How to use delta math

Answer:

length = 4 cm

Width = 5 cm

Step-by-step explanation:

      Area of rectangle = length * width

length = (x - 3) meters

Width = (x - 2) meter

Area = 20 square meters

  (x - 3)*(x - 2) = 20

Use FOIL method.

   x*x + (x)(-2) + (-3)*x + (-3)*(-2) = 20

                         x² -2x  - 3x + 6 =20

         Combine like terms

                        x² - 5x + 6  = 20

Now subtract 20 from both side

                     x² - 5x + 6 - 20 = 0

                           x² - 5x - 14  = 0

Factorize the equation and find the roots

         Sum = -5

   Product = -14

    Factors =  (-7) , 2

When we add (-7) + 2 = -5 and when we multiply (-7)*2 = -14

x² + 2x - 7x - 14 = 0

 x(x + 2) -7(x + 2) = 0

 (x + 2)(x - 7)  = 0

  x - 7 = 0    {Ignore (x + 2 = 0) as measurements wont't be in negative}

x = 7

length = x - 3

          = 7 - 3

   [tex]\sf \boxed{\bf length = 4 \ cm}[/tex]

width = x - 2

         = 7 - 2

    [tex]\sf \boxed{\bf width = 5 \ cm }[/tex]

Answer:

v ≥ 5

Step-by-step explanation:

v ≥ 5

Answer:

- 439

Step-by-step explanation:

evaluate f(- 7) and substitute the value obtained into s(x)

f(- 7) = 3(- 7) = - 21 , then

s(- 21) = 2 - (- 21)² = 2 - 441 = - 439

Answer:

A. (s*t)(-7)=-439

Step-by-step explanation:

(s*t)(-7) is the same as s(t(-7)). First find t(-7)

t(-7)=3(-7)=-21

t(-7)=-21

Plug -21 into s(t(-7)) for t(-7).

Find s(-21).

s(-21)=2-(-21)^2=-441+2=-439

Hope this helps!

If not, I am sorry.

Answer:

18.75 inches

Step-by-step explanation:

Inches:feet

3. : 8

X. : 50

(Cross multiply)

8x=150

X=150÷8=18.75

The profits at x = $185 is 0 and the graph is attached below:

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Function is to model the profits of a new pet-monitoring system, so, if the profits are y and x then y = f(x)

The curve shows that y is negative at values of x< $95, then the profits increase when x varies between $95 and $140.

The profits reach a maximum at $140 and then the profits start to reduce as x increases again.

So, the profits at x = $185 is 0.

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Answer:

a on edge

Step-by-step explanation:

I js did it

The loss on the sale of equipment of $25 will appear in cash flow for operating activities section.

The cash flow statement is a financial statement that gives aggregate data regarding the cash inflows that a company receives.

The loss on sales of equipment will be:

Cost of equipment = $500

Less accumulated depreciation = $375

Less sale of equipment = $25

Here, the loss on the sale of equipment of $25 will appear in cash flow for operating activities section.

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The volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

Given that, the length of copper wire=200 m=200000 mm and the diameter of the copper wire=1.2 mm.

We need to find the volume of the copper wire.

The formula to find the volume of a cylinder is πr²h.

Now, the volume of the copper wire=πr²h=[tex]\frac{22}{7} \times (0.6)^{2} \times 200000=2,26,080[/tex] mm³=226.080 cm³

If the density of copper is 8.9 g/cm³, find the mass of the wire.

We know that [tex]Density=\frac{Mass}{Volume} }[/tex].

⇒8.9 g/cm³=[tex]\frac{Mass}{226.080}[/tex]

⇒Mass=2,012.112 g/cm³

Therefore, the volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

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The function which is used to represent the graphed geometric sequence is

[tex]f(x) = 80{( \frac{1}{4}) }^{x - 1} [/tex]

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is of the form a,ar,ar^2, ...

The common ratio will be ar/a.

From the graph, we can find out the sequence as 80,20,5, ...

Here we can see that the sequence is in Geometric Progression.

First term a=80

Common ratio r= ar/a

= 20/80

=1/4

General term of Geometric sequence is

[tex]f(x) = a {r}^{x - 1} [/tex]

Substituting the value a = 80 and r = 1/4,

we get,

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

Hence, the correct answer is

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

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The polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved. Example, x² + 3x + 5.

As per the given informations, the first polynomial is 2x² + 2x + 1.

The second polynomial equal is 5x² + 4x + 6.

Now, the sum of the two polynomial can be written as,

Sum = 5x² + 4x + 6 + 2x² + 2x + 1 = 7x² + 6x + 7

Therefore, the polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

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Answer:

33

Step-by-step explanation:

Apply BODMAS(Brackets Of Division Multiplication Addition Subtraction)

Answer:

+33

Step-by-step explanation:

first (24÷8), 8x(3), 14-8+3+24 =33

Answer:

A) 2

Step-by-step explanation:

Because the slope is negative of line 2 the distance is getting smaller

The number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120

Permutation is the number of ways of arrangement for a given set.

The formula for a permutation is given as P(n, r) = n! / (n-r)!

Where n = items chosen from = 5

r is the number of items = 4

Substitute values into the formula

P(5, 4) = [tex]\frac{5!}{5-4!}[/tex]

P(5,4) = [tex]\frac{5 * 4* 3*2*1}{1}[/tex]

P(5,4) = [tex]\frac{120}{1}[/tex]

P(5,4) = 120

Therefore, the number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120

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Answer:

The answer is actually 120.

Step-by-step explanation:

I have the keysheet to the questions.

Answer:

p =43

Step-by-step explanation:

Finding the angle in a triangle

The angle next to 133, angle a,  is 180-133 = 47 because the angles form a straight line

The angle next to 90, angle b, is 180-90 = 90,  because the angles form a straight line

We have a triangle.  The angles in a triangle equal 180 degrees

a+b+ p =180

47+90+p = 180

137 + p = 180

p = 180-137

p =43

The attached graph represents the solution set of [tex]3e^x > \frac 12^x[/tex]

The complete options are not given.

So, I would plot the graph that represents the solution set

The inequality is given as:

[tex]3e^x > \frac 12^x[/tex]

Start by splitting the inequalities as follows:

[tex]f(x) > 3e^x[/tex]

[tex]g(x) > \frac 12^x[/tex]

The above means that we plot the graphs of f(x) and g(x) to represent the solution set

See attachment

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Answer:

Step-by-step explanation:

A function can only have one output for an input.  That is, for any value of x, there must be a unique value of y.

{(-6,-1), (13,8), (1,6), (1,-10)}   Not a  Function:  (1,6) and (1,-10)

{(10,5), (10,-5), (5,10), (5,-10)}  Not a  Function:  (10,5) and (10,-5)

{(3,5), (-17,-5), (3,-5), (-17,5)}   Not a Function:  (3,5) and (3,-5)

{(10,5), (-10,-5), (5,10), (-5,-10)}  Function:  No duplicate values of y for a value of x.

The surface area is multiplied by a factor of 16

The dimensions are given as:

The factor of the surface area is calculated as:

Surface area = Factor^2

So, we have:

Surface area = 4^2

Evaluate

Surface area = 16

Hence, the surface area is multiplied by a factor of 16

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16

Step-by-step explanation:

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The parameters are given as follows:

[tex]\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24[/tex]

Item a:

The probability is one subtracted by the p-value of Z when X = 984, hence:

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

[tex]Z = \frac{984 - 959}{263}[/tex]

Z = 0.1

Z = 0.1 has a p-value of 0.5398.

1 - 0.5398 = 0.4602.

Item b:

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

By the Central Limit Theorem:

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

[tex]Z = \frac{984 - 959}{43.24}[/tex]

Z = 0.58

Z = 0.58 has a p-value of 0.7190.

1 - 0.719 = 0.281.

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The number of hamburgers he could cook is 14 if he chopped 100 potatoes with the machine option (B) is correct.

A mathematical notion called the graph of the best estimate connects points spread throughout a graph.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have shown a graph in the picture that shows the number of hamburgers cooked versus the number of potatoes chopped.

As we can see in the graph,

Number of potatoes chopped = 80

number of hamburgers cooked = 30

Number of potatoes chopped = 90

number of hamburgers cooked = 20

Number of potatoes chopped = 95

number of hamburgers cooked = 10

Number of potatoes chopped = 100

number of hamburgers cooked = 14 (best estimate)

Thus, the number of hamburgers he could cook is 14 if he chopped 100 potatoes with the machine option (B) is correct.

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Answer:

80 m is distance traveled

Step-by-step explanation:

if object moves at 20m/s, then in 4 seconds the expression 20 x 4 is used to get 80. 80 m traveled

Answer:

B

Step-by-step explanation:

right on edg3

Answer:       B.     [–4, 0)  ∪  [2, ∞)

To find the range, find out what y-values are possible for the function in the graph.

We need to pay attention to what symbols to use.

Solid circle

Empty circle

Arrow

Square brackets: [ and ]

Curved brackets: ( and )

Union of sets: ∪

Let's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.

The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is:     [tex]-4[/tex]

If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include:     [tex]0[/tex]

So, the first part of our range is:

The blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value:    [tex]2[/tex]

If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol:    [tex]\infty[/tex]

So, the second part of our range is:

Put the lower and upper blue lines together with the union of sets symbol. The range is expressed as:    [–4, 0)  ∪  [2, ∞)

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The statement that is true about this function is C. As x approaches positive infinity, h(t) approaches positive infinity

Given that we have:

Therefore, when x approaches to negative infinity,

[tex]\lim_{x \to \infty} h(x)[/tex]

= 2^(-∞-5)

= 2^(-∞)

= 1/2^∞

=0

Also, as x approaches negative infinity, function h(x) approaches 0.

Then when x approaches to positive infinity,

[tex]\lim_{x \to \infty} h(x)[/tex]

2^(∞-5)

= 2^(∞)

= ∞

Therefore, As x approaches positive Infinity, h(x) approaches positive infinity.

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Answer:

y+3=10

solution,

y+3=10

y+3-3=10-3

y=7

thus,

y=7ans

Answer:

Here's a little trick I learned in 8th grade. The first numbers don't matter all that matters are the 2nd numbers, and if you have 2 of the same kind of numbers then it's not a function so your answer would be B.

The simplified product of [tex]2\sqrt{5x^{3} }[/tex] and -3[tex]\sqrt{10x^{2} }[/tex] is -30[tex]x^{5/2} \sqrt{2}[/tex].

Given Two expressions: -3[tex]\sqrt{10x^{2} }[/tex] and 2[tex]\sqrt{5x^{3} }[/tex].

We have to multiply both the expressions and it can be done as under:

-3[tex]\sqrt{10x^{2} }[/tex] *2[tex]\sqrt{5x^{3} }[/tex]

Firstly we have to multiply -3 with 2 to get

=-6[tex]\sqrt{10x^{2} }\sqrt{5x^{3} }[/tex]

Then we have to find square root of x cube and x square which is x to the power 3/2 and x to the power 1.

=[tex]-6x^{3/2} x\sqrt{10}\sqrt{5}[/tex]

Now we have to multiply both the numbers in the root to get the answer;

=-6[tex]x^{5/2} \sqrt{50}[/tex]

Square root of 50 is 5 root 2.

=-6*5[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]

=-30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]

Hence the simplified product is -30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex].

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The trigonometric relation is solved and the length of side DE is given by the relation DE = 3.8 ( tan 40° )

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔEFD

Now , the measure of side EF = 5 units

The measure of side DF = 3.8 units

And , from the trigonometric relations , we get

tan θ = opposite / adjacent

On simplifying , we get

tan 40° = DE / DF

Multiply by DF on both sides , we get

DE = 3.8 ( tan 40° )

Hence , the trigonometric relation is solved

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Answer:

5377

Step-by-step explanation:

this is a vector question where how far is the Resultant. that is, it is determined by the magnitude of the Hypotenuse.

using Pythagoras theorem

Hypotenuse ²= Opposite ²+Adjacent²

Hypotenuse ²= 2865²+4550²

Hypotenuse ²= 8208225+20702500

Hypotenuse ²=28910725

Hypotenuse=√28910725

Hypotenuse=5376.86944234282

Hypotenuse= 5377 approximated

Answer:

dSutlrysl07tris5eiruwf3rtst47er747y3utgxgudjdudufnlgjfngvi