Which is the next number in this pattern. What is the rule ? 0,1,1.5,1.75
A.2
B.1.875
C.1.85
D.1.8

The length of the base is 4  inch.

It is required to find the length of the base.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given:

Let b be the length of the base.

h=3  inch.

Area = 6 square inches

a=1/2bh

6=1/2b*3

b=4  inch.

Therefore, the length of the base is 4  inch.

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The required point of tangency if the curve y=sqrt(1+2x) is the tangent line perpendicular to the line 6x+2y=1 is (4, 3)

Given the curve expressed as y = √1+2x

Also, given the equation 6x + 2y = 1

Get the slope of the line

6x + 2y = 1

2y = -6x + 1

y = -3x + 1

The slope of the line is -3

The slope of the line perpendicular will be 1/3

The equation of the tangent line perpendicular to the line 6x+2y=1, hence;

y = 1/3 x + b

Equate the equation with the equation of the curve;

√1+2x =  1/3 x + b

Square both sides

(√1+2x)² =  (1/3 x + b)²

1 + 2x = 1/9x² + 2/3bx + b²

Multiply through by 9

9 + 18x = x² + 6bx + 9b²

x²+ 6bx-18x-9+9b² = 0

x²+(6b-18)x-(9-9b²) = 0

x²+(6b-18)x+9b²-9 = 0

If the discriminant b²-4ac = 0, hence;

(6b-18)² - 4(9b²-9) = 0

36b² - 216b + 324 - 36b²+36 = 0

- 216b + 360 = 0

216b = 360

b = 360/216

b = 5/3

Get the value of x by substituting b = 5/3 into x²+(6b-18)x+9b²-9 = 0

x² + [6(5/3) - 18]x + [9(5/3)² - 9] = 0  

x² - [10 - 18]x + [9(25/9)- 9] = 0

x² + 8x + [25- 9] = 0

x² + 8x + 16 = 0

x² + 4x + 4x + 16 = 0

(x - 4)² = 0  

x = 4

Substitute x = 4 into the y value

y = √(1 + 2(4))

y = √9

y = 3

Hence the required coordinate is (4, 3)

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Todd can use the polynomial function [tex]9x^2 - 1[/tex] to calculate his average profit based on the amount of raw materials his furniture company currently has.

The question is asking for a polynomial function that Todd can use to calculate the average profit based on the amount of raw materials the company currently has. To find this, Todd will need to multiply the profit from each piece of furniture (3x + 1) with the amount of furniture he can produce (3x - 1). Thus, the polynomial function will be [tex](3x + 1)(3x - 1)[/tex]. After simplifying we get [tex]9x^2 - 1.[/tex] So this is the polynomial function that Todd can use to predict his average profit.

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Answer:

c  $12

If the cost c is at least $12 then it could be equal to 12, or could also be a cost greater than $12. So, c is greater than or equal to 12, expressed as c  $12

Step-by-step explanation:

Answer:

∠8 , ∠4 are Corresponding angle.

Step-by-step explanation:

Given : Two parallel line l ,m and transveral line .

To find : what is the relationship between angle 8 and angle 4.

Solution : We have given two parallel line l ,m and transveral line .

Corresponding angle :  The angles in matching corners are called Corresponding Angles.

Corresponding angle are equal.

Therefore, ∠8 , ∠4 are Corresponding angle.

The relation between the angles 8 and 4 is that, they are corresponding angles.

Hence, the correct option is a.

Given that are two lines l and m, intersected by a transversal line,

We need to determine the relationship between angle 8 and angle 4.

According to the definition of corresponding angles we get, that 8 and 4 are a set of corresponding angles,

Corresponding angles :-

Corresponding angles are formed when a transversal intersects two lines. The angles that are in the same position on the intersected lines are called corresponding angles.

Hence angles are corresponding angles.

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The value of x = 5.3.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The equation is,

0.3x +5.14 = 2.1x -4.4

The equation here formed is made of two expressions,

Expression 1:  0.3x +5.14 and,

Expression 2 : 2.1x -4.4

In the expressions, the variable is x, and the constants are 0.3, 5.14, 2.1, -4.4

Solving for x,

0.3x +5.14 = 2.1x -4.4

Taking variable on the left side, and the constants on the right side.

Taking the like terms on one side,

0.3x - 2.1x = -4.4 -5.14

The negative sign gets cancelled,

-1.8x = -9.54

Dividing 1.8 on both sides.

x = (-9.54 / -1.8)

x = 5.3

The value of x is 5.3.

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Answer:

Step-by-step explanation:

Given is a statement as

[tex]If you play the tuba, then you play an instrument.[/tex]

We have to write the converse, inverse and contrapositive of the above statement.

If x, then y has converse as if y, then x, inverse as if no y then no x, contrapositive as if no x, then no y.

Using the above we find

Converse: If you play an instrument, then you play the tuba

Inverse: if you do not play the tuba, then you do not play an instrument

Contra positive:  If you do not play an instrument, you do not play the tuba.

2 numbers win

4 numbers lose

 so answer would be The probability of losing is higher than that of winning.

Answer:

Option C

Step-by-step explanation:

We are given that a spinner has 6 parts numbered 1-6.

If the result is 1 or 6 then a player wins the number times $10.00.If the result is 2-5 then the player loses the number times $5.

Number of cases when the player wins number times $10.00=1 or 6=2

Number of cases when the player loses the number times $5=2,3,4,5=4

Total number of cases =6

Formula for finding probability

P(E)=[tex]\frac{Number \;of\; favourable\; cases}{Total \; number\; of \; cases}[/tex]

Applying this formula

The probability of wining=[tex]\frac{2}{6}[/tex]

The probability of wining=[tex]\frac{1}{3}[/tex]

The probability of wining=0.33

The probability of losing=[tex]\frac{4}{6}[/tex]

The probability of losing=[tex]\frac{2}{3}[/tex]

The probability of losing=0.66

Hence, the probability of losing is higher than that of winning.

Therefore, option C is true.

Answer: 15%

Step-by-step explanation:

Given: The original value of car : [tex]\$5,200[/tex]

The value of car after one year : [tex]\$4,420[/tex]

Now, the percent of decrease in the value of her car is given by :-

[tex]\dfrac{\text{Change in price}}{\text{Original price}}\times100\\\\\\=\dfrac{5200-4420}{5200}\times100=15\%[/tex]

Hence, the percent of decrease in the value of her car = 15%

The ratio of surface area to volume of the moon is [tex]\boxed{\bf 1.9\text{\bf\ times}}[/tex] of the ratio of surface area to volume of the mars.

Further explanation:

The volume of the spherical shape can be calculated as,

[tex]\boxed{\text{Volume of sphere}=\dfrac{4}{3}\pi r^{3}}[/tex]    

The surface area of the spherical shape can be calculated as,

[tex]\boxed{\text{Surface atrea of sphere}=4\pi r^{2}}[/tex]  

Here, [tex]r[/tex] is the radius of the sphere.

Calculation:

Step 1:

First we will calculate the ratio of surface area of the sphere to the volume of the sphere.  

The ratio of these quantities can be calculated as,

[tex]\begin{aligned}\dfrac{\text{Surface area}}{\text{Volume}}&=\dfrac{4\pi r^{2}}{\dfrac{4}{3}\pi r^{3}}\\&=\dfrac{3}{r}\end{aligned}[/tex]    

Therefore, the ratio of the surface area to the volume of the sphere is [tex]\frac{3}{r}[/tex].

Step 2:

Second we will calculate the ratio of surface area of the moon to the volume of the moon.

The radius of the moon is [tex]1738\text{ km}[/tex].

Substitute [tex]r=1738[/tex] in the ratio of the surface area to the volume of the sphere.

[tex]\begin{aligned}\dfrac{\text{Surface area of the moon}}{\text{Volume of the moon}}&=\dfrac{3}{r}\\&=\dfrac{3}{1738}\end{aligned}[/tex]    

Step 3:

Third we will calculate the ratio of surface area of the mars to the volume of the mars.

The radius of the mars is [tex]3397\text{ km}[/tex].

Substitute [tex]r=3397[/tex] in the ratio of the surface area to the volume of the sphere.

[tex]\begin{aligned}\dfrac{\text{Surface area of the mars}}{\text{Volume of the mars}}&=\dfrac{3}{r}\\&=\dfrac{3}{3397}\end{aligned}[/tex]  

Step 4:

Now compare the ratios of the surface area to volume of moon with ratios of the surface area to volume of mars.

Divide the ratios of the moon by the ratio of the mars to compare.

[tex]\begin{aligned}\dfrac{\text{ratio for moon}}{\text{ratio for mars}}&=\dfrac{1738}{3}\times\dfrac{3}{3397}\\&=\dfrac{1738}{3397}\\&=1.9\end{aligned}[/tex]  

Clearly we can see that the ratio surface area to volume of the moon is [tex]\boxed{\bf 1.9\text{\bf\ times}}[/tex] of the ratio surface area to volume of the mars.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Mensuration

Keywords: Mensuration, volume, surface area, sphere, ratio, moon, mars, comparision, spherical shape, curved surface area, radius of the sphere.

The surface area-to-volume ratio of the Moon is larger than that of Mars.

The surface area-to-volume ratio of an object is a measure of how much surface area it has compared to its volume. It is calculated by dividing the surface area of the object by its volume.

To compare the surface area-to-volume ratios of the Moon and Mars, we need to first calculate the surface area and volume of both objects. The Moon has a diameter of approximately 3,474 km and Mars has a diameter of approximately 6,779 km. Using the formula for the surface area and volume of a sphere, we can find the surface area and volume of each planet.

For the Moon:

For Mars:

Now we can calculate the surface area-to-volume ratios:

Therefore, the surface area-to-volume ratio of the Moon is larger than that of Mars.

Final answer:

The graph of the inequality y ≥ |x + 2| − 3 is represented by a shaded region above a solid V-shaped boundary line that has its vertex at the point (-2, -3).

Explanation:

To determine which description matches the graph of the inequality y ≥ |x + 2| − 3, it is essential to understand the properties of the inequality and the properties of absolute value functions. The absolute value function |x + 2| creates a V-shaped graph with a vertex at the point (-2, 0). When this is adjusted by subtracting 3, the vertex of the V shape is moved down to (-2, -3).

The inequality sign ≥ indicates that we are looking for the region that includes all y-values that are greater than or equal to the function |x + 2| − 3. Therefore, the region of the graph that we are interested in is above this V-shaped graph. The equal part of the inequality ≥ allows us to use a solid boundary line rather than a dashed line, because the points on the graph of y = |x + 2| − 3 are included in the solutions for the inequality.

So, the correct description is a shaded region above a solid boundary line, which represents all the points (x, y) where y is greater than or equal to the value of |x + 2| minus 3.

Answer:

the answer is

22.75

The number will be 6.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The algebraic expression is,

''A number to the 11th power divided by the same number to the 8th power equals 216.''

Now,

Let a number = x

So, we can formulate;

⇒ x¹¹ / x⁸ = 216

⇒ x ¹¹ ⁻ ⁸ = 216

⇒ x³ = 216

Take cube root both side, we get;

⇒ x = ∛216

⇒ x = 6

Thus, The number will be 6.

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The numbers are -19 and 34.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing.

Given:

Sum of two number= 15.

let the number be x and y.

So, three times one of the numbers is 11 less than five times the other

3x = 5y- 11

and, x+ y= 15

On solving above two equations

3(15- y)  =  5y - 11

45 - 3y = 11-5y

38 = -2y

y= -19

and, x= 34.

Hence, the numbers are -19 and 34.

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