Compare 9/15 and 10/15

The ordered pair that solves the system of equations 2y = 5x + 13 through the substitution method is (-6, -5). To solve the system of equations using the substitution method, we need to isolate one variable in one of the equations and substitute it into the other equation.

Let's begin by isolating y in terms of x in the given equation 2y = 5x + 13:

2y = 5x + 13

Dividing both sides by 2, we get:

y = (5/2)x + 13/2

Now, we substitute this expression for y into the second equation:

3x + 4y = 7

Replacing y with (5/2)x + 13/2, we have:

3x + 4((5/2)x + 13/2) = 7

Simplifying and solving for x, we get:

3x + 10x + 26 = 7

13x + 26 = 7

13x = 7 - 26

13x = -19

x = -19/13

Substituting this value of x back into the first equation to find y:

2y = 5(-19/13) + 13

2y = -95/13 + 169/13

2y = 74/13

y = 37/13

Therefore, the solution to the system of equations is (x, y) = (-19/13, 37/13). This can be simplified to (-6, -5) by multiplying both the numerator and denominator by 13 to get integers.

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Answer:

408 square inches

Step-by-step explanation:

The top of the desk is Rectangular.

The area of a rectangle = Length × Width

Length = 24 inches

Width = 17 inches

Area of the rectangular top = 24 inches × 17 inches

= 408 square inches

Therefore, the area of the top of Kathleen's desk in square inches is 408 square inches

Therefore ,the answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.

Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign.  For an unknown quantity represented by an unknown variable, equations can be solved to determine its value.

Here,

The number of solutions is unlimited if there are more variables than linear independent equations.

A single solution or no solution is possible if there are the same number of linearly independent equations and variables.

In the following scenarios, we are at a loss for solutions:

y = x + 3

y = x - 3

this causes:

x + 3 = x - 3

+3 = -3

Consequently, this system lacks a solution.

The first set of equations is

y = x + 5

y = 2x + 5

You can see that there is only one solution for this system because there are only two variables and two linear independent equations.

Thus, "One solution, the graph of these lines should connect at one point" is what we have here. The key idea is (0, 5)

Another system is:

y =x+x+5 = 2x + 5

y = 2x+ 5

Since both equations are identical and there are just two variables in this situation, there are an endless number of solutions to the system.

The answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.

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Answer:

Given:

Cashew = $7 per pound ; represented by x

Almond = $5 per pound ; represented by y

makes less than 6 pounds

x + y < 6

7x + 5y < 30

Step-by-step explanation:

i hope this help mark me as brailiest

Answer:

x+y≤6

Step-by-step explanation:

it has to be less than 6 so that's why they paid 30 dollars

The Department of Energy was also eager to sign on, in part because it wanted to learn about how radiation causes genetic mutations.

An modification in the nucleic acid sequence of an organism's, virus's, or extrachromosomal DNA is referred to as a mutation. DNA or RNA can be found in the viral genome.

Any alteration to a cell's DNA sequence. Mistakes in cell division can result in mutations, as can exposure to environmental DNA-damaging substances.

Ionizing radiation may harm genetic material (mutations) in gonads or germ cells, which can result in disorders with a genetic component (hereditary defects). Malformations, metabolic issues, immune system deficits, etc. might occur from them.

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Answer:

111 meters, break each area into a rectangle, find the areas, then add.

Of the choices, the best definition for a circle is:

OA. the set of all points in a plane that are the same distance from each other surrounding a given point called the center

Some key points in this definition:

1) It refers to a set of points, indicating it is a geometric shape.

2) The points are in a plane, showing it is a 2D shape.

3) The points have the same distance from each other, indicating they lie on a curve.

4) There is a given center point, showing the points surround the center point.

5) The points surround the center point, indicating it is a closed shape.

So choice OA captures all these key aspects in defining a circle. The other choices are too vague or incomplete.

Answer:

The probability that the next customer will pay with a credit card will be 0.26 or 26%.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.

Then the probability that the next customer will pay with a credit card will be

P

=

32

123

�

=

0.26

P=

123

32

P=0.26

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Step-by-step explanation:

I hope this helps :-)

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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Answer:

145°

Step-by-step explanation:

< 6 + <2 = 180° {being linear pair }

70° + < 2 = 180°

< 2 = 180° - 70°

< 2 = 110°

Now

< 4 = < 1 + < 2 (exterior angle of a triangle is equal to the sum of two opposite interior angles)

<4 = 35° + 110°

= 145°

Hope it will help :)

Answer:

Step-by-step explanation:

\(5t=30 \implies \frac{5t}{5}=\frac{30}{5} \implies t=\boxed{6}\)

The answer is:

t = 6

Work/explanation:

This is a one step equation, so we will arrive at our answer after performing one operation.

To solve this equation, I divide each side by 5:

\(\sf{5t=30}\)

\(\sf{t=6}\)

Hence, t = 6.

Answer:

1

Step-by-step explanation:

\(\frac{2}{3} * \frac{3}{2} = \frac{6}{6}\)\(=\frac{1}{1}=1\)

This shows how to multiply fractions. When you multiply fractions, you just multiply across, and then simplify.

Answer:

1

answers? i think thanks

Answer:24

Step-by-step explanation:

9+((1 divided by 2)x30)

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation is

y = - 2x - 1

Comparing with the general equation above

Slope = - 2

Y - intercept = - 1

Hope this helps you

Answer:

9c + (-15c) + (-3c) = -9c

Step-by-step explanation:

9c + (-15c) + (-3c) =

9c - 15c - 3c =

-6c - 3c =

-9c

The x-coordinate for the center of gravity is 16.1, and the y-coordinate is 15.4 which is determined using average.

To find the center of gravity (also known as the centroid), we need to calculate the weighted average of the x and y coordinates using the given data points and their respective weights. The weights are represented by the "dc coordinates demand a" value for each data point.

Let's calculate the x-coordinate first:

x-coordinate = (1040 + 2525 + 830 + 1120 + 25*6) / (40 + 25 + 30 + 20 + 6) = 16.1

Now let's calculate the y-coordinate:

y-coordinate = (1240 + 3025 + 1530 + 2011 + 6*25) / (40 + 25 + 30 + 20 + 6) = 15.4

Therefore, the center of gravity is located at approximately (16.1, 15.4) in terms of x and y coordinates.

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The answers of all the parts are solved below:

1. Significant digits:

12.03: 4 significant digits

58.2: 3 significant digits

0.002: 1 significant digit

0.0030: 4 significant digits

0.00050004: 7 significant digits

2: 1 significant digit

2. Conversions:

0.05 km to mm: 0.05 km = 0.05 x 10^6 mm = 50,000 mm

0.15 hm to cm: 0.15 hm = 0.15 x 100 cm = 15 cm

280 dm to dam: 280 dm = 280 x 10 dam = 2,800 dam

500,000 mm to km: 500,000 mm = 500,000/10^6 km = 0.5 km

85 m to hm: 85 m = 85/100 hm = 0.85 hm

3. Significant digits in calculation:

(a) 25.3456 +888.010 + 53.11 + 7-10: 925.456, 4 significant digits

(b) (45.805 * 2.00) / 5.0 + 0.1: 13.52, 4 significant digits

4. Scientific notation with significant digits:

(a) 70,000,000 * 9.8540 * 2.00 * 10^8 = 1.38 x 10^18, 2 significant digits

(b) 8.888 * 10^14 * 4.00 * 10^-6 - 3.0 * 10^7 = 3.555 x 10^7, 4 significant digits

Trigonometry:

Given triangle ABC with angle B = 56, angle C = 35 and side A = 10. To find side B.

Using the law of cosines, B = sqrt(A^2 + C^2 - 2 * A * C * cos(B)) = sqrt(10^2 + 56^2 - 2 * 10 * 56 * cos(56)) = 115, 3 significant digits.

Thus, All the answers are solved above.

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Answer: 75

Step-by-step explanation:

To find the sum of these numbers, we simply add them together:

15 + 28 + 12 + 20 = 75

Therefore, the sum of 15, 28, 12, and 20 is 75.

Step-by-step explanation:

Image 1:

Blank 1: (0,5)

Blank 2: (5,0)

Blank 3: (0,-5)

Blank 4: (-5,0)

Image 2:

C, Both B and D only have one line of symmetry. Choice A has more than 2 because you can evenly split the kite by its vertices and its lengths.

Image 3:

B, a regular quadrilateral is named this way because it contains both the point and linear symmetry. By definition, a regular quadrilateral must have 4 equal sides and angles and must have its diagonals bisect each other.

Image 4:

B, Point symmetry only. This is because when flipped upside down, the shape would still look the same. This would not be rotational symmetry because it does not look 100% like the original after rotating it to a certain degree.

Answer:

x = \(\frac{1}{19}\)

Step-by-step explanation:

2 = 19x + 1  Subtract 1 from both sides

2 - 1 = 19x + 1 - 1

1 = 19x  Divide both sides by 19

\(\frac{1}{19}\) = \(\frac{19x}{19}\)

\(\frac{1}{19}\) = x

The quadrilateral is a parallelogram so it is Yes.

If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:

The opposite sides are parallel and equal

The opposite angles are equal

The consecutive or adjacent angles are supplementary

If any one of the angles is a right angle, then all the other angles will be at right angle.

The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°

In conclusion, yes, the figure is a parallelogram.

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Answer:

h(4)=17

Step-by-step explanation:

h(g(x)), h(x)= 2x+9; g(x)=4

2(4)+9= 8+9=17

Answer:

The answer is A

Step-by-step explanation:

Answer: We can use the following formula for the union of two sets:

n(A U B) = n(A) + n(B) - n(A ∩ B)

where n(A ∩ B) is the number of elements in the intersection of A and B.

Substituting the given values, we get:

n(A U B) = n(A) + n(B) - n(A ∩ B)

n(A U B) = 25 + 18 - 7

n(A U B) = 36

Therefore, the value of n(A U B) is 36.

Answer:

\(y<-\frac{4}{3}x+5\)

Step-by-step explanation:

Since, the given line in the graph is a dotted, line will represent an inequality with no sign of equal to (=).

Since, the shaded area is below the dotted line, inequality will have the sign less than (<).

Therefore, equation of the inequality will be in the form of,

y < mx + b

Here, m = slope of the line

b = y-intercept

Slope of the line passing through two points (0, 5) and (3, 1),

m = \(\frac{y_2-y_1}{x_2-x_1}\)

   = \(\frac{5-1}{0-3}\)

   = \(-\frac{4}{3}\)

Y-intercept (at x = 0),

b = 5

Therefore, equation of the inequality will be,

\(y<-\frac{4}{3}x+5\)

The area of the cone that was painted black is given by 47.66 ft²

For a right circular cone of radius 'r', height 'h', and slant height 'l', we have; Curved surface area of the right circular cone = π r l. The total surface area of a right circular cone = π(r + l) r. The volume of a right circular cone = 1/3π r2 h.

Given here: The height of the cone is 12 feet and circumference of the base of the cone is 8π

We know the base of the cross section is always a circle.

Thus  we have

2πr=8π

2r=8

r=4

Now slant height of the cone is given using the pythagoraes theorem as follows

l=\(\sqrt{4^2+12^2}\)

=12.65 feet

Thus lateral surface area of the cone is L= πrl

                                                                   =3.14×4×12.65

                                                                   =158.884 ft²

Now we can infer from the question that 30% of the lateral surface area is painted black thus

Area painted black is = 30%×158.884

                                    =0.3×158.884

                                    =47.66 ft²

Hence, The area of the cone that was painted black is given by 47.66 ft²

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Answer: 47.7

Step-by-step explanation:i took the quiz the guy on top is wrong

The level of confidence is approximately 1 - 0.0505 = 0.9495 or 94.95%.

The level of confidence given the confidence coefficient z(α/2) = 1.63 is approximately 94.95%.

We need to find the level of confidence that corresponds to the confidence coefficient z(/2) = 1.63 in order to determine the level of confidence.

The desired confidence level is represented by the confidence coefficient, which is the number of standard deviations from the mean.

To determine the level of confidence, use the following formula:

Since z(/2) represents the number of standard deviations from the mean, and /2 represents the area in the distribution's tails, the level of confidence is equal to 100%. As a result, denotes the entire tail area.

The relationship can be used to find:

α = 1 - Certainty Level

Given z(α/2) = 1.63, we can find α by looking into the related esteem in the standard typical circulation table or utilizing a mini-computer.

We determine that the area to the left of z(/2) = 1.63 is approximately 0.9495 using the standard normal distribution table or calculator. This indicates that the tail area is:

= 1 - 0.9495 = 0.0505, so the level of confidence is roughly 94.95%, or 1 - 0.0505 = 0.9495.

The confidence level is approximately 94.95% with the confidence coefficient z(/2) = 1.63.

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