Which system(s) of linear equations has (have) (2,−1) as its (their) unique solution? Select the THREE (3) systems that apply. Responses

Answer:

40 days

Step-by-step explanation:

We know

A certain insect eats 1/8 gram of food each day.

How many days would the insect take 5 grams of the food?

We take

5 divided by 1/8 = 40 days

So, it would take the insect 40 days to eat 5 grams of the food.

Answer:40 days

Step-by-step explanation: first, how many days would it take for the insect to eat 1 gram of food? it would take 8 days so if it wants to eat 5 grams of food 8x5=40 so it would take 40 days for the insect to eat the food

The image showing the locus points equidistant from X, Y, and Z is B. See the attached image.

If the distances between a point and each object in the set are equal, the point is said to be equidistant from the set.

When a point is equidistant from two other points, it is at the same distance from both of them. The distance between two points may be computed using the distance formula and the coordinates of the two points.

In geometry, a locus is a set of points that satisfy a specific condition or circumstance for a form or figure. The locus is pluralized as loci. The region is the location of the locus. The term locus comes from the word location.

Thus, the point that is equidistant from X, Y, and Z is B.

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The engine's speed at which the vehicle's estimated horsepower at the wheels is greatest is given as follows:

1905 rpm.

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which:

The value of h for this problem is given as follows:

h = 1905 rpm.

As the leading coefficient is negative, for h = 1905, the output has the maximum value.

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Answer:-12x

Step-by-step explanation:

just trust me on this

The  slope and the y-intercept of the line are -1 and 5 respectively

It is important to note the general formula for the equation of a line is expressed with the formula;

y = mx+ c

Where the noted parameters of the equation are;

From the information given, we have the equation of the line as;

y = -x + 5

Now, we can have the parameters as;

Intercept, c = 5

Slope of the line, m = -1

Hence, the values are 5 and -1

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Saeng's third race is between race 2 and race 3.

Ascending order: Arranging the numbers from lowest number to highest number.

Descending order: Arranging the numbers from highest number to lowest number.

The times for 5 races are given in the table  

  Race       timings

      1              -1.2

      2             [tex]+1\frac{1}{10}=1.1[/tex]    

      3              [tex]-1\frac{1}{4}=-1.25[/tex]

      4              - 1.4

      5               [tex]+1\frac{1}{2}=1.5[/tex]

Arranging the timings in ascending order we get,

-1.4,-1.25,-1.2,1.1,1.5

Hence third race is -1.2 it lies between race 2 and race 3.

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Answer:

599 and 550

Step-by-step explanation:

I'm not sure but I think it's 599 and 550

The linear equation is 12y = 5x. Then the number of bagels when you buy for $50 will be 120 bagels.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A shop sells bagels for $5 per dozen.

Let 'x' be the number of bagels and 'y' be the total cost. Then the equation is given as,

y / x = 5 / 12

12y = 5x

The number of bagels when you buy for $50 will be given as,

12(50) = 5x

600 = 5x

5x = 600

x = 120

The number of bagels when you buy for $50 will be 120 bagels.

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For the triangle ABC the interior angles measures ∠A = 48°, ∠B = 82°, and ∠C = 50°.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

According to the angles of a triangle theorem, the sum of angles of a triangle is 180°.

The measure of ∠A = 4x.

The measure of ∠B = 7x - 2.

The measure of ∠C = 5x - 10.

The equation is -

∠A + ∠B + ∠C = 180°

Substitute the values into the equation -

4x + 7x - 2 + 5x - 10 = 180

Collect the like terms -

4x + 7x + 5x = 180 + 2 + 10

16x = 192

x = 192/16

x = 12°

So, the measure of ∠A = 4(12) = 48°.

The measure of ∠B = 7(12) - 2 = 82°

The measure of ∠B = 5(12) - 10 = 50°

The interior angles of the triangle are 48°, 82° and 50°.

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An equation, in slope-intercept form, to represent the total cost, y, for x toppings on a jumbo pizza is y = 1.35 x + 15.

As per the data given:

A local restaurant charges $15 for a jumbo size cheese pizza.

Each of the additional topping costs $1.35.

Here we have to determine an equation, in the slope-intercept form, to represent the total cost, y, for x toppings on a jumbo pizza.

Considering y as the cost of pizza and x be the amount of topping added.

Cost of a pizza with toppings

y = 1.35 x + 15

The equation for the slope-intercept form is y = mx + c

m will be the slope of the equation.

Here, the slope of the equation is 1.35

The Y-intercept is equivalent to the price of the base pizza i.e. 15

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Answer:

what we should do when we leave for every 25minutes

The perimeter of scale drawing of rectangular classroom floor is 42 inches.

Based on the mentioned information, let us first calculate the width of floor of classroom according to the scale drawing.

Length/width of original classroom floor = length/width of scale drawing

30/33 = 10/width

As we know, 1 foot = 12 inches

So, length = 360 inches and width = 396 inches

Width = (396 × 10)/360

Cancelling zero as it is common in both numerator and denominator

Width = 396/36

Performing division on Right Hand Side of the equation

Width = 11 inches

Perimeter of scale drawing = 2 (length + width)

Perimeter = 2( 10 + 11)

Performing addition

Perimeter = 2 × 21

Performing multiplication

Perimeter = 42 inches

Thus, perimeter of the rectangle is 42 inches.

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In the given choices, both (D) n = 300 and (E) n = 312 satisfies the inequality. So for both these options, the inequality is true.

We can solve for n by adding 93 to both sides of the inequality:

n - 93 > 175

Adding 93 on both sides

n - 93 + 93 > 175 + 93

n > 268

Therefore, the value of n that makes the inequality true is greater than 268.In the given options, n = 300 and n = 312 satisfy this condition. So this is inequality is true for both cases. The answer choice that fits this is (D) n = 300 and (E) n =312.

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Answer:

x = 11/90 = 0.122

Step-by-step explanation:

7[tex]\frac{1}{2}[/tex]x - [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{3}[/tex]

15/2x - 1/4 = 2/3

90/12x - 3/12 = 8/12

90/12x = 8/12 + 3/12

90/12x = 11/12

x = (11/12)(12/90) = 132/1080 = 11/90

The table in the question which the values from the graph of the parabola is inputed is presented as follows;

Name [tex]{}[/tex]                     Key Feature             Name           Key Feature
x-intercepts[tex]{}[/tex]             (-1, 0), (3, 0)                Increasing      (-∞, 1)      

y-intercept[tex]{}[/tex]               (0, 3)                          Decreasing     (4, ∞)

Vertex[tex]{}[/tex]                      (1, 4)                            Positive           (-1, 3)

Axis of symmetry[tex]{}[/tex]     x = 1                           Negative        (-∞, 1), (3, ∞)

Domain[tex]{}[/tex]                    (-∞, ∞)                         Range            (-∞, 4]

The graph of a parabola is a u (or n) shaped curve obtained by the intersection of a cone and a plane which is parallel to the slant of the cone.

The x-intercepts are the point the graph intersects the x-axis, where the y-value is zero, y = 0. From the graph, the x-intercepts are;(-1, 0), and (3, 0)

The y-intercept is the point at which the graph intersects the y-axis, which is the point the x-value is 0, (x = 0). The graph indicates that the y-intercept is (0, 3)

The vertex of the parabolic graph is the highest (or lowest) point on the graph, therefore, from the graph in the question, the vertex point is; (1, 4)

The axis of symmetry is the line that divides the graph into two mirror halves, which is the line passing through the vertex and parallel to the y-axis. The axis of symmetry is therefore the line; x = 1

The domain is the set of the possible input values of the graph of the function, which is the set of the possinble x-values.

The graph indicates that the x-values can decrease and increase to -∞ and ∞. The domain is therefore; (-∞, ∞).

The region where the graph is increasing is fro x = -∞ to just before x = 1. The interval where the graph is increasing is therefore; (-∞, 1)

Similarly, the interval the graph is decreasing is; (4, ∞)

The graph is positive in the region above the x-axis. The interval over which the graph is positive is therefore between the x-intercepts, which is; (-1, 3)

The graph is negative in the region below the x-axis. The interval in which the graph is negative are; (-∞, 1), and (3, ∞)

The range is the set of possible output of the graph, therefore, the range is the set of the possible y-values, which is; (-∞, 4]

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The value of equation is -3.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

T-5/t-3=t-3/t+3+1/t-3

Now

T-5/t-3=t-3/t+4/t-3

-5t=-2t+9

-3t=9

t=-3

Therefore, the answer of the equation will be -3.

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The value of the missing angles x , y, and z are 63⁰ , 63⁰  and 72⁰ respectively.

The value of the missing angles is calculated by applying the following mathematical method.

x + 85⁰ + 32⁰ = 180⁰ ( sum of angles in a triangle )

x = 180 - 117 = 63⁰

y = x = 63 ⁰ ( opposite angles )

z + y + 45⁰  = 180⁰ ( sum of angles in a triangle )

z + 63 ⁰  + 45⁰ = 180

z = 72⁰

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There are 56 possible ways to make a selection of coins so that the value is at least 25 cents.

The total number of possible ways to make a selection of coins so that the value is at least 25 cents is calculated using the formula:

# of ways = (n+r-1Cr-1)

Where n is the number of coin denominations available and r is the number of coins needed to make the selection.

In this case, n = 5 (1 cent, 5 cents, 10 cents, 25 cents, 50 cents) and r = 4. Therefore, the number of ways to make a selection of coins so that the value is at least 25 cents is calculated as:

of ways = (5+4-1C4-1)

of ways = (8C3)

of ways = 56

Therefore, there are 56 possible ways to make a selection of coins so that the value is at least 25 cents.

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The value 0.00073 feet per millisecond. in scientific notation is 7. 3 × 10⁴ feet per millisecond

Index forms are described as mathematical methods of writing or representing numbers that are too large or two small in more convenient forms.

They are written in the forms of exponents of numbers or variables,

There are other names for index forms which are scientific notation and standard forms.

From the information given, we have that;

The seahorse moves 0.5 miles per hour, or 0.00073 feet per millisecond

In converting 0.00073 feet per millisecond into index forms

count the number of zeros to the first significant number

7. 3 × 10⁴ feet per millisecond

Hence, the value is 7. 3 × 10⁴ feet per millisecond

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Answer: In math End Behavior describes a graph at its end values. To explain, it is the high values and what the graph would like like as x values get very high and how it would look for the y values. Also, in terms of graph looks, this could be an exponential or logarithmic curve as values get very high. Think about End Behavior as the graphical patterns when the values get high. Hope this helps! Please give this a brainiest if this was helpful as I am one away from the next rank.

Step-by-step explanation:

Answer:I hope this helps

Step-by-step explanation:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

End behavior refers to the appearance of a graph as it is followed indefinitely in either horizontal direction. Leading coefficient POSITIVE: both "ends" are UP. Leading coefficient NEGATIVE: both "ends" are DOWN. Leading coefficient POSITIVE: left end is DOWN and right end is UP.

If the degree is odd and the lead coefficient is positive, then the right end of the graph will point up and the left end will point down. If the degree is odd and the lead coefficient is negative, then the right end of the graph will point down and the left end will point up

The proof for UX || VW is shown below.

According to the midpoint theorem, "The line segment in a triangle joining the midpoint of any two of the triangle's sides is said to be parallel to its third side and is also half the length of the third side."

Given:

As, TUX and TVW are similar.

So, the ratio of their corresponding sides are equal.

So, TU/ TV = UX/ VW = TX / TW = 1/2  {TU/ TV = 1/2}

By using mid point Theorem

UX = 1/2 VW

Then, UX || VW.

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Answer:

B

Step-by-step explanation:

We always look original price for 1 or 100%, now increase 1/2, that is 50%

So now it is 100%+50%=150%

Answer:

[tex] \sf \: x = 6[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ 4x + 10 = 34

Then the value of x will be,

→ 4x + 10 = 34

→ 4x = 34 - 10

→ 4x = 24

→ x = 24 ÷ 4

→ [ x = 6 ]

Hence, the value of x is 6.

The solution is, 53.5 sec was her time, in seconds, for the third lap.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Given

Number of times Lucia ran the race=n=3

Slowest time= x_1=56.3 sec

Fastest Time= x_2=52.2 sec

Average time=54.0 sec

Since, we know the average time and two of the three race times, we can use the average formula to calculate the third race’s time.

Let  

x_3=the third race^' s time

So,

Average=(Sum of values)/(Number of values)

Average =  (x_1+ x_2+ x_3)/n

Putting the values

54.0=  (56.3+ 52.2+ x_3)/3

Multiplying 3 with 54.0 and adding 56.3 and 52.2

162= 56.3+52.2+ x_3

162= 108.5+ x_3

x_(3 )=162-108.5

x_(3 )=53.5 sec

Hence, The solution is, 53.5 sec was her time, in seconds, for the third lap.

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The solution to the system of linear equations using the Equal Value Method is Y = -(8y / 6) - 21.

The Equal Value Method is a technique used to solve a system of linear equations. To solve a system of linear equations using the Equal Value Method, we first write out the two equations. In this case, we have the two equations:

Y = -8x - 21

y = 6x + 7

Next, we need to solve one of the equations for one of the variables. We can solve for x in the first equation, giving us x = (-21 - Y) / -8. We can then substitute this into the second equation, giving us y = (6(-21 - Y) / -8) + 7. We can then expand and simplify this equation, giving us y = (126 + 6Y) / -8.

Finally, we can set the two equations equal to each other and solve for Y. This will give us 126 + 6Y = -8y, which simplifies to 6Y = -8y - 126. We can then divide both sides by 6 to get Y = -(8y / 6) - 21.

Therefore, the solution to the system of linear equations using the Equal Value Method is Y = -(8y / 6) - 21.

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The possible set of dimensions for the container

radius = 8 inches, height = 21 inches:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

A) radius = 21 inches, height = 21 inches:

The inequality h > 0.3r² is satisfied (21 > 0.3 * 21^2).

The height must be no more than 15 inches greater than the radius

=21 - 21 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches

= πr² ≥ 36pi, which is not satisfied ( πr² < 36π).

So, option A is not a possible set of dimensions.

B) radius = 8 inches, height = 21 inches:

The inequality  h > 0.3r² is satisfied (21 > 0.3 x  8²).

So, The height must be no more than 15 inches greater than the radius (21 - 8 ≤ 15), which is satisfied.

The area of the base must be at least 36π square inches

= π(8²) ≥ 36π

So, option B is a possible set of dimensions.

C) radius = 7 inches, height = 23 inches:

The inequality h > 0.3r^2 is satisfied (23 > 0.3 x 7^2).

The height must be no more than 15 inches greater than the radius

= (23 - 7 ≤ 15), which is satisfied.

and, Area of the base

= (π (7)² < 36pi) not satisficed.

So, option C is not a possible set of dimensions.

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Answer:

Below

Step-by-step explanation:

1)   The domain can be ANY value of 'x' except 'x' that cause the denominator to = 0    and it cannot be 'x' values that cause the denominator to be negative    as this is not allowed

so   x cannot be 5 or greater

       (-∞ , 5)   is the domain in interval notation

    or you could just write   x < 5      

2) you cannot have a negative square root so the domain would be all 'a'

       that the numerator would be 0 or greater (you CAN have a square root of '0' in the numerator)

             7-5a ≥ 0

               7 ≥ 5a

               7/5 ≥ a     or flipping it around    a ≤ 7/5

3) 15x^3y^2 + 10x^2 y - 20 x^2 y^3

you can factor out a   x^2    5  and  y from all three terms to get :

   5 x^2 y ( 3xy + 2 - 4 y^2 )       there ya have it !

Equating both equations, Nayati and Tatiana will have the same amount of savings after 21 weeks.

Equations are mathematical statements that show that there is equality between two or more mathematical expressions.

Equations are depicted using the equation symbol (=).

                       Nayati   Tatiana

Savings            $240     $450

Weekly savings $40       $30

Nayati total savings = 40w + 240

Tatiana total savings = 30w + 450

To determine the number of weeks when their savings will be equal, the two equations will be equated as follows:

40w + 240 = 30w - 450

10w = 210

w = 21

= 21 weeks

Thus, we expect Nayati and Tatiana to embark on their road trip after 21 weeks.

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