Can someone pls write these in algebraic expression simplify if possible,

The sum of twice a number and -1 added to the sum of five times a number and -10

Triple a number, minus the sum of the number and three

Answer:

200+400=600

400/600=2/3=66.6%

Answer:

191.56

Step-by-step explanation:

Given

191.5638

Required

Approximate

Approximating to the nearest hundredth implies that, only to digits after the decimal point is needed

This is:

191._ _

The third digit after the decimal point will approximated using the approximation rule;

Since, the third digit after the decimal point (3) is not up to 5, it'll be approximated to 0 and added to the second digit (6)

So, we have:

191.5 _

The next digit is calculated as 6 + 0 = 6

Hence, the full approximated number is 191.56

Answer:

Hmm...giraffe perhaps?

Answer:

\( - {2k}^{3} - {k}^{2} + 8k\)

Step-by-step explanation:

1) Remove parentheses.

\( - {2k}^{3} - {7k}^{2} + 5k + {6k}^{2} + 3k\)

2) Collect like terms.

\( - {2k}^{3} + ( - 7k^{2} + {6k}^{2} ) + (5k + 3k)\)

3)Simplify.

\( - {2k}^{3} - {k}^{2} + 8k\)

Therefor, the answer is -2k³ - k² + 8k.

Answer:

  a) see attachment

  b) negative values for miles or gallons are not possible

  c) 45 miles

Step-by-step explanation:

See the attachment for a graph

__

Graphing in the first quadrant is all that is necessary, because the number of gallons and the number of miles cannot be negative.

__

Use 2.5 for g and evaluate:

  d = 18(2.5) = 45

Rick can drive 45 miles on 2.5 gallons of gas.

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

37°

Step-by-step explanation:

Here it is given that there are two flagpoles which are 20 m apart. One of them is 12m high and the other is 27m high .And we are interested in finding the angle of depression from the top of taller pole to the top of shorter pole .

For illustration, refer to the attachment or below ,

Illustration :-

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(0,1){6}}\put(0,0){\line(1,0){4}}\put(4,0){\line(0,1){4}}\multiput(0,4)(0.6,0){7}{\qbezier(0,0)(0,0)(0.5,0)}\qbezier(0,6)(0,6)(4,4)\put(0,6){\vector(1,0){3}}\qbezier(0.8,6)(1,5.8)(0.6,5.7)\put(1,5.6){$\theta$}\qbezier(3.2,4.42)(3,4.1)(3.25,4)\put(2.4,4.15){$\theta$}\put(-0.5,-0.5){A}\put(-0.5,6){E}\put(-0.5,3.8){D}\put(-0.8,5){15m}\put(4.3,-0.5){B}\put(-1.2,2){$ 27m $}\put(3.2,6){$ F $}\put(4.5,2){$ 12m $}\put(4.3,3.8){C}\put(-1,1.8){\vector(0,-1){1.8}}\put(-1,2.4){\vector(0,1){3.7}}\put(2,-0.5){$ 20m$}\put(2,3.5){$ 20m$}\end{picture} \)

Here the angle of depression will be ,

\(\longrightarrow\sf \angle_{of \ depression}=\angle FEC \)

Also ,

\(\sf\longrightarrow \angle FEC =\angle ECD \ (alternate \ interior \ angles)\)

Let ,

\(\sf\longrightarrow \angle FEC =\angle ECD = \theta \ ( say ) \)

Now in ∆ EDC , we have;

\(\sf\longrightarrow tan\theta =\dfrac{perpendicular}{base}\\ \)

\(\sf\longrightarrow tan\theta =\dfrac{15m}{20m}\\\)

\(\sf\longrightarrow tan\theta =\dfrac{3}{4}\\ \)

\(\sf\longrightarrow \theta =tan^{-1}\bigg\lgroup \dfrac{3}{4}\bigg\rgroup\\ \)

\(\sf\longrightarrow \underline{\boxed{\textsf{\textbf{$\boldsymbol{\theta}$= 37$^{\bf o }$ }}}} \)

And we are done!

Answer:

θ = 37°

Step-by-step explanation:

In the figure,

Distance between the poles = DC = 20 m

Height of the smaller pole = ED = 12 m

Height of the larger pole = AC = 27 m

Now, by using the properties of a rectangle,

DC = EB = 20 m

ED = BC = 12 m

Then,

AB

= AC - BC

= 27 - 12

= 15 m

We know that,

tan (θ) = opposite side / base side

Then, in △ ABE,

(Here, θ = missing angle)

tan (θ) = AB / BE

tan (θ) = 15/20

tan (θ) = 3/4

=》 θ = 37°

___________

Note:

Ray A & BE are parallel horizontal lines with AE as the transversal, so both the angles are equal to each other as then they will be alternate interior angles & they are represented in this question as 'θ'.

[Refer to the attachment for the figure]

____________________

Hope it helps ⚜

Answer:

\(6\sqrt{3}\)

Step-by-step explanation:

because of the 90-60-30 theorem

which \(6*\sqrt{3}=6\sqrt{3}\)

Using the theorems of vertical and linear pair angles, the angle measures are:

m∠1 = 146°

m∠3 = 146°

m∠4 = 34°

Based on the vertical angles theorem, two non-adjacent angles that are directly opposite each other are vertical angles that have the same angle measure.

On the other hand, angles that lie on a straight line that are adjacent angles are called a linear pair and they have a sum of 180 degrees (supplementary angles).

Given that, m∠2 = 34°

m∠1 = 180 - m∠2 [linear pair]

m∠1 = 180 - 34

m∠1 = 146°

m∠3 = m∠1 [vertical angles]

m∠3 = 146° [substitution]

m∠4 = m∠2 [vertical angles]

m∠4 = 34° [substitution]

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Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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10 cars and 10 trains in 100 hours

it approximately take him 10 hours to build one car and one train how 6+4=10 how many times can 10 go into 100 10 times hope this helps a little

Answer:

130 degrees

Step-by-step explanation:

No hate but it literally tells you the answer by the picture.

:)

Answer:

Step-by-step explanation:

well the answer is 90 degress  but it also adds up to 360 degress

A centimeter (cm) is a unit of length in the metric system, equal to one hundredth of a meter, commonly used to measure small distances or dimensions such as the length or width of an object.

To convert 44cm to meters, we need to divide 44 by 100 (since there are 100 centimeters in 1 meter) to get:

44/100 = 0.44 meters

To express this in simplest form, we can leave it as 44/100 or simplify it by dividing both the numerator and denominator by the greatest common factor (GCF) of 44 and 100, which is 4:

44/100 = (44 ÷ 4)/(100 ÷ 4) = 11/25

Therefore, 44 cm is equivalent to 0.44 meters or 11/25 meters in simplest form.

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Answer:

The money

Step-by-step explanation:

The drive to the farmers market is a certain distance away, which costs him a specific amount of money. If the distance were to change, then so would the price it took to get there per week. Additionally, as the amount of boxes increases, so does the price.

A dependent variable is a variable that directly changes as the independent variable(s) change. In this scenario, the money, or cost is what's changing based on other factors.

hope this helps :)

Answer:

A

Step-by-step explanation:

The vertical asymptote is 3 so our constant add to our function e^x is 3.

So naturally that leaves us which Only Option A.

Option A is the option because in the parent function, e^x, the y intercept occurs at (0,1). After the vertical shift upwards 3, the graphs becomes

\( {e}^{x} + 3\)

We then have to move to the left 2 units to we add 2 to the x variable

\( {e}^{x + 2} + 3\)

Answer:

The cafe sold 40 single shot espressos.

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

she got 35 is positive 35

she bought something for 15 and something for 7 is negative 15 and 7

she got 10 is positive 10

+35  +  (-15)  +  (-7)  +  10

35-15-7+10

Answer:

10

Step-by-step explanation:

use permutations with repetitions formula

\(\large{\rm{\underline{\underline{Answer:}}}}\)

Angle AEB and Angle DEC are opposite angles which means they are equal in measure. Hence,

⇛ Angle AEB = Angle DEC

⇛ 9x + 8° = 3x + 42°

⇛ 9x - 3x = 42° - 8°

⇛ 6x = 34°

⇛ x = (34/6)°

To find: Angle DEC = 3(

34/6 °) + 42° = 59° (Ans)

Answer:

  ₹35,100

Step-by-step explanation:

You want to know the university cost if it is ₹45,000 reduced by 22%.

The discounted price of tuition and fees will be ...

   ₹45,000 - 0.22 × ₹45,000

  = 0.78 × ₹45,000 = ₹35,100

Mandla will pay ₹35,100 for the year.

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

Answer:

5< r or r>5

Step-by-step explanation:

-25 > -6r+5

-5            -5

-30> -6r

-30/-6< -6r/-6   when dividing a negative number, the symbol switches

5< r or r>5

Hope this helps!

Answer:

15% = $5100

7% = 900

Step-by-step explanation:

With simultaneous equations we can take the easier number like numbers that end in 0 or 5 or 2 etc.

We have 7% which is a prime and 15 so we call and name 'x' = amount

invested at 15%

x = the amount invested at 15%

Then 6000-x = the amount invested at 7%

The total interest earned is $710.

Therefore solve the simultaneous equation by substituting the 6000-x

0.15x + 0.08 (6000-x) = 710

Solve for x:

0.15x - 0.07x + 353 = 780 -> x = 357/0.07= $5100

Therefore the amount invested at 7% interest = 6000 - 5100 = $900

and here, 6000-900 = 5100 = 15%

The absolute value of the elevation difference between the valley and sea level is 94 feet.

The absolute value of a number is the distance of that number from zero on the number line. It represents the magnitude or size of a quantity without considering its direction. In the given scenario, we are dealing with the elevation difference between a valley and sea level.

The valley is described as being 94 feet below sea level. To find the absolute value of the elevation difference, we need to ignore the negative sign and consider the magnitude of the difference.

In this case, since the valley is below sea level, the elevation difference is negative. However, when we take the absolute value, we disregard the negative sign and focus solely on the numerical value of the difference.

By applying the absolute value to the elevation difference of -94 feet, we remove the negative sign and consider only the magnitude. Thus, the absolute value of -94 is simply 94.

Therefore, the absolute value of the elevation difference between the valley and sea level is 94 feet. It indicates that the valley is 94 feet away from sea level in terms of elevation, regardless of the direction (above or below sea level). The absolute value provides a measure of the magnitude of the difference while disregarding the direction or sign associated with it.

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The term in the AP whose value is 201 / 2 is 71.3.

The first term of an arithmetic progression is 5 and the common difference is - 3/2.

The formula of the arithmetic progression can be described as follows:

nth term = a + (n - 1)d

where

Therefore, using the arithmetic progression formula,

a = 5

d = 3 / 2

nth term = 201 / 2

let's find the term(n)

Therefore,

- 201 / 2 = 5 + (n - 1) - 3 / 2

- 201 / 2 = 5  - 3 / 2 n  + 3 / 2

- 201 / 2  - 3 / 2 - 5 =  - 3 / 2 n

- 107  =  -3 / 2 n

-3n = - 214

n = 214 / 3

n = 71.3

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The number in the problem whose result is 40, will be 3,600 and 90.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Use the digits nine, six, and three one time each in the following Multi-digit division problem then rewrite the problem.

Then the problem whose result is 40 will be given as the division of 3600 by 90.

3,600 / 90 = 40

The number in the problem whose result is 40, will be 3,600 and 90.

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Answer:

Concept: Algebraic Representation

Answer:

y=0.50x+20

X represents pizzas sold and y represents total pay