Robert is building a deck in his backyard. Each piece of wood measures 42.5 inches. If he has 8 boards, how long are they altogether?

The length BC of the right triangle is 18 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:

Therefore, using proportion because triangle ABC is similar to triangle BDC.

x / 36 = 9 / x

cross multiply

x × x = 36 × 9

x² = 324

square root both sides of the equation

x = √324

x = 18 units

Therefore,

BC = 18 units

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[tex](69)(5.6\times 10^{5})\implies (69)(560000)\implies 3\underset{\leftarrow 7\to }{\underline{8640000}}\implies 3.864\times 10^{7}[/tex]

The cost of filling the cone to its full capacity would be = 189.4 cents

A cone is a three-dimensional figure in geometry that tapers from a flat base (usually a circular base) to a point called a vertex or longitude (which forms an axis through the center of the base).

The formula for the volume of a cone = πr²h/3

Height (h) = 5 inches

Radius (r) = 3 inches

π = 3.14

volume = 3.14 × 3² × 5/3

= 3.15 × 9 × 1.67

= 47.35 in³

But 1 in³ = 4 cents

47.35 in³ = X

Make X the subject of formula;

X = 47.35 × 4 = 189.4 cents.

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Answer:

y = 95°

Step-by-step explanation:

x + 120° = 180°

x = 180° - 120°

x = 60°

25° + y + x = 180°

25° + y + 60° = 180°

y + 85° = 180°

y = 180° - 85°

y = 95°

The required,
1. figure 1, domain and range are (0, ∞) and {25000, 0}, the graph shows the exponential decay.
2.  figure 2, domain and range are (-∞, ∞) and {0, ∞}, the graph shows the exponential growth.

The function which is in format f(x) =aˣ  where, a is constant and x is variable,  the domain of this exponential function  lies   (-∞, ∞).

As mentioned in the question, the graph of two exponential functions are given, we have to determine the domain and range of both function and justify which graph shows the exponential growth and decay.

1.
A general exponential equation is given as,
y = aˣ
Graph 1, the graph shows the exponential decay because the value of the function is getting decreasing for the domain 0 to ∞. For this domain, the value of the function starts from point A which is at 25000 and ends at point B where y = 0, so the range is {25000, 0}.

Similarly,
Graph 2 shows exponential growth,
Domain and range are (-∞, ∞) and (0, ∞).

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Step-by-step explanation:

what do you not understand ? please let me know where you need more instructions.

the basic rule : every term of one side has to be multiplied with every term of the other side, and the results are added (by using the correct signs of the products).

remember :

+ × + = +

- × - = +

+ × - = -

- × + = -

(3x - 3)(5x - 4) = 3x × 5x + 3x × -4 + -3 × 5x + -3 × -4 =

= 15x² - 12x - 15x + 12 = 15x² - 27x + 12

All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

2(3y + 4) − 3 (y − 2) = 2⁢y

Simplify the equation, then we have

2(3y + 4) − 3 (y − 2) = 2⁢y

6y + 8 − 3y + 6 = 2y

3y + 14 = 2y

14 = 2y - 3y

14 = - y

y = - 14

All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.

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The given triangles are congruent by SAS criteria.

Congruent triangles have both the same shape and the same size.

Given are two right angled triangles as shown in the image.

In the right angled triangles -

Two corresponding sides are equal.

They both have one right angle common.

We can conclude them as congruent by SAS Rule.

Therefore, the given triangles are congruent by SAS criteria.

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In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.

given

the points (5.-4) and (-1,8)

slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

slope intercept form = y = mx + c

To find the equation of the line that passes through the points (5, -4) and (-1, 8),

The slope and the intercept by the slope intercept form = y = mx + c .

The slope is -4 and the intercept is 8.

In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .

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The degree of the polynomial  [tex]2yA^2yA^32y^8[/tex] is 15

A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.

The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).

Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]

The polynomial has a degree of 6.

This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.

As per question, polynomial is: [tex]2yA^2yA^32y^8[/tex]

The total sum of power is: 1+2+1+3+8=15

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The equations of the commissions are

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have:

This means that:

Commission = Unit rate * Commission proportion * Number of pieces

Using the above as a guide, we have the following:

Sara: y = 25 * 60% * x

Ravi: y = 2000 * 25% * x

Evaluate

Sara: y = 15x

Ravi: y = 500x

See attachment for the graph of the commission equations

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To find the missing side length of the acute angled triangle apply the cosine law as follow:

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = b² + a² - 2abcosC

As given in the question,

Given triangle is acute angled triangle.

Let us consider the measure of two sides and its included angle of the acute angled triangle is given.

Let the triangle be ABC,

Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.

Apply cosine law to find the measure of the missing side in the acute angled triangle:

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = b² + a² - 2abcosC

Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.

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The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.

Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)

Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

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A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is (0.2301, 0.2759).

(0.2301, 0.2759).

This interval is calculated using the following formula:

(sample proportion - margin of error, sample proportion + margin of error)

Where the sample proportion is the number of favorable voters (100) divided by the sample size (432), and the margin of error is calculated using the standard error and a critical value from a normal distribution table.

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He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.

The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.

As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.

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Answer:

the answer is 1

Step-by-step explanation:

4(2x-3)=6x+2

8x-12=6x+2

+6x   +6x

14x-12 =2

    +12 +12

14x=14

x=1 and don't worry we all make mistakes

You can ride in many places, so be sure to look for hazards that could cause injury or other risks while bicycling.

The number of miles you can cycle in a single day is unlimited. It depends on your level of fitness, your exercise regimen, and the distance you cycle. Starting out, 10 kilometres per day is OK.

If you're an experienced cyclist who can pedal 25–30 miles every day, 45 miles is a realistic limit.  You can ride a certain bike trail. By riding a bike to work, you can get in shape. If you've never rode a bike before, start out slowly. If you ride your bike for at least three miles every day, you might be able to travel further.

You may be able to make the most of your speed sensor’s accuracy, depending on how accurate it is. You need to know exactly how much effort you put in during your rides.

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On solving the provided question we can say that - her in the equation  14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex]14w + 3p = 70.50 \\[/tex]

10w+7p = 62.50 ,

[tex]w = 12\\[/tex]

p = 18

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From figure A to figure B, the scale factors are 1/8 and 1/2. To scale shapes in various dimensions, utilize the scale factor.

A polygon is a closed object in a two-dimensional plane comprised of line segments rather than curves. The word "polygon" is a combination of the words "poly" (which meaning many) and "gon" (means sides). A closed figure must include a minimum of three line segments that connect end to end. A polygon is any three or more-sided closed two-dimensional shape. In addition to more complex designs like a dodecagon with twelve sides, polygons include triangles and squares. Polygons include shapes like quadrilaterals, triangles, hexagons, and pentagons. The number of sides the form has is indicated by the name.

given

the scale factor of figure A to figure B

=  smaller dimension / larger dimension

= 2/16

= 1/8

and 4/8

= 1/2

From figure A to figure B, the scale factors are 1/8 and 1/2. To scale shapes in various dimensions, utilize the scale factor.

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The dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape.

A square has sides of equal dimensions.

A rectangle has length and width as its dimensions that define the area of a rectangle.

Also, dimension is used widely to term the figure as one-dimensional, two-dimensional or three-dimensional.

Wood = 1.5 cm by 30 cm

Each cut = .15 mm by 4 mm

Steps = 21

The remaining dimension is calculated as:

Remaining = 1.5 cm - 21 * .15 mm by 30 cm - 21 * 4 mm

Express mm as cm

Remaining = 1.5 cm - 21 * .015 cm by 30 cm - 21 * 0.4 cm

Evaluate the difference

Remaining = 1.185 cm by 21.6 cm

Hence, the dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm

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Answer:

Step-by-step explanation:

26° + 100°

= 126°

360° - 126°

234°

The point (2, 3) lies in the first quadrant.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.

These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).

Cartesian system

The Cartesian coordinate system uses a horizontal axis that is called the x-axis and a vertical axis called the y-axis. Equations for lines in this system will have both the x and y variable.

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For the given expression, x has a value of 6.5.

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables.

A number is 6 times larger than the other number, x, by a factor of 2.

The equation x/2 + 6 in mathematics represents this claim.

Here, we have the equation:

-3(4x - 5) = 2(1 - 5x)

Find the value of x by solving the expression:

-3(4x - 5) = 2(1 - 5x)

-12x + 15 = 2 - 10x

-2x = -13

x = -13/-2

x = 13/2

x = 6.5

Therefore, for the given expression, x has a value of 6.5.

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Correct question:

What value of x satisfies the equation -3(4x - 5) = 2(1 - 5x)?

Answer: No, 3x-2 and 3x^2 are not reciprocals.

Step-by-step explanation: The reciprocal of a number is defined as the multiplicative inverse of that number, which means that when a number is multiplied by its reciprocal, the result is 1. For example, the reciprocal of 2 is 1/2, because 2 * (1/2) = 1.

In contrast, 3x-2 and 3x^2 are not numbers, they are expressions that contain variables. It is not possible to determine their reciprocals without knowing the values of the variables.

For example, if x=1, then the reciprocal of 3x-2 would be (1/3)/(1-2) = -1/3, and the reciprocal of 3x^2 would be (1/3)/(1^2) = 1/3. However, if x=2, then the reciprocal of 3x-2 would be (1/3)/(2-2) = undefined, and the reciprocal of 3x^2 would be (1/3)/(2^2) = 1/12.

So it is not accurate to say that 3x-2 and 3x^2 are reciprocals.

No

The only thing stopping these from being reciprocals is the -2. Say x becomes 3

First we get 3(9)-2.

Next, we'd get 3(3)(2)

In Week 1,

Salesman C got larger paycheck than Salesman A and Salesman B.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.

Given,

Commission of salesman A per sale = $65

Commission of salesman B per sale = $40

Commission of salesman C per sale = $0

Salary of salesman A per week = $0

Salary of salesman B per week = $300

Salary of salesman C per week = $900

No. of sales × commission + salary = total earning

In week 1.

Earning of A

11 × $65 + $0 = $715

Earning of B

14 × $40 + $300 = $860

Earning of C

16 ×$0 + $900 = $900

In week 2.

Earning of A

14 × $65 + $0 = $910

Earning of B

15 × $40 + $300 = $900

Earning of C

12 ×$0 + $900 = $900

In week 3.

Earning of A

16 × $65 + $0 = $1040

Earning of B

13 × $40 + $300 = $820

Earning of C

111 ×$0 + $900 = $900

By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.

In week 2 and week 3 his paycheck is smaller than both of the other salesman.

Hence, Salesman C  received larger paycheck than both of the other salesmen in Week 1.

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Determine how many square centimeters make up a square meter in order to determine how long Marc will have brownies before they run out.

We must first determine the number of square centimeters in a square meter in order to determine how many days Marc has left of brownies before they run out. A square meter has 3.6 square meters in it.

Because of this, Marc has access to brownies for 3.6 days until they are finished.

Knowing the dimensions of a square or rectangle will allow you to compute its square meters. Also known as the shape's area, this term is used. Length times width equals m2, which is the formula used to calculate square meters. As an illustration, if your square is 3 meters long and 2 meters wide, 3 x 2 equals 6 meters2.

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55

11 = 20% × y

11 = 20/100 × y

multiply both sides by 100 and divide both sides by 20

y = 11 x 100/20

y = 11 × 100 ÷ 20

y = 55

Answer:

35° and 100°

Step-by-step explanation:

The total angle of a triangle = 180°
The total angle of two angles = 180° - 45° = 135°
One part of the ratio = 135° : (20 + 7) = 5°
The smaller angle = 5° x 7  = 35°
The bigger angle = 5° x 20 = 100°

Answer:

35° and 100°

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180°

the ratio of 2 angles is 7 : 20 = 7x : 20x ( x is a multiplier )

equate the sum to the 3 angles to 180 and solve for x

45 + 7x + 20x = 180

45 + 27x = 180 ( subtract 45 from both sides )

27x = 135 ( divide both sides by 27 )

x = 5

Then

7x = 7 × 5 = 35

20x = 20 × 5 = 100

the measure of the 2 angles is 35° and 100°

The length AC will be 5.83 and the angle ACD will be 34.45°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The length AC will be calculated as,

AC² = 5² + 3²

AC = √ ( 25 + 9 )

AC = √34

AC = 5.83

The angle ACD will be,

tanθ = P / B

θ = tan⁻¹ = ( 4 / 5.83)

θ = 34.45°

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