A company sells furniture for home assembly. Their largest bookcase has shelves that should be 105 cm, with a tolerance of 0.8 cm (105cm 0.8cm). A set of six shelves had lengths of 105.3 cm, 105.2 cm, 104.1 cm, 105.1 cm, and 105.9 cm. Find the minimum and maximum allowable shelf length. Which , if any, of the shelves are not within the specified tolerance?

Answer:

Therefore both Ken and Billy ran the same amount of the training course.

Step-by-step explanation:

i) Billy was going to [tex]\frac{3}{4}[/tex] th of the training course.

ii) Ken was going to run [tex]\dfrac{1}{2}[/tex] of the training course.

iii) Billy finished [tex]\frac{1}{3}[/tex] of his run Therefore Billy finished only [tex]\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}[/tex] of the training course.

iv) Ken finished [tex]\dfrac{1}{2}[/tex] of his run Therefore Billy finished only [tex]\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}[/tex] of the training course.

v) Therefore both Ken and Billy ran the same amount of the training course.

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: Can you attach a copy of the triangles?

Step-by-step explanation:

True, [tex]f(x)[/tex] is a function.

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.

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:

34.246

Just divide both numbers

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:

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 ;)

Answer:

EF = 6m.

Step-by-step explanation:

Given that:

1) All the edges of the pyramid in the model have length 12m.

So, AB = 12m

2) E is the middle of AT, F is the middle of BT

So, EF is a line segment connecting the midpoints of ΔATB

So, by applying The Triangle Mid-segment Theorem

EF // AB and EF = 0.5 AB

So, EF = 0.5 AB = 0.5 * 12 = 6m

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

The Triangle Mid-segment Theorem:

The line segment connecting the midpoints of any two sides of a triangle has the following properties:

1) The line segment will be parallel to the third side.

2) The length of the line segment will be a half of the length of the third side.

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: 2

Step-by-step explanation:

to find this you use the equation

y2-y1

--------

x2-x1

so with your points tuat would be

5+3/4-0 (it becomes a plus bc two negatives= a positive

8/4=2

Answer: 0.112485

Step-by-step explanation: Look below for an attached explanation

Hope this helps!

To find 0.06 divided by 0.5334, multiply both numbers to convert them into whole numbers and then perform long division. The result of the division is approximately 0.1125.

The question asks for the division of two decimal numbers, specifically 0.06 divided by 0.5334. To divide these decimals, you can use long division or a calculator. Here's how to divide them step-by-step using long division:

In this case, 0.06 divided by 0.5334 is approximately 0.1125.

This type of math problem is common in various science calculations, such as determining the concentration of a solution in chemistry or the rate of a reaction in physics.

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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:

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.

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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)

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:

1979.25

Step-by-step explanation:

Answer:

3x + 1 <-5 is x<−2

5x-1> 29 is x>6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x<−2

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x>6

Final answer:

To solve the compound inequality 3x + 1 < -5 OR 5x - 1 > 29, solve each inequality separately. The solution is all real numbers that are either less than -2 or greater than 6.

Explanation:

To solve the compound inequality 3x + 1 < -5 OR 5x - 1 > 29, we need to solve each inequality separately and then find the union of the two solutions, since the word 'OR' indicates that a solution to either inequality will satisfy the compound inequality.

Solving the first inequality:

3x + 1 < -5

Solving the second inequality:

5x - 1 > 29

The solution to the compound inequality is the set of all real numbers that are either less than -2 or greater than 6.

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.

Step-by-step explanation:

15x + 21= 3 (5x + 7)

Therefore, greatest common factor is (5x + 7)

Answer:

18

Step-by-step explanation:

2(x - 5) + 4 = 30

2x - 10 + 4 = 30

2x - 6 = 30

2x = 36

x = 18

Answer:

18

Step-by-step explanation:

2(x-5)+4=30

2(x-5)=30-4

2(x-5)=26

x-5=26/2

x-5=13

x=13+5

x=18

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:

Answer:$135

Step-by-step explanation: you divide it and get that answer

Answer:

$135

Step-by-step explanation:

90×1.5= 135 Hope this helps

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.

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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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.

[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