Solve the system of equations using substitution.

3x + 2y = 7
x = 3y + 6

Answer:

£23, 490

Step-by-step explanation:

10% deposit by Carol of £234,900

10/100 *£234,900

0.1*£234,900=£23,490

The slope of the line from the given points will be equal to 3/2 in the simplest form.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given points in the question,

(1, -9) and (4, -7).

x1 = 1 and x2 = 4

y1 = -9 and y2= -7

Slope  = (x2- x1)/(y2- y1)

= (4 - 1)/(-7 - (-9))

Slope = 3/2

Therefore, the slope of the line will be 3/2.

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Answer: m (slope) = 3

Step-by-step explanation: Slope Solution

m=rise run=ΔyΔx

m=y2−y1x2−x1

m=8−53−2

m=31

m = 3

Point Slope Form

y−y1=m(x−x1)

y−5=3(x−2)

Slope Intercept Form

Find the Equation of the Line:

y=mx+b

by solving for y using the Point Slope Equation.

y−y1=m(x−x1)

y−5=3(x−2)

y−5=3x−(3×2)

y−5=3x−6

y=3x−6+5

y=3x−1

m=3

b=−1

Hope this helps :)

The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

Given that,

The points (-7,9).

We have to find the image of the point after a rotation of 90° counterclockwise.

Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.

Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.

(x,y)→(y,-x)

(-7,9)→(9,7)

Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

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To balanced hanger, adding a circle to the left and a square to the right. To both sides, add two triangles. The option 1, 2, and 5 are correct.

What is balanced hanger?

Adding two circles to the left side and a square to the right would adjust the hanger's balance in accordance with the lesson's emphasis on maintaining the equation in balance.

adding a circle to the left and a square to the right. To both sides, add two triangles.

Hence the option 1, 2, and 5 are correct.

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The equation is y = 4x. And the value of the function at x = 6 will be 24.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If y varies directly to x. Then the relationship between them is written as,

y ∝ x

y = kx

When y = 8 and x = 2, then the value of the constant k is given as,

8 = k (2)

k = 8 / 2

k = 4

Then the equation is written as,

y = 4x

Then the value of the function at x = 6 will be given as,

y = 4 (6)

y = 24

The equation is y = 4x. And the value of the function at x = 6 will be 24.

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The representation of the composite function (fg)(x) is (fg)(x) = 10x

From the question, we have the following function definitions

f(x) = √2x

g(x) = √50x

The function to calculate is given as (fg)x

This can be calculated using

(fg)(x) = f(x) * g(x)

Substitute √2x for f(x) and √50x for g(x) in the above equation

So, we have

(fg)(x) = √2x  * √50x

Evaluate the products

(fg)(x) = √100x²

Evaluate the exponents

(fg)(x) = 10x

Hence, the possible equation is (fg)(x) = 10x

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The amount of fat in Cherry ice-cream is 24 grams.

The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.

Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)

Multiplying equation (2) by 3 and then subtracting equation (1) from

the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12

The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12  

grams C + 12*3 = 60C = 60-36 = 24

The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.

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The number of views in the four weeks round to the whole number is 48.

Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.

We have to find the number of views in the fourth week.

On the first week the increase = 25 + 25× 18%

                                                   = 25 + 25 × 18/100

                                                   = 25 + 4.5

                                                   = 29.5

The second week increase = 29.5 + 29.5 × 18%

                                              = 29.5 + 5.31

                                                = 34.81

The third week increase = 34.81 + 34.81 × 18%

                                         = 34.81 + 6.2658

                                         = 41.0758

The fourth week increase = 41.0758 + 41.0758 × 18%

                                           = 41.0758 + 7.393644

                                            = 48.469444

Therefore the number of views in the four weeks is 48.

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The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.

First find out the selling price of the clarinet:

= Discounted price / ( 1 - discount rate)

= 93.60 / ( 1 - 20%)

= $117

This selling price is 30% more than what the store paid so the price the store paid was:

= Selling price / ( 1 + rate of increase)

= 117 / ( 1 + 30%)

= $90

In conclusion, the amount the store paid was $90.

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Complete question

A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.

How much did the store pay for the clarinet?

Answer:

2 , 3 , 4

Step-by-step explanation:

Corresponding angles:  When two parallel lines are intersected by a transversal, the angles on the same side and same position of the transversal are same.

            ∠3 = ∠1

Vertically opposite angles: When two lines intersect, the opposite angles are congruent.

             ∠2 = ∠1

            ∠4 = ∠3

So, ∠1 = ∠2 = ∠3 = ∠4 = 60°

The number -58 is a real number and it cannot be represented as a complex number

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

Expression = -58

The given expression above is a number

And also, it is a negative number

Negative numbers of this form are real numbers

This means that the such numbers cannot be represented as a complex number

Hence, the number -58 does not have a complex equivalent

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The enclosure can be as large as 606 m2 in total.

Given that,

Let x be length of y be width of enclosure

fencing material cost $ 30 / m

Partition material cost $25/m

Total cost = (x+x+y+y)x 30+(y + y) x 25

c= 60(x+y) + 50y = 60 x + 110 y

4000 = 60 x + 110y

y = ( 400 - 6x / 11)

Now,Area of enclosure = x*y

A = x*(400 - 6x / 11)

A'(x)= 400-12x/11

for maximum area A'(x) = 0

400 - 12x/11 = 0,12x = 400,x = 100/3

A " ( x) = - 12/11 < 0  i.e., maximum

y = 400 - 6( 400/12 ) = 200/11 m

Maximum area = xy = 100/3 * 200/11 = 20000/33

                                                            =606.0606

A max = 606m²

Hence, the maximum area you can achieve for the enclosure is 606m²

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Answer:

Triangular prism

Step-by-step explanation:

If you were to fold all the creases and glue it together you would get a tent shape which is a triangular prism

If he arranges them into 6 equal rows, 4 posters will be in each row.

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.

Given,

Total posters = 24

Arranging them into 6 equal rows,

Dividing:

24÷ 6

Reciprocating,

24 × 1/6

4

If he arranges them into 6 equal rows, 4 posters will be in each row.

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According to the integer N,

a) The smallest possible value of N is 6.5 if N >= 6.5

b) The largest possible value of N is -2 if N < - 3

c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.

Integer

Integer refers a collection of whole numbers and negative numbers.

Given,

Here we have the integer N.

And we need to find the following:

a. the smallest possible value of N if N >= 6.5

b. the largest possible of N if N < -3

c. the possible values of N if N >= -2 and N <2.

Part a). smallest possible value of N if N >= 6.5

Here the smallest number is 6.5 because other value are greater than this one.

Part b). the largest possible of N if N < -3

The largest possible number is -2, because the other values on N are less than -2.

Part c). the possible values of N if N >= -2 and N <2.

Here the possible values between these are {-2, -1, 0, 1}.

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Use the compass to join the two circles together, this statement is not a step used when constructing an inscribed equilateral triangle.

A polygon having three vertices and three sides are called a triangle. The triangle's angles are created by joining its three sides end to end at a single point.

The triangle's construction does not include claim D, which is the case. Use the compass to join the two circles together.

It is necessary to keep the compass at a width equal to the circle's radius and to position it at the point where the circle and radius connect while building an inscribed equilateral triangle.

Additionally, it's crucial to pivot an arc the radius's length away from the circle's point. It is not a part of the steps to join the two circles using the compass.

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Each text will cost Hassan $0.09

A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.

Similarly $5.31 is the cost of 59 text messages

Therefore a text message will cost $5.31/12=$0.09

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We can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.

Given, that there are 3 boxes and we have to put 8 balls in them such that no box is empty.

Let, a + b + c = 8, where a , b , c represent three different boxes.

The equation be reduced by allotting 1 ball to each box so that no box remains empty.

Hence, a + b + c = 5

Now, using the formula of "no. of ways in which 'n' objects can be grouped into 'r' groups" i.e. C(n+r-1 , r-1)

So, the required number of ways = C(5+3-1 , 3-1) = C(7 , 2)

Calculating, C(7 , 2) = (7×6)/2 = 21

Hence, we can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.

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The equation of the line that passes through the point (-8,-3) and has a slope of -3/4 is y = -3/4x - 9

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

Slope, m = -3/4

Points, (x₁, y₁) = (-8, -3)

A linear equation can be represented as

y = slope * x + y-intercept i.e. y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = -3/4(x + 8) - 3

Open the brackets

So, we have the following equation

y = -3/4x - 6 - 3

Evaluate the like terms in the above equation

So, we have the following representation

y = -3/4x - 9

The above equation cannot be further simplified

Hence. the linear equation is y = -3/4x - 9

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An ordered pair that is not marked on the coordinate plane of this graph is (8, 0).

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which represent the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

An ordered pair can be defined as a pair of two (2) data points that are commonly written in a fixed order within parentheses as (x, y), in order to represent the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

By critically observing the given graph, we can reasonably and logically deduce that data point (8, 0) is the missing ordered pair on the coordinate plane.

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Answer:

3.6

................................

The values of x after applying congruency to solve the complete shape is 3.5.

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. The symbol to represent two congruent shapes is ≅.

To calculate the values of x in the diagram, we need to first join point Q to point H and point G to form ΔQHG also, we join point Q to point E and point F to form ΔQFE.

Comparing ΔQHG and  ΔQFE, we can deduce that

Therefore,

Hence, the values of x in is 3.5.

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The the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is the function -

x = y

We have the function -

y = x

Now, we can define locus as -

A curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.

This equation -

y = x

is a straight line.

Refer to the graph attached.

The slope of the line is [m] = 1

The [y] intercept is at [c] = 0

Therefore, the the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

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Yes, there is causation between the two given variables, as the weight is related at some point with the amount of calories consumed.

For two variables x and y, we say that there is causation when, if we modify one of the variables, the other changes in response.

Correlation just means that the variables are related in some way (maybe both have a causation relationship with the same other variable)

So causation implies correlation.

Correlation does not imply causation.

In this case, we have the example:

x = The number of additional calories consumed

y =  amount of weight gained.

Clearly, we have causation between x and y as larger is the value of x, larger will be the value of x.-

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The solution to the inequality is X  > 4

Inequality  is a set of mathematical expression which the individual side is not equal to other side

To solve for  x  in the inequality  x - 1 . 5 > 2, we followed the step;

Step 1: Add 1.5 to both sides

x - 1.5 + 1.5 > 2 . 5 + 1.5

X  > 4

Therefore, the solution to the inequality is X  > 4

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Answer:

x + 3 = 18

Step-by-step explanation:

original number of kids: x

additional kids: 3

new total number of kids: x + 3

actual total number of kids: 18

Equation: x + 3 = 18

31 Americans should be surveyed  by Z mean.

What does critical value of Z mean?

If the prior population proportion is unavailable then the formula to find the sample size is given by

           n = 0.25[tex](\frac{z^{*} }{E} )^{2}[/tex]

where z* = Critical z-value

E = margin of error

Given,  Confidence level = 98%

The critical z-value for 98% confidence interval is 2.326  ( BY z-table)

Margin of error : E= 0.21

             n = 0.25 [tex](\frac{2.326}{0.21})^{2}[/tex]

             n = 0.25 * ( 11 .07)²

             n = 0.25 * 122.5449

             n =  30.363225  ≈ 31

Hence,  31 Americans should be surveyed.

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1. The angles measures are larger than the original angle measures is a false statement.

2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.

3. The final angle measure are the same as the original angle measure is false statement.

4. The original figure and the final figure may not be congruent is true statement.

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Answer:

that is a quadratic function so yes it is a function

Step-by-step explanation:

it is a function becausr you can write an equation with it. Hope I could help!