On a winters day, the average temperature during the daytime is 40°F. At night the temperature falls to 24°F. What is the percentage decrease?

The equation is 36 - 4x = 6.

Solution:

To write the equation without fraction.

[tex]$4-\frac{4}{9} x=\frac{2}{3}[/tex]

[tex]$\frac{4}{1} -\frac{4}{9} x=\frac{2}{3}[/tex]

The denominators must be same to add/subtract the fractions.

LCM of 1, 9 and 3 = 9.

Multiply first term by [tex]\frac{9}{9}[/tex] and [tex]\frac{2}{3}[/tex] by [tex]\frac{3}{3}[/tex] to make the denominator same.

[tex]$\frac{4\times9}{1\times9} -\frac{4}{9} x=\frac{2\times3}{3\times3}[/tex]

[tex]$\frac{36}{9} -\frac{4}{9} x=\frac{6}{9}[/tex]

[tex]$\frac{36-4x}{9} =\frac{6}{9}[/tex]

Multiply by 9 on both sides.

[tex]$\frac{36-4x}{9}\times9 =\frac{6}{9}\times9[/tex]

Both 9 in the numerator and denominator get canceled.

36 - 4x = 6

This term does not have fraction.

Hence the equation is 36 - 4x = 6.

Step-by-step explanation:

The centroid divides the length of each median in 2:1 ratio.

The length of the part between the vertex and the centroid is twice the length between the centroid and the mid-point of the opposite side.

In case of median KM,

K is the vertex and M is the midpoint of the side JL

KT = 2× TM

5y+3 = 2(y+3)

5y+3= 2y +6

5y-2y= 6-3

3y = 3

y= 1

Answer:

C)x^2 - 6x-6

Step-by-step explanation:

-3(x + 2) + (x – 3)x=

-3x-6+x^2-3x=

x^2 - 6x-6

Answer:

C

Step-by-step explanation:

-3(x + 2) + (x – 3)x = -3*x + (-3)*2 +x*x - 3*x

                              = -3x - 6  +x² - 3x

                              = x² - 3x -3x - 6

                               = x² - 6x - 6

Answer:

80 in.

Step-by-step explanation:

to find the perimeter of a shape you add all of the side lengths together

20+20+20+20

Answer:

  c = V/((r^3)-72.25r)

Step-by-step explanation:

V is proportional to c, so you can simply divide by the coefficient of c.

  c = V/((r^3)-72.25r)

Answer:

B) 0:15=0

Step-by-step explanation:

Answer:

12(2 + 3)

Step-by-step explanation:

To use the distributive property, we must find a common factor between the two numbers. The greatest common factor or 24 and 36 is 12. Let's just use that. We get:

[tex]12(2+3) = 24+36[/tex]

That's our answer!

Answer:

12 ( 2 + 3 )= + 36

Step-by-step explanation: GCF between 24 and 36 by prime factorization should be:

24 = 2 * 2 * 2 * 3

36 = 2 * 2 * 3 * 3. what they both have in common between the prime factorization of both of the numbers are 2*2*3 which is GCF and equivlent to 12.

Answer:

The answer is 12

Step-by-step explanation:

Step 1:  Convert words into an equation

What do you is you multiply -2 by something to get -24

-2 * something = -24

We can represent something with a variable called x.

-2 * x = -24

-2x = -24

Step 2:  Solve for x by dividing both sides by -2

-2x / -2 = -24 / -2

x = 12

Answer:  The number we can multiply -2 by to get -24 is 12

Lets write this into an expression.

-2x = -24

Now, lets solve for x.

~Divide -2 to both sides

-2x/-2 = -24/-2

~Simplify

x = 12

Best of Luck!

Answer:

431

Step-by-step explanation:

Let

[tex]p(x) = {x}^{6} - 4 {x}^{4} + 4 {x}^{2} - 10[/tex]

We want to find the remainder when this polynomial is divided by x+3.

We use the remainder theorem.

Which says that, when p(x) is divided by x-a, the remainder is p(a)=R.

Therefore the remainder when p(x) is divided by x+3 is p(-3).

[tex]p( - 3) = {( - 3)}^{6} - 4 { (- 3)}^{4} + 4 {( - 3)}^{2} - 10[/tex]

We evaluate:

[tex]p( - 3) = 729 - 4 (81)+ 4 {( 9)} - 10[/tex]

We multiply to get;

[tex]p( - 3) = 729 - 324+ 36- 10[/tex]

We simplify to get:

[tex]p( - 3) =431[/tex]

Therefore the remainder is 431

Answer:

33.33%

Step-by-step explanation:

6 bikini styles and 2 other types

so, total types is 3

so, bikinis is only 1 of the 3, which is 1/3 or 33.33%

Bikini styles: 6

Othe types: 2

Overall: 6+2=8

Bikini percentage: 6/8=3/4=75%

Answer: 3/4 or 75%

Answer: The answer is C

Based on the information given, the best description of the data is the data cluster along a line and there is no outlier.

Option A is the correct answer.

A scatterplot is a type of graph used to display the relationship between two variables.

It is a collection of points on a two-dimensional plane, where each point represents a pair of values for the two variables being plotted.

One variable is typically plotted on the x-axis (horizontal axis), and the other variable is plotted on the y-axis (vertical axis).

We have,

The scatter plot shows a linear pattern where the data points are clustered around a line.

As the number of hours spent studying increases, the quiz score tends to increase as well.

There do not appear to be any outliers in the data that would significantly affect the relationship between the hours spent studying and the quiz scores.

Thus,

Based on the information given, the best description of the data is the data cluster along a line and there is no outlier.

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Option C:

[tex]2 g^{3}-5 g^{2}+6[/tex]

Solution:

Given expression:

[tex]$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}[/tex]

To find which expression is equal to the given expression.

[tex]$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}[/tex]

Expand the term [tex]-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right):-3 g^{4}-6 g^{3}+7 g^{2}+12[/tex]

         [tex]$=\frac{5 g^{4}+5 g^{3}-17 g^{2}+6 g- 3 g^{4}-6 g^{3}+7 g^{2}+12}{g+2}[/tex]

Arrange the like terms together.

         [tex]$=\frac{5 g^{4}- 3 g^{4}+5 g^{3}-6 g^{3}-17 g^{2}+7 g^{2}+6 g+12}{g+2}[/tex]

         [tex]$=\frac{2 g^{4}- g^{3}-10 g^{2}+6 g+12}{g+2}[/tex]

Factor the numerator [tex]2 g^{4}-g^{3}-10 g^{2}+6 g+12=(g+2)\left(2 g^{3}-5 g^{2}+6\right)[/tex]

         [tex]$=\frac{(g+2)\left(2 g^{3}-5 g^{2}+6\right)}{g+2}[/tex]

Cancel the common factor g + 2, we get

         [tex]=2 g^{3}-5 g^{2}+6[/tex]

Hence option C is the correct answer.

Answer:

C.

Step-by-step explanation:

Answer:

False.

Step-by-step explanation:

xy is one term.

Each term in an algebraic expression is separated by a + or - sign.

For example, x^2 - xy + y^2  has 3 terms

The volume of the smaller room is B. 768 cubic feet.

Step-by-step explanation:

Step 1:

The entire length for both rooms is 20 feet. As the large room has a length of 12 feet, the length of the smaller room is [tex]20-12=[/tex] 18 feet long.

The width of the prism is 12 feet and a height of 8 feet.

The volume of a rectangular prism is determined by multiplying its length, its width, and its height.

The small room's length = 8 feet,

The small room's width = 12 feet, and

The small room's height = 8 feet.

Step 2:

The volume of a rectangular prism [tex]= (l)(w)(h).[/tex]

The volume of the smaller room [tex]= (8)(12)(8)= 768.[/tex]

So the volume of the smaller room is 768 cubic feet which is option B.

A second linear equation that forms a system with exactly one solution with 3x+9y=-8 could be y = -2x + 4, as it has a different slope and y-intercept, ensuring the lines intersect at one point.

To create a system of equations with exactly one solution, you need to write a second linear equation that has a different slope than the first equation (3x+9y=-8) but does not share any points with it. The slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, will be used to construct our new equation.

Given the slope-intercept form y = 9 + 3x as an example, we see that the slope (m) is 3 and the y-intercept (b) is 9. To ensure our second equation has only one solution when paired with the first equation, we can select a different slope and y-intercept. For instance, an equation such as y = -2x + 4 would suffice, as it has a different slope (-2) and intercept (4), ensuring that the two lines will cross at exactly one point on the graph.

In summary, the original equation 3x+9y=-8 and the second equation y = -2x + 4 when graphed will intersect at exactly one point, forming a system of linear equations with one solution. This process involves selecting different values for the slope and y-intercept to make sure the lines are not parallel and do not coincide.

Answer: No

Step-by-step explanation:

When graphing [tex]y=2x+4[/tex] it comes out not being a proportion relationship.

*(revised answer)

So the answer is no, a proportional relationship has to run through the origin, and y=2x+4 has a y-intercept of 4, meaning that even though x increases when y does, the y-intercept means that this equation is not a proportional relationship.

Hope this helps!

(Thx for helping)

Answer:

x = 39

Step-by-step explanation:

The sum of all three angles of a triangle will ALWAYS be 180 degrees.

So, simply subtract 39 and 103 from 180 and you will find your answer.

180 - 39 - 102 = 39

Answer:

39

Step-by-step explanation:

There are 180degrees in a triangle. So 102+39=141than we have to do 180-141 to get out answer of 39

Step-by-step explanation:

Let the required line bisects the segment joining the point (5,3) and (4,4) at point M (x, y).

Therefore, M is the mid point of segment joining the point (5,3) and (4,4).

Now by mid-point formula we have:

[tex]M = ( \frac{5 + 4}{2} \: \: \frac{3 + 4}{2} ) = ( \frac{9}{2} \: \: \frac{7}{2} ) \\ \\ \therefore \: M \: = ( 4.5 \: \: 3.5 ) = (x_1 \: \: y_1)\\ \\ \because \: Line \: makes \: 45 \degree \: angle \: with \: positive \: \\ \: \: \: \: \: direction \: of \: x - axis. \\ \\ \therefore \: Slope \: of \: line: \: \\ \: \: \: \: \: \: \: m = tan \: 45 \degree = 1 \\ \\ Equation \: of \: line \: in \: slope \: point \: form\\ \: is \: given \: as: \\ y-y_1 =m(x-x_1) \\ \therefore \: y - 3.5 = 1(x - 4.5) \\ \therefore \: y - 3.5 = x - 4.5 \\ \therefore \: y = x - 4.5 + 3.5 \\ \therefore \: y = x - 1\\ \huge \purple { \boxed{\therefore \: x - y - 1 = 0}} \\ [/tex]

is the equation of required line.

Answer: x = -9

Step-by-step explanation:

Subtract 10 from both sides:

4x + 10 - 10 = -26 - 10

Simplify:

4x = -36

Divide both sides by 4:

4x/4 = -36/4

simplify:

-36/4 = -9

Answer: x = -9

Answer:

x = -9

Step-by-step explanation:

4x+10 = -26

    -10    -10

[tex]\frac{4x=-30}{4}[/tex]

x = -9

Answer:

Sometimes true

Step-by-step explanation:

Examples:

Denominators are 2 & 3

LCM is 6 (2×3 = 6)

True here

Denominators are 2 & 6

LCM is 6 (2×6 = 12)

Not true here

The product of -7p³ and the trinomial (4p² + 3p - 1) is obtained by multiplying -7p³ by each term of the trinomial and combining like terms, resulting in -28p⁵ - 21p⁴ + 7p³.

The question involves multiplying a monomial by a trinomial in algebra, which is a process of using the distributive property. To multiply -7p³ by (4p² + 3p - 1), you distribute -7p³ across each term in the trinomial:

Combine the results to get the final product:

-28p⁵ - 21p⁴ + 7p³

Answer:

with what

Step-by-step explanation:

Answer:

48.30 kph

Step-by-step explanation:

55mph - 88.50kph

1mph - 1.61 kph

30 mph - 48.30 kph

Horses can reach speeds of 55 mph (approximately 88.50 kph), while most donkeys top out at 30 mph over short distances.

A conversion factor is a number that is used to multiply or divide one set of units into another. The acceptable factor to an equivalent value must be utilized when a conversion is crucial.

Given that,

Horses can reach speeds of 55 mph (approximately 88.50 kph).

Most donkeys have a top speed of 30 mph over short distances.

Here the top speed of most donkeys is asked.

To convert miles per hour (mph) to kilometers per hour (kph),

Use the conversion factor of 1.60934.

Calculate the top speed of most donkeys in kph:

Given: Top speed of most donkeys = 30 mph

Conversion: 30  x 1.60934

≈ 48.28 kph

Hence, the top speed of most donkeys, rounded to two decimal places, is approximately 48.28 kph.

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The dimensions of the rectangle are: Width = 3 feet, Length = 7 feet.

The formula for Area of rectangle

Area = length x width

Given:

Area of rectangle = 21 square feet.

Let the width of the rectangle is w feet.

According to the given information, the length of the rectangle is four feet longer than the width,

So, length = w + 4 feet.

So, Area of rectangle = length x width

21 = w (w+4)

[tex]\[21 = w^2 + 4w\][/tex]

[tex]\[w^2 + 4w - 21 = 0\][/tex]

Solve this quadratic equation, set it equal to zero:

w² + 7w -3w -21 =0

w(w+7)-3 (w+7)= 0

(w+7)(w-3) =0

Setting each factor equal to zero:

w+ 7 =0

w= -7

or, w - 3 =0

w = 3

So, the length of rectangle is

= 3+ 4

= 7 feet

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Answer:

24:6

Step-by-step explanation:

It is 4 to 1. The ratios added up is 5. So 30 divided by 5 is 6. So 1 (the ratio) is 6 games. 4x6=24. So the new ratio is 24 to 6. 24 wins and 6 losses.

The team won 24 games and lost 6, calculated by first solving for x in the equation 5x = 30 and then applying the 4:1 win-to-loss ratio.

If the ratio of wins to losses for Loyola basketball is 4 to 1, and they played 30 games, we want to find how many of those games were wins and how many were losses. Let's say the number of wins is 4x and the number of losses is x. According to the ratio, there are 4 wins for every loss, which makes the total number of games 4x + x = 5x.

Since we know 5x is 30 games, we can solve for x to find out the number of losses. Dividing 30 by 5, we get x = 6. That's the number of losses. To find the number of wins, we multiply 4 times the number of losses (4x), which gives us 4 * 6 = 24 wins.

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

Answer:

Step-by-step explanation

Length of pipe =2/3yard

3/4 of pipe = 3/4 × 2/3

= 2/4 = 1/2 yard

Answer:

  4096

Step-by-step explanation:

You want to evaluate (-8)⁴.

The exponent of 4 signifies the base (-8) is a factor 4 times in the product:

  (-8)⁴ = (-8)×(-8)×(-8)×(-8)

The multiplication is accomplished in the usual way. There are an even number of minus signs, so the product will be positive. The value is ...

  (-8)×(-8)×(-8)×(-8) = 8·8·8·8 = 64·8·8 = 512·8 = 4096

  (-8)⁴ = 4096

__

Additional comment

It can be faster to decompose the exponent into powers of 2. This makes it possible to use squaring to reduce the number of operations required.

  (-8)⁴ = (8²)² = 64·64 = 4096

Answer:

[tex]x = \frac{\pi}{2} [/tex]

[tex]x = \frac{3\pi}{2} [/tex]

Step-by-step explanation:

The tangent function is

[tex]y = \tan(x) [/tex]

We can rewrite it as:

[tex]y = \frac{ \sin(x) }{ \cos(x) } [/tex]

This graph has vertical asymptotes at where the denominator is zero.

[tex] \cos(x) = 0 \\ \implies \: x = \frac{\pi}{2} \: or \: \frac{3\pi}{2} [/tex]

The correct options are : (b) [tex]\( x = \frac{\pi}{2} \)[/tex] and (d) [tex]\( x = \frac{3\pi}{2} \)[/tex]

The asymptotes of the tangent graph are the vertical lines where the tangent function is undefined. The tangent function, [tex]\(\tan(x)\)[/tex], is undefined where the cosine function is zero, which happens at:

[tex]\[ x = \frac{\pi}{2} + k\pi \quad \text{for integer values of } k \][/tex]

So, let's check each given value to see if it fits this form.

1. [tex]\( x = \frac{\pi}{4} \)[/tex]

[tex]\[ \frac{\pi}{4} \neq \frac{\pi}{2} + k\pi \][/tex]

This is not an asymptote.

2. [tex]\( x = \frac{\pi}{2} \)[/tex]

[tex]\[ \frac{\pi}{2} = \frac{\pi}{2} + 0 \times \pi \][/tex]

This is an asymptote.

3.[tex]\( x = \pi \)[/tex]

[tex]\[ \pi \neq \frac{\pi}{2} + k\pi \][/tex]

This is not an asymptote.

4. [tex]\( x = \frac{3\pi}{2} \)[/tex]

[tex]\[ \frac{3\pi}{2} = \frac{\pi}{2} + \pi \][/tex]

This is an asymptote.

5.[tex]\( x = 3\pi \)[/tex]

[tex]\[ 3\pi \neq \frac{\pi}{2} + k\pi \][/tex]

This is not an asymptote.

The asymptotes of the tangent graph from the given options are:

[tex]\( x = \frac{\pi}{2} \)[/tex]

[tex]\( x = \frac{3\pi}{2} \)[/tex]

The complete Question is

Select all that are asymptotes of the

tangent graph.

a. x = pi/4

b. x=pi/2

c. x=pi

d. x=3pi/2

e. x=3pi

Answer:

V ≈ 143.91938 ft

Step-by-step explanation:

V = π r² h

V = π r² h = π · 49² · 180

V ≈ 1.35773 × 10⁶

V ≈ 143.91938 ft

volume of the cylinder is 13577335.51 cubic feet

A 3-dimensional solid geometric figure with straight parallel sides and a circular or oval cross section is called a cylinder.

                                             V = πr²h

     where,                              V =  volume of the cylinder

                                               r= the radius of base

                                               h = height of the cylinder

According to the problem, volume of the cylinder = π(49)²( 180)

                                                                  =13577335.51 cubic feet

∴   volume of the cylinder is 13577335.51 cubic feet

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Answer:0

Step-by-step explanation:

-8 + 8 (opposite)

=0

Answer:

0

Step-by-step explanation:

the oppisite of -8 is 8 the sum of 8+(-8)

is the same as 8-8