which of the following represents the ratio of the short leg to the hypotenus in the right triangle shown below​.


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The ordered pairs (x, y) which are the solutions to the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)

Given,

The equation: 4x - 5y = 24

We have to find the ordered pairs in the form (x, y) which are the solutions to the equation:

Lets check:

Option A: (6, 0)

Substitute this in the equation:

We get

4 × 6 - 5 × 0 = 24

24 - 0 = 24

24 = 24

(6, 0) satisfies the equation.

Option B: (4, 8)

Substitute this in the equation:

We get

4 × 4 - 5 × 8 = 24

16 - 40 = 24

-24 ≠ 24

(4, 8) does not satisfies the equation.

Option C: (1, -4)

Substitute this in the equation:

We get

4 × 1 - 5 × -4 = 24

4 - (-20) = 24

4 + 20 = 24

24 = 24

(1, -4) satisfies the equation

Option D: (-9, -12)

Substitute this in the equation:

We get

4 × -9 - 5 × -12 = 24

-36 + 60 = 24

24 = 24

(-9, -12) satisfies the equation

Therefore, the solutions for the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)

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after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.

We are given the logarithm expression as:

log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24

Now, we can also write 2log₆ 3 as:

2log₆ 3 = log₆ 3²

So, the logarithm expression will become:

log₆ 8 + log₆ 3² + log₆ 12 - log₆ 24

Now, we will use the property that is:

logₐ x + logₐ y = logₐ (x × y)

So, we get the logarithm expression as:

log₆ ( 8 × 3² × 12   / 24)

=log₆ (8 × 9 × 12  / 24)

= log₆ (36)

= log₆ 36

Therefore, after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.

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Using the given linear function, we have that:

a) The equation in standard form is: h - 3.34r - 81.2 = 0.

b) The intercepts are given as follows: h-intercept = 81.2, r-intercept = -24.31.

c) The predicted height is of 164.7 centimeters.

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

y = mx + b

In standard format, the equation is given by:

y - mx - b = 0.

In which:

For this problem, the equation is:

h = 81.2 + 3.34r.

In standard format, the equation is:

h - 3.34r - 81.2 = 0.

From the equation, the h-intercept is of 81.2. To find the r-intercept, we have to solve for r when h = 0, hence:

3.34r + 81.2 = 0.

3.34r = -81.2

r = -81.2/3.34

r = -24.31.

For item c, the radius is given by r = 25, hence the height will be given as follows:

h = 81.2 + 3.34(25) = 164.7.

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Answer:

x=15, y=7

Step-by-step explanation:

Angles that form a linear pair are supplementary, so:

[tex]2(5x-5)+3x-5=180 \\ \\ 10x-10+3x-5=180 \\ \\ 13x-15=180 \\ \\ 13x=195 \\ \\ x=15 \\ \\ \\ \\ 5y+5+20y=180 \\ \\ 25y+5=180 \\ \\ 25y=175 \\ \\ y=7[/tex]

Answer:

The answer is 1

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: f = 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Let's consider two points (1 , 3) and (7 , f), now we can write the slope (m) of line in form of these points as :

[tex] \qquad \tt \rightarrow \: m = \cfrac{y2 - y1}{x2 - x1} [/tex]

[tex]\qquad \tt \rightarrow \: - \dfrac{1}{6} = \dfrac{f - 3}{7 - 1} [/tex]

[tex]\qquad \tt \rightarrow \: - (7 - 1) = 6(f - 3)[/tex]

[tex]\qquad \tt \rightarrow \: - 6 = 6(f - 3)[/tex]

[tex]\qquad \tt \rightarrow \: f - 3 = - \dfrac{6}{6} [/tex]

[tex]\qquad \tt \rightarrow \: f - 3 = - 1[/tex]

[tex]\qquad \tt \rightarrow \: f = - 1 + 3[/tex]

[tex]\qquad \tt \rightarrow \: f = 2[/tex]

Value of f is 2, so the point is : (7 , 2)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

the slope of the line on the graph is 3 .

Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.

to find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .

the points i m choosing is (-2,0) and (-1,3)

now for finding the slope we will use the formula

m = (y2-y1)/(x2-x1)

m = (3 - 0 ) / (-1+2)

m = 3 / 1

m = 3

so the slope of the line on the graph is 3 .

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Prove that x = 50 in the following equation: 1/5x – 5 = 5

Write the equation:

1/5x – 5 = 5

Add 5 to both sides:

1/5x – 5 + 5 = 5 + 5

1/5x = 10

Multiply each side by 5:

5 × 1/5x = 10 × 5

–5 + 5 cancels out, leaving you with:

1x = 10 × 5

1x = 50

Divide both sides by 1 to get x:

1x/1 = 50/1

The 1 cancels out:

x = 50/1

Answer:

x = 50 ✔

Check your work by plugging in 50 as x:

1/5x – 5 = 5

1/5 × 50 – 5 = 5

Multiply:

1/5 × 50/1 – 5 = 5

50/5 – 5 = 5

Get rid of the fraction by dividing:

50 ÷ 5 = 10

10 – 5 = 5

Subtract:

10 – 5 = 5

5 = 5 ✔

I have just proven that x = 50 because the answer I got when I checked my work was balanced. Hope that helps! Have an amazing rest of your day! :)

The number of weeks that they will they have same number of baseball cards is 5 weeks.

From the information given, Ty and Elijah each decide to collect baseball cards. It should take about Ty has 37 cards and Elijah has 42 cards to begin with. Ty decides to buy 4 more cards each week and Elijah decides to buy 3.

Therefore, the expression for Ty will be:

= 37 + 4x

The expression for Elijah will be:

= 42 + 3x

where x = number of cards

Therefore, this will be:

37 + 4x = 42 + 3x

4x - 3x = 42 - 37.

x = 5

The number of weeks is 5.

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Ty and Elijah each decide to collect baseball cards. Ty has 37 cards and Elijah has 42 cards to begin with. Ty decides to buy 4 more cards each week and Elijah decides to buy 3. In how many weeks will they have same number of baseball cards?

The cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

The formula for converting currencies is Original Currency / New Currency = Exchange Rate.

Given:

Cost of 7 t-shirts at a special deal = $97.93

Now, she wants to purchase 5 t-shirts for her family members at this special rate.

Total Cost of 5 shirts in dollars = (97.93 * 5)/7 = $69.95

The exchange rate of the currency is 1 U.S. Dollar = 8.6964 Krona

So, $69.95 = (69.95 * 8.6964)/1 = 608.313 Krona

Therefore, the cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

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Considering the numerical representation of integers with n bits, it is found that 8 bits would have to be set aside in order to store the number of high school students taking CS105 across the nation.

For this problem, we work with unsigned numbers, excluding negatives, as the number of students is a discrete amount that starts with 0 and increases by 1 for each new student.

For unsigned integers with n bits, we have that:

For this problem, we want to represent an amount of 220, hence the number of bits needed is found as follows:

2^n - 1 ≥ 220

2^n ≥ 221

log2(2^n) ≥ log(2)(221)

n ≥ 7.8.

The number of bits cannot be a decimal amount, hence n is rounded up, and thus, 8 bits are needed to represent the amount.

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well, the bill was $59.17, if we round it by the "tens", the closest to 59 is 60, since 59 is farther from 50 but closer to 60, so it rounds up to 60

[tex]50\stackrel{farther}{\rule[0.35em]{18em}{0.25pt}59.17}\stackrel{closer}{\rule[0.35em]{2em}{0.25pt}}60 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]

The nonlinear system of the equation has two solutions as it intersects at two points.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

From the given figure we observe that the straight line intersects the parabolic curve at two distinct points, Therefore this nonlinear system of equation has two solutions.

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c = All real numbers are solutions.

How is the equation 8(c - 9) = 6(2c - 12) - 4c solved?

8(c - 9) = 6(2c - 12) - 4c

8c- 72 = 12c- 72- 4c

8c- 72 = 8c - 72

0=0

L.H.S = R.H.S

Both sides are equal and this stands true for all real number values as c.

For example:

Let c = 10

8(10) - 72= 8(10) - 72

8 = 8

L.H.S = R.H.S

What are real numbers?

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Hello!

To find f(12):

 ⇒ must plug in '12' into the x's position in the equation

  [tex]f(12)=-2(12) +1=-24+1=-23[/tex]

Hope that helps!

The value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that:

The quadratic equation is:

y² = 144

As we know, the polynomial equation is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

Taking square root on both sides:

y = ±√144

y = ±12

Thus, the value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

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The first term of the geometric progression will be 128.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

Given that the common ratio of the geometric series is ( 1 / 4 ) and the sum of the first four terms is 170.

The first term of the geometric series will be calculated as:-

[tex]S_n = a_1\dfrac{(r^n-1)}{r-1}[/tex]

[tex]170 = a_1\dfrac{(\dfrac{1}{4}^4-1)}{\dfrac{1}{4}-1}[/tex]

a₁ = ( 170 x 64 ) / 85

a₁ = 2 x 64

a₁ = 128

Therefore, the first term of the geometric progression will be 128.

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The value of x that makes this equation (X-2)/2= (X+4)/4  to be true is 8.

An equation ca be described as the mathematical terms which can contains different digits as well we a as alphabet and it can simplified so that a particular expression or term can be found, in the given equation we were told to find the value of x by simplify the equation which is done below.

(X-2)/2= (X+4)/4

Then if we cross multiply we will have

(4x - 8) =(2x+8)

then we can simplify further and collect the like terms which is

2x=16

x=8

There, the correct option is B

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Based on the height climbed, and the yards climbed per feet, the distance west you would have moved from the foot of the hill is 66 yards

For every 2 feet that you climb higher, you would be moving about 11 yards to the west.

This means that the distance climbed is directly proportional to the number of yards to the west.

Every 2 feet that one climbs higher will meant they move 11 yards to the west so the yards to the west for 12 feet is:

=  12 / 2 x 11

= 6 x 11

= 66 yards

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The answer is 3.4

Because the 3 is in the tenths place. Since 6 is greater than 5 it gives 1 to the 3 which makes it a 4.

From the given graph, the numeric values of the expressions are given as follows:

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

On the graph of the function, the equivalent to this is that we have to find where the x-axis has the value, and find the value of y for which the function passes through the y-axis.

From the graph, when x = -1, f(x) passes the point at y = 12, hence f(-1) = 12.

For the second item, applying the same logic, we have that:

Hence:

f(1) - g(1) = 10 - 2 = 8.

For the third item, we have to look at the graph of g(x), and find the value of x when y = 4, hence g(x) = 4 when x = 2.

For the fourth item, the functions intersect at point (3,8), hence f(x) = g(x) when x = 3.

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Answer:

False

Step-by-step explanation:

Scale copies are indicated by proportional changes in the lengths of the sides of a figure. in this image, we can see that the bottom side of the figure is different while the shorter segments on each figure are the same length. Because of this, the answer is False as they can not be scale copies.

Using percentages we can conclude that the total commission the salesman gets is of $540.

So, the total commission:

5% of 10,000 -

8% of remaining (10,500 - 10,000 = 500) $500 -

Total commission: $500 + $40 = $540

Therefore, using percentages we can conclude that the total commission the salesman gets is of $540.

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Inversely proportion - The work out value of R and A is 3.6 and 2 respectively.

What is inversely proportion?

They are said to be inversely proportional when one quantity's value rises relative to another's decline or vice versa. It implies that the two quantities behave inherently differently. For instance, time and speed have an inverse relationship. The time decreases as you increase the speed. Inverse proportion, varying inversely, inverse variation, and reciprocal proportion are additional terms used here to describe this kind of proportion.

Given, R [tex]\alpha[/tex] 1/A

R = k/A

When R = 12 and A = 1.5

12= k× 1.5

k= 18

Now, when A=5, R= 18/5 = 3.6

And when R= 9, A = 18/9=2

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Cube roots - The two numbers that are solutions to the equation x³ = 27 are +3 and -3.

What are cube roots?

A number's cube root is a quantity that, when multiplied by itself three or more times, returns the original quantity. The cube root of 27, represented as 327, for instance, is 3 because 3 x 3 x 3 = 27 = 33 when we multiply 3 by itself three times. As a result, we can state that the cube root yields a value that is essentially cubed. Here, 27 is referred to as the ideal cube. We may deduce what the cube's root is from the word "cube root." It denotes the integer that brought about the cube under the root. Typically, we use the prime factorization technique to determine the cubic root of perfect cubes. We can discover the importance of square root in a similar way.

We are given the equation,

[tex]x^{3}[/tex] = 27

taking cube root on both the sides to find the value of x,

we get,

x = ±[tex]\sqrt[3]{27}[/tex]

further solving,

x = ±3.

Hence the two solutions of the  x³ = 27 equation will be ±3 or +3 and -3.

Because 3x3x3 Equals 27, the cube root of 27 is 3.

Since 4x4x4 = 64, the cube root of 64 is also 4, and so on.

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LET US FIRST FIND m<FEG using sum of angles in a triangle

[tex]58 + 90 + < feg = 180 \\ < feg = 180 - 90 - 58 \\ < feg = 32[/tex]

NOW WE CAN SEE THAT <FEG +<E =180° BECAUSE THEY ARE ON A STRAIGHT LINE.

[tex] < feg + 4x = 180 \\ 32 + 4x = 180 \\ 4x = 180 - 32 \\ 4x = 148 \\ \frac{4x}{4} = \frac{148}{4} \\ x = 37[/tex]

THEREFORE x=37°