Put the known terms together on one o
equation.
Example: 3x + 6 = 30
3x = 30 - 6
1. 2b10 =12
2.8 + 5x = 41
3 6 - 42 = 12.
4. 3n = 60 +n
5. 7a+ 5 = 54
ale
ACTIVITY 2:
Solve and check. Show your complete solutions.
1. x+ 5 = 2
2 X – 10 = 22
3. 41 + 3x = -29-18
4. x-27 = 8 + 10
5. 5x + (-55) = 20
ACTIVITY 3:
Solve each problem. Show your solution.
1. What is the number if twice a number is increased by 9
2. If twelve less than a thrice a number is 3, what is the n​

Answer:

answer below

Step-by-step explanation:

1) when multiplying you add the powers so

7^-9 x 7^-3 = 7^x

-9 + -3 = -12

2) when dividing you subtract the powers

so -4 - -8= 4

hope this helps!

In parabοla, the fοcal width, well, |4p| is pretty much the fοcal width, in this  case,  20.

What is parabοla in math?  

The set οf all pοints (x, y) οn a plane that are spaced apart by the same amοunt frοm the directrix—a fixed line—and frοm a fixed pοint (the fοcus) that is nοt οn the directrix is referred tο as a parabοla. It is pοssible tο graph the parabοla using its standard fοrm, which has vertex (0,0) and the x-axis as its axis οf symmetry.

vertical parabοla vertex frοm with fοcus pοint distance.

4p(y - k) = (x - h)²

 -1/20 x² = y

 x²/-20 = y

 x² = -20y

(x - 0)² = 20(y - 0)

(x - 0)² = 4(-5)(y - 0)

vertex is at (0,0)

the fοcus pοint is "p" οr 5 units dοwn frοm there, namely at (0, -5)

the directrix is "p" units οn the οppοsite directiοn, up, namely at y = 5

the fοcal width, well, |4p| is pretty much the fοcal width, in this  case, is simply yeap, yοu guessed it, 20.

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The complete question is -

Find the vertex, focus, directrix, and focal width of the parabola.

-1/20x²= y

Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

Answer:

6 numbers

Step-by-step explanation:

Given

\(x = \{1,2,3,4,5,6,7,8,9,10\}\)

Required

Pairs that add up to 11

The pairs are:

\(x = \{\{1,10\},\{2,9\},\{3,8\},\{4,7\},\{5,6\}\}\)

In the above set, we have:

\(n(x) =5\)

Using pigeonhole principle

This principle implies that, there is at least 1 more pair.

Hence, the numbers that must be selected to guarantee the required sum of 11 is:

\(n= 5+1\) --- The 1 represents (at least 1 more)

\(n=6\)

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then I'll help you
the questions is in my page

A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

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Answer:

47.1cm²

Step-by-step explanation:

diameter=15cm

circumference of circle= d×3.14

circumference=15×3.14

circumference=47.1

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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Answer:

x = 180-95=85

z=180-52=128

y=85(x)+52+x=180

so =180-137=43

so y=180-43=137of y

Step-by-step explanation:

this is done because of the rule of triangle that is sum of all angle is 180

Given

The value of the cosine of the angle of (a - b) will be 0.80.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

It is a function that repeats itself in a particular time interval.

Suppose that sin(a) = 4/6 and cos(b) = 1/5.

Then the value of 'a' is given as,

sin(a) = 4/6

sin(a) = 2/3

a = 41.81°

Then the value of 'b' is given as,

cos(b) = 1/5

b = 78.46°

Then the value of the cosine of the angle of (a - b) will be given as,

⇒ cos(41.81° - 78.46°)

⇒ cos(-36.65°)

⇒ cos 36.65°

⇒ 0.80

The value of the cosine of the angle of (a - b) will be 0.80.

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Answer:

C.)

Step-by-step explanation:

that is exactly the definition of the derivative.

the derivative is the limit of

(f(x+h) - f(x))/((x+h) - x) = (f(x+h) - f(x))/h

with h going to 0.

this is the limit of the standard rate of change concentrated on a single point = the slope of the tangent at that point.

Answer:

\(59^{\circ}\)

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary.

\(5x-11+11x-33=180 \\ \\ 16x-44=180 \\ \\ 16x=224 \\ \\ x=14\)

Opposite angles of a parallelogram are congruent.

\(m\angle N =m\angle P \implies m\angle P=5(14)-11=59^{\circ}\)

Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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Answer:

The 3.907 is approximate.

====================================

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

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

Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

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

Extra info:

Answer:

3) x = -4 and y = 6

4) x = -1 and y = 0

5) x = 1 and y = -3

6) x = -4 and y = -3

Step-by-step explanation:

3) Add the equations:

(3x + 4y = 12) + (-3x - y = 6) (eliminate the x)

= 3y = 18

y = 18/3

y = 6

3x + 4(6) = 12

3x = 12 - 24

x = -12/3 = 4

4) Add the equations:

(-5x - 6y = 5) + (-6x + 6y = 6)

-11x = 11

x = -1

-5(-1) -6y = 5

-6y = 5 - 5

y = 0

5) 7x -4y = 19

10x - 2y = 16

Multiply the second equation by -2 to eliminate the y and add both equations.

-2(10x -2y = 16) =

(-20x + 4y = -32) + (7x - 4y = 19)

-13x = -13

x = 1

7(1) - 4y = 19

-4y = 19-7

y = 12/-4

y = 3

6) multiply the second equation by -2 to eliminate the x and then add the equations.

-2(5x - 3y = - 11) =

(-10x + 6y = 22) + (10x - 9y = - 13)

= -3y = 9

y = - 3

10x - 9(-3) = - 13

10x = -13 - 27

x = -40/10

x = -4

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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Dear Editor,


I am writing to express my concern about the issue of leakages in Zambia. The constant leakages of natural resources such as oil, gas and minerals have been a major setback to the country's economic growth and development.


It is disheartening to note that despite the country being rich in natural resources, the benefits of these resources have not been fully realized due to leakages. This has led to a loss of revenue that could have been used to improve the lives of citizens through investments in education, healthcare, and infrastructure.


Furthermore, leakages also have negative environmental impacts, which can affect the health and wellbeing of communities living in the vicinity of these resources.


As a concerned citizen, I urge the government to take decisive action to curb leakages and ensure that the country's natural resources are utilized for the benefit of all Zambians.


Sincerely, [Your Name]

The probability that a Statistics student is also in African-American Literature is 18%.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Let, The total number of students is 100.

Given, 30% of the seniors are in statistics.

Therefore, The probability of choosing a student in statistics is,

= 30/100.

= 3/10.

Similarly, The probability of choosing a student in African-American Literature is,

= 18/100.

= 9/50.

We know the probability of A given B is P(A∩B)/P(B).

Therefore, The likelihood that a student majoring in statistics will also study African-American literature is,

= [(3/10)×(9/50)]/(3/10).

= 0.054/0.3.

= 0.18 Or 18%.

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Answer:

English?

Step-by-step explanation:

Answer:

sorry wish I could've helped you

Answer:

\(100 {in}^{2} \)

Step-by-step explanation:

Answer:

100 sq.inches

Step-by-step explanation:

Area of the square = Side x Side

So, Area= 10 x 10

= 100 sq.inches

Answer: C equals 2.

Step-by-step explanation:

37 + (-2c - 3) = 4c + 20 +c (distribute)

34 - 2c = 5c +20 (combine like terms)

14 = 7c (divide)

c = 2

Answer:

C

Step-by-step explanation:

reciprocal of z=1/z

\(z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}\)

Hi there!

To make n+1>4 true, you must have n be a numebr greater than 3...

The reason why is because if it is less than 3 or 3, it’ll have to be <.

The two numbers that can make this equation true is 4 and 5...

\(4+1=5>4\)

\(5+1=6>4\)

And if it is 1,2, and 3 it would be:

\(1+1=2<4\)

\(2+1=3<4\)

\(3+1=4=4\)