part 1:
Which set of angle measures could be the interior angles of a triangle?
A.
15°, 25°, 50°
B.
23°, 67°, 90°
C.
25°, 58°, 102°
D.
38°, 42°, 80°
part 2:
Which set of side lengths could be the sides of a triangle?
A.
1 cm, 2 cm, 3 cm
B.
5 cm, 9 cm, 18 cm
C.
7 cm, 16 cm, 24 cm
D.
10 cm, 24 cm, 26 cm

The interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

In this question we have an expression that combines polynomic and exponential expression, whose variable x cannot be cleared by analytical approaches, but by numerical and graphical methods. Herein we decide to find the interval by graphical methods, using a graphing tool:

First, write the function in explicit form (f(x) = 3 · x - eˣ). Second, find the two points such that the function goes through the x-axis (horizontal axis). Third, define the set of possible x-values by interval notation such that y > 0.

Then, the points of the function that are on the x-axis are (x₁, y₁) = (0.6191, 0) and (x₂, y₂) = (1.5121, 0). Then, the interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

To learn more on functions: https://brainly.com/question/12431044

#SPJ1

Given, equation of curve is

\(y = \frac{(x - 7)}{(x - 2)(x - 3)} .....(1)\\\)

To find the intersection of given curve with X-axis, Put y = 0 in equation 1, we get,

\(0 = \frac{(x - 7)}{(x - 2)(x - 3)} ......(2) \\ \)

x − 7 = 0 ⟹ x = 7

Thus, the curve cut the X-axis at (7,0).

Now, on differentiating equation of curve w.r.t. x, we get,

\( \frac{dy}{dx} \\ = \frac{(x - 2)(x - 3).1 - (x - 7)[(x - 2).1 + (x - 3).1]}{[(x-2)(x - 3) {}^{2}]} \)

Next answer is in pic.

Answer: x² + 3x - 10

Step-by-step explanation:

(x + 5)(x - 2)

Distribute:

x² - 2x + 5x - 10

Combine like terms:

x² + 3x - 10

Hope this helps!

Answer:

alternate interior angles are congruent

Answer:

Solution,

f(X)= 2x-1

g(X)= 7x-12

Now,

\(h(x) = f(x) + g(x) \\ \: \: \: \: \: = 2x - 1 + 7x - 12 \\ \: \: \: \: = 2x + 7x - 1 - 12 \\ \: \: \: \: \: = 9x - 13\)

Hope this helps...

Good luck on your assignment...

Answer:

[6, 8).

Step-by-step explanation:

When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.

In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.

Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.

Applying internal notation, the range of this function is:

[6, 8).

Learn more about interval notation here:

1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.

2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.

Answer:

C: EAF Is the correct answer

Answer:

science only is 220

math only is 180

either math or science is 60

(1) The sample size (n)>30 and population standard deviation (σ) is unknown then we use one sample t-test we get.

(2) There is sufficient evidence to conclude that, the customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised.

Test the hypothesis that the client is prepared to buy a watch unless it can be shown that the average lifespan is shorter than what is claimed using a significance level of α=0.05.

Given that,

Sample size (n)=50

Sample mean (x−)=738.44

Sample standard deviation (S)=38.2 where (S)2=1,459.24

The null and alternative hypothesis are,

H(0): μ≥800

vs

H(1): μ<800

(1) In the given question we have to explain why the test statistic has a normal distribution despite the experimenter being unaware of the distribution of the population of digital watches.

The sample size (n)>30 and population standard deviation (σ) is unknown then we use one sample t-test we get.

(2) In the given question we have to devise an appropriate hypothesis test to determine whether the given customer is willing to purchase a digital watch.

Then test statistic becomes,

t = x−μ/(s/√n)

t = 738.44−800/(38.2/√50)

t = −61.56/5.40229

t = −11.40

Here the test is one tailed (left tailed) at α=0.05

Then degrees of freedom=(n-1)=(50−1)=49

Thus P-value becomes,

P-value = <0.00001

The P-value is less than or equal to α=0.05

Then we reject the null hypothesis H(0).

We use excel command to find the P-value we get,

=T.DIST( x, deg _freedom, TRUE)

=T.DIST(-11.40 , 49,TRUE)

=<0.00001

There is sufficient evidence to conclude that, the customer is willing to purchase a watch unless it can be demonstrated that the average lifetime is shorter than what is advertised.

To learn more about Hypothesis Test link is here

brainly.com/question/17099835

#SPJ4

The right question is given below:

Answer: 6/10

Step-by-step explanation: Six parts are shaded and even though the shaded parts are not touching each other, they will still count as shaded. 4 parts are not shaded and there is a total of 10 parts so the answer would be 6/10.

Hoped This Helped!

Answer:

If it is asking for the fraction of shaded parts the answer is A

If it is asking for the fraction of non-shaded parts the answer is B

Step-by-step explanation:

I would most likely go with A, because I have very rarely gotten a question asking for the non-shaded parts.

Answer:

What do we have to do in this? Find x? Let me know I'll explain it in the comment section

Answer:

Step-by-step explanation:

Answer:

the approximate distance between the points is

√25+25 = 5√2

=7.07

Step-by-step explanation:

The rectangular coordinates for the given point are.

x = cos(60°) = 1/2

y = sin(60°) = √3/2

For a polar point (R, θ), the rectangular coordinates are:

x = R*cos(θ)

y = R*sin(θ)

Here we have the unit circle, so R = 1.

And we can see that θ = 60°

Then the coordinates are:

x = cos(60°) = 1/2

y = sin(60°) = √3/2

These are the coordinates.

Learn more about polar coordinates at:

https://brainly.com/question/14965899

#SPJ1

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

Laern more about continuous functions at:

https://brainly.com/question/18102431

#SPJ1

Step-by-step explanation:

what's the problem ?

you need to calculate the area of each rectangle and sum them all up.

that is then the total surface area of the whole prism (or "box").

we have 2 rectangles of 4×3.8

2 rectangles of 11.5×3.8

and 2 rectangles of 11.5×4

so, the total is

2×4×3.8 + 2×11.5×3.8 + 2×11.5×4 = 30.4 + 87.4 + 92 =

= 209.8 m²

Answer:

16 boys

Step-by-step explanation:

Answer:

16 boys

Step-by-step explanation:

24 x 2 = 48

48/3 = 16

The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

For more question on return visit:

https://brainly.com/question/30761579

#SPJ8

Answer:

13, 8, 4, 0

Step-by-step explanation:

The absolute value symbol turns the number into positive numbers. After that, all you need to do is find is greatest to least order.

Hope This Helps :)

Answer:

Step-by-step explanation:

how

how you get 800 in 8000000 to 87777

The coordinates of A' and B' include the following:

A' (4, 7).

B' (10, 9).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 2 centered at the point (6, 3) by using the following mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A', we have;

Coordinate A' = (5, 5)  →  (2(5 - 6) + 6, 2(5 - 3) + 3)

Coordinate A' = (5, 5)  →  (2(-1) + 6, 2(2) + 3)

Coordinate A' = (5, 5)  →  (-2 + 6, 4 + 3)

Coordinate A' = (5, 5)  →  (4, 7)

For coordinate B', we have;

Coordinate B' = (8, 6)  →  (2(8 - 6) + 6, 2(6 - 3) + 3)

Coordinate B' = (5, 5)  →  (2(2) + 6, 2(3) + 3)

Coordinate B' = (5, 5)  →  (4 + 6, 6 + 3)

Coordinate B' = (5, 5)  →  (10, 9)

Read more on dilation here: brainly.com/question/20482938

#SPJ1

Step-by-step explanation:

10×10+24×24= third side ×third side

third side ×third side =100+576

third side × third side=676

third side=√676

third side=26

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

For such more questions on translated

https://brainly.com/question/12861087

#SPJ8

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

For similar question on proportion.

https://brainly.com/question/29864115  

#SPJ8

The solution of the system of equations are  x = - 6 , y = 44 and z = 2

Given,

The system of equations;

3x + y - 2z = 22

x + 5y + z = 4

x = -3z

We have to solve the given equations;

Substitute x = -3z in both equations;

3x + y - 2z = 22

⇒ 3 × -3z + y - 2z = 22

⇒ - 9z + y - 2z = 22

⇒ - 11z + y = 22

And,

x + 5y + z = 4

⇒ - 3z + 5y + z = 4

⇒ 5y - 2z = 4  

Solve the equations  - 11z + y = 22  and 5y - 2z = 4  

We get,

⇒ y = 44 and z = 2

So, x = - 3z    

⇒ x = - 3 × 2

⇒ x = - 6

Thus, The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

Learn more about solution for system of equations here;

https://brainly.com/question/29040805

#SPJ1

Solution:

Note that:

Using cross multiplication:

Using the division property of equality.

Each day, Cornell ate 11/60 gallons of soup.

The amount of gallons of soup Cornell ate each day was 11/60

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total \(x\) parts, where \(x\) is the number of parts the given number is divided.

Thus, \(a \div b\) = a divided in b equal parts.

Also, we can write: \(a \div b = a \times \dfrac{1}{b}\)

(it is since a = a times 1 so \(a/b = 1 \times (a/b) = (1/b) \times a\))

For the given case, we're given that:

Total amount of soup Cornell ate in 5 days = 11/12 gallons.
Cornell ate equal amount of soup each day.

Due to this equal amount of soup eating, we can use division.

The amount of soup Cornell ate each day = 11/12 divided in  5 equal parts

The amount of soup Cornell ate each day = \(\dfrac{11}{12} \div 5 = \dfrac{11}{12} \times {1}{5} = \dfrac{11}{60}\)

Thus, the amount of gallons of soup Cornell ate each day was 11/60

Learn more about division here:

https://brainly.com/question/26411682

Answer:

angle 1 is 45 degrees

Step-by-step explanation:

all triangles are equal to 180 degrees

59+76 + x = 180

x =45

The complete question is;

when graphed on a coordinate plane, Bumby avenue can be represented by the equation y = -4x - 7. Primrose Avenue can be represented by the equation 8x + 2y = 17. Are these two parallel?

A) They are parallel because their slopes are the same

B) They are not parallel because their slopes are the same

C) They are parallel because their slopes are opposite reciprocals

D) They are not parallel because their slopes are opposite reciprocals

Answer:

Option D: They are not parallel because their slopes are opposite reciprocals

Step-by-step explanation:

Bumby avenue is represented by the equation y = -4x - 7 while Primrose Avenue can be represented by the equation 8x + 2y = 17.

Now, the general formula for slope intercept is;. y = mx + c.

Where m is the slope and c is the y - intercept.

This means the slope of bamby is - 4 while that of Primrose is 8.

The slopes are not the same and so options A and B are not correct.

Now, -4 is an opposite reciprocal of 8/-2.

But an opposite reciprocal means that both lines on the graph are perpendicular to each other.

Thus, option C is wrong because they are not parallel.

So correct option is D.