Phillip added 15 pencils to his collection. He then gave 30 pencils to a friend. Write and evaluate an expression

Answer: y-intercept is 12

Step-by-step explanation:

y = mx +b

m = slope

b = y-intercept

y | = | x | + | b

f(x) | = | 4x | + | 12

b = y-intercept

Answer: CD<AD

Step-by-step explanation:

Just got it right on the test.

Answer: CD<AD

Step-by-step explanation:

Took the test!

a. It should be noted that the equation illustrates that the value of 6a + 9b is 24.

b. The value of 2x + 5y is 25.

a. From the information, 2a + 3b = 8. The value of 6a + 9b will be:

6a + 9b = 3(2a + 3b)

This implies that the value will be multiplied by 3. Therefore, 8 × 3 = 24

(ii) What is the value of 2x + 5y?

4x + 10y = 50

It should be noted that this can be divided through by 2. This will be;

(4x + 10y = 50) / 2

2x + 5y = 25

The value is 25.

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Answer: 87, 295,000,000 or eighty-seven two hundred ninety-five Billion

Im pretty sure

Answer:

  a)  x³, 1/x, x, sin(x)

Step-by-step explanation:

You want to know which list of functions has the same graph when reflected across both the y- and x-axes.

Reflection across the y-axis transforms the function to ...

  f(x) ⇒ f(-x)

Reflection across the x-axis transforms the function to ...

  f(x) ⇒ -f(x)

Hence, reflection across both axes transforms the function to ...

  f(x) ⇒ -f(-x)

A function that has the characteristic that f(x) = -f(-x) is an odd function. Its graph is symmetrical about the origin. We can check to see if the functions of interest match this definition of an odd function:

  x³ = -(-x)³ . . . . true

  1/x = -(1/-x) . . . . true

  x = -(-x) . . . . true

  sin(x) = -sin(-x) . . . . true

  cos(x) = -cos(-x) . . . . false

  e^x = -e^-x . . . . false

  |x| = -|-x| . . . . false

The basic functions that are odd are ...

  x³, 1/x, x, sin(x)

Answer:

x=-1/4 or -.25

Step-by-step explanation:

I took the test and double checked it

Answer:

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

Step-by-step explanation:

ASA: Angle, Side, Angle

AAS: Angle, Angle, Side

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

I am going to use the drawer to show the differences:

Nothing tricky here:

[tex]\displaystyle \int_{-\infty}^0 \sqrt{1+2^2} \, e^{2\theta} \, d\theta = \sqrt5 \int_{-\infty}^0 e^{2\theta} \, d \theta \\\\ ~~~~~~~~ = \frac{\sqrt5}2 \left(e^0 - \lim_{\theta\to-\infty} e^{2\theta}\right) \\\\ ~~~~~~~~ = \frac{\sqrt5}2[/tex]

Recall that

[tex]\phi = \dfrac{1+\sqrt5}2[/tex]

and this is exactly 1/2 more than the value of the integral.

So, 13 games were played each month, if each month had the same number of games.

Compared to multiplication, division is the opposite. If three groups of four add up to 12, then division of 12 into three groups of equal size yields four in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. It is referred to as a method of division to divide anything. According to the degree of difficulty, there are three different sorts of division procedures. These include the bus stop approach, the chunking method, and the long division method. The chunking method is also known as division by repeated subtraction.

Given Data

A total of 117 football games in the season, and 33 were played at night.

The season was nine months long.

Each month same numbers of game were played.

So,

117 ÷ 9

13

So, 13 games were played each month, if each month had the same number of games.

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Answer:

578.0 yd^2

Explanation:

The formula for finding the surface area of a cylinder is given as;

where A = surface area

pi = 3.14

r = radius of the base of the circle = diameter/2 = 8/2 = 4 yd

h = height = 19yd

Let's go ahead and substitute these values into our formula and solve for A;

The scale is 1/2 to 7 feet. That means that for each half of an inch of the original picture, the scaled figure will have 7 feet.

Now,

That means that 1 inch corresponds to 7ft +7ft= 14ft.

Therefore, if my original figure is 1 inch in height the scaled picture will be 14 ft in height.

Answer: The scaled figure will fit in the billboard.

The dilated polygon image is attached below under a dilation with a scale factor of 3 and center of dilation (0,0)​

In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the points where two sides meet.

Transformation is the movement of a point from one location to another. Transformations include rotation, reflection, translation, and dilation.

Dilation is the process of increasing or decreasing the size of a figure by a factor k. If a point A(x, y) is dilated about the origin by a factor k, the new point is A' (kx, ky).

Assume the polygon has vertices at A(0, 0), B(3, 3) and C. (-3, 3). If the polygon is dilated by a factor of three with the center of dilation at (0, 0), the new vertices are as follows:

A'(0,0), B'(1, 1) and C'(-1, 1)

Therefore, the polygon graph is attached in which the polygon is dilated by a factor of three with the center of dilation at (0, 0),

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Answer:

400 < m< 430 kg

Step-by-step explanation:

the mass of horse is 429 kg

estimated to the nearest hundred is 400  kg

estimated to the nearest  tens is 430 kg

thus the value of m mass lies between 400 to 430

therefore

400 < m< 430 kg

The answer is 400 < m< 430 kg

Step-by-step explanation:

Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.

How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?

..

please post full questions

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

The given system of equations:

x  +  2y  =  8              (Equation - 1)

-3x - 2y  =  12            (Equation - 2)

This can be written in matrix form as shown:

[tex]\left[\begin{array}{ccc}1&2&\\-3&-2&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]  [tex]= \left[\begin{array}{ccc}8\\12\\\end{array}\right][/tex]

Let us assume, D = [tex]\left[\begin{array}{ccc}1&2\\-3&-2\\\end{array}\right][/tex]

We can use cross multiplication,

= (-2)(1) - (-3)(2)

= -2 + 6

= 4 ≠ 0

So the system has a unique solution,

Then,

[tex]D_{1} = \left[\begin{array}{ccc}8&2\\12&-2\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{1} = (8)(-2)-(12)(2)\\D_{1} = -16-24\\D_{1} = -40[/tex]

[tex]D_{2} =\left[\begin{array}{ccc}1&8\\-3&12\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{2} = (12)(1)-(-3)(8)\\D_{2} = 12+24\\D_{2} = 36[/tex]

So, they can solve the X and Y values,

X = D1 / D

X = -40/4

X = -10

Y = D2 / D

Y = 36/4

Y = 9

Therefore,

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

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EXPLANATION:

Solution first(a) exercise part b:

All the internal angles of a right triangle must add up to 180, so to order the internal angles from least to greatest we must find the missing angle;

The exercise is as follows:

Now we must order them from lowest to highest, the order is as follows:

a) g(3) = -182

b) g(0) = 7

c) g(-1) = 70

a) g(3): To get this, we will substitute 3 for x in the function g(x)

b) g(0): To get this, we will substitute 0 for x in function g(x)

c) g(-1): To get this, we will substitute -1 for x in function g(x)

The domain for the rational function is the set of all real numbers except for 8, this is written as:

{x | x ∈ R, x≠8}

For any function f(x), the domain is the set of the possible inputs.

In this case, we have the rational function:

f(x) = (x - 3)/(x - 8)

Now, we start by assuming that the domain is the set of all real numbers, and then we remove all the problematic values.

Now, we can't divide by zero, so the value of x that makes the denominator zero needs to be removed, that is such:

x - 8 = 0

x = 8

So the domain is the set of all real numbers except for 8, this is written as:

{x | x ∈ R, x≠8}

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Answer:

83

Step-by-step explanation:

3x³+2y-6

x= 3 and y = 4, we will plug in what x equals to for the x value, then we will plug in what y equals to for the y value

3(3³) + 2(4) - 6

now let's use order of operations (PEMDAS: parenthesis exponent multiplication division addition subtraction)

parenthesis first

3³ = 3·3·3= 27

3(27) + 2(4) - 6

there are no exponents so we will use multiplication

3·27 = 81

2·4=8

81 + 8 - 6

83

Answer:

  x = 8

Step-by-step explanation:

You want the value of x for a right triangle with side lengths (x+1) and (x-3) and an area of 22.5 cm².

The area of a triangle is given by the formula ...

  A = 1/2bh

Then the area of this triangle is ...

  22.5 = 1/2(x -3)(x +1)

  45 = x² -2x -3

  48 = x(x -2) . . . . . . . add 3 and factor out x

We know that 48 can be factored as (8)(6). Comparing this to x(x-2), we see that x=8.

__

Additional comment

x could also be -6, but that would make the side lengths be negative. The only applicable solution for this geometry is x=8.

The total possible outcome for the experiment is 36.

The ossible outcomes for same number on each dice is 6.

So probability for the same number on dice is,

So probability for the same number on dice is 1/6. So first statement "The probability of rolling the same digit with each die is 1/4" is false.

You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.

a) At t = 0

temperature of turkey is 67 degree  Fahrenheit

b) At t = 3.75

temperature of turkey is 165 degree  Fahrenheit

c) t = 3

temperature of turkey is 4 degree  Fahrenheit

d) at t = 3.75

temperature of turkey is 169 degree  Fahrenheit

Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done.

Given that : You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.

a) At t = 0

temperature of turkey is 67 degree  Fahrenheit

b) At t = 3.75

temperature of turkey is 165 degree  Fahrenheit

c) t = 3

temperature of turkey is 4 degree  Fahrenheit

d) at t = 3.75

temperature of turkey is 169 degree  Fahrenheit

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We know that

• The probability of a head is 1/2.

• The probability of a tail is 1/2.

Notice that the number of times they flip a coin is 7. Since both probabilities are the same, we just have to multiply 1/2 seven times by itself.

Now, we multiply the probability with 7 since there are 7 possibilities.

Then, we multiply by 100 to express it as a percentage.

Probability that first three price winners are omar, kira and elsa is     [tex]\frac{1}{84}[/tex]

Probability that omar is first prize winner and kira is second prize winner and elsa is third price winner is  [tex]\frac{1}{504}[/tex]

When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.

(i)First 3 prizes must be given to 3 persons regardless of order

Hence they can also be arranged in 3! ways.

est 6 can be arranged in 6! ways.

positions                   ___ ___ ___ ___ ___ ___ ___ ___ ___

number of ways         3     2       1     6     5    4       3     2     1

total number of ways to arrange 9 people = 9!

[tex]P(A)= \frac{(3)(2)(1)(6)(5)(4)(3)(2)}{(9).(8).(7).(6).(5).(4).(3).(2))}[/tex][tex]P(A)=\frac{6}{9.8.7}[/tex][tex]P(A)= \frac{1}{84}[/tex]

(ii)Event A

In event A three positions are fixed .

Omar -1 Kira -2 Elsa -3

Therefore there is only 1 way to fill the 1st,2nd and 3rd position

Permutations can only be made among the other positions.

Positions -           ___  ___ ___ ___ ___ ___ ___ ___  ___

Number of ways-  1        1      1       6     5     4      3      2    1

Total number of ways of arranging  9 people =9×8×7×6×5×4×3×2×1

Number of ways to satisfy event A =1×1×1×6×5×4×3×2×1

P(A)=   [tex]\frac{(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}[/tex]

P(A)= [tex]\frac{1}{504}[/tex]

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The z-score of the given expression P(-a < z < a) = 0.4314 is; 0.55

We are told that P(-a < z < a) = 0.4314. Thus;

P(-a < z < a) = 0.4314 is represented by the area about mean. This means that; 0.4314/2 = 0.2157 is the area each on the left side and right side of mean.

Now, from online z-score calculator, we see that the z value corresponding to 0.2157 is 0.55.

Assume that ​z-scores are normally distributed with a mean of 0 and a standard deviation of 1, if P(-a < z < a) = 0.4314, then it means that the z score is 0.55.

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Complete question is;

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−a < z < a) = 0.4314, find d a. Round to two decimal places

SOLUTION

Step1:

hence from the diagram above, the dimension of the rug is

Since we have area of the rug,

then we have

We now solve the equation above quadratically

Then we have

Solve using factor method we obtain

Equating each factor to zero we have

Since x can not be 28, the value of x is 1

The Dimension of the rug becomes

Hence the dimension of the rug is 32 ft by 22ft (22,32)