A politician's support increases from 34% to 50% Determine the actual and relative change in this sitation.

Answer: The area of the base of the triangular pyramid is given as 15.6 in² and each side of the base is 6 in, so we can use the formula for the area of an equilateral triangle to find the height of the base:

A = (s^2 * sqrt(3)) / 4

where s is the side length of the triangle. Plugging in the values, we get:

15.6 = (6^2 * sqrt(3)) / 4

Solving for the height of the base, h:

h = (4 * 15.6) / (6^2 * sqrt(3)) = 4 / sqrt(3)

Next, we can use the Pythagorean theorem to find the height of the pyramid, since the slant height is given:

h^2 + (base/2)^2 = slant height^2

where base is the length of one side of the base of the pyramid. Plugging in the values, we get:

h^2 + (6/2)^2 = 8^2

Solving for h:

h = sqrt(64 - 9) = sqrt(55)

Finally, the surface area of the pyramid can be found using the formula:

SA = base area + (perimeter * slant height) / 2

where perimeter is the total length of the sides of the base. Plugging in the values, we get:

SA = 15.6 + (3 * 6 * 8) / 2 = 15.6 + 36 = 51.6 in²

So, the surface area of the triangular pyramid is 51.6 in².

Step-by-step explanation:

The equation of the line that is parallel to this line and passes through the point (-4,-6) is y = 7x + 22

The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is y = -(1/7)x - 46/7

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Two lines are parallel if they have the same slope and are perpendicular if the product of their slope is -1.

Given the line:

y = 7x - 3

The slope is 7. The line parallel to this line would also have a slope of 7, while the line perpendicular have a slope of -1/7

The equation of the line that is parallel to this line and passes through the point (-4,-6) is:

y - (-6) = 7(x - (-4))

y = 7x + 22

The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is:

y - (-6) = (-1/7)(x - (-4))

y = -(1/7)x - 46/7

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Step-by-step explanation:

The average speed is 42 km/hr.

To calculate the average speed, you divide the total distance by the time it took to travel that distance:

189 km / 4.5 hours = 42 km/hr

[tex]\texttt{speed}=\dfrac{d}{t}[/tex]

distance = 189 km

time = 4.5 hours

[tex]\texttt{speed}=\dfrac{189}{4.5}[/tex]

[tex]\fbox{speed = 42 km/hr}[/tex]

The equation of line having a slope of 2 and passing through the point (1,4) is y = 2x + 2.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line has a gradient of 2 and passes through the point (1, 4).

Plug the given values into the point-slope formula and solve for y.

y - y₁ = m( x - x₁ )

y - 4 = 2( x - 1 )

y - 4 = 2x - 2

Add 4 to both sides of the equation

y - 4 + 4 = 2x - 2 + 4

y = 2x - 2 + 4

y = 2x + 2

Therefore, the equation of the line is y = 2x + 2.

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Answer:

13 since the second power (-3) is doubled.

Answer:

4 4/10 is greater.

Step-by-step explanation:

4 = 40/10

then:

4 4/10 = 4 + 4/10 = 40/10 + 4/10 = (40+4)/10 = 44/10

Then:

44 > 32

44 is greater.

Answer:

5/2 or 2.5

Step-by-step explanation:

Divide both sides by 2.

The equations are 4x - y - 2 = 0 and x + 3y + 6 = 0. The solution has been obtained using two-point form.

What is two-point form?

One of the crucial forms for algebraically representing a straight line is the two-point form. Each and every point on a line fulfils the equation for that line, making it the representation of the entire line.

We are given two lines on the graph

Both the lines meet on the y-axis at (0,-2)

This means (0,-2) is the common solution.

Another point of the steeper line is (1,2)

Another point of the flatter line is (3,-3)

Now, as we know the two points of the line, using the two-point form, we get

[tex]\frac{y - y_{1}}{x-x_{1} } = \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]

⇒ (y+2)/(x-0) = (2+2)/(1-0)

⇒ y+2 = 4x

⇒ y = 4x-2

⇒ 4x - y - 2 = 0

Similarly,

⇒ (y+3)/(x-3) = (-2+3)/(0-3)

⇒ (y+3)/(x-3) = -1/3

⇒ (y+3) = -(x-3)/3

⇒ y+3 = -x/3 + 1

⇒ y = -x/3 - 2

⇒x + 3y + 6 = 0

Hence, the equations are 4x - y - 2 = 0 and x + 3y + 6 = 0.

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Since there are multiple questions so, the question answered above is attached below

Answer:

Well, it depends, but I'd reckon kilograms.

Step-by-step explanation:

2.2 pounds is approximately 0.998 kg, which can be rounded off to 1 kg. However, you really do have to be precise, you may measure it in grams (that's, 998 grams).

So, the most appropriate way is to use 1 kilogram, as a hailstone can be considered quite heavy and we may not be keen on looking for a really precise measurements, as they're measured in hundreds of grams!
Hope this helps :)

The total number of hours for Jim to drive 900 miles is given by the proportion A = 25 hours

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the number of hours for Jim to drive 900 miles be A

Now , the number of hours = 5 hours

The total distance traveled by Jim in 5 hours = 180 miles

Now , the distance traveled by Jim = 900 miles

And , the proportion will be

A / 900 = 5 / 180

Multiply both sides of the equation by 900 , we get

A = ( 5 x 900 ) / 180

On simplifying the equation , we get

A = 5 x 5

A = 25 hours

Hence , the number of hours is 25 hours

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The exponential grows at the same rate as the quadratic in the interval

0 ≤ x ≤ 1.

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

[tex](f(a) - f(b))/(b-a)[/tex].

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

 = (2-1)/1 = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

=(1 - 0)/1  = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

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Answer:

B

Step-by-step explanation:

Factor Trees are diagrams that show the prime factorization of a number by breaking it down into smaller factors until only prime numbers are left.

Here are the factor trees for the numbers you provided:

8:

8

/

2 4

/

2 2

20:

20

/

2 10

/

2 5

27:

27

/

3 9

/

3 3

36:

36

/

2 18

/

2 9

/

3 3

72:

72

/

2 36

/

2 18

/

2 9

/

3 3.

To solve this, I used the process of prime factorization. Prime factorization is the process of finding the prime numbers that multiply together to form a given number.

The steps I followed to solve this problem are:

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The only table that represents both a linear and proportional relationship is table 4

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.

In the first table, we see that the proportion of y to x are;

-4/-2 = 2

-3/0 = undefined

-2/2 = -1

Second table shows that;

0/-1 = 0

2/0 = undefined

4/1 = 4

Third table shows that;

-4/-1 = 4

-1/0 = undefined

2/1 = 2

Fourth table shows that;

-1/-3 = 1/3

0/0 = 0

1/3 = 1/3

Looking at the tables. the only one that is a proportional relationship is table 4

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Answer:

The only table that represents both a linear and proportional relationship is table 4

How to identify a proportional relationship?

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.

In the first table, we see that the proportion of y to x are;

-4/-2 = 2

-3/0 = undefined

-2/2 = -1

Second table shows that;

0/-1 = 0

2/0 = undefined

4/1 = 4

Third table shows that;

-4/-1 = 4

-1/0 = undefined

2/1 = 2

Fourth table shows that;

-1/-3 = 1/3

0/0 = 0

1/3 = 1/3

Looking at the tables. the only one that is a proportional relationship is table 4

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Step-by-step explanation:

Answer:

Mixed number: 1  3/8

Improper fraction: 11/8

Step-by-step explanation:

The first circle is 1 whole  1 = 8/8

The second circle is 3/8 *

8/8 + 3/8 = 11/8

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

If you want to write a mixed number as improper fraction just multiply the whole number by the denominator and add the numerator's fraction.

1  3/8 Mixed number

1x8=8

8+3=11

11/8 Improper fraction

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

* the second circle is not divided into 4 parts. It is divided into 8 equal parts. Each part is 1/8. There are three shaded parts which means 3/8.

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

I hope this helps!

Answer:

1

Step-by-step explanation:

Y intercept is 1

Y intercept is the point where the line crosses the y axis (point where x=0, you see the line crosses y axis at 1). Thus even if you put 0 in equation 9^x you will get 9^0 and anything power of 0 is 1.

From the graph, the coordinates of the points of the equation y=(x-1)(x-3): (1,0) (4,0), P(0,3) and turning point (2.5,2)

You should know that these are possible reading from the graph

The scale of the graph is [laced at 1 com to 1 unit on both axes

From the graph, the coordinates of A are (1, 0) This is where x=1 and y=0

The coordinates of B = (4, 0) This is where x=4 and y=0

b)  The coordinates of point P are (0,3) This is where x=0 and y= 3

c) The coordinates of the turning point are (2.5, 2) This is the minimum value of the curve

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Answer:

Below

Step-by-step explanation:

Solve the given equation for y

3x+9y = 18

9y = -3x + 18       divide by 9

y = - 1/3 x + 2     done

The change will be approximately $100 million by solving through simple algebra.

The use of percentages is widespread and diverse. For instance, percentages are used to convey discounts in stores, bank interest rates, inflation rates, and various statistics in the media. For comprehending the financial aspects of daily life, percentages are crucial.

Divide the whole number by 100, then multiply the result by the requested percentage to find a percentage of the given number: For instance, 12% of 250 equals (250 100) x 12 = 30.

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Answer: n= 4

Step-by-step explanation:

n+10=2(n+6) where n represents the number

you solve this.

n+10=2n+6

n+10-6=2n

n+4=2n

n=4

The radius is the center of circle to its edge or half of a diameter so half of 4/5 is 0.4 since 0.8 / 2 = 0.4.

To find the volume we need to do the equation π r² h.

So, π x 0.4^2 x 10 = 5.02654825.

Round 5.02654825 to the nearest hundredth and it is 5.03.

Volume is 5.03.

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Answer: i don't know give me more info

Step-by-step explanation:

The amount invested at 10% by $568.65 and investment rate is -

amount invested at 13%. is $5275

amount invested at 10%.  is $1171

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

here, we have,

Let x represent the amount invested at 13%.

Let y represent the amount invested at 10%.

$6,446 is invested, part at 13 % and the rest at 11%.

This means that

x + y = 6,446

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested at 13%,

P = x

R = 13%

T =1 year

I = (x × 13 × 1)/100 = 0.13x

Considering the amount invested at 10%,

P = y

R =10%

T = 1 year

I = (x × 10 × 1)/100 = 0.10y

If the interest earned from the amount invested at

13% exceeds the interest earned from the amount invested at

10% 10 % by $568.65, it means that

0.13x - 0.10y = 568.65,- - -- - - - - -1

Substituting x = 6,446 - y into equation 1, it becomes

0.13(6,446- y) - 0.10y =568.65

i.e. y= 1171

solving, we get,

x=5275

y= 1171

amount invested at 13%. is $5275

amount invested at 11%.  is $1171

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The required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.

Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,

here,
The decimal value is shown in the image,
= 31 / 100

= 0.31

From the options,
0.31 > 0.1
0.31 < 0.5
0.31 < 0.32
0.31 < 0.4

Thus, the required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.

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The exponential grows at the same rate as the quadratic in the interval

0 ≤ x ≤ 1.

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

[tex](f(a) - f(b))/(b-a)[/tex].

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

 = (2-1)/1 = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

=(1 - 0)/1  = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

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Answer:

Step-by-step explanation

y≥  2x + 3 is -6,2

(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.

Therefore, we must first determine this's slope.

-3x - 7y = 10

To both sides, add three.

-7y = 3x + 10

Add -7 to both sides.

y = -3/7x - 10/7

Our slope is thus -3/7.

The slopes always remain the same when searching for a line that is parallel to something.

Remember that y = mx+b is the slope-intercept form as well.

Where b is the y-intercept and m is the slope.

Our y-intercept is -3 since the coordinates (-5,-3) are available.

The slope here is -3/7.

Put those numbers into the slope-intercept form equation, then, to solve.

y = mx + b

y = -3/7x - 3

(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.

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The equation of the line parallel to the given line is y = -3x/7 + 47/7

The equation of the perpendicular will be  y = 7x/3 -13/3

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope. The slope of the original line's perpendicular line is -2, which is the original line's negative reciprocal.

The equation of the line is 3x + 7y = 8

The slope of the line is = -3/7

so the equation of the line parallel to the given line is y = -3x/7 + c

the point given as (4,5)

The line is 5 = -3*4/7 + c

or, c = 5 + 12/7 = 47/7

the equation of the line parallel to the given line is y = -3x/7 + 47/7

The slope of the line perpendicular to the given line is 7/3

So, the equation of the line is y = 7x/3 + c

The intercept is 5 = 7*4/3 + c

or, c = 5 - 28/3 = -13/3

The equation of the perpendicular will be  y = 7x/3 -13/3

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For a dozen cookies, 0.75 cups of sugar are needed in total.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

given, A cookie recipe calls for 1.5 cups of sugar for two dozen cookies.

Since,

For two dozen of cookies, there are a total of 1.5 cups of sugar required.

In 2 dozen cookies, required sugar = 1.5 cups

In 1 dozen cookies, required sugar = 1.5/2 cups

In 1 dozen cookies, required sugar = 0.75 cups

Therefore, The total number of cups of sugar required for one dozen cookies is 0.75.

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The total number of students in the class given the percentage of unhappy students is 263 students.

Percentage of unhappy students= 7.23%

Number of unhappy students= 19

Total number of students in class= x

Number of unhappy students = Percentage of unhappy students × Total number of students in class

19 = 7.23% × x

19 = 0.0723 × x

19 = 0.0723x

divide both sides by 0.0723

x = 19/0.0723

x = 262.7939142461964

Approximately,

x = 263 students

Therefore, there are 263 students in the class.

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