The longer leg of a right triangle is 7m longer than the shorter leg. The hypotenuse is 9m longer than the shorter leg. Find the side lengths of the triangle.

Answer:

Look at the variables and numbers in the equation, and what it equals

Step-by-step explanation:

Expressions that are the exact same have infinite solutions

[tex]5x+3=5x+3[/tex]

Expressions that are different have 1 solution

[tex]6x+7=5x-2[/tex]

Expressions that are the same with different operands have no solution

[tex]5x-3=5x+3[/tex]

Explanation:

The short of it is that when the equations are in the same form, if one equation is the same as or a multiple of the other, there are infinite solutions. If one equation is the same as or a multiple of the other, except for the constant terms, there are no solutions. Otherwise, there is one solution.

Example:

If one equation is x +2y = 3, then you can consider the other equation:

  3x +6y = 9 . . . . 3 times the first equation: infinite solutions

  3x +6y = 6 . . . . 3 times the first equation; constants differ: no solutions

  3x -6y = 9 . . . .  not a multiple of the first equation: one solution

_____

Here's a more formal method.

Put both equations of the linear system of two equations into general form:

  ax +by +c = 0

  dx +ey +g = 0

Perform the following arithmetic:

  p = ae -db . . . . . this is called the system "determinant"

  q = bg -ec

  r = cd -ga

If p = q = r = 0, the equations describe the same line, so there are infinite solutions.

If p = 0 and either of q ≠ 0 or r ≠ 0, the equations describe parallel lines, so there are no solutions.

If p ≠ 0, there is one solution: (x, y) = (q/p, r/p).

_____

Additional comment

This method can always be used to find the solution to a system that is known to have one solution. It often requires fewer arithmetic operations than other solution methods. It is a variation of what is sometimes called the "cross multiplication method."

Answer:

Let x = salary of the architect, in thousands

Let 2x - 25 = salary of a lawyer, in thousands

2x + 2x - 25 = 206 (combined salaries, in thousands)

4x - 24 = 206

4x = 206 - 25 = 181

x = 45.25, in thousands.

The architect earns $45,250 yearly

The lawyer earns $65,500 yearly

If you want to set up a system of equations with 2 variables.

Let x = the salary of the architect, in thousands.

Let y = the salary of the lawyer, in thousands.

x + y = 206

y = 2x - 25

Solving by substitution will yield the same equation as above: x = 45.25 or $45,250

Then y = 2(45,250) - 25,000 = $66,500

Hi!

I can help you with joy!

Remember that

* Zeros in the beginning of decimals are not significant figures.

For example, 0.021 has only 2 significant figures: 2 and 1.

* Zeros in the end of decimals are significant.

For example, 2.100 has 4 significant digits.

Now, let's round 0.02852 to 3 significant digits.

Right now it has 4.

Recall the Rounding Rules:

[tex]\text{5 is followed by a number less than 5, so we round down.}[/tex]

[tex]\text{0.02852 Round down: 0.0285 (Answer)}[/tex]

Hope it helps!

Enjoy your day!

Answered by

~Silent~

The percentage by which it is less than the other is 10%

From the question we are asked to find the percentage of which the difference of the two numbers are. To do this, we take the subtraction of both

110 - 100 = 10

Then we find the percentage of this number.

10/100 * 100 = 10%

To learn more about percentage visit here, https://brainly.com/question/24304697

Answer:

<DEF = 107

Step-by-step explanation:

The way to best solve this problem is by starting with angle F. Remember that all angles in a straight line must add up to 180. So by subtracting 135 from 180 we get 45 for angle F.

180 - 135 = 45

After that, we can figure out the measure of <DEF. All the angles of a triangle must add up to 180. So:

180 - 28 - 45 = 107

Making the answer 107 for the measure of <DEF

Answer:

399.77 yd³

Step-by-step explanation:

Circumference: 2πr

Solve for r:

Solve for volume: 4/3(πr³)

-Chetan K

Answer:

-2y=10-5x

Step-by-step explanation:

5x-2y=10

you want to get the y by itself

so you would subtract the 5x from both sides

-2y=10-5x

Considering the definition of probability, the probability that the next customer will pay with a debit card is [tex]\frac{12}{139}[/tex].

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases.

[tex]P(A)=\frac{number of favorable events}{ total number of possible events}[/tex]

The probability of event A can only be a number between 0 and 1; although it can also be written as a percentage.

In this case, you know:

Replacing in the definition of probability:

[tex]P(A)=\frac{12}{ 139}[/tex]

Finally, the probability that the next customer will pay with a debit card is [tex]\frac{12}{139}[/tex].

Learn more about probability:

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Answer:

420 miles after lunch

Step-by-step explanation:

Day 1 is 630 miles travelled - total amount of travelling.

After lunch is twice the amount of m.

Twice means 2.

So,

2xm + m (they'd have travelled) = 630 total miles

(2xm = 2m & 1m is the same as m)

2m + 1m = 630

3m = 630

÷3

m = 210 miles

Initial miles travelled before lunch was 210.

After lunch is double that amount.

Thus, 210 x 2 = 420 miles

Check:

210 + 420 = 630 miles.

Hope this helps!

Answer:

1 foot is 12 inch so the tail of boeing will be 63 2/3 x 12

Step-by-step explanation:

https://brainly.com/question/3663351

Hoped this helped and have a nice day

Answer:

22

Step-by-step explanation:

Answer: -25

Step-by-step explanation:

-3/5t=15   mulitply both sides of the equation by -5/3.

-5/3x3/5t= -5/3x15   multiplying an even number makes it positive.

t= -5x5   multiply remaining numbers.

Answer: t = -25

Brainliest pls :)

Answer:

[tex]\huge\boxed{\sd -9, \ 1}[/tex]

Step-by-step explanation:

Given quadratic equation is:

x² + 8x - 9 = 0

Using mid-term break formula

x² + 9x - x - 9 = 0 (When we multiply middle terms, we get side terms as answer which is mid term break formula.)

Taking common

x(x + 9) - 1(x + 9) = 0

Take (x + 9) common

(x + 9)(x - 1) = 0

According to zero's method:

Either:

x + 9 = 0      OR    x - 1 = 0

x = -9           OR       x = 1

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer: 12 and 8

Step-by-step explanation:

there not

The integer m whose factors are 15,12,10 and 6 is 60 and 8 is not, therefore, for integer 60, 8 will be not the factor so option (D) is correct.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer ; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

The factors of 10 ⇒ 2 × 5

The factors of 12 ⇒  2 × 2 × 3

The factors of 10 × 12  ⇒  2 × 5 × 2 × 2 × 3

We can make all factors by 2 × 5 × 2 × 2 × 3 like 5 × 3 = 15 , 2 × 2 × 2 = 8.

So find a number whose all will be a factor except one.

The factor of 60 ⇒ 2 × 2 × 3 × 5

We cannot make 8 by this factor but can make 15,12,10,6.

Example 15 = 3 × 5 , 12 = 2 × 2 × 3

Hence "The integer m whose factors are 15,12,10 and 6 is 60 and 8 is not, therefore, for integer 60, 8 will be not the factor".

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Answer:

B is the correct answer

Step-by-step explanation:

B os the correct answer

Answer:

here may be more than one correct answer.  

Cubic, f(x)=x^3

Quadratic, f(x)=x^2

Square root, f(x)=√x

Constant, f(x)=c

Linear, f(x)=x

Step-by-step explanation:

The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.

A function is a relation between a dependent variable f(x) and an independent variable x, where for every value of x in its domain, there is one and only one value of f(x).

The domain of a function is the set of values of x, for which f(x) exists.

The range of a function is the set of values of f(x), in a given domain of x.

We are asked why is the domain of the square root parent function x ≥ 0 and the domain of the cube root parent function all real numbers.

We know that the domain of a function is the set of values of x, for which f(x) exists.

Let the square root parent function be f(x) = √x.

The domain of this function is x ≥ 0, as the square root of negative values does not exist in the real number system.

Let the cube root parent function be g(x) = ∛x.

The domain of this function is all real numbers, as the cube root of all values does exist in the real number system.

∴ The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.

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Answer: y=2/(x-1)

Step-by-step explanation:

We can tell this is a rational function that looks somewhat like y=1/x, execpt that the asymptote is at x=1, not x=0. This means we have y=k/(x-1), where k is a constant.

Substituting in the coordinates of a point on the graph, say (0, -2), we get that -2=k/-1, meaning k=2.

So y=2/(x-1).

Answer:

10.99

Step-by-step explanation:

I JUST HAD THAT AND GOT IT RIGHT TRUST ME NOW GIVE ME BRAINLY I SWEARRR

Answer:

8 science fiction movies

Step-by-step explanation:

2+s=10

-2   -2

s=8

Travis streamed 8 science fiction movies

Answer:

My best recommendation is to find the median.

Step-by-step explanation:

To find a median, find the averaging number and divide by 2. Round them up for odd numbers. For even numbers, leave them and if it's a decimal, find a remainder. If the median method does not work, put the numbers on a ratio comparison and see if that gives you the next patterns.

I tried my best so I really do hope this helps you.

Answer:

height = 4.8 cm

area = 120 cm²

perimeter = 62 cm

Step-by-step explanation:

**Please refer to the attached diagram when following the step-by-step**

First, find m∠C (green angle on diagram) by using the cosine rule:

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

[tex]\implies 29^2=6^2+25^2-2(6)(25)cos(C)[/tex]

[tex]\implies cos(C)= \frac{29^2-6^2-25^2}{-2(6)(25)}[/tex]

[tex]\implies cos(C)= \frac{180}{-300}=-\frac{3}{5}[/tex]

[tex]\implies cos(C)=126.8698976... \textdegree[/tex]

Therefore, the interior angle of the right triangle at point C (blue angle on diagram) is:

[tex]180-cos^{-1}(-\frac{3}{5})=53.13010235... \textdegree[/tex]

Now use the Sine Rule (for finding sides) to determine height (h):

[tex]\frac{6}{sin(90)}=\frac{h}{sin(53.13..)}[/tex]

[tex]\implies \frac{6}{1}=\frac{h}{\frac{4}{5}}[/tex]

[tex]\implies 6 \times \frac{4}{5}=h[/tex]

[tex]\implies h=\frac{24}{5}=4.8[/tex]

So the height = 4.8 cm

Now we have determined the height, we can calculate the area by using the area of a parallelogram formula:

Area of a parallelogram = base x perpendicular height

⇒ area = 25 x 4.8 = 120 cm²

Parallelogram is a four-sided shape made up of two pairs of straight parallel lines that are equal in length.

Perimeter = sum of the sides

⇒ perimeter = 6 + 6 + 25 + 25 = 62 cm

Answer:

decreasing

Step-by-step explanation:

it is decreasing

Answer:

7^2, 10^2, 23^2

Step-by-step explanation:

49 + 100 + 529 = 678

7^2 + 10^2 + 23^2 = 678

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Answer:

The answer is 140 cubic in

Step-by-step explanation:

The formula for the volume of a prism is V=Bh, where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw. Hope this helped! :) (ps. I am sorry if it does not help.)

Answer:

140 cubic inches

Step-by-step explanation:

8x5x3.5

8x5 = 40

40x 3.5= 140

The amount of kobo you can get in the naira is; 100 kobo

There are different types of currencies in the world such as dollars, pounds, euros, naira e.t.c

Now, for the naira, we know that a conversion;

100 kobo = 1 naira

Thus, we can conclude that the amount of kobo you can get in the naira is 100 kobo

Read more about currency conversions at; https://brainly.com/question/1306721

100 Kobo is equal to 1 Nigerian Naira (NGN). However, please note that currency exchange rates can fluctuate over time, so it's always a wise idea to check for the most up-to-date information from a reliable source such as a bank or financial institution.

Answer:

[tex]y=\frac{7}{2}x+11[/tex]

Step-by-step explanation:

To solve, we need to find the y-intercept (b). In order to find the y-intercept, we can plug in the slope and the (x,y) coordinate pair given to us into the equation to solve for the y-intercept:

y=mx+b

4=(-7/-2)*-2+b

4=14/-2+b

4=-7+b

Add 7 to both sides

b=11

Therefore the equation is:

[tex]y=\frac{7}{2}x+11[/tex] (note that the fraction is positive since the two negatives cancel out)