question 5 (10 points)

Answer:

p= -16.1

Step-by-step explanation:

-4.8=0.5(p+6.5)

first you want to multiply 0.5 by p and 6.5.

-4.8=0.5(p)+0.5(6.5)

then solve it:

-4.8=0.5p+3.25

next you want to isolate p so you'd subtract 3.25 on both sides so:

(-4.8-3.25)=0.5p+(3.25-3.25)

solve:

-8.05=0.5p

lastly, divide 0.5 on both sides:

-16.1=p or p= -16.1

hope this helps :)

The value of x is 1.5

The parallel lines are the coplanar straight lines  that are at equal distance from each other and never meet.

When two parallel lines are cut by a transversal, the formed alternate exterior angles will be congruent

Here two parallel lines L1 and L2 cut by a transversal L3, the marked angles in the given picture is called alternate exterior angles. The alternate angles are congruent.

Therefore

x+1 = 3x-2

Move 3x to left hand side and 1 to right hand side of the equation

x-3x = -2-1

-2x = -3

x = -3/-2

x = 1.5

Hence, the value of x is 1.5

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The slope or gradient of the line is 0.15 .

The slope or gradient of a line in mathematics is a numerical expression of the steepness and direction of the line.

We know that slope can be calculated by the change in the height by the change in the length.

1 mile = 5280 feet

therefore 4.9 miles = 25872

Therefore slope = 4000/25872 = 0.1546...≈ 0.15

Hence the slope or gradient of the line is 0.15 .

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Answer:

545

Step-by-step explanation:

Answer:

Your answer is [tex]4\sqrt{2x} \sqrt{x} +6\sqrt{2x}[/tex]

Step-by-step explanation:

(attached)

To remove a common factor and transform a polynomial into the union of two polynomials:According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC.

what is common factor and distributive property?

To remove a common factor and transform a polynomial into the union of two polynomials: Discover the most prevalent factor that is a whole number (no variables). Put the product of dividing all polynomial terms by that factor in parenthesis. The factor should be written without parentheses.

According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC. This distributive law, which is represented as A (B - C) = AB - AC, also applies to subtraction. This indicates that the distribution of operand A among the other two operands.

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Given that

Hence,

Similarly,

Therefore,

The length of the given building is equal to 186ft

To calculate the length of the building whose shadow is 248ft, we can simply find the ratio of the height of Tim to his shadow and compare it with the building.

The ratio of the height to the shadow is 6:8

Or we can simply set it out as an equation, cross multiply and solve.

[tex]height = shadow length[/tex]

Let's use this system to solve

[tex]height = shadow length\\6ft = 8ft\\x = 248\\[/tex]

We can cross multiply here and solve for x

[tex]x = \frac{6 * 248}{8}\\x = 186ft[/tex]

The height of the building is 186ft

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The center  ( x - 6)² + (y + 4)² = 1 of circle does not lies in second quadrant.

it lies in fourth quadrant.

A circle equation with centers (h, k) and radius r is ,

                       ( x - h)² + (y - k)² = r²

Regarding the given question,

The circle equations have been given to us.

Each circle's center is located.

We know that any point in the second quadrant has coordinates of the form (-x, y)

The x-coordinate must be a negative number, and the Y-coordinate must be a positive number.

( x - 6)² + (y + 4)² = 1

( x - 6)² + (y + 4)² = 1²

By comparing the above circle equation with ( x - h)² + (y - k)² = r²,  

we get the center = (6, -4) and the radius = 1.

The circle's center is located in the fourth quadrant. The x-axis in this quadrant is positive, while the y-axis is negative.

So here  ( x - 6)² + (y + 4)² = 1 does not lies in second quadrant .

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The factored expression of the expression given as -6x² + 18x is -6x(x - 3)

The expression is given as

-6x² + 18x

Group the expression in 2's

So, we have

-6x² + 18x= (-6x² + 18x)

Factor each group

So, we have

-6x² + 18x= x(-6x + 18)

Rewrite as

-6x² + 18x= -6x(x - 3)

Hence, the factored expression is -6x² + 18x= -6x(x - 3)

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Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to create an equation for x, and to solve it.}[/tex]

[tex]\textsf{There's an infinite amount of equations that we can create, but let's keep it simple.}[/tex]

[tex]\large\underline{\textsf{Example:}}[/tex]

[tex]\mathtt{9x+5x= 70}[/tex]

[tex]\textsf{Let's begin solving for x since we've just created an equation.}[/tex]

[tex]\large\underline{\textsf{Solving:}}[/tex]

[tex]\textsf{This equation involves combining like terms.}[/tex]

[tex]\Large\underline{\textsf{What are Like Terms?}}[/tex]

[tex]\textsf{Like terms are 2 or more terms that have similar \underline{whole numbers, variables, and/or exponents}.}[/tex]

[tex]\textsf{For this specific equation, 9x and 5x are like terms.}[/tex]

[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]

[tex]\mathtt{9x+5x= 70}[/tex]

[tex]\mathtt{14x= 70}[/tex]

[tex]\large\underline{\textsf{Divide by 5 to find x:}}[/tex]

[tex]\mathtt{\frac{14x}{14}=\frac{70}{14} }[/tex]

[tex]\large\boxed{\mathtt{x=5}}[/tex]

Answer:

3rd option

Step-by-step explanation:

(5y - 16) and (3y + 20) are a linear pair and sum to 180° , that is

5y - 16 + 3y + 20 = 180

8y + 4 = 180 ( subtract 4 from both sides )

8y = 176 ( divide both sides by 8 )

y = 22

then

5y - 16 = 5(22) - 16 = 110 - 16 = 94°

3y + 20 = 3(22) + 20 = 66 + 20 = 86°

Answer:

The price per unit of chocolate bars is £0.3.

Step-by-step explanation:

The cost of 4 chocolates bars is  £1.20.

The cost of 1 chocolate bars is [tex]\frac{1.20}{4}[/tex]

The cost of 1 chocolate bars is £0.3.

Answer: $4.80 (us dollars)

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

The domain and the range are 0 ≤ t ≤ 6 and 2 ≤ d(t) ≤ 5, respectively

The domain of the function is the set of input values the function can take

The function is given as

d(t) = 1/2t + 2

Where t represents the number of days

And d represents the inches of rainfall

From the question, we have

Total number of days = 6

This means that the domain is 0 to 6.

This is represented as 0 ≤ t ≤ 6

For the range, we have

Set t = 0 in d(t) = 1/2t + 2

d(0) = 1/2(0) + 2 = 2

Set t = 6 in d(t) = 1/2t + 2

d(6) = 1/2(6) + 2 = 5

This means that the range is 2 to 5.

This is represented as 2 ≤ d(t) ≤ 5

Hence, the domain is 0 ≤ t ≤ 6 and the range is 2 ≤ d(t) ≤ 5

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Answer:

b < -21

Step-by-step explanation:

1/3b + 1 < -6

1/3b < -7

b < -21

The linear model is represented as

A. An increasing lines goes up from left to right. This is shown from 0 to 2

B. A horizontal line would show the height remaining the same. This is shown from 2 to 3

C. The steeper the line the faster the decrease. This is shown from 3 to 4

D. The height of the balloon at 10 seconds would be O as it hits the zero mark at 6 seconds and the arrow continues along the O line.

What is Linear Model ?

A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.

Part A  the balloons height is increasing when the line is going up

It is increasing between 0 and 2

0 ≤ t ≤ 2

Part B  the balloons height remains the same when the line is flat

It is constant between 2 and 3

2 ≤ t ≤ 3

Part C the balloons height is decreasing when the line is going down

It is decreasing the fastest when the line is going down the quickly and that is between 3 and 4. The slope is (80-20)/(4-3)= 60/160. The larger the slope, the faster the height decreases.

3 ≤ t ≤ 4

Part D  At 10 second the balloon will be on the ground. At 6 second the height is zero and remains at 0.

The linear model is represented as

A. An increasing lines goes up from left to right. This is shown from 0 to 2

B. A horizontal line would show the height remaining the same. This is shown from 2 to 3

C. The steeper the line the faster the decrease. This is shown from 3 to 4

D. The height of the balloon at 10 seconds would be O as it hits the zero mark at 6 seconds and the arrow continues along the O line.

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Answer:

-80

Step-by-step explanation:

PEMDAS is Parentheses, exponent, multiplication, division, addition, subtraction.

the '-' is not a subtract sign, it is saying it is negative. Therefore, 4 * -20 = -80

Answer:the answer is -80

Step-by-step explanation:

The value of x is 3. The order in which you perform operations in arithmetic and algebra is governed by a number of laws.

Given,

[tex]$9^{-1 / 2}=27^{1 / 4} \div 3^{x+1}$[/tex]

[tex]${\left[3^2\right]^{-1 / 2}=\left[(3)^4\right]^{1 / 4} \div 3^{x+1} }$[/tex]

[tex]$3^{-1}=3 \div 3^{x+1}$[/tex]

[tex]$3^{-1}=\frac{3}{3^{x+1}}$[/tex]

[tex]$3^{-1}=3^{1-x+1}$[/tex]

[tex]$3^{-1}=3^{2-x}$[/tex]

On comparing we get,

-1=2-x

x= 3

Hence, the value of x is 3.

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It is to be noted that the graph comprises two inherent traits:
The domain and the range. Each of these qualities helps the user interpret and analyze data.

The domain of a graph consists of all the input values represented on the x-axis since the domain refers to the set of potential input values. The range represents the set of potential output values, which are shown on the y-axis.

In mathematics, domain and range are significant because they allow us to determine the set of all possible values for a function. Understanding a function's domain and range allows us to identify its inverse, graph it, and solve issues involving the function.

To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).

It is to be noted that the question contains very limited information hence the general answer.

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Probability that in a random sample of 400 headache sufferers, less than 58. 1% obtain relief has a Z score -1.79

P = 62.4%

The sample proportion p = 58.1% of 400 = 232.4

This implies that 232  person of 400 headache sufferes obtain relief with just two asprins

n = 400

np = 400 x 62.4% = 249.6

n(1 - p) = 400 x (1 - 62.4%) = 150.4

The sample proportion p is assumed to follow a normal distribution.

The mean of the sample proportion μ' = p = 0.624

The standard error of the sample proportion

σ'  [tex]\sqrt{\frac{p(1 - p)}{n} }\\ \sqrt{\frac{0.624(1 - 0.624)}{400} }\\\\= 0.0240\\[/tex]

Standardize 0.581 to a Z score

P(p'< 0.581) = P(Z>(0.581-0.624)/0.024) = -1.791

Probability that in a random sample of 400 headache sufferers, less than 58. 1% obtain relief has a Z score -1.79

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The value of p for given inequality would be:

p is greater than or equal to negative twenty one halves

In this question, we have been given a statement for an inequality.

two thirds times p plus 10 is greater than or equal to 3

i.e., (2/3)p + 10 ≥ 3

We need to find the value of p

(2/3)p + 10 ≥ 3

(2/3)p + 10 -10 ≥ 3 - 10

(2/3)p ≥ -7

(2/3)p * (3/2) ≥ -7 (3/2)

p ≥ -21/2

This means, p is greater than or equal to negative twenty one halves

Therefore, the value of p for given inequality would be:

p is greater than or equal to negative twenty one halves

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The new length is 35+10=45 and the new width is 18+10=28.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

Given that enclosure at the zoo is 35 feet long by 18 feet wide. It means length is 35 feet and width is 18 feet.

Area of rectangle is length times of breadth.

Area of Rectangle=Length × Width

=35×18

=630

The zoo wants to double the area of the enclosure by adding the same distance x to the length and width.

(35+x)×(18+x)=1260

630+35x+18x+x²=1260

x²+53x+630-1260=0

x²+53x-630

Now use the quadratic formula we get

x = 10.

The new length is 35+10 = 45

The new width is 18+10 = 28.

Hence the new length is 35+10 = 45 and the new width is 18+10=28.

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Part a: Inverse of the function- g⁻¹(x) =  3 - 7x.

Part b: Composite function, (g⁻¹o g)(3) = -18.

Part c: The value of h⁻¹(9) = 0.

Part a: Inverse of the function- g⁻¹(x).

For the given question.

The one-to-one function is given as;

g(x) = (-x + 3)/7

As, it is one-to-one function, its inverse is possible.

Let y = g(x) = (-x + 3)/7

Write function in terms of y.

7y = -x + 3

x = 3 - 7y

Now, replace y with x in the function.

g⁻¹(x) = 3 - 7x

Part b: Composite function, (g⁻¹o g)(3)

First find the composite value of g(3).

g(x) = (-x + 3)/7

Put x = 3

g(3) = (-3 + 3)/7 = 0

Now, put the value of g(3) in g⁻¹(x).

(g⁻¹o g)(3) =  3 - 7x

(g⁻¹o g)(3) =  3 - 7×3

(g⁻¹o g)(3) = -18

Part c: The value of h⁻¹(9).

Check the domain and ranges given for the 'h' function.

h⁻¹(9) has the domain of 0

Thus, h⁻¹(9) = 0.

Thus, the values for the one-to-one function are found.

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To determine the distance rolled by the tire in 24 revolutions, use the following formula:

where r is the radius (14 in) and θ the degrees of the revolutions. Consider each revoutions represents 180 degrees or 2π radians, the, 24 revolutions are 24x2π = 48π.

Replace the values of r and θ into the formula for s:

Hence, the tire rolls 2,110 in

Answer:

B

Step-by-step explanation:

Circumference = pi * d  =   28 pi   inches

  twenty four of these is   24 *  28 pi inches = 2111.15 in = 175.9 ft

The division for 514 / 28 is 18 remainder 10.

Long Division is a method for dividing large numbers, that breaks the division problem into multiple steps

Step 1: Here, the digits to first use is 51. This means 51 divided by 28 will give 1.

Step 2: Subtract 28 from 51 and this is 23. Bring the third digit of the dividend down and place it beside 23. This will be 234.

Step 3: Now, 234 divided by 28 will be 18.

Step 4: Multiply 18 by 28 and subtract the value. The remainder will be 10.

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The approximate weight of all the ants in the worlds in scientific notation is  3×10¹⁰ kg .

Values that are either too large or too little to be conveniently stated in decimal form can be indicated using scientific notation (typically would result in a long string of digits).

Weight of 1 ant = 3×10⁻⁶ kg

number of ants =  1×10¹⁶

Total weight = 3×10⁻⁶ × 1×10¹⁶ =  3×10¹⁰ kg

Therefore the weight of all the ants in the world is approximately

3×10¹⁰ kg

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Answer:

x = 2, x = 5, c = 3, c = 7, t = 4, t = -4

Step-by-step explanation:

x^2 - 7x + 10 = (x-2)(x-5) = 0

c^2 - 10c + 21 = (c-3)(c-7) = 0

t^2 - 16 = (t-4)(t+4) = 0

Given:

Required:

We need to solve for L.

Explanation:

Consider the given equation.

Subtract 2W from both sides.

Divide both sides by 2.

Final answer: