What is the common ratio of this geometric sequence? 64, 16, 4, 1 ...

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

• 1 + tan²x = sec²x

• cot x = [tex]\frac{1}{tanx}[/tex]

Given

secΘ = [tex]\frac{4}{3}[/tex], then

tan²Θ = sec²Θ - 1 = ([tex]\frac{4}{3}[/tex] )² - 1 = [tex]\frac{16}{9}[/tex] - 1 = [tex]\frac{7}{9}[/tex], hence

tanΘ = ± [tex]\sqrt{\frac{7}{9} }[/tex] = ± [tex]\frac{\sqrt{7} }{3}[/tex]

Since 270° < Θ < 360° ← fourth quadrant where tanΘ < 0

Hence tanΘ = - [tex]\frac{\sqrt{7} }{3}[/tex]

and

cotΘ = [tex]\frac{1}{-\frac{\sqrt{7} }{3} }[/tex] = - [tex]\frac{3}{\sqrt{7} }[/tex] = - [tex]\frac{3\sqrt{7} }{7}[/tex]

We can solve the problem in two equivalent ways:

if we compute the 45% of the price, we have

[tex]320\cdot \dfrac{45}{100} = 14.4[/tex]

and we subtract the discount from the original price:

[tex]320-144=176[/tex]

Alternatively, we can think as follows: if we discount the 45%, it means that we pay the remaining 55%, i.e. we pay

[tex]320\cdot \dfrac{55}{100} = 176[/tex]

To calculate the sale price, first calculate the discount by multiplying the original price by the discount percentage - 320 * 0.45. Then, subtract the value of the discount from the original price to get the sale price.

The subject of this question is mathematics, specifically percentages. In order to calculate the sale price of the television, we first need to calculate the amount of the discount. The discount can be calculated by multiplying the original price of the TV (£320) by the percentage of the discount (45%). In mathematical terms, this equation can be written as 320 * 0.45. Now, subtract the discount from the original price to find the sale price: 320 - (320 * 0.45).

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Answer:

The solutions are the points (1,3) and (4,0)

Step-by-step explanation:

we have

[tex]y=x^{2} -6x+8[/tex] ----> equation A

[tex]y=-x+4[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations are the intersection points both graphs

using a graphing tool

The graph has two intersection points

therefore

the system of equations has two solutions

The solutions are the points (1,3) and (4,0)

see the attached figure

Answer:

its c on edge

Step-by-step explanation:

cause um if you look at c on edge it looks like the bestes answer

Answer:

Sets A and B . choice D

Step-by-step explanation:

A relation from a set X to a set Y is said to be a function if each individual element of X is related to exactly one element in Y. In other words, given an element x contained in X, there is only one element in Y that x is related to.

Going by this definition, Sets A and B are functions since each element in x is related to exactly one element in y.

On the other hand, Set C is not a function since the element x = 2 has two corresponding y elements, 1 and 4

Answer:

sets A and B

Step-by-step explanation:

The value of the constant in the equation is 0.4

An equation is a mathematical statement that shows the equality of two expressions. It consists of two sides, with an equal sign (=) separating them.

The expressions on either side of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to solve for an unknown value, model real-world situations, or describe relationships between different quantities.

We have the equation: Height = Constant/Width

This implies, Constant = Height * Width

Since the graph represents the plot of Height against Width, just pick any point and multiply the values to get the Constant. That is:

Constant = 0.5 * 0.8 = 0.4

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The answer is bike just do some simple math

Answer:

The solutions of the equation are √3 - 1/2 and -√3 - 1/2

Step-by-step explanation:

* Lets revise how to make the completing square

- The form of the completing square is (x - h)² + k, where h , k

 are constant

- The general form of the quadratic is x² + bx + c, where b , c

 are constant

- To change the general form to the completing square form equate  

 them and find the constant h , k

* Now lets solve the problem

∵ x² + x = 11/4 ⇒ subtract 11/4 from both sides

∴ x² + x - 11/4 = 0

- Put the equation equal the form of the completing square

∵ x² + x - 11/4 = (x - h)² + k ⇒ solve the bracket power 2

∴ x² + x - 11/4 = x² - 2hx + h² + k

- Equate the like terms

∵ x = -2hx ⇒ divide both sides by x

∴ 1 = -2h ⇒ divide both sides by -2

∴ -1/2 = h

∴ the value of h = -1/2

∵ -11/4 = h² + k

- Substitute the value of h

∴ -11/4 = (-1/2)² + k

∴ -11/4 = 1/4 + k ⇒ subtract 1/4 from both sides

∴ -12/4 = k

∴ k = -3

∴ The value of k is -3

- Substitute the value of h and k in the completing square form

∴ (x - -1/2)² + (-3) = 0

∴ (x + 1/2)² - 3 = 0 ⇒ add 3 to both sides

∴ (x + 1/2)² = 3 ⇒ take square root for both sides

∴ x + 1/2 = √3 OR x + 1/2 = -√3

∵ x + 1/2 = √3 ⇒ subtract 1/2 from both sides

∴ x = √3 - 1/2

OR

∵ x + 1/2 = -√3 ⇒ subtract 1/2 from both sides

∴ x = -√3 - 1/2

* The solutions of the equation are √3 - 1/2 and -√3 - 1/2

Answer:

5x-13=7

Step-by-step explanation:

because we have "a number" we substitute that with x.

and the rest you just plug in. hope this helps :) <3

The required number is 4.

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1.

It is given that,

[tex]5x-13=7[/tex]

Now, solve the above equation.

[tex]5x-13=7\\5x=7+13\\5x=20\\x=4[/tex]

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Answer:

[tex]\large\boxed{x=\dfrac{5\pm3\sqrt3}{2}}[/tex]

Step-by-step explanation:

[tex]Domain:\ x-5\neq0\to x\neq5\\\\\dfrac{2}{x-5}=4x\\\\\dfrac{2}{x-5}=\dfrac{4x}{1}\qquad\text{cross multiply}\\\\(4x)(x-5)=(2)(1)\qquad\text{use the distributive property}\\\\(4x)(x)+(4x)(-5)=2\\\\4x^2-20x=2\\\\2^2x^2-20x=2\\\\(2x)^2-2(2x)(5)=2\qquad\text{add}\ 5^2\ \text{to both sides}\\\\(2x)^2-2(2x)(5)+5^2=2+5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(2x-5)^2=2+25\\\\(2x-5)^2=27\to2x-5=\pm\sqrt{27}\qquad\text{add 5 to both sides}[/tex]

[tex]2x=5\pm\sqrt{9\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\2x=5\pm\sqrt9\cdot\sqrt3\\\\2x=5\pm3\sqrt3\qquad\text{divide both sides by 2}\\\\x=\dfrac{5\pm3\sqrt3}{2}[/tex]

Add/subtract common factors.

3 - 11 + 4x = -32

-8 + 4x = -32

4x = -32 + 8

4x = -24

Then, isolate the x by using division/multiplication. But for this problem, use division.

x = -24 / 4

x = -6

Answer:

see below

Step-by-step explanation:

the pattern between the numbers is that you add;

4+1=5

5+2=7

7+3=10

10+4=14

14+5=19

19+6=25

hope this helps

You add 6 to 19 in order to get to 25

Answer:

Part A: Data summary is given in the table

Part B: out of the total 100 students, 15 students do not like either tennis or track

[tex]\frac{15}{100}[/tex]  = 0.15

0.15 × [tex]\frac{100}{100}[/tex] = 15%

Part C:

Total no. of students that dislike track = 60

Total no. of students that dislike tennis = 40

According to the survey results, more people dislike track.

Answer:

Step-by-step explanation:

Given that in a survey of 100 students,  60 liked tennis, out of this 60, 15 also liked track

i.e. people who like tennis and track = 15

people who liked only tennis = 45

Peoplewho like track = 40

a)                                     Like tennis    Do not like tennis    Total

Like track                             15                     25                       40

do not like track                  45                     15                       60

Total                                     60                     40                     100

B) Percentage of the survey respondents did not like either tennis or track

= [tex]\frac{15}{100} =15%[/tex]

C) Dislike for tennis

To graph the function f(x) = -15x + 4, plot the points (0,4) and (1,-11) on the graph. The slope of the line is -15 and the y-intercept is 4.

To graph the equation f(x) = -15x + 4, you need to plot two points on a graph then draw a line through those points. First, plug in value x = 0 into the equation, you get f(0) = -15*(0) + 4 = 4. So, one point is (0,4). Second, let's plug another x value, for example, x = 1, into the function. Hence, f(1) = -15*(1) + 4 = -11, giving you the second point (1,-11).

Also remember that this is a linear function and you'll see that it forms a straight line when graphed. The slope of the line is -15, which means the line will fall to the right. The y-intercept of the line is 4, which is the point where the line crosses the y-axis.

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The graph of f(x) = -15x + 4 is a line with a slope of -15 and a y-intercept of 4. Connecting points (0, 4) and (1, -11) depicts the downward-sloping trend.

To graph the linear function f(x) = -15x + 4, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is -15, and the y-intercept (b) is 4.

To create the graph, we choose two points and connect them with a line. Let's select x = 0 and x = 1 to find the corresponding y-values.

For x = 0: y = -15(0) + 4 = 4. So, the point (0, 4) is on the graph.

For x = 1: y = -15(1) + 4 = -11. The point (1, -11) is on the graph.

Now, we can use these two points to draw the line on the coordinate plane. The line will have a negative slope, indicating a downward trend, and it intersects the y-axis at 4.

In summary, the graph of f(x) = -15x + 4 is a downward-sloping line that passes through the point (0, 4) and (1, -11).

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Answer:

Option D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Step-by-step explanation:

step 1

we know that

The SSS Similarity Theorem , states that If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar

In this problem

Verify

substitute the values

---> is true

therefore

The triangles are similar by SSS similarity theorem

step 2

we know that

The SAS Similarity Theorem , states that two triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

In this problem

Two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

therefore

The triangles are similar by SAS similarity theorem

The true statement is The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Hence, the correct answer is option (d).

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Answer:

The figure PEST is a rhombus

Step-by-step explanation:

* Lets talk about the difference between all these shapes

- At first to prove the shape is a parallelogram you must have one

 of these conditions

# Each two opposite sides are parallel OR

# Each two opposite sides are equal in length OR

# Its two diagonals bisect each other

- After that to prove the parallelogram is:

* A rectangle you must have one of these conditions

# Two adjacent sides are perpendicular to each other OR

# Its two diagonals are equal in length

* A rhombus you must have one of these conditions

# Two adjacent sides are equal in length OR

# Its two diagonals perpendicular to each other OR

# Its diagonals bisect its vertices angles

* A square you must have two of these conditions

# Its diagonals are equal and perpendicular OR

# Two adjacent sides are equal and perpendicular

* Now lets solve the problem

∵ The vertices of the quadrilateral PEST are

   P (-1 , -5) , E (8 , 2) , S (11 , 13) , T (2 , 6)

- Lets find the slope from each two points using this rule :

 m = (y2 - y1)/(x2 - x1), where m is the slope and (x1 , y1) , (x2 , y2)

 are two points on the line

- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)

∴ m of PE = (2 - -5)/(8 - -1) = 7/9

- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)

∴ m of ES = (13 - 2)/(11 - 8) = 11/3  

- Let (x1 , y1) is (11 , 13) and (x2 , y2) is (2 , 6)

∴ m of ST = (6 - 13)/(2 - 11) = -7/-9 = 7/9

- Let (x1 , y1) is (2 , 6) and (x2 , y2) is (-1 , -5)

∴ m of TP = (-5 - 6)/(-1 - 2) = -11/-3 = 11/3

∵ m PE = m ST = 7/9

∴ PE // ST ⇒ opposite sides

∵ m ES = m TP = 11/3

∴ ES // TP ⇒ opposite sides

- Each two opposite sides are parallel

∴ PEST is a parallelogram

- Lets check if the parallelogram can be rectangle or rhombus or

 square by one of the condition above

∵ If two line perpendicular , then the product of their slops = -1

- Lets check the slopes of two adjacent sides (PE an ES)

∵ m PE = 7/9

∵ m ES = 11/3

∵ m PE × m ES = 7/9 × 11/3 = 77/27 ≠ -1

∴ PE and ES are not perpendicular

∴ PEST not a rectangle or a square (the sides of the rectangle and

  the square are perpendicular to each other)

- Now lets check the length of two adjacent side by using the rule

 of distance between two points (x1 , y1) and (x2 , y2)

 d = √[(x2 - x1)² + (y2 - y1)²]

- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)

∴ PE = √[(8 - -1)² + (2 - -5)²] = √[9² + 7²] = √[81 + 49] = √130 units

- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)

∴ ES = √[(11 - 8)² + (13 - 2)²] = √[3² + 11²] = √[9 + 121] = √130 units

∴ PE = ES ⇒ two adjacent sides in parallelogram

∴ The four sides are equal

* The figure PEST is a rhombus

Answer:

Diane purchased 7 pens

Step-by-step explanation:

Let

x----> the number of pens

y----> the number of pencils

we know that

x+y=17

y=17-x -----> equation A

0.60x+0.40y=8.20 -----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for x

0.60x+0.40(17-x)=8.20

0.60x+6.8-0.40x=8.20

0.20x=8.20 -6.8

x=1.4/0.2=7 pens

Answer:  The number of pen purchased by Diane is 7.

Step-by-step explanation:  Given that Joe’s department store sells pens for 60 cents each and pencils for 40 cents each.

Diane purchased a total of 17 items for $8.20.

We are to find the number of pen that Diane purchased.

We know that

1 cent = $ 0.01.

Let x and y represents the number of pen and pencils that Diane purchased.

Then, according to the given information, we have

[tex]60\times0.01x+40\times 0.01y=8.20\\\\\Rightarrow 0.6x+0.4y=8.20\\\\\Rightarrow 6x+4y=82~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]x+y=17\\\\\Rightarrow y=17-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of y from equation (ii) in equation (i), we get

[tex]6x+4y=82\\\\\Rightarrow 6x+4(17-x)=82\\\\\Rightarrow 6x+68-4x=82\\\\\Rightarrow 2x=82-68\\\\\Rightarrow 2x=14\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]

Thus, the number of pen purchased by Diane is 7.

Final answer:

The projectile reaches its maximum height after 22 seconds, which is determined by the vertex formula t = -b/(2a) applied to the given quadratic function representing the height over time.

Explanation:

To determine after how many seconds the projectile reaches its maximum height, we need to analyze the function h(t) = -16t2 + 704t. This is a quadratic function, and the maximum height will be reached at the vertex of the parabola represented by this function.

The vertex of a parabola given by ax2 + bx + c can be found using the formula t = -b/(2a), where a, b, and c are coefficients from the quadratic equation. In this case, a = -16 and b = 704.

Using the formula to find the time t when the projectile reaches its maximum height, we calculate: t = -704/(2 × -16) = 704/32 = 22. Therefore, the projectile reaches its maximum height after 22 seconds.

Answer:

8:12, which reduces to 2:3

Step-by-step explanation:

The tennis team played 12 total matches if they won 8 and lost 4. (8+4=12). They're asking for ratio of wins to total matches. They won 8 and played twelve in total so: 8:12. Ratios are like fractions and must be reduced. So it's 2:3.

Answer:

The ratio of wins of the total number of matches played is 2/3

Step-by-step explanation:

A tennis team won 8 matches and lost 4 which means that the tennis team have played 12 matches in total.

So, the ratio of wins to the total numbers of matches played is:

Ratio of wins = won matches/total matches

Ratio of wins =  8/12 = 2/3

Without more information on the shape, it's not possible to provide the area of the figure from just the provided dimensions. Assuming it's a rectangle and using significant figures, the example calculation yields an area of 4.1 cm² when multiplying 0.6238 cm by 6.6 cm and rounding to two significant figures.

To find the area of a figure with given dimensions, one would typically multiply the length by the width. However, the question provided seems to be missing specific details about the shape of the figure. Given the figure's dimensions, if we assume it is a rectangle, the calculation would be straightforward: multiply the length by the width. Unfortunately, without additional information about the exact shape or context provided by equations or a figure reference, it is not possible to provide an accurate answer. It's essential to verify the shape and relevant equations before proceeding with the area calculation.

However, based on the examples given, to calculate the area with significant figures, one must consider the number of significant figures in the given dimensions. For example, if we multiply 0.6238 cm by 6.6 cm, the result is 4.11708 cm², which we round to 4.1 cm² (to two significant figures) because we are multiplying a number with four significant figures by a number with two significant figures.

Answer:

2 < s

Step-by-step explanation:

We need to write expression for 2 less than s

The expression 2 less than s is equal to:

2 < s

The symbol < is used for less than.

Answer:

[tex]\$20,400[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

step 1

Find the rate of interest

in this problem we have

[tex]t=4\ years\\ P=\$18,000\\ A=\$21,600\\r=?[/tex]

substitute in the formula above and solve for r

[tex]\$21,600=\$18,000(1+4r)[/tex]

[tex]1.2=(1+4r)[/tex]

[tex]4r=1.2-1[/tex]

[tex]r=0.2/4=0.05[/tex]

The rate of interest is [tex]5\%[/tex]

step 2

Find the sum of  money that will amount to 25,500 in 5 years, at the same rate of interest

in this part we have

[tex]t=5\ years\\ P=?\\ A=\$25,500\\r=0.05[/tex]

substitute in the formula above and solve for P

[tex]\$25,500=P(1+0.05*5)[/tex]

[tex]P=\$25,500/(1.25)=\$20,400[/tex]

The answer would be 17n+6.

Answer:

17n+6

Step-by-step explanation:

you add 5n and 12n and get 17n and you can't add 6 to 17n so your answer is 17n+6

Answer:

Step-by-step explanation:

The Ruler Postulate:

A distance between a number A and a number B:

AB = |B - A|

We have A = -60, and B = 13. Substitute:

|13 - (-60)| = |13 + 60| = |73| = 73

Answer:

The solutions are [tex]x=2(+/-)\sqrt{11}[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-4x-7=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}-4x=7[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]x^{2}-4x+4=7+4[/tex]

[tex]x^{2}-4x+4=11[/tex]

Rewrite as perfect squares

[tex](x-2)^{2}=11[/tex]

Take square root both sides

[tex]x-2=(+/-)\sqrt{11}[/tex]

[tex]x=2(+/-)\sqrt{11}[/tex]

The equation of the line parallel to y= (1/2) x−4 and passing through (-4, 2) is y= (1/2) x+4. The equation of the line perpendicular is y=−2x−6.

1. To find the slope of a line parallel to the given line y = (1/2)x - 4, we use the fact that parallel lines have the same slope. Therefore, the parallel line will also have a slope of 1/2.
2. Now, we can use point-slope form of linear equation, given by
[tex]y-y_1 =m(x-x_1),[/tex] where [tex](x_1 , y_1)[/tex] is a point on the line, m is the slope.
3. For the parallel line passing through (-4, 2),substitute [tex]x_1=-4, y_1 =2,[/tex] and m=1/2 into the point-slope form:
y−2= (1/2) (x+4)
4. Now, let's simplify equation to get in slope-intercept form (y=mx+b):
y−2= (1/2) x+2
5. Add 2 to both sides:
y= (1/2) x+4
6. So, the equation of the line parallel to y= (1/2) x−4 and passing through (-4, 2) is y= (1/2) x+4.
7. Now, to find the slope of a line perpendicular to the given line, we use the fact that perpendicular slopes are negative reciprocals. The slope of y= (1/2) x−4 is 1/2, so the perpendicular slope is -2.
8. Now, use the point-slope form again to find the equation of the line perpendicular to y= (1/2) x−4 and passing through (-4, 2):
y−2=−2(x+4)
9. Simplify:
y−2=−2x−8
10. Add 2 to both sides:
y=−2x−6
11. So, the equation of the line perpendicular to y= (1/2) x−4 and passing through (-4, 2) is y=−2x−6.

Complete and correct question:

Consider the graph of the line y = one-halfx – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on the line parallel to the given line, passing through (−4, 2), is . The slope of a line perpendicular to the given line is . A point on the line perpendicular to the given line, passing through (−4, 2), is .

Answer: X= -3/4, -1/2

Step-by-step explanation:

Answer:

left

Step-by-step explanation:

Answer:

left

Step-by-step explanation:

because it is a negative number you would subtract that from +5

hope this helps :)

Answer: DGC

Step-by-step explanation:

Congruent means it's equal, basically the same. In this case the question means to find a triangle that is the same shape as FGA. DGC is FGA flipped backwards, so it's the correct answer

Answer:

DGC

Step-by-step explanation:

Answer is negative 2

Answer:

The probability of not getting yellow is 2/3 ⇒ 3rd answer

Step-by-step explanation:

* Lets describe the meaning of experimental probability

- Experimental probability is the ratio of the number of times an

  event occurs to the total number of trials

∵ There are 6 blue marbles , 4 yellow marble and 2 red marbles

∴ the total number of marbles = 6 + 4 + 2 = 12 marbles

- The probability of each color is the number of the marbles have the

 same color divided by the total number of the marbles

∴ The probability of blue marbles = 6/12 = 1/2

∴ The probability of yellow marbles = 4/12 = 1/3

∴ The probability of red marbles = 2/12 = 1/6

- To find the probability of not yellow you can add the probability of

  blue and red OR subtract the probability of yellow from 1 because

  the total of probability of all colors is 1

∴ The probability of not yellow = 6/12 + 2/12 = 8/12 = 2/3

OR

∴ The probability of not yellow = 1 - 4/12 = 12/12 - 4/12 = 8/12 = 2/3

* The probability of not getting yellow is 2/3

Answer:

The correct answer is  3rd option

The probability of getting not yellow = 2/3

Step-by-step explanation:

It is given that, there are 6 blue marbles, 4 yellow marbles and 2 red marbles

To find the probability

Total number of marbles = 12 marbles

number of yellow marbles = 4 marbles

probability of getting yellow = 4/12 = 1/3

probability of getting not yellow = 1 - 1/3 = 2/3

Therefore the correct answer is 3rd option