find the missing terms

_,-9,_,3,9

answer: they spend $27.92 on goodie bags

the hourly rate is $37.5

they spend $177.92 in total

When he wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up is 1/4.

It should be noted that from the information, in the art class, Mr. Jacobs compared the amount of glitter left on students' plates and the dot plot shows this data

It should be noted that the least two plates of glitters will be:

= 1/4 + 2/4

= 3/4

Therefore, when e wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up will be:

= 3/4 ÷ 3

= 3/4 × 1/3

= 1/3

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The heat of the sun penetrates the atmosphere and warms the Earth's surface. The warmed rEarth Radiates and this heat back into the atmosphere.The gases the surround the atmosphere such as carbon dioxide , methane , nitrous oxide and water vapour absorb some of the radiated heat and send it back to the Earth . This trapping of heat from the Sun by excess carbon dioxide and other gases present in the atmosphere is known as the greenhouse effect. The gases involved in the phenomenon are called greenhouse gases.

The given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.

Notice that the given conjecture does not necessarily be always true.

To be precise; there are no reasons as to why A, B and C must be noncollinear.

1.  we are given If AB, BC, and AC are congruent, then A, B, and C and colllinear.

A,B ,C are not collinear so it will be false

Therefore, the given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.

A Counter- example of the given statement is that  A, B, C are three points that lie on the same line and so they are collinear.

2. We are given If <1 is complementary to <2, and <1 is complementary to <3, then <2 ≅ <3.

It may be true.

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Answer:

Step-by-step explanation:

The questions tests on indices. Write 125 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 125 = 5×5×5

125 = 5^3

(125^3)^(1/3) = 5^(3×1/3) = 5

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The 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.

The formula of the potential energy of each driver:

Replace the value of PE for driver 1 with the driver 2 formula.

Now, solve for (h) height:

Therefore, the 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.

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They travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.

This is solved by unitary method.

Distance travelled by (4 and 2/3) or 14/3 gallons of gas = 143 miles.

So, we get that for 1 gallon of gas it will be given as:

Distance travelled by 1 gallon of gas = 143 miles × 3/14

= 30.64 miles

So, they travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.

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If you are filling traffic cones with sand to keep them from blowing over and the cone has a radius of 7 inches and a height of 28 inches, then 1436 cubic inches of sand can fit inside the cone.

The volume of the cone can be described as the measure of a 3-D space occupied by matter.

The volume of sand in cubic inches that can fit inside the traffic cone can be calculated by the formula,

v = πr²h / 3

As the radius of the cone = 7 inches

Height of the cone = 28 inches

v = π(7)²28 / 3

v = (π)(49)(28) / 3

v = (π)(1372) / 3

As π = 3.14

v = (3.14)(1372) / 3

v = 4308.08 / 3

v = 1436.02 ≈ 1436 cubic inches

Hence, 1436 cubic inches of sand is calculated to fit inside the cone.

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The value of the expression when a = 6 and b = -4 is -1

The expression is given as

2a/3b

The values are given as

a = 6 and b = -4

Substitute a = 6 and b = -4 in the expression 2a/3b

2a/3b = 2 * 6/3 * --4

Evaluate the products

2a/3b = 12/-12

Evaluate the quotient

2a/3b = -1

Hence, the value of the expression when a = 6 and b = -4 is -1

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Complete question

What is the value of the expression when a = 6 and b = -4? 2a/3b

The error Jacy made was that the hypothesis or if part and the conclusion part was not appropriate . The correct conditional statement is  "If water is below 0°C then water freezes."

Conditional statement is a statement which contain both hypothesis and conclusion . Thus there are two parts in conditional statement, first is the hypothesis part or the if part then the second part is the conclusion part or then part.

According to the question the conditional statement is

  " Water freezes if it is below 0°C."

Which is not correct as the error is that the first part should be hypothesis part or if part and the second part should be the conclusion of the hypothesis.

Hence the correct conditional statement is :

      "If water is below 0°C then water freezes."

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The logarithmic form is 2log₁₀6

Logarithm is a mathematical tool used to make high value calculations simple.

It is the exponent to the power of which a number must be raised to give a certain result.

Some of the important formulas in logarithm are:

loga where a is considered as base of the logarithm and b is the argument

is given as nlogab

when base and the argument is same , log is given as 1

logabc where a is the base is given as logab+logc

loga b/c where a is the base is given as logab-logac

Now it is given to us to find the logarithmic form of 36=6^2

Let us consider the base of the logarithm to be 10

thus log₁₀36=log₁₀[tex]6^{2}[/tex]

log₁₀36=2 log 6

Hence the expression becomes 2log6

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The area of a parallelogram when the dimensions are a base of 440 miles and a height of 120 miles is 52800 miles²

It should be noted that the area of a parallelogram is calculated by multiplying the base by the height.

The dimensions are a base of 440 miles and a height of 120 miles.

The area of the parallelogram will be:

= Base × Height

= 440 × 120

= 52800 miles²

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The integers that will make the inequality false are integers greater than 3

The inequality expression is given as

5x + 6 ≤ 2x + 15

Collect the like terms.

So, we have

5x - 2x  ≤ -6 + 15

Evaluate the like terms.

So, we have

3x ≤ 9

Divide both sides of the expression by 3

So, we have

x ≤ 3

Hence, the integers that will make the inequality false are integers greater than 3

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The height in feet that the water from the hose hits the wall is; 7x + 12 ft

Let the height where the spray from a fire extinguisher hits the wall be denoted as x.

Now, we are told that Water from their firetruck hose hits the wall 12 feet

higher than 7 times where the spray from a fire extinguisher hits the wall.

Thus, the algebraic equation that expresses this statement is;

7x + 12

Thus, the height in feet that the water from the hose hits the wall is; 7x + 12 ft

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Answer:

A) Vertical angles are congruent

B) 40 and b are vertical angles and c and a are vertical angles.

C) <a = 40

<b = 140

<c = 140

Step-by-step explanation:

A straight angle is a straight line.  It is 180°

Answer:

162 kg

Step-by-step explanation:

135 + .2(135) = is the elephant's weight now

135 + 27 = 162 kg

Answer:

20% of 135 is 27 so you just add that to the original weight and you would get 162kg!

Step-by-step explanation:

Hope it helps! =D

The simplified form of given number is 16

We are given the number 64 with exponent ²/₃

Now, as per the known fact, cube of 4 is equal to 64. As, 4 multiplied with 4 gives 16. Further multiplying 16 and 4 gives 64. So, rewriting the number using 4 as follows -

Number = [tex]4^{3(2/3) }[/tex]

Cancelling 3 from exponent as it is present in both numerator and denominator. Rewriting the number with remaining exponent to find the simplified form of the number-

Number =  4²  

Taking square of the number to find the simplified form of the number given in question

Number = 16

Hence, the simplified form of the number is 16

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Applying the definition of a midpoint, the value of x is calculated as: x = 10.

The midpoint of a segment, for example, point M, is a point that bisects a segment into two equal parts with the same measurement.

Thus, this means that:

PM = MQ

PM = 9x + 3

MQ = 11x - 17

Substitute

9x + 3 = 11x - 17

Combine like terms

9x + 3 - 11x = 11x - 17 - 11x

-2x + 3 = -17

-2x + 3 - 3 = -17 - 3

-2x = -20

-2x/-2 = -20/-2

x = 10

Thus, applying the definition of a midpoint, the value of x is calculated as: x = 10.

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The correct answer to the given question is 5 .

If a mathematical equation has real roots, then its solutions or roots are real numbers. If an equation has distinct roots, we contend that all of its solutions or roots are not equal. A quadratic equation has real and distinct roots if its discriminant is bigger than.

In the case where the discriminant is positive or zero, a quadratic equation has real roots (not negative). This indicates that, in terms of algebra, b² >= 4ac. This indicates visually that the quadratic's parabola-shaped graph crosses the x axis at least once.

We have been given to evaluate √25 .

√25 = √(5 × 5)

= √5²

= 5

Therefore, the value of the given question is 5.

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After solving the given inequality the answer is x∈(5/6, ∞).

So,

Given: 3(2) x¹>5

Then,

Therefore, after solving the given inequality the answer is x∈(5/6, ∞).

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Answer:14.12

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

pizza has rotational symmetry of 60 degrees. Thus, the order of symmetry will be 6.

Answer:

[tex]\textsf{a)} \quad g'(x)=2x-4[/tex]

[tex]\textsf{b)} \quad y=2x[/tex]

[tex]\textsf{c)} \quad x=5[/tex]

Step-by-step explanation:

Given function:

[tex]g(x) = x^2-4x+9[/tex]

Differentiate the given function with respect to x:

[tex]\begin{aligned}g(x) & = x^2-4x+9\\\implies g'(x) & = 2 \cdot x^{2-1}-1 \cdot 4x^{1-1}+0\\& = 2x^{1}-4x^{0}\\& = 2x-4(1)\\& = 2x-4 \end{aligned}[/tex]

The y-value of the function at x = 3:

[tex]\begin{aligned}\implies g(3) & = (3)^2-4(3)+9\\& = 9-12+9\\& = -3+9\\& = 6\end{aligned}[/tex]

Therefore: (3, 6).

To find the slope of the function at x = 3, substitute x = 3 into the differentiated function:

[tex]\begin{aligned}\implies g'(x) & = 2(3)-4\\& = 6-4\\& = 2\end{aligned}[/tex]

Therefore, the slope of the function at x = 3 is 2.

Substitute the found slope and point (3, 6) into the point-slope form of linear equation to find the equation of the tangent line of g(x) at x = 3:

[tex]\begin{aligned} y-y_1 & =m(x-x_1)\\\implies y-6 & = 2(x-3)\\y-6 & = 2-6\\y & = 2x-6+6\\y&=2x\end{aligned}[/tex]

To find the value of x for which the slope of the graph is equal to 6, set the differentiated function to 6 and solve for x:

[tex]\begin{aligned}g'(x) & = 6\\\implies 2x-4 & = 6\\2x & = 6+4\\2x & = 10\\x & = \dfrac{10}{2}\\x & = 5\end{aligned}[/tex]

The best estimate for the total Aisha spent organizing is; 1/2 hour

We are told that Aisha organized her books for 1/6 and her coin collection for 3/7.

Now, normally when we want to find the total, we just add both fractions in this manner;

1/6 + 3/7 = 25/42

Now, since we want to find the best estimate, we will just approximate each fraction individually to get;

1/6 hour is closer to 0 hours than 1/2 hour. Thus;

1/6 hr ≈ 0 hour

3/7 hour is closer to 1/2 hour than 0 hours. Thus;

3/7 hr ≈ 1/2 hour

Thus;

Best estimate for total spent = 0 + 1/2 = 1/2 hour

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The value of  f(x) . g(x) is [tex]2x^2+28x[/tex] by using multiplication of functions.

By considering the given functions

f(x)=4 x

g(x)=1/2 x+7

f(x) . g(x)

=4 x (1/2 x+7 )

[tex]=2x^2+28x[/tex]

A y-intercept, a horizontal asymptote, a domain (the range of x values at which the function exists), and a constant growth factor, b, are the four main characteristics of exponential functions.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.

Four broad categories can be used to classify different types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

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It is untrue to claim that words like grid, linear, quadrant, zone, and spiral are frequently used to refer to datum points.

A location that acts as a base or reference for the measurement of other quantities is known as a datum point. It can be located at any reference point where known or guessed coordinates can be used to make calculations or measurements.

Datum references, which the maker can choose, are used when marking out an object as a reference point from which all measurements are obtained. Accuracy can be increased and maintained by measuring from a limited selection of fixed points.

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