Algebra 1
> J.10 Solve one-step and two-step equations: word problems UFG
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At Dapper Dave's annual end-of-season sale, every necktie in the shop gets marked down.
Dillon purchased 6 neckties during the sale. Each necktie cost $5 less than its full price. He
paid a total of $162. What is the cost of each necktie at full price?

Answer:

x=-12

y=11/3

z=28/3

Step-by-step explanation:

The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6)

The equations are given as: y = 1.5x - 4 & y = -x

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables

Substitute y = -x in the first equation

-x = 1.5x - 4

Collect like terms

-1.5x - x = -4

Any set of values of x1, x2, x2,…xn which simultaneously satisfies the system of linear equations given above is called a solution of the system. If the system of equations has one or more solutions, the equations are called consistent. Also, if the system of equations does not admit any solution, then the equations are called inconsistent.

This gives

-2.5x = -4

Divide both sides by -2.5

x = 1.6

Substitute x = 1.6 in y = -x

y = -1.6

Hence, the solution to the system of equations is (1.6,-1.6).

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To simplify, we multiply each single one in the first bracket with both in the second bracket :

\((3x+1)(3x-5) = 9x^{2} -15x + 3x - 5\)

Answer:

a^5x^5, 10a^5x^4, 40a^5x^3

Step-by-step explanation:

Use pascal's triangle for the first one

(2+x)^5 * a^5

= x^5a^5 + 5*2^1*x^4*a^5 + 10*2^2*x^3*a^5 ...

= a^5x^5 + 10a^5x^4+ 40a^5x^3 ...

Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

The ratio of $1.60 to $2.00 in the simplest form or lowest terms is 4:5.

To write the ratio of 1.60 dollars to 2.00 dollars as a ratio of whole numbers in the lowest terms, we can divide both the numerator and the denominator by the Greatest Common Divisor (GCD) of the two terms.

GCD of 1.60 and 2.00 can be found by listing down the multiples of both the terms until we find the first common factor, which is 0.20, and that is the GCD of 1.60 and 2.00.

So,Dividing both terms by 0.20, we get,

1.60/0.20 = 8 and 2.00/0.20 = 10

Now, we can write the ratio of 1.60 dollars to 2.00 dollars as a ratio of whole numbers in lowest terms by dividing both terms by their GCD 0.20 and then simplifying it.

Thus, the ratio as a ratio of whole numbers in lowest terms is:

8:10 or 4:5

In other words, the ratio of $1.60 to $2.00 in the simplest form or lowest terms is 4:5.

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The value of x is 6 when the equation is √x+2= x-4.

Given that,

The equation is

√x+2= x-4

The value of x must be determined.

Equations are mathematical expressions with two algebraic expressions on either side of the equals (=) sign. It shows that the expressions written on the left and right sides have an equal relationship. A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.

Take the equation,

√x+2= x-4

√x=x-4-2

√x=x-6

√x-x=-6

x=6

Therefore, The value of x is 6 when the equation is √x+2= x-4.

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Answer:

The equivalent ratio to the given ratio is;

Explanation:

Given the ratio;

We want to select an equivalent ratio from the given options.

Let's divide the ratio all through by 3;

Therefore, the equivalent ratio to the given ratio is;

Answer:

-13/10

Step-by-step explanation:

It wont be -7/10 because to change a mixed number to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.

An expression is in its simplest form when it can no longer be simplified or reduced any further.

When an expression is in its simplest form , it means that it has been reduced to its most basic and concise form, with no unnecessary terms or factors.

This makes it easier to evaluate and work with the expression . In some cases , the simplest form of an expression may also reveal certain properties or relationships that were not immediately apparent in its original form.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

The exact value of \(sin(\(\theta + \phi\))\)can be found using trigonometric identities and the given values of \(tan\(\theta\) and cot\(\phi\).\)

We can start by using the given values of \(tan\(\theta\) and cot\(\phi\) to find the corresponding values of sin\(\theta\) and cos\(\phi\). Since tan\(\theta\)\)is the ratio of the opposite side to the adjacent side in a right triangle, we can assign the opposite side as 4 and the adjacent side as 9. Using the Pythagorean theorem, we can find the hypotenuse as \\((\sqrt{4^2 + 9^2} = \sqrt{97}\). Therefore, sin\(\theta\) is \(\frac{4}{\sqrt{97}}\).\)Similarly, cot\(\phi\) is the ratio of the adjacent side to the opposite side in a right triangle, so we can assign the adjacent side as 5 and the opposite side as 3. Again, using the Pythagorean theorem, the hypotenuse is \(\(\sqrt{5^2 + 3^2} = \sqrt{34}\). Therefore, cos\(\phi\) is \(\frac{5}{\sqrt{34}}\).To find sin(\(\theta + \phi\)),\) we can use the trigonometric identity: \(sin(\(\theta + \phi\)) = sin\(\theta\)cos\(\phi\) + cos\(\theta\)sin\(\phi\). Substituting the values we found earlier, we have:sin(\(\theta + \phi\)) = \(\frac{4}{\sqrt{97}}\) \(\cdot\) \(\frac{5}{\sqrt{34}}\) + \(\frac{9}{\sqrt{97}}\) \(\cdot\) \(\frac{3}{\sqrt{34}}\).Multiplying and simplifying, we get:sin(\(\theta + \phi\)) = \(\frac{20}{\sqrt{3338}}\) + \(\frac{27}{\sqrt{3338}}\) = \(\frac{47}{\sqrt{3338}}\).Therefore, the exact value of sin(\(\theta + \phi\)) is \(\frac{47}{\sqrt{3338}}\).\)



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The solution to the equation x plus 16 all over 3 = 3x  is x = 2

The mathematical statement is given as:

x plus 16 all over 3 = 3x

Rewrite the equation as:

(x + 16)/3 = 3x

Multiply both sides of the equation by 3

x  + 16 = 9x

Subtract x from both sides of the equation

8x = 16

Divide both sides of the equation by 8

x = 2

Hence, the solution to the equation x plus 16 all over 3 = 3x  is x = 2

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Answer:

5=2x

Step-by-step explanation:

poopu

Answer:

it should be two

Step-by-step explanation:

I hope this helps!

It would take around 902 trillion (902,000,000,000,000) gum balls to fill a sphere the size of Pluto, assuming the given diameter and the size of a gum ball.

To determine the number of gum balls it would take to fill a sphere the size of Pluto, we need to make a few assumptions and calculations.

Approximating the Size of Pluto:

The diameter of Pluto is approximately 2,374 kilometers (1,473 miles). We'll use this value as the diameter of our hypothetical sphere.

Calculating the Volume of the Sphere:

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius. Since we have the diameter, we can calculate the radius as half the diameter: r = 1,187 kilometers (736.5 miles). Substituting these values into the formula, we find the volume of the sphere is approximately 3.778 × 10^9 cubic kilometers (9.04 × 10^8 cubic miles).

Determining the Size of a Gum Ball:

Assuming a gum ball has a diameter of 2 centimeters, we can calculate its radius as 1 centimeter (0.01 meters).

Calculating the Volume of a Gum Ball:

Using the formula V = (4/3)πr³, where V is the volume and r is the radius, we find the volume of a gum ball is approximately 0.0042 cubic meters (4.2 × 10^-6 cubic kilometers).

Finding the Number of Gum Balls:

To find the number of gum balls needed, we divide the volume of the sphere (Pluto) by the volume of a gum ball. This gives us approximately 9.02 × 10^14 gum balls.

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The volume of a hexagonal pyramid in cubic feet with the same dimensions = 1220 ft³

A hexagοnal pyramid is a three-dimensiοnal geοmetric shape that cοnsists οf a base that is a regular hexagοn (a six-sided pοlygοn with all sides and angles equal) and six triangular faces that meet at a single pοint abοve the base, called the apex.  The six triangular faces fοrm a pyramid shape with the base, which is why it's called a hexagοnal pyramid.

This relatiοnship can be derived using the fοrmula fοr the vοlume οf a pyramid  V = (1/3)Bh, where B is  area οf  base and h is  height οf pyramid. Since the base οf the pyramid is a hexagοn inscribed within the hexagοnal base οf the prism, the area οf the base is (3√3/2)a², where a is the side length οf the hexagοn. The height οf the pyramid is the same as the height οf the prism, which we can call h.

Thus, the volume of pyramid is

\(\rm V_p\) = (1/3)(3√3/2)a²h

= (√3/2)a²h, while the volume of prism is

\(\rm V_p\)r = \(\rm B_p\)r h = (3√3/2)a²h.

Dividing \(\rm V_p\)r by 3 gives \(\rm V_p\)

so we have \(\rm V_p\) = \(\rm V_p\)r/3, as claimed. so

\(\rm V_p\) = 3360/3 ft³

\(\rm V_p\) = 1220ft³

volume of a hexagonal pyramid in cubic feet 1220ft³

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The probability that an ear of corn selected at random with no borers is 0.5488

Given,

The farmer counted 3000 borers in the 5000 ears.

The probability mass function of Poisson distribution: \(P(X=x)=\frac{e^{-\beta }\beta ^{x} }{x!}\)

Here, \(\beta\) is the parameter.

Then the value of parameter is:

\(\beta =\frac{3000}{5000}\) = 0.6

Now determine the probability that an ear of corn selected random will contain no borers:

P(X=0) = \(\frac{e^{-0.6}0.6^{*} }{0!}\)

P(X=0) = \(\frac{e^{-0.6} }{1}\)

P(X=0) ≈ 0.5488

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In a binomial experiment, there are only two possible outcomes for each of the n trials. True statement.

These outcomes are typically labeled as "success" and "failure," and they are mutually exclusive (meaning that only one outcome can occur per trial) and collectively exhaustive (meaning that one of the two outcomes must occur per trial).

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Yes (-3,-2) is true.

No (1,6) is false

No (0,4)  is false

To determine if an ordered pair is a point of intersection between the line and the parabola, we need to check if the coordinates satisfy both equations.

(-3, -2)

y = 2x + 4 => -2

= 2(-3) + 4 => -2 = -2 (True)

y = x² + 4x + 1 => -2

= (-3)² + 4(-3) + 1 => -2 = -2 (True)

Answer: Yes

(1, 6)

y = 2x + 4 => 6

= 2(1) + 4 => 6 = 6 (True)

y = x² + 4x + 1 => 6

= (1)² + 4(1) + 1 => 6 ≠ 6 (False)

Answer: No

(0, 4)

y = 2x + 4 => 4

= 2(0) + 4 => 4 = 4 (True)

y = x² + 4x + 1 => 4

= (0)² + 4(0) + 1 => 4 ≠ 1 (False)

Answer: No

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Answer:

6+6=12 cm

4+4=8 cm

6+6= 12 cm

Add all together and it equals 32

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

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4x6=24

24x0.5=12

12x4=48

4x4=16

48+16=64

Answer:

1,2,3,4,6,8,12,24

Step-by-step explanation:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).

Step-by-step explanation:

Answer:15

Step-by-step explanation:

distance = Sqrt((x2-x1)^2 +(y2-y1)^2)

15-3 =12

16-7=9

12^2 = 144

9^2 = 81

144+81 = 225

square root of 225 = 15

the distance is 15

Answer:

d/2 = r if you are talking about circles, if that's the case then the r would be 5

The probability that the coin is fair given that it lands heads is 0.3571.

Given that a coin is picked from the box and flipped, the probability of the coin being fair is 1/3.

The probability of the coin being biased towards heads and the coin being biased towards tails is 1/3.

Therefore, the probability that the coin is fair and lands heads is (1/3) x 0.5

= 0.1667.

The probability that the coin is biased towards heads and lands heads is (1/3) x 0.8

= 0.2667.

The probability that the coin is biased towards tails and lands heads is (1/3) x 0.1

= 0.0333.

Therefore, the total probability that the coin lands heads is 0.1667 + 0.2667 + 0.0333

= 0.4667.

Using Bayes' Theorem, the probability of the coin being fair given that it lands heads is:

P(fair|heads)

= P(heads|fair) * P(fair) / P(heads)

= 0.5 * 1/3 / 0.4667

= 0.3571.

Thus, the probability that the coin is fair given that it lands heads is 0.3571.

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Answer:

Step-by-step explanation: the nearest hundredth to 12.0683 is 12.068  because 3 is  below five

Answer:

kathryn= 6 years old

her mother= 38 years old

Step-by-step explanation:

kathryn=x

mother= x²+2

x²+2 +x=44

x=6

kathryn= 6 years old

her mother= 38 years old