The expressions (x²-ax-b) and (2x² + b) have a common factor (x + c),
where a, b and c #0
(i) Show that b=2ac/3
(ii) Given that a = -b = -3c, find the common factors.

Answer:

t < 23

Step-by-step explanation:

t - 2 < 21

Step 1 : Add 2 on both sides.

t - 2 + 2 < 21 + 2

t < 23

The height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

It is given that:

Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

D = 39.75 m

d = 34.9 m

H:h = D:d

H/1.85 = 39.75/34.9

H = 2.11 m

Thus, the height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

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Answer:

  53

Step-by-step explanation:

You want the value of a^2 +b^2, given that 'a' and 'b' are roots of the polynomial x^2 +7x -2.

If the roots are 'a' and 'b', then the factored form is ...

  (x -a)(x -b) = x^2 -(a+b)x +ab

Comparing this to the given polynomial, we see that ...

  -(a+b) = 7

  ab = -2

The expression a^2 +b^2 can be written as the sum ...

  a^2 +b^2 = a^2 +2ab +b^2 -2ab = (a+b)^2 -2ab

Using the values of (a+b) and ab from above, we see that ...

  a^2 +b^2 = (-7)^2 -2(-2) = 49 +4 = 53

The given expression has a value of 53.

Answer:

Step-by-step explanation:

The result of the expression given is 3x - 3

To solve this problem, we have to simplify the equation, and write the expression.

Given that

[tex]\sqrt{x^2}+ 2x -3[/tex]

In the square root, we can eliminate the square and square root using the square root rule.

Lets apply that in this expression

[tex]\sqrt{x^2} + 2x - 3\\x + 2x - 3[/tex]

Lets solve the expression

[tex]x + 2x - 3\\3x - 3[/tex]

The value of the expression given is 3x - 3

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Answer:

From the bit that you have given , we can say = 5a + ab = to the rest of the equation

The half life obtained to the nearest tenth is 5.0 days.

The half life is the time taken for only half of the initial amount of the radioactive substance to remain. We know that we have to use the formula;

N=N0e^-kt

N = amount present at time t

No = Amount initially present

k = The constant

t = The half life

We now have that;

HALF LIFE = O.693/k

We have to recall that the term k is the decay constant for the process as shown.

Half life = O.693/0.1394

Half life = 5.0 days

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Answer:

Question 4

Answer: Alternative C - 0

Step-by-step explanation:

Since x→∞, we can substitute the values of x for values as 10, 100, 1000 and see the tendency of the function when the values are getting higher (closer to ∞):

For x = 10

f(10) = 0.5*10^(-3/4)

f(10) = 0.089

For x = 100

f(10) = 0.5*100^(-3/4)

f(10) = 0.016

For x = 1000

f(10) = 0.5*1000^(-3/4)

f(10) = 0.003

As we can see, when the x-values are getting closer to infinite, the y-values tends to zero. Thus, alternative C is correct.

Given data

Ammy has a piece of wood that measures 42 inches

Ammy cut from the 42-inch piece of wood is calculated as

Thus, Amy cut from the 42-inch piece of wood is 33 inches

Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:

2x² + 5x + 1.

In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:

8, 26, 19 and 3.

The divisor is found as follows:

4x + 3 = 0

4x = -3

x = -3/4

x = -0.75.

The resulting coefficients of the quotient are given as follows:

8, 20, 4 and remainder of 0.

Hence the quotient is:

8x² + 20x + 4.

Which can be simplified as:

2x² + 5x + 1.

The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.

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Jacinda get 12% of commission

How to find percentage :

The cost of shoe that customer purchased is $259.50

The amount that Jacinda get commission is $31.14

To calculate the percentage of commission divide 31.14 by 259.50 and multiply by 100.

That is percentage of commission = 31.14/259.50 * 100

                                                         = 12%

Jacinda get 12% of commission.

What is percentage ?

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Answer:

1/4

Step-by-step explanation:

The points (-4, 5) and (0, 6) lie on the line. Substituting into the slope formula,

[tex]\frac{6-5}{0-(-4)}=\frac{1}{4}[/tex]

Answer: No the input 3 has two out puts

Step-by-step explanation:

Use ur eyes

The probability that a value selected at random from this distribution is greater than 20 is 0.5.

What is a probability with normal distribution?

The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. The probabilities for values that are farther from the mean taper off equally in both directions.

Here,

Let us assume that X follows a normal distribution.

If X follows a normal distribution, then

z = (X−μ) /σ, follows a standard normal distribution.

The probability of a value selected at random from this distribution is greater than 20:

P (X > 20) = 1 − P (X ≤ 20)

P ((X − μ) / σ > 20) = 1−P((X − μ) / σ ≤ 20)

P (z > (20 − 20) /5) = 1 − P (z ≤ (20−20 / 5))

P (z > 0) = 1 − P (z ≤ 0)

The value of probability is obtained from the standard normal table as:

P (z > 0) = 1 − P (z ≤ 0)

             = 1 - 0.5

            = 0.5

Hence, the probability that a value selected at random from this distribution is greater than 20 is 0.5.

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Answer:

A function is a relation where each input value is assigned to only one output value. The domain of a function is the set of all input values, or x-values, for which the function is defined. The range of a function is the set of all output values, or y-values, for which the function is defined. To write the equation y = ax + b in function notation, substitute f(x) for y.

Step-by-step explanation:

Brainlest, Please!

We will see that the linear equation that passes through the two given points is:

y = 4x + 28

So the y-intercept is y = 28.

First, we need to find the linear equation that passes through the two given points. Remember that for a line that passes through two points (x₁, y₁) and (x₂, y₂), the slope is:

m = (y₂ - y₁)/(x₂ - x₁)

Here our line passes through (-8,-5) and (10, 67), then the slope is:

m = (67 + 5)/(10 + 8) = 4

So we can write:

y = 4*x + b

To find the value of b we can use the point (-8,-5), replacing these values we get:

-5 = 4*-8 + b

-4 + 4*8 = b

28 = b

So the y-intercept is 28.

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a) We know that in the northern Hemisphere we have 4 seasons: Summer where is more sun, Spring, and autumn that the sun is like 50/50 and winter that is the season with less sun. So we can made a graph with this so:

b) In this case if we have a simple interest is going to be a streight light that is going to increase. So the graph will be:

c) An item that increase it's price by 50% is going to be increasing each time more, so this case will be an exponential so the graph will be:

d) The high of a triangle and the base of the triangle are going to to have a constant rate. so the graph will be a horizontal line so:

Answer:

The slope is 0.

Step-by-step explanation:

Using the slope formula which is m= y2 - y1 / x2 - x1, plug in the x values and y values of the two points. (12,-18) is x1 and y1. (-15,-18) is x2 and y2.

When plugging it in we get -18 - (-18)/ -15 - 12.  You cannot subtract a negative so it turns from subtraction to addition. So, -18 + 18 / -15 - 12 which equals 0/-27. 0 divided by any number is 0. So the slope is 0, m=0.

Hope this helps :)

Answer:

D

Step-by-step explanation:

22.5÷3 is 7.5 and 52.5÷3 is 7.5 as well

Money is y axis (x,y) and candles is x axis (x,y)

(a) Let "X" be the random variable that represents the time in minutes required to assemble the product.

(b) The random variable may assume the values in the interval (0, ∞).

(c) The random variable "X" is continuous in nature.

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Answer:

I gotchu

Step-by-step explanation:

1= 155

2= 222

3= 44

4= 132

5= 163

Answer:

c and e

Step-by-step explanation:

(a)

x² - 4x + 3 = 0 ← is a quadratic and not linear

(b)

6x - 2y = 7 ← is a linear equation in 2 variables, x and y

(c)

3x - 1 = - 2x ( add 2x to both sides )

5x - 1 = 0 ← is a linear equation in 1 variable

(d)

pq - 3 = p ← is a linear equation in 2 variables , p and q

(e)

3x + 2 = 4(x + 7) + 9 ← is a linear equation in 1 variable

The no. of schnauzers in the annual dog show are 20.

Assume that there are x Schnauzers at the annual dog show.

Scotties entered in the yearly dog show: x + 3

There are 2x - 5 Wirehaired Terriers entered in the annual dog show.

There are 78 dogs in all competing in the yearly dog show.

Consequently, the equation becomes

x + x + 3 + 2x - 5 = 78.

4x - 2 = 78

4x = 78 + 2

4x = 80

x = 80/4

  = 20

In the yearly dog show, there are 20 Schnauzers. I hope you can understand the process without too much trouble. It is crucial to thoroughly study the equation so that you can easily solve the issue.

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The minutes will it be until they complete a lap at the same time is 2.4 minutes

From the information, Lana can walk around the track in 4 minutes and Raul can walk around the track in 6 minutes.

Lana will cover a distance of 1/4 while Raul will be represented as 1/6.

This will be illustrated as:

1/4 + 1/6 = 1

3/12 + 2/12 = 1

5x/12 = 1

Cross multiply

5x = 12

x = 12/5

x = 2.4 minutes

Note that x = number of minutes

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1. The total number of cases of cancer x that could be prevented if each one of the exposures were eliminated is 900.

2. The suggestion to the public health agencies if they requested the one exposure that would have a greater impact on reducing the prevalence of cancer x if eliminated is smoking.

The prevalence rate refers to the proportion of the population who have a particular disease or attribute or can be exposed to risks at a specified time or over a specified period.

The assumed population size in Epiland  = 1,000

Prevalence of smoking in Epiland = 60%

The number of Epiland smokers = 600 persons (1,000 x 60%)

Percentage of people drinking water with a high concentration of heavy metals = 30%

The number of people drinking the water = 300 (1,000 x 30%)

The total number of people exposed to cancer x = 900 (600 + 300).

Thus, 90% of the population in Epiland is exposed to cancer x based on the prevalence rate of smoking and the high concentration of heavy metals in their drinking water.

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x² -16=0

1) Since we have two roots and any quadratic equation can be rewritten as once we have the roots:

So let's find one equation whose roots are 4 and -4, with coefficient a=1

(x-4)(x+4)=0

x² -16=0

2) So the equation x² -16= 0 has roots x_1=4 and x_2= -4 S={-4,4}

Answer:what photo

Step-by-step explanation:

where

1) There exists a 3.82% probability that at least one right-handed student in this class is forced to utilize a seat designed for a left-hander.

2) There exists a 68.35% probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander.

The binomial probability exists the probability of exactly x successes on n repeated trials, and X can only contain two outcomes.

[tex]$P(X=x)=C_{n, x} \cdot \pi^x .(1-\pi)^{n-x}$$[/tex]

In which [tex]$C_{n, x}$[/tex] exists the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]$C_{n, x}=\frac{n !}{x !(n-x) !}[/tex]

And π exists the probability of X happening.

Given: 13 % of the students are left-handed and 100 - 13 = 87 % are right handed.

There are 220 sets. Of them, 25 exists designed for left handers and 220-25 = 195 for right handers.

There are 215 students, so n = 215.

In this case, a success is a student being right-handed. So [tex]$\pi=0.87$[/tex].

There are 195 seats for right handed students. If there are 196 or more right handed students, they will have to use a seat designed for a left hander. We have to find [tex]$P(X \geq 196)$[/tex]. Utilizing a binomial probability calculator, we find that [tex]$P(X \geq 196)=0.0382$[/tex]

So, there is a 3.82 % probability that at least one right-handed student in this class exists forced to utilize a seat designed for a left-hander.

There are 25 seats for left-handed students. If there exists 26 , or more, at least one exists going to be forced to utilize a seat designed for a right-hander.

In this case, a success is a student being left-handed. So [tex]$\pi=0.13$[/tex].

We have to find [tex]$P(X \geq 26)$[/tex].

Using a binomial probability calculator, we have that [tex]$P(X \geq 26)=0.6835$[/tex]

There exists a 68.35 % probability that at least one left-handed student in this class is forced to utilize a seat designed for a right-hander.

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