At the beginning of the year, Salma had $35 in savings and saved an additional $8 each week thereafter. Henry started the year with $95 and saved $5 every week. Let SS represent the amount of money Salma has saved tt weeks after the beginning of the year and let HH represent the amount of money Henry has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the number of weeks after the beginning of the year until Salma and Henry have the same amount of money saved.

Answer:

the 66th term is 1095

The following results of the quadratic equation are summarized below:

Vertex: (h, k) = (3, 1)

Axis of symmetry: x = 3

Min/Max value: f(3) = 1 (Maximum)

y-Intercept: - 8

x-Intercepts: (2, 0), (4, 0)

Domain: All real numbers.

Range: y ≤ 1.

Sketch of the graph: Please see image.

Standard form: f(x) = x² - 6 · x + 8

Rigid transformations: Horizontal translation / Reflection about x-axis / Vertical translation

In this problem we have a quadratic equation in standard form, whose definition is shown below:

f(x) - h = C · (x - h)²        (1)

Where:

Now we proceed to determine each of the required features:

Vertex

The quadratic equation has a vertex at point (3, 1).

Axis of symmetry

The axis of symmetry of the parabola is x = 3.

Min/Max value

For as the vertex constant is a negative number, then the vertex represents a maximum. Then, we evaluate the function at x = 3:

f(3) = 1

y-Intercept

The y-intercept is the value of the quadratic equation evaluated at x = 0.

f(0) = - (0 - 3)² + 1

f(0) = - 9 + 1

f(0) = - 8

x-Intercepts

The x-intercepts are the values of x such that f(x) = 0, all these can be found by using algebra properties:

- (x - 3)² + 1 = 0

- (x² - 6 · x + 9) + 1 = 0

- x² + 6 · x - 9 + 1 = 0

x² - 6 · x + 8 = 0

(x - 2) · (x - 4) = 0

Then, the x-intercepts of the parabola are (2, 0) and (4, 0).

Domain

The domain of all quadratic equations are all real numbers.

Range

Since the vertex constant is negative, the range of the quadratic equation is the subset of all real numbers equal or less than the y-value of the vertex.

Sketch of the graph

Please check the image attached below to see the graph.

Standard form

The standard form of the quadratic equation is:

f(x) = x² - 6 · x + 8

Rigid transformations done

Let be g(x) = x², it is transformed into f(x) = - (x - 3)² + 1 by using the following rigid transformations:

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Answer: 59

Step-by-step explanation:

[tex]51+x+70=180\\\\121+x=180\\\\x=59[/tex]

Answer:

1.  3 and -5

2.  7

Step-by-step explanation:

The zeros of functions are the x-values when y = 0, i.e the point(s) at which the line crosses the x-axis.

To find the zeros of the given functions, set the function to zero and solve for x.

Given function:

[tex]y=5(x-3)(x+5)[/tex]

Set the function to zero:

[tex]\implies 5(x-3)(x+5)=0[/tex]

[tex]\implies \dfrac{5(x-3)(x+5)}{5}=\dfrac{0}{5}\\[/tex]

[tex]\implies (x-3)(x+5)=0[/tex]

Using the Zero Product Property, set each factor equal to zero and solve for x:

[tex]\implies (x-3)=0 \implies x=3[/tex]

[tex]\implies (x+5)=0 \implies x=-5[/tex]

Therefore, the zeros of the function are 3 and -5.

Given function:

[tex]y=(x-7)^2[/tex]

Set the function to zero and solve for x

[tex]\implies (x-7)^2=0[/tex]

[tex]\implies \sqrt{(x-7)^2}=\sqrt{0}[/tex]

[tex]\implies x-7=0[/tex]

[tex]\implies x=7[/tex]

Therefore, the zero of the function is 7 (with multiplicity 2).

The integer in the solution set of 5/6m - 4 < 1/3m + 5 that would make it false is 20

The set is given as

S:{−18, 2, 15, 20}

The inequality expression is given as

five sixths m minus four is less than one third m plus 5

Rewrite the inequality expression properly

So, we have

5/6m - 4 < 1/3m + 5

Subtract 1/3m from both sides of the inequality expression

So, we have

1/2m - 4 < 5

Add 4 to both sides of the inequality expression

So, we have

1/2m < 9

Divide both sides of the inequality expression hy 1/2

So, we have

m < 18

This means that the integers in the solution set are integers that are less than 18

These integers are −18, 2, 15

All other integers would make the inequality false

Hence, the solution is 20

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By solving a simple linear equation, we will get that:

36° = m∠AOB

We can write a simple linear equation here, we know that:

m∠AOC = 108°

And we also know that:

m∠AOC = 3*m∠AOB

If we replace the first equation into the second one, then we will have the linear equation:

108° = 3*m∠AOB

And we want to solve this for m∠AOB, to do so, we just need to divid both sides by 3, we will get:

108°/3 = m∠AOB

36° = m∠AOB

We conclude that the measure of angle ∠AOB is 36°

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Answer:

Step-by-step explanation:

31/2x-7

Based on the given graph and line, the distance between the pair of points is 5

To find the distance between two points on a line or a pair of points, first find the coordinates of the points:

(-1, -2) and (-1, 3)

The distance then be found by applying the formula:

=√((x2 – x1)² + (y2 – y1)²)

Solving for the distance gives:

=√((-1 – (-1))² + (3 – (-2))²)

= 5

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The equation that can be use to find the how many miles, x, Omar ran each day after work is x =  (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days  after work

The total number of days he run = 7 days

Total distance he ran in one week = 63 miles

The distance he run before the work = 3 miles

The total distance he run before the work in one week= 7×3

= 21 miles

The total distance he run after the work = 63 - 21

= 42 miles

The equation that can use to find how many mile x, Omar ran each day after work = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7

Substitute the values in the equation

= 42/7

= 6 miles

Hence, the equation that can be use to find the how many miles, x, Omar ran each day after work is x =  (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days  after work

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The value of x is 67°.

To determine the value of x,

Draw a line parallel to lines l and m passing through the vertex at angle x dividing it into two angles a and b.

∠a  = 35°   (Interior Alternate angles are congruent)

∠b + 148°  = 180°  (Co-Interior angles are supplementary)

⇒ ∠b = 32°

∠x  = ∠a + ∠b

⇒ ∠x  = 35° + 32°

⇒ ∠x = 67°

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Answer:

0.79 greater than 0.789 by 0.001

Step-by-step explanation:

[tex]{ \tt{ \delta x + 0.79 = 0.789}} \\ { \tt{ \delta x = 0.001}}[/tex]

[tex]4 {x}^{3} - 36x = 0 \\ 4x( {x}^{2} - 9) = 0 \\ 4x = 0 \\ \\ or \\ {x}^{2} - 9 = 0 \\ \\ \frac{4x}{4} = \frac{0}{4} =0 \\ \\ \\ (x - 3)(x + 3) = 0 \\ \\ x + 3 = 0 \\ \\ or \\ x - 3 = 0 \\ \\ \\ x = 0 \\ or \\ x = - 3 \\ \\ or \\ \\ x = 3[/tex]

ATTACHED IS THE SOLUTION

Answer:

5 clusters

Step-by-step explanation:

This is because she went to the market with 50 pesos and buys one bag of papayas for 20 pesos.

That means that her the remaining money she would have would be 50-20=30.

she would have 30 pesos.

Each banana cost 6 pesos so, she would buy 5 clusters because 30÷6=5

Answer:

Step-by-step explanation:

Hope it helps :D

The slope and equation of line with the coordinates (5,6) and (3,4) are 1 and y = x + 1 respectively.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point A(5,6)

Point B(3,4)

Slope m = ?

To determine the slope, plug the given coordinates into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 4 - 6 )/( 3 - 5 )

Slope m = ( -2 )/( -2 )

Slope m = ( -1 )/( -1 )

Slope m = 1/1

Slope m = 1

Next, use the the formula for the equation of line to determine the y-intercept 'b'.

y = mx + b

Plug in slope m = 1 and point (5,6)

6 = 1(5) + b

6 = 5 + b

b = 6 - 5

b = 1

Now that we have both the slope m ( 1 ) and y-intercept b ( 1 ), plug these values into y = mx + b to find the linear equation.

y = mx + b

y = 1x + 1

y = x + 1

Therefore, the slope is 1 and equation of line is y = x + 1.

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The length of the edge of the box is 6 cm.

Here, we are given that the volume of a box is 216 cm cube.

Here, we assume that the box is a cube and not a cuboid since only then we will be able to find the edge of the box.

The volume of a cube is given by the formula-

Volume = side × side × side

Let the side of the given cube be x.

Then we can form the following equation-

[tex]x^{3}[/tex] = 216

x = (216)^1/3

we can find the 216 is the cube of 6. Thus,

x = 6

Hence, the length of the edge of the box comes out to be 6 cm.

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Answer:

x < -7/6

Step-by-step explanation:

In a equation that show a greater than or less than sign can be a equal sign .

Answer:

Quotient = 3x² - 2x + 3

Remainder = 1

Step-by-step explanation:

We have to solve: [tex]\dfrac{3 x^{3} + 4 x^{2} - x + 7}{x + 2}[/tex]

We will use synthetic division to calculate this divisor

First, take the constant term of the divisor with the opposite sign and write it to the left. Write the coefficients of the dividend expression to the right Where there is no coefficient for a specific x term, use 0

Step 1: Write down the first coefficient asis

   |  x³      x²       x¹       x⁰
2  |  3       4        -1        7           ←    Coefficient row
   |
   ---------------------------------

       3                                           ← Result Row

Step 2: Multiply the entry in the left part of the table by the last entry in the result row and add he obtained result to the next coefficient of the dividend, and write down the sum.

    |  x³      x²       x¹       x⁰
-2  |  3       4        -1        7          
     |          -6                                         -6 = -2 x 3
   ---------------------------------

       3     -2                                          -2 = 4 + (-6)

Repeat step 2 until we have finished with all the entries. These are the snapshots of each computation. Current operands are in bold

   |  x³      x²       x¹       x⁰
-2 |  3       4        -1        7          
    |          -6        4                              
   ---------------------------------

       3     -2         3

   |  x³      x²       x¹       x⁰
-2 |  3       4        -1        7          
    |          -6        4      -6                        
   ---------------------------------

       3     -2         3       1

The last entry in the result table shows the remainder of the division

The resultant coefficients are 3, -2, 3, 1

Therefore the answer is
Quotient = 3x² - 2x + 3
Remainder = 1

Using the slope of the linear function, it is found that 50 megabytes are transferred every 10 seconds.

A linear function is modeled according to the following rule, in slope-intercept form:

y = mx + b

In which:

For this problem, the function is given as follows:

S(t) = 5t + 45.

The slope of m = 5 means that every one second, 5 megabytes are transferred, hence the amount transferred every 10 seconds is given by:

Amount = 5 x 10 = 50 MB.

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Answer:

3, 4, 5

6, 8, 10

5, 12, 13

Step-by-step explanation:

If you are given side lengths and must determine if it is a right angle, you will use the Pythagorean Theorem. Which states that the square length of the hypotenuse (longest side of a triangle) must equal to the sum of the square length of the two shortest.

Formula: a² + b² = c²

2, 4, 6

a² + b² = c²

(2)² + (4)² ≟ (6)²

4 + 16 ≟ 36

20 ≠ 36

3, 4, 5

a² + b² = c²

(3)² + (4)² ≟ (5)²

9 + 16 ≟ 25

25 = 25

6, 7, 9

a² + b² = c²

(6)² + (7)² ≟ (9)²

36 + 49 ≟ 81

85 ≠ 81

6, 8, 10

a² + b² = c²
(6)² + (8)² ≟ (10)²

36 + 64 ≟ 100

100 = 100

5, 12, 13

a² + b² = c²

(5)² + (12)² ≟ (13)²

25 + 144 ≟ 169

169 = 169

With an income of $57,890, you need to pay $12,735.8 in taxes.

What is mean by proportion?

A proportion is a fraction of a total amount, in which two ratios are set equal to each other.

Given that;

For incomes from $38,701 up to $82,500, you need to pay 22% in taxes.

And, No federal taxes up to $9,525, 12% for income from $9,526 up to $38,700, 22% for income from $38,701 up to $82,500.

Now,

An income of $57,890 is in this range, hence the amount paid is given by;

Amount paid = 57890 x 22%

                    = 57890 x 0.22

                    = $12,735.8.

So, Paid amount for the tax = $12,735.8

Thus, With an income of $57,890, you need to pay $12,735.8 in taxes.

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Using permutation and combination we can calculate that she can get 63 different types of pizza.

Permutations and combinations are the various ways in which elements from a set may be chosen, typically without replacement, to create subsets. This choice of subsets is known as a permutation when the order of the selection is taken into account, and as a combination when it is not.

The total of the decisions we make given an initial set of n items is known as a combination. Permutation, on the other hand, counts the number of possible arrangements of n separate items. This will help us recall that combinations place more emphasis on choice than on placement, order, or arrangement.

Now Cody can get any two toppings out of the 7.

Number of ways in which Cody can pick 2 toppings out of 7 is given by the use of combination,

7C2 = 21 different ways.

Again the number of ways in which 3 different pizza s can be selected is given by 21 × 3 = 63 ways.

Hence Cody can create 63 different pizzas.

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After losing 4 Kg ,the weight of Artur is 14 Kg .

In the question ,

it is given that ,

the ratio of weight of Max : Artur is 5 : 9 .

So the weights of Max and Artur before dieting is 5x and 9x .

Now Artur goes on dieting and lose 4 Kg weight and

the ratio of weight of Max and Artur becomes 5:7  .

and the weights of Max and Artur after dieting is  5x and 7x .

Present weight of Artur = 7x .

As we can see that the change in Artur weight is 9x - 7x = 2x

According to the question

2x = 4

x = 2

hence Artur now weighs 7*(2) = 14 Kg

Therefore , after losing, 4 Kg the weight of Artur is 14 Kg .

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Using properties of exponents, the simplified expression for 5³ x 5^(-5) is given by:

A. 1/(5²).

The exponent property applied to multiply the terms with the same base but different exponents is that we keep the bases and then add the exponents.

For this problem, the expression is given as follows:

5³ x 5^(-5)

Hence:

Adding the exponents, we have that:

3 + (- 5) = 3 - 5 = -2.

Hence the simplified expression is:

5³ x 5^(-5) = 5^(-2).

When a number has a negative exponent, we can move it to the denominator, then the exponent becomes positive, hence:

5^(-2) = (1/5)² = 1/5² = 1/25.

Meaning that option A is correct.

The expression in this problem is 5³ x 5^(-5), and the correct options are given by the image at the end of the answer.

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Probability of choosing a red gumball choosing a blue gumball and choosing a green gumball are 2/9,  3/9,   4/9   RESPECTIVELY.

four green balls three blue gumballs and two red gumballs all the same size and shape.

total number of balls =9;

red ball =2

green ball=4

blue ball =3

as we know, the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

so, according to the question;

probability of choosing a red gumball choosing= no. of red balls/total number of balls

=>2/9=0.22

probability of choosing a blue gumball choosing= no. of blue balls/total number of balls

=>3/9=0.33

probability of choosing a green gumball choosing= no. of green balls/total number of balls

=>4/9=0.44;

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Answer:

the coordinate of point P is (14/5, -1)

Step-by-step explanation:

The domain and the range for the relations are given as follows:

For items 13 and 16, the functions are continuous, hence it is over the real numbers, and both the domain and range are all real values.

For items 14 and 15, the functions are discrete, hence it is over the integer numbers, and the domain is composed by the values assumed by x and the range is composed by the values assumed by y.

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Answer:

interior = 150° , exterior = 30°

Step-by-step explanation:

the sum of the exterior angles of a polygon = 360°

since the polygon is regular then each exterior angle is

360° ÷ 12 = 30°

the sum of the exterior angle and interior angle = 180° then

interior angle = 180° - 30° = 150°

Using the special parallelograms the proof with regard to the EFGH rectangle that triangle FJG is an isosceles is completed and attached. See further explanations below.

Proofs are examples of exhaustive deductive reasoning that establishes logical certainty, as opposed to empirical arguments or non-exhaustive inductive reasoning that establishes "reasonable expectation."

The following are various kinds of proof:

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Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius. The circumference is 471 yards

Do not worry; we have you covered. Simply enter the diameter into this formula, C=[tex]\pi[/tex]d, if you know it. Instead, did you receive the radius? No issue, just use the equation C=2[tex]\pi[/tex]r. For all the information you need on calculating a circle's circumference using its diameter or radius, keep reading. To make things simple, we even provide a circumference calculator.

To determine the circumference using the radius, use the formula C = 2[tex]\pi[/tex]r. The radius of the circle is denoted by "r" in this expression. Again, you can enter the number value of, which is a closer approximation of 3.14, into your calculator.

Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius.

You might have noticed that this resembles the formula C = [tex]\pi[/tex]d. This is due to the fact that the diameter can be thought of as 2[tex]\pi[/tex]r because the radius is only half as long as the diameter.

Circumference= 2[tex]\pi[/tex]r

                         = 2*3.14*75 yards

                          = 471 yards

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