Seamus has a truck of chairs and tables for a party. There are 8 times as many chairs as tables, for a total of 56 chairs in the truck. How many tables are in the truck?

Answer:

x = 65

Step-by-step explanation:

The angle labeled with the expression " ( 2x + 15 ) " and the angle with the measure of 145° are vertical angles

Vertical angles are congruent (In other words, they are equal to each other)

Hence, 2x + 15 = 145

                   ^ ( Note that we just created an equation  that we can use

                       to solve for x )

Using that same equation we then solve for x

2x + 15 = 145

step 1 subtract 15 from each side

15 - 15 cancels out

145 - 15 = 130

we now have 130 = 2x

step 2 divide each side by 2

130 / 2 = 65

2x / 2 = x

we're left with x = 65

Answer:

200

Step-by-step explanation:

you subtract

Answer:  you would need to cross the bridge 5 times

Step-by-step explanation:

costing a total of $42.50 for each option.

hope this helps

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

We have,

In a parallelogram,

- Opposite sides are congruent:

The opposite sides of a parallelogram have equal lengths.

- Opposite angles are congruent:

The opposite angles of a parallelogram have equal

Now,

a)

Opposite angles are congruent:

So,

5x + 29 = 7x - 11

29 + 11 = 7x - 5x

40 = 2x

2x = 40

x = 40/2

x = 20

And,

3y + 15 = 5y - 9

15 + 9 = 5y - 3y

24 = 2y

y = 24/2

y = 12

b)

Opposite sides are congruent:

So,

-6x = -4x + 6

-6x + 4x = 6

-2x = 6

x = -3

And,

7y + 3 = 12y - 7

12y - 7y = 3 + 7

5y = 10

y = 2

Thus,

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

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Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

The calculated volume of the solid figure is 421.08 cubic feet

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

Base area = 38.28 square feet

Height = 11 feet

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

Volume = Base area * Height

substitute the known values in the above equation, so, we have the following representation

Volume = 38.28  * 11

Evaluate

Volume = 421.08

Hence, the volume of the solid figure is 421.08 cubic feet

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The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer:

F.3p < 10.2

G.13.6 ≤ 3.9p

H.5p > 17.1

J.8.5

For the positive integer n, \(\langle n\rangle\) denote the sum of all the positive divisors of n with the exception of n itself is an option (A). 6.

We start by calculating the value of \(\langle 6 \rangle\), which is the sum of the positive divisors of 6 excluding 6 itself.

Since the divisors of 6 are 1, 2, 3, and 6, we have \(\langle 6 \rangle = 1 + 2 + 3 = 6\).

Next, we need to calculate \(\langle\langle 6 \rangle\rangle\), which is the sum of the positive divisors of 6 excluding 6 itself, and the positive divisors of 6 excluding 6 itself and \(\langle 6 \rangle\).

The divisors of 6 excluding 6 itself are 1, 2, and 3, so \(\langle\langle 6 \rangle\rangle\) is the sum of the positive divisors of 1, 2, and 3.

The divisors of 1 are just 1, the divisors of 2 are 1 and 2, and the divisors of 3 are 1 and 3.

Thus, \(\langle\langle 6 \rangle\rangle = 1 + 2 + 1 + 3 = 7\).

Finally, we need to calculate \(\langle\langle\langle 6\rangle\rangle\rangle\),

which is the sum of the positive divisors of 1, 2, 3, and 7.

The divisors of 1 are just 1, the divisors of 2 are 1 and 2, the divisors of 3 are 1 and 3, and the only divisor of 7 is 1.

Thus, \(\langle\langle\langle 6\rangle\rangle\rangle = 1 + 2 + 1 + 3 + 1 = \boxed{8}\).

For the positive integer n, \(\langle n\rangle\) denote the sum of all the positive divisors of n with the exception of n itself is 6

Hence option A is correct choice.

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Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

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

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

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

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

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

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

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

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer: 280

Step-by-step explanation:

The products of each pair of numbers are:

1 x 33 = 33

4 x 30 = 120

8 x 26 = 208

14 x 20 = 280

b. To find the pair of numbers that will produce the largest possible product, we need to look for the pair with the closest product to 340 (the square of 17, which is the average of the two numbers).

The pair of numbers with the closest product to 340 is 14 and 20, whose product is 280. Therefore, the pair of numbers that will produce the largest possible product is 14 and 20, and the product is 280.

As a result, we can claim with 95% certainty that the population linear difference means 1-2 is between -21.48 and -2.52 units of small appliances.

In algebra, a linear equation has the form y=mx+b. The slope is denoted by B, while the y-intercept is denoted by m. Because y and x are variables, the preceding sentence is sometimes referred to as a "linear equation with two variables." Bivariate linear equations are two-variable linear equations. Linear equations may be found in various places: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the form y=mx+b, where m represents the slope and b represents the y-intercept, it is said to be linear. A linear equation is one that contains the formula y=mx+b, with m signifying the slope and b denoting the y-intercept.

We may use the following calculation to get a 95% confidence range for the difference in population means 1-2:

\((x1 - x2) t(\alpha/2, df) * \sqrt(s12/n1 + s22/n2)\)

where:

Initially, we must compute the degrees of freedom:

\(df = ((s12/n1) + s22/n2)2/((s12/n1) + (s22/n2)2/(n2-1))\\df = ((13^2/36 + 16^2/49)^2) / ((13^2/36)^2/35 + (16^2/49)^2/48) = 67.94\\(78 - 90) 2.00 * \sqrt(132/36 + 162/49)\\CI = -12 +2.00 * 4.742\\CI = -12+ 9.484\\CI = (-21.48, -2.52) (-21.48, -2.52)\)

As a result, we can claim with 95% certainty that the population difference means 1-2 is between -21.48 and -2.52 units of small appliances.

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The translation form of each shape is given as follows:

a) X to Z: (x, y) -> (x + 5, y + 2).

b) Z to X: (x, y) -> (x - 5, y - 2).

The four translation rules are defined as follows:

For the composition of translations, we add the coordinates, hence:

Hence the rule from X to Z is given as follows:

(x, y) -> (x + 5, y + 2).

From Z to X, we have the inverse rule, hence:

(x, y) -> (x - 5, y - 2).

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Answer:

i dont know how to help you:(

The measures of the non-right angles of each triangle are 40 degrees and 50 degrees.

The sum of the interior angles of a regular 18-gon can be found using the formula:

S = (n - 2) × 180 degrees

n is the number of sides of the polygon.

Substituting n = 18 we get:

S = (18 - 2) × 180 degrees

= 2880 degrees

The 18-gon into 36 right triangles need to draw 18 lines from the center of the polygon to its vertices dividing the polygon into 36 congruent sectors each with a central angle of 360 degrees / 18 = 20 degrees.

Each sector is an isosceles triangle with two sides of equal length radiating from the center of the polygon.

The vertex angle of each isosceles triangle is equal to twice the central angle or 40 degrees.

Since the vertex angle of a right triangle is 90 degrees the two non-right angles of each right triangle are 40 degrees and 50 degrees.

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Answer:

44.59 divided by 5.25= 8.49

Hope this helps!!

Answer:

44.5÷56 that how you answer

The value of {h} is equivalent to 6/5.

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is the function as follows -

(1/5) + h = (7/5)

We can write the function as -

(1/5) + h = (7/5)

h = 7/5 - 1/5

h = (7 - 1)/5

h = 6/5

Therefore, the value of {h} is equivalent to 6/5.

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The triangles are not similar

Given data ,

Let the first triangle be ΔJKL

Let the second triangle be ΔMNP

Now , the corresponding sides are

JK / JL ≠ NM / MP

where the corresponding sides of similar triangles are not in the same ratio

And , the common angle to both the triangles is ∠J = ∠M

So , ∠J = ∠M and JK / JL ≠ NM / MP

Hence , the triangles are not similar

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Answer:

E

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{a}{sin64}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a = \(\frac{9.3sin64}{sin31}\) ≈ 16.23 ( to 2 decimal places )

then to find b , using

\(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

\(\frac{b}{sin85}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b = \(\frac{9.3sin85}{sin31}\) ≈ 17.99 ( to 2 decimal places )

Answer:

113 meters long

Step-by-step explanation:

If each part is all equal in length, then each part is 1/4 the total length of the obstacle course. Therefore, each part of the course was 1/4(452)=113 meters long

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Answer:

y=1/2x-2

Step-by-step explanation:

perpendicular lines have a neg. reciprocal for the slope.

for example:

in this equation y=-2x+1

-2 is the slope and the negative reciprocal would be 1/2

hence, the slop of our new line is 1/2

y=1/2x+b

we can substitute the coordinates given for x and y:

2=1/2(8)+b

2=4+b

-2=b

hence the new equation is y=1/2x-2

Answer:

40 and 56.

Step-by-step explanation:

x - y = 16    where x is the greater number

If the ratio is 5:7 one number must be 7/12 of the total of the 2 numbers, so:

x =  7/12(x + y)

From first equation x = y + 16, so substituting for x:-

y + 16 = 7/12( 2y + 16)

Multiplying through by 12:

12y + 192 = 7(2y + 16)

12y + 192 = 14y + 112

2y = 192 - 112 = 80

y = 40

So x = 40+ 16 = 56.

Answer:

The numbers are:

56 and 40

Step-by-step explanation:

a - b = 16    eq. 1

5a = 7b      eq. 2

from eq. 1:

a = 16 + b

relacing this last eq. in eq. 2

5(16+b) = 7b

5*16 + 5*b = 7b

80 + 5b = 7b

80 = 7b - 5b

80 = 2b

80/2 = b

40 = b

From eq. 1

a - b = 16

a - 40 = 16

a = 16 + 40

a = 56

Check:

from eq. 2:

5a = 7b

5*56 = 7*40 = 280

The capacity of the container is equal to 7.6 × 10⁻³ kiloliters.

This is a unit conversion question, in which we need to determine how many kiloliters are equivalent to the capacity of a container.

According to capacity tables, a cubic decimeter or 1000 cubic centimeters equals a liter. Then, we can determine the number of kiloliters by using the following cross multiplication:

x = 7.6 dm³ × (1 L / 1 dm³) × (1 kL / 1000 L)

x = 7.6 × 10⁻³ kL

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Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

The physical diameter of the sun will be 1309000km and the percentage of difference between the diameters will be 5.8%.

From the information, the sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. The angular diameter in radians will be:

= 0.5π / 180

= 0.008727 radians

Distance from the sun = 150 × 10^6

The physical diameter of the sun will be:

= 150 × 10^6 × 0.008727

= 1309000km

The difference between the diameters will be:

= 1390000 - 1309000

= 8.1 × 10^4.

The percentage of difference will be:

= (8.1 * 10^4) / 1390000 × 100

= 5.8%

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Possible Answer 1:

Positive values represent elevations above sea level, while negative values are elevations below sea level. For example, a building may be +100 or simply 100 feet high. Another example: going scuba diving could lead the diver to reach a elevation of -10 meters. The value 0 is the exact location of sea level itself. In other words, if your elevation is 0, then you are at the surface of the water.

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

Possible Answer 2:

Often in money, loans and borrowing happens. If so, then we use negative numbers to indicate debt. If someone has a bank balance of say -10 dollars, then they owe the bank $10. Positive values mean that they don't owe the money and it's entirely theirs to spend however they want. A balance of 0 means they neither have money, nor do they owe anyone.

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

Possible Answer 3:

Let's say we define negative distance to mean that you walk some amount to the left (to match up with the fact the negative x values point left). So for instance, we could say the number -14 indicates you walked 14 feet to the left. Positive values on the other hand will mean you walk some amount to the right. Drawing an x axis number line is very recommended. The value 0 indicates that no walking has occurred at all.

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

Of course, when you write your answer, it should be in your words only. Those answers posted above are just a springboard to get you started.

To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.

To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.

What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).

What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value

step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)

Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)

Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11

Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)

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Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!