Consider the formula 4(h-3k)= h+7.
(a) Make k the subject of the above formula.
(b) If the value of h is decreased by 8, write down the change in the value of k.

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Answer:

8√3 ≈ 13.86

Step-by-step explanation:

6√2 - 4√3 + | 3√(2²•2) -8√3 | + 2√2²•3

Every 2² get our from the square root and loses the ² :

6√2 -4√3 + | 2•3√2 -8√3 | + 2•2√3

Solve the multiplications and taking of the | | , the signal inside it changes:

6√2 - 4√3 +8√3 -6√2 +4√3

Now you group the similar terms and solve the possible operations:

6√2 - 6√2 +4√3 - 4√3 + 8√3

8√3 ≈ 13.86

Step-by-step explanation:

4(3_/2-2_/3)

SEE the IMAGE for Solution

Answer:

2√5

Step-by-step explanation:

hypotenuse of the second triangle = √(9²-5²)

= 2√14

so,

x = √{(2√14)²-6²}

= 2√5

Answer:

2sqrt(5)

Step-by-step explanation:

The left triangle is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs  and c is the hypotenuse

5^2 + b^2 = 9^2

b^2 = 9^2 - 5^2

b^2 = 81-25

b^2 =56

Taking the square root of each side

b = sqrt(56) = sqrt(4*14) = 2 sqrt(14)

The right side is also a right triangle so we can  use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs  and c is the hypotenuse

x^2 + 6^2 = (sqrt(56))^2

x^2 +36 = 56

x^2 = 56-36

x^2 = 20

Taking the square root

sqrt(x^2) = sqrt(20) = sqrt(4*5) = 2sqrt(5)

Answer:

True

Step-by-step explanation:

We actually can use Sine, Cos, or Tangent to solve for the angles, which would give the angle, but graphing it came up with an Obtuse Scalene triangle.

Answer:

The additive inverse of -61 is 61. For additive inverse just reverse the sign.

Answer:

3x³ + 16x² + 12x - 16

Step-by-step explanation:

(x - -4)(3x² + 4x - 4)

(x + 4) (3x² + 4x - 4)

3x³ + 4x² - 4x + 12x² + 16x - 16

3x³ + 4x² + 12x² - 4x + 16x - 16

3x³ + 16x² + 12x - 16

Answer:

2000 milligrams —> 2 grams

6000 milligrams —> 6 grams

7000 milligrams —> 7 grams

10000 milligrams —> 10 grams

I hope I helped you^_^

Answer:

Does the answer help you?

Answer:

5/3

Step-by-step explanation:

1) The denominator will be multiply to the whole number to find the improper fraction. 3 (denominator) x 1 (whole number)

2) 1 plus 2 (numerator) equal 5

3) Always keep the denominator (3) for you improper fraction.

4) 5 will be the numerator and 3 will be the denominator.

5/3

Answer:

c = 12

Step-by-step explanation:

i'm Attaching the work

Answer:

4500

Step-by-step explanation:

The first digit can't be 0. so it will be a number from 1000 to 9999. That's a total of 9000 numbers (9999-1000+1=9000). Since the last digit must be an even number that is one half of the 9000 numbers which is 4500.

Answer:

It's 5 which is A.

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

Fraction =2/5

In decimal =0.4

Answer:

d=1, r=4/3

Step-by-step explanation:

For aritmetic sequence

a1=9

a1+3d=a4    9+3d=a4.

a1+7d=a8    9+7d=a8.

For geometric sequence

b1*r=b2

b2=a4, b1=a1=9

9*r=a4

b3= b1*r^2

b3=a8

a8=9*r^2

So 9+3d=a4

9+3d=9r

9+7d= a8=9r^2

So we have a system of equations

9+3d=9r

9+7d=9r^2

Multiply 9+3d=9r by -7 It is equal to -63-21d=-63r

And multiply 9+7d=9r^2 by 3. It is equal to 27+21d=27r^2

Then add them

-63-21d+ (27+21d)= -63r+27r^2

-36+63r-27r^2=0 /9

-4+7r-3r^2=0

3r^2-7r+4=0

r=1 r=4/3

If r=1 9+3d=9

d=0 (It is not right, d isn't equal to 0)

If r=4/3

9+3d= 9*4/3

9+3d=12

d=1

The value of the common difference,  d is 9

The value of the common ratio r is 2

The nth term of an arithmetic sequence is:

[tex]T_n=a+(n-1)d[/tex]

The first, fourth, and eighth terms are therefore:

a,  a + 3d,  a + 7d

The nth term of a geometric sequence is:

[tex]T_n=ar^{n-1}[/tex]

The first three terms of the arithmetic sequence are:

[tex]a, ar^2, ar^3[/tex]

For both sequences, the first term is 9

That is, a = 9

[tex]a+3d=ar^2\\\\9+3d=9r^2..............(1)\\\\a+7d=ar^3\\\\9+7d=9r^3..........(2)[/tex]

Make d the subject of the formula in equation (1) and substitute to equation (2)

[tex]d=\frac{9r^2-9}{3} \\\\d=3r^2-3[/tex]

Substitute equation (3) into equation (2)

[tex]9+7(3r^2-3)=9r^3\\\\9+21r^2-21=9r^3\\\\21r^2-9r^3=12\\\\7r^2-3r^3=4\\\\r=1, \frac{-2}{3}, 2[/tex]

Substitute r = 2 into (1)

[tex]9+3d=9(2^2)\\\\d = 9[/tex]

The value of the common difference,  d is 9

The value of the common ratio r is 2

Learn more on sequences here: https://brainly.com/question/6561461

Step-by-step explanation:

Let SP1 be x

P%=10%

CP=SP×100/100+%P

= x+100/100+10

= 100x/110

SP2= x+55

CP= SP×100/100+%P

or 100x/110= x+55×100/120

or x/110=x+55/120

or 24x-22x=22×55

or 2x=1210

or x=1210/2

or x=605

Now,

CP=100x/110

=100×605/110

=60500/110

=Rs 550

Let assume hours be x.

1 hour = 60 minutes

x hour = 330 minutes

[tex] \bf \large \rightarrow \: \: \frac{1}{60} \: \times \: \frac{x}{330} \: \: \: \small\rm({\red{ Cross \: \: Multiplying }}) \\ [/tex]

[tex]\bf \large \rightarrow \: \: 60x \: = \: 330[/tex]

[tex]\bf \large \rightarrow \: \: x \: = \: \cancel \frac{330}{60} \: = \: 5.5 \\ [/tex]

Total hours in a day is 5.5

The average American student is in class 5.5 hours a day.

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

We have to given that;

The average American student is in class 330 minutes a day.

We know that;

⇒ 1 hours = 60 minutes

⇒ 1 minute = 1/60 hours

Hence, We can change the unit as;

⇒ 330 minutes = 330 / 60 hours

                        = 5.5 hours

Thus, It is equal to 5.5 hours.

Learn more about the measurement unit visit:

https://brainly.com/question/777464

#SPJ2

Answer:

If the area of a circular rose garden is 44 square meters, then we can write:

44 = πr^2

And since π is equal to  22/7, we have:

44 = 22/7(r^2)

Multiply both sides by 7/22 to cancel the 22/7:

14 = r^2

And finally, we see that the radius of the garden is:

[tex]\sqrt{14}[/tex]

Let me know if this helps!

Answer:

r = sqrt(14)

Step-by-step explanation:

The area of a circle is

A = pi r^2

44 = 22/7 * r^2

Multiply each side by 7/22

44 * 7/22 = 22/7 * 7/22 r^2

14 = r^2

Take the square root of each side

±sqrt(14) = r

The radius must be a positive length

r = sqrt(14)

Answer:

B. -2

Step-by-step explanation:

Slope (m) =  

ΔY

ΔX

=  

-2

1

= -2

θ =  

arctan( ΔY ) + 360°

ΔX

= 296.56505117708°

ΔX = 3 – 0 = 3

ΔY = -2 – 4 = -6

Distance (d) = √ΔX2 + ΔY2 = √45 = 6.7082039324994

Answer from Gauth math

Answer:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Answer:

Step-by-step explanation:

Im gonna guess C, not sure. good luck tho

Answer:

total number of marble=22

probability of picking 1 blue marble= 1/22

=45×10^-2

probability of getting a green ball= 5/21

= 238×10^-3

Answer:   1.4

Work Shown:

42 cupcakes : 30 minutes

42/30 cupcakes : 30/30 minutes

1.4 cupcakes : 1 minute

The unit rate is 1.4 cupcakes per minute. This assumes that the rate is kept the same.

Answer:

£200

Step-by-step explanation:

4 friends - 4 tickets

They need to BUY 3 tickets.

3 tickets will cost £1200

Divide the £1200 between the 4 friends which is £300.

They will then get the other 1 ticket for free and have 4 altogether!

Using pythagorean theorem

[tex]\\ \sf\longmapsto B^2=H^2-P^2[/tex]

[tex]\\ \sf\longmapsto x^2=13^2-5^2[/tex]

[tex]\\ \sf\longmapsto x^2=169-25[/tex]

[tex]\\ \sf\longmapsto x^2=144[/tex]

[tex]\\ \sf\longmapsto x=\sqrt{144}[/tex]

[tex]\\ \sf\longmapsto x=12[/tex]

Answer:

x = 12

Step-by-step explanation:

→ State Pythagoras theorem

a² + b² = c²

→ Rearrange to make b the subject

b² = c² - a²

→ Square root everything

b = √c² - a²

→ Substitute in the numbers

b = √13² - 5²

→ Simplify

b = 12

Answer:

D

Step-by-step explanation:

Simply because 25 is divisible by 5.

Answer:

x^2-12x+31

Step-by-step explanation:

Standard form of the quadratic equation (x-6)^2-5 is x^2-12x+36-5=x^2-12x+31

Answer:

A

Step-by-step explanation:

for a function there is only 1 output value for every input and the first option is the only one which meets that requirement

Answer:

x=10

y=-9

Step-by-step explanation:

eqn 2-1

-1x+10=0

x=10

in eqn 1

y=-2 ×10+11

-20+11

-9