MATH
Devon is making table runners for his niece's wedding. The short tables are 6 feet
(ft) long, and the long tables are 10 ft long. Each runner will overhang its table by 8
inches (in.) on each end. Devon was told there will be 12 small tables and twice that
number of long tables. How many total yards (yd) of fabric will he need to make the
table runners, assuming no waste? (Note: 12 in. = 1 ft and 3 ft = 1 yd.)

Answer:

[tex]6 \frac{5}{12} \: {ft}^{2} [/tex]

Step-by-step explanation:

[tex]area \: of \: rectangle = length \times width \\ \\ = 1 \frac{1}{6} \times 5 \frac{1}{2} \\ \\ = \frac{7}{6} \times \frac{11}{2} \\ \\ = \frac{77}{12} \\ \\ = 6 \frac{5}{12} \: {ft}^{2} [/tex]

Answer:

[tex]x = \frac{1}{3} [/tex]

or x = 0.33

Step-by-step explanation:

[tex] {5}^{3x} - {5}^{3x - 1} = 4 \\ \\ \implies{5}^{3x} - {5}^{3x} . {5}^{ - 1} = 4 \\ \\ \implies{5}^{3x}(1 - {5}^{ - 1} )= 4 \\ \\ \implies{5}^{3x} \bigg(1 - \frac{1}{5} \bigg)= 4 \\ \\ \implies{5}^{3x} \bigg(\frac{5 - 1}{5} \bigg)= 4 \\ \\ \implies{5}^{3x} \times \frac{4}{5} = 4 \\ \\ \implies{5}^{3x} = 4 \times\frac{5}{4} \\ \\ \implies{5}^{3x} =5 \\ \\ \implies \: 3x = 1 \\ \\ \huge \implies \: x = \frac{1}{3} \\\\ \huge \implies \: x = 0.33[/tex]

Answer:

a) 2x + 3; b) 0

Step-by-step explanation:

Area = [tex]4\pi x^2+12\pi x+9\pi =\pi (4x^2+12x+9)=\pi (2x+3)^2[/tex]

Area = [tex]\pi r^2[/tex]

a) radius r = 2x + 3

b) 2x + 3 > 0

x > -3/2

The least possible integer value of x is 0

Answer:

[tex]cos\theta=\frac{3}{5}[/tex]

Step-by-step explanation:

Since [tex]sin\theta=0.8[/tex] is the same as [tex]sin\theta=\frac{4}{5}[/tex] and [tex]sin\theta=\frac{opposite}{hypotenuse}[/tex], then we know that the side opposite to the angle [tex]\theta[/tex] is 4 units and the hypotenuse is 5 units.

Because [tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex], then we have to find the adjacent side to the angle [tex]\theta[/tex] using the Pythagorean Theorem:

[tex]a^2+b^2=c^2\\\\(adjacent)^2+(opposite)^2=(hypotenuse)^2\\\\(adjacent)^2+4^2=5^2\\\\(adjacent)^2+16=25\\\\(adjacent)^2=9\\\\adjacent=3[/tex]

Therefore, since the adjacent side is 3 units, then [tex]cos\theta=\frac{3}{5}[/tex]

Explanation:

AB = AX+XB = 8+22 = 30

The ratio of AB to AX is AB/AX = 30/8 = 3.75

AC = AY+YC = 9+33 = 42

The ratio of AC to AY is AC/AY = 42/9 = 4.67 approximately

Since we don't get the same result, this means that the equation AB/AX = AC/AY is not true. The sides are not in proportion with one another, and therefore the triangles aren't similar.

The sides need to be in proportion with one another so we could use the SAS similarity rule.

Considering the SAS similarity theorem, triangles ABC and AXY are not similar triangles.

The SAS Similarity postulate or theorem, states that, when two triangles have two pairs of corresponding sides whose ratios are the same, and also has a pair congruent included angles, then, both triangles are similar.

Triangles ABC and AXY have a pair of congruent included angles, ∠BAC ≅ XAY.

Let's find out if their corresponding sides have equal ratios.

Thus:

AB/AX = 30/8 = 3.75

AC/AY = 42/9 = 4.67

Their ratios are not equal.

Therefore, considering the SAS similarity theorem, triangles ABC and AXY are not similar triangles.

Learn more about SAS similarity theorem on:

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Answer:

[tex]f^-1 (x) = \sqrt[3]{x - 8}[/tex]

Step-by-step explanation:

Custom file created rather than math ML for neatness.

Answer:

8/10 > 5/8

Step-by-step explanation:

8/10 > 5/8

Hope this helps!

Answer:

See Below

Step-by-step explanation:

For each of these, you just replace x with what's in the parenthesis.

f(-2) = 4(-2)^2 - 2(-2) + 1

f(-2) = 16 + 4 + 1

f(-2) = 21

g(5) = [tex]\sqrt{4(5) - 16}[/tex]

g(5) = [tex]\sqrt{20-16}[/tex]

g(5) = [tex]\sqrt{4}[/tex]

g(5) = 2

f(3r) = 4(3r)^2 - 2(3r) + 1

f(3r) = 4(9r^2) - 6r + 1

f(3r) = 36r^2 - 6r + 1

f(a+b) = 4(a+b)^2 - 2(a+b) +1

f(a+b) = 4 (a^2 + 2ab + b^2) - 2a - 2b + 1

f(a+b) = 4a^2 + 8ab + 4b^2 - 2a - 2b + 1

Answer:

6 bags.

Step-by-step explanation:

Subtract 38 from 75 to represent the remaining amount of Matthew's money.

[tex]75-38=37.[/tex]

Matthew has $37 left over from buying flowers.

Divide 37 by 6 to represent how many bags of soil he can buy.

[tex]37\div6=6\frac{1}{6}[/tex]

Matthew can only buy 6 bags of soil, 1/6 isn't included because you can't buy a fraction of a bag.

Answer:

C

Step-by-step explanation:

hope this helps :)

Answer:

Example 1) sin(42) ×25=16.73

Example 2) 12÷tan(75)=3.22

Example 3) 19÷cos(36)=23.49

Example 4) tan(53)×7=9.29

Answer:

yup it is ...

x²-2x = -6+2x

=> x²-4x +6

By expanding the equation, we can see that it is quadratic.

A quadratic equation is any polynomial of degree 2.

Here we have:

x^2 - 2x = (-2)*(3 - x)

Expanding this we get:

x^2 - 2x = -6 + 2x

Moving all to the same side:

x^2 - 2x - 2x + 6 = 0

x^2 - 4x + 6 = 0

This is a polynomial of degree 2, so this is a quadratic equation.

If you want to learn more about quadratic equations, you can read:

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Answer:

ABCD is the quadrilateral

Answer:

The x -intercept is (3, 0)

The y -intercept is (0, - 2)

Step-by-step explanation:

Given equation is: -6x + 9y = -18

To find x - intercept:

Plug y = 0 in the given equation.

-6x + 9(0) = - 18

-6x + 0 = -18

-6x = - 18

x = (-18)/(-6)

x = 3

The x -intercept is (3, 0)

To find y - intercept:

Plug x = 0 in the given equation.

-6(0) + 9y= - 18

0 + 9y = -18

9y = - 18

y = (-18)/(9)

y = - 2

The y -intercept is (0, - 2)

Answer:

216 units^2

Step-by-step explanation:

the formula to calculate area of triangle is 1/2 b×h

so...

[tex] \frac{1}{2} (27) \times (16) \\ = 216 {units}^{2} [/tex]

Answer:

Step-by-step explanation:

144 units^3

Answer:

Yes, it is a right triangle. The distance is 6,2.

Step-by-step explanation:

The square of 15 is 225, and the square of 12 is 144. The square of 9 is 81. 144 + 81 = 225, so it's a right triangle.

9y

(space fillerrrrr)

Answer:

Step-by-step explanation:

10 cubes ÷2 stacks = 5, so in each stack 5.

one stack has 5

Second stack has 4 more cubes than the other. (5+4=9)

So the answer is 5 and 9

The number of cubes is 3 and 7 in two stacks consisting of 10 stacks total.

Suppose Ebony has 'x' cubes in one stack

So, the number of cubes in another stack =x+4

A cube is a solid having all three dimensions i.e. length, breadth, and height equal to each other.

According to the question,

Total number of cubes = 10

x+(x+4) = 10

2x+4 =10

2x=6

x=3

So, Ebony has 3 cubes in one stack

Number of cubes in another stack =3+4 =7cubes

Therefore, The number of cubes is 3 and 7 in two stacks consisting of 10 stacks total.

To get more about cubes visit:

https://brainly.com/question/1972490

Answer:

The sum of the three mixed numbers is 11 and 9.5/16.

Step-by-step explanation:

5 and 13/16

2 and 1/8 = 2 and 0.5/16

3 and 3/4 = 3 and 12/16

10 and 25.5/16

11 and 9.5/16

Answer:

[tex]11\frac{11}{16\\} \\[/tex]

Step-by-step explanation:

Separate fractions and whole numbers

5 2 3   13/16 1/8 3/4

Add whole numbers and fractions (where the denominator is 16)

5+2+3=1                    

13/16+1/8+3/4 =

13/16+2/16+12/6=

27/16 =

[tex]1\frac{11}{16\\} \\[/tex]

27/16+10 = [tex]11\frac{11}{16\\}[/tex]

Carla would have about 795 pictures on May 16th.

A linear equation is in the form:

y = mx + b

where y,x are variables, m is the rate of change and b is the y intercept.

Let y represent the number of pictures after x days.

At April 30th, Carla sees that she has 235 pictures, hence b = 235. Also,  she takes 35 pictures each day, hence m = 35. The equation is:

y = 35x + 235

On May 16th, x = 16 hence:

y = 35(16) + 235 = 795

Carla would have about 795 pictures on May 16th.

Find out more on Linear equation at: https://brainly.com/question/14323743

=======================================================

Explanation:

In a standard deck, there are 52 cards.

If this deck is missing the queen of hearts and 2 of clubs, then we really have 52-2 = 50 cards in the deck.

There are 4 aces and 13 spades. Those values add to 4+13 = 17, but we need to subtract off 1 to account for the ace of spades counted twice. We have 17-1 = 16 cards that are either an ace, a spade, or both.

Or you can think of it like saying 13 spades + 1 ace of hearts + 1 ace of diamonds + 1 ace of clubs = 16 cards total.

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

The event space has A = 16 cards in it, while the sample space has B = 50 cards.

The probability we're after is A/B = 16/50 = 8/25

Answer:

[tex]4x^{9} y^{8} \sqrt{5y}[/tex]

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

This is the Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
The hypotenuse is c so we need to make c the subject:
[tex]c = \sqrt{a^{2}+b^{2} }[/tex]
To do this I simply square rooted both sides.
Now we substitute values given to get the answer of the hypotenuse:
[tex]c = \sqrt{3^{2} + 4^{2} }[/tex]
[tex]c = \sqrt{9+16}[/tex]
[tex]c = \sqrt{25}[/tex]
c=5
The lengths 3,4,5 of a triangle are known as a Pythagorean triple.
A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².