Let A = [-5 2 ]and B = [1 0] . Find 2A + 3B

The volume, surface area, and ratio of the height of the box to the length will be 296.98 cubic inches, 292.35 square inches, and 0.88, respectively.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

A rectangular box has a length of √90 inches, a width of √14 inches, and a height of √70 inches.

The volume of the box is given as,

V = LBW

V = (√90) x (√14) x (√70)

V = 296.98 cubic inches

The area of the top of the box is given as,

SA = 2(LW + WB + BL)

SA = 2(√90 x √14 + √14 x √70 + √70 x √90)

SA = 292.35 square inches

The ratio of the height of the box to the length of the box is given as,

H / L = √70 / √90

H / L = 0.88

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Answer:

6[tex]x^{2}[/tex] + 8x

Step-by-step explanation:

4x(3x + 2) = 12[tex]x^{2}[/tex] + 8x  is the area of the big rectangle

2x(3x) = 6[tex]x^{2}[/tex]  is the area of the small rectangle.

Subtract the small rectangle from the large rectangle to find the area of the shaded region

12[tex]x^{2}[/tex] + 8x - 6[tex]x^{2}[/tex]

6[tex]x^{2}[/tex] + 8x

The distance across the river (BD) is 800 yards

An equation is an expression that shows the relationship between two or more numbers and variables. Types of equation are linear, quadratic, cubic and so on.

From the image shown, triangle ABC and triangle ADE are similar triangles. For similar triangles, the ratio of corresponding sides are proportional to each other. Hence:

AD/AB = DE/BC

substituting values:

AD / 200 = 500/100

AD = 1000 yards

AD = AB + BD

substituting:

1000 = BD + 200

BD = 800 yards

The value of BD is 800 yards

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in the form ax²+bx+c, in which a, b, and c are constants, the value of given quadratic equation a+b+c is 0.

Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.

For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as [tex]2x^2 + 4x = 2x(x+2).[/tex]

The goal of simplification is to make the expression or equation easier to understand, manipulate, or solve.

The expression given is already in the form ax^(2) + bx + c, so we can simply add the coefficients of the x^(2), x and constant terms to find the value of a+b+c:

[tex](2x^{(2)} -3x+1)-(-2x^{(2)}-3x+2) = 2x^{(2)} - (-2x^{(2)}) + (-3x) - (-3x) + 1 - 2[/tex]

a+b+c = 2 - (-2) + (-3) - (-3) + 1 - 2 = 2 + 2 - 3 - 3 + 1 - 2 = 0

Therefore, the value of a+b+c is 0.

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Answer:

119 cm²

Step-by-step explanation:

Area of white triangle:

             base = 9 cm

           height = 14 cm

       [tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base *height}[/tex]

                                    [tex]\sf =\dfrac{1}{2}*9*14\\\\ = 9*7\\\\= 63 \ cm^2\\[/tex]

Area of trapezium:

          [tex]\sf \boxed{Area \ of \ trapezium =\dfrac{(a+b)*h}{2}}[/tex]

Here, a and b are the parallel sides of trapezium & h is the height.

           a = 9 cm ; b = 17 cm and h =14 cm

[tex]\sf Area \ of \ trapezium = \dfrac{(9+17)*14}{2}[/tex]

                           [tex]= \dfrac{26*14}{2}\\\\\\=13*14\\\\= 182 \ cm^2[/tex]

Area of shaded region = area of trapezium - area of white triangle

                                      = 182 - 63

                                      = 119 cm²

Answer:

area of shaded region = 119 cm²

Step-by-step explanation:

the outer figure has one pair of parallel sides and is a trapezium.

the shaded area (A) is calculated as

A = area of trapezium - area of white triangle

the area of a trapezium is calculated as

area = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 14 , b₁ = 9 , b₂ = 17 , then

area = [tex]\frac{1}{2}[/tex] × 14 × (9 + 17) = 7 × 26 = 182 cm²

the area of the triangle is calculated as

area = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 9 and h = 14 , then

area = [tex]\frac{1}{2}[/tex] × 9 × 14 = 4.5 × 14 = 63 cm²

then area of shaded region (A) is

A = 182 - 63 = 119 cm²

The total cost of the rectangular frame is C = $240.

After a small search online, I found the original question, it is written at the end of the answer.

Remember that for a rectangle of length L and width W, the perimeter is given by:

P = 2*(L + W)

In this case, we know that the frame is 6 inches by 14 inches, then the perimeter will be:

P = 2*(6in + 14in)

P = 2*20in = 40in

And we know that the framing material costs $6 per inch, then the total cost of the frame will be:

cost = 40*$6 = $240

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After a small search online, I found that the complete question is:

"You decide to buy a custom frame for a painting which measures 4 by 6 inches. If the framing material costs $2 per inch, what is the total cost of framing material?"

The value of the liquid assets of the salesperson is; D: $613,570

Liquid assets are defined as a set of property or investment that can be converted easily into cash. These liquid assets include raw cash, fast selling and marketable securities that can be traded and converted into cash within a short time.

Hence the liquid assets of the person, along with their values, are listed as follows:

The returns from someone's retirement portfolio will supplement your Social Security benefits, and it can even prevent you from having to live squarely on a fixed income. Due to the fact that a retirement portfolio is diversified, it can protect you from market volatility by balancing different income classes. Retirement Portfolio in this question is given as  $473,906 (It is called the Retirement fund)

Investments = $139,664

The total value of the person's liquid assets is given by the sum of the values of each of these two assets, hence:

473,906 + 139664 = $613,570

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2 3 as an exponent is written as 2^3 and it represents 2 multiplied by itself 3 times. 2^3 = 2 * 2 * 2 = 8

In the notation 2^3, the number 2 is the base and the number 3 is the exponent. The exponent tells you how many times the base is being multiplied by itself. In this case, 2 is multiplied by itself 3 times.

It's important to note that the exponent is also known as the power, so 2^3 is also read as 2 to the power of 3.

In summary, 2 3 as an exponent is written as 2^3 and it represents 2 multiplied by itself 3 times, or 2 to the power of 3 which is equal to 8. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.

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Answer:

An exponent refers to the number of times a number is multiplied by itself.

Step-by-step explanation:

For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

In the overlapping triangles, the statements needed to be match to the reasons are explained below.

A triangle is sometimes referred to as trigon because it is bounded by three straight sides, and has a measure of internal angles which add up to 180^o.

Considering the overlapping triangles given in the question, the statements  to be matched to the reasons are given below:

                 STATEMENT                                      REASON

1. ΔRTN ≅ ΔSTM                                        Side-Angle-Side (SAS)

2. <T ≅ <T                                                   Betweenness

3. RN = SM                                                  Reflexive property

4. RM = SM, TM = TN                                 Given

5. RT = ST                                                   Substitution

6. RM + TM = TN  + SN                              CPCTE

7. RM + TM = SN + TM                                Addition property of equality

The match of statements with the reasons are required to proof that RN = SM

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Answer: 439.2 miles

Step-by-step explanation:

213.5/3.5=61

61*7.2=439.2 miles in total

The slope and the y-intercept of the line are 3 and 5 respectively.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of a straight line → y = 3x + 5

The equation of the straight line given is -

y = 3x + 5

We can compare and conclude that -

m = 3

c = 5

Therefore, the slope and the y-intercept of the line are 3 and 5 respectively.

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Answer:

2.4

Step-by-step explanation:

2/5=AB/6

=>AB=2.4

Substitute the values into the Pythagorean theorem and show that a false statement results.

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The rate of change for a linear function, also known as the slope, can be found by calculating the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between two points on the line. The slope of a line describes how steep the line is and whether it is increasing or decreasing.

In this case, the slope of the linear function can be found by using the coordinates of points E and F:

Slope = (y2 - y1) / (x2 - x1)

Slope = (-8 - 27) / (5 - 0)

Slope = -35/5

The slope of the linear function is -35/5 or -7.

The initial value of a linear function is the y-intercept, which is the point where the line crosses the y-axis. To find the y-intercept, we can use the slope and one point on the line (in this case point E (0,27)):

y = mx + b

27 = -7(0) + b

b = 27

The y-intercept of the linear function is 27.

So, the linear function starts at point E (0,27) with an initial value of 27, and has a rate of change or slope of -7.

The function's value at x = 1, y = - 1 Or f(1) = -1.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The x-coordinate represents the input and the y-coordinate represents the output.

From the given points in the graph, we can conclude that when x = 1, y = -1.

Therefore, The value of the function f(1) = -1.

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An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.

In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;

h + 178 = T

Substituting the given parameters into the algebraic equation, we have the following;

h + 178 = 214

Solving for h, we have the following;

h = 214 - 178

h = 36 hours.

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The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.

The unit technique is a method of problem-solving that entails calculating the value of a single unit, multiplying that value, and then calculating the required value. To put it simply, the unit method is used to extract a single unit value from a specified multiple. One pen costs 400 rupees, thus 40 pens would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mathematics of matrices or operators, linear algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.

given

The price of a 500 g packet of Healthy Flakes is €3.20.

Healthy Flakes come in packets of 750 g for €4.50.

A better size packet of 500 g costs €3.20. A two-pack of 750 g costs €166.66.

The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.

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Using quadratic equation, the value of x is 5 and -1/3

3x²+16x-5

3x² +16x -5= 0

Split the middle term using two factors

3x² -15x -x -5= 0

Take out the common factors

(3x-1)(x-5)= 0

3x+1= 0

3x= 0-1

3x= -1

x= -1/3

x-5= 0

x= 0+5

x= 5

Hence x = 5 and x= -1/3

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Answer: Would it just be 2/3? It says 2/3 are alley cats.

Step-by-step explanation:

Answer:

1/3 of them are alley cats

Step-by-step explanation:

The length of the side BD is;  8

The measure of the angle DAB is; ∠DAB = 53°

Two triangles are said to be congruent by any of the following postulates;

1) SSS (Side Side Side) Congruence Postulate.

2) SAS (Side Angle Side) Congruence Postulate.

3) ASA (Angle Side Angle) Congruence Postulate.

4) AAS (Angle Angle Side) Congruence Postulate.

5) HL (Hypotenuse Leg) Congruence Postulate

Now, for the given triangles that are congruent, we can say that;

∠ADC ≅ ∠ACB

∠DAB ≅ ∠CAB

BD ≅ BC

AC ≅ AD

Thus;

BD = 8

∠DAB 53°

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Answer:

y = 2x + 5

Figure 505

Step-by-step explanation:

(3,11) ( 4,13)

Find the slope

Change in y over the change in x

[tex]\frac{13-11}{4-3}[/tex] = [tex]\frac{2}{1}[/tex] = 2

slope (m) is 2.

Part A

Find the y -intercept

m = 2

x = 3     from the point (3,11)

y = 11    from the point (3,11)

y = mx + b  Substitute what I know and solve for b

11 = (2)(3) + b

11 = 6 + b  Subtract 6 from both sides

11 - 6 = 6 -6 + b

5 = b

The y intercept (b) is 5

y = mx + b

y = 2x + 5

Part B

y =  2x + 5

1015 = 2x + 5  Subtract 5 from both sides

1015 - 5 = 2x + 5 - 5                                                    

1010 = 2x  Divide both sides by 2

505  

It is "3 pairs" not "3 pair", because a pair is a set of two things, so if you have 3 of them it would be 3 sets of two things or 3 pairs.

The equation in slope intercept form is

y = 5/2x + 5

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

Two points on the line are (-2,0) and (0,5)

The slope intercept form is

y = mx + c

so when y = 0 and x = -2

0 = -2(m) + c

or,  2m -c = 0 ..(i)

again when x= 0 y = 5

5 = 0*m + c

c = 5

so putting c= 5 in equation (i) we get

m = 5/2

so the equation in slope intercept form is

y = 5/2x + 5

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The value of exponential 2 is 2^2, or 4. This means two multiplied by itself two times or squared.

Exponential notation is a way of expressing a number, usually greater than 10, as a base number, the number 2 in this case, raised to a power, which in this case is 2. Therefore, exponential 2 is written as 2^2, which means two multiplied by itself two times or squared.

For example, if we wanted to find the value of exponential 8, we could easily calculate 2^8, or 256, which is much faster than multiplying 2 by itself 8 times. Exponential notation is also helpful when calculating exponents with variables.

For example, if we wanted to find the value of 3^x, we could use exponential notation to find the answer quickly. In summary, exponential notation is a useful tool for quickly finding the value of a number raised to a power.

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The balance on the credit card after three years would be $20,111.25.

What is continuous compound interest?

Continuous compounding means that there is no limit to how often interest can compound. Compounding continuously can occur an infinite number of times, meaning a balance is earning interest at all times.

The balance on the credit card after three years can be calculated using the formula for continuous compound interest:

A = P * e^(rt)

where A is the final balance, P is the initial principle (the amount of the loan), r is the annual interest rate as a decimal, and t is the number of years.

In this case, P = $12,500, r = 0.1599 (15.99% as a decimal), and t = 3.

Plugging these values into the formula:

A = $12,500 * e^(0.1599 * 3)

A = $12,500 * e^0.4797

A = $12,500 * 1.6089

A = $20,111.25

Rounded to the nearest penny: $20,111.25

Hence, the balance on the credit card after three years would be $20,111.25.

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The population of the Boom town increased by 25% compared to last year, present population is 6000 then last year population is equal to 4800.

As given in the question,

Given population of the present year is equal to 6000

Let us consider 'x' be the last year population.

Increased in population compared to last year = 25%

Required equation is given by :

x + (25/100)x = 6000

⇒ (125 / 100 )x = 6000

⇒ x = ( 6000 × 100 ) / 125

⇒ x = 4800

Therefore, the population of the last year as per given data of the present year is equal to 4800.

The above question is incomplete, the complete question is:

Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?

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Answer:

x=14

Step-by-step explanation:

The angles inside a triangle add up to 180 degress all the time, therefore

58+80+3x=180

simplify

138+3x=180

subtract 138 from both sides of the equation

3x=42

divide both sides by 3

x=14

Answer:

Step-by-step explanation:

x36 + 24

x39x² + 24x - 28

x3(x2 + 9x - 28/3)

x3(x + 28/3)(x - 3)

Answer:

a = 2

b = 7

Step-by-step explanation:

The given rectangle is a parallelogram.

10b + 1 = 9b + 8

10b - 9b = 8 - 1

b = 7

2. WX = ZY

6a + 4 = a + 14

6a - a = 14 - 4

5a = 10

a = 2