Write an algebraic expression for the verbal description.
The amount of acid in x liters of a 45% acid solution

The inequality will be 3.70x ≤ 145 and the number of items that you can by is  x ≤ 39

Total budget that you have = $145

The price of each item = $3.70

Consider the number of items = x

The inequality will be

3.70x ≤ 145

We have to solve the inequality to find the number of items

3.70x ≤ 145

Divide 3.70 on the both side of the inequality

3.70x / 3.70 ≤ 145 / 3.70

x ≤ 39.18

x ≤ 39

The number of items that you can buy is x ≤ 39

Hence, the inequality will be 3.70x ≤ 145 and the number of items that you can by is  x ≤ 39

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The daily production level that will minimize the costs is 106300 units.

From the information, the function is given as C = 0.04x² - 8.504x + 25302.

c = cost

From the function, the following can be deduced:

a = 0.04

b = 8.504

c = 25302

Then, -b/(2a) will be:

= -8.504 / (2 × 0.04)

= 106.300

Note that production level will minimize the cost in thousands.

The production level will now be:

= 106.300 × 1000

= 106300 units

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The value of x is 17, y is 2 and length of DF is 20.

Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

For x

DG = GE ( Given )

DG + GE = DE

DE = 2(DG)

DG/DE = 1/2

hence GH/EF = 1/2

By Basic Proportionality Theorem ( BPT )

(x – 3) / 28 = 1/2

after cross multiplication

2(x – 3) = 28

2x – 6 = 28

2x = 34

x = 17

For y

By Basic Proportionality Theorem (BPT) to side DF

DF = 2(DH)

DH/DF = 1/2

(y + 8) / (y + 8 + x – 7) = 1/2

after cross multiplication

2(y + 8) = y + 8 + x – 7

put x = 17

2(y + 8) = y + 8 + 17 – 7

2(y + 8) = y + 18

2y + 16 = y + 18

2y = y + 2

2y – y = 2

y = 2

DF = 2(2+8)

     = 2(10)

     = 20

Hence, x is 17, y is 2 and DF is 20.

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The percent increase between the total without Daya's employer contribution and the total with is A. 94%.

From the information, Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement and her employer also contributes a set percentage, which will increase her total by $161,531.00.

Therefore, the percentage increase will be:

= Increase in amount / Original amount × 100

= 161,531/172486 × 100

= 94%

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The simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.

We will solve the given expression using laws of exponents.

Some laws of exponents are:

We are given:

(3.7 x 10^-9) - (8.2 x 10^-8)

= (3.7 x 10^(-1 -9)) - (8.2 x 10^-8)

= (3.7 x 10^-1 x 10^-8) - (8.2 x 10^-8)

= (0.37 x 10^-8) - (8.2 x 10^-8)

= (0.37 - 8.2) x 10^-8

= - 7.83 x 10^-8

So, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) is - 7.83 x 10^-8.

Thus, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.

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x = -2, n(-2) = -1 - (-2) + 4 = 5

x = 0, n(0) = -1 - 0 + 4 = 3

x = 5, n(5) = -1 - 5 + 4 = -2

Answer:

sin(79°) - cos(11°) = 0

Step-by-step explanation:

Based on the rule sin(90-x) = cos(x), we can transform the expression. See the attached for more details

Answer:

(- 1, 3 )

Step-by-step explanation:

2x + 3y = 7 → (1)

- 2x + 4y = 14 → (2)

add (1) and (2) term by term to eliminate x

(2x - 2x) + (3y + 4y) = (7 + 14)

0 + 7y = 21

7y = 21 ( divide both sides by 7 )

y = 3

substitute y = 3 into either of the 2 equations and solve for x

substituting into (1)

2x + 3(3) = 7

2x + 9 = 7 ( subtract 9 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

As a check

substitute the values of x and y into the left side of both equations and if equal to the right side in both equations then the values of x and y are true.

(1) 2(- 1) + 3(3) = - 2 + 9 = 7 ← true

(2) - 2(- 1) + 4(3) = 2 + 12 = 14 ← true

then (- 1, 3 ) is the solution to the system

Answer:(- 1, 3 )

Step-by-step explanation:

Answer:

no chart

Step-by-step explanation:

show chart let us see what to use

The system of equations is:

x + y = 20

2x + 3y  = 48

And its graph can be seen in the image at the end.

Let's define the variables:

Each bicycle has 2 wheels, each tricycle has 3 weels, and we know that there are 20 boxes and 48 wheels, then the system of equations is:

x + y = 20

2x + 3y = 48

To solve the system graphically we just need to graph both lines on the same coordinate axis and see at which point do the lines intersect, the graph is below.

The solution is x = 12, y = 8.

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Answer:

Alexa has 13 quarters and 15 dimes.

Step-by-step explanation:

First, we should set up a system of equations using the given information. We can use q to represent the number of quarters and d to represent the number of dimes.

Since quarters are $0.25, dimes are $0.10, and the total is $4.75 we know 0.25q + 0.1d = 4.75

The problem tells us that there are 2 more dimes than quarters, so d = q + 2

To solve for the number of quarters, we can substitute the second equation into the first equation.

0.25q + 0.1 (q + 2) = 4.75

0.25q + 0.1q + 0.2 = 4.75

0.35q = 4.55

q = 13

Then, to solve for the number of dimes, we can substitute q into the second equation.

d = q + 2

d = 13 + 2

d = 15

Circumcenter is equidistant from the vertices, perpendicular bisectors will cross. Incentre is equidistant from the sides. Where the angle bisector cross incenter

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to choose the properties of circumcenter.

Circumcenter is equidistant from the vertices.

It is equidistant from the three vertices of the triangle, and thus you can construct a circle centered at the circumcenter and circumscribing the triangle.

and perpendicular bisectors will cross.

We have to choose the properties of incenter.

Incentre is equidistant from the sides.

Where the angle bisector cross incenter

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Answer:

-x-12

Step-by-step explanation:

1/2x+6

first divide by -1/2 or multiply by -2(its the reciprocal)

-2(1/2x+6)

-2*1/2x+6*-2

-x-12

Answer:

-6

Step-by-step explanation:

to solve you need to substitute the value of x in the equation which is given as 2so if you rewrite the equation it will be

-2(2)+10

=(-2*2)+10

=-4+10

=6

The integers in the set S:{-24, -6, 12, 24) that will make the inequality 1/3(m - 3) ≤ 1/6(m - 12) false are: S:{12, 24}​.

In order to determine which integers are true and false with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;

For integers (-24, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(-24 - 3) ≤ 1/6(-24 - 12)

1/3(-27) ≤ 1/6(-36)

-9 ≤ -6 (True).

For integers (-24, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/3(27) ≤ 1/6(36)

9 ≤ 6 (False).

For integers (-24, -6), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(-6 - 3) ≤ 1/6(-6 - 12)

1/3(-9) ≤ 1/6(-18)

-3 ≤ -3 (True).

For integers (-6, 12), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

For integers (12, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/3(27) ≤ 1/6(36)

9 ≤ 6 (False).

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The monthly bill for 20 gallons of water is $88.

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 water bottling company charges $8 per month for their water dispenser and $4 for each gallon of water delivered.

If you have g gallons of water delivered in a month.

Then, the equation to represent the  amount of your bill for that month.

8+ 4g

Now, for g=20 the amount of bill would be

= 8 +4(20)

= 8+ 80

= $88

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Answer:

  A.  -5

Step-by-step explanation:

You want the slope of a graphed line that crosses grid points (0, 2) and (1, -3).

The sign of the slope is positive if the line goes up to the right. This line goes down to the right, so the sign of its slope is negative. (Eliminates choices C and D)

The magnitude of the slope is the ratio of vertical distance to horizontal distance between two points. This line drops 5 vertical squares for each square to the right, so its slope is ...

  rise/run = -5/1 = -5

The slope is best represented by -5.

__

Additional comment

From a point on the line that is a crossing of grid lines, if the line crosses the next vertical grid line before it crosses the next horizontal grid line, the magnitude of its slope is less than 1.

Here, the line crosses several horizontal grid lines before it crosses another vertical grid line, so its slope has a magnitude greater than 1. When the choice is between -5 and -1/5, the larger magnitude number is -5.

From two points on the line, you can find the slope using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -2)/(1 -0) = -5/1 = -5 . . . . . . using points (0, 2) and (1, -3)

∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.

A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.

Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and

m∠2 = 9x+12, and x = 10.

Putting the value of x, we get,

m∠1 = 6x + 18 = 6*10 + 18 = 78°

m∠2 = 9x+12 = 9*10 + 12 = 102°

m∠1 + m∠2 = 180°

Therefore, ∠1 and ∠2 are consecutive angles pairs.

We can prove that oars are parallel by converse of consecutive angles theorem.

Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel

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The function rule that gives the height of a stack of cups is h(c) = 8+ 2(c)

Looking at the image,  1 paper cup has a body height of 8cm (total height = 10cm) and the height of the cups increases by 2cm for each cup added.

If you add three cups, for example, the height increases by 6cm (3 x 2cm). If you add n cups the height will increase by 2n and the total height will be 8+2n  

Number of cups, c  >>>>>  Process >>>>>  Height of stack, h(cm)

         c                                  8+ 2(c)                       h

h(c) = 8+ 2(c)

Note: It is h(c) because c is the input and h is the output

Therefore, the function rule that gives the height of a stack of cups in terms of the number of cups in a stack is h(c) = 8+ 2(c)

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Answer: False, adding two negatives does not make a bigger number. I know this because when adding the two negatives, the absolute value will get bigger. However, the value of the number gets smaller.

Using the concepts of probability, we got that  0.063 is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time

We know very well that probability is defined as the fraction of number of favorable outcomes to the total number of outcomes.

Here, we are rolling a 6-faced dice.

Getting 3 on the top face of dice is same as the any number getting from 1 to 6 on the top face of the dice.

So, every number has equal probability to come on the top face,  therefore the probability of getting 3 on the top face of dice is (1/6)

Now, similarly total number of marbles in the bag=6 blue +3 black+8 orange marble=17 marbles.

Now, picking one marble from 17 marble is can be done in [tex]^1^7C_1[/tex]  ways, similarly  choosing 1 blue marble from 6 marble can be done in [tex]^6C_1[/tex] ways.

So, probability of picking 1 blue marble randomly=6/17

Now, the probability of picking 1 blue marble from 17 marbles along with rolling dice probability is given by =(6/17)×(1/6)=(1/17)=0.063

Hence, the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time is 0.063

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Answer: ( -2, -3 )

Step-by-step explanation:

Answer: 58

Step-by-step explanation:

First you substitute the values, so

4-9*-6

Then you solve using order of operations

Answer:

58

Step-by-step explanation:

y-9a

Let a = -6 and y=4

Substitute the values in

4 -9(-6)

Multiply first

4 + 54

Add

58

By using normal distribution, it is obtained that weight of a randomly selected chicken egg is 28.39 grams

What is normal distribution?

Normal distribution is a continuous type probability distribution whose probability density function is

[tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}[/tex]

where,  z = [tex]\frac{x - \mu}{\sigma}[/tex]

[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

In case of normal distribution

Formula for z = [tex]\frac{x - \mu}{\sigma}[/tex]

[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

Let the weight of the egg be x grams

Here, z = -1.41, [tex]\mu[/tex] = 58 and [tex]\sigma[/tex] = 21

[tex]-1.41 = \frac{x - 58}{21}\\[/tex]

x = -1.41 [tex]\times[/tex] 21 + 58

x = 28.39 grams

Weight of a randomly selected chicken egg is 28.39 grams

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Answer:

2.5 dhs

Step-by-step explanation:

5% of AED50

50x5/100=250/100

=AED2.5

The number of bushels of wheat does the farmer harvest is 7251 bushels of wheat

The farmer's estimated number of bushels of wheat in the harvest = 7250 bushels

The weather is perfect during the growing season

The number of additional bushels of wheats harvested = 1 bushels

The number of bushels of wheat does the farmer harvest = The farmer's estimated number of bushels of wheat in the harvest + The number of additional bushels of wheats harvested

Substitute the values in the equation

The number of bushels of wheat does the farmer harvest = 7250 + 1

Here we haver to use the addition

Add the terms

= 7251 bushels of wheat

Hence, the number of bushels of wheat does the farmer harvest is 7251 bushels of wheat

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The equation that compares the time (t) with the distance (d) would be; 80 (t) = d

An expression that depicts the relationship between two or more numbers and variables is called an equation. Two or more equations that can be solved to get a singular result are referred to as a system of equations. The equation's power must be in one degree.

Given that A train travels at 80 miles per hour. We need to find the equation that compares the time (t) with the distance (d)

where t means time so if the train travels 2 hours then it will travel;

80 × 2 = 160 miles

Therefore, the equation that compares the time (t) with the distance (d) would be; d = 80t.

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Answer:

x = 8

Step-by-step explanation:

the exterior angles of a triangle sum to 360° , that is

20x + 8x + 17x = 360

45x = 360 ( divide both sides by 45 )

x = 8