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Express in the form n : 1
14:7
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The interior angle of any triangle sum to 180° in measure, so that angle ACB has measure

m∠ACB = 180° - 67° - 35° = 78°

Angles ACB and BCD are supplementary because they occur on the same ray AD, which means they also sum to 180° in measure. Then angle BCD has measure

m∠BCD = 180° - 78° = 102°

Answer:

102 degrees

Step-by-step explanation:

for this problem, add the angles given to 180 degrees to find the remaining angle ACB in the triangle. Once you have that angle, you can subtract it from 180 degrees to find BCD, because side ACD is straight. By adding Angle CAB (67 degrees) and Angle ABC (35 degrees), you end up with the missing 98 degrees to reach 180 degrees. thus, when subtracting to find BCD on the straight of ACD, a value of 102 degrees remains for Angle BCD

Answer:

1. x = 6 cm

2. The coordinates of the x-intercept are (-15.798879, 0) and (8.177004, 0)

b) The maximum value of is y is approximately 459.874

The value of 'x' for which the maximum occurs is x is -3.8109375

c) 'k' is approximately -15.63748 or 'k' is approximately 8.0156

Step-by-step explanation:

1. The area of rectangle ABCD - Area of triangle ABP = 114 cm²

Therefore, we have;

The area of rectangle ABCD = (2·x - 3)·(3·x + 1)

∴ The area of rectangle ABCD = 6·x² + 2·x - 9·x - 3 = 6·x² - 7·x - 3

The area of triangle ABP = 1/2 × (3·x + 1)·x = 3·x²/2 + x/2

The area of rectangle ABCD - Area of triangle ABP = 6·x² - 7·x - 3 - 3·x²/2 - x/2

6·x² - 7·x - 3 - 3·x²/2 + x/2 = 9·x²/2 - 13·x/2 - 3 = 114

9·x²/2 - 15·x/2 - 3 = 114

9·x² - 15·x - 6 - 228 = 0

9·x² - 15·x - 234 = 0

x = (15 ± √((-15)² - 4 × 9 × (-234)))/(2 × 9) = (15 ± 93)/18

∴ x = 6 or x = -13/3

Given that x is a natural number, we have that x = 6 cm

2. The given equation is 'y = -3.2·x² - 24.39·x + 413.4'

Therefore, we have;

The x-intercept are the values of 'x', where the value of 'y' is 0

Therefore, we have, at the x-intercept;

y = 0 = -3.2·x² - 24.39·x + 413.4

By the quadratic formula, we have;

x = (24.39 ± (√((-24.39)² - 4×(-3.2)×413.4)))/(2 × (-3.2))

x ≈ -15.798879 or x ≈ 8.177004

The coordinates of the x-intercept are;

(-15.798879, 0) and (8.177004, 0)

b) The maximum is given at dy/dx = 0

Therefore, at the maximum point, we have;

dy/dx = d(-3.2·x² - 24.39·x + 413.4)/dx = -6.4·x - 24.39 = 0

dy/dx = -6.4·x - 24.39 = 0

∴ x = 24.39/(-6.4) = -3.8109375

x = -3.8109375 at the maximum point

At the maximum point, we have;

y = -3.2·x² - 24.39·x + 413.4 = -3.2·(-3.8109375)² - 24.39·(-3.8109375) + 413.4 ≈ 459.874

y ≈ 459.874

Therefore, the maximum value of 'y' is given as follows

[tex]y_{max}[/tex]  ≈ 459.874

The value of 'x' for which the maximum occurs is x = -3.8109375

c) The coordinate of the point is (12.3, k), therefore, we have;

y = -3.2·x² - 24.39·x + 413.4

When y = 12.3, therefore, -3.2·x² - 24.39·x + 413.4 = 12.3

-3.2·x² - 24.39·x + 413.4 = 12.3

-3.2·x² - 24.39·x + 413.4 - 12.3 = -3.2·x² - 24.39·x + 401.1 = 0

By the quadratic formula, we have;

x = (24.39 ± √((-24.39)² - 4×(-3.2)×401.1))/(2 × (-3.2))

x ≈ -15.63748 or x ≈ 8.015600

Therefore, k ≈ -15.63748 or k ≈ 8.015600

Answer:

$3.07

Step-by-step explanation:

36.84/12=3.07

ndixbslwofbnslaoqhfb

Answer: 254, 255, 256

Step-by-step explanation:

Divide the total by 3 to get the integer in the middle. 255.

Subtract 1 to get the first integer, 254.

Add 255 + 1 to get the third integer, 256.

Answer:

cx

Step-by-step explanation:

Answer:

Quotient: 56 Remainder: 3

Answer: It is a strong positive correlation,and it is not likely causal.

Step-by-step explanation: Correlation Coefficient value is used to determine the strength of linear relationship between two variables. The value ranges from - 1 to +1.with negative values depicting a negative relationship and positive values showing positive relationship. Value of 0 implies that, no relationship exists. The closer the correlation Coefficient value is to +1 or - 1, the greater the strength of the relationship between them. Also correlation does not mean causation. Hence, a correlation coefficient of 0.74 depicts a strong positive relationship. However it doesn't imply causation.

The given correlation is strong positive correlation,and it is not likely causal.

We have given that,

The correlation coefficient relating the two variables is 0.74.

Correlation coefficient value is used to determine the strength of linear relationship between two variables. The value ranges from - 1 to +1.

The correlation coefficient value is used to determine the strength of linear relationship between two variables. The value ranges from - 1 to +1.

with negative values depicting a negative relationship and positive values showing positive relationship.

The value of 0 implies that, no relationship exists.

The closer the correlation coefficient value is to +1 or - 1, the greater the strength of the relationship between them.

Also correlation does not mean causation.

Hence, a correlation coefficient of 0.74 depicts a strong positive relationship.

However it doesn't imply causation.

We have the given correlation coefficient relating the two variables is 0.74 and it is near +1

Therefore,the given correlation is strong positive correlation,and it is not likely causal.

To learn more about the correlation coefficient visit:

https://brainly.com/question/4219149

Answer:

Last one

Step-by-step explanation:

The slope intercept form is: y=mx +b

m=the slope and b is the y intercept

so it would be the last one

Answer:

Step-by-step explanation:

Make a quadratic:

2[tex]x^{2}[/tex]-8x+7=0

Then use quadratic formula to solve.

It would be x=   2 ±   [tex]\frac{2}{\sqrt{2} }[/tex]

Answer:

(helps)

Step-by-step explanation:

Answer:

simplified: (16/81)

rewritten: (2/3)^4

Step-by-step explanation:

hope this helps! if wrong you can delete it :)

Answer:

Elena's run for 1.17 miles in ten minutes

Step-by-step explanation:

From the question

y = 8.5 x ; where x is Distance in miles, and y is time in minutes

and y= 10 minutes

thus on substituting the respected values we get

10 = 8.5 x

⇒ x  = [tex]\frac{10}{8.5}[/tex]  = 1.17 miles

Therefore Elena's run for 1.17 miles in ten minutes

The required equation that models the bee population (b) is y = 2000x + 500

The equation of a line in slope-intercept form is expressed as y = mx + b

where;

Using the coordinate points on the graph (2, 2000) and (3, 4000)

Get the slope of the line

[tex]m=\frac{4000-2000}{3-2}\\m=\frac{2000}{1}\\m=2000[/tex]

Since one of the coordinate points lies on the y-axis at (0, 500), hence the y-intercept is 500.

The required equation that models the bee population (b) is y = 2000x + 500

Learn more on equation of a line here: https://brainly.com/question/13763238

Step-by-step explanation:

Scale factor

= Side length of big triangle / Side length of small triangle

= 12/5 = 24/10 = 33.6/14 = 2.4.

Answer: 2.4

Step-by-step explanation:

10 × 2.4 = 24

5 × 2.4 = 12

14 × 2.4 = 33.6

Answer:

The greatest common factor in that expression is 3x², giving you the expression:

3x²(-x² + 4x -7)

Step-by-step explanation:

All three terms are divisible by three:

3(-x⁴ + 4x³ - 7x²)

Each term is also divisible by x²:

3x²(-x² + 4x -7)

So the greatest common factor is 3x²

Answer:

14c-16

Step-by-step explanation:

Answer:

14c - 16

Step-by-step explanation:

2( 7c - 8 )  All you do is distribute:

14c - 16

Ace

Answer:

3

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

From the question, we are informed that a survey was conducted of 880 college students attending the same university and that they were offered a list of 10 different internet service providers and were asked to select the one they prefer.

Basee on this information, if everyone selected equal numbers, each service provider will get (880 / 10 = 88 students). In this case, if someone has 89 votes, this means that another person will get 87 votes while the remaining 8 service providers gets 88 students each. Therefore, the device provider with 89 votes can come out on top.

Answer:

I think the answer would be 3.92682926829

Step-by-step explanation:

Honestly i dont think i did this right at all. But i hope i did.

Here is what i did:

0.95 + 1.10 = 2.05

8.05 divided by 2.05 = 3.92682926829

Im so sorry if you get this wrong. I honestly am having an off day. Good luck :(

Answer:

The correct answer is 9.15625

✧brainliest appreciated✧

Answer:

9.15625

Step-by-step explanation:

step 1- Convert the proper fraction to decimal: Divide the numerator by the denominator: 5 ÷ 32 = 0.15625

step 2- Add this decimal number to the whole number of the mixed fraction: 9+ 0.15625 = 9.15625

Therefore, the mixed number 9 5/32 converted to decimal number is: 9.15625

(can i get brainliest)

Answer:

17

Step-by-step explanation:

7(3) - 4

21 - 4

17

Answer:

i dont know

Step-by-step explanation:

i dont know

Answer:

3b/4a²

Step-by-step explanation:

3a²*4b³/16(a²b)²

12a²b³/16a⁴b²

12b/16a²

3b/4a²

Is it a 3 or 4 choice question?

Answer:

7/12 lb of sugar.

Step-by-step explanation:

first we add 1 2/3 and 2 3/4, which will give you 4 5/12 then subtract 5 lb by 4 5/12 and your answer will be 7/12

I performed a transcriptome analysis (Clariom D Array, Affymetrix) of two groups of subjects (human tissue) by using Transcriptome Analysis Console (TAC; Affymetrix) and Partek software and same cutoff (n=20; FC greater than 1.5 and P value less than 0.05). However, the overlap between differential expressed genes between both software was quite low.

someone has some comment about why this may be happening?

Answer:

8.9 meters

Step-by-step explanation:

this seems like a problem where you can use the pythagorean theorem:

you know one of the two legs (6m) and  the hypotenuse (9m), you must find the other leg

a^2 + 6^2 = 9^2

a^2 + 36 = 81

a^2 = 45

a = [tex]\sqrt{45}[/tex] or [tex]\sqrt{9}[/tex] · [tex]\sqrt{5}[/tex] which simplifies to be 3[tex]\sqrt{5}[/tex] or approx. 8.9 meters

Answer:

[tex]7^{-4}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](7^2)^{-2}[/tex]

= [tex]7^{2(-2))}[/tex]

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