1. calculate the angles marked with letters​

Answer:Your answer would be x=1/10

Step-by-step explanation:

The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.

The Scale Factor is employed to scale shapes in different dimensions. Geometry teaches us about numerous geometrical shapes in two and three dimensions. The scale factor is a metric considering similar figures that appear the same but have distinct scales or measures.

The basic formula for computing this same scale factor is, Scale factor = Dimension of the new shape x Dimension of the original shape If indeed the original figure is scaled up, then the formula is expressed as Scale factor = Larger figure dimensions /Smaller figure dimensions.

The size of the ant = 1/2 inch.

the model size is = 1 foot.

                             = 1 foot = 12 inch

The scale factor of the model  =  Larger figure dimensions ÷ Smaller figure dimensions.

                                                  = 12/.5

                                                  = 24 inch or 2 foot

The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.

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The cost of 8 oranges is $7.52

The first step is to find the cost of one orange

6 oranges cost 5.65

1 orange= 5.64/6

= 0.94

Therefore the cost of 8 oranges can be calculated as follows

= 0.94×8

= 7.52

Hence 8 oranges cost $7.52

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Answer:

It will take approximately 20 years for the investment to double. The amount after 10 years will be $17,033.

Step-by-step explanation:

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The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.  

With an example, what is compound interest?

Principal - $400

rate of interest is compounded annually

g(x) =  400( 1.03)ˣ equation 1.

Formula used

A = P( 1 + r )ⁿ

here n = x

Solution:

Putting the value of n, and principal in the formula

A = P( 1 + r )ⁿ ................... equation 2

now comparing both equation 1 and equation 2,

400( 1.05)ˣ =  400( 1 + r )ˣ

( 1.05)ˣ = ( 1 + r  )ˣ

1.05 = 1 + r

r = 1.05 - 1

r = 0.05

r % = 0.05 × 100

r % = 5 %

thus, the constant percent rate of change =  5 %

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Using a system of equations, it is found that there were a total of 825,000 Arabic speakers, and the diagram is completed as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

There were 639,000 French Creole speakers, hence:

f = 639,000.

There were 186,000 more Arabic speakers than French Creole speakers, hence:

a = 186,000 + f = 186,000 + 639,000 = 825,000.

There were a total of 825,000 Arabic speakers, and the diagram is completed as follows:

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Answer:

It's B

Step-by-step explanation:

Step-by-step explanation:

[tex]\displaystyle\\12-15x > 22\\12-15x+15x > 22+15x\\12 > 22+15x\\12-22 > 22+15x-22\\-10 > 15x\\Divide\ both\ parts\ of \ the \ equation\ by\ 15:\\-\frac{10}{15} > x\\\\-\frac{5*2}{5*3} > x\\\\-\frac{2}{3} > x \\\\Thus,\\\\x < \frac{-2}{3}[/tex]

Answer: A

[tex]\displaystyle\\4\leq 3x+10 < 19\\\\4-10\leq 3x+10-10 < 19-10\\\\-6\leq 3x < 9\\\\Divide\ the\ inequality\ by \ 3:\\\\-2\leq x < 3\\\\Answer:\ -2\leq x < 3[/tex]

The number of apples Chee bought is 2, and the number of peaches she bought is 8

From the question, we are to determine the number of apples, x, and the number of peaches, y, that Chee bought

From the given information,

She bought $6 worth of apples and peaches

and

Each apple costs $1 and each peach costs $0.50

Then, we can write that

$1 × x + $0.50 × y = $6

x + 0.50y = 6

Also,

She bought 4 times as many peaches as apples

That is,

y = 4x

Now, we will solve the system of equations graphically

x + 0.50y = 6

y = 4x

From the graph, the solution to the system of equations is x = 2, y = 8.

Hence, the number of apples Chee bought is 2, and the number of peaches she bought is 8

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The positive interval is (0,2) and the negative range is calculated as (-4,0) and (2,4).

A graph is used to show the relationship between variables on a coordinate plane.

The domain of the function is [-4,4].

The zeros are: -2,0 and 2.

The positive interval is between (0,2).

The range of negative values is (-4,0) to (2,4). This is the set of x values in the graph. The graph demonstrates that the x value is between -4 and 4.

Thus, the domain is [-4,4]. The zeros of the function: Where it crosses the x- axis. The graph touches the x-axis when it is at -2,0 and 2. As a result, the function has the following zeros:-2,0 and 2.

Positive interval:

On the graph, positive values range from x = 0 to x = 2.

Consequently, the positive interval is (0,2).

Negative duration:

This is the x values when the function gives a negative result.

The graph shows negative values from x = -4 to x = 0, then from x = 2 to x = 4.

The negative range is therefore (-4,0) and (2,4).

Hence, the positive interval is (0,2) and the negative range is (-4,0) and (2,4).

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The equation of the line, with slope equal to 0 and passing through the point located at (4 , -2), is y = -2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 0 and (x1 , y1) = (4 , -2)

(y - -2) = 0(x - 4)

(y + 2) = 0

y = -2

In slope-intercept form, the equation of the line is:

(y + 2) = 0

y = -2

In standard form, the equation of the line is:

y = -2

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Answer:

[tex]4x^2+2x+1[/tex]

Step-by-step explanation:

[tex]f(x)=4x^2+5\\g(x)=2x-4\\\\f(x)+g(x)=(4x^2+5)+(2x-4)\\\\4x^2+5+2x-4\\\\4x^2+2x+1[/tex]

The solution using the square root property for given complex numbers would be x = 10i where i is an imaginary number.

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,

where a, and b are real numbers and i is an imaginary number.

We have been given the equation of complex numbers x² = -100

Using the square roots property to solve the above equation

⇒ x² = -100

⇒ x = √-100

⇒ x = √(-1×10×10)

∵ i² = - 1 or i = √-1

Here i is an imaginary number.

⇒ x = 10(√-1)

⇒ x = 10i

Therefore, the solution of given complex numbers would be x = 10i where i is an imaginary number.

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Answer: If you're solving for the substitution method then your answer would be (1,3)

Step-by-step explanation:

Answer:

x = -4/5

y = 9/5

Step-by-step explanation:

-3y + 2x = -7

8x - 3y = -1

make one of the equations y=....

-3y + 2x = -7

-3y = -7 - 2x

  y = (-7 - 2x)/3

now put (-7 - 2x)/3 where y is in the other equation

8x - 3y = -1

8x - 3((-7 - 2x)/3) = -1

8x - 1*(-7 - 2x) = -1

8x + 7 + 2x = -1

solve for x

8x + 7 + 2x = -1

8x+2x = -8

10x = -8

x = -8/10

x = -4/5

now put -8/10 in one of the equations to get what y is

-3y + 2x = -7

-3y + 2(-8/10) = -7

-3y - 16/10 = -7

-3y = -7 + 16/10

-3y = -70/10 + 16/10

-3y = -54/10

y = -54/10 * -1/3

y = 18/10

y = 9/5

The given lograthimic expression  log₃ y + 4 log₃ t can be written as log₃(yt^4).

According to the given question.

We have an logarithmic expression

log₃ y + 4 log₃ t

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the product  and power rule we know that

log(mn) = logm + logn

Thereofore, the given lograthimic expression  log₃ y + 4 log₃ t can be written as

log₃ y + 4 log₃ t

= log₃ y + log₃ t ^4

= log₃(yt^4)

Hence, the given lograthimic expression  log₃ y + 4 log₃ t can be written as log₃(yt^4).

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Domain - { 3, 11, 121, 34 , 23 , } is domain of  each relation is a function.

What is domain and range ?

How are the domain and range determined?

  Domain - { 3, 11, 121, 34 , 23 , }

 Range  -  { 9, 21 , 34 , 1 , 45 }

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The lowest possible integer value of x is 3 such that (x ≥ 3).

For the given question;

The area of rectangle A is bigger than the area of rectangle B.

The sides of the rectangle A are 2x-3 and 5 cm.

Area = length×breadth

Area A = (2x - 3)(5)

Area A = 10x - 15

The sides of the rectangle B are x = 2 and 3 cm.

Area = length×breadth

Area B = (x + 2)3

Area B = 3x + 6

As area B > area B

Then,

10x - 15 ≥  3x + 6

Solving the inequality;

10x - 3x ≥ 6 + 15

7x ≥ 21

x ≥ 3

Thus, the minimum value of the x is 3 to make the area A bigger than Area B.

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Answer:

[tex]{ \tt{f•g(x) = 4(2x + 5) {}^{2} }} \\ = { \tt{4(4 {x}^{2} + 20x + 25)}} \\ = { \tt{ {8x}^{2} + 80x + 100}} \\ \\ { \tt{f•g( - 3) = 8 {( - 3)}^{2} + 80( - 3) + 100 }} \\ { \tt{f•g( - 3) = 72 - 240 + 100}} \\ { \tt{f•g( - 3) = - 68}} \\ \\ \\ { \tt{g•f(x) = 2( {4x}^{2}) + 5 }} \\ { \tt{ = {8x}^{2} + 5 }} \\ { \tt{g•f( - 3) = 8 {( - 3)}^{2} + 5}} \\ { \tt{g•f( - 3) = 77}}[/tex]

Using system of three equations, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.

The standard form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Substituting the values of the x and y coordinates of each point to the standard form of the equation of a circle, the three system of equations are:

(x - h)^2 + (y - k)^2 = r^2

(0 , 0) : (0 - h)^2 + (0 - k)^2 = r^2

(6 , 8) : (6 - h)^2 + (8 - k)^2 = r^2

(7 , 7) : (7 - h)^2 + (7 - k)^2 = r^2

Expanding these equations,

(0 , 0) : h^2 + k^2 = r^2     (equation 1)

(6 , 8) : 36 - 12h + h^2 + 64 - 16k + k^2 = r^2     (equation 2)

(7 , 7) : 49 - 14h + h^2 + 49 - 14k + k^2 = r^2     (equation 3)

Subtracting equation 1 from equation 2 and 3.

36 - 12h + h^2 + 64 - 16k + k^2 = r^2

-                (h^2 +                 k^2 = r^2)

36 - 12h           + 64 - 16k           = 0

100 - 12h - 16k = 0

12h + 16k = 100

Dividing both sides by 4,

3h + 4k = 25     (equation 4)

49 - 14h + h^2 + 49 - 14k + k^2 = r^2

-                (h^2 +                 k^2 = r^2)

49 - 14h            + 49 - 14k          = 0

98 - 14h - 14k = 0

14h - 14k = 98

h + k = 4     (equation 5)

h = 7 - k

Substitute h = 7 - k to equation 4 and solve for k.

3h + 4k = 25     (equation 4)

3(7 - k) + 4k = 25

21 - 3k + 4k = 25

k = 25 - 21

k = 4

Substitute the value of k to equation 5 and solve for h.

h = 7 - k     (equation 5)

h = 7 - 4

h = 3

Substitute the value of h and k to equation 1 and solve for r.

h^2 + k^2 = r^2     (equation 1)

3^2 + 4^2 = r^2

9 + 16 = r^2

r^2 = 25

r = 5

Hence, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.

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Answer: A

Step-by-step explanation: took the quiz got it right

Answer:

1.76.

Step-by-step explanation:

1.32 ÷ 12 = 0.11

16 x 0.11 = 1.76.

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The midpoint is at ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

In the given statement is

To find the midpoint of the line segment joining the pair of points

B(√3, 2,2√2) and C(-2√3, 4,4√2)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2} ,[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points B(√3, 2,2√2) and C(-2√3, 4,4√2)

Solving for the midpoint , we have,

m = ([tex]\frac{\sqrt{3}+(-2\sqrt{3} ) }{2}, \ \frac{2+4}{2}, \frac{2\sqrt{2} +4\sqrt{2} }{2}[/tex])

m = [tex]\frac{-2\sqrt{3} }{2} ,\frac{6}{2},\frac{6\sqrt{2} }{2}[/tex]

m = ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

Therefore, the midpoint is at( [tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

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Kittens without black markings to kittens with black markings: 2:5

Kittens without black markings to total kittens: 2:7

Kittens with black markings to total kittens: 5:7

The value of the function  (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.

We are given the functions:

f(x) = x + 3

g(x) = x² − 2

Now,

(f + g) (−8) × (f + g)(−8)

= [ (f + g) (−8) ]²

Substituting the values of the functions, we get that:

=(x + 3 + x² - 2)² ,   where x = -8

= ( -8 + 3 + 64 - 2 )²

= ( -5 + 62)²

= (57) ²

= 3249

So, the value of the function  (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.

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According to the question, determine whether the given sequence converges or diverges.

The given sequence is: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} }[/tex]

Taking limits tends to infinity on both sides. And dividing numerator and denominator by [tex]n^{2}[/tex]

Therefore, the final term can be re-written as: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} } = \frac{3}{8}[/tex].

Hence, the given sequence converges and the limit is [tex]\frac{3}{8}[/tex].

What converges and diverges in limits?

When the limits of the sequence exist and have finite value that means the sequence is a convergent sequence. The calculated value is a real number. And the tem divergence means limits do not exist.

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The y-intercept is the amount she got as gifts during her graduation.

The equation in slope intercept form is $630 + $60b

The slope intercept form is used to write equations for equations for linear equations with two variables. The graph for a  slope intercept form is a straight line.

The form for  slope intercept form is: y = mx + b

Where:

The y-intercept is the constant. It represents the point where the slope touches the y-axis.

The first step is to determine how much are earnings are and how much the gift is.

The equations that would be used to determine this are:

a +2b = 750 equation 1

a + 4b = 870 equation 2

Where:

a = gift

b = amount earned weekly while working on the golf course

Subtract equation 2 from equation 1: 2b = 120

Divide both sides of the equation by 4: b = $60

Substitute for b in equation 1

a + 2(60) = 750

a + 120 = 750

a = 750 - 120

a = 630

The y-intercept is $630.

The equation in slope intercept form is: $630 + $60w

Where w is the number of weeks that Betty works.

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The equation of the line in slope-intercept form with a slope of -3/8 and y-intercept of (0 , 12) is y = (-3/8)x + 12.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given that the slope of the line is -3/8 and the y-intercept is (0 , 12), write the equation of the line by simply plugging in its values.

y = mx + b

y = (-3/8)x + 12

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The two consecutive odd integers are less than 76 is the numbers are 37 and 39.

Any integer's reverse and sum are both equal to zero.

A positive sum results from adding two positive numbers, whereas a negative sum results from adding two negative integers.

Take the absolute value of each integer, then subtraction, to obtain the total of a positive and a negative integer.

Let two consecutive odd numbers be x and x+2

According to question

⇒ x........... equation (1)

⇒ x+2........equation (2)

by adding equation 1 and 2

⇒ x+x+2=76

⇒ 2x+2=76

⇒ 2x=76-2

⇒ 2x=74    

⇒  x=74/2

⇒ x=37

We apply the value of x=37 in equation (2)

⇒ x+2

⇒ 37+2

⇒ 39

so, the numbers are 37 and 39.

Therefore, the two consecutive odd integers are less than 76 is the numbers are 37 and 39

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