Solve the system of linear equations by substitution.

y=4x
x+y=-10

The amount of time they rest in 8 hours is 40 minutes.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

In the problem, it is stated that a couple rests for 25 minutes in 5 hours during a dance-a-thon. We can use this information to find out how long they rest each hour. To do this, we simply divide the total amount of time they rest (25 minutes) by the number of hours (5 hours). That is:

rest time in 1 hour = 25 minutes / 5 hours = 5 minutes.

So, if they dance for 8 hours, the amount of time they rest will be:

8 hours * 5 minutes/hour = 40 minutes.

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Answer:

  C.  17 units

Step-by-step explanation:

You want the hypotenuse of a right triangle with legs 8 and 15.

The Pythagorean theorem tells you the relation between the sides of a right triangle is ...

  c² = a² +b² . . . . . . where c is the hypotenuse, and a, b are the legs

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17 . . . . units

The missing side length is 17 units.

__

Additional comment

A set of integers that satisfies the Pythagorean theorem is called a "Pythagorean triple." Perhaps the first one you run across is {3, 4, 5}. Other triples commonly seen are {5, 12, 13}, and {7, 24, 25}. This one, {8, 15, 17} also shows up in algebra and trig problems. It can be worthwhile to remember a few of these.

Their multiples are also seen. For example, {6, 8, 10} is the {3, 4, 5} triple times 2.

The heaviest pack's maximum allowable weight is d = 46 - 39 = 7 kg.

Let the four packs each weight a, b, c, and d (with a <= b <= c <= d).

Using the given data, we can formulate the following six equations:

a + b = 34

a + c = 37

a + d = 39

b + c = 41

b + d = 43

c + d = 46

the fourth equation and the first equation added:

2a + 2b = 34 + 41 = 75

Solving for a, we get:

a = (75 - 2b) / 2

Substituting this into the first equation:

(75 - 2b) / 2 + b = 34

Multiplying both sides by 2:

75 - 2b + 2b = 68

Solving for b, we get:

b = 34 - (75 - 68) / 2 = 34 - 3.5 = 30.5

Substituting this value into the equation for a:

a = (75 - 2 * 30.5) / 2 = (75 - 61) / 2 = 7

The greatest possible weight of the heaviest pack is d = 46 - c. Since c <= 46 - a = 46 - 7 = 39,

The greatest possible weight of the heaviest pack is d = 46 - 39 = 7 kg.

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Answer:2 i think im not sure

Step-by-step explanation:

Expression is; 29 - x = 16 an expression to represent this situation.

Where in mathematics is an expression?

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

                               Term is a mathematical concept that refers to a constant, a single variable, or a mixture of variables and constants along with multiplication or division. Example of an algebraic expression: 3x + 9; 5x + 10

We are told that at lunchtime, it was 29 degrees Celsius and that by sunset, the temperature had dropped to 16 degrees Celsius.

Let the drop be x.

Thus;

29 - x = 16

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The complete question is -

On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

Answer:

50 grams

Step-by-step explanation:

A line must have a 2 1/2 slope in order to be perpendicular to the line whose equation is 6x + 15y = 225.

A line's slope is determined by its inclination.

M is used to signify it.

m = (y₂ - y1)/(x₂ -x₁).

Consider Point 1 and Point 2 as the two points on a line.

The coordinates for Point 1 are (x1,y1), while the coordinates for Point 2 are (x2,y2).

The line equation was provided to us as follows:

⇒ 6x + 15y = 225

⇒ 15y = -6x + 255

⇒ y = -6/15 x + 255/15

The slope, m = -6/15

The angle of perpendicularity = -1/m

⇒ -1/(-6/15)

Reciprocal the term of denominator, and we get    

⇒ 15/6  = 2 1/2

Therefore, a line must have a 2 1/2 slope in order to be perpendicular to the line whose equation is 6x + 15y = 225.

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Answer:

To solve for x in the equation AX - B = 4, if A does not equal 0, we can isolate x by adding B to both sides and then dividing both sides by A:

AX - B + B = 4 + B

AX = 4 + B

X = (4 + B) / A

So, the solution for x is given by: X = (4 + B) / A, where A is not equal to 0.

Step-by-step explanation:

The figure which is made by placing a triangle on the small side of a rectangle has a area of 95 in.²

According to question, there is a figure made by placing a triangle with a height of 4 inches on the small side of a rectangle that measures 5 inches by 17 inches.

Small side of rectangle is 5 inches, on which triangle is placed so it becomes the base of triangle.

Area of rectangle = length × breadth

Area of rectangle = 17 × 5

so, area of rectangle is 85 in.²

Now calculate the area of triangle

Area of triangle = [tex]\frac{1}{2}[/tex] × base × height

Area of triangle = [tex]\frac{1}{2}[/tex] × 5 × 4

so, area of triangle is 10 in.²

Area of the whole figure = Area of rectangle + Area of triangle

Area of the whole figure = 85 + 10 = 95 in.²

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Answer:

22

Step-by-step explanation:

1 Simplify 14-6 to 8.

78-2^4 ÷ 8 × 28

2 Simplify 24 to 16.

78 - 68 ÷ 18 x 28

3 Simplify 16 ÷ 8 to 2.

78-2 × 28

4 Simplify 2 x 28 to 56.

78 - 56

5 Simplify.

22

The problem can be written as:

x/(5 - 4) = 12

which simplifies to:

x/1 = 12

x = 12

Therefore, the number is 12.

The probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is 0.4

We can calculate the probability by finding the number of favorable outcomes, i.e., the number of ways that Sergio can choose a number that is larger than the sum of the two numbers chosen by Tina, and dividing it by the total number of possible outcomes, which is

5C2 * 10C1 = (5!/(2! * 3!)) * 10

= 100

Tina's sum   Sergio's favorable outcomes  

3           7

4           6

5           5

6           4

7           3

8           2

9           1

For example the sum 5 can be achieved by two ways, that is 1+4 and 2+3. So

Tina's sum   Number of ways to achieve that sum

3           1

4           1

5           2

6           2

7           2

8           1

9           1

The number of favourable outcomes is

= 1*7 + 1*6 + 2*5 + 2*4 + 2*3 + 1*2 +1*1

= 40

So probability is

= 40/ 100

= 0.4

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Answer:

C = 24 inches

Step-by-step explanation:

the fraction of the circumference (C) that the arc AB subtends is

[tex]\frac{45}{360}[/tex] = [tex]\frac{1}{8}[/tex]

thus C is 8 times length of arc AB

C = 8 × 3 = 24 inches

Answer:102

Step-by-step explanation: add 2

Answer:

102

Step-by-step explanation:

=2+100

=102

So the answer is.. 102

I'll do the first one for you.

Step-by-step explanation:

a)

First find the gradient using the coordinates given.

(-4, -2), (6, 8)

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

m = (-2 - 8)/(-4 - 6)

m = -10 / -10 = 1

Then use tanθ = m,

tanθ = 1

θ = tan -1(1)

θ = 45 degrees.

If you want to know why we use tanθ, refer to this -> https://amsi.org.au/ESA_Senior_Years/SeniorTopic1/1b/1b_2content_4.html

The probability of randomly selecting an individual in this community who has red hair or is​ left-handed is 0.23

The probability of an event refers to the likelihood of the event occurring, expressed as a number between 0 and 1.

In other words, the probability of the union of two events can be expressed as follows:

P(A or B) = P(A) + P(B) - P(A and B)

Where A represents the event of having red hair, B represents the event of being left-handed, and P(A and B) represents the probability of the intersection of the two events. In this case, P(A) = 0.08 and P(B) = 0.15.

Therefore, to find the probability of a randomly selected individual in this community who has red hair or is left-handed, we would need to know the probability of the intersection of the two events, P(A and B).

This would allow us to subtract it from the sum of the individual probabilities, P(A) + P(B), to find the total probability of having red hair or being left-handed.

=> P(A) + P(B) = 0.08 + 0.15 = 0.23

In conclusion, to find the probability of having red hair or being left-handed in this community, we would need to know the probability of the intersection of the two events, P(A and B).

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Step-by-step explanation:

The general solution of the differential equation can be found as follows:

dQ/dx = k/x^2

Integrating both sides, we get:

Q = k * ln|x| + C

where C is the constant of integration.

Based on the above, it can be inferred that the arrow is expected to stop on the number 3 space at least 13 times in the 104 shots.

To calculate how many times the arrow will stop at number 3 we must perform the following mathematical operation:

1 / 8 = 0.125

0.125 is equivalent to 12.5% of the pitches.

Therefore, we must make a rule of three.

According to the above, the arrow must stop at least 13 times at the number 3.

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Answer:

Quadrilateral

Step-by-step explanation:

Quadrilateral = 4 sides

The cost of the computer in Mexican pesos would be 839,779 Mexican pesos.

To convert an amount in American dollars to Mexican pesos, we can multiply by the exchange rate of 18.4398 Mexican pesos per American dollar.

That is, 18.4398 in Mexican peso is equal to one American dollar.

So, if an order of American computer hardware costs $45,000, the cost in Mexican pesos would be $45,000 * 18.4398 = 839,779 Mexican pesos.

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Taylor had $788.50 left over from her paycheck after making the house payment and the car payment.

Let's calculate the amount spent on the house payment first:

$1575 * 0.30 = $472.50

Now, let's calculate the amount that was left after the house payment:

$1575 - $472.50 = $1102.50

Next, let's calculate the amount spent on the car payment:

$1102.50 - $314 = $788.50

Here's a step by step breakdown of the calculation:

Taylor received a paycheck of $1575.

She spent 30% of her paycheck on the house payment, which is $1575 * 0.30 = $472.50.

After making the house payment, Taylor had $1575 - $472.50 = $1102.50 left. She then spent $314 on the car payment, leaving her with $1102.50 - $314 = $788.50.

So, Taylor had $788.50 left over from her paycheck after making the house payment and the car payment.

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Answer:

x= the square root of 7 and the negative square root of 7

Step-by-step explanation:

basically

x^2=7

can be converted into

x=7^1/2 (^1/2 is another way to say square root or represent square root)

x= 2.645751311 or -2.645751311

negative is included as a negative value to the power of 2 gives a positive value

hope this helps

Answer:

P(Red) = [tex]\frac{12}{50}[/tex] = [tex]\frac{6}{25}[/tex]

P(not green)

= 1 - [tex]\frac{8}{50}[/tex]

= [tex]\frac{21}{25}[/tex]

P(Blue or yellow)

= P(Blue) + P(Yellow)

= [tex]\frac{7}{50}[/tex] + [tex]\frac{9}{50}[/tex]

= [tex]\frac{8}{25}[/tex]

Answer:

ΔGAS ≅ ΔIOLby AAS

Step-by-step explanation:

We can prove congruence by the AAS Theorem

AAS Theorem

By definition, AAS congruence rule states that if any two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle, the two triangles must be congruent

In triangles ΔGAS and ΔIOL

We have:
∠G ≅ ∠I
m∠A ≅ m∠O

AS ≅ OL

AS is the non-included side of ΔGAS and OL is the non-included side of ΔIOL

Therefore we have two corresponding angles congruent and the non-included side of each of these triangles also congruent

Therefore by the AAS (Angle-Angle-Side) theorem, the two triangles are congruent

ΔGAS ≅ ΔIOL by AAS

Answer:

ΔGAS ≅ ΔIOL by AAS

Step-by-step explanation:

From the dashes on the angles and sides of the given triangles:

Therefore, the two triangles have two corresponding congruent angles and a congruent corresponding non-included side.  This means we can show that the triangles are congruent by the AAS congruence Theorem.

If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Therefore:

Answer:

Step-by-step explanation:

The expression "15/18 - 7/36" can be simplified as follows:

Step 1: Find a common denominator for the two fractions. In this case, the least common denominator is 36.

Step 2: Convert both fractions to have a denominator of 36.

15/18 can be converted to 30/36 by multiplying both the numerator and denominator by 2.

7/36 can be expressed as 7/36.

Step 3: Subtract the two fractions to simplify the expression:

30/36 - 7/36 = 23/36

So the expression simplifies to 23/36.

P' would have coordinates  d. (8, -5).

What is Reflection across a line?

It is discovered using reflections principles that:

1) When a function is reflected across the x-axis, the x-coordinates remain unchanged, however the y-coordinates have the opposite signal.

2) When a function is reflected across the y-axis, the y-coordinates remain unchanged, whereas the x-coordinates have the opposite signal.

Given that,

      Triangle is reflected across the dashed line with coordinates of P' if P(8, 5).

Reflection across a line means taking a shape and flipping it over the line so that it appears as its mirror image.

In the case of the point P(8,5), reflecting it across the dashed line would result in a new point P' whose y-coordinate is the opposite of the y-coordinate of P.

Therefore, P' would have coordinates (8, -5).

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Answer:

Step-by-step explanation:

First find the hyp..

6^2 + 20^2 = x^2

x = 20.88

Using x, we now know the extra height missing from the original tree height, so we add 6 to find the original.

20.88 + 6 = 26.88ft

The tree was 26.88 feet tall before the storm.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have Perpendicular = 6 feet

and, base = 20 feet

Using Pythagoras theorem we get

H² = P² + B²

H² = 6²+ 20²

H²= 36+400

H² = 436

H = 20.88 feet

thus, the height of the tree = 20.88 + 6 = 26.88 feet

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The original price of the pair of jeans is

equals to the $120.

Jodi wants to buy a pair of jeans.

The purchase price of pair of jeans on sale = $90

Discount on price of jeans = 75%

Let the original price of pair of jeans be equal to "$y". As we know, percentage is an important concept of mathematics. It is a number calculated by dividing the part of number to the whole number, then resultant multiply by 100. It's symbol is %. The formula is % = (part/whole )x100

Here, it is said that the price of pair of jeans, $90, is only 75% of the original price. So, we can write it as the following way 75% of y = 90

=> (75/100) of y = 90

=> (75/100) x y = 90

=> y = 90x 100/75

=> y = 9000/75

=> y = 120

Hence, required value of y is $120.

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Answer: 5

Step-by-step explanation:

1st piece = x

2nd piece = 2x

3rd piece = 2x + 2

All of these pieces add up to 27, which means =>

5x + 2 = 27

5x = 27 - 2 = 25

x = 5