5. Find the lowest number which is exactly divisible by 14 and 16.

The answer of -1/5 - (1/2 + -1/4) divided by 1/3 is [tex]-\frac{27}{20}[/tex]

We have given an expression [tex]-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))[/tex] .

On simplifying , we get

  [tex]-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=-\frac{1}{5}-(\frac{1}{2} -\frac{1}{4} )\\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))= - \frac{1}{5}-(\frac{2-1}{4} )\\\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))= - \frac{1}{5}-\frac{1}{4} \\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=\frac{-4-5}{20} \\\\-\frac{1}{5}-(\frac{1}{2} +(-\frac{1}{4} ))=\frac{-9}{20}[/tex]

Now , we are asked to divide -9 /20 by 1 /3 .

On dividing, we get

           [tex]\frac{\frac{-9}{20} }{\frac{1}{3} } =\frac{-9}{20} \times\frac{3}{1} \\\\=\frac{-27}{20}[/tex]

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Answer:

-55

Step-by-step explanation:

The pattern here is subtracting by 2 higher than the previous term.

As you can see

1 -2 = -1

-1 - 4= -5

-5 - 6 = -11

etc.

Continuing until the eighth term gets you   - 41 - 14 = -55

he started with 90 dollars and spent $3.50 each day

The value of given expression for x=0 is 0, x=-2 is -1.25 and x=2 is -1.25.

Given the expression is -5x⁻².

Firstly, we will simplify the given expression -5x⁻² for x=0.

Substitute the value x=0 in given expression, we get

-5x⁻²=-5(0)⁻²

-5x⁻²=-5(0)

As we know that something multiply with 0 is zero.

So, we get

-5x⁻²=0

Now, we will simplify the given expression -5x⁻² for x=2.

Substitute the value x=2 in given expression, we get

-5x⁻²=-5(2)⁻²

Now, we will square the expression to simplify it, we get

-5x⁻²=-5(4)⁻¹

Further, we will divide it above expression by 1 to remove negative sign, we get

-5x⁻²=-5/4

-5x⁻²=-1.25

Furthermore, we will simplify the given expression for x=-2.

Substitute the value x=-2 in given expression, we get

-5x⁻²=-5(-2)⁻²

Now, we will square the given expression, we get

-5x⁻²=-5(4)⁻¹

Further, we will divide it above expression by 1 to remove negative sign, we get

-5x⁻²=-5/4

-5x⁻²=-1.25

Hence, the value of expression -5x⁻²  for x=0, 2 and -2 is 0, -1.25 and -1.25.

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When the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2 ,the value of HJ is 27.

Fronxrye information, the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2.

Therefore, the value of HJ will be:

= (1 + 2)/(1 + 2 + 3) × 45

= 3/5 × 45

= 27

Therefore, the value of HJ is 27.

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Answer:

14x+18

Step-by-step explanation:

2(5x+7) + 2(2x+2)

10x+14+4x+4

14x+18

Answer:solve for x

x>3

Step-by-step explanation: 12x<9(2x−3)+9

Use the distributive property to multiply 9 by 2x−3.

12x<18x−27+9

Add −27 and 9 to get −18.

12x<18x−18

Subtract 18x from both sides.

12x−18x<−18

Combine 12x and −18x to get −6x.

−6x<−18

Divide both sides by −6. Since −6 is negative, the inequality direction is changed.

x>

−6

−18

​

Divide −18 by −6 to get 3.

x>3

For each annual rate of change , the corresponding growth or decay factor is - 0.75 .

Given : annual rate of change = - 75 % .

To find : corresponding growth or decay factor .

For an exponential growth function ,

y = a ( [tex]1 + r^{t}[/tex] ) ,

( 1 + r ) is the growth factor and

for an exponential decay function y = a ( [tex]1 - r ^{t}[/tex] ) ,

( 1 - r ) is the decay factor .

According to question ,

( - 75 ) / 100 = - 0 .75

Hence , for each annual rate of change , the corresponding growth or decay factor is - 0.75 .

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By solving the improper fractions, there are 18 water stations in all.

This problem can be solved by two methods:

Method 1 :

First of all, calculate 13²/₃ miles in fraction. The value is 13.5 miles. Then calculate 3/4 mile in fraction. The value is .75 miles.

Now divide 13.5 miles by 0.75 miles.

13.5 ÷ 0.75 = 18

So, 18 water stations are there in all.

Method 2 :

Convert 13 ¹/₂ miles into an improper fraction from 27/2 miles.

Now, again divide 27/2 miles by 3/4.

27/2 ÷ 3/4 = ²⁷/₂ ₓ ⁴/₃ = 18

So, 18 water stations are there in all.

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Answer:

40 cm^2

Step-by-step explanation:

Area of rectangle = length * width.
Area of square = length^2

To find the area of the given shape, we must subtract the area of the square from the area of the rectangle.

Area of the given rectangle = 8 * 7 = 56 cm^2
Area of the given square = 4^2 = 16 cm^2

56 - 16 = 40 cm^2

When y= 105 then x= 15.

A proportion is an equation in which two ratios are set equal to each other.

given:

At x=3, y=21

at y= 105 , x=?

So, creating proportionality

105/x= 21/3

105/x = 7

x= 105/7

x=15

Hence, when y= 105 then x= 15.

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The question attached here is incomplete.

The complete question is

The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?

Answer:

7.25, 0​, -9.8

Step-by-step explanation:

Reflexive Property of congruence justifies the statement

∠K ≅ ∠K

The Reflexive Property of congruence states that any geometric figure is congruent to itself. The figures are being the reflection of itself. They have the line segments of same length, an angle has the same angle measure and the figure has same shape and size as itself.

If two triangles have a common side or a common angle, then Reflexive Property of congruence is used to prove that the two triangles are congruent.

Since the given angle is K, therefore by the Reflexive Property of congruence  we could say that the angle K is congruence to angle K.

⇒ ∠K ≅ ∠K

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The values for

[tex]f(g(x)) = 6x^3 +2 \\g(f(x)) = 6x^2 + 4[/tex]

[tex]Given : f(x)=3 x²+2, g(x)=2 x[/tex]

1.

[tex](f.g)(x) = f(g(x)) \\g(x) = 2x \\f(x) = 3 x^2+2 \\f(2x) = 6x^3 +2[/tex]

2.

[tex](g.f)x = g(f(x)) \\fx = 3x^2 + 2 \\g(3x^2 + 2) = 2 (3x^2 + 2) = 6x^2 + 4[/tex]

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The inverse of the function y= 10 - 2x² is y =√ (10 - x) / 2. .

Inverse Variation:

A connection between two variables is said to have inverse variation when one of the variables rises while the other falls.

When two variables, let's say X and Y, are coupled in such a way that raising X results in a drop in Y and vice versa, this is known as indirect or inverse variation.

All we have to do to find the inverse of a function is switch the variables x and y.

x = 10 - 2y²

Now, solve for y as follows:

2y² = 10 - x

y² = (10 - x)/2

y = √ (10 - x) / 2

Therefore,  the inverse of the function y=10 - 2x² is y = √ (10 - x) / 2.

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The year in which we predict the population to reach 1,000,000 based on annual growth rate of 5% is 2009

How many years would population will be 1,000,000?

The year that the population of the city would reach 1,000,000 can be determined by first of all computing the number of years beginning from 1990 that it would take the population size of 400,000 to reach 1,000,000

FV=PV*(1+G)^n

FV=future population size=1,000,000

PV=present population size=400,000

g=population growth rate per year=5%

N=number of years it takes population to become 1,000,000=unknown

1,000,000=400,000*(1+5%)^N

1,000,000/400,000=(1+5%)^N

2.50=(1.05)^N

take log of both sides

ln(2.50)=N*ln(1.05)

N=ln(2.50)/ln(1.05)

N=19(rounded to the nearest whole number)

number of years before population reach 1m=1990+19

number of years before population reach 1m=2009

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The range of the quadratic function is {y |0 ≤ y < 9}

The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.

From the question, we have the following parameters:

Write out the vertex

So, we have

Vertex = (0, 0)

Remove the x value

y = 0

From the question, we have

The parabola opens upward

This means that the vertex is a minimum

So, the range is

y ≥ 0

Rewrite as

0 ≤ y

Recall that:

Closed circle point = (-2, 4)

Open circle point = (3, 9)

Remove the x values

Closed circle point = 4

Open circle point = 9

Remove the smaller y value

Open circle point = 9

This means that the highest value of y is at open circle point = 9

This is represented as

y < 9

So, we have

0 ≤ y and y < 9

Combine both

0 ≤ y < 9

Rewrite properly as

{y |0 ≤ y < 9}

Hence, the range of the quadratic function is {y |0 ≤ y < 9}

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{y |0 ≤ y < 9}

The person above need the shine, im just making it simple

Answer:

Measures of each angle are as follows:

4.     ∠BXC = 20°

5.     ∠FXE = 85°

6.     ∠GXD = 75°

7.     ∠BXF = 75°

Step-by-step explanation:

#4
 ∠BXC is opposite ∠EXD and so it is the same as ∠EXD = 20°

#5
∠FXE is opposite ∠CXG and so it is the same as ∠CXG = 85°

#6
Angles  ∠CXG, ∠GXD and ∠EXD line on a straight line so the sum of these angles must be 180°
∴ m∠CXG + m∠GXD + m∠EXD = 180°

Substituting known values for ∠CXG and ∠EXD we get
85 + ∠GXD + 20 = 180°
105 + m∠GXD = 180°
m∠GXD = 180-105 = 75°

#7
∠BXF is opposite ∠GXD which we computed in #6 to be 75°
So m∠BXF = m∠GXD = 75°

The diagonal of the given brick using the Pythagorean Theorem is 5√2.

So, let the diagonal be 'x'.

Pythagorean formula: x² = b² + h²

Now,

Therefore, the diagonal of the given brick using the Pythagorean Theorem is 5√2.

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Given the radius and height, the volume of the cone to the nearest hundredth is 25.12 in³.

Option b)25.12 in³ is the correct answer.

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The volume of a cone is expressed as;

V = (1/3)πr²h

Given the data in the question;

Plug the given values into the volume formula above and simplify.

V = (1/3)πr²h

V = (1/3) × 3.14 × (2in)² × 6in

V = (1/3) × 3.14 × 2in² × 6in

V = (1/3) × 3.14 × 4in² × 6in

V = 25.12 in³

Given the radius and height, the volume of the cone to the nearest hundredth is 25.12 in³.

Option b)25.12 in³ is the correct answer.

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Based on the data points given, the type of function shown is a Quadratic function.

A quadratic function is one where the values of x and y form data points that lead to a parabola being formed.

This parabola forms when the values of the data points start away from 0 and then reach zero and rise again. This is what happens with these points so the function must be a quadratic function.

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Answer:

4

Step-by-step explanation:

9 - 5 = 4

The x coordinate of the solution to the system is 4

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

x + 2y = 6

5x - 4y = 16

Next, we plot the graph of x + 2y = 6  and 5x - 4y = 16 (see attachment)

From the attached graph, the point of intersection is

(x, y) = (4, 1)

Remove the y coordinate

x = 4

Hence. the x coordinate of the solution to the system is 4

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[tex]\bf \implies{The \: correct \: option \: is \: (c) \: 240}[/tex]

[tex] \large \frac{40}{5} . \: 6 \: . \: \frac{10}{2} [/tex]

Step 1) : Cross out the common factor

[tex] \bf \longrightarrow\frac{ \cancel{40}}{ \cancel{5}} . \: 6 \: . \: \frac{ \cancel{10}}{ \cancel{2} } \\ \\ \bf \longrightarrow8 \times 6 \times 5[/tex]

Step 2 : Multiply it

[tex] \bf \longrightarrow8 \times 6 \times 5 \\ \bf \longrightarrow8 \times 5 \times 6 \\\bf \longrightarrow 40 \times 6 \\ \bf \longrightarrow240[/tex]

Answer:

the 1st value represents x, the independent value

the 2nd value represents y, the dependent value

I think that is what it is asking

It is a vague question

Answer:

Step-by-step explanation:

You want to know the meaning of the first and second values in the ordered pairs that represent the relation shown in the diagram.

The ordered pairs representing a relation are understood to be ...

  (first value, second value) = (input value, output value)

  = (value at arrow tail, value at arrow head)

The diagram labels the ends of the arrows as "Grade" and "Hours Studied." That tells you the values mean ...

 first value: Grade

  second value: Hours Studied

The approximate population 3 years after the population started being recorded is 2584.

What is an exponential function:

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Given that,

The population of a community is modeled by this exponential function, where x represents the number of years since the population started being recorded:

p(x) = 2,400(1.025)×

Plug x = 3 years in the above function.

P(3) = 2400(1.025)³

P(3) = 2400x1.0768

P(3) = 2584.53 ≈ 2584 people

Therefore,

The approximate population 3 years after the population started being recorded is 2584 people.

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We need to know about logarithm to solve this problem. The logarithm expanded is [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]

Logarithm is the power to which a base should be raised to get a given number. Expanding logarithm is writing logarithms usisng addition, subtraction, simplifying the logarithm. In logarithm, log ab can be written as log a+ log b and log a/b can be written as log a -log b, [tex]log_{a} b[/tex] can be written as log b/log a. We will be using these rules to expand the given logarithm. In the given logarithm we have the base of the log as 3 and we have logarithm of fraction, which we can expand.

[tex]log_{3} \frac{250}{37} =log_{3} 250 - log_{3} 37=\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]

So we found the expansion of the given algorithm using the rules for expansion of algorithm to be [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex].

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Answer:

-a^2*(a^2+21a+22)

best I can do