1 Which of the following equations are
true? Select all that apply.
A 7+(-7) = 14
B -4+9=5
C 3-(-10) = -7
D -2-6=-8

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 terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.

Let's check all the options. Then we have

a) √6, 2.5, 8/3, convert the numbers into a decimal form. Then we have

⇒ 2.449, 2.5, 2.667, order is in ascending form.

b) √8, 11/4, 2.9, convert the numbers into a decimal form. Then we have

⇒ 2.828, 2.75, 2.667, order is not in ascending form.

c) 9/5, 1.9, √5, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.9, 2.236, order is in ascending form.

d) 13/5, 2.8, √7, convert the numbers into a decimal form. Then we have

⇒ 2.6, 2.8, 2.645, order is not in ascending form.

e) 1.8, 7/4, √3, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.75, 1.732, order is not in ascending form.

The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

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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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Answer:

Her piggy bank can hold 720 pennies.

Step-by-step explanation:

1/2= 3/6, and 2/3=4/6, meaning the difference of 1/6=120 pennies. 120x6=720.

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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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

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!

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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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 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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Answer:

3.6

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

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 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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The newly translated function of  f(x) = 7x + 1 is; g(x) = 7(x - 1) + 1

In transformation of functions, there are different operations such as translation, reflection, dilation, rotation.

Now, we are told that the function is given as;

f ( x ) = 7x + 1

We are told that it is translated by 5 units to the right.

It is pertinent to note that when talking about translation, it is as good as saying moving from one point to the other without changing the dimensions or shape.

Now, when we shift a function f(x) = x - 1 by a units to the left, it means the translated function is; f'(x) = (x + 1) - 1

However, when we shift a function f(x) = x - 1 by a units to the right, it means the translated function is; f'(x) = (x - 1) - 1

Now, applying that translation rule to our given function gives;

g(x) = 7(x - 1) + 1

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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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The congruency can be proved using SAS rule.

What are congruent triangles?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles is slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of harmoniousness is’ ≅’.

Main Body:

In ΔPQR and ΔRST

PR = RT           ---(1)

as both the sides are congruent , the third sides of triangles is also equal.

QR = RS          ----(2)

∠PRQ = ∠SRT   ----(3)

Hence by side- angle -side

ΔPQR and ΔRST are congruent.

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The function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

The function is  

f(x) =[tex]2(\frac{1}{2})^x[/tex]

The function is defined as the expression that represents the relationship between one variable and another variable.

The function is in the form of

f(x) = a × [tex]b^x[/tex]

Such functions are called exponential function

Here  

The value of a = 2

The value of b = 1/2

If the value of b > 1, the function is called exponential growth function.

If the value of b < 1, the function is called exponential decay function.

Here b < 1

Therefore it is exponential decay function

Hence, the function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

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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

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 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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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 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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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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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?

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 best question is that if they can examine a sample of tires used for 60,000 miles and determine the proportion that is worn out, then how likely is that proportion to be 3.6% or less?

we are given the information that an A tire manufacturer has a 60,000-mile warranty and the manufacturer considers the overall tire quality to be accepted if less than 5% are worn out at 60,000 miles, also the manufacturer tested 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. So here the Hypotheses can be that:

1) The proportion of tires that are worn out after 60,000 miles is equal to 0.05 and

2) The proportion of tires that are worn out after 60,000 miles is less than 0.05.

We need to deny the first hypothesis with an alternative one. You cannot demonstrate that the average is 3.6%, but if you by one means or another decide that the probability the average is greater than 3.6% is lower than 100% minus your confidence level, at that point you'll be able to deny the first hypothesis and acknowledge the second one as new average.

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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 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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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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