Write the equation for each line. Use slope-intercept form. m = 4/5 and the y -intercept is (0,7) .

The product of given integers 28, -5 and 17 is -2380.

The given numbers are the product of 28, -5 and 17.

We need to find the product of the given numbers.

The product of two integers with like signs is equal to the product of their absolute values.

(i) The product of two positive integers is positive.

(ii) The product of two negative integers is positive.

(iii) The product of one positive and one negative integer is negative.

The product of 28, -5 and 17 is calculated as follows:

Now, 28 × (-5) × 17

= (28 × (-5)) × 17

= (-140) × 17

= -2,380

Therefore, the product of given integers 28, -5 and 17 is -2380.

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Answer:

-2380 (None of the option)

Step-by-step explanation:

Now we have to,

→ find the product of 28, -5 and 17.

Let's solve the problem,

→ x = 28 × ((-5) × 17)

→ x = 28 × -85

→ [ x = -2380 ]

Hence, the answer is -2380.

The distance between the pair of parallel lines given by the equations y = -4x - 6 and y = -4x + 11 is √17 units.

The shortest distance between two parallel lines is the length of the perpendicular segment between them.

First, determine the slope of the segment perpendicular to the parallel lines.

y = -4x - 6

m = -4

slope of perpendicular segment = 1/4

Consider a point that one of the equation passes through. Line y = -4x - 6 passes through (0 , -6).

Write the equation for the perpendicular line using the point-slope form.

(y - y1) = m(x - x1)

(y - -6) = 1/4(x - 0)

y + 6 = 1/4 x

y = 1/4x - 6

Determine the point where this perpendicular line intersects with the 2nd parallel line by equating both equations.

y = 1/4x - 6 = -4x + 11

1/4x + 4x = 11 + 6

17/4 x = 17

x = 4

Substitute this value of x in the previous equations,

y = 1/4x - 6

y = 1/4(4) - 6

y = 1 - 6

y = -5

Now, the distance between the two points (0 , -6) and (4 , -5) is the distance between the two parallel lines.

d = √(x2 - x1)^2 + (y2 - y1)^2

d = √(4 - 0)^2 + (-5 - -6)^2

d = √4^2 + 1^2

d = √16 + 1

d = √17

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The solution to the linear inequation is x>1/2 .

It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

For solving this exercise, it is necessary to find a number solution for the given inequality.

15−2(2x−1)<15

15-4x+2 < 15

-4x < -2

4x > 2

x > 2/4

x> 1/2

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The inequality can be simplified to:

x > -1

And the graph can be seen in the image below.

Here we have the inequality:

5x + 8 > 3

To solve this, we need to isolate the variable x in one side of the inequality.

5x + 8 > 3

We subtract 8 in both sides:

5x > 3 - 8

5x > -5

Now we divide both sides of the inequality by 5.

x > -5/5

x > -1

Now, to graph this, we need to do an open circle at x = -1, and shade all the region to the right of this point, like in the example below.

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Answer:

B -3>(-11)

Step-by-step explanation:

because of integers

Answer:

1) m = rise/run = x - x/y - y

2) Slope(m) = -2

    Question 2

m = 1 - (-5)/ -3 - (0)

m = 1 + 5/-3 - (0)

m = 6/-3 - (0)

m = 6/-3 + 0

m = 6/-3

= -2

Answer:

$650

Step-by-step explanation:

You need to get at least $65 in savings to make the card worthwhile

10% of x is 65

multiply both sides by 10

100% of 10x is 65

get rid of 10x since we don't need that

100% of our answer is 650

Answer:

Question 4 : 10 m

Question 5 : Square root 37

Step-by-step explanation:

QUESTION 4: So for the this one here we need to make a drawing (unfortunately). Lets break down the question because having a math problem with a ton of words is confusing sometimes. So we have a pole that is 8m high, so we can draw that out. So we take some cable and go 6 m from the bottom of the pole. So now we want to know how long the cable is and if we go from the top of the pole to the bottom 6m away it looks like this. (Below I'll put what I have written) Since now it's a 90 degrees angle there is a specific formula we can use in situations like this. Where we know 2 sides and need 1 more. a^2 + b^2 = c^2 should look familiar if it doesn't its all good! :D a^2 + b^2 = c^2 is called 'Pythagorean's theorem' (we don't really need to know that part) but basically we use it whenever we need to figure out a side when we already know the other two. We know that the straight line is 8, and the horizontal line is 6. So we can use that formula to get the last number. just know that whenever we have the right triangle, we can use the a^2 + b^2 = c^2 to get all the sides for it. The a and b in the formula are always the straight lines. The c is always the slanted line (the red line I drew). We don't know what it is, so we'll just put c^2 into our equation but we can solve for it! So 8^2 would equal to 64. 6^2 would equal to 36. 64 + 36 here gets us 100. Here's another trick you might need to memorize. Whenever there is a number squared like c^2, we can take the square root of both sides to get rid of it. So c^2 just becomes c. It's a little weird but very useful to remember.  But if you remember the a^2 + b^2 = c^2 and use that square root technique you can get an A+ every time. :D Now all we need to know is the square root of 100. It's a big one so using a calculator is fine, here its just 10. Therefore our answer is 10.

QUESTION 5:  We'll start off by reading 'distance between points' is a big thing to note here. There is a formula that we can directly use here. (I'll write under the picture in black). So distance between points always uses this formula: (In black). Okay, so the formula in black has more letters in it (which sucks) but we can break it down. When we have numbers like this (3, 0) it means (x, y). So I wrote down what the x1, y1, x2, y2, are here. X1 is just the first number, y1 is the second, x2 is the third, and y2 is the fourth. I just plugged in all the numbers from above in the order we put (x2, x1, y2, y1). Basically we can just solve this now! As of right now we'll need to solve (-3 -3)^2 when we solve that we should get 36. Next we're gonna solve  (-1 - 0)^2 and we should get the answer of 1. Now we need to solve 36 +1 and we should know that it equals 37. Therefore we'd get answer: square root 37.

Answer:

Step-by-step explanation:

45 / 2.25 = 20 games

A cyclic polygon is inscribed in a circle, and the circle is its circumscribed circle or circumcircle. The radius of the inscribed circle or sphere, if it exists, is the inradius or filling radius of a given outer figure.

An inscribed angle in geometry is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle formed by two given points on a circle at a given point on the circle.

An inscribed polygon is one with all of its vertices on a circle. The circle is encircled by the polygon, and the polygon is encircled by the circle. (It's a polygon inside a circle) A circumscribed polygon is one with each side tangent to a circle.

A cyclic polygon is inscribed in a circle, and the circle is its circumscribed circle or circumcircle. The radius of the inscribed circle or sphere, if it exists, is the inradius or filling radius of a given outer figure.

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Simplification form of the given complex fraction [tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }[/tex] is  (xy)/ (xy+1).

As given in the question,

Given complex fraction is [tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }[/tex]

Simplify the given complex fraction by taking the least common multiple,

[tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }\\\\\\=\frac{x}{\frac{1}{\frac{xy+1}{y} } } \\\\\\=\frac{xy}{xy+1}[/tex]

Therefore, the simplification form of the given complex fraction [tex]\frac{x}{\frac{1}{x+\frac{1}{y} } }[/tex] is  (xy)/ (xy+1).

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The equation of the line 5y = -3x - 10 expressed in slope-intercept form is y = -3/5 x - 2 with a slope equal to -3/5.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 5y = -3x - 10, which the variable y is already isolated in one side, divide both sides by 5.

5y = -3x - 10

y = -3/5 x - 2

Hence, the equation of the line in slope-intercept form is y = -3/5 x - 2 where the slope, m, is equal to -3/5.

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Answer:

128,256,512

Step-by-step explanation:

Because 64×2=128, 128×2=256,...

If  x = ≥ 7/3 this equation gives an Imaginary value for y, so it is still a function; it is just not a real valued function.

What is function explain?

the Domain of x will be limited (assuming by "function" we mean a "real value function")

y² = 3x - 7

[tex]y = \sqrt{3x - 7}[/tex]

which gives a unique value provided x = ≥ 7/3

If  x = ≥ 7/3 this equation gives an Imaginary value for y, so it is still a function; it is just not a real valued function).

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Using the Fundamental Counting Theorem, it is found that 1,835,008 numbers are possible.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem, we have that:

Hence:

N = 7 x 8 x 8 x 8 x 8 x 8 x 8 = 1,835,008.

1,835,008 numbers are possible.

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Answer:

-41.6 repeating

Step-by-step explanation:

Not sure if this is for homework or anything, but...

y3=-125

y/3=-125/3

y=-41.6 repeating

Answer:

-5

Step-by-step explanation:

5^3 is 5×5×5

Which gives 125

since the y3 = −125.

then y=-5

The equation of line for the given values of m and y - intercept is y = 6x + 5,

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The standard equation of the line is y = mx + c

Now, we are given,

m = 6 and y - intercepts = (0,5)

Now, putting it in the equation,

y = 6x + 5, which is our desired equation

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The final answer in scientific notation is 6×10¹⁴.

When the numbers are in scientific notation, the multiplication is accompanied with addition of exponents. So, the numbers will be multiplied and exponents will be added.

Writing the equation to find the product by performing the calculation -

Product = 2×10⁷ × 3×10⁷

To perform addition of exponent of the number 10⁷ and to perform the multiplication of the number rewriting the equation

Product = (10⁷⁺⁷)×(2×3)

Adding the exponent and performing multiplication of the numbers to find the product of the given numbers in scientific notation

Product = 10¹⁴×6

Hence, the final answer on multiplication of given numbers is 6×10¹⁴.

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x is equal to the -10 or less than the -10

Inequality:

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. Inequalities can be posed either as questions, much like equations, and solved by similar techniques, or as statements of fact in the form of theorems. For example, triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than or equal to the length of the remaining side. The mathematical analysis relies on many such inequalities (e.g., the Cauchy-Schwarz inequality) in the proofs of its most important theorems.

In mathematics, an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.[1] It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities:

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

In either case, a is not equal to b. These relations are known as strict inequalities,[1] meaning that a is strictly less than or strictly greater than b. Equivalence is excluded.

In contrast to strict inequalities, there are two types of inequality relations that are not strict:

The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).

The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).

The relation not greater than can also be represented by a ≯ b, the symbol for "greater than" bisected by a slash, "not". The same is true for not less than and a ≮ b.

The notation a ≠ b means that a is not equal to b; this inequation sometimes is considered a form of strict inequality.[2] It does not say that one is greater than the other; it does not even require a and b to be member of an ordered set.

In engineering sciences, less formal use of the notation is to state that one quantity is "much greater" than another,[3] normally by several orders of magnitude.

The notation a ≪ b means that a is much less than b.[4]

The notation a ≫ b means that a is much greater than b.[5]

This implies that the lesser value can be neglected with little effect on the accuracy of an approximation (such as the case of ultra relativistic limit in physics).

In all of the cases above, any two symbols mirroring each other are symmetrical; a < b and b > a are equivalent, etc.

Solution :

1/2x+8 [tex]\leq[/tex] 3

1/2x [tex]\leq[/tex] 3-8

1/2x[tex]\leq[/tex]-5

x  [tex]\leq[/tex] -5 x 2

x[tex]\leq[/tex] -10

x is equal to the -10 or less than the -10

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The area of the polygon become 24.5.

According to the statement

We have to find that the area of the polygon.

So, For this purpose, we know that the

Polygon is a plane shape (two-dimensional) with straight sides.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

From the given information:

The given vertices are:

J(-3,\ 4),\ K(4,\ 4),\ L(3,-3)

And then the base of the polygon become:

Base = [tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]

Then

Base = [tex]\sqrt{(-3 - 4)^{2} + (4 -4)^{2} }[/tex]

Base = 7

Then

Height = [tex]\sqrt{(y_{1} - y_{2})^{2} +(z_{1} - z_{2})^{2} }[/tex]

Height = [tex]\sqrt{(4 - 4)^{2} +(4 - (-3))^{2} }[/tex]

Height = 7

Then the area of the polygon becomes:

Area = 1/2 *Base*Height

Area = 1/2 *7*7

Area = 1/2*49

Area = 24.5

Thus, The area of the polygon become 24.5.

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The value of different f(x) for different value of 'x' in the given graph is f(-3) = -1 , f(-2)=0. f(-5)= 3, f(-4) =0

Given that, The f(x) graph we can observe that it is a shifted parabola.

We can translate the parabola vertically to produce a new parabola that is similar to the basic parabola. The function [tex]y=x^2 + b[/tex] has a graph which simply looks like the standard parabola with the vertex shifted b units along the y-axis. Thus the vertex is located at (0,b). If b is positive, then the parabola moves upwards and, if b is negative, it moves downwards.

Similarly, we can translate the parabola horizontally. The function[tex]y =(x-a)^2[/tex]has a graph which looks like the standard parabola with the vertex shifted a units along the x-axis. The vertex is then located at (a,0). Notice that, if a is positive, we shift to the right and, if a is negative, we shift to the left.

So, for the given question

b = parabola shift unit along y-axis = -1 units

a = parabola shift unit along x-axis = -3 units

So, equation of parabola = [tex]f(x)=y = (x+3)^2-1[/tex]

Now,

for x = -3. f(-3)=[tex](-3+3)^2-1=-1[/tex]

So, f(-3)= -1

x = -2. f(-2)=[tex](-2+3)^2-1=0[/tex]

So, f(-2)= 0

x = -5. f(-5)=[tex](-5+3)^2-1 = 3[/tex]

So, f(-5)= 3

x = -4. f(-4)=[tex](-4+3)^2-1=0[/tex]

So, f(-4)= 0

Therefore, from the graph f(x),  value of f(x) for diiferent value of x is f(-3)=-1. f(-2)=0.f(-5)=3.f(-4)=0.

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[tex]y = 49x^2 - 1\implies \stackrel{y}{0}=49x^2 -1\implies 1=49x^2\implies \cfrac{1}{49}=x^2 \\\\\\ \sqrt{\cfrac{1}{49}}=x\implies \cfrac{\sqrt{1}}{\sqrt{49}}=x\implies \cfrac{1}{7}=x[/tex]

The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.

The coordinates of the orthocenter of Δ RST is (3, 6).

An orthocenter of a triangle is the point at which altitudes drawn perpendicular from the vertex to the opposite sides of a triangle intersect. A triangle typically has three altitudes, and the intersection of all three altitudes is known as the orthocenter.

The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.

The midpoint of AD is (-1+3/2, 11+1/2) or (1, 6). Note that DC is a line that connects the vertex C and D, the midpoint of AB. The distance from D(1, 6) to C(7, 6) is 7 - 1 or 6 units.

If P is the centroid of the triangle XYZ, then PC = (2/3) DC.

So, the centroid is 2/3(6) or 4 units to the left of C. The coordinates of the centroid (P) are (7 - 4, 6) or (3, 6).

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The standard deviation of the number of residents in the sample who were born in Colorado is 7.82

PC = Indicates the real population of residents born in Colorado  

PC = 0.427 shows estimated proportion for residents born in Colorado

nC = 250 sample size selected

Let X = random variable of interest

n = 250 , p = 0.427

Now the probability mass function is given by

P(X) =  (nCx)(p)^x(1-p)^n-x

Here (nCx) means combinatory and its formula is:

nCx = n! / (n-x)!x!

Let's calculate the expected value by the given formula.

E(X) = np = 250 x 0.427 = 106.75

The standard deviation for the random variable is given by:

sd(X) = √np(1-p)

sd(X) = √250 x 0.427 x (1-0.427) = 7.82

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The additional cost required to pay for a 30 minutes call is 49.4 cents.

What is a word problem?

A word problem is defined as a mathematical problem written in form of words or sentences. These are assigned to students to determine their hold on the concepts.

Calculation of cost of calling 30 minutes

The cost for calling 4 minutes is 7.6 cents

The cost for calling 1 minute is 7.6 / 4

= 1.9

The cost for calling 30 minutes = 1.9 × 30

= 57 cents

The word 'more' in the word problem specifies the additional cost needed to make a 30-minute call i.e. it requires the difference between the cost of a 4-minute call and a 30 minutes call.

More cost = còst for calling 30 minutes- cost for calling 4 minutes

= 57 - 7.6

= 49.4 cents

Hence, the additional cost required to pay for a 30 minutes call is 49.4 cents.

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Answer:

AH

Step-by-step explanation:

the two lines that are vertical on both lines show that they are both congruent (the same length)

Using adjacent angles, The value of a given figure, the value of E = 132°

What is an Adjacent angle?

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.

draw a line EOF parallel to AB

now EF || AB and CD||AB

∵ AB || EF and AO is a transversal

we have

∠AOF+∠OAB=180°

∠AOF+108 = 180 °

∠AOF=72 °

∵ EF|| CD and OC is transversal

so

∠COF+∠OCD=180°

∠COF+112° = 180°

∠COF=60°

∴∠AOC=∠AOF+∠COF

=72 ° + 60°

=132°

Hence the value of E = 132°

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Answer:

x

Step-by-step explanation:

When you add them, you get 4/4x which is also known as 1x.

Answer:

-1

Step-by-step explanation:

This quadratic function shows this equation:

[tex]g(x)=(x-3)^2-1[/tex]

But you shouldn't need to know that! By observation, the minimum value of g is -1, because that is the lowest y value at the vertex on the graph! Since this is a parabola, we know that the graph will not have another minimum anywhere else!

Answer:

Step-by-step explanation:

20/3 * (- 21/5) = -84/3 =  - 28