These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
Town B
10 15 20
H
5
ㅏ
20
30
30
40
55
55
05 10 15 20 25 30 35 40 45 50 55 60
Degrees (F)

An error exists in the distinction between the exact length of an object and its measured length.

The closest to the percent error for Diego's measurement exists at 4.3%.

An error exists in the distinction between the exact length of an object and its measured length.

Error = Actual length - Measured length

= 23cm - 22cm

= 1 cm

Percent error = Error/ Actual length × 100

= 1 /23 × 10

= 4.35%

Therefore, the closest to the percent error for Diego's measurement exists at 4.3%.

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The radius of the hemisphere is 9.5 inches.

The diameter of the hemisphere is 19 inches.

The surface area of the hemisphere is 850.2 inches²

circumference of a circle = 2πr

where

Therefore,

19π = 2πr

2r = 19

r = 19 / 2

r = 9.5 inches

diameter = 9.5 × 2 = 19 inches

Therefore,

surface area of an hemisphere = 3πr²

surface area of an hemisphere = 3 × 3.14 × 9.5²

surface area of an hemisphere = 850.155 inches²

surface area of an hemisphere = 850.2 inches²

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The value of cos A is √(1 + x²)/ (1 - x²) /√1 + x

It is important to note that

sin A = opposite/ hypotenuse

cos A = adjacent/ hypotenuse

Then,

opposite = [tex]\sqrt{1} - x[/tex]

Hypotenuse = [tex]\sqrt{1} + x[/tex]

Let's find the adjacent side using the Pythagorean theroem

[tex](\sqrt{1} + x)^2 = (\sqrt{1 -x } )^2 + x^2[/tex]

[tex]1 + x^2 = 1 - x^2 + x^2[/tex]

[tex]x = \sqrt{\frac{1 + x^2}{1 -x^2} }[/tex]

cos A = x/hypotenuse

[tex]cos A = \frac{\sqrt{\frac{1+x^2}{1 -x^2} } }{\sqrt{1} +x}[/tex]

cos A = √(1 + x²)/ (1 - x²) /√1 + x

Thus, the value of cos A is √(1 + x²)/ (1 - x²) /√1 + x

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Answer:

Each number is increasing by [tex]\frac{1}{4}[/tex].  The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

I am not sure what the question is.  I am wondering if they are asking how is the list growing or what would be the next number.

Each number is increasing by 1/4

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex]  you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1

Answer:

C

Step-by-step explanation:

y is greater or equal to 0

x is also greater or equal to 0

you can see that only one answer choice can be the answer

the line is x-y = 2

the upper side is x-y <= 2

proves that c is the answer

x-y ≤ 2

y ≥ 0

x ≥ 0 satisfies this graph. Thus option C is correct.

A schematic or visual presentation that organizes the depiction of data or quantities is known as a graph. The relationships connecting two or more objects are frequently represented by the spots on a graph. They are employed to arrange data in order to highlight correlations and patterns. This data is presented as a pattern on a graph.

When y is bigger than 0 and x is also.

The equation is 2x-y.

x-y ≤ 2 on the upper side of the graph is represented in this same way.

x-y ≤ 2; y ≥ 0 and x ≥ 0 will be the correct represented points in the graph. Therefore, option C is the correct option.

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Answer:

1) 0.10

2) 0.15

3) 0.100

4) No

Answer:

[tex]-4\leq x[/tex] is what it looks like simplifed. In word form this means x is greater than all values equal to or greater than four. This means that the FOURTH graph is correct.

Step-by-step explanation:

[tex]13-2x\leq 37+4x = -24\leq 6x.[/tex]

Simplify this into [tex]-4\leq x[/tex] or [tex]x\geq -4[/tex]

This in words translates into x is greater than or equal to the value of four. Meaning all values larger than 4 and 4 are equal to x

Meaning the 4th graph is correct because it shows exactly what the word form says.

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

Have a great day,

Nish

Answer:

86.

Step-by-step explanation:

His total score is 99 + 85 + x where x is score on third test,

99 + 85 + x = 3 *90   (as his average must be 90, so:

184 + x = 270

x = 270 - 184

  =   86.

Answer:

86

Step-by-step explanation:

Let x be the required score for Lamar's third test in order to get an average of 90 or higher.

Start with the initial equation:

[tex]\frac{99+85+x}{3}\geq 90[/tex]

Simplify the numerator in the fraction:

[tex]\frac{184+x}{3}\geq90[/tex]

Multiply both sides by 3 to cancel out division on left side of equation:

[tex]184+x\geq 270[/tex]

Subtract 184 from both sides to isolate the x variable:

[tex]x\geq86[/tex]

Leaving us with x must be greater than or equal to 86.

The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

The area of triangle A = 1728 square feet

The base length of the triangle b = 72 feet

Let h be the height of the triangle

Area = (1/2)b×h

1728 = (1/2)72×h

h = 48 feet

Half of the 72 is 72/2 = 36

As we know,

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

Applying trigonometric ratio:

tan(x) = 48/36

tan(x) = 1.333

x = 53.13 degrees

Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

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Answer: -9

Step-by-step explanation:  You might think that the smallest two numbers are 11 and 1 but there are negative numbers. 1 - (-9) is equal to 10. 1 x (-9) is -9.

Answer:

x = 75

Step-by-step explanation:

Given information from the question:

x - 3y = 30

y = 15

We can substitute y = 15 into the equation to find x.

x - 3(15) = 30

x - 45 = 30

x - 45 + 45 = 30 + 45

x = 75

Answer:

75

Step-by-step explanation:

x-3y=30

x-3×15=30

x-45=30

x=30+45

x=75

Answer:

40 vanilla cookies

Step-by-step explanation:

Lets say that

N = No-bake cookies

V = Vanilla cookies

C = Cinnamon cookies

If the ratio is 2 : 2 : 2

And there are 40 no-bake cookies

It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same

( N : V : C )

( 40 : 40 : 40 )

Hope this helps  (๑ > ᴗ <)وxx

( I am so sorry if this is wrong!!)

The midpoint between A and E is (0,1)

The coordinates of the cities are given as:

A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).

From the above, we have:

A = (-2,3)

E = (2,-1)

The midpoint between A and E is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

Midpoint = 1/2 * (-2 + 2, 3 - 1)

This gives

Midpoint = 1/2 * (0, 2)

Evaluate the product

Midpoint = (0, 1)

Hence, the midpoint between A and E is (0,1)

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Applying the angle bisector and triangle proportionality theorem, the solutions are:

16. x = 1/2 or x = 4

17. x = 5

18. x = −1 or x = 6.

The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.

16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]

Cross multiply

(x - 1)(x + 4) = 3x(x - 2)

x² + 3x - 4 = 3x² - 6x

x² - 3x² + 3x - 4 + 6x = 0

-2x² + 9x - 4 = 0

Factorize -2x² + 9x - 4

(−2x + 1)(x − 4)

-2x = -1

x = 1/2

or

x = 4

17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)

(2x + 2)(2x + 2) = (4x - 2)(x + 3)

4x² + 8x + 4 = 4x² + 10x - 6

Combine like terms

4x² - 4x² + 8x - 10x = -4 - 6

-2x = -10

x = -10/-2

x = 5

18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]

Cross multiply

(2x + 3)(x - 2) = x(x + 4)

Expand

2x² - x - 6 = x² + 4x

2x² - x - 6 - x² - 4x = 0

x² - 5x - 6 = 0

Factorize x² - 5x - 6 = 0

(x+1)(x−6) = 0

x = −1 or x = 6

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The missing side length of the right triangle are as follows;

v = 1 units

u = 2 units

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Therefore,

tan 60 = opposite / adjacent

tan 60 = √3 / v

cross multiply

v = √3 / tan 6-

v = √3 / √3

v = 1

Hence,

sin 60 = opposite / hypotenuse

sin 60 = √3 / u

cross multiply

u = √3 / sin 60

u = √3 × 2 / √3

u = 2√3 / √3

u = 2

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Answer:

5x^2+22x-12         x cannot be -5, -4, -2

(x+5)(x+4)(x+2)

Step-by-step explanation:

In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:

x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)

x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)

Now that you have factored out the two quadratics, plug them into the equation.

    5x        -       3

(x+4)(x+2)      (x+5)(x+2)

Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.

5x (x+5)             -           3(x+4)  

(x+5)(x+4)(x+2)      (x+5)(x+4)(x+2)

Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:

5x^2+25x - (3x+12)     =    5x^2+22x-12         x cannot be -5, -4, -2

 (x+5)(x+4)(x+2)               (x+5)(x+4)(x+2)

To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then [tex]$g(x) =x^2-10[/tex] exists g(10) = 90.

The value of g(10), we have to substitute in every x of f(x), the

[tex]f(x) = 2x + 1[/tex] exists f(90) = 181

Therefore, the value of f[g(10)] exists 181.

To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then

[tex]$g(x) =x^2-10[/tex]

substitute the value of x = 10

[tex]$g(10) = (10)^2-10[/tex]

simplifying the equation, we get

g(10) = 100 - 10

g(10) = 90

We have the value of g(10), we have to substitute in every x of f(x), then

f(x) = 2x + 1

substitute the value of x = 90

f(90) = 2(90) + 1

simplifying the equation, we get

f(90) = 180 + 1

f(90) = 181

The value of f[g(10)] exists 181.

Therefore, the correct answer is option b) 181.

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The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.

The numeric value of an expression is found replacing each letter by it's attributed value.

In this problem, the expression is:

-a² - 2bc - |c|

The attributed values are:

a = -3, b = -5 and c = 2

Hence the numeric value will be given by:

-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.

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Answer:

I x² +12x I = -32

Step-by-step explanation:

Absolute value equation:

  x = -4  ; x = -8

x + 4 = 0  and     x + 8 = 0

(x +4)(x + 8) = 0

x*x + x*8 + 4*x + 4*8 = 0

     x² + 4x + 8x  + 32 = 0

         x² + 12x   + 32   = 0

Absolute value equation:

  I x² + 12x I = -32

Answer:

18.0  cm to 1 decimal point.

Step-by-step explanation:

First  work out the unknown side (s) of the right triangle using the Pythagoras theorem:

s^2  = 13^2 - 5^2

       = 169 - 25 = 144

s = sqrt 144 = 12 cm.

Now consider the other triangle:

s = 12

The missing angle = 180 - 65 - 40 = 75 degrees.

By the Sine Rule:

x / sin 75 = 12 / sin40

x = 12 sin 75 / sin 40

  = 18.03

    -

The meaning of the y-intercept exists in the time required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind.  [tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.

The time it takes the plane to travel 2,000 kilometers with the tailwind, t(x), exists determined by the function

[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]

where x exists the increase in speed when the plane travels with the wind (tailwind).

The y-intercept exists at x=0, then

[tex]$&t(0)=\frac{2,000}{900}+x \\[/tex]

[tex]$&t(0)=\frac{20}{9}=2 \frac{2}{9}[/tex] hours

[tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.

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The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

For given question,

We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]

We need to find the sum of given convergent series.

Given series is a geometric series with ratio r = sin(1)

The first term of the given geometric series is [tex]a_1=sin(1)[/tex]

So, the sum is,

= [tex]\frac{a_1}{1-r}[/tex]

= sin(1) / [1 - sin(1)]

This means, the series converges to sin(1) / [1 - sin(1)]

[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]

= [tex]\frac{sin(1)}{1-sin(1)}[/tex]

= [tex]\frac{0.8415}{1-0.8415}[/tex]

= [tex]\frac{0.8415}{0.1585}[/tex]

= 5.31

Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31

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The characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

A linear equation is given as:

y = mx + b

Where m represents the slope of the linear equation.

When the value of  is 0

i.e. m = 0, the equation becomes

y = 0 *x + b

Evaluate

y= b

The above equation is a horizontal line that passes through the y-axis at y= b

Hence, the characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

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Answer:

m = -x

Step-by-step explanation:

The percentage form of given fraction is 60% and the hundredths form is 0.60

According to the statement

we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.

So, For this purpose,

The given fraction is 12/20.

Then the definition of the percentage is that

The Percentage, a relative value indicating hundredth parts of any quantity.

so, the percentage of given fraction is :

Percentage fraction = 12/20 * 100

After solving it, The percentage fraction will become:

Percentage fraction = 60%

and Now convert into the hundredths form then

In the hundredths form it will become

from 60% to 0.60.

So, The percentage form of given fraction is 60% and the hundredths form is 0.60

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The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)

In this question we must find a kind of polynomial whose form offers the best approximation to the point set, that is, the least polynomial whose mean square error is reasonable.

In a graphing tool we notice that the least polynomial must be a cubic polynomial, as there is no enough symmetry between (10, 9.37) and (14, 8.79), and the points (6, 3.88), (8, 6.48) and (10, 9.37) exhibits a pseudo-linear behavior.

The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)

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For the given function f(x) = 5x² + 2x - 3,

Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).

Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).

Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.

The x-intercepts of a function or equation are obtained at y = 0.

Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.

To calculate the x coordinate of vertex(h, k), use the formula mentioned below:

h = -b/2a

When the function is in the form of ax² + bx + c.

Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.

Thus, the required coordinates of the vertex are obtained as (h, k).

It is given that,

f(x) = 5x² + 2x - 3

Part A: Finding the x-intercepts:

Substituting y = 0 i.e., f(x) = 0;

⇒ 5x² + 2x - 3 = 0

On simplifying/factorizing,

⇒ 5x² + 5x - 3x - 3 = 0

⇒ 5x(x + 1) - 3(x +1) = 0

⇒ (5x - 3)(x + 1) =0

∴ x = 3/5 or x = -1

Thus, the x-intercepts are (3/5, 0) and (-1, 0).

Part B: Finding the vertex of the given function:

We have h = -b/2a

From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3

So, h = -2/2(5) = -1/5 = -0.2

Then, on substituting h = x = -0.2 in the function we get

k = 5(-0.2)² + 2(-0.2) - 3

k = -3.2

Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).

Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.

Part C: Steps to graph f(X):

Step 1: Plot the x-intercepts in the coordinate plane

Step 2: Plot the vertex of the function

Step 3: draw a curve line passing through them, opening towards up.

Thus, the graph of the given function is plotted as shown below.

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Answer:

3 3/4 hour

Step-by-step explanation:

(3/4) ÷ (1/5) = (3*5) / (4*1)

= 15/4 hour

15/4 = 12/4 + 3/4 = 3 + 3/4 hour

= 3 3/4 hour

The standard form of the given quadratic equation in  factored form is

(x+2) (x-6) = x²-4x-12

(x-4) (x+3) = x²-x-12

(x-12) (X+1) = x²-11x-12

(x-3) (x+4) = x²+x-12

what are quadratic equations?

A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero

To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.

f(x) = (x+2) (x-6)

x²+2x-6x-12

x²-4x-12

similarly, the standard form of equations 2,3 and 4 are :

(x²-x-12)

(x²-11x-12)

(x²+x-12)

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Answer:

B, D, A, C

Step-by-step explanation:

f(x) = (x + 2)(x – 6)

✔ B

f(x) = (x – 4)(x + 3)

✔ D

f(x) = (x – 12)(x + 1)

✔ A

f(x) = (x – 3)(x + 4)

✔ C

The number of different integers there are for the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

According to the task content, the square of the square of such integers must be a two-digit number, that is, less than or equal to 99.

The numbers in discuss, x must satisfy;

x⁴ < 99.

The numbers in this regard are therefore, -2, -3, 2, 3.

Ultimately, the integers which satisfy the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

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