2.
Technology required. ABCD is a rectangle. Find the length of AC and the measures of a
and e.





Help pleaseee

The exponential function is given by f(x) = 7ˣ

An exponential function is in the form:

y = abˣ

Where a is the initial value of y, b is the multiplier, y and x are variables.

Given the y-intercept is (0,1), hence:

1 = ab⁰

a = 1

Also f(2) = 49, hence:

49 = (1)(b)²

b = 7

The exponential function is given by f(x) = 7ˣ

Find out more on Exponential Function at: https://brainly.com/question/12940982

Answer:

Solution to Problem 1:

Use the fact that the sum of all three angles of a triangle is equal to 180 o to write an equation in C.

A + B + C = 180 o

Solve for C.

C = 180 o - (A + B) = 43 o

Use sine law to write an equation in b.

a / sin(A) = b / sin(B)

Solve for b.

b = a sin (B) / sin(A) = (approximately) 5.4 cm

Use the sine law to write an equation in c.

a / sin(A) = c / sin(C)

Solve for c.

c = a sin (C) / sin(A) = (approximately) 7.1 cm

Problem 2

The angle of elevation to the top C of a building from two points A and B on level ground are 50 degrees and 60 degrees respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building(round your answer to the nearest unit).

diagram problem 2

Solution to Problem 2:

We consider triangle ABC. Angle B internal to triangle ABC is equal to

B = 180 o - 60 o = 120 o

In the same triangle, angle C is given by.

C = 180 o - (50 o + 120 o) = 10 o

Use sine law to find d.

d / sin(50) = 30 / sin(10)

Solve for d.

d = 30 *sin(50) / sin(10)

We now consider the right triangle.

sin (60) = h / d

Solve for h.

h = d * sin(60)

Substitute d by the expression found above.

h = 30 *sin(50) * sin(60) / sin(10)

Use calculator to approximate h.

h = (approximately) 115 meters.

Problem 3

A triangle ABC has side a = 12 cm, side b = 19 cm and angle A = 80 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).

Solution to Problem 3:

Use sine law to write an equation in sin(B).

a / sin(A) = b / sin(B)

Solve for sin(B).

sin (B) = (b / a) sin(A) = (19/12) sin(80) = (approximately) 1.6

No real angle B satisfies the equation

sin (B) = 1.6

The given problem has no solution.

Problem 4

A triangle ABC has side a = 14 cm, side b = 19 cm and angle A = 32 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).

Solution to Problem 4

Use sine law to write an equation in sin(B).

a / sin(A) = b / sin(B)

Solve for sin(B).

sin (B) = (b / a) sin(A) = (19/14) sin(32) = (approximately) 0.7192

Two angles satisfy the equation sin (B) = 0.7192 and the given problem has two solutions

B1 = 46.0 o and B2 = 134 o

Solution 1: Find angle C1 corresponding to B1

C1 = 180 - B1 - A = 102 o

Solution 1: Find side c1 corresponding to C1

c1 / sin(C1) = a / sin(A)

c1 = 14 sin(102) / sin(32) = (approximately) 25.8 cm

Solution 2: Find angle C2 corresponding to B2

C2 = 180 - B2 - A = 14 o

Solution 2: Find side c2 corresponding to C2

c2 / sin(C2) = a / sin(A)

c1 = 14 sin(14) / sin(32) = (approximately) 6.4 cm

Exercises

1. A triangle ABC has angle A = 104 o, angle C = 33 o and side c = 9 m. Solve the triangle ABC by finding angle B and sides a and b.(round answers to 1 decimal place).

2. Redo problem 2 with the distance between points A and B equal to 50 meters.

Solutions to Above Exercises

1. B = 43 o, a = 16.0 m , b = 11.3 m

2. 191 meters.

More References and Links to Sine and Cosine Laws

sine law

Sine Law Calculator and Solver.

Geometry Tutorials, Problems and Interactive Applets.

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Cosine Law Calculator and Solver.

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Sine Law Calculator and Solver

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Triangles

Triangle Problems

Answer:

10, 12, 30 - no

6, 8, 10 - yes

8, 16, 24 - no

20, 21, 28 - no

Step-by-step explanation:

Just plug them into the Pythagorean Theorem equation (a² + b² = c²)

Brₐinliest plz close to leveling up

Answer:

Man yur tripping playstation better jhit

Step-by-step explanation:

Answer:

0%

Step-by-step explanation:

Since there are no red marbles in the bag, there is no chance that a red marble will be picked.

Answer:

Step-by-step explanation:

An investment banker received a bonus and invested that money in two investments. He put a certain sum

of money in the first investment that returned 7% interest after one year. In the second investment he

Invested four times that of the first investment and got a 12% interest return after one year. If the total

interest from his investments after one year was $8,525.00, find the amount invested at each interest rate.

Answer:

The possible locations are;

(3, 4), (3, 12), (7, 4), and (7, 12)

Please find attached the plot of the points created with Microsoft Excel      

Step-by-step explanation:

The given parameters of the plot of Oliver's backyard are;

The area of the right triangular plant bed Oliver wants to design, A = 8 yd²

The length of a/each unit of the plot = 1 yard

The location of one of the vertex of the right triangular area = (3, 8)

The location of the other vertex of the right triangular area = (7, 8)

We note that the area of a triangle, A = 1/2 × Base length, B × Height, h

Let the distance between the two plotted point represent the base length, 'B', therefore;

B = 7 - 3 = 4 (We subtract only the x-values (7 and 3) given that the y-values (8 and 8) are the same;

Therefore, the base length, B = 4 yards

A = 1/2 × B × h

∴ A = 8 yd.² = 1/2 × 4 yd. × h

h = 8 yd.²/ 2 yd. = 4 yd.

The height of the right triangle, h = 4 yd.

Therefore the possible locations of the last vertex the right triangle on the coordinate plane, given that the first two points are parallel with the x-axis, are points 4 units above or the y-axis value of the plotted points with the x-value of the last vertex being either 3, or 7 as follows;

(3, 8 ± 4) or (7, 8 ± 4) which give points, (3, 4), (3, 12), (7, 4), and (7, 12).

Answer:

3,4 7,4

Step-by-step explanation:

Answer:

4/3 or 1 1/3

Step-by-step explanation:

Answer:

The shape that has the smallest standard deviation is;

Uniform distribution

Step-by-step explanation:

A uniform distribution is a probability distribution where the outcomes are equally likely such as the probability of landing any face of a die, or the probability of landing a head or a tail, or a perfect random number distribution

Therefore, the outcome of a uniform distribution are all the same and the standard deviation is zero (0)

Therefore, the uniform distribution has the smallest standard deviation.

Answer:

36%

Step-by-step explanation:

34-25=9

9/25=36%

Answer:

x= 40°

Step-by-step explanation:

since the angles of the quadrilateral add up to 360°

then to find the agle x:

step:1

add alll the angles given in the quadrilateral

100+120+100

= 320

step:2

now subtract the sum of the quadrilateral from the sum of alll angles

360°-320° = 40°

therefore the answer equates to 40°

Answer:

360-(100+120+100)

360-320

40

Answer:

1

Step-by-step explanation:

Hope This helps! : )

Answer:

the answer i got is 10

im taking the same test right now

Step-by-step explanation:

Answer:

1. their

2. your

3. there

4. You're

5. they're

6. it's

Step-by-step explanation:

Answer: Below

1. Their

2. i dont know sorry

3. There

4. Your're ( I think, I am not good at the Ys

5. They're

6. I think it's

Please do not take these answer for granted I am trying my best

Thank you and have a great nae nae

Answer:

The expression is A that is -b

Answer:

B) <

Step-by-step explanation:

b is the answer because -1 is bigger than 0 so, the answer is b.

Answer:

B. 15

Step-by-step explanation:

Step by Step Solution

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "11.3" was replaced by "(113/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    b-((113/10))>0  

Step by step solution :

STEP

1

:

           113

Simplify   ———

           10  

Equation at the end of step

1

:

      113

 b -  ———  > 0  

      10  

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

         b     b • 10

    b =  —  =  ——————

         1       10  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

b • 10 - (113)     10b - 113

——————————————  =  —————————

      10              10    

Equation at the end of step

2

:

 10b - 113

 —————————  > 0  

    10    

STEP

3

:

3.1    Multiply both sides by  10  

3.2    Divide both sides by  10  

     b-(113/10)  > 0

Solve Basic Inequality :

3.3      Add  113/10  to both sides

            b > 113/10

Inequality Plot :

3.4      Inequality plot for

        b  - 11.300  >  0

One solution was found :

b > 113/10

Which number is a solution of the inequality?

b > 11.3

The answers are 15,9,-14, and 4

15

Answer:

31

Step-by-step explanation:

They're technically asking you to find the missing angle. 61+57 is 118. 180-118 is 62. Since they're asking  2x, you do 62 divided by 2, which is 31.

Answer:

[tex]x=4;\ y=4\sqrt{2}[/tex]

Step-by-step explanation:

[tex]x=4[/tex] since it is an isosceles triangle.

[tex]y=\sqrt{4^2+4^2}=\sqrt{32}=4\sqrt{2}[/tex] due to Pythagoras' theorem.

Hi there!

To begin, we can distribute sec²x with (1 - sin²x):

= sec²x - sec²xsin²x

Which simplifies to:

= sec²x - tan²x

Recall the Pythagorean identity:

1 + tan²x = sec²x

Rearrange alike to the solved for expression above:

1 = sec²x  - tan²x

Thus, using the Pythagorean Identity, sec²x(1 - sin²x) = 1.

Answer:

Step-by-step explanation:

Dimensions:

Area is:

-10 and -1

Step-by-step explanation:

Answer:

-10, and -1

Step-by-step explanation:

4/14 does not = 6/20

2/12 does not = 3/18

Thus, NEITHER is the answer.

Answer:

hello your question is incomplete attached below is the complete question

answer : option A

Step-by-step explanation:

The correct box-and-whisker plot is option A

75% is between 1st quartile and maximum value ( age )

also given that No one is older than 36 years and About 50% of the member are at least 28 years hence option A is the correct Box and whisker plot

Answer:

2x-6

Step-by-step explanation:

4(3x-5)-2(5x-7)

(12x-20)-(10x-14)

12x-20-10x+14

12x-10x-20+14

2x-6

Answer:

=> first multiply the numbers in bracket

4(3x-5)-2(5x-7) when we multiply for 4 and -2

12x-20-10x+14

=> then collect the like terms

12x-10x-20+14

=> 2x-6

Answer:

$198

Step-by-step explanation:

Take 220 then multiply it by .10 (10%)=22

Then subtract that from 220

220*.10=22

220-22=198

Answer:

arc EI = 103°

arc EGI = 257°

Step-by-step explanation:

arc HI = 77° because they are alternate angles

arc EI = (360° - 77° - 77°)/2 = 103°

arc EGI = 360° - 103° = 257°

Answer:

n<

9/8

explanation

simplify n+ -7/4 < -5/8

add 7/4 to both sides

= n< 9/8