Select the reason that supports the
following statement:
Statement Reason
2x-2 = 8 Given
2x-2+2 = 8+2 [ ?
]
A. Subtraction property of equality
B. Addition property of equality
C. Substitution

Answer:

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

Step-by-step explanation:

Given

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

Required

Solve

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

In trigonometry;

[tex]1 - cos^2x = sin^2x[/tex]

So, make substitution

[tex](1-cos^2 x ).(1+tan^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(1+tan^2 x)[/tex]

Also; in trigonometry:

[tex]1 + tan^2x = sec^2x[/tex]

Make another substitution

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex]

Recall that [tex]secx = \frac{1}{cosx}[/tex]

So;

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(\frac{1}{cos^2 x})[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = \frac{sin^2 x }{cos^2 x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = (\frac{sin x }{cosx})^2[/tex]

In trigonometry;

[tex]tan x = \frac{sin x}{cos x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

The expression cannot be further simplified

Answer:

Answer:

3 < c < 13

Step-by-step explanation:

A triangle is known to have 3 sides: Side a, Side b and Side c.

For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).

To solve the above question, we would be using the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.

Side a + Side b > Side c

Side a + Side c > Side b

Side b + Side c > Side a

For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,

side (a) = 5

side (b) = 8

Let's represent the third side as c

To solve for the above question,we would be having the following Inequality.

= b - a < c < b + a

= 8 - 5 < c < 8 + 5

= 3 < c < 13

Answer:

the correct answer is 47

Answer:

The value of x is 66°

Hope it helps!

Step-by-step explanation:

The sum of exterior angles of a polygon is always 360°

So since the angles are given

40+45+77+2x+x = 360

(40+45+77)+(2x+x)= 360

162 + 3x = 360

3x = 360-162

= 198

x= 198/3

= 66°

Answer:

(-9/2 , -10)

Step-by-step explanation:

2x-3y=21

-6x+2y=7

Multiply the first equation by 3

3(2x-3y)=21*3

6x - 9y = 63

Add this to the second equation to eliminate x

6x - 9y = 63

-6x+2y=7

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

0x -7y = 70

Divide by -7

-7y/-7 = 70/-7

y = -10

Now find x

2x- 3y = 21

2x -3(-10) = 21

2x +30 =21

subtract 30 from each side

2x = 21-30

2x= -9

Divide by 2

x = -9/2

(-9/2 , -10)

Now lets solve it by elemination method !

[tex]:\implies\sf 2x-3y=21--------(1)\\ \\ \\ :\implies\sf -6x+2y=7-------(2)\\ \\ \\ \sf Eleminate\ (x) \\ \\ \\ \it Multiply\ first \ equation \ with \ 3\ \ \ and \ 2nd \ \ with \ 1 \\ \\ \\ :\implies\sf (2x-3y=21)\times 3 \\ \\ \\ :\implies\sf (-6x+2y=7)\times 1\\ \\ \\ :\implies\sf 6x-9y=63------(3) \\ \\ \\ :\implies\sf -6x+2y=7-----(4)\\ \\ \\ \it\ \ Add \ equation\ 3\ \ and \ 4\\ \\ \\ :\implies\sf 6x-9y=63+ (-6x+2y= 7)\\ \\ \\ :\implies\sf (6x-6x)+(-9y+2y) = 63+7\\ \\ \\ :\implies\sf 0-7y=70\\ \\ \\ :\implies\sf y= \cancel{\dfrac{70}{-7}}= - 10\\ \\ \\ :\implies\sf y= -10 [/tex]

★ Now find the value of x

let's substitute the value of y in equation 4

[tex]:\implies\sf -6x+2y=7\ \ \ \ \ \ (y= -10)\\ \\ \\ :\implies\sf -6x+2\times (-10)=7\\ \\ \\ :\implies\sf -6x-20= 7\\ \\ \\ :\implies\sf -6x = 7+20 \\ \\ \\ :\implies\sf x= \cancel{\dfrac{27}{-6}}= \dfrac{-9}{2}[/tex]

[tex]\underline{\textit{ \ \ So, \ the \ value \ of \ x\ and \ y }}[/tex]

[tex]\bigstar{\boxed{\sf x= \dfrac{-9}{2}}}[/tex]

[tex]\bigstar{\boxed{\sf\ y= (-10)}}[/tex]

Answer:

A:

(4x+5)(3x+10)=

(12x^2) + (40x) + (15x) + (50)

12x^2 + 55x + 50

B: 2nd degree trinomial.

C:  it is demonstrated in part A because when we added it, the variable do not change and neither do the  exponents.  

Step-by-step explanation:

do not copy. used this on my test.

Answer:

Step-by-step explanation:Jo's Mobile Plan:

Fixed monthly charge = £16

Monthly 150 free minutes, post that 13p (or £0.13) per minute,

Monthly 150 free texts, post that 15p (or £0.15) per text

Jo's mobile phone usage details:

170 minutes of calls

182 texts

Total Charges for Jo = Fixed Monthly Charge + Charges for Calls + Charges for Texts

⇒ Total Charges for Jo = 16 + (170-150) × 0.13 + (182-150) × 0.15

⇒ Total Charges for Jo = 16 + (20) × 0.13 + (32) × 0.15

⇒ Total Charges for Jo = 16 + 2.6 + 4.8

⇒ Total Charges for Jo = 23.4

Hence, Jo should be charged £23.4 for the month.

Answer:

If you use a graphing calculator, at x= 0   (t =0)  the graph starts at 60 mb   and then climbs 4 mb per sec   (slope = 4 mb/sec)  from there until Agent Hunt gets caught and executed for espionage.

Hope this helps!

Answer:

hi

Step-by-step explanation:

Answer: its 3

Step-by-step explanation:

Answer:   2

Step-by-step explanation: Because their are 2 squares

Answer: B $2.22

Step-by-step explanation:

2 controllers will cost

= 2 x 18.50 = 37

6% tax = 37 x 0.06 = 2.22

Answer:

B

Step-by-step explanation:

i took the test

The probability distribution is given below:

[tex]\left|\begin{array}{c|ccccc}Outcome& 0& 1& 5& 10& 1000\\Probability& 0.33& 0.32& 0.24& 0.10& 0.01\end{array}\right|[/tex]

Answer:

C. 12.52

Step-by-step explanation:

Given the probability distribution below:

[tex]\left|\begin{array}{c|ccccc}Outcome& 0& 1& 5& 10& 1000\\Probability& 0.33& 0.32& 0.24& 0.10& 0.01\end{array}\right|[/tex]

Expected Value of the random variable

=(0 X 0.33)+(1 X 0.32) +(5 X 0.24) +(10 X 0.10) + (1000 X 0.01)

=0+ 0.32+1.2+1+10

=12.52

The correct option is C.

Answer:

D

Step-by-step explanation:

Answer:

Q(-4,4)R' (4,4)S' (4,-4)T'(-4,-4)

Step-by-step explanation:

Given

Quadrilateral QRST

Dilated Factor  = 2

Required

Find the coordinates of Q'R'S'T'

To do this, we first have to identify the coordinates of QRST

[tex]Q = (-2,2)\\R = (2,2)\\S = (2,-2)\\T = (-2,-2)[/tex]

Being dilated by scale factor of 2 means we have to multiply each coordinates by 2; This is as shown below

Q'R'S'T' = 2 * QRST

Q' = 2 * (-2,2)

Q(-4,4)R' (4,4)S' (4,-4)T'(-4,-4)

Answer:a

Step-by-step explanation:

Q′ (–4, 4), R′ (4, 4), S′ (4, –4), T′ (–4, –4)

Answer:

Question 1:

The smallest 5-digit no. is 10,000

The product of its prime factors is:

=> 10,000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

Question 2:

The prime factors of 1729 are:

=> 1729 = 7 × 13 × 19

The relation between their 2 consecutive prime factor is that when they both are subtracted, they give the result 6

Such as :

=> 13-7 = 6

=> 19-13 = 6

Hope this helps!

Don't hesitate asking anything regarding this question!

Answer:

1. The smallest 5-digit number is: 10000

10000= 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

2. 1729= 7 × 13 × 19

7= 6+1

13= 6*2+1

19= 6*3+1

Answer:

3f(x)  

3x^2  

12  

-x+6

0

Step-by-step explanation:

Fashoo

Answer:

614

Step-by-step explanation:

Let the number be x.

50% × x = 307

0.5x = 307

x = 307/0.5

x = 614

50% of 614 is 307.

Answer:

614

Step-by-step explanation:

50% means half. So,

x ÷ 2 = 307

x = 307 × 2

x = 614

Have a blessed day!

Answer:

C, D and E

Step-by-step explanation:

From the congruence postulate, CPCTC(Corresponding parts of congruent triangles are congruent) The following are congruent and corresponding:

=> AC = DF

=> <A = <D

=> BC = EF

Answer: If you have different answers the answers are

C=F and AB=DE

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Distribute

1/2 x + 3 = 18

Subtract 3 from each side

1/2x +3-3 = 18-3

1/2x = 15

Multiply each side by 2

1/2x*2 = 15*2

x = 30

10 L of a 25% acid solution contains 0.25 * (10 L) = 2.5 L of acid.

Adding x L of pure water dilutes the solution to a concentration of 10%, such that

(2.5 L)/(10 L + x L) = 0.10

Solve for x :

2.5 = 0.10 * (10 + x)

2.5 = 1 + 0.10x

1.5 = 0.10x

15 = x

so 15 L of pure water are needed.

Answer:

x-intercept is equal to 2 (Option 3)

Step-by-step explanation:

Slope = m = -3/2

y-intercept = b =  3

Putting in the slope-intercept form

=> y = [tex]\frac{-3}{2} x+3[/tex]

For finding x- intercept, y must be equal to 0

=> 0 = (-3/2)x+3

=> -3/2 x = -3

=> 3/2 x = 3

=> 3x = 6

Dividing both sides by 3

=> x = 2

Answer:

the third option 2

Step-by-step explanation:

Answer:

1) Length  22 and 26 have the same amount of desks that have the same length

2) Lengths 21, 23, 25, and 27 have the equal amount of tables

Step-by-step explanation:

3) There are 12 desks in total  

Explanation of Sentence 1 is that lengths 22 and 26 both have 3 tables that are its length

Explaination of Setence 2 is that lengths 21, 23, 25, and 27 all have 1 desk that is its length

Explaination of sentence 3 is that there are 12 desks that are measured.

If this helped please mark me brainliest :)  

Answer: I'm guessing it's acute

Step-by-step explanation:

Since all the angles are less that 90 degrees, it can't be right or obtuse. I'm gonna say acute

Answer:

See below

Step-by-step explanation:

You have to find the number in the middle of all of the heights and multiply them by the all of the frequency. When you have those answers, add them together and divide the answer by 40. That is why, our answer in part (a) is an estimate.

The mean is the average value of an observation, the mean of the grouped data is 129.3 cm

The mean value can be calculated using the relation :

ΣF = (7 + 8 + 13 + 9 + 3) = 40

Σfx = (7 × 122) + (8 × 126) + (13 × 130) + (9 × 134) + (3 × 138) = 5172

Mean = ΣFx /ΣF

Mean = 5172 / 40 = 129.3 cm

B.)

The mean value obtained is an estimate because, calculation used the midpoint value existing within a certain range, and not the exact height value of individual student.

Learn more :https://brainly.com/question/17007926

Answer:

10 meters

Step-by-step explanation:because they are square and they would have to be 5 meters long and she dose not want any left over so...

Answer:

A. x = 5, y = 6

Step-by-step explanation:

The directions tell you to do steps on the calculator, so I can't explain or show how to use it in the calc. But simply just plug it into the calc as a matrix and do rref.

Answer:

x= 5, y= 6

Step-by-step explanation:

5x - 4y = 1

4x - 2y =8

Multiply the second equation by -2

-8x + 4y = -16

Add this to the first equation

5x - 4y = 1

-8x + 4y = -16

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

-3x = -15

Divide by -3

-3x/-3 = -15/-3

x = 5

Now find y

4x -2y = 8

4(5) -2y = 8

20-2y = 8

Subtract 20

-2y = -12

Divide by -2

y = 6

Answer:

x=-3 y=19/7 z=7

Step-by-step explanation:

Answer:

average speed of sprinter will be 10.42m/s

Step-by-step explanation:

distance covered=s=100m

time taken=t=9.67m/s

average speed=[tex]\frac{distance covered}{time taken}[/tex]

average speed=[tex]\frac{100m}{9.67s}[/tex]

average speed=10.42m/s

Answer:

The height is 5 units

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

30 = 1/2 (12) h

30 = 6h

Divide each side by 6

30/6 = 6h/6

5 = h

The height is 5 units

Answer:

[tex]Fraction = \frac{3}{14}[/tex]

Step-by-step explanation:

Given:

[tex]Total\ Length = 5\frac{5}{6}[/tex]

[tex]Straight\ Section = 1\frac{1}{4}[/tex]

Required:

Fraction of the circuit that is straight section

To solve this, we simply divide the length of the straight section by the total length of the circuit;

This is done as follows;

[tex]Fraction = 1\frac{1}{4} / 5\frac{5}{6}[/tex]

Convert both fractions to improper fractions

[tex]Fraction = \frac{5}{4} / \frac{35}{6}[/tex]

Change division sign (/) to multiplication (*)

[tex]Fraction = \frac{5}{4} * \frac{6}{35}[/tex]

Combine to form a single fraction

[tex]Fraction = \frac{5*6}{4*35}[/tex]

[tex]Fraction = \frac{30}{140}[/tex]

Divide numerator and denominator by 10

[tex]Fraction = \frac{3}{14}[/tex]

Hence, the fraction of the straight section is; [tex]Fraction = \frac{3}{14}[/tex]

Answer:

132 dollars, I think

Step-by-step explanation:

15*2=30

66*2=132

Answer:

D

Step-by-step explanation:since 15 cases is $66 multiply 66 by 2 to get $132

Answer:

risk

Step-by-step explanation:

Lenders rely on credit scores to determine risk.

Answer:

risk

Step-by-step explanation:

Lenders rely on credit scores to determine risk.