1
Solve these simultaneous equations using the elimination method

4x + y = 23
x + y = 8​

Answer:

[tex]\log_5(\frac{x}{4})^2 = 2\log_5(x) - 2\log_5(4)[/tex]

Step-by-step explanation:

Given

[tex]\log_5(\frac{x}{4})^2[/tex]

Required

The equivalent expression

To do this, we apply the following law of indices:

[tex]\log_a(b)^c = c\log_a(b)[/tex]

So, we have:

[tex]\log_5(\frac{x}{4})^2 = 2\log_5(\frac{x}{4})[/tex]

To further simplify:

[tex]\log(\frac{a}{b}) = \log(a) - \log(b)[/tex]

So, we have:

[tex]\log_5(\frac{x}{4})^2 = 2(\log_5(x) - \log_5(4))[/tex]

Open brackets

[tex]\log_5(\frac{x}{4})^2 = 2\log_5(x) - 2\log_5(4)[/tex]

Answer:

C.

Explanation:

Edge 2021

Answer:

0.77

Step-by-step explanation:

Given that:

P(A) = 0.64

P(B) = 0.25

P(AnB) = 0.12

Probability that customer buys either pet or baby supplies ; P(AuB)

P(AuB) = P(A) + p(B) - p(Ann)

P(AuB) = 0.64 + 0.25 - 0.12

P(AuB) = 0.77

Answer:

D

Step-by-step explanation:

its just rabdom numbers

Answer:

D thats just a number no sequence or any thing

Step-by-step explanation:

Answer:

[tex]{ \tt{formular :}} \\ { \boxed{ \bf{centripental \: acceleration = \frac{ {v}^{2} }{r} }}} \\ \\ { \tt{30= \frac{ {3.7}^{2} }{r} }} \\ \\ { \tt{r = \frac{ {3.7}^{2} }{30} }} \\ \\ { \tt{radius = 0.456 \: meters}}[/tex]

Answer:

The answer is 3

For the steps, Im leaving it blank for you to figure it out first.

If you really need help, ask anytime and I'll reply as soon as i can :)

Answer:

234

Step-by-step explanation:

182/7= 26 9x26=234

why is there a minimum number of characters needed

Answer:

e-154

f-648

Step-by-step explanation:

rttyyuuguguvuhuhihihuhuhuhihihih7

Answer:

for e

[tex] v = \frac{1}{ 2} \times 8 \times 7 \times 5.5 = 154[/tex]

for f

v=6×9×12=648

Answer:

yes

Yes; the graph passes the vertical line test.

Step-by-step explanation:

if it were a graph of a circle it would not pass

the vertical line test because the vertical line would touch at least 2 points

graph is probably a cubic function

something like

y = x^3-4x+6

Answer:

m<I, m<G, m<H

Step-by-step explanation:

The angle that sees the longest side length has the biggest measurement

so

if we were to list the angles from largest to smallest

m<I, m<G, m<H

Answer:

2p + 9 = 3

2p = 3 - 9

2p = -6

p = -6/2

p = -3

Step-by-step explanation:

Refer Fig 1 as attached

1a. angle a = angle b = 25°

AM = 8 x cos 35° = 6.553

so AB = AM x 2 = 13.1

1b. Area of sector OAB / Area of the circle

= 130 / 360

Area of sector OAB = 8x8xpi x 130/360

= 23pi

1c. Area OAB = 2 X ( AM x OM) /2 = AM x OM

OM = AM x tan (angle a) = 13.1 x tan 25°

= 6.109

so Area OAB = 6.553 x 6.109 = 40.03

1d. Area of the minor segment

= Area of sector OAB - Area of triangle OAB

= 23pi - 40.03

= 32.23

2, 3 Please refering the approach as above to find the answers

4. Refer Fig 2 as attached

a = 3

the cord is 3 cm from the centre

5. Repeat the approach of 4 above please.

Answer:

∠ J = 71°

Step-by-step explanation:

Given that the triangles are congruent then corresponding angles are congruent, so

∠ H = ∠ Y  = 38°

Since GH = JH then Δ GHJ is isosceles and the 2 base angles are congruent

∠ J = [tex]\frac{180-38}{2}[/tex]= [tex]\frac{142}{2}[/tex] = 71°

Answer:

(672-640)/640 x 100 = 5%

Answer:

Length = 6cm

Step-by-step explanation:

You would get 6cm as the length, because 6 ÷ 3 = 2, that is your width. So in the same way, you would divide 18 by 3 and get 6, thus the length of the second rectangle is 6 centimeters

Hope it helps :D

6 cm po tama to mag quandary pi akyu

Answer: x=pi/8+npi    and x=5pi/8+npi

Step-by-step explanation:

Answer:

Graph the system on linear equations.

Step-by-step explanation:

(-4, 4) & (-4, -6)

Answer:

(- 3, - 7 )

Step-by-step explanation:

Given the 2 equations

y = 4x + 5 → (1)

y = x - 4 → (2)

Substitute y = 4x + 5 into (2)

4x + 5 = x - 4 ( subtract x from both sides )

3x + 5 = - 4 ( subtract 5 from both sides )

3x = - 9 ( divide both sides by 3 )

x = - 3

Substitute x = - 3 into either of the 2 equations and evaluate for y

Substituting into (2)

y = x - 4 = - 3 - 4 = - 7

solution is (- 3, - 7 )

Answer:

y=1/3x+7

Step-by-step explanation:

Hi there!

We're given the equation x-3y=21 and we want to find the equation of the line parallel to x-3y=21 that passes through (-6,5)

Parallel lines have the same slopes, but different y intercepts

So we need to find the slope of x-3y=21

To do that, we can convert x-3y=21 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept).

We'll need to isolate y onto one side

subtract x from both sides

-3y=-x+21

divide both sides by -3

y=1/3x-7

1/3 is in the place where m is, so 1/3 is the slope of the line

it's also the slope of the line parallel to x-3y=21

here's the equation of the line parallel to x-3y=21 so far:

y=1/3x+b

we need to find b

as the line passes through (-6,5), we can use it to solve for b

substitute -6 as x and 5 as y

5=1/3(-6)+b

multiply

5=-2+b

add 2 to both sides

7=b

Substitute 7 as b into the equation

y=1/3x+7

Hope this helps!

Answer:

Let's see each case.

a) 2

We know that a number is divisible by two if it ends in {0, 2, 4, 6, 8}

In our case, we have 240,720

We can see that it ends with a zero, so it is divisible by 2.

b) 3

A number is divisible by 3 only if the sum of its digits is a multiple of 3.

For our number, the sum of the digits gives:

2 + 4 + 0 + 7 + 2 + 0 = 2 + 4 + 7 + 2 = 6 + 9 = 15

15 is a multiple of 3, then 15 is divisible by 3.

then 240,720 is divisible by 3.

c) 4

A number is divisible by 4 if the last two digits form a number that is divisible by 4.

In this case, the last two digits are 2 and 0, so they form the number 20

and we know that 20 = 4*5 is a multiple of 4.

then 20 is divisible by 40

then 240,720 is divisible by 4

d) 5

A number is divisible by 5 if it ends in 0 or 5.

Our number ends in a 0, so it is divisible by 5.

e) 6

A number is divisible by 6 if it is divisible by 2 and 3.

We already know that our number is divisible by 2 and 3, so we can conclude that it is also divisible by 6.

f) 8

A number is divisible by 8 if, in the case where the hundreds digit is odd, the number obtained from the last two digits plus 4 must be divisible by 8.

in the case where the hundreds digit is even, the number formed by the last two digits must be divisible by 8.

In our case the hundreds digit is 7, so it is odd, so we will use the first criteria.

The last two digits form the number 20

if we add 4, we get:

20 + 4 = 24

And 24 is a multiple if 8:  8*3 = 24

Then 24 is divisible by 8, then 240,720 is divisible by 8.

g) 9

Similar for the case of the 3, a number is divisible by 9 if the sum of its digits is divisible by 3.

We know that the sum of the digits of our number is 15, which is not divisible by 9, then our number is not divisible by 9

h) 10

A number is divisible by 10 if the last digit is a zero.

In this case the last digit is a zero, so  240,720 is divisible by 10.

i) 11

A number is divisible by 11 if:

starting from the left, you need to add and subtract each subsequent digit, if this is divisible from 11, then the original number is divisible by 11.

Then for  240,720 we have:

2 - 4 + 0 - 7 + 2 - 0 = -2 - 5 = -7

-7 is not divisible by 11, so our number is not divisible by 11

Answer:

choice: A

Step-by-step explanation:

Answer:

There are 105 pennies in the piggy bank.

There are 42 nickels in the piggy bank.

Step-by-step explanation:

there are:

p pennies in the piggy bank

n nickels in the piggy bank

Then we can define T, the total number of coins, as:

T = p + n

We know that 2/7 of the total number of coins are nickels.

This can be written as:

n = (2/7)*T = (2/7)*(n + p)

And if we remove 84 pennies, 1/3 of the remaining coins are pennies.

This can be written as:

p - 84 = (1/3)*(n + p - 84)

Then we have a system of two equations:

n = (2/7)*(n + p)

p - 84 = (1/3)*(n + p - 84)

Let's solve the system, to do it, we first need to isolate one of the variables in one of the equations.

We can isolate n in the first one, to get:

n = (2/7)*(n + p) = (2/7)*n + (2/7)*p

n - (2/7)*n = (2/7)*p

n*(5/7) = (2/7)*p

n = (7/5)*(2/7)*p = (2/5)*p

n = (2/5)*p

Now we can replace this in the other equation:

p - 84 = (1/3)*(n + p - 84)

p - 84 = (1/3)*( (2/5)*p + p - 84)

Let's solve this for p

p - 84 = (1/3)*( (7/5)*p - 84)

3*(p - 84) = (7/5)*p - 84

3p - 252 = (7/5)*p - 84

3*p - (7/5)*p = 252 - 84

(15/5)*p - (7/5)*p = 168

(8/5)*p = 168

p = (5/8)*168 = 105

There are 105 pennies in the piggy bank.

And we know that:

n = (2/5)*p = (2/5)*105 = 42

There are 42 nickels in the piggy bank.

Answer:

the average probability of all possible outcomes of a future event occurring, weighted by each possible outcome individually

Step-by-step explanation:

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

In Statistics, an expected value can be defined as the average probability of all possible outcomes of a future event occurring in an experiment, weighted by each possible outcome individually. Thus, an expected value in theory refers to the outcome an individual expect to obtain from an experiment in the long-run.

Mathematically, an expected value can be calculated by summing the products of each distinct outcome and their probability respectively.

my answer is in the image above

Answer:

C

Step-by-step explanation:

2x+4=16-x

2x-x=16-4

x=12

So C

Answer and Step-by-step explanation:

The parent function, f(x) = |x|, has no transformations applied to it.

When the number is with the x, it translates the graph horizontally. <->

When the number is outside of the absolute box, it translates the graph vertically. ^ V

When the number is multiply the absolute box on the outside with the x inside, it scales the graph.

So, first lets apply the translations of horizontal and vertical shift.

The graph translated 1 units downwards.

The graph translates 2 units to the right.

g(x) = |x - 2| - 1

We subtract the 2 because that makes it go right, while if we added it would go left.

Now for the scale.

The lines have a slope of [tex]\frac{1}{4}[/tex], so that is what we are multiplying.

g(x) = [tex]\frac{1}{4}[/tex]|x - 2| - 1

^That is your transformed function.

#teamtrees #PAW (Plant And Water)

Answer:

These people are using the representativeness heuristic to make this faulty guess. A correct guess would have been made if they had used base rate information.

Step-by-step explanation:

Representativeness heuristic occurs when the similarity of items or events causes individuals to be perplexed about the likelihood of a given result. People usually make the error of guessing that two comparable things or occurrences are more closely related than they are. Therefore, the similarity of an engineer and a calculator confuse the people to guess that Albert is an engineer.

Base rate information refers to the information provided by base rates which are a type of statistic that is used to describe the percentage of a population that exhibits a certain feature. Base rates suggest the likelihood of something based on the lack of other facts. Using the information in the question as an example, if 20% of the employees were engineers and 80% were lawyers, the base rate of lawyers is simply 80%. This implies that Albert is a lawyer, but we won't know for sure until we look at the total number of workers that the base rate information reveals that he is a lawyer.

Therefore, these people are using the representativeness heuristic to make this faulty guess. A correct guess would have been made if they had used base rate information.