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The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.

I assume that the question is to describe or graph the equation r² - 15 = t + 19.

The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.

4p(y - k) = (x - h)² is the common equation for a parabola that faces up and down and has a vertex at (h, k) and a focal length of |p|.

Let us re-write the given equation in the standard form.

r² - 15 = t + 19

⇒ r² = t + 19 + 15

⇒ r² = t + 34

⇒ (r - 0)² = t + 34 (r can be written as r - 0)

⇒ (r - 0)² = t - (-34) (+34 is written as -(-34))

⇒ (r - 0)² = 4 × 1/4 × (t - (-34))

(4 × 1/4 is equal to 1. The given equation is unaffected by a multiplication by 1.)

⇒ 4 × 1/4 × (t - (-34)) = (r - 0)²  this equation is in the standard form. And here we have |p| = 1/4 and (h, k) = (0, -34).

Refer to the attached image for the graph of this equation.

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Answer:

just use the calculator

Step-by-step explanation:

We know that the irrational number is between:

6 < √45 < 7

And a good estimation is √45 = 6.71

Here we just need to find a lower and upper bound for the given irrational number.

To do it, we just need to find a square number larger and a square number smaller than the number inside the square root.

The larger one will be:

7*7 = 49

The smaller one will be:

6*6 = 36

Then we can write:

√36 < √45 < √49

6 < √45 < 7

So we now know that our number is between 6 and 7, that is already a good estimation, now you can also try to see if it is closer to 6 or 7, by taking the direct square root you will get:

Now just take the product between numbers of the form:

6.10*6.10 = 37.21

And so on, until we almost reach 45.

We will get:

6.71*6.71 = 45.02

So a good estimation is √45 = 6.71

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Answer:

49x=70

Step-by-step explanation:

Answer:

3/20 = 15%

Step-by-step explanation:

Answer:

3/20 = 0.15 = 15%

We're given:

Determine f(-5):

[tex]f(a) = 3a - a^2\\f(-5) = 3(-5) - (-5)^2\\f(-5) = -15 - 25\\f(-5) = -40[/tex]

Therefore, this statement is true.

Determine f(4):

[tex]f(a) = 3a - a^2\\f(4) = 3(4) - (4)^2\\f(4) = 12 - 16\\f(4) = -4[/tex]

Therefore, this statement is true as well.

Determine f(-1):

[tex]f(a) = 3a - a^2\\f(-1) = 3(-1) - (-1)^2\\f(-1) = -3 - 1\\f(-1) = -4[/tex]

Therefore, this statement is not true.

Determine f(0):

[tex]f(a) = 3a - a^2\\f(0) = 3(0) - (0)^2\\f(0) = 0 - 0\\f(0)=0[/tex]

Therefore, this statement is also not true.

f(-5) = -40

f(4) = -4

We get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

We are given a graph of a function.

A graph of a function is a special case of a relation.

In mathematics, the graph of a function f is the set of ordered pairs, where f(x)=y.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Here, we can see that function increases before x = - 2, then it decreases till x = 0, then it again increases from x = 0 to x = 2 and then it again decreases.

Therefore, we get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

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Answer:

-7

Step-by-step explanation:

f(x)=4x+5
f(-3)=4x+5
=4(-3)+5
-12+5
f(-3)= -7

The "x" in f(x) is the "x" in the equation

By critically observing the graph shown above, the set of ordered pairs include the following:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.

Note: Let each box/cell in the graph represent 1 unit.

By critically observing the graph shown above, we can logically deduce that the set of ordered pairs include the following:

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Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

-7 + 3 = -4

-11 + 9 = -2

-4 + -2 = 6

Mr. Farley used 0.4 pounds of hamburger per patty.

The unitary method is a technique used to find the solution by first finding the value of a single unit and then multiplying the value to get the required answer.

Here, we are given that Mr. Farley used 4 pounds of hamburger to

make 10 hamburger patties.

Given that all of these patties are of the same size, an equal amount of hamburger will be used to make each patty.

We have,

For 10 patties, we need ⇒ 4 pounds of hamburger.

Therefore, for 1 patty we will need ⇒ 4/10 pounds

= 0.4 pounds

Thus, Mr. Farley used 0.4 pounds of hamburger per patty.

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Answer:57368

Step-by-step explanation:

put all them on top like this 573                                                                                                                                                                       you can do this                     68

Answer:

It literally means either find out what the fractions divided by each other would be or find the answer to the fraction.

Ex: 5/10 divided by 1/2= 1

Ex: 5/10 is equal to 0.5

Step-by-step explanation:

Answer: means either find out what the fractions divided by each other would be or find the answer to the fraction.

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Formula

h(x) = 4x + 3

Givens

x = 4

Comment

h(x) is the same thing as y. So the equation can be written as y = 4x + 3

Now it is a simple matter of solving 4x  + 3 given that x = 4.

Solution

f(4) = 4*4 + 3          Combine

f(4) = 16 + 3            Add

Answer

f(4) = 19

It is given that Dodi has two cups of liquid starch

2 cups =16 fluid ounces

1 container  can hold 6 fluid ounces

We are required to find that how many containers are required

1 container contains 6 ounces

Hence 16 ounces will be contained in 3 containers

Hence Dodi will required 3 containers.

Disclaimer:

The question is incomplete and jumbled

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So, we are to solve: [tex] {8}^{15} \div {8}^{7} \times 8[/tex]

Using the exponential rule of multiplication and division with the same bases, which are:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

and:

[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]

Therefore:

[tex] {8}^{15} \div {8}^{7} \times {8}^{1} = {8}^{15 - 7 + 1} [/tex]

→[tex] {8}^{9} = 134217728[/tex]

Therefore: 134217728 is the final answer

We get the distance between the coordinates of the point S and T as 5 √2 units.

We are given the coordinates of two points as:

S = ( - 2, 4 )

T = ( 3, 9 )

We have to find the distance between the points S and T.

We will use the distance formula for this.

Distance = √(x₂ - x₁)² + ( y₂ - y₁)²

Here, we have:

x₁ = -2

x₂ = 3

y₁ = 4

y₂ = 9

Substituting the values in the formula, we get that:

Distance = √(3 + 2)² + ( 9 - 4)² units

Distance = √(5)² + ( 5)² units

Distance = √25 + 25 units

Distance = √50 units

Distance = 5 √2 units

Therefore, we get the distance between the coordinates of the point S and T as 5 √2 units.

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The compound inequality is: x<20 and x>10

Given,  a quantity of x is greater than 10 and less than 20.

A compound inequality (also known as a compounded inequality) is created when two or more inequalities are coupled with and. One part of an inequality must be true for a value to be a solution to an or inequality. It must make both parts true in order to be the solution to an inequality. X<3 or X>2, for instance.

Divide a compound inequality into two independent ones before attempting to solve it. Choose either a union of sets ("or") and an intersection of sets as the appropriate response ("and"). Then, resolve the graph and all inequalities.

Simply put, a compound inequality is more than one inequality that we want to address simultaneously. When referring to the resolution of both inequalities, we can either use the term "and" or "or."

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The population of Tacoma in 2017 would be 865,527.

If the population grows by 9% every year, the population would grow at a compound rate each year and the equation that can be used to determine the population in 2017 would be an exponential equation.

Compound growth is when both the existing population and the increase in population every year.

The equation that can be used to determine the population of Tacoma in 2017 is:

The formula for calculating future value:

FV = P (1 + r)^n

Where:

200,000 x (1 + 0.09)^17

200,000 x (1.09^17) = 865,526.68

In order to round  865,526.68 to the nearest whole number , look at the tenth figure, if it is greater or equal to 5, add one to the units digit and change the tenth and hundredth digit to 0. So,  865,526.68 becomes  865,527.

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Answer:

45

Step-by-step explanation:

=4+10×2÷4+36

=4+5+36

=45

Answer: 144

Step-by-step explanation:

Product =(12^-5)*(12^7) = 144

Using Distributive Property, we have;

13) 5(m - 2) = ((5*m) + (5 * -2))

14) 8(y + 2) = ((8*y) + (8 * 2))

15) -3(m + 4) = ((-3*m) + (-3 * 4))

16) a(a + 3) = ((a*a) + (a * 3))

17) h(h - 2) = ((h*h) + (h * -2))

18) 2m(m + 4) = ((2m*m) + (2m * 4))

19) -2(z - 8) = ((-2*z) + (-2 * -8))

20) -4x(x - 10) = ((-4x*x) + (-4x * -10))

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC

13) 5(m - 2) expressed using distributive property is;

((5*m) + (5 * -2))

14) 8(y + 2) expressed using distributive property is;

((8*y) + (8 * 2))

15) -3(m + 4) expressed using distributive property is;

((-3*m) + (-3 * 4))

16) a(a + 3) expressed using distributive property is;

((a*a) + (a * 3))

17) h(h - 2) expressed using distributive property is;

((h*h) + (h * -2))

18) 2m(m + 4) expressed using distributive property is;

((2m*m) + (2m * 4))

19) -2(z - 8) expressed using distributive property is;

((-2*z) + (-2 * -8))

20) -4x(x - 10) expressed using distributive property is;

((-4x*x) + (-4x * -10))

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Answer:

x = -17

Step-by-step explanation:

You can plug in answer choices, or you can get x by itself.

I got x by itself because it is faster. Simply subtract 15 from both sides.

So, you would get x = -2 - 15. Keep change change to subtract negative numbers => -2 + -15 which equals to -17.

So x = -17.

You can also plug it in: 15 + -17 does equal -2.

The solution to the geometric sequence in the question are;

First part;

r = 3

[tex]a_{8} = 8748 [/tex]

Second part;

r = 4

[tex]a_{6} = 9216 [/tex]

Practice:

r = 8

[tex]a_{7} = 0.3125 [/tex]

Third part;

Please see the detailed reasons in following section

Fourth part;

[tex] {a}_{n} = 4 × {a}_{n-1}[/tex]

[tex] {a}_{n} = 0.2 × {a}_{n-1}[/tex]

First part;

The formula for geometric progression can be presented as follows;

[tex] a_{n} = a_{1} \times {r}^{n - 1} [/tex]

[tex]a_{4} =108 = a_{1} \times {r}^{4 - 1} [/tex]

Where;

[tex]a_{1} = 4 \: and \: a_{4} = 108[/tex]

We have;

[tex]a_{4} =108 = 4 \times {r}^{4 - 1} = 4 \cdot {r}^{3} [/tex]

Which gives;

[tex] {r}^{3} = \frac{108}{4} = 27[/tex]

[tex]r = \sqrt[3]{27} = 3[/tex]

r = 3

Therefore;

[tex]a_{8} = 4 \times {3}^{7} = 8748 [/tex]

Second part;

Where;

[tex]a_{1} = 9 \: and \: a_{3} = 144[/tex]

Therefore;

[tex] {r}^{2} = \frac{144}{9} = 16[/tex]

[tex]r = \sqrt{16} = 4[/tex]

r = 4

Which gives;

[tex]a_{6} = 9 \times {4}^{5} = 9216 [/tex]

Practice;

[tex]a_{1} = 3 \: and \: a_{4} = 1536[/tex]

Therefore;

[tex] {r}^{3} = \frac{1536}{3} = 512[/tex]

[tex]r = \sqrt[3]{512} = 8[/tex]

r = 8

[tex]a_{1} = 20 \: and \: a_{3} = 5[/tex]

Therefore;

[tex] {r}^{2} = \frac{5}{20} = 0.25[/tex]

[tex]r = \sqrt{0.25} = 0.5[/tex]

Which gives;

[tex]a_{7} = 20 \times {0.5}^{6} = 0.3125 [/tex]

Third part

Recursively means expression in terms of previous terms

The meaning of the equation is that each term of a geometric sequence is given by the product of the common ratio and the previous term

Fourth part;

The recursive formula for the sequence, {2, 8, 32, 128...} is found as follows;

r = 8/2 = 4

Therefore;

[tex] {a}_{n} = 4 × {a}_{n-1}[/tex]

Part;

The sequence is {200, 40, 8, 1.6...}

The common ratio is; 40/200 = 0.2

The recursive formula is therefore;

[tex] {a}_{n} = 0.2 × {a}_{n-1}[/tex]

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