x-y=5 and x+y=-10 is this parallel, perpendicular, or neither?

Answer:

X = 8.5, Y = 6.5

Step-by-step explanation:

X = # of children's books

Y = # of puzzle books

Amelie wants to buy 2 more children's books than puzzle books.

15 - 2 = 13 (Save the 2)

13 / 2 = 6.5

6.5 + 2 = 8.5

So; 8.5 + 6.5 = 15

X = 8.5

Y = 6.5

Answer:

450.

Step-by-step explanation:

The given equation is

\(\dfrac{150}{170}=\dfrac{x}{510}\)

We need to solve the proportion to find the value of x.

Multiply both sides by 510, to isolate x on one side.

\(\dfrac{150}{170}\times 510=\dfrac{x}{510}\times 510\)

Cancel out common factors.

\(150\times 3=x\)

\(450=x\)

On interchanging the sides, we get

\(x=450\)

Therefore, the value of x is 450.

Answer:

450

Step-by-step explanation:

Answer:

If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.

But if you multiply or divide both sides of an inequality by a negative number, the inequality is no longer true.

Step-by-step explanation:

Answer:

The multiplication property of inequality states that if one side of the inequality is multiplied or divided by a positive number, we can multiply and divide the other side of the inequality by the same number without changing or disturbing the direction sign of the inequality.

Step-by-step explanation:

The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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Answer:

D

Step-by-step explanation:

Answer:

rectangle

Step-by-step explanation:

If you place those points on a grid, you would obtain a rectangle as the slopes are opposite reciprocals when forming lines showing perpendicular and parallel lines that are seen in a rectangle

Answer:

6 yards

45 inches

\(2 \frac{1}{4}\) feet

Hope this helps :)

Step-by-step explanation:

1 yard = 3 feet

1 foot = 12 inches

6 yards = 18 feet = 216 inches

\(2 \frac{1}{4}\) feet = 27 inches

Greatest to least

6 yards

45 inches

\(2 \frac{1}{4}\) feet

Assuming the population standard deviation is known and the standard deviation of the sample mean x : option (b) is correct : the standard error of the sample mean decreases.

In probability theory, the central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution (i.e., a “bell curve”) as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.

Standard deviation is a calculation of the dispersion or variation in a set of numbers. If the standard deviation is a small number, it means the data points are close to their average value. If the deviation is large, it means the numbers are spread out, further from the mean or average.

There are different ways to write out the steps of the population standard deviation calculation into an equation. A common equation is:

                          σ = ([Σ(x - u)2]/N)1/2

Where:

σ is the population standard deviation

Σ represents the sum or total from 1 to N

x is an individual value

u is the average of the population

N is the total number of the population

A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.

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Answer:

15

Step-by-step explanation:

Since, we need a number that if added to -14, it'll give a positive result. The first number is gonna be 15, . Because, it's the first number that can give a positive number if summed up with -14.

a) The  total expenditure if the job takes 13 days is  $36400.

b) Money will be spent on the job from the 13th day to the 24th day is $83600.

c) If the company wants to spend no more than SI 01,200 on the job, in 224 days must it complete the job.

A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by the function below, where x is the number of days since the start of the job.

E(x) = 4x + 2

where x is the number of days since the start of the job.

a.) Find the total expenditure if the job takes 13 days

We Integrate

E(x) =∫E'(x) dx

=∫4x + 2  in hundreds of dollars

(2x² + 2x + c) in hundreds of dollars

now,

(2x² + 2x + c) in hundreds of dollars

x is the number of days since the start of the job.

x = 13

2x² + 2x

[2(13)² + 2(13)] in hundred of dollars

=[ 338 + 26] in hundreds of dollars

=[364] in hundreds of dollars

Hence the expenditure is 364 in hundreds of dollars

This means, 364 × $100

= $36400

similarly we get,

b.) Money will be spent on the job from the 13th day to the 24th day

= ∫4x + 2  in hundreds of dollars [from 13 to 24]

solving we get,

= $83600

c.) let the job complete in t days.

so, we get,

I 01,200 = ∫4x + 2  in hundreds of dollars [from 0 to t]

solving we get,

t = 224 days

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Answer:

b=Ah

Step-by-step explanation:

multiply both sides by h

The price of the carpet per square meter is $32.13. It will cost $1,556.86 to carpet an area of 1475 square feet.

1. To find the price of the carpet per square meter, first convert $28.99 per square yard to meters.

1 yard = 0.9144 meters

$28.99 per yard x (1 meter/ 0.9144 meters) = $32.13 per square meter

2. To find the cost of carpeting an area of 1475 square feet, first convert 1475 square feet to square yards.

1 square foot = 0.11111 square yards

1475 square feet x (1 square yard/ 0.11111 square yards) = 13,333.33 square yards

3. Multiply the cost per square yard by the number of square yards needed to carpet the area.

$28.99 per square yard x 13,333.33 square yards = $1,556.86

The complete question is:

a carpet sells for $28.99 a square yard. what is the price of the carpet per square meter? how much will it cost to carpet an area of 1475 square feet? 1 yard is equal to 0.9144 meters

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The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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The function has a minimum of -4.35125

From the question, the equation of tis given as

f(x)=2x^2-9.1x+6

Rewrite the function as follows

f(x) = 2x² -9.1x + 6

Next, we differentiate the function

This is represented as

f'(x) = 2 * 2x - 1 * 9.1 + 0 * 6

Evaluate

f'(x) = 4x - 9.1

Set the differentiated function to 0

This is represented as

f'(x) = 0

So, we have

4x - 9.1 = 0

This gives

4x = 9.1

Divide by 4

x = 2.275

Substitute x = 2.275  in f(x) = 2x² -9.1x + 6

f(2.275) = 2(2.275)² - 9.1(2.275) + 6

Evaluate

f(2.275) = -4.35125

Hence, the minimum is -4.35125

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Answer:

  13. x = 52.8°

  14. 663.65 ft

  15. 30.7 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and trig functions of the acute angles.

__

The sides adjacent and opposite the angle are marked. The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(x°) = 2.5/1.9

The angle is found using the inverse tangent function:

  x° = arctan(2.5/1.9) ≈ 52.8°

__

Again, the tangent relation comes into play. The given values are the side opposite and the angle, and we are asked for the side adjacent.

  Tan = Opposite/Adjacent

  tan(11°) = (129 ft)/(distance to shore)

  distance to shore = (129 ft)/tan(11°)

  distance to shore ≈ 663.65 ft

__

In this scenario, the given angle is opposite the given side of the triangle. The measure of the hypotenuse is needed.

  Sin = Opposite/Hypotenuse

  sin(71°) = (29 ft)/(ladder length) . . . . substitute given information

  ladder length = (29 ft)/sin(71°) . . . . . . solve for ladder length

  ladder length ≈ 30.7 ft

if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.

Let us pull out the critical elements

Population: Normally distributed with mean of 2870

population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180

As population sigma is known, we do not have apply any corrections

P(xbar < $2500) = ?    

Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.

Ztest = (2500-2870 )/ 180  or -370/180 = -2.055

As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma  being 95.44% to get a close estimate.   If the area between -2 and 2 sigma = .9544 then the area outside = .0456.  Half of this (the amount under the curve LESS THAN -2) would be .0228

Using a calculator or computer for an exact answer we find (using a TI-83/86):

nmcdf(-9E6,2500,2870,180) = .0199

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The number of solutions can be found using the stars and bars formula, which states that the number of ways to distribute k indistinguishable objects into n distinguishable boxes is (k+n-1) choose (n-1).

In this case, we can think of the integers a, b, c, d, and e as the indistinguishable objects, and the plus signs between them as the distinguishable boxes. Since each integer must be at least 10, we can subtract 10 from each integer to get a new equation a' + b' + c' + d' + e' = 450, where each of the new variables is a nonnegative integer. We can then apply the stars and bars formula with k = 450 and n = 5 to get the number of solutions to the original equation, which is (450+5-1) choose (5-1) = 454,686.

Therefore, there are 454,686 solutions to the equation a + b + c + d + e = 500, where each of a, b, c, d, and e is an integer that is at least 10. These solutions can be found by distributing the integers 460 (i.e., 450+10 for each integer) into the five boxes separated by plus signs in all possible ways. The solutions can also be enumerated by using generating functions or other combinatorial techniques.

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The given situation can be represented in inequality as t ≤ 45 °F.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, we are instructed to use t to denote the refrigerator's temperature (in°F).

Additionally, we are informed that the lab refrigerator's maximum temperature is 45 °F.

It must be either lower than or equal to 45 °F for the temperature inside the refrigerator to be no higher than that.

As a result, t must be lower than or equal to 45 °F.

Therefore, it can be expressed as inequality as follows:

t ≤ 45 °F

Therefore, the given situation can be represented in inequality as t ≤ 45 °F.

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Complete question:
The temperature inside the lab refrigerator is at most 35 Fahrenheit used to represent the temperature in Fahrenheit of the refrigerator in inequality.

Answer:

The insurance company will pay $350 to get the car repaired.

Step-by-step explanation:

Insurance is as a business arrangement between the insured and the insurer, whereby  the insurer, usually a company or the state, agrees to provide some guaranteed compensations for some specific losses upon the payment of some specified premiums by the insured.  The insured is the person taking up the insurance policy, while the insurer is the company guaranteeing the compensation for the insured risk.  It offers protection to the insured to restore the person to the former position before the occurrence of the risk.

Answer:

Area of shaded region is 160.14m²

Step-by-step explanation:

To find the area of the shaded region, subtract the area of inner circle from the area of outer one

a=πr²

(3.14)7²=153.86

(3.14)10²=314

314-153.86=160.14

Remainder 11. We are aware that when a number is split by three, the remainder is created by dividing the digit sum by three. The law of three's divisibility asserts that a number is entirely divisible by three if the sum of its digits is also three-digit divisible.

If a polynomial f(x) is divided by xa, the result is the constant f(a) and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.

The remainder theorem asserts that "when a polynomial of degree p(x) is divided by a linear polynomial of degree x - a, the remaining is p(a)" (OR) "when a polynomial of degree p(x) is divided by a linear polynomial of degree ax + b, the remainder is p(-b/a)".

The law of three's divisibility asserts that a number is entirely divisible by three if the sum of its digits is also three-digit divisible. We are aware that when a number is split by three, the remainder is created by dividing the digit sum by three.

The formula reads as follows: f(x)/x + 3.

A 0 x + 3 = 0 divisor should be used.

Calculate x x = -3.

The remainder of the quotient is 11.

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The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).

Equation of a circle

A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.

We know that,

Equation of the circle passing through the origin is given by:-

\(x^2+y^2=r^2\)

Where,

r is the radius of the circle, and

(x,y) are the coordinates of each point of the circle.

Hence, we can write,

The radius of the circle will be :-

\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)

Hence, r = 4 units.

Hence, the equation of the circle is given by:-

\(x^2+y^2=16\)

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300 milligrams is 0.3 grams of protein.

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.

To convert a value or expression between two different forms. • Measurement: converting between different units, for as from inches to millimeters or liters to gallons. For instance, change 12 inches to millimeters. 304.8 millimeters are equal to 12 inches multiplied by the inch-to-millimeter ratio of 25.4.

Given Data

100 grams of honey  contains about 0.3 grams of protein.

1 gram = 1000 milligrams

To find milligrams in protein:

0.3 grams multiplied by 1000

0.3(1000)

300

300 milligrams is 0.3 grams of protein.

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The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped. Answer is 8.212°.

The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped.

The ratio of the opposite side to the hypotenuse is called sin(), and the ratio of the adjacent side to the hypotenuse is called cos(), when viewed from a vertex with angle.

So, the Pythagorean identity-based formula for sin is sin²x = 1 - cos²x.

Hypotenuse²=base²+perp²

(8)²=(7)²+(perp)²

64=49+(perp)²

64/49=perp²

1.306=perp²

Now taking square root on both sides

Perp=√1.306

Perp=1.142

Sin C=opposite/hypotenuse

Sin =1.142/8

Sin C=0.14285

C=Sin^-1 0.14285

C=8.212°

Answer is 8.212°.

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The provided equation has a straight graph and no typical axis of symmetry because it is a linear function. As a result, the equation y = -8x does not have an axis of symmetry.

The graph of a linear function is a direct line. The form of the a linear function is as follows. a + bx Equals y = f (x). A regression line is composed of one independence variable and one dependent variable. The variables that are dependent and independent are X and Y, respectively.

A perfect line just on coordinate plane is expressed by a linear function. As an illustration, the equation y = 3x – 2 depicts a function f because it refers to a line inside the reference system.

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