 inch.

The circumference of a circle can be found by multiplying its diameter by π (pi). In this case, the diameter of the circle is given as inch. To find the circumference, we need to multiply the diameter by π.

Circumference = Diameter × π

Since the diameter is inch, the circumference of the circle is ( inch) × π = inch × π = 3.14 inch.

The circumference of the circle with diameter 6.2 cm, using (pi) equal to 3, is calculated as 18.6 cm using the formula C = (pi)d.

The question asks to calculate the length of the circumference of a circle with a diameter of 6.2 cm, using an approximate value for (pi) as 3. To find the circumference of a circle, the formula C = (pi)d is used, where C is the circumference and d is the diameter. Since we are provided with the diameter (6.2 cm) and an approximate value for
(pi) as 3, the calculation is straightforward.

Using the formula,

Thus, the circumference of the circle is 18.6 cm.

Answer:

It's a probability problem to find the odds of picking a green or red shirt out of the 10 shirts on Thursday, Friday and Saturday since you have randomly already know you have picked a blue shirt on the other days. Probability = Number favorable outcomes / total number of outcomes

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Step-by-step explanation:

We can cut a total of 4 sections of 1.4 meters through 6-meter long rope.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

Length of rope = 6 meter

Length of section = 1.4 meter

Number of sections = Length of rope ÷ Length of section

Number of sections = 6/1.4 = 4.28 since 0.28 part is not complete section so we will not consider it.

Hence "We can cut a total of 4 sections of 1.4 meters through 6-meter long rope".

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As they both are tangents of the same circle, their lengths must be equal.

RS = RT

x/4 = x-6.3

x = 4x - 25.2

4x-x = 25.2

3x = 25.2

x = 8.4

As, RS = x/4, it will be equal to 8.4/4 = 2.1

SO, YOUR FINAL ANSWER IS RS = 2.1

To find the length of segment RS, we can use the tangent-radius theorem and the Pythagorean theorem. Segment RS is perpendicular to the radius of circle Q that passes through point S. By using the Pythagorean theorem, we can solve for the length of RS.

The length of segment RS can be found using the tangent-radius theorem. According to this theorem, if a line is tangent to a circle at a certain point, then the line is perpendicular to the radius that passes through that point. Therefore, segment RS is perpendicular to the radius of circle Q that passes through point S.

Since RS is perpendicular to the radius, RS and the radius form a right triangle. The length of RS can be found using the Pythagorean theorem. Let's denote the length of the radius as r and the length of RS as x. The radius is the hypotenuse of the right triangle, so we have:

x^2 + RS^2 = r^2

Since RS is the only unknown, we can solve for it. Once we have the value of the radius, we can substitute it into the equation to find the length of RS.

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