given angle2 and angle 4 are vertical angels. prove angle 2 cong angle 4

Step-by-step explanation:

8x(7y+2)-4(7y+2)

=56xy+16x-28y-8

Answer:

56xy+16x-28y-8

Step-by-step explanation:

you have to use the FOIL method to solve this is problem which is

F-First

O-Outer

I-Inner

F-Last

Answer:

Y=15 when x=5

Step-by-step explanation:

if y= -6 when x= -2

So y=? When x=5

Y=15

Hope this helps

Good Luck

Answer:

x = 12:15=×5

36

060

Step-by-step explanation:

12:15=0

x=0

Answer:

4

Step-by-step explanation:

Divide the left side by 3

12:15

12/3 : 15/3

4:5

x would be 4

Answer:

[tex]900[/tex]

Step-by-step explanation:

[tex]892/10=89.2\\893/10=89.3\\894/10=89.4\\895/10=89.5\\896/10=89.6\\897/10=89.7\\898/10=89.8\\899/10=89.9\\900/10=90\\901/10=90.1\\902/10=90.2\\903/10=90.3\\904/10=90.4\\905/10=90.5\\906/10=90.6\\907/10=90.7\\908/10=90.8\\909/10=90.9[/tex]

Answer:

4

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

[tex]a_{n}[/tex] = 11 +(n - 1)4 , then

d = 4

The recursive formula allows a term in the sequence to be found by adding d to the previous term, thus

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 4

Answer:

The answer is 4

Step-by-step explanation:

Answer:

so 2a+3b=±13

Step-by-step explanation:

4a²+9b²=97

ab=6

2a+3b=?

by using formula

(a+b)²=a²+b²+2ab

(2a+3b)²=(2a)²+(3b)²+2(2a)(3b)

(2a+3b)²=4a²+9b²+12ab

putting values

(2a+3b)²=97+12(6)

(2a+3b)²=97+72

(2a+3b)²=169

taking square root on both sides

√(2a+3b)²=√169

2a+3b=±13

i hope it will help you

Answer:

2a+3b = 13

Step-by-step explanation:

Using this formula

[tex](x+y)^2 = x^2+y^2+2xy[/tex]

Where,

x = 2a and y = 3b

Putting in the above formula

=> [tex](2a+3b)^2=4a^2+9b^2+12ab[/tex]

Putting  4a²+9b² = 97 and ab = 6

=> (2a+3b)² = 97+12(6)

=> (2a+3b)² = 97+72

=> (2a+3b)² = 169

Taking sqrt on both sides

=> 2a+3b = 13

Answer:

t ≤ 4.24

Step-by-step explanation:

P(t) ≥ 40000 implies

500t/(2t²+9) ≥ 40000

Multiplying through by t², we have

500t ≥ 40000(2t²+9)

500t/40000 ≥ 2t²+9

Collecting like terms

0.0125t  ≥ 2t²+9

0  ≥ 2t²+ 9 - 0.0125t

2t²+ 9 - 0.0125t  ≤ 0

2t²- 0.0125t + 9 ≤ 0

Using the quadratic formula,

[tex]t = \frac{-(-0.0125) +/-\sqrt{(-.0125)^{2} - 4 X 2 X 9} }{2 X 2} \\= \frac{0.0125 +/-\sqrt{(0.00015625 - 288} }{4}\\= \frac{0.0125 +/-\sqrt{-287.9998} }{4}\\= \frac{0.0125 +/-16.97i }{4}\\=0.00313 + 4.24i or 0.00313 - 4.24i[/tex]

The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)

So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0

(t - 0.00313)² - 4.24² ≤ 0

(t - 0.00313)² ≤ 4.24²

taking square-root of both sides,

√(t - 0.00313)² ≤ √4.24²  

t - 0.00313 ≤ 4.24

t ≤ 4.24 + 0.00313

t ≤ 4.24313 ≅ 4.24

t ≤ 4.24

Answer: y = 1/2x - 6

Step-by-step explanation:

#4 We are going to use slope intercept form, (y = mx+b)

1. The line crossing the y-intercept at (0,-6)

2. The slope is 1/2 (increasing by 1 then over 2 --> RISE OVER RUN)

3. Make the equation: y= 1/2x - 6

Answer: 3 . y = -1/3 + 4/3   4. y= 1/2x -6

Step-by-step explanation:

3.   In the first graph  they have the coordinates,  (-2,2)  and (4,0). We have to solve for the slope and the y-intercept in other to write and equation.

To find the slope we have to find the change in the y values  and divide it by the difference in the x values.

2-0 = 2

-2 -4 = -6

2/-6 =  -1/3  Now we know that the slope is -1/3  so we need to  find the y-intercept.

2= -1/3(-2) +b   where be is the y intercept.

2= 2/3 + b

-2/3  -2/3

b= 4/3  

Now we could write the equation as  y= -1/3 + 4/3  

4. The same with number 4.  

We will find the slope and the y intercept by using some points on the number line.

(0,-6)  This already have the y-intercept graphed so we will need to just find the slope.

(0,-6)

(4,-4)  

-6 - (-4) = -2

0 - 4 =  -4

-2/-4 = 1/2

Equation: y = 1/2x  -6

Answer: 0.5

Step-by-step explanation:

Total bags (U) = 140

Number of bags with both button and zip:

(48 + 47 + x + 22) = 140

117 + x = 140

x = 140 - 117

x = 23

Therefore, probability that bag has button :

Total Number of bags with button:

(Bags with button alone + bags with both button and zip)

(47 + 23) = 70

Probability = (required outcome / Total possible outcomes)

P(bag has button) = (number of bags with button / total number of bags)

P(bag has button) = 70/140 = 0.5

P(bag has button) = 0.5

Step-by-step explanation:

We have,

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :

[tex]h=-16t^2 + 36t + 10[/tex] ......(1)

Part (a) :

The maximum height reached by the ball is given by :

[tex]\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s[/tex]

Part (b) :

The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :

[tex]h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m[/tex]

Answer:

9.31?

Step-by-step explanation:

Answer:

Do it your self

Step-by-step explanation:

Answer:

A car can travel 45 miles every hour, because I multiply 3/4 (0.75) by 60. Because of this, 60 minutes is an hour.

Step-by-step explanation:

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer:

280 ft2

Step-by-step explanation:

The lateral area of this prism consists of seven rectangles, each one with dimensions 4 feet by 10 feet.

The area of one of these rectangles is:

[tex]A = base * height = 4 * 10 = 40\ ft^2[/tex]

Then, the area of the seven rectangles is:

[tex]Lateral\ area = 7*A = 7*40 = 280\ ft^2[/tex]

So the lateral area of this prism is 280 ft2.

1 pound = 1.62 dollars.

Multiply total pounds by 1.62 for total dollars.

650 x 1.62 = $1,053

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

https://brainly.com/question/17615619

#SPJ2

Answer:

20 red sweets

Step-by-step explanation:

do two thirds of 30 and the part that cane out is the red sweets

Answer:

12

Step-by-step explanation:

Sum the parts of the ratio, 2 + 3 = 5 parts

Divide the number of sweets by 5 to find the value of one part of the ratio

30 ÷ 5 = 6 sweets ← value of 1 part of the ratio, thus

2 × 6 = 12 ← number of red sweets

Answer:

(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

Step-by-step explanation:

When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]

PART A

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]

PART B

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]

ii) Not a perfect square  

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]

iii) A multiple of 5  

Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

[tex]=\dfrac{15}{64}\\=0.234375[/tex]

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]

Answer:

unanswerable,don't censore the question

Step-by-step explanation:

sorry pal

Answer:

n is the seventh term=5832

Step-by-step explanation:

a1=8

r=3

a(n)=a1*r^(n-1)=

an=8*3(n-1)

8+24+72+216+648+1944+5832=8744

Answer: [tex]y \leq \frac{1}{2} x+3[/tex]

Step-by-step explanation:

If a function has a positive slope, that means the y value is increasing with respect to x. As you go down the x-axis, the y value will continuously increase.

First you want to plot the two sets of coords that they gave you, or else you wont know what the line looks like. Or, you could visually do it in your head. We're going down -4 on the x-axis and down 1 on the y-axis. Then for our second coords, we are going to 0 on the x-axis, then up 3 on the y-axis.

You could plot this for yourself, but im going to do it in my head for simplicity. We also need to find the slope of this function in order for us to find the y-intercept. The slope is change in y divided by the change in x. Subtract the initial position from the final position.

3 - 1 = 2

0 - (-4) = 4

2/4 = 1/2

The new equation is:

[tex]y=\frac{1}{2} x+b\\plugin(0,3)\\3=\frac{1}{2} (0)+b\\b=3[/tex]

Everything is shaded below and to the right of the line. They said the line was solid, so that means less than or equal to, [tex]\leq[/tex]

Answer:

B

Step-by-step explanation:

Answer:

35 cm

Step-by-step explanation:

As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,

The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:

2(length + width) = Perimeter

2(2x + x) = 21

2(3x) = 21

6x = 21

x = 21/6 = 3.5 cm

x = 3.5 cm

From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:

2(length + width) = Perimeter

2(3x + 2x) = Perimeter

Perimeter = 2(5x)

Perimeter = 10x

Perimeter = 10(3.5)

Perimeter = 35 cm

Answer:

Option (3)

Step-by-step explanation:

Given expression in this question represents the partial sum of an infinite geometric series in the sigma notation.

[tex]S_{n}=\sum_{n=1}^{\infty}6(2)^{n-1}[/tex]

First term of this series 'a' = 6

Common ratio 'r' = 2

We have to find the sum of 4 terms of this infinite series (n = 4).

Sum of n terms of a geometric series is,

[tex]S_n=\frac{a(r^n-1)}{(r-1)}[/tex]

[tex]S_4=\frac{6(2^4-1)}{(2-1)}[/tex]

    [tex]=\frac{6(16-1)}{(1)}[/tex]

    [tex]=90[/tex]

Therefore, sum of 4 terms of the given series will be 90.

Option (3) will be the answer.

Step-by-step explanation:

5f

5 + n times of a number

Answer:

-1.67

Step-by-step explanation:

Answer:

63 cm

Step-by-step explanation:

piece 1: x

piece 2: x - 18

First you would subtract 2x - 18 = 108

Second you would add 108 + 18 = 2x

Third you would divide 126 divided by 2x = 63

So that would mean x = 63

Answer:

63cm

Step-by-step explanation:

2 pieces of rope, and one is shorter by 18cm.

piece 1: x

piece 2: x-18

Add the equations together, combine both pieces

2x-18

2x-18 = 108

108+18 = 2x

126 = 2x

x = 63

Answer:

2/6 or 1/3

Step-by-step explanation:

There are two numbers who are equal or less than 2 its 1 and 2

And the total is 6 so its 2/6 which is 1/3

Sorry if this is late

Answer:

0.33

Step-by-step explanation:

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x