The sum of the squares of the lengths of the legs of an isosceles triangle is equal to the square of the length of the hypotenuse

Answer:

Step-by-step explanation:

Let's solve your system by substitution.

2x+3y=15;x+y=6

Rewrite equations:

x+y=6;2x+3y=15

Step: Solvex+y=6for x:

x+y=6

x+y+−y=6+−y(Add -y to both sides)

x=−y+6

Step: Substitute−y+6forxin2x+3y=15:

2x+3y=15

2(−y+6)+3y=15

y+12=15(Simplify both sides of the equation)

y+12+−12=15+−12(Add -12 to both sides)

y=3

Step: Substitute3foryinx=−y+6:

x=−y+6

x=−3+6

x=3(Simplify both sides of the equation)

Answer:

x=3 and y=3

Answer:

x = 3, y = 3

Step-by-step explanation:

Given the 2 equations

2x + 3y = 15 → (1)

x + y = 6 → (2)

Multiplying 2) by - 2 and adding to (1) will eliminate x

- 2x - 2y = - 6 → (3)

Add (1) and (3) term by term to eliminate x

y = 3

Substitute y = 3 into either of the 2 equations and solve for x

Substituting into (1)

2x + 3(3) = 15

2x + 9 = 15 ( subtract 9 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

The amount of wrapping paper needed for the square pyramid gift box is: 96.72 in.².

Surface area of a square pyramid = area of the square base + area of the 4 triangular faces = s² + 4(1/2bh).

We are asked to find the amount of wrapping paper that would be needed to wrap the gift box, which is the surface area of the gift box that has a square pyramid shape.

Given the following dimensions of the gift box:

s = 5.2 in.

b = 5.2 in.

h = 6.7 in.

Plug in the values into s² + 4(1/2bh):

Surface area of a square pyramid = 5.2² + 4(1/2 × 5.2 × 6.7).

Surface area of a square pyramid = 96.72 in.²

Therefore, the amount of wrapping paper needed for the square pyramid gift box is: 96.72 in.².

Learn more about square pyramid on:

https://brainly.com/question/25823102

An equation is formed of two equal expressions. The equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The transformation of the equation from x²+6x+5 into the form a(x − h)²+k can be done in the following steps as shown below,

1. Taking +5 on the right-hand side of the equation,

\(x^2+6x+5 = 0\\\\x^2+6x = -5\)

2. Now if we add +9 on both sides of the equation, we will get,

\(x^2+6x = -5\\\\x^2+6x+9 = -5+9\)

3. Now we look at the left side of the equation as the square of the binomial expression (x+3).

\(x^2+6x+9 = -5+9\\\\(x+3)^2 =4\)

4. Taking +4 from the right side of the equation to the left side of the equation,

\((x+3)^2 =4\\\\(x+3)^2 -4=0\)

Thus, the equation is in the form of a(x − h)²+k, where the value of a is 1, h is -3 and the value of k is -4.

Hence, the equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.

Learn more about Equation:

https://brainly.com/question/2263981

Answer:

2x2 is 4 but you have 3 apples?

Step-by-step explanation:

Answer: 243.6

Step-by-step explanation:

For us to solve the question and round off 243.583 to the nearest tenth. First, we need to look at the number beside the tenth number which is 8.

Since 8 is more than 4, we simply add 1 to the tenth number which implies that we add 1 to the number in tenth place which is 5. Adding one means the number change to 6. Therefore, rounding 243.583 to the nearest tenth will be 243.6.

Answer:

-2(-11v-4)

Step-by-step explanation:

The probability P(n < 10 | n is prime) is 4/6, which simplifies to 2/3 or approximately 0.67 (rounded to the nearest hundredth).

To find the probability P(n < 10 | n is prime), we need to determine the number of prime integers less than 10 and divide it by the total number of integers from 1 to 15 that are prime.

The prime numbers less than 10 are 2, 3, 5, and 7. So, there are 4 prime numbers less than 10.

The total number of integers from 1 to 15 that are prime is 6 (2, 3, 5, 7, 11, and 13).

As a result, the chance P(n 10 | n is prime) is 4/6, which can be expressed as 2/3 or, rounded to the nearest hundredth, as around 0.67.

Thus, 0.67 is the answer.

for such more question on probability

https://brainly.com/question/13604758

#SPJ8

The largest open interval where f(x) is decreasing is (-2√(1/3), 2√(1/3)). In interval notation, this can be written as (-2√(1/3), 2√(1/3)).

To determine where the function f(x) = x^3 - 4x is decreasing, we need to find the intervals where the derivative is negative. Let's calculate the derivative of f(x) first:

f'(x) = 3x² - 4

To find where f'(x) < 0, let's solve the inequality:

3x² - 4 < 0

Adding 4 to both sides gives:

3x² < 4

Dividing both sides by 3 gives:

x² < 4/3

Taking the square root of both sides (and considering both the positive and negative square root) gives:

x < √(4/3) and x > -√(4/3)

Simplifying further, we have:

x < 2√(1/3) and x > -2√(1/3)

The largest open interval where f(x) is decreasing is (-2√(1/3), 2√(1/3)). In interval notation, this can be written as (-2√(1/3), 2√(1/3)).

To know more about interval notation;

https://brainly.com/question/13048073

We need to investigate the behavior of the derivative of the feature. If the spinoff is negative inside a c program language period, then the quality is lowering over that c language.

Let's begin by finding the derivative of the function f(x) = x^3 - 4x:

f'(x) = 3x^2 - 4

we set f'(x) < zero:

3x^2 - four < zero.

Now, permit's remedy this inequality:

3x^2 < 4,

x^2 < four/three,

x^2 - 4/three < 0.

To find the critical points, we set x^2 - 4/three = zero:

x^2 = 4/three,

x = ±√(4/three),

x = ±2/√3.

We need to test the durations among the essential factors and beyond.

For x < -2/√3, allow's select x = -1. Plugging this cost into f'(x):

'(-1) = three(-1)^2 - four = -1.

Since f'(-1) < zero, the characteristic is decreasing for x < -2/√3.

For -2/√three < x < 2/√three, permits select x = zero. Plugging this price into f'(x):

f'(0) = 3(0)^2 - four = -four.

Since f'(0) < zero, the characteristic is lowering for -2/√three < x < 2/√3.

For x > 2/√three, permits choose x = 1. Plugging this cost into f'(x):

f'(1) = three(1)^2 - four = -1.

Since f'(1) < 0, the function is decreasing for x > 2/√3.

Therefore, the largest open c language in which the characteristic f(x) = x^3 - 4x is lowering is (-∞, 2/√three).

Answer:

∡x = 30°

∡y = 70°

∡z = 80°

Step-by-step explanation:

Answer: 4 and a half

Step-by-step explanation:

Answer:

24x + 41

Step-by-step explanation:

Distribute the 6.

6(4x + 5) + 11 = 24x + 30 + 11

Now we just add the 30 and the 11 which are at the back of the expression.

24x + 30 + 11 = 24x + 41

Therefore the answer is 24x + 41. Please mark brainliest if possible and i hope you get a good grade on your homework

The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.

He comes to a river that he must cross from east to west, and there is a boat available to do so.  Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."

The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.

To know more about riddle visit:

brainly.com/question/10914267

#SPJ11

The probability that one player gets all aces is 0.0467

From the question, we have the following parameters that can be used in our computation:

Cards, n = 52

Players, r = 4

The 52 cards can be shared to the the 4 players in C(n + r - 1, r - 1) ways

So, we have

C(52 + 4 - 1, 4 - 1) = C(55, 3)

When evaluated, we have

C(52 + 4 - 1, 4 - 1) = 26235

Next:

The remaining 48 cards can be shared to the other 3 players in C(n + r - 1, r - 1) ways

C(48 + 3 - 1, 3 - 1) = C(50, 2)

C(48 + 3 - 1, 3 - 1) = 1225

So, we have

P = 1225/26235

Evaluate

P = 0.0467

Hence, the probability is 0.0467

Read more about probability at

https://brainly.com/question/31649379

#SPJ4

Answer:

the 1st - 840,000 2nd-96,600

Therefore, the solution of the equation 2(4(x-1)+3)= 5(2(x-2)+5) is x = 5.

Given that the equation is 2(4(x-1)+3)= 5(2(x-2)+5).To find the solution of the equation, simplify the equation by applying the distributive property, and solve for x as follows

2(4x - 4 + 3) = 5(2x - 4 + 5)8x - 8 + 6 = 10x - 20 + 2538x - 2 = 10x + 5

Combine the like terms by bringing 10x to the left side and subtracting 2 from both sides.

38x - 10x = 5 + 238x = 40Divide by 8 on both sides.

x = 5Therefore, the solution of the equation 2(4(x-1)+3)= 5(2(x-2)+5) is x = 5.

To know more about distributive property visit:

https://brainly.com/question/30321732

#SPJ11

Answer:

Blue Box / First answer choice

Step-by-step explanation:

Plug in d1:8.6 and d2:10.2 into d1 x d2/2 to find the area.

d1 x d2/2

8.6 x 10.2/2

87.72/2

Area=43.86

Answer:

Step-by-step explanation:

first plug 362.50 in for y since that is our office supply expense

362.50 = 10.50x + 100

then we solve for x

362.50 = 10.50x + 100

262.50 = 10.50x

25 = x

so 25 are working in the office that month

hope this helps <3

The predicted grade for a student with 11 absences can be calculated using the equation y = mx + b, where y = predicted grade, m = the slope of the linear regression line, x = the number of absences, and b = the y-intercept. The predicted grade for a student with 11 absences is 79.5.

The linear regression equation is used to predict the value of a dependent variable (y) based on the value of an independent variable (x). The equation takes the form y = mx + b, where m is the slope of the regression line and b is the y-intercept. To calculate the predicted grade for a student with 11 absences, we first need to determine the value of m and b. This can be done by plotting the data points on a graph and calculating the slope and y-intercept of the regression line. Once we have the values of m and b, we can plug them into the linear regression equation. For example, if the slope is -0.5 and the y-intercept is 90, then the predicted grade for a student with 11 absences would be y = (-0.5 * 11) + 90 = 79.5. In this way, the linear regression equation can be used to predict the grade of a student based on the number of absences.

Learn more about equation here

https://brainly.com/question/10413253

#SPJ4

The distance from his hotel to his home is 89 miles.

Given - Ronald's home is located 33 miles west and 56 miles north of his hotel.

To find the distance between Ronald's hotel to his home, add the distance.

∴ \(33 + 56 = 89\)

Therefore, the distance from his hotel to his home is 89 miles.

Know more about direction here:

https://brainly.com/question/2748145

#SPJ2

\(Let$p_1$ - true proportion of California residents who reported insufficient rest or sleep during the preceding 30 days$p_2$ - true proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days$\hat{p}_1$ - sample proportion of California residents who reported insufficient rest or sleep during the preceding 30 days $=0.08$$\hat{q}_1=1-\hat{p}_1=1-0.08=0.92$$n_1$ - sample size of CA residents $=11,545$\)\($\hat{p}_2$ - sample proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days $=0.088$$\hat{q}_2=1-\hat{p}_2=1-0.088=0.912$$n_2$ - sample size of OR residents $=4,691$The $95 \%$ Confidence Interval for $\left(p_1-p_2\right)$ is given by,$$\)\(\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{p_1 q_1}{n_1}+\frac{p_2 q_2}{n_2}}$$if $p_1$ and $p_2$ are unknown we use$$\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}}$$where $Z^*=Z_{\frac{\alpha}{2}}=Z_{0.0250}$\)\(Plugging in, we get$$\begin{aligned}\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}} \\(0.08-0.088) & \pm 1.96 \sqrt{\frac{0.08(0.92)}{11545}+\frac{0.088(0.912)}{4691}} \\&-0.008 \pm 0.009498026 \\&(-0.017498026,0.001498026) \\& \approx(-0.0175,0.0015)\end{aligned}$$\)\(a) For the Hypothesis Test we have,- i) State the hypotheses.$$\begin{aligned}&H_0: p_1-p_2=0 \\&H_1: p_1-p_2 \neq 0\end{aligned}$$\)

A hypothesis test examines a suggested mathematical model to see if a sample of data contains enough evidence to disprove the null hypothesis.

To know more about hypothesis, visit;

https://brainly.com/question/13025783

#SPJ4

Answer:

C. 3×(h-6)

Step-by-step explanation:

Sana makatulong

Answer:

35.26m

Step-by-step explanation:

6.7/ 2 = 3.35

Radius = 3.35^2

Circle = pie x 3.35^2

pie x 11.2225 = 35.25652355

35.25652355 estimated = 35.26

Therefore, the formula for converting 35 liters to milliliters is 35000, with a conversion factor of 1000.

This is further explained below.

Generally,  The amount that is supplied in liters must be multiplied by 1000 in order to be converted to milliliters.

A conversion factor is a number that may be multiplied or divided to shift the units of measurement used for one set to another.

In situations when a conversion is required, the correct conversion factor that results in the same value must be used. For the purpose of converting inches to feet, for instance, the correct value for the conversion is 12 inches equaling 1 foot.

In conclusion, Therefore 35 liters to milliliters is given as 35000, conversion factor of 1000

Read more about the conversion factors

https://brainly.com/question/20822566

#SPJ4

Answer:

1000ml and 1 liter

Step-by-step explanation:

Answer:

The unit rate is $.80 per can.

Step-by-step explanation:

All you have to do is divide $4.80 by 6.

$4.80÷6=$.80

This means that each can cost 80 cents,

In other words the unit rate is $.80

Hope this helps!

(a) The number of ways that the event can occur is 6.

(b) Probabilities are :

1) 1/2, 2) 1/6 and 3) 1/3.

(a) Given a bag of different shapes.

Total number of shapes = 6

So, if we select one shape from random,

total number of ways that the event can occur = 6

(b) Number of squares in the bag = 3

Probability of choosing a square = 3/6 = 1/2

Number of circles in the bag = 1

Probability of choosing a circle = 1/6

Number of stars in the bag = 2

Probability of choosing a star = 2/6 = 1/3

Hence the required probabilities are found.

Learn more about Probability here :

https://brainly.com/question/14210034

#SPJ1

The snapshot graph of the wave at t=0s is a graph of the displacement of the wave along the x-axis at time t=0s.

It is a graph of the wave's initial position, which is usually a sinusoidal graph with a maximum value at the center and decreasing values as x increases. This is because the wave is traveling from left to right and its amplitude decreases as it moves further from its source. To explain in more detail, a sinusoidal wave is a wave that oscillates up and down in a regular pattern.

The snapshot graph at t=0s will show the wave at its highest point, which is the amplitude of the wave. As the wave moves along the x-axis, its amplitude will decrease as it moves further from its source. The graph will also show the wave's wavelength, which is the distance between two successive crests or troughs.

Learn more about Graph here:

https://brainly.com/question/347428

#SPJ4

Answer:

Scale factor 3

Step-by-step explanation:

First, we solve for y in the expression:

So, the y-intercept is (0, -4).

The error is that you are given the wrong y-intercept and the wrong x-intercept; they are swapped in the place of writting.