4. If a = 1+ 1/b where b>1, find the value of a ?

Answer:

12

Step-by-step explanation:

The area of a triangle is calculated with the following formula:

[tex]\frac{1}{2} *b*h[/tex] (b: base, h: height (or legs))

We can use this formula to find the length of the other leg:

30 = [tex]\frac{1}{2} *b*h[/tex] multiply both sides with 2 to get rid of fraction

60 = b*h one of the leg's length is given as 5 so

60 = 5*h divide both sides by 5

12 = h is the length of the missing leg.

The polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.

In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.

To find the solutions, we do as follows:

x³ - 4x² - 7x + 28 = 0,

or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},

or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},

or, (x - 4)(x² - 7) = 0 {Grouping},

or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex]}.

By the zero-product rule, the solutions are:

x - 4 = 0, or, x = 4,

x + √7 = 0, or, x = -√7,

x - √7 = 0, or, x = √7.

Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.

Thus, the polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.

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The complete question is:

"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?

x³-4x²-7x+28=0

a. two or zero

b. three or one

c. one

d. two"

Answer:

Two or zero.

Step-by-step explanation:

The cost spent on fill the box with sand is 405$.

According to the statement

we have given a square sandbox with length 9 ft and depth of 1 ft.

and the rupees of sand per cubic ft is $5

then

Now, we have to find the volume of sandbox with the given length and depth.

So, for this purpose we use Volume formula

V = (a)^3

V = 9*9*1

V = 81 cubic feet

And the cost of sand per cubic feet is $5.

then

The cost of sand for 81 cubic per feet is calculate by multiplication formula then

Total cost of sand = 81*5

Total cost of sand = 405$

So, The cost spent on fill the box with sand is 405$.

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The equivalent equation is (4x² + 9)(4x² - 9) and the zero's are x =± 3 / 2 and x = ± 3 / 2i

The equivalent equation can be found by factoring. Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.

Therefore,

f(x) = 16x⁴ - 81 = 0

Hence,

9 × 9 = 81

4x² × 4x² = 16x⁴

Therefore,

16x⁴ - 81  = (4x² + 9)(4x² - 9)

Hence,

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

The zero's of the function are as follows:

4x²  = 9

x² = 9 / 4

x =± 3 / 2

4x² = -9

x² = - 9 / 4

x =√-9 / 2

x = ± 3 / 2i

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The answers are as follows:

a. There are 6 ways of tossing a coin and then drawing a marble from the bag. (Tree diagram is shown in the diagram below) The probability is 1/12.

b. These are independent events since tossing a coin does not affect the drawing of marble from the bag.

c. From the tree diagram, the probability of tossing a head and drawing a red marble is 1/6(since they are independent events).

d. The probability of drawing two blue marbles if the first marble is not replaced is 1/5(since they are dependent events).

It is given that a bag contains,

Number of white marbles(W) = 1

Number of Blue marbles (B) = 3

Number of Red marbles (R) = 2

Thus, there are 6 marbles in the bag. So, the sample space for drawing a marble = 6

a. Finding all the possible outcomes using a tree diagram:

The possible outcomes from the tree diagram are

(H, W), (H, B), (H, R), (T, W), (T, B),  and (T, R)

The probability of tossing head or tail = 1/2

The probability of drawing a marble from the bag = 1/6

So, the compound probability = (1/2)(1/6) = (1/12)

The sample space for this is 12.

b. Independent or dependent events:

These are independent events since the tossing of a coin does not affect the drawing of marble from the bag.

c. Finding the probability of tossing a head and drawing a red marble:

The probability of tossing a head = 1/2

The probability of drawing a red marble = 2/6 = 1/2

Since they are independent events,

The required probability = (1/2)(1/2) = 1/4

d. Finding the probability of drawing two blue marbles if the first marble is not replaced:

The probability of drawing a blue marble from the bag(1st attempt) = 3/6

The probability of drawing another blue marble from the bag (2nd attempt) = 2/5 (From the leftover marbles after the first attempt)

Since they are dependent events, the probability of the 2nd event is calculated only after the first event is calculated.

So, the required probability = (3/6)(2/5) = 1/5

Thus, all the probabilities are calculated.

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That year FTE was 26.

According to statement

Labor hours worked that year = 55,267

Total number of hours paid that year = 59,995

The total number of hours during the year

8 hours × 5 days × 52 weeks = 2080 hours

Now we find the FTE per year

So, FTE/YEAR = Labour works on that year / total number of hours in year

Substitute the values in it then

FTE/YEAR = 55267/2080

FTE/YEAR = 26

So, That year FTE was 26.

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Answer:

9,240

Step-by-step explanation:

For the first number, there are 22 numbers available to choose from. For the second number, there are 21 numbers available, since the first number cannot be the same as the second number. And for the last number, there are 20 remaining numbers to choose from. So, there are 22*21*20=9240 possible sequences.

The number of apples in the basket are; 24 apples

Let there be X number of apples and Y number of oranges.

Thus by the given ratio we can say that;

x/y = 3/8   -----(1)

(x — 1)/y = 1/3

3x — 3 = y   ----(2)

Substitute 3x - 3 for y in eq 1 to get;

x/(3x - 3) = 3/8

8x = 9x - 9

9x - 8x = 9

x = 9

Thus;

y = 3(9) - 3

y = 24 apples

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Answer:

Step-by-step explanation:

Let the length be l and the width be y. We have the following:

l + w = 37

lw = 342

From here, we can find the factor pairs of 342, and see which pair has a sum of 37. Our desired pair is 18 & 19, so the dimensions of the field are 18 by 19 feet.

The length of side DF is 3.75.

Given that within the figure there are two triangles that are similar.

Congruent triangles will be triangles that have a comparable measure and shape. This infers that the comparing sides are comparable and the relating focuses are equivalent.

Two comparative triangles are given.

If two triangles are comparable at that point their comparing sides are relative and comparing points are congruent.

DF/AB=EF/BC

Substitute the values from the given figure

DF/15=6/24

Cross multiply both sides, and we get

DF×24=6×15

DF×24=90

Divide both sides by 24, we get

(DF×24)/24=90/24

DF=15/4

DF=3.75

Hence, the length of side DF from the given figure is 3.75.

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The probability you will roll a sum of 9 is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability you will roll a sum of 9 = total times a sum of 9 is derived / total sample spaces

The probability you will roll a sum of 9 = 4/36 = 1/9

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Hello,

an other method

Pythagorean theorem :

x² + x² = 6²

2x² = 36

x² = 36/2

x² = 18

x = √18 (and not -√18 because x ≥ 0)

x = √(9 × 2)

x = √(3² × 2)

x = 3√2

Answer A

Answer:

605

Step-by-step explanation:

We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.

110 + 1/2(1100 - 110)  Subtract what is in the parentheses

110 + 1/2(990) Find 1/2 of 990

110 + 495

604

Answer:

[tex]AC = \bf 4.13 \space\ cm[/tex]

Step-by-step explanation:

Using Pythagoras's theorem:

[tex]\boxed {a^2 = b^2 + c^2}[/tex],

where:

a ⇒ hypotenuse (AC, ? cm)

b, c ⇒ the two other sides of the triangle (AB = 2.2 cm, BC = 3.5 cm),

we can find the length of AC.

[tex]AC^2 = AB^2 + BC^2[/tex]

⇒ [tex]AC^2 = (2.2)^2 + (3.5)^2[/tex]

⇒ [tex]AC = \sqrt{(2.2)^2 + ((3.5)^2}[/tex]

⇒ [tex]AC = \sqrt{17.9}[/tex]

⇒ [tex]AC = \bf 4.13 \space\ cm[/tex]

Answer:

probability of all the four women chosen over people needed in a committee=4 over 4 =1

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

An equation is an expression that shows the relationship between two or more number and variables.

[tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18} \\\\=\frac{(x +3)(x +4)}{x-3} .\frac{(x-3)(x-3)}{2(x+3)(x-3)} =\frac{x+4}{2}[/tex]

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

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Answer:

C.  (x,y) ⇒ (x + 8, y − 3)

Step-by-step explanation:

See attached image.

Ms. Drake will earn [tex]\$ 170[/tex] in this time from the investment of [tex]\$ 1000[/tex] at a simple interest with rate of interest [tex]8.5\%[/tex]

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Formula for finding simple interest is [tex]\frac{principal \times rate \ of \ interest \times time}{100}[/tex]

Given principal of Ms. Drake is [tex]\$1000[/tex]

Rate of interest is [tex]8.5 \%[/tex]

Time is [tex]2[/tex] years.

Interest [tex]=\frac{1000 \times 8.5 \times 2}{100}[/tex]

            [tex]=\frac{17000}{100}\\=170[/tex]

Therefore, Ms. Drake will earn [tex]\$ 170[/tex] in this time.

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The parent function of g(x) = |x - 7| +6 is f(x) = |x|

The function is given as:

g(x) = |x - 7| +6

The above function is an absolute function, and the parent function is f(x) = |x|

Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|

When f(x) is reflected across the x-axis, we have:

f'(x) = -|x|

When f(x) is reflected across the y-axis, we have:

f'(x) = |x|

When f(x) is stretched horizontally by a factor k

g'(x) = |kx|

When f(x) is stretched vertically by a factor k

g'(x) = k|x|

When f(x) is shifted horizontally by k units

f'(x) = |x ± k|

When f(x) is shifted vertical by k units

f'(x) = |x| ± k

See attachment for the graph of g(x)

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a) ∠PQR=65° (alternate interior angles theorem)

∠PRQ = 60° (linear pair)

x = 55° (angles in a triangle add to 180°)

b) ∠APQ and ∠PQR are congruent alternate interior angles.

Answer:

1

Step-by-step explanation:

[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]

The probability of event X or Y is P = 0.7, or, in percentage form, the probability is 70%.

First, two events are mutually exclusive if these events can't happen at the same time.

This means that if happens X, with a 30% of probability, then Y can't happen.

If happens Y, with a 40% of probability, then X can't happen.

Then the probability of X or Y (the probability that one of these two events happens, not both) is just the addition of the two individual probabilities.

Then we have:

P(X or Y) = 0.3 + 0.4 = 0.7

Or, in percent form, we get:

P(X or Y) = 70%

The probability of event X or Y is just 70%.

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Check the picture below, so the parabola looks more or less like that one, with a "p" distance of 2 units that is positive, whilst the vertex, which is always half-way between the focus point and the directrix is where you see it there, thus

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-1\\ k=2\\ p=2 \end{cases}\implies 4(2)( ~~ x-(-1) ~~ )~~ = ~~(y-2)^2\implies 8(x+1)=(y-2)^2 \\\\\\ x+1=\cfrac{1}{8}(y-2)^2\implies \boxed{x=\cfrac{1}{8}(y-2)^2-1}[/tex]

Answer: UR WELCOME

Step-by-step explanation: ANSWER ON EDMENTUM

Answer:

Step-by-step explanation:

380 rows in total

bcs

use sense

Intermediaries who are independent, but agree to cooperate have likely formed a(n) contractual distribution system.

The most commonplace form of Contractual VMS is Franchising. In franchising, the manufacturer authorizes the distributor to promote its product below the producer's call against some annual license rate. For example, McDonald's, Dominos, Pizza Hut, etc. are all styles of a franchise that might be operating on a contractual foundation.

A form of vertical advertising machine in which unbiased firms at unique degrees of distribution are tied together by using contracts to achieve economies of scale and more income impact.

A vertical advertising system refers to a marketing system that aims to draw and attain organizations running inside the same industry. then again, horizontal advertising and marketing device refers to an advertising and marketing system whereby corporations which can be on equal degree join collectively to advantage economies of scale.

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Answer: -8 points

Step-by-step explanation: because he lost 50, and he originally had 42, a smaller number, the answer will go into the negatives.

42-50= -8, which is how you get the answer!

Answer:

-8

Step-by-step explanation:

42-50 is the same as 50-42, except the answer is negative

Answer:

the scale factor is :

[tex]\frac{9}{15}[/tex]

Step-by-step explanation:

The trapezoids TUVW and ABCD are similar

and AB is the corresponding side of the side TU

Then the function that transform TUVW to ABCD is of scale factor :

[tex]= \frac{AB}{TU}[/tex]

[tex]= \frac{9}{15}[/tex]

Generally speaking, Harriot's notation was clearer than Viète's, which made it simple for him to connect Viète's identities.

Harriot made significant contributions to the theory of equations and developed a more straightforward notation for algebra.

The employment of special notation is algebra's most evident characteristic. Variables are the symbols that are used to represent numbers.

A symbolic system known as notation is used to represent mathematical concepts and objects.

The primary components of notation are letters, symbols, figures, and signs. Notation can be made using symbols, characters, numbers, or a combination of these, such as the factorial symbol.

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