An artist uses 49.4 centimeters of decorative molding to make a square picture frame . How long is each side of the frame

Answer:

[tex]57.2\ ft[/tex]

Step-by-step explanation:

we know that

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In this problem

The tangent of angle of 5 degrees is equal to the quotient of "rise over run"

Let

y ----> the rise of the ramp

x ----> the run of the ramp

[tex]tan(5^o)=\frac{y}{x}[/tex]

we have

[tex]y=5\ ft[/tex]

substitute and solve for x

[tex]tan(5^o)=\frac{5}{x}[/tex]

[tex]x=\frac{5}{tan(5^o)}[/tex]

[tex]x=57.2\ ft[/tex]

[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6) = 8x^3+5x^2+2x+3[/tex]

Solution:

Given that we have to perform the indicated operation

Given polynomial is:

[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)[/tex]

Polynomial addition\subtraction is similar to arithmetic addition\subtraction

Add\subtract the terms of coefficients with same variable with same exponent

For example: [tex]x^3 -2x^3 = -x^3[/tex]

To subtract Polynomials, first reverse the sign of each term we are subtracting

Which means, reverse the sign of each term in second bracket

[tex]\rightarrow (7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)\\\\\rightarrow (7x^3 + 11x^2 + 4x + 9)+x^3 - 6x^2 - 2x-6\\\\\text{Remove the parenthesis in first bracket }\\\\\rightarrow 7x^3 + 11x^2 + 4x + 9+x^3 - 6x^2 - 2x-6\\\\\text{Group the similar terms }\\\\\rightarrow 7x^3+x^3+11x^2-6x^2+4x-2x+9-6\\\\\text{Combine the similar terms }\\\\\rightarrow 8x^3+5x^2+2x+3[/tex]

Thus the given operation is performed

Answer:

122 degree

Step-by-step explanation:

As we know that

Sum of all angles of triangle = 180 degree

Angle A + Angle B + Angle C = 180

Angle A + 43 + 15 = 180

Angle A + 58 = 180

Angle A = 180-58

Angle A = 122

Answer: Can you attach a copy of the triangles?

Step-by-step explanation:

Answer:the answer  is a

Step-by-step explanation:

Answer:

[tex]1\frac{1}{2}x + 4[/tex]

Step-by-step explanation:

We are given the Perimeter: P = Perimeter[tex]3\frac{1}{2}x + 18[/tex]    in decimal 3.5x+18

we know that a Perimeter is equal to all sides added up: S1+S2+S3+S4=P

we know that this is a rectangle so that means that it has 4 sides and two sides are the same and the other 2 are the same.

We are given the the height on the image

Height: H = [tex]\frac{1}{4}x + 5[/tex]  in decimal 0.25x + 5

That height is one side so we know another of the sides is the same.

Perimeter is equal to all sides added up. So we have to subtract the sides to find out each ones measurements.

(Height x 2) + (Width x 2) = Perimeter

Therefore we know the height which is given on the image is 0.25x+5 so that times 2 = 0.5x+10    (height x 2)

so now we can subtract the heights from the perimeter.

  3.5x  +  18

-  0.5x  +  10

--------------------

  3x     +    8

So we got rid of both heights. Now we are left with our two lengths:

3x+8  = (length x 2)

To get the length of one side we divide that by 2 because there are 2 sides that have the same length and get 1.5x+4  in fractions that is:

  [tex]1\frac{1}{2}x + 4[/tex]

I hope this helped you or anyone else that needs the answer :)

Answer:

A dodecagon.

Answer:

(0 , -1)

Step-by-step explanation:

WR = 4 + 2 = 6

WS = 1/3 x WR = 2   .... the point of 1:2 of WR

S (-2 + 2 , -4) i.e. (0,4)

The same reason: RQ = 1/3 x RY = 1/3 x (5 + 4) = 3

Q (-4 , -4 + 3) i.e. (-4, -1)

QP // RW

p (0 , -1)

Step-by-step explanation:

100%=245

x%=40

Let's see what part 40 is of 245. 40/245=0.16. so 0.16×245=40. Therefore 0.16×100%=x=16% roughly.

Answer:

A man drove x miles per hour for 3 hours and (2x-60) miles per hour for the next 4.75 hours.Express the total distance traveled in terms of x.

Total distance covered by the man in terms of 'x' = (12.5x-285)miles

Step-by-step explanation:

Given:

Speed of  a man = 'x' miles/hour

Time taken = [tex]3[/tex] hour

So, distance = product of speed and time.

Distance covered in term of 'x' [tex]=(d_1=3x)[/tex]

Now,

Speed = [tex](2x-60)[/tex] miles/hour

Time taken= [tex]4.75[/tex] hours

Distance [tex](d_2)[/tex]  = [tex](2x-60)\times 4.75[/tex]

                      = [tex](2x\times 4.75) -(60\times 4.75)[/tex]

                      = [tex](9.5x - 285)[/tex] miles

Total distance covered by the man = Summation of  [tex]d_1[/tex] and [tex]d_2[/tex]

                                                           = [tex](9.5x-285+3x)[/tex]

                                                           = [tex](12.5x-285)[/tex] miles

So the total distance covered by the man in terms of 'x' = (12.5x-285) miles.

ANSWER: Exact Form: [tex]\sqrt{10}[/tex]

Decimal Form:  3.16227766

STEP-BY-STEP EXPLANATION:

(1, 2) and (4,3)

Use the distance formula to determine the distance between the two points.

Distance = \sqrt{(X2-X1)^{2  }+ (Y2-Y1)^{2} }

Substitute the actual values of the points into the distance formula.

\sqrt{(4-1)^{2  }+ (3-2)^{2} }

The result can be shown in multiple forms.

Exact Form: [tex]\sqrt{10}[/tex]

Decimal Form:  3.16227766

The distance between the given points is approximately 3.16 units.

To find the distance between the points (1, 2) and (4, 3), we use the distance formula derived from the Pythagorean Theorem, which calculates the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²).
Using this formula, we plug in the coordinates of the two points:

Let (x₁, y₁) = (1, 2)

Let (x₂, y₂) = (4, 3)

Substituting these values into the formula gives us:

d = √((4 - 1)² + (3 - 2)²)
d = √(32 + 12)
d = √(9 + 1)
d = √10
d ≈ 3.16

Therefore, the distance between the two points is approximately 3.16 units.

Answer:

–43p + (–25)  is  EQUIVALENT to  –43p – 25.

Step-by-step explanation:

The options are MISSING.

The needed options are:

1. 25 – 43p

2. 25 – 43p

3. –25p –43

4. –43p + (–25)

Now, here the given expression is:  –43p – 25

Taking each option and simplifying it , we get:

1. 25 – 43p

Here, the second term is NEGATIVE, but the first term (25) is POSITIVE.

⇒  25 – 43p  ≠ –43p – 25

Hence, 25 – 43p is  NOT EQUIVALENT.

2. 25 – 43p

Here, the second term is NEGATIVE, but the first term (25) is POSITIVE.

⇒  25 – 43p  ≠ –43p – 25

Hence, 25 – 43p is  NOT EQUIVALENT.

3. –25p –43

Here, the variable p is multiplied with (-25) and NOT (-43).

⇒   –25p –43 ≠ –43p – 25

Hence,  –25p –43 is  NOT EQUIVALENT.

4. –43p + (–25)

Here, both the given terms (43) and (25) are NEGATIVE.

Also, the varibale p is multiplied with (-43)

⇒  –43p + (–25) = –43p – 25

Hence, –43p + (–25)  is  EQUIVALENT.

Answer:

no no no no

Step-by-step explanation:

Answer:

For the first scatter plot, the variables have a negative association, which matches the option D. X is the amount of time in the mall and Y is the remaining money.

For the second scatter plot, it is a positive association. This plot could match A, B, or E.

The third scatter plot shows no correlation whatsoever, which represents C. Tomika's friends' heights did not associate with how much time they watched TV.

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Brainliest would be appreciated! I'd be Expert by now, but I never get brainliest. You don't have to though, but it would make me happy. Thanks!

Answer:

2z +3

Step-by-step explanation:

This question simply involves understanding what like terms are, and how to combine them.

Here, 5z and -3z are like terms, so we combine them by going 5z-3z = 2z

(i.e. we minus the coefficients, but the z stays unchanged).

Next, the number term of 3 in the middle cannot be combined with any other term, so it just stays in the expression.

If there are 29 students in class and they need to collect a total of 168, we can divide 168 by 29 to get $5.79. This means that each student must collect $5.79 in order for them to be able to purchase everything.

Answer:

[tex]4x^2+72x+259=0[/tex]

Step-by-step explanation:

If [tex]x_1[/tex] and [tex]x_2[/tex] are the solutions to the quadratic equation, then this equation can be written as

[tex](x-x_1)(x-x_2)=0[/tex]

In your case,

[tex]x_1=-9+\dfrac{\sqrt{65}}{2}\\ \\x_1=-9-\dfrac{\sqrt{65}}{2}[/tex]

Then the equation is

[tex]\left(x-\left(-9+\dfrac{\sqrt{65}}{2}\right)\right) \left(x-\left(-9-\dfrac{\sqrt{65}}{2}\right)\right)=0\\ \\\left(x+9-\dfrac{\sqrt{65}}{2}\right)\left(x+9+\dfrac{\sqrt{65}}{2}\right)=0\\ \\x^2+9x+\dfrac{\sqrt{65}}{2}x+9x+81+\dfrac{9\sqrt{65}}{2}-\dfrac{\sqrt{65}}{2}x-\dfrac{9\sqrt{65}}{2}-\dfrac{65}{4}=0\\ \\x^2+18x+\dfrac{259}{4}=0\\ \\4x^2+72x+259=0[/tex]

Answer:

(2x+5)(x+3)

Step-by-step explanation:

2x^2+11x+15

(2x+5)(x+3)

Answer:

(2x+5)(x+3)

Step-by-step explanation:

1) Quotient = [tex]x^2+x-3[/tex].

   Reminder= 8.

2) Quotient = x-3.

    Reminder = 7x-9.

Step-by-step explanation:

The Polynomial division is same as the regular division using long division method.

The quotient and reminder can be either polynomial or number.

1) For [tex]\frac{x^4-3x^2+4x+5}{x^2-x+1}[/tex] , the quotient is [tex]x^2+x-3[/tex] and the reminder is 8.

2) For [tex]\frac{x^3-3x^2+5x-3}{x^2-2}[/tex],  the quotient is  x-3 and the reminder is 7x-9.

( The steps are uploaded in the image).

The value of two figures that are similar to the 2 by 6 figure are shown in figure 2 and figure 4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The figure is type of 2 by 6.

Now,

Since, The figure is type of 2 by 6.

Which is equal to 1 by 3.

Clearly, In figure 1;

The size is 2 by 4.

It is equal to 1 by 2.

In figure 2;

The size is 1 by 3.

It is equal to 1 by 3.

In figure 3;

The size is 1 by 6.

It is equal to 1 by 6.

In figure 4;

The size is 3 by 9.

It is equal to 1 by 3.

Thus, The figure 2 and figure 4 is equal to the figure 2 by 6.

Learn more about the divide visit:

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Answer:

300

Step-by-step explanation:

22% means 22 of 100

for every 100 persons 22 voted

for every x persons 66 voted.lets do the math to find what is the x

[tex] \frac{22}{100} = \frac{66}{x} [/tex]

[tex]x = \frac{66 \times 100}{22} [/tex]

x=300

Answer: 300

Step-by-step explanation:

we know that 22% is the same as 22/100 ( 22 over 100). We are trying to find the whole, which means we are already given the part which is 66. how can we get from 22 to 66? 22 multiples by 3 = 66 do the same to the bottom 100 multiplied by 3 is 300.

Answer:

Divide 2 by 1/6 and you should get the value of x.

Step-by-step explanation:

simple 2 step equation.

Answer: x = 12

Step-by-step explanation: In this equation, notice that x is being multiplied by a fraction. In this situation, in order to get x by itself, we must multiply both sides of the equation by the reciprocal of that fraction. The reciprocal of a fraction is just that fraction flipped so the reciprocal of 1/6 is just 6/1.

So here, in order to get x by itself, we multiply both sides of the equation by 6/1. On the left our 6's cancel and our 1's cancel and we're left with x. On the right we have 2 x 6 which simplifies to 12 so x = 12.

The statement is true. The rational roots of a polynomial can be written in the form p/q. The rational root theorem is used to determine these potential roots.

The statement in the question is true.

The rational roots of a polynomial function can indeed be written in the form p/q, where p is a factor of the leading coefficient and q is a factor of the constant term. This is known as the Rational Root Theorem.

For example, if we have the polynomial function f(x) = 3x^3 - 7x^2 + 4x - 2, the leading coefficient is 3 and the constant term is -2. The potential rational roots would be of the form p/q, where p is a factor of -2 and q is a factor of 3. The factors of -2 are -1, 1, -2, and 2, while the factors of 3 are -1 and 3. Therefore, the potential rational roots would be:

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Answer:

  x less 16.5

Step-by-step explanation:

"x -16.5" means 16.5 is subtracted from x. The resulting value is 16.5 less than x. The wording "x less 16.5" basically means "x minus 16.5" and/or "x reduced by 16.5".

__

Subtraction is not commutative, so "16.5 decreased (or reduced) by x", meaning "16.5 -x" or "16.5 minus x", is not the same thing.

Answer:

$69

Step-by-step explanation:

1 - 0.25 = 0.75

original price * (1 - markdown) = sale price

$92 * 0.75 = sale price = $69

Answer:

-17

Step-by-step explanation:

f(n)=-5n-2

f(3)=-5(3)-2

f(3)=-15-2

f(3)=-17

Answer:

if your dividing then 3 but if you want 21 sevenths as a mixed number then it would be 3.

Step-by-step explanation:

to find the quotient, you need to find out what multiplied by 7 gives you 21. (thats easy 3) so there is your answer. to find the mixed version of 21 sevenths you need to divide 21 by 7 ( literally what  i just showed...) and you get 3.

HOPE THIS HELPS!!!

Answer:

That would be 3 because 7x3 is 21.

Step-by-step explanation:

Answer:

When solving equations the goal is to get the variable by itself so

4.5+1.5k=18-3k (first step is to subtract 4.5 from each side)

1.5k=13.5-3k (4.5-4.5=0, 18-4.5=13.5) (Next is to add 3k to each side)

4.5k=13.5 (1.5k+3k=4.5k, -3k+3k=0) (Last you divide both sides by 4.5)

k=3 (4.5/4.5=1, 13.5/4.5=3)

k=3

Hope this helps ;)

Final answer:

To find an equivalent length for a wooden board that is 3 yards and 1 foot long, you convert yards to feet, using the fact that 1 yard equals 3 feet, and then add any remaining feet. The board is therefore 10 feet long in total.

Explanation:

Converting Yards to Feet:

A wooden board is 3 yards and 1 foot long. To find an equivalent length, we need to convert yards to feet because there are 3 feet in 1 yard. The calculation goes as follows:

 First, we know that 1 yard equals 3 feet.

 To convert 3 yards to feet, we multiply by 3: 3 yards × 3 feet/yard = 9 feet.

 Next, we add the extra foot: 9 feet + 1 foot = 10 feet.

 Therefore, the board is 10 feet long in total.

This process involves using equalities and conversion factors to change one unit of measurement to another while maintaining the same quantity.

Answer:

[tex] \frac{4}{15} [/tex]

Step-by-step explanation:

[tex] 3 \frac{1}{10} - 2 \ \frac{5}{6} [/tex]

Convert the above mixed numbers to improper fractions through this simple approach: 3 × 10 + 1 /10 = 31/10. Similarly, 2 × 6 + 5 /6 = 17/6

[tex] \frac{31}{10} - \frac{17}{6} [/tex]

Take the LCM of the denominators and simplify. LCM = 60. Thus, 60/10 = 6; 6 × 31 = 186. Also, 60/6 =10; 10×17 =170 all divide by 60:

[tex] = \frac{186 - 170}{60} [/tex]

Common factors between the numerator and denominator is 4, therefore 16/4 = 4 and 60/4 = 15.

[tex] = \frac{16}{60} = \frac{4}{15} [/tex]

Therefore the answer is 4/15 in simplest form.

Answer:

1979.25

Step-by-step explanation: