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Answer:

Step-by-step explanation:

let a be the first term and r be common ratio.

[tex]a_{3}=ar^2=-45\\a_{5}=ar^4=-405\\divide\\\frac{ar^4}{ar^2} =\frac{-405}{-45} =9\\r^2=9\\r=\pm3\\9a=-45\\a=-5\\a_{7}=ar^{7-1}=ar^6=ar^4 \times r^2=-405 \times 9=-3645[/tex]

Answer: True

Step-by-step explanation: The angles given are the same AND the side given us the same. The triangle has been reflected, but the reflection is still congruent.

The two triangles given are congruent according to the ASA congruence rule.

Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.

The given triangles are both right angled triangles.

The side 12 units is the included side between the angles 45° and 90° in both the triangles. This is the required condition for ASA congruence rule.

Hence we can say that the triangles are congruent according to the ASA congruence rule. The answer is A.True.

Learn more about congruence of triangles here:

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Answer:

Step-by-step explanation:

Equation of line:  y = mx + c

 y = x - 6

Slope m = 1

y-intercept c = -6

Answer:

m = 1

c = -6

Step-by-step explanation:

Formula for a  line is y = mx+c

m = gradient

c  = intercept.

Here:

m = 1

c = -6

Hope this helps

Good Luck

Answer:

sin θ = +/- (2√2)/3

Step-by-step explanation:

cos θ  = 1/3

cos²θ  + sin²θ  = 1

(1/3)² + sin²θ  = 1

sin²θ  = 1 - 1/9

√(sin²θ) = +/-√(8/9)

sin θ = +/- (2√2)/3

Answer:

[tex]\dfrac{47}{42} \ \ \ \ \ OR \ \ \ \ 1.1[/tex]

Step-by-step explanation:

The objective of this question is to find the  sum of the greatest and least numbers below:

[tex]\[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\][/tex]

To do this ; we will need to find the decimal component of each of them and equate them on a number line before summing the greatest and least numbers.

[tex]8 \frac{1}{5} = \dfrac{8*5+1}{5} \\ \\ = \dfrac{41}{5} \\ \\ = 8.2[/tex]

[tex]-8 \frac{2}{5} =- \dfrac{8*5+2}{5} \\ \\ =- \dfrac{42}{5} \\ \\ = -8.4[/tex]

[tex]-\dfrac{26}{3}= - 8.7[/tex]

[tex]-\dfrac{54}{7} = - 7.7[/tex]

[tex]\dfrac{53}{6}= 8.8[/tex]

Thus; the above decimal component of the fractions given are :

8.2, -8.4, -8.7 , -7.7 and 8.8

We are to find the sum of the greatest and the smallest number ; on a number line; we will realize that the positive side is greater than the negative side , As such the greatest number from the positive side will be 8.8 and the smallest number will be -7.7

The sum of 8.8 + ( -7.7 ) = 8.8 - 7.7

= 1.1

i.e

[tex]\dfrac{53}{6} + (- \dfrac{54}{7} )[/tex]

[tex]\dfrac{53}{6} - \dfrac{54}{7}[/tex]

[tex]\dfrac{53}{6} - \dfrac{54}{7} = \dfrac{53*7 - 6*54}{42} \\ \\ = \dfrac{47}{42} \\ \\ = 1.1[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Answer is 20.

1: First, add up all the temperatures that has been provided, 21 + 21 + 19 + 19. It should give you 80.

2: Divide 80 by how many temperatures has been shown. There were 4 temperatures shown, so 80/4 = 20. Hope this helps you!

Answer:

180 millimeters.

Step-by-step explanation:

To find the height of the replica, a ratio can be set up:

[tex]\frac{x}{50}= \frac{1}{275}[/tex]

Cross multiply:

[tex]275x = 50[/tex]

Divide both sides by '275:

x≈0.18 meters

Convert 'meters' to 'millimeters' by multiplying by a thousand:

0.18 × 1000 = 180 millimeters.

Answer:

RT is more appropriate, though even SU could be called a secant.

Step-by-step explanation:

Answer:

(x+5)²(x²+5)

Step-by-step explanation:

Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25

On factorising we have:

x²+5x+5x+25

= x(x+5) +5(x+5

= (x+5)(x+5)

= (x+5)²

The LCM can be calculated as thus

| x²+5, (x+5)²

x+5| x²+5, (x+5)

x+5| x²+5, 1

x²+5| 1, 1

The factors of both equation are x+5 × x+5 × x²+5

The LCM will be the product of the three functions i.e

(x+5)²(x²+5)

This hives the required expression.

Answer:

two times a number

Step-by-step explanation:

Answer:

$ 60

Step-by-step explanation:

p(x) = 7x + 25

f(1) = 2.1² + 3 = 5

p(f(1)) = p(5) = 7 . 5 + 25 = 35 + 25 = 60

so he get $ 60 for 5 hours work with tips

Answer:

3. 324+432=756 in cubed

4. 2100+7200=9300 yd cubed

Answer:

$178,000

Check my explanation for further details

Step-by-step explanation:

$8200 in his pension fund for 15 years

=8200×15

=$123,000

By 2031

Tom will have a total of $55 000+$123,000

=$178,000

If by saying E55,000 you mean 55,000 Euro

Then,

$62,174.99=E55000

$62,174.99+$123,000

=$185,174.99

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πr^2 = area

Half the diameter to get the radius

Substitute the values in:

area = 3.142 x (7)^2

area = 153.958 cm^2

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Answer:

153.958cm^2

Step-by-step explanation:

r=d/2=14/2=7cm

A=πr^2

A=3.142×7^2

A=3.142×49cm^2

A=153.958cm^2

Answer:

Area_square = 4 cm2

Area_triangle = 4 cm2

Step-by-step explanation:

The first thing to do is calculate the area of both figures.

The area of the square is given by:

Area_square = side * side

The side of the square is 2 cm, so:

Area_square = 2 * 2 = 4 cm2

The area of the triangle is given by:

Area_triangle = base * height / 2

The base is 2 cm, and the height is 4 cm, so we have:

Area_triangle = 2 * 4 / 2 = 4 cm2

So we have that Area_square = Area_triangle = 4 cm2

Answer:

[tex]135<t_{minutes}\:<315[/tex]

Step-by-step explanation:

Malik's goal is a minimum total of 135 (45 x 3) minutes per week, in three session of 45 minutes.

Notice that it is at least.

So He can do sessions from 3 , 4, 5, 6 up to 7 nights per week

Hence, we can write his goals in minutes per week:

[tex]G_{w}=3*45<t_{minutes}<7*45\\G_{w}=135<t_{minutes}<315[/tex]

Answer:

3.44571

Step-by-step explanation:

look at the number to the right of the decimal. if the number is higher than or is 5 round the number up, but if the number is less than 5 it will stay the same.

The number after rounding off to nearest hundred-thousandth or  5 decimal places will be -

3.44571

We have the following number - 3.44570830811

We have to round it of nearest hundred-thousandth or 5 decimal places.

Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. For example - 53 rounded to the nearest ten is 50.

According to the question, we have the following number -

3.44570830811

Rounding it off One by one until we get 5 digits after decimal -

R1 -  3.44570830811

R2 - 3.4457083081

R3 - 3.445708308

R4 - 3.44570831

R5 - 3.44570831

R6 - 3.4457083

R7 - 3.445708

R8 - 3.44571

Hence, the number after rounding off to nearest hundred-thousandth or  5 decimal places will be -

3.44571

To solve more questions on Rounding Numbers, visit the link below-

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Answer:

e. 29.840

Step-by-step explanation:

The cat, the floor and the foot pole form the shape of a right angled triangle.

The opposite is the height of the foot pole = 32 ft

The adjacent is the distance of the cat from the base of the foot pole.

The hypotenuse is the direct distance of the cat from the bird.

The angle of elevation, x, is 47°

To find the distance of the cat from the foot of the foot pole, we can use to TAN part of the trigonometric function SOHCAHTOA:

tan(x) = opposite / adjacent

=> tan(47) = 32 / adj

adj = 32 / tan(47)

adj = 29.840 ft

Therefore, the cat is 29.840 feet from the base of the foot pole.

Answer:

Yes it is 7 cuz it has the equation of 3-5a

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Plug in -3 as a

h(-3) = (3+15)/3

h(-3) = 18/3

h(-3) = 6

Answer:

y=1/6x

Step-by-step explanation:

y=1/x

the rule for horizontal compression is f(k.x) since we have the equation of y=1/x and k=6 then y=1/6x

Answer:

[tex]\frac{27}{1000}[/tex]

Step-by-step explanation:

=> [tex](\frac{3}{10} ) ^3[/tex]

=> [tex]\frac{(3)^3}{(10)^3}[/tex]

=> [tex]\frac{27}{1000}[/tex]

Answer:

It's 0.003.

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

because i said

Answer:

c is the correct option

Step-by-step explanation:

Answer: 20/27

Step-by-step explanation:

So it is non- mutually exclusive;

Let B for the boys and H for the blond hair.

P(B) = 15/27; P(H) 11/27; P(B and H) = 6/27

Then, we have,

P(B or H) = 15/27 + 11/27 - 6/27

P(B or H) = 20/27 

Therefore,  the probability of selecting a boy or a blond-haired person is 20/27.

Answer:

- 18y = 1

Step-by-step explanation:

Adding the 2 equations term by term on both sides gives

(- 5x + 5x) + (- 9y - 9y) = (3 - 2), that is

0 + (- 18y) = 1

- 18y = 1

Answer:

12/5hours=2.4 hours

Step-by-step explanation:

Sam:6hours

Tom:4hours

This is a rate problem

Sam's rate is one job completed in 6 hours which is 1/6

Tom's rate is one job completed in 4 hours which is 1/4

Together, they could complete 1/4+1/6 of the job in y hours

We are trying to find the rate at which Sam and Tom could complete the job together, or one job in x days, for a rate of 1/y

1/4+1/6=1/y

The least common denominator is 12y

Multiplying through by the LCD which gives:

12y(1/4)+ 12y (1/6)= 12y (1/y)

3y + 2y=12

5y = 12

y=12/5 hours=2.4hours

Therefore it will take 12/5 hours or 2.4 hours to complete the job if they work together

Answer:

2.4

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

4.7 - 2.3

Step 2: Evaluate

Subtract

2.4

Answer:

2.4

Step-by-step explanation:

Answer:

Optimal investment amount = $300

Step-by-step explanation:

discount = x

original price = 10,000

discount% = 7%

x/10,000 = 7/100

x · 100 = 7 · 10,000

100x = 70,000

100x/100 = 70,000/100

x = 700

discount = x

original price = 10,000

discount% = 8%

x/10,000 = 8/100

x · 100 = 8 · 10,000

100x = 80,000

100x/100 = 80,000/100

x = 800

discount = x

original price = 10,000

discount% = 12%

x/10,000 = 12/100

x · 100 = 12 · 10,000

100x = 120,000

100x/100 = 120,000/100

x = 1,200

So:

$1,200 - $800 - $700 = $300

We max out the high return investment, $2000 for 12%.

We have $8000 left to invest and we want to put as much in CDs at 8% as possible.  Let's call b the bond investment and c the CD investment.  We have

b ≥ 3c

Since munis have the lower return we want as many CDs as possible.  So we choose:

b = 3c

b + c = 8000

3c + c = 8000

4c = 8000

c = 2000

That leaves b=3c=6000 for bonds.

Answer: $6000 in bonds, $2000 in CDs, $2000 in high-risk.

Step-by-step explanation:

6 - 4s = - 8 - 6s

Bringing like terms on one side

-4s + 6s = - 8 - 6

2s = - 14

S = - 14/2

S = - 7

Answer:

-35 - 5

Step-by-step explanation:

2 + 12 = 14, which is positive

(-3) * (-8) = 24, which is positive

10 - (-18) = 10 + 18 = 28, which is positive

-35 - 5 = -40, which is negative

Answer:

[tex]-35-5[/tex]

Step-by-step explanation:

[tex]2+12=14[/tex]

The result is a positive value.

[tex]-3 \times -8=24[/tex]

The result is a positive value.

[tex]10-(-8)\\10+8=18[/tex]

The result is a positive value.

[tex]-35-5=-40[/tex]

The result is a negative value.