What are two numbers that when multiplied equal 5/9 and when added together equal -2?

if Fred has 40 balls in his room then there are 7 pits in his room.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that there are 12 balls to every 2 pits

Fred has 40 balls in his room

We have to find the number of pits for 40 balls

Let x be the number of pits for 40 balls.

Form an proportional equation

12/2=40/x

6=40/x

x=40/6=20/3

x=6.667=7

Hence, if Fred has 40 balls in his room then there are 7 pits in his room.

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The congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

For the given triangles ABC and triangle LMN we can see that:

Line segment AB = LM

Segment AC= LN

and, CB = MN

Hence, the congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.

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The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.

Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.

The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.

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Answer:

if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months. you will have 800,000 after 20 years.

Step-by-step explanation:

rate of return is 5.3% compounded monthly.

number of years = 40.

future value = 800,000

interest rate per month is 5.3% / 12 = .4416666....%

number of time periods if 40 * 12 = 480

payment required at the end of each month is equal to 484.5267545

your total payments are 480 * 484.5267545 = 232,572.8422

total interest earned would be 800,000 minus 232,572.8422 = 567,427.1578

if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months.

you will have 800,000 after 20 years.

if you deposit that money for an additional 10 years at the same rate of interest per year compounded annually, then you will have 1,357,560.674.

you can use an online calculator to get the results similar to this.

they might not be right on because of possible rounding errors, but they'll be close.

Answer:

81

Step-by-step explanation:

[tex]2\frac{1}{4}*36\\ \\\frac{9}{4}*\frac{36}{1} \\ \\\frac{324}{4} =81[/tex]

a) The locus of points that are less than 5 cm from P is (A)

b) The  locus of points that are closer to Q than to P is (F)

c) The locus of points that are more than 5 cm from Q is (D),

A locus is a curve or other shape created in mathematics from all the points that meet a specific equation describing the relationship between the coordinates, or from a point, line, or moving surface. The locus defines all shapes as a set of points, including circles, ellipses, parabolas, and hyperbolas.

Given:

a) The point A is less than 5cm away from point P is int he circle centered on P.

b) The option E is point closer to P than Q.

The option F is point closer to Q than P.

c) The option D point more than 5 cm away from Q on the outside of the circle centered on Q.

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Answer: t=-5

Step-by-step explanation:

Multiply by -6 on both sides to get rid of the -1/6

Subtract 12 on both sides
Divide 18 by -90 on the other side

[tex](-1/6(12+18t))(-6)=13(-6)\\12+18t=-78\\18t=-90\\\\t=-5[/tex]

The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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It will take Rachel 5 months to pay off her debt at her current monthly payment rate.

Interest rate is a percentage that represents the amount of interest charged by a lender to a borrower for the use of money. It is used to calculate the interest that will accrue on a loan or deposit over a specific period of time, and is usually expressed as an annual rate. It is a key component in determining the cost of borrowing money, and affects the amount that must be paid back to the lender, including the principal amount and any additional interest charges.

Rachel's monthly payment of $320 will only cover the interest on her debt and will not significantly reduce the outstanding balance. She would need to pay more each month or find a way to reduce the interest rate in order to pay off her debt in a reasonable amount of time.

To calculate the time it will take for Rachel to pay off her debt, we can use the following formula:

n = ceil(log(P/A) / log(1 + r))

where n is the number of payments, P is the initial balance, A is the monthly payment, and r is the monthly interest rate (expressed as a decimal).

In this case, P = $8,975, A = $320, and r = 17% / 12 = 0.17 / 12 = 0.01417.

So, n = ceil(log($8975 / $320) / log(1 + 0.01417)) = ceil(log(28.09375) / log(1.01417)) = ceil(4.3626) = 5.

It will take Rachel 5 months to pay off her debt at her current monthly payment rate. This means that it will take her just over 4 years to pay off the debt, assuming no additional purchases are made on the card and the interest rate does not change.

As for shopping for a new card, Rachel should consider a card with a lower interest rate. This will allow her to pay off her debt more quickly and save money in interest charges. She may also consider a balance transfer card with an introductory 0% interest rate, which would give her time to pay off the debt without accruing interest. However, she should be aware of any balance transfer fees that may apply. It is best for Rachel to compare options and read the fine print before making a decision.

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Answer:

Step-by-step explanation:

When someone has a growth mindset they believe that they can continue to learn and become more intelligent with effort.

"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

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The amount of money Camilla gave the cashier is

$11.68

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.

For example, if there are 20mangoes and 20 oranges are in a basket, the total number of fruit is 20+20 = 40 fruits

Camilla bought a duffel bag for $10.73 and he collected $0.95 as change.

Therefore the total money he gave to the cashier is $10.73+$0.95 = $11.68

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On solving the provided question, we can say that In rectangle, the two diagonals are in congruence , the diagonals bisect each other. PT=TR=ST=TQ=1/2PR=1/2QS =1/2×22.8=11.4

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Rectangle, two diagonals are in congruence

⇒PR=QS=22.8

The diagonals bisect each other.

⇒PT=TR=ST=TQ=1/2PR=1/2QS

=1/2×22.8=11.4

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Step-by-step explanation:

To find the probability of getting an even number, we need to count the number of even numbers and divide it by the total number of sides of the die:

Number of even numbers = 10 (2, 4, 6, 8, 10, 12, 14, 16, 18, 19)

Total number of sides = 19

P(even number) = Number of even numbers / Total number of sides = 10/19 = 0.526 (or 52.6%)

The decimal number 0.4 is greater than 0.25.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

There are 25 out of 100 shaded cubic part.

That means, the number is 0.25.

From the given choices:

0.4 > 0.25.

Therefore, 0.4 is the required decimal number.

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Answer:

5, second choice

Step-by-step explanation:

When x is 3, the purple line's y-value is between 4 and 6, which is 5.

Answer:

B

Step-by-step explanation:

You have two black lines with the arrows at the end. The one going left and right is your X-Axis. The one going up and down is the Y-Axis.

What they want to know is what is f(x) when x = 3

f(x) is another term for y

So they want to know, what is the value of the y-axis when x is 3 on the x-axis.

So on the line going left and right you find the line 3, between 2 and 4, then going up until you hit the purple line. Once you hit the purple line, go left until you hit the up and down line. That will give you an answer of 5

If you already chopped 4 walnuts and you have only gotten 1/4 cup of the chopped walnuts, it means that each walnut yields 1/4 cup / 4 walnuts = 1/16 cup of chopped walnuts.

To find out how much more chopped walnuts you need, we can subtract the amount you have from the total amount the recipe calls for:

1 cup - 1/4 cup = 3/4 cup

So you need 3/4 cup of chopped walnuts more.

To find out how many more walnuts you should chop, divide the amount you need by the amount each walnut yields:

3/4 cup / (1/16 cup/walnut) = 12 walnuts

So you should chop 12 more walnuts to get the desired amount.

The number of students that signed up for only language art is 116

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

n( of Math and language only) = 20-2 = 18

n( of Math and humanities only) = 5-2 = 3

n( of humanities and language only) = 10-2 = 8

n( math only) = 68-(18+2+3)

= 68 - 23 = 45

n( humanities only) = 40-( 8+3+2)

= 40-13 = 27

represent number of student Who signed up for language by x

n( of language only) = x-( 18+2+8)

=x- 28

219 = 45+27+18+2+3+8+x-28

219 = 75 +x

x = 219-75

x= 144

therefore number of students that signed from language art only = 144-28

= 116

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Answer:

see below

Step-by-step explanation:

tricycles = x

bicycles = y

x+y =10 so y=10-x

3x+2y=23

so 3x + 2(10-x) =x+20 =23

so x=3

y = 7

The amount of the fabric is 4 / 3 yards.

Let's call the amount of fabric used to make each pillow "x".

Then, the total amount of fabric used was 12 * x = 16 yards.

Solving for x, we get x = 16 / 12 = 4 / 3 yards.

Since fabric is typically sold in whole yards, the answer lies between 1 and 2 yards.

The answer, 4 / 3 yards,

This can be rounded up to 1 yard or rounded down to 1 1/3 yards.

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Answer: We can use the Law of Cosines to find the length of side k in ΔJKL:

k^2 = j^2 + l^2 - 2 * j * l * cos(m∠K)

k = √(j^2 + l^2 - 2 * j * l * cos(m∠K))

Substituting the given values, we get:

k = √(1.7^2 + l^2 - 2 * 1.7 * l * cos(47°))

k = √(2.89 + l^2 - 2.94 * l * cos(47°))

To the nearest 10th of an inch, k = √(2.89 + l^2 - 2.94 * l * cos(47°)) = 3.3 inches.

Step-by-step explanation:

Step-by-step explanation:

The probability of selecting a defective watch is 400/10,000 = 2/50.

The probability of selecting 50 defective watches out of 100 selected is given by the binomial distribution:

(100 choose 50) * (2/50)^50 * (1/2)^(100-50) = 0.072.

So the probability that exactly 50 out of 100 selected watches are defective is approximately 0.072.

The triangle ABC is vertically translated only. Then the correct option is B.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

We know that;

Reflection does not change the size and shape of the geometry.

Rotation does not change the size and shape of the geometry.

Translation does not change the size and shape of the geometry.

Here, On a coordinate plane, triangle ABC is shifted 5 units up to form triangle A'B'C'.

The diagram is given below.

From the diagram, we can clearly observe that the triangle ABC is vertically translated only.

Then, The correct option is B.

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Answer:  A; The probability of landing on blue is greater than the probability of landing on purple.

Step-by-step explanation: This statement is true because you need to analyze the problem. Since there is a 3/6 or 1/2 chance of getting a blue, it is higher than getting a purple spot, which is 2/6 or 1/3. So, we can model our answer as:

3/6 > 2/6

or

1/2 > 1/3

I hope this helped!

Answer:

Step-by-step explanation:

To show that x-3 and x+5 are factors of x^4+2x^3-16x^2-2x+15, we can use polynomial division, synthetic division, and the Remainder theorem.

Using long division, we can divide x^4+2x^3-16x^2-2x+15 by x-3:

x^4 + 2x^3 - 16x^2 - 2x + 15

÷ x - 3

_________________________

  x^3 + 5x^2 - 14x - 12

   |__________

      -3x^3 + 17x^2 + 26x + 36

          |_________

                -14x^2 - 23x - 36

                     |_________

                          -15x + 72

                               |___

                                  57

So, the remainder is 57, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x - 3)(x^3 + 5x^2 - 14x - 12) + 57.

Using synthetic division, we can divide x^4 + 2x^3 - 16x^2 - 2x + 15 by x+5:

1   2    -16   -2   15

   x + 5 |x^4 + 2x^3 - 16x^2 - 2x + 15|

____________________________

        x^3 - 3x^2 + 21x + 75

So, the remainder is 0, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x + 5)(x^3 - 3x^2 + 21x + 75).

Using the Remainder theorem, we know that if a polynomial p(x) is divided by x-a, the remainder is p(a). So, when we plug in x=3, the remainder should be p(3) = 57. When we plug in x=-5, the remainder should be p(-5) = 0. This confirms that x-3 and x+5 are indeed factors of x^4 + 2x^3 - 16x^2 - 2x + 15.

Therefore , the solution of the given problem of triangle comes out to be m∠x = 30° they are congruent.

Triangles are included in polygons because they have four aspects or more. It is simple and geometric in design. The triangle formed by the letters ABC has a square angle. A single rectangles or square is produced by euclidean geometry when the sides are not coinciding. Triangles are polygons because they have three parts and three corners. The intersection of a triangle's three sides forms its corners. A triangle has 180 degrees of angles in all.

Here,

Given :

=> ΔEFG ≅ ΔXYZ

In ΔEFG

=> 90° + 60° + x = 180°

=> 150° + x = 180°

=> x = 180° - 150°

=> x = 30°

Since . they are congruent .

So m∠x = 30°

Therefore , the solution of the given problem of triangle comes out to be m∠x = 30° they are congruent.

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Answer:

∠YPV = 50°

∠XPV = 130°

∠WPZ = 85°

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc.

6. Arc ZVW is a major arc.

7. Arc YWZ is a major arc.

8. Arc ZXW is a major arc.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc.  

Step-by-step explanation:

As WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.

As VW is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPX + ∠XPV = 180°

⇒ 50° + ∠XPV = 180°

⇒ ∠XPV = 130°

As XY is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°

⇒ ∠WPZ + 45° + 50° = 180°

⇒ ∠WPZ + 95° = 180°

⇒ ∠WPZ = 85°

Add the central angles to the given circle diagram (see attachment).

Note that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.

Note that three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.

As WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle.

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 50° + 45° = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.

6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.

7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.

8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.  

The answers to the respective arcs are given as follows:

The arcs are defined as follows:

It is to be noted that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.

Also, three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.

To solve for the arcs:

Given that WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.

As VW is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPX + ∠XPV = 180°

⇒ 50° + ∠XPV = 180°

⇒ ∠XPV = 130°

Since XY is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°

⇒ ∠WPZ + 45° + 50° = 180°

⇒ ∠WPZ + 95° = 180°

⇒ ∠WPZ = 85°

Given that WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle. Thus,

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 50° + 45° = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.

6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.

7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.

8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.  

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Answer:

3.844, 3.840, 3.836, 3.832, 3.828 ,3.824, 3.820 - minus by 4

30.565, 31.065, 31.565, 32.065, 32.565, 33.065, - minus 0.5 , -0.5 , 0.5 .......

The Answer is B because we use pemdas (parentheses)(exponents)(multiplication)(division)(addition)(subtraction)

so first is what is inside of the parentheses which is a subtracting equation number b is subtraction so the answer is b

If the economy is producing 12 units of guns and 4 units of butter, the opportunity cost of increasing the production of butter from 4 units to 11 units is 4 units of guns.

In Economics, an opportunity cost is sometimes referred to as alternative forgone and it can be defined as the value, profit or benefits that are given up and forfeited by an individual or business organization, in order to choose or acquire something that is deemed most significant at a particular point in time.

This ultimately implies that, the opportunity cost of owning or earning a thing is the alternative that is foregone in the attainment or earning of another value, profit or benefits.

Cost increase = 11 units - 4 units = 7 units of butter.

In this context, we can reasonably infer and logically deduce that the opportunity cost of 7 more units of butter would be 4 units of guns.

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