Please help with this math question graph

Answer:

The length of the short leg is 5 inches and the leg of the long leg is 12 inches

Step-by-step explanation:

Let

a -----> the long leg of a right triangle

b ----> the short leg of a right triangle

c ----> the hypotenuse of a right triangle

we know that

Applying the Pythagoras Theorem

[tex]c^{2} =a^{2}+b^{2}[/tex] -----> equation A

we have that

[tex]a=b+7[/tex] -----> equation B

[tex]c=13\ in[/tex] ----> equation C

Substitute equation B and equation C in equation A and solve for b

[tex]13^{2} =(b+7)^{2}+b^{2}[/tex]

[tex]169=b^2+14b+49+b^2[/tex]

[tex]2b^2+14b+49-169=0[/tex]

[tex]2b^2+14b-120=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]b=5\ in[/tex]

see the attached figure

Find the value of a

[tex]a=b+7[/tex] ----> [tex]a=5+7=12\ in[/tex]

therefore

The length of the short leg is 5 inches and the leg of the long leg is 12 inches

The lengths of the leg : 12 and 5

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

[tex]\large {\boxed {\bold {f (x) = ax ^ 2 + bx + c}}}[/tex]

where a, b, and c are real numbers and a ≠ 0.

There are 3 ways to solve quadratic equations

a. factoring b. perfect squared c. quadratic formula

We use the factoring method

Quadratic equation x² + bx + c = 0 is equivalent to quadratic equation

[tex]{\displaystyle {x ^ 2 + (p + q) \times \: pq}}[/tex]

where p + q = b and px q = c

for a = 1, the result of factoring is (x + p) (x + q)

If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle

There is a hypotenuse in this triangle which is the sum of the two sides

where c = hypotenuse

This formula is known as the Pythagorean theorem which states that:

the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.

then c = 13

then a = b + 7

Then the phytagorean equation becomes:

(b + 7)² + b² = 13²

49+14b+b²+b²=169

49+14b+2b²=169

2b²+14b-120=0

b²+7b-60=0

factoring

(b-5)(b+12)=0

b=5 or b=-12

we use positive number ⇒5

So :

the long leg = b+7=5+7=12

the short leg = b = 5

the triangle angle

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Prove the converse of the Pythagorean Theorem

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Use Pythagoras' theorem

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Keywords :  Pythagorean Theorem , hypotenuse, the long leg

Answer:

C on Plato

Step-by-step explanation:

Answer:x             f(x) = 2.5x − 10.5              g(x) = 64(0.5x)

2            f(2) = 2.5(2) - 10.5             g(2) = 64(0.5*2)

             f(2) = 5 - 10.5                    g(2) = 64(1)

             f(2) = -5.5                          g(2) = 64

3            f(3) = 2.5(3) - 10.5             g(3) = 64(0.5*3)

             f(3) = 7.5 - 10.5                 g(3) = 64(1.5)

             f(3) = -3                             g(3) = 96

4            f(4) = 2.5(4) - 10.5             g(4) = 64(0.5*4)

             f(4) = 10 - 10.5                  g(4) = 64(2)

             f(4) = -0.5                          g(4) = 128

5            f(5) = 2.5(5) - 10.5             g(5) = 64(0.5*5)

             f(5) = 12.5 - 10.5               g(5) = 64(2.5)

             f(5) = 2                              g(5) = 160

6            f(6) = 2.5(6) - 10.5             g(6) = 64(0.5*6) 

             f(6) = 15 - 10.5                  g(6) = 64(3)

             f(6) = 4.5                           g(6) = 192

Answer:

Step-by-step explanation:

X=1.125 hope this helps!

Answer:

10.9

Step-by-step explanation:

So you add or subtract the number, leaving the bottom number the same and then simplify if you need to.

Answer:

It makes 5/3 it is less than two!

Step-by-step explanation:

Topic: Fractions and Mixed Numbers

You have to remember the concept of fractions, let's represent by cake diagrams, it says that Gary says that 3, let's say it's 3 cakes, as the fractions are represented in terms of thirds, let's draw the cakes each one divided in 3.

and the statement says that taking away 1 and 1/3 it will make more than 2.

As you can see in the picture below, we take away 1 cake and we will take away another third of a second cake represented by the brown region of the cakes. it means that the yellow region is what's left after taking the 1 and 1/3. as you can see it doesn't make two, makes less than two exactly 5/3.

PS: Try and do it mathematically now!

Answer:

2.967741935

Step-by-step explanation:

Answer:

Width 15 feet

Step-by-step explanation:

Use formula

[tex]A_{rectangle}=\text{Width}\cdot \text{Length}[/tex]

Let x feet be the width of the rectangle.

If the length of a rectangle is 4 times the width of the rectangle, then the length is 4x feet.

The area of the rectangle is 900 square feet, so

[tex]900=x\cdot 4x\\ \\900=4x^2\\ \\x^2=225\ [\text{Divided by 4}]\\ \\x=\pm 15[/tex]

The width cannot be negative, then x=15 feet and 4x=60 feet.

Final answer:

To find the width of the rectangle when the length is 4 times the width and the area is 900 square feet.

Explanation:

To find the width of the rectangle:

Let the width be w feet.

Since the length is 4 times the width, the length is 4w feet.

Given that the area is 900 square feet, we can set up the equation w * 4w = 900 to solve for w.

4w² = 900

w² = 225

w = 15 feet

Therefore, the width of the rectangle is 15 feet.

Answer:

x ≥ -6

Step-by-step explanation:

Answer:

(x+7, y-3)

Step-by-step explanation:

7 units to the right and 3 units down

this probably isn't right but this is what the internet says 31/400

To convert 7 3/4% to a fraction in simplest form, add the whole number and the fractional part together, find a common denominator, and simplify if necessary.

To convert 7 3/4% to a fraction in simplest form, we first need to convert the mixed number to an improper fraction. The whole number part, 7, can be written as 7/1. Adding the fractional part, we have (7/1) + (3/4). To add fractions, we need a common denominator, which in this case is 4. So, we rewrite the fractions as (28/4) + (3/4). Adding the numerators, we get 31/4. Since we want the fraction in simplest form, we can simplify 31/4 by dividing both the numerator and the denominator by their greatest common factor, which is 1. Therefore, 7 3/4% as a fraction in simplest form is 31/4.

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Answer:

4

Step-by-step explanation:

$21-$13=$8

$8÷$2=4 bottles

Answer:

t=-5

Step-by-step explanation:

Answer:

t = -5

Step-by-step explanation:

Distribute by multiplication -2(t + 2), obtaining

-2t - 4 + 5t = 6t + 11.

Combine the t terms; this yields -4 = 3t + 11.  Solving for 3t, we get

3t = -4 -11, or 3t = -15.  Thus t must be -5.

Answer:

Part 1)  441km in 45s   --> Has the same speed as Saige's spaceship

Part 2) 215km in 25s --> Does not have the same speed as  Saige's spaceship

Part 3) 649km in 110s --> Does not have the same speed as  Saige's spaceship

Step-by-step explanation:

The complete question is

Saige's spaceship traveled 588 kilometers in 60 seconds.

Determine whether or not each spaceship trip below has the same speed as Saige's spaceship.

441km in 45s

215km in 25s

649km in 110s

we know that

The speed is equal to divide the total distance traveled by the total time

In this problem we have that

The speed of Saiges spaceship is equal to

[tex]\frac{588}{60}=9.8\ \frac{km}{sec}[/tex]

case 1) we have

441km in 45s

Find out the speed of the  spaceship trip

[tex]\frac{441}{45}=9.8\ \frac{km}{sec}[/tex]

Compare the speed of the spaceship trip with the speed of Saiges spaceship

[tex]9.8\ \frac{km}{sec}=9.8\ \frac{km}{sec}[/tex]

therefore

Has the same speed as Saige's spaceship

case 2) we have

215km in 25

s

Find out the speed of the  spaceship trip

[tex]\frac{215}{25}=8.6\ \frac{km}{sec}[/tex]

Compare the speed of the spaceship trip with the speed of Saiges spaceship

[tex]8.6\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}[/tex]

therefore

Does not have the same speed as  Saige's spaceship

case 3) we have

649km in 110s

Find out the speed of the  spaceship trip

[tex]\frac{649}{110}=5.9\ \frac{km}{sec}[/tex]

Compare the speed of the spaceship trip with the speed of Saiges spaceship

[tex]5.9\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}[/tex]

therefore

Does not have the same speed as  Saige's spaceship

Answer:

4.5 foot shadow

Step-by-step explanation:

By looking at this you can make a ratio that very every 5 feet there is a 1.5 foot shadow.

So 1.5 x 3 = 4.5 foot shadow

(Very sorry If it is incorrect Good luck!)

Answer:

no solution

Step-by-step explanation:

30n-18+2n-14-64=30n-18+2n-14

32n-96=32n-32

-96=-32<-----false statement, therfore it is no solution

Answer:

Absolute value is a number's distance from 0, so when comparing quantities, such as positive and negative, the greater absolute value is of that number.

For ex:

|-11| > |6| ,  because |-11| = 11, |6| = 6, and 11 > 6.

So, |-11| > |6|

Absolute values are used to describe the distance of any values from the point 0. Hence, absolute values are used to express the positive value a quantity.

Quantities may be positive or negative depending on their relative position from Zero.

Positive values are to the right of Zero; While negative values are to the left of Zero.

Since quantities maintain equal distance either to the left or right of Zero; Absolute values are only concerned with the magnitude of a quantity from Zero and not the direction.

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Answer:

the answer is 8.5

Step-by-step explanation:

yeet

Answer:

I think the closest would be 8 :3

Answer:

205  miles per hour.

Step-by-step explanation:

1 mile = 5280 feet so:

300 ft / second = 300/ 5280 miles/second.

There are 3600 seconds in an hour so

this converts to  300 * 3600 / 5280 miles per hour

= 204.55 miles per hour.

Hey!

-----------------------------------------------

Solution:

Let's use dimensional analysis!

[tex]= \frac{1mi}{5280ft} * \frac{3600}{1hr} * \frac{300ft}{1sec}[/tex]

[tex]= \frac{1,080,000}{5,280}[/tex]

[tex]= 204.454545...[/tex]

[tex]= 205[/tex]

-----------------------------------------------

Answer:

205

-----------------------------------------------

Hope This Helped! Good Luck!

Answer:

0 because it doesn't cross the x-axis

Step-by-step explanation:

Interpreting the graph, it is found that the function has no real solutions.

The number of different real solutions that a function has is given by the number of times it crosses the x-axis(also known as the horizontal axis) on the graph.

In this problem, the function never crosses the x-axis, thus, it has zero real solutions.

A similar problem, in which the real solutions are taken from a graph, is given at https://brainly.com/question/16349072

Final answer:

[tex]9 \times 10^{-2 }(0.09)[/tex] is greater than [tex]3 \times 10^{-4} (0.0003)[/tex], and is 300 times greater.

Explanation:

To determine which is greater between  [tex]9 \times 10^{-2 }[/tex] and  [tex]3 \times 10^{-4}[/tex]we need to understand how to interpret numbers in scientific notation. The expression  [tex]9 \times 10^{-2 }[/tex] means 9 times 1 following 2 zeroes to the left, resulting in 0.09. In the case of   [tex]3\times 10^{-4}.[/tex] it means 3 times 1 following 4 zeroes to the left, producing 0.0003.

Comparing these values,  [tex]9 \times 10^{-2 }[/tex] is clearly the larger number because 0.09 is greater than 0.0003. To find out how many times greater it is, we divide the larger number by the smaller one: 0.09 / 0.0003 equals 300. Therefore,  [tex]9 \times 10^{-2 }[/tex]is 300 times greater than [tex]3\times 10^{-4}.[/tex]

Answer:

Forty and three hundred two thousandths.

Step-by-step explanation:

40 = forty

300 = three hundred

.02 = two thousandths

Hope this helps.

Answer:

Step-by-step explanation:

Forty and three hundred two thousandths.

Answer:

m∠QRT = 90°

m∠QRT = m∠SRT

Step-by-step explanation:

Triangle QST is isosceles with QT ≅ ST. In isoscels triangle QST, angles STR and RTQ are congruent.

RT is angle T bisector, so angles QTR and STR are congruent.

Consider two triangles QTR and STR. In these triangles:

By SAS postulate, these two triangles are congruent. Two congruent triangles have congruent corresponding sides, so

Angles QRT and SRT are supplementary (add up to 180°). Since these two angles are congruent, they have the same measure equal to [tex]\frac{1}{2}\cdot 180^{\circ}=90^{\circ}[/tex]

So, true options are

m∠QRT = 90°

m∠QRT = m∠SRT

Answer:

The correct options are;

m[tex]\angle[/tex]QRT [tex]=90^o[/tex]

m[tex]\angle[/tex]QRT [tex]=[/tex] m[tex]\angle[/tex]SRT

Step-by-step explanation:

Given information;

The triangle QST is isosceles with QT ≅ ST.

The angle STR ans RTQ are congruent.

Now, consider two triangles QTR and STR

In the following triangle

1. TR  ≅  TR (having reflective property)

2. [tex]\angle[/tex]QTR ≅ [tex]\angle[/tex]STR (as given in question)

3. QT ≅ ST (as given in information)

Now, according to SAS postulate , two congruent triangle have congruent corresponding to their sides ,

Hence ,

1. QR ≅ SR

2. [tex]\angle[/tex]QRT ≅ [tex]\angle[/tex]SRT

Since, this above two angles are congruent they will have same measure

That will be

[tex]=(180/2)\\=90 ^o[/tex]

Hence, The correct options are;

m[tex]\angle[/tex]QRT [tex]=90^o[/tex]

m[tex]\angle[/tex]QRT [tex]=[/tex] m[tex]\angle[/tex]SRT

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Answer:

27

Step-by-step explanation:

The square root of 10 lies between two whole numbers, 3 and 4. This concept can be understood using number sense and geometry.

The square root of 10 falls between two whole numbers. To determine these two numbers, we need to consider the closest perfect square numbers to 10. These are 9 (the square root of 9 is 3) and 16 (the square root of 16 is 4). Hence, the square root of 10 must be somewhere between 3 and 4. Using a calculator, we find the approximate square root of 10 to be around 3.16. So, the square root of 10 lies between 3 and 4.

This kind of problem is related to number sense and geometry, especially when it comes to understanding square roots.

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Answer:

the answer is -8 13/30

Step-by-step explanation:

Answer:

N/A

p-by-step explanation:

x minus 1 is already a simplified expression (can only be solved if you know x)