7. (a) A line has the equation y = 6x – 3 and goes through the point (4, a).
Calculate the value of a.

Answer:

  1/(8b^2a^8)

Step-by-step explanation:

The given expression can be simplified using the rules of exponents.

  [tex]ba^4\times(2ba^4)^{-3}=\dfrac{ba^4}{(2ba^4)^3}=\dfrac{ba^4}{8(ba^4)^3}=\dfrac{1}{8(ba^4)^2}=\boxed{\dfrac{1}{8b^2a^8}}[/tex]

__

The applicable rules of exponents are ...

  a^-b = 1/a^b

  (a^b)^c = a^(bc)

  (ab)^c = (a^c)(b^c)

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Additional comment

It can be useful to think of an exponent as indicating repeated multiplication: 2^3 = 2×2×2, for example. Of course, the repeated multiplication can be nested: (4^2)^3 = (4^2)×(4^2)×(4^2) = (4×4)×(4×4)×(4×4) = 4^6

Numerator and denominator factors cancel in the usual way.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$25000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]25000=P\left(1+\frac{0.08}{12}\right)^{12\cdot 5}\implies 25000=P\left( \frac{151}{150} \right)^{60} \\\\\\ \cfrac{25000}{\left( \frac{151}{150} \right)^{60}}=P\implies 16780.26 \approx P[/tex]

Answer:

x = y = - 1

Step-by-step explanation:

y = - 2x - 3

y = 7x + 6 -----> equation 1.

So,

7x + 6 = - 2x - 3

7x + 2x = - 3 - 6

9x = - 9

Divide 9 on both sides,

9x / 9 = - 9 / 9

x = - 1

Substitute x = - 1 in equation 1,

y = 7x + 6

  = 7 ( - 1 ) + 6

  = - 7 + 6

  = 6 - 7

y = - 1

Therefore,

x = y = - 1

Step-by-step explanation:

please mark me as brainlest

Answer:

D

Step-by-step explanation:

this is not standard form

Answer:

D

Step-by-step explanation:

The first number should be equal to or greater than one but less than 10

Answer:

x = 4

y = -6

Step-by-step explanation:

5x + 2y = 8

8x + 4y = 8

-2(5x + 2y) = -2(8)

8x + 4y = 8

-10x -4y = -16

8x + 4y = 8

-10x -4y + 8x + 4y = -16 + 8

-2x = -8

x = 4

plug 4 into x so y = -6

Answer:

four sixths + three fifths.

Step-by-step explanation:

1 8/30 = 38/30.

4/6 + 3/5

= 20/30 + 18/30 = 38/30.

Answer:

36ft

Step-by-step explanation:

9ft times 4ft= 36ft

Answer:

They have 23 miles left to travel.

Step-by-step explanation:

If they have 65 miles total to travel and they've already gone 42 miles, 65-42=23

Answer:

x = 61

y = 29

Step-by-step explanation:

The angle with the measure of 58 degrees and the angle represented by 2x are supplementary because they form a straight line.

2x + 58 = 180 subtract 58 from both sides

2x = 122 divide both sides by 2

x = 61

The angle represented by 2x and the angle represented by 58 are corresponding and their measure is equal to each other

2y = 58 divide both sides by 2

y = 29

Answer:

h= 7/6 mm

Step-by-step explanation:

hello :

the area is :  A= (b+B)×h/2

calculate h the height  : 2A = (b+B)×h

so:  h = 2A/(b+B)

you have : A=21/5   and  b= 3    and B= 21/5

h= 2(21/5)/(3+21/5)

h= (42/5) /(36/5)

h= 42/36

h= 7/6 mm

Step-by-step explanation:

please mark me as brainlest

Answer:

for profit percentage

p% =(sp-cp/cp)×100%

=(25-20/20)×100%

=25%

The profit percentage is 25%

Answer:

2.3 miles

Step-by-step explanation:

Given by the circular pattern as shown in the diagram:

Ranger station to Nature Center = 90°

Nature center to petting zoo= 40°

Petting zoo to Tennis court =120°

Tennis court to Pool = 65°

Pool to Ranger station= 45°

The radius of the circular pattern = 1 mile

Formula:

Arc length = 2πr angle / 360° where r is radius and π=3.14

Solution:

Thus,

Arc length = 2×3.14×1×90°/360°

Arc length=2×3.14×1×1/4 =1.57 miles

Distance from Nature Center to Petting Zoo

Arc length= 2×3.14×1×40°/360°

Arc length= 2×3.14×1×1/9 = 0.70 miles

Total =1.57+0.70 =2.27 miles

Answer to the nearest tenth = 2.3 miles

For more information:

https://brainly.com/question/11692709

~lenvy~

Answer:

found in a toys store and cost more than 50$

Step-by-step explanation:

it makes the most sense don't you think?

Answer: 3.75 is at it's lowest terms. if you mean fractions its 15/4 or 3 & 3/4

Step-by-step explanation:

Answer:

800m

Step-by-step explanation:

If 100cm is equivalent to a meter (1 Meter). 8 Meters would be equivalent to 8 Meters multiplied by 100cm and divided by a meter (1 Meter)

Answers:

10.) [tex]\displaystyle \pm{5}[/tex]

9.) [tex]\displaystyle 1\frac{1}{2}[/tex]

8.) [tex]\displaystyle \pm{1\frac{1}{2}}[/tex]

7.) [tex]\displaystyle \pm{1\frac{1}{2}}[/tex]

6.) [tex]\displaystyle \pm{\frac{1}{2}}[/tex]

Step-by-step explanations:

10.) [tex]\displaystyle \frac{\sqrt{200}}{\sqrt{8}} \hookrightarrow \sqrt{25} \hookrightarrow \frac{\pm{10\sqrt{2}}}{\pm{2\sqrt{2}}} \\ \\ \boxed{\pm{5}}[/tex]

9.) [tex]\displaystyle \frac{\sqrt[3]{135}}{\sqrt[3]{40}} \hookrightarrow \sqrt[3]{3\frac{3}{8}} \hookrightarrow \frac{3\sqrt[3]{5}}{2\sqrt[3]{5}} \\ \\ \boxed{1\frac{1}{2}}[/tex]

8.) [tex]\displaystyle \frac{\sqrt[4]{162}}{\sqrt[4]{32}} \hookrightarrow \sqrt[4]{5\frac{1}{16}} \hookrightarrow \frac{\pm{3\sqrt[4]{2}}}{\pm{2\sqrt[4]{2}}} \\ \\ \boxed{\pm{1\frac{1}{2}}}[/tex]

7.) [tex]\displaystyle \frac{\sqrt{63}}{\sqrt{28}} \hookrightarrow \sqrt{2\frac{1}{4}} \hookrightarrow \frac{\pm{3\sqrt{7}}}{\pm{2\sqrt{7}}} \\ \\ \boxed{\pm{1\frac{1}{2}}}[/tex]

6.) [tex]\displaystyle \frac{\sqrt{12}}{\sqrt{48}} \hookrightarrow \sqrt{\frac{1}{4}} \hookrightarrow \frac{\pm{2\sqrt{3}}}{\pm{4\sqrt{3}}} \\ \\ \boxed{\pm{\frac{1}{2}}}[/tex]

I am joyous to assist you at any time.

Answer: -63.5 feet per mintue

Step-by-step explanation:

      We can look at what the problem is asking for, and solve. It says average change in altitude per minute:

[tex]\frac{altitude}{minute}[/tex] = [tex]\frac{1,524}{24}[/tex] = 63.5 feet per mintue

      Since she is hiking down the mountainside, this will be negative. We arrive at our final answer of:

      -63.5 feet per mintue

The graph with an equation y = 6x has a slope of 6. If the slope is changed to 0, the equation becomes y = 0.

A linear function is in the form:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept

The graph with an equation y = 6x has a slope of 6. If the slope is changed to 0, the equation becomes y = 0.

Find out more on linear function at: https://brainly.com/question/4025726

Answer:

Theories used

Angles on a straight line will always add up to 180°

The sum of interior angles in a triangle is 180°

Question 7

a + 134° = 180°

⇒ a = 180° - 134°

⇒ a = 46°

b + 119° = 180°

⇒ b = 180° - 119°

⇒ b = 61°

a + b + c = 180°

⇒ 46° + 61° + c = 180°

⇒ c = 180° - 46° - 61°

⇒ c = 73°

Question 8

r + 126° = 180°

⇒ r = 180° - 126°

⇒ r = 54°

s + 145° = 180°

⇒ s = 180° - 145°

⇒ s = 35°

r + s + t = 180°

⇒ 54° + 35° + t = 180°

⇒ t = 180° - 54° - 35°

⇒ t = 91°

#7

c=

#8

Answer:

At both 0.78 and 1.3 seconds, to the nearest hundredth, the ball will be at 20 feet.  

Step-by-step explanation:

We can use two approaches to finding the answer:  Calculation and Graphing.

Calculation:

Set h to 20 feet and solve the equation using the quadratic formula.

h= 4 + 33t - 16t^2

20= 4 + 33t - 16t^2

- 16t^2 + 33t + 4 = 20

- 16t^2 + 33t + -16 = 0

Solve using the quadratic formula.  I find solutions of 0.779 and 1.28 seconds.

Graphing:

See the attached graph.

The ball is at 20 feet at 0.783 seconds on the way up and 1.28 seconds on the way back down.

===

Both approaches agree:  0.78 and 1.3 seconds, to the nearest hundredth, the ball will be at 20 feet.  

Answer:

a = 2

b = 4

Step-by-step explanation:

Δy   = 2x + a.................for turning point, Δy/Δx = 0.

Δx

0 = 2x + a

x = -a/2.........from ( -1, 3), x = -1...............so,

-1 = -a/2.................a = 2.

y = x^2 + ax + b.

y = 3  ,    a = 2.................substitute.

3 = (-1)^2 + 2(-1) + b

3 = 1 -2 + b

b = 4

Answer:

The turning point of a parabola is the vertex

Vertex form of a quadratic equation: [tex]\sf y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex and a is the coefficient of the variable x²)

Given:

Therefore, a = 1

Substituting a = 1 and the given vertex into the equation:

[tex]\sf \implies y=1(x-(-1))^2+3[/tex]

[tex]\sf \implies y=(x+1)^2+3[/tex]

[tex]\sf \implies y=x^2+2x+1+3[/tex]

[tex]\sf \implies y=x^2+2x+4[/tex]

Therefore, a = 2 and b = 4

Answer: 343pi/18

Step-by-step explanation:

Answer:

215 minutes

Step-by-step explanation:

1 hour = 60 min

3x60=180

180+35=215

Answer:

The answer is 215 minutes

Step-by-step explanation:

1 hour is 60mintues

you have 3 hours so you would do

60+60+60=180 or 60*3=180

then take the 35 minutes you have and add those together.

180+35=215 total minutes

Hope this helps mark brainliest please! :)

X/6 = 15/18

Cross multiply:

18x = 15 times 6

18x = 90

Divide both sides by 18

X = 5

5/6 = 15/18

Answer:

Step-by-step explanation:

X= 15  x6

     18

I guess it is correct

Answer:Cost = $33 per month + Fee 1.  C(m) = 33m + F 33(6) + F = 228198 + F = 228F = $30 membership fee C(m) = 33m + 30 2.  At 9 months:  33(9) + 30 = $327

Step-by-step explanation:

Answer:

(x - 3)² + (y - 5)² = 16

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

given (h, k ) = (3, 5 ) we require to find r

r is the distance from the centre to a point on the circle

given x = - 1 is a tangent the r is the distance between the x- coordinates

r = | 3 - (- 1) | = | 3 + 1 | = | 4 | = 4

then equation of circle is

(x - 3)² + (y - 5)² = 4² , that is

(x - 3)² + (y - 5)² = 16

Answer:

there is not enough information to solve

Step-by-step explanation:

You need two ordered pairs to calculate the average rate of change.

Let's say the value of the function at n = 1 is a, and the value of the function at n = 3 is b, then the average rate of change from n = 1 to n = 3 is

(b - a)/(3 - 1) = (b - a)/2