Select the statement that correctly describes the solution to this system of equations.

X+3y=5
Y=4x-7


A. There is no solution
B. There are infinitely many solutions.
C. There is exactly one solution at (2,1).
D. There is exactly one solution at (4,2).


Which 1?

The domain of the ordered pairs {(4, 9), (–6, 1), (–2, 5), (3, 1)} is  (c) {–6, –2, 3, 4}

From the question, we have the following parameters that can be used in our computation:

{(4, 9), (–6, 1), (–2, 5), (3, 1)}

Rewrite as

(x, y) = {(4, 9), (–6, 1), (–2, 5), (3, 1)}

The domain is the set of the x values

So, we have the following representation

x = {4,–6, –2, 3}

Remove repeated entries and reorder

x = {–6, –2, 3, 4}

So, the domain is x = {–6, –2, 3, 4}

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The temperature change that is required is; A reduction in temperature by 8°C.

We are told that;

The freezer should be working at -18°C.

The temperature on the freezer marks -10°C.

Now, what we see here is basic arithmetic because we simply want to find the additional temperature that will make the current reading to be equal to the ideal temperature required for it to wor. Thus, what we will do is to simply subtract the current temperature from the ideal one to find out the temperature required to make it work well.

Thus;

Temperature change = -18 - (-10)

Temperature change = -18 + 10

Temperature change = -8°C.

We see that the freezer still needs its' temperature to be reduced by 8°C.

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Complete question is;

Tom works in the cold food department in a supermarket. The thermometer shows the temperature of one of the freezers. The freezer should be working at -18°C. The temperature on the freezer marks -10 The temperature should increase or decrease by how many °C?

Pool A is filling up slower than Pool B because slope of the graph of Pool A is less than that of the graph for Pool B.

The slope of the graph tells you the unit-rate in gallons per minute.

Graphs are an essential type of computing tool in mathematics. The nodes and edges that make up a graph are referred to as its elements. Whether "directed" or "undirected," nodes can only move through a graph in a single direction (either direction may be traversed from node to node).

In contrast to a chart, a graph is a representation of linked values in a multidimensional space. Graphs are helpful for examining the various relationships among specific data points.

A graph's search algorithm seeks out the shortest route between any two nodes. The best path is determined by an algorithm that considers the weight of each path on a graph.

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The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex]

A symbolic expression, also known as a mathematical expression, is a combination of numbers, variables, and mathematical operators (such as +, -, *, /) that can be evaluated to produce a numerical result.

Symbolic expressions can also contain functions, constants, and mathematical operations like logarithms, trigonometric functions, etc. They can be used to model physical phenomena or to solve mathematical problems.

A logarithmic function is a mathematical function that expresses the power (or exponent) to which a fixed number (the base) must be raised to produce a given value.

It is typically written in the form "logb(x)" where b is the base and x is the value being evaluated. The most common base used is 10 (common logarithm) or e (natural logarithm)

These expressions can be used to represent mathematical concepts, relationships, or equations.

Therefore, The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex].

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{n^2 - 5n + 8}[/tex]

[tex]\mathsf{= 2^2 - 5(2) + 8}[/tex]

[tex]\mathsf{= 2\times 2 - 10 + 8}[/tex]

[tex]\mathsf{= 4 - 10 + 8}[/tex]

[tex]\mathsf{= -6 + 8}[/tex]

[tex]\mathsf{= 2}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

36,323-17,000

Step-by-step explanation:

just go to the thousands place and look back one place value

the best deal for holly to do shopping from the first store.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Holly needs to buy some cloth to make masks. The following deals are available at various stores.

For the first store:

Price per yard = 16.52/6$

Price per yard = 2.7533$

For the second store:

Price per yard = 13.85/5$

Price per yard = 2.77$

therefore, it is best for her to buy from the first store.

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Complete question:

The following deals are available at various stores. Choose the best deal.

a

$16.52 for 6 yd

b

$13.85 for 5 yd

c

Neither

Answer:

0.39 is the answer to this question

6.2353535353535 as a fraction is 623535353535/1000000.

This fraction is written as a mixed number by dividing the numerator by the denominator to get 623,535,353,535/1,000,000. This can be further simplified to 623,535/1,000, which is the same as 623 5/8.

Answer:ok

Step-by-step explanation:

ol

The value of x is 7.

Two or more angles are said to be vertical angles if only they are formed by same two lines intersecting at a point. Thus the two angles have equal measure of value.

Given that A and B are vertical angles, then this implies that there is a relationship between them i.e they are opposite and equal.

Such that;

m<A = m<B

(x + 27) = (2x + 20)

x + 27 = 2x + 20

collect like terms,

-20 + 27 = 2x - x

7 = x

x = 7

Therefore, the value of x is 7.

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A function is defined as a relation between a set of inputs, each with an output. The sketch of the function f(x,y) = 9 - 9x² - y² is given below.

f(x,y) = 9 - 9x² - y²

Let the given function is equal to 0, Then

           9 - 9x² - y² = 0

                         y²  = 9 - 9x²

The function can be written as

                          y²  = 9 - 9x²

A function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. Functions are commonly denoted by f(x). x is the input. Here's the technical definition of the function:

A relationship from a set of inputs to a set of possible outputs.

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Answer:

1/7

Step-by-step explanation:

4/4 is 1 and 28/4 is 7 so 1/7

The answer is 1/7.

To simplify : 4/28

To simplify fractions, we should follow these steps:

Here, the given fraction is 4/28.

At first, we need to write the factors of the numerator and the denominator

Factors of the numerator, 4 = 1, 2, 4.

Factors of the denominator, 28 = 1, 2, 4, 7, 14, 28.

So, the common factors are 1, 2 and 4.

Dividing the numerator and denominator by the common factor, 2;

(4/2) / (28/2)   or,

2/14

And,

(2/2) / (14/2)    or,

1 / 7.

Hence, 1/7 is the simplified fraction of 4/28.

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The solution set x<-5.2 or x>5.2 is true for the inequality |x|>5.2.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

The given inequality is |x|>5.2.

So, the value of x should be greater than 5.2.

For example take x=6, then the given inequality will be -

|6|>5.2 = 6>5.2, so this is true.

Now take x=-6, then the given inequality will be -

|-6|>5.2 = 6>5.2, so this is also true.

Similarly, among the different choices x<-5.2 or x>5.2

The condition x>5.2 is already true.

Also, the condition x<-5.2 is also true for x if the value is lower than -5.2.

Therefore, the inequality x<-5.2 or x>5.2 is true.

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Answer: 3a − 2/2a(3a + 1)(3a − 1)

Step-by-step explanation:

I simplified it and got 3a − 2/2a(3a + 1)(3a − 1)

Both lessons will be on the same day again after 21 days.

We will determine the least common multiple when two events occur simultaneously.

If I take tuba lessons every third day and piano lessons every seventh day,

Least common multiple of 3 and 7 will be,

Multiples of 3 = 1 × 3

Multiples of 7 = 1 × 7

Least common multiple (LCM) of 3 and 7 = 1 × 3 × 7

                                                                    =21

Therefore, I will have both the lessons after 21 days.

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Height and contour: The matrix band should not extend more than 2 mm beyond the occlusogingival height of the crown of the tooth.

A dental matrix band can be defined as a properly shaped piece of metal, or other material, inserted. To support and give form to the restoration during placement, and hardening of the restorative material.

The primary function of a matrix band is to compensate for missing walls and thus provide containment of the filling material.

Matrix band systems have evolved over time and newer systems are made to give ease of use to operators and also cover for flaws and difficulties in older systems.

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A parallelogram is a quadrilateral with congruent and parallel opposite sides. Thus, to justify that the given quadrilateral is a parallelogram, option E is correct.

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

Quadrilaterals are shaped with four straight sides. Examples are; square, rectangle, parallelogram, trapezium, etc.

A parallelogram is a type of quadrilateral that has opposite sides to be equal and parallel. It has some distinguishing properties which can be used to differentiate it from other quadrilaterals. Some of the are:

Thus, in the given question the required option is C. consecutive angles are supplementary.

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Subtract the sum that appears on the same side of the equation as the "x" to isolate the "x" on one side of the algebraic equation. For instance, rewrite the equation "x + 5 = 12" as "x = 12 - 5" and then find "x" in the new equation. The answer is "x = 7"

Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the numbers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

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The first step in isolating the variable in this equation is to subtract 75 from both sides. Option A is correct.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
Given expression,
1/2p + 75 = 100

In order to isolate the variable our first step should be to subtract 75 from both sides
1/2P = 25

Then, multiply by 2 on both sides
P = 50

Thus, the first step in isolating the variable in this equation is to subtract 75 from both sides. Option A is correct.

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x = 2

All the sides are 2 so if the length on the bottom is 2, then it would be the same for the top :)

Answer:

x=2

Step-by-step explanation:

This shape is a regular polygon so all the sides are the same length

At the height of the swing forth, the swing seat would be at a maximum height of 2 + (6 * (1 - cos(pi/4))) = 4 feet above the ground.

Cosine is a trigonometric function that relates the length of the adjacent side of a right triangle to the length of the opposite side to the hypotenuse. It is represented by "cos" and its formula is cos(x) = adjacent / hypotenuse. It is commonly used in mathematics, physics, and engineering to solve problems related to angles and vectors.

Cosine is a fundamental trigonometric function that is used in many areas of mathematics, physics, and engineering. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. It can also be defined as the dot product of the unit vector pointing in the direction of the angle and the unit vector pointing in the direction of the adjacent side. Cosine is periodic with a period of 2π and is always between -1 and 1, inclusive. It has many important properties and relationships with other trigonometric functions such as sine, tangent, and cotangent.

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Answer:

88 square cm

Step-by-step explanation:

Surface area of down rectangular prism:

      l = 6cm ; w = 3 cm & h = 2 cm

   [tex]\sf \boxed{Total \ surface \ area \ of \ rectangular \ prism = 2*(lw + wh+hl)}[/tex]

                                                                       = 2*(6*3 + 3*2 + 2*6)

                                                                        = 2* (18 + 6 + 12)

                                                                         = 2 * 36

                                                                          = 72 cm²

Lateral surface area of the top rectangular prism:

    l = 3 cm

    w = 1 cm

     h =  4 - 2 = 2 cm

         LSA = 2h( l + w)

                = 2*2 *( 3 + 1)

                 = 4 * 4

                 = 16 cm²

Surface area of the shape = 72 + 16

                                              = 88 cm²

Answer:

a = 88 cm2

Step-by-step explanation:

[tex]a=(4)(3)+2(4)(1)+2(5)(2)+2(3)(2)+(1)(3)+6(3)+5(3)=12+8+20+12+3+18+15[/tex]

[tex]a=88cm^{2}[/tex]  

Hope this helps

Answer:

Here is a process on how to solve it:

Step-by-step explanation:

The midline theorem states that a seg that connects the midpoints of 2 sides is parallel and equal to 1/2 (50%) of the other side.

Look for the line that is drawn from one midpoint of another (you can see because it is usually drawn or you can see bisected segs) then multiply it by 2 to find the value of the other side.

Hope this helps!

The equation that represent y, the total number of letters Natasha put in an envelope in x hours is y = 42x.

Natasha has a job putting letters to the envelope to be mailed. In one hour she put 42 letters in the envelope.

Therefore, the equation that best represent y, the total number of letters Natasha put in an envelope in x hours if she continue at the same rate can be calculated as follows;

1 hours = 42 envelopes

x hours = ?

cross multiply

Therefore,

y = 42x

where

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The iterated integral by converting to polar coordinates is  [tex]\frac{2a^{2} }{5}[/tex]

Evaluating an iterated integral by converting it to polar coordinates involves the following steps:

Here, [tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]

Now, converting it into the polar form:

[tex]\int\limits^\pi _\frac{\pi }{2} \int\limits^a_0} {6\cos^{2}\theta}\ {sin\theta\ r^{4} dr\ d \theta[/tex]

[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6cos^2\theta}{5}\ r^5 sin\theta]^{a}_{0} \, d\theta[/tex]

[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6\ a^2 \cos^2\theta sin\theta}{5}] \, d\theta[/tex]

[tex]= [-\frac{2a^{2} }{5}\ cos^{3}\theta ]^{{\pi} }_\frac{\pi}{2}[/tex]

[tex]= \frac{2a^{2} }{5}[/tex]

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The complete question is:

Evaluate the iterated integral by converting it to polar coordinates:

[tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]

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The size of the animal population in year 2004 (t=0) is 200 thousands individuals.

Population is a term used to describe the total number of people that live in a specific geographic area. This can be a country, a state, a city, or any other area of the world. Population size and density are important factors in understanding the landscape of an area and its resources.

The size of the animal population in year 2004 (t=0) can be calculated by substituting t=0 into the given equation:

P(t)=210t+400/(t+2)

P(0)=210 × 0 + 400/(0+2)

P(0)=400/2

P(0)=200
Therefore, the size of the animal population in year 2004 (t=0) is 200 thousands individuals.

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Interval notation: [0, ∞). To arrange the intervals in interval notation, use brackets and parenthesis.

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