The segments shown below could form a triangle.

Answer:

Value of ∠ BFG = 135°

Step-by-step explanation:

Given:

AB || CD

∠ AFG = (3x + 15)°

∠ FGD = (5x - 5)°

Find:

∠ BFG

Computation:

We know that;

∠ AFG = ∠ FGD

3x + 15 = 5x - 5

3x - 5x = - 5 - 15

- 2x = - 20

2x = 20

x = 10

Value of ∠ AFG = 3x + 15

Value of ∠ AFG = 3(10) + 15

Value of ∠ AFG = 45°

∠ BFG = 180° - Value of ∠ AFG

∠ BFG = 180° - 45°

∠ BFG = 135°

Value of ∠ BFG = 135°

Answer:

Samuel had RM8 previously

Step-by-step explanation:

24÷3=8

Answer:

7x = 42

Step-by-step explanation:

"Product" refers to multiplication and "is" refers to equal to.

Hi! I'm happy to help!

This equation will be written like this

x×7=42

To make this easier to solve, we can use the inverse operation, division.

42÷7=x

42 divided by 7 is 6, so the answer is 6.

I hope this was helpful, keep learning! :D

Step-by-step explanation:

70+1

Steps:

write tens and then ones

9514 1404 393

Answer:

  138.77

Step-by-step explanation:

Your scientific or graphing calculator will have exponential functions for bases 10 and e. On the calculator shown in the first attachment, they are shifted (2nd) functions on the log and ln keys. Consult your calculator manual for the use of these functions.

The value can be found using Desmos, the Go.ogle calculator, or any spreadsheet by typing 10^2.1423 as input. (In a spreadsheet, that will need to be =10^2.1423.) The result using the Go.ogle calculator is shown in the second attachment.

You can also use the y^x key or the ^ key (shown to the left of the log key in the first attachment). Again, you would calculate 10^2.1423.

__

We have assumed your log is to the base 10. If it is base e (a natural logarithm), then you use the e^x key instead. Desmos, and most spreadsheets, will make use of the EXP( ) function for the purpose of computing e^( ). You can type e^2.1423 into the Go.ogle calculator.

_____

Additional comment

There are also printed logarithm tables available that you can use to look up the number whose log is 0.1423. You may have to do some interpolation of table values. You should get a value of 1.3877 as the antilog. The characteristic of 2 tells you this value is multiplied by 10^2 = 100 to get the final antilog value.

The logarithm 2.1423 has a "characteristic" (integer part) of 2, and a "mantissa" (fractional part) of 0.1423.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

760

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\(35+5)[16+(12\div 4)]\\------------------\\\text{Follow \textbf{PEMDAS}}\\\\\rightarrow 35+ 5 = 40\\\\40[16+(12\div 4)]\\\\\rightarrow 12\div4 = 3\\\\\rightarrow 16 + 3 = 19\\\\40(19)\\\\\rightarrow 40 * 19\\\\\boxed{760}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

217

Step-by-step explanation:

53 + 44 + 46 = 143

360 - 143 = 217

Answer:

Step-by-step explanation:

The answer is C.

That's another way of using the vertical line test. Put a ruler perpendicular to the x axis and going through a point. If the ruler hits only one point, then then if all the points plotted do the same thing, then the points make a function.

C says the same thing. Only 1 element in the domain (x) can be associated with 1 y value (the range). If there is more than 1 y value, then you do not have a function.

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{pq+1}{9}[/tex]

= [tex]\frac{(3x+1)(3x-1)+1}{9}[/tex]

= [tex]\frac{9x^2- 1+1}{9}[/tex]

= [tex]\frac{9x^2}{9}[/tex]

= x²

Answer:

Hello,

Step-by-step explanation:

[tex]Using\ the\ formula\ (a+b)(a-b)=a^2-b^2\\p=3x+1\\q=3x-1\\\\p*q=(3x+1)*(3x-1)=9x²-1\\\\p*q+1=9x^2\\\\x^2=\dfrac{p*q+1}{9} \\[/tex]

Answer:

27 1/2 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = 5 * 5 1/2

Change to an improper fraction

A = 5 * (2*5+1)/2

A = 5*11/2

A = 55/2

Change back to a mixed number

A = 27 1/2

Step-by-step explanation:

the number which has the highest value as8 is

6586.34

Answer:

x = 1, y = 5

x = 5, y = 13

Step-by-step explanation:

y = x² − 4x + 8 .......(1)

y = 2x + 3 .......(2)

Substitute the value of y in equation 2 into equation 1

y = x² − 4x + 8

y = 2x + 3

x² − 4x + 8 = 2x + 3

Rearrange

x² − 4x − 2x + 8 − 3 = 0

x² − 6x + 5 = 0

Solve by factorization

Find the product you x² and 5. The result is 5x²

Find the factors of 5x² such that their sum will result in −6x. The factors are −x and −5x.

Replace −6x in the equation above with −x and −5x. This is illustrated below:

x² − x − 5x + 5 = 0

x(x − 1) − 5(x − 1) = 0

(x − 1)(x − 5) = 0

x − 1 = 0 or x − 5 = 0

x = 1 or x = 5

Substitute the value of x into equation 2 to obtain the value of y.

y = 2x + 3

x = 1

y = 2(1) + 3

y = 2 + 3

y = 5

x = 5

y = 2x + 3

y = 2(5) + 3

y = 10 + 3

y = 13

SUMMARY:

x = 1, y = 5

x = 5, y = 13

1 - 580squaredcm

2 - 540

Answer:

-

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

-6(x - 2) + 3x = -3(x + 3) + 21

-6x + 12 + 3x = -3x - 9 + 21

Collect like terms

-6x + 3x + 3x = -9 + 21 - 12

-6x + 6x = - 9 + 9

0 = 0

In this scenario, it can be deduced that there is no solution to Kenya's equation.

Answer:

infinitely many solutions

Step-by-step explanation:

i got it right

Answer:

The diameter would be 11 feet

Step-by-step explanation:

C = pi * d

we don't know D so we rearrange the equation to solve for D by dividing both sides by pi:

C/pi = d

Now we plug in everything

11pi/pi = d

The pi cancel each other out leaving with 11 feet

Therefore D = 11 feet

Answer:

The net change is -.30

Step-by-step explanation:

increase means add

decrease means subtract

+3.50

-3.70

+3.30

-3.40

-------------

-.30

The net change is -.30

Answer:

Each box of buns weighs 18 pounds and each box of potatoes weighs 35 pounds

Step-by-step explanation:

Let's say each bun box weighs b pounds and each potato box weighs p pounds. For each box of buns, we add b pounds. Therefore, for 40 boxes of buns, we add 40 * b pounds. Similarly, for 35 boxes of potatoes, we add 35 * p pounds.

For Tuesday, the total weight of the buns boxes is equal to 40 * b. The total weight of the potato boxes is equal to 35 * p. Adding these two together, we get the total weight of the boxes to be equal to

40 * b + 35 * p = 1945

For Friday, we can apply similar techniques to get

60 * b + 70 * p = 3530

We therefore have the two equations

40 * b + 35 * p = 1945

60 * b + 70 * p = 3530

One way to solve this would be to convert this into a matrix and use Guass-Jordan Elimination. With the amount of bun boxes representing the first column, the amount of potato boxes representing the second, and the total weight of each day representing the third, we have

[tex]\left[\begin{array}{ccc}40&35&1945\\60&70&3530\end{array}\right][/tex]

One thing that we can do here is multiply the first row by -2 and add it to the second. That way, there would be a 0 in the 2nd column in the 2nd row, making an equation of the form

something * b = something else, enabling us to solve for b.

We thus have

[tex]\left[\begin{array}{ccc}40&35&1945\\(-40*2+60)&(-35*2+70)&(-1945*2 +3530)\end{array}\right] = \left[\begin{array}{ccc}40&35&1945\\-20&0&-360\end{array}\right][/tex]

Therefore, we can say that

-20 * b = -360

divide both sides by 20 to isolate b

b = 18

Therefore, each box of bunds weighs 18 pounds. Plugging that into an equation, we have

40 * b + 35 * p = 1945

40 * 18 + 35 * p = 1945

720 + 35 * p = 1945

subtract 720 from both sides to isolate the p and its coefficient

1225 = 35 * p

divide both sides by 35 to isolate p

p = 35

Therefore, each box of potatoes weighs 35 pounds

yfd sat fltfurjbhviccyvihkjobkb 47 I have

Answer:

The distribution is positively skewed.

Step-by-step explanation:

It's not symmetric because the distribution in the chart isn't equally shown or marked. It's not negative skewed either because for it to be negative the graph would have to go down in a negative direction, usually the left, but in the picture you posted the graph is going down in the right direction. Lastly, positively skewed graphs or charts look like the one you posted. They go down in the right direction, hence why they're called "positively" skewed. The right tail of the distribution is longer in positively skewed graphs or charts.

Answer:

i think it the measured of the indicated angle is 55

Answer:

(k) cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

From trigonometric identities, we have;

1 + cot²θ = cosec²θ

On the Left Hand Side of the equation, we get;

cos(θ)·√(1 + cot²θ) = cos(θ) × cosec(θ) = cot(θ)

On the Right Hand Side of the equation, we have;

√(cosec²(θ) - 1) = √(1 + cot²(θ) - 1) = √(cot²(θ)) = cot(θ)

∴ √(cosec²θ - 1) = cot(θ)

By transitive property of equality, therefore;

cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

(l) sin⁶A + cos⁶A = 1 - 3·sin²A·cos²A

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³

(sin²A)³ + (cos²A)³ = ((sin²A) + (cos²A))³ - 3·((sin²A)·(cos²A))·((sin²A) + (cos²A))

∴ (sin²A)³ + (cos²A)³ = (1)³ - 3·((sin²A)·(cos²A))·(1) = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³ = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = 1 - 3·((sin²A)·(cos²A))

(m) (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(sinA - cosecA)²  = sin²A - 2×sinA×cosecA + cosec²A = sin²A - 2 + cosec²A

(cosA - secA)² = cos²A - 2×cosA×secA + sec²A = cos²A - 2 + sec²A

∴ (sinA - cosecA)² + (cosA - secA)² = sin²A - 2 + cosec²A + cos²A - 2 + sec²A

Where;

sin²A - 2 + cosec²A + cos²A - 2 + sec²A = sin²A + cos²A  - 2  - 2 + cosec²A + sec²A

sin²A + cos²A  - 2  - 2 + cosec²A + sec²A = 1 - 4 + cosec²A + sec²A

1 - 4 + cosec²A + sec²A = cosec²A + sec²A - 3

Where;

cosec²A = cot²A + 1

sec²A = tan²A + 1

∴ cosec²A + sec²A - 3 = cot²A + 1 + tan²A + 1 - 3 = cot²A + tan²A - 1 = The Right Hand Side of the equation

∴ (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(n) [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Squaring the Right Hand Side of the equation, we get;

(sinA - cosA)² = sin²A -2·sinA·cosA + cos²A = sin²A + cos²A -2·sinA·cosA

sin²A + cos²A -2·sinA·cosA = 1 - 2·sinA·cosA

∴ (sinA - cosA)² =  1 - 2·sinA·cosA

Taking the square root of both sides gives;

√((sinA - cosA)²) = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

∴ sinA - cosA = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

By symmetric property of equality, we have;

[tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Step-by-step explanation:

Answer:

20 mm^3, 20 cubic millimeters

Step-by-step explanation:

The volume of a prism is length times width times height.

Length, width, and height can have units of mm.

mm * mm * mm = mm^3

The units of a volume must be cubic units.

Answer: 20 mm^3, 20 cubic millimeters

Answer:

x ≈ 55.5°

Step-by-step explanation:

Using the Sine rule in the triangle

[tex]\frac{5}{sinx}[/tex] = [tex]\frac{5.7}{sin70}[/tex] ( cross- multiply )

5.7 sinx = 5 sin70° ( divide both sides by 5.7 )

sin x = [tex]\frac{5sin70}{5.7}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{5sin70}{5.7}[/tex] ) ≈ 55.5° ( to the nearest tenth )

Answer:

[tex]x =55[/tex]°

Step-by-step explanation:

An isosceles triangle is a triangle with two congruent sides. One can see that the given triangle is an isosceles triangle, as two sides have a side length of (5) units. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. In this situation, this means that two angles have a measure of (x) degrees. As a given, the sum of angles in any triangle is (180) degrees. Thus, one can form an equation, and solve for the unknown, (x):

[tex]x + x + 70 = 180[/tex]

Simplify,

[tex]2x + 70 =180[/tex]

Inverse operations,

[tex]2x + 70 =180[/tex]

[tex]2x = 110[/tex]

[tex]x =55[/tex]

Answer:

The speed of the balloon is 0.16 m/s.

Step-by-step explanation:

CD = 300 m

Let AD = x

AB = y

time, t = 3 min

Triangle, ADC

[tex]tan 15 = \frac{AD}{BC}\\\\0.27 \times 300 = x \\\\x = 80.4 m[/tex]

Triangle, BCD

[tex]tan 20 = \frac{BD}{BC}\\\\0.36 \times 300 = x + y \\\\x + y = 109.2 m[/tex]

So, y = 109.2 - 80.4 = 28.8 m

Speed = 28.8/180 = 0.16 m/s

Answer:

C. $1,260

Step-by-step explanation:

80 × 14.5 = 1,160

2,500 × 0.04 = 100

Answer:

C. $1260

Step-by-step explanation:

Answer:

R = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

Step-by-step explanation:

P - Q + R = I ( I is the identity matrix )

[tex]\left[\begin{array}{ccc}2&4\\3&5\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}-2&2\\4&1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( subtract corresponding elements )

[tex]\left[\begin{array}{ccc}2-(-2)&4-2\\3-4&5-1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

Hi!

[tex]|15x+2|=8\\\\\\15x+2=8\\15x=8-2\\15x=6 \ \ |:15\\\boxed{x_1=0,4}\\\\\\15x+2=-8\\15x=-8-2\\15x=-10 \ \ |:15\\\boxed{x_2=-\frac{2}{3}}[/tex]

Answer:

x = 2/5      x = -2/3

Step-by-step explanation:

|15x + 2 |= 8

There are two solutions, one positive and one negative

15x + 2 = 8  and 15x + 2 = -8

Subtract 2 from each side

15x + 2-2 = 8-2  and 15x + 2-2 = -8-2

15x = 6                             15x = -10

Divide by 15

15x/15 = 6/15                   15x /15 = -10/15

x = 2/5                               x = -2/3

Answer:

C

Step-by-step explanation:

degree 1 ( linear function