Write a quadratic equation in a such that the sum of its roots is -8 and the product
of its roots is -15

Answer: C

Step-by-step explanation:

pythagorean theorem : a^2 + b^2 = c^2

8^2 + 8^2 = x^2

64 + 64 = x^2

128 = x^2

x = sqrt(128) square root both sides

x = 8sqrt(2) simplified

Answer: c, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

     Since this is a right triangle, we will use the Pythagorean theorem to help us solve for x.

    Theorem:

a² + b² = c²

    Substitue values:

8² + 8² = c²

    To the power of 2:

64 + 64 = c²

    Addition:

128 = c²

   Square root both sides of the equation:

[tex]\sqrt{128}[/tex] = c

    Reflexive property and breaking up 128 into two factors:

c = [tex]\sqrt{64*2}[/tex]

    Square root of 64:

c = 8[tex]\sqrt{2}[/tex]

   So, x = 8[tex]\sqrt{2}[/tex]

A 60-inch piece is the shorter one. 180 inches long is the longer piece.

Step-by-step explanation:

L + S = 240

L = 3 S

L + S = 240 ( 3 S ) + S = 240 \s 4 S = 240 \s S = 60

L = 3 S L = 3 ( 60 )

L =180

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The required number of employees does it have in total is 68877.

A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 as opposed to as a small portion. Something is all 100%, a big part of it is 50%, none of something is zero percent. To decide a rate, you partition the piece of the entire by the actual entire and duplicate by 100.

Let total population of the company be X

So,

19.6% of x = 13500

x(19.6/100) = 13500

X = 13500×100/19.6 = 68877 employees

Thus, required number of employees is 68877.

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The interval of the domain where the function is decreasing are (0, 1) and (3, 4)

From the question, we have the graph that represents the given parameters that can be used in our computation

To determine the decreasing interval on the graph, we look for the points where

The intervals that represent the above highlights are

This can be represented as (0, 1) and (3, 4)

Hence, the intervals are (0, 1) and (3, 4)

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The triangles are similar triangles. Then the value of the variable 'x' will be 6.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Similar triangles are shown below.

We know that the ratio of the corresponding sides of similar triangles remains constant. Then the equation is given as,

(6x - 1) / 15 = 14 / 6

Simplify the equation, then we have

(6x - 1) / 15 = 14 / 6

(6x - 1) / 5 = 7

6x - 1 = 35

6x = 36

x = 6

The triangles are comparable triangles. Then, at that point, the worth of the variable 'x' will be 6.

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The numbers are -19 and -13 by the given conditions.

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach. Aloud to yourself, read the issue.

Let the two numbers be x and y

One number is six less than a second number: x = y - 6 ⇒ i

Four times the first is 2 more than 6 times the second: 4x = 6y + 2 ⇒ ii

Substitute the value of x in (ii)

4(y-6) = 6y + 2

4y - 24 = 6y + 2

2y = -26

y = -13

Now substitute the value of y in (i);

x = -13 - 6

x = -19

Hence, the numbers are -19 and -13 by the given conditions.

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Answer:

2/5 ≠ 25

Step-by-step explanation:

Given question,

→ Is 2/5 equivalent to 25?

Let's check the problem,

→ 2/5 = 25

→ 0.4 ≠ 25

The equivalent fractions of 2/5 are,

→ 2/5 = 4/10

→ 2/5 = 6/15

→ 2/5 = 8/20

→ 2/5 = 10/25

Hence, 2/5 is not equivalent to 25.

Answer: B C and D

Step-by-step explanation:

To determine whether Juakali can successfully save the document on the flash disk, you can calculate the total number of words in the document and compare it to the amount of free space on the flash disk.

First, calculate the total number of lines in the document by multiplying the number of pages by the number of lines per page:

Total number of lines = 123 pages * 70 lines/page

= 8610 lines

Next, calculate the number of lines with 14 words by multiplying the total number of lines by the proportion of lines with 14 words:

Number of lines with 14 words = 8610 lines * 36/70

= 4380 lines

Calculate the total number of words in the lines with 14 words by multiplying the number of lines by the number of words per line:

Total number of words in lines with 14 words = 4380 lines * 14 words/line

= 61320 words

Calculate the number of lines with 18 words by subtracting the number of lines with 14 words from the total number of lines:

Number of lines with 18 words = 8610 lines - 4380 lines

= 4230 lines

Calculate the total number of words in the lines with 18 words by multiplying the number of lines by the number of words per line:

Total number of words in lines with 18 words = 4230 lines * 18 words/line

= 76140 words

Finally, add the total number of words in the lines with 14 words and the total number of words in the lines with 18 words to find the total number of words in the document:

Total number of words = 61320 words + 76140 words

= 137,460 words

To determine whether Juakali can successfully save the document on the flash disk, you can compare the total number of words in the document to the amount of free space on the flash disk. Since the flash disk has 256 KB of free space and there are 137,460 words in the document, Juakali will not be able to save the document on the flash disk. This is because the document is larger than the amount of free space available on the flash disk.

It is important to note that the capacity of a storage device is usually measured in bytes, and 1 KB is equal to 1024 bytes.

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Answer: about 61290 employees total

Step-by-step explanation:

18.6% is equal to 11400 employees in one country

18.6% of X = 11400

x=11400/0.186

x=61290

Note that the answer is rounded

The value of a is 71°, and the value of b is 109°.

A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.

When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;

From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.

That is 180 - 71 = 109°

Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.

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The substance will weigh 9 pounds after  4.5123 hours.

Here it is given that every 3 hours the weight of the substance doubles.

At 12 noon it weighed 2 pounds. Hence we will consider the initial weight to be 2.

Let the weight after x hours be w(x)

Here it doubles in 3 hours, hence the growth rate is 100%

Since the growth rate is given, the equation for the growth rate will be

w(x) = w₀.eˣ

where x = no. of 3-hour spans.

Here

w₀ = 2

and w(x) is given 9

Hence,

2eˣ = 9

or, e²ˣ = 9/2

Taking log on both sides we get

loge²ˣ = ln(9/2)

or, 2xloge = ln(9/2)

Since loge = 1 we get

2x = log(9/2)

or, x = 1.5041

Hence they will become 9 pounds after

3 X 1.5041 hours

= 4.5123 hours

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Answer:

11

Step-by-step explanation:

The range is the set of outputs, or the second element in each ordered pair.

The sum of these values is [tex]5+2+1+3=11[/tex].

Answer:

2.213

2×1+2(1÷10)+1(1÷100)+3(1÷1000)

2×1+2×0.1+0.01+3×0.001

2+0.2+0.01+0.003

2.213 #

hope this will help ig

Answer:

2.213

Step-by-step explanation:

2×1+2(1÷10)+1(1÷100)+3(1÷1000)

2×1+2×0.1+0.01+3×0.001

2+0.2+0.01+0.003

2.213

Answer: the equations has no solution

Step-by-step explanation:

[tex]9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution[/tex]

Using listing method the elements in the set are +2 and -2.

What is listing method ?

The listing approach involves writing the members of the set as a list, with commas separating the items and curly brackets enclosing the list. The rule or condition that may be used to determine if an object can belong to the set is specified when using the rule method for sets.

The members of a set are listed using this technique, with commas used to separate them and curly braces used to enclose the list. The four distinct seasons, for instance, can all be written as "Summer, Autumn, Spring, and Winter." The list's elements can be in any order, so don't worry.

We are given the set [tex]\left\{x \mid x^2=4\right\}[/tex]

all such x such that the perfect square is 4. Now, we have

[tex]$x^2=4 \Rightarrow x=\pm 2$[/tex]

Therefore, the elements in the set are +2 and -2.

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The new perimeter will be 2 times larger then the old perimeter, if both dimensions of rectangle are doubled.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width.

The figure's length is essentially revealed by the perimeter. Assume that the perimeter of a square with equal sides will be four times that square's sides. The perimeter of a circle, which is determined by its radius, is known as its circumference.

The new dimensions  of rectangle = 4mm and 9mm

The original dimension = 2mm and 4.5 mm

Perimeter of rectangle = P=2(l+w) = 2 (4.5 +2 ) = 13 mm

Perimeter of rectangle after doubled dimension = 2 (9 + 4) = 26

So, the new perimeter will be 2 times larger then the old perimeter

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The relative frequency probability that the forecast for tomorrow will be accurate = 16/33.

What is probability?

P(A) = Number of accurate days/ Total number of days

Here, the number of accurate days is 25 and total number of days is 37.

Substitute the above values as follows:

P(A) = 25/37

Hence, the relative frequency probability that the forecast for tomorrow will be accurate = 16/33.

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The Medals are as follows:

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A + B + C = 119

Country B won 9 more than Country C so:

B = C + 9

Also, Country A won 39 more than the other two combined so:

A = B + C + 39

  = (C + 9) + C + 39

  = 2C + 48

Now we substitute into the equation:

A + B + C = 129

(2C + 48) + (C + 9) + C = 129

4C + 57 = 129

4C = 72

C = 18

So, if B = C + 9  then B = 27

and, A = 2C + 48 = 36+ 48 = 84

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1) The mean and the standard deviation of the total amount of money that she earns in a month are of:

2) The probability that she earns more than $2750 in a given month is of: 0.3192 = 31.92%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

When two variables are added, the mean is given by the sum of the means, hence:

[tex]\mu = 2100 + 550 = 2650[/tex]

The standard deviation is given by the square root of the sum of the variances, hence:

[tex]\sigma = \sqrt{200^2 + 70^2} = 211.9[/tex]

The probability that she earns more than $2750 in a given month is  one subtracted by the p-value of Z = 2750, hence:

Z = (2750 - 2650)/211.9

Z = 0.47

Z = 0.47 has a p-value of 0.6808.

1 - 0.6808 = 0.3192 = 31.92%.

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Answer:  The percent that the house's value is going up each year is given by the factor 1.04 - 1, which is 0.04. This represents a 4% increase in the value of the house each year.

ii) To find the value of the home in 15 years, you can substitute x = 15 into the equation to get:

A = 400,000 (1.04)^15

= 400,000 (1.7589)

= 700,356

Therefore, the value of the home in 15 years is $700,356.

iii) To find when the value of the home will double, you can set the value of A equal to 2*400,000 and solve for x:

2*400,000 = 400,000 (1.04)^x

2 = (1.04)^x

x = log(2)/log(1.04)

= 10.67

Therefore, it will take approximately 10.67 years for the value of the home to double, assuming the trend continues.

95% confidence that machine calibrated properly is (48.536, 51.424).

We have given that,

n = 25

mean of x = 49.98 mm

S = 0.14 mm

μ = 50.00 mm

and CI = 95%

from t-table we know that,

t at 95% and n - 1 = 25 - 1 = 24 is 2.064

Therefore 95% of CI means that

(x - 2.064 × S√n, x + 2.064 × S√n)

(49.98 - 2.064 × 0.14√25, 49.98 + 2.064 × 0.14√25)

(49.98 - 2.064 × 0.7, 49.98 + 2.064 × 0.7)

(49.98 - 1.444 , 49.98 + 1.444)

(48.536, 51.424)

Therefore 95% confidence that machine calibrated properly is

(48.536, 51.424).

The 95% confidence interval is a range of values that you can be 95% confident contains the true mean of the population.

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If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.

The rational zero theorem is used to determine the rational roots of a polynomial function.

Rational Zero Theorem statement:-

The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients

f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,

p is a factor of the constant a₀,

q  is a factor of the leading coefficient an,

and p and q are relatively prime.

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For an average intake of 2200 calories per day, the number of acres of land is approximately 2.

If we are given all a function so in that case, we just need to substitute values given in question and solve for unknown variable that is to be determined.

C(x) is a variable that tells the number of calories consumed daily by a person

x is the number of acres that person own.

C(x) = 270㏑(x+1) +1900

In the given question number of acres ask a person to have who consumed 2200 calories in a day.

Therefore,

C(x)=2200

2200=270㏑(x+1) +1900

2200-1900=270㏑(x+1)

300=270㏑(x+1)

300/270 = ㏑(x+1)

10/9 = ㏑ (x+1)

x+1 = [tex]e^{\frac{10}{9} }[/tex]

x+1 = 3.037

x= 3.037-1

x=2.037

x=2(round off)

Therefore, 2 acres of land a person can consume 2200 calories in a day.

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Answer:

the answer will be the options A

The simplified form of [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex] is [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex].

= [tex]\sqrt{4 - 4\sqrt{5} + 5}+ \sqrt{4 + 4\sqrt{5} + 5}[/tex].

= [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].

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{25} is the solution set of the equation  {10, 24, 25, 36}.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given set of equation is {10, 24, 25, 36}

Since, The equation is represented by the sentence that is 5/6 of a number is 30.

So the required solution,

5/6 of the number 30 = 25

The solution set of the equation is {25}.

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