Position and label each triangle on the coordinate plane. (Lesson 4-8)
Right ΔXYZ with hypotenuse XZ, Z Y is twice X Y , and XY is b units long.

The constant of variation in 4 y-5 x=0 is (5/4)

y = kx                           (Where k is the constant)

Here,

⇒ 4y - 5x = 0

⇒ 4y = 5x

⇒ y = 5x/4

⇒ y = (5/4) x

So, k = (5/4)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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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.

The solution of the formula  A = 1/2h(b₁ + b₂) for the indicated variable b₂ is (2A/h) -  b₁.

According to the given question.

We have a formula  A = 1/2h(b₁ + b₂).

Since, we have to solve the given formula A = 1/2h(b₁ + b₂) for the indicated variable b₂.

Therefore, the solution of the formula  A = 1/2h(b₁ + b₂) for the indicated variable b₂ is given by

A = 1/2h(b₁ + b₂)

⇒ 2A = h(b₁ + b₂)   (multiplying both the sides by 2)

⇒ 2A/h = b₁ + b₂    (dividing both the sides by h)

⇒  2A/h -  b₁  = b₂   ( subtracting b₁ from both the sides)

⇒ b₂ = (2A/h) -  b₁

Hence, the solution of the formula  A = 1/2h(b₁ + b₂) for the indicated variable b₂ is (2A/h) -  b₁.

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Part a

x = number of months

43x = amount saved at $43 per month

43x ≥ 250  is the inequality

===============================================

Part b

43x ≥ 250

43x/43 ≥ 250/43

x ≥ 5.81395 approximately

Since x is a positive integer, the value 5.81395 rounds to 6

So it would be x ≥ 6

================================================

Part c

He needs 6 months to be able to save at least $250.

Five months gets him 43x = 43*5 = 215 which is 35 dollars short of the goal of 250.

But 6 months gets him 43x = 43*6 = 258 which is 8 dollars over the goal of 250.

The two consecutive integer numbers are 24 and 25.

We can write the two consecutive integers as x and x + 1, where the larger one is x + 1.

We know that 1/5 of the larger is 7 less than 1/2 of the lesser one, then we can write the linear equation:

1/5*(x + 1) = 1/2*x - 7

1/5*x + 1/5 = 1/2*x - 7

So we need to solve that for x:

1/5 + 7 = 1/2*x - 1/5*x

1/5 + 35/5 = 5/10*x - 2/10*x

36/5 = 3/10*x

(36/5)*(10/3) = x = 24

So the smaller is 24, and the larger is x + 1 = 25.

The two consecutive integer numbers are 24 and 25.

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Answer:

Step-by-step explanation:

2.25 times 9 equals 20.25 dollars hope it helped

The total cost f(x) of the candy is given by the expression -0.7x + 35, where x is the weight of the less expensive candy

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the weight of the less expensive candy and y represent that of the other candy, hence:

x + y = 10

y = 10 - x

Total cost = f(x)

Hence:

f(x) = 2.8x + 3.5(10 - x) = -0.7x + 35

The total cost f(x) of the candy is given by the expression -0.7x + 35, where x is the weight of the less expensive candy

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From the calculation below, the number of books bought by Mr. Ankomah was 87 books.

Let x represent present the number of books bought.

Therefore, we have:

Number of books sold = x - 12

Total revenue from units sold = Number of books sold  * Unit selling price = (x - 12) * 7 = 7x - 84

Total cost of units sold = Number of books sold  * Cost price per unit = (x - 12) * 5 = 5x - 60

Profit = Total revenue from units sold - Total cost of units sold ........... (1)

Since he made a profit of Ghc150.00, we substitute all the relevant values into equation (1) and solve for x as follows:

150 = (7x - 84) - (5x - 60)

150 = 7x - 84 - 5x + 60

150 + 84 - 60 = 7x - 5x

174 = 2x

x = 174 / 2

x = 87

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The solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

According to the given question.

We have a linear equation in one variable.

4y - 6 = 2y + 8

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is given by

4y - 6 = 2y + 8

⇒ 4y - 2y - 6 = 8     ( subtracting 2y from both the sides)

⇒ 2y -6 -8 = 0           (subtracting 8 from both the sides)

⇒ 2y - 14 = 0

⇒ 2y = 14

⇒ y = 14/2

⇒ y = 7

Hence, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

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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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Answer:2,166

Step-by-step explanation:

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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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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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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The equation of the circle (x + 3)^2 + (y - 5)^2 = 38 has a radius of √38 and a center located at (-3 , 5).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x + 3)^2 + (y - 5)^2 = 38, is in standard form, then

h = -3

k = 5

r = √38

Hence, the equation of the circle (x + 3)^2 + (y - 5)^2 = 38 has a radius of √38 and a center located at (-3 , 5).

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Answer:

52 cm

Step-by-step explanation:

since all sides of a square is equal u do 4*13 and get 52 cm!

Answer: 52

Step-by-step explanation:

Square has 4 equal sides

13 x 4

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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if you already have the answer and just need the graph, you can look for it on Desmos. Just write the answer and it will show you. Hope this helps.

Answer:

I think dividing them by the same number is a solution so , 15/5 to 25/5

= 3:5

Answer:

Step-by-step explanation:

20/3 * (- 21/5) = -84/3 =  - 28

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:

Perhaps this could help :) xx

Answer:

Step-by-step explanation:

A: D:(-6,6)

B: D:(-7,5]

C: Not a function D: -5

D: Not a function D:(-4,4)

E: Not a function D:(0,∞)

F:  D:[0,∞)
G: D:[-3,5)

H: D:(-4,2)

I: D:[-3,4]

J: Not a function D:(-3.-4)

K: D:(-∞,∞)

L: D:(-∞,∞)

Answer:

Step-by-step explanation:

45 / 2.25 = 20 games

Answer:0.86

Step-by-step explanation:

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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According to the given statement the given data is true.

we can see that the number 5 is a perfect square of 25.

Informally: When someone multiplies an integer (a "whole" number, positive, negative, or zero) by itself, mathematics resulting product is known as a square number, a perfect square, or simply "a square." So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.

To check the accuracy of your square, simply calculate the exact square root of something like a given value. If the square root seems to be an integer, your number is the perfect square. Let's compute the squares of something like the following numbers: 49 and 53. 49 = 7 - 7 is an integer number 49 is a perfect square.

As can be seen, the calculated value is:

x²=25 , then x=5

While find the square root of the given number of:

x²=25

x = √25

x=5

So,

we can see that the number 5 is a perfect square of 25.

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Congruent transformations can be divided into three categories: rotation, translation, and reflection. We can accurately characterize translations by using vectors.

What is the name of a congruence transformation?

A congruent transformation, also known as a congruence transformation, is: Isometry's other name; see congruence (geometry).

Is reflection a transition that congruence?

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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]

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

Non-Integer numbers are those that are not whole numbers, whole numbers that are negative numbers, or zero.

The first non-integer number in this pattern is 4.5

The pattern is as follows,

144/2 = 72

72/2 = 36

36/2 = 18

18/2 = 9

9/2 = 4.5.

4.5 is the first non-integer number in this pattern.

Therefore, the first non-integer number in this pattern is 4.5.

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