The two possible pairs of numbers that fit the given equations are (√7, 2) and (-√7, -2). We find these by setting up two equations based on the provided conditions and solving them simultaneously.
Explanation:Let's denote the first number as 'x' and the second number as 'y'. We have two equations from the given information:
1. x² - y² = 5
2. 3x² - 2y² = 19
We can solve these equations simultaneously to find the values of 'x' and 'y'. The first step in solving a system of linear equations is to multiply the equations by what's needed to get the coefficients of one of the variables to match, so it can be eliminated when the equations are added or subtracted. Let's multiply the first equation by 3 and the second equation by 1. We then have:
3x² - 3y² = 15
3x² - 2y² = 19
If we subtract the second equation from the first, we get:
-y² = -4
which leads to y = 2 or y = -2 (squared numbers are always positive). Substituting '2' for 'y' in the first original equation, we find that x = √7 or x = -√7. Therefore, the possible pairs of numbers are (√7, 2) and (-√7, -2).
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wendy is paid $9 per hour and plans to work between 20 and 25 hours per week. indetify the independent and dependent quanity in the situation. find reasonable domain and range values
- Independent quantity: Number of hours worked per week
- Dependent quantity: Earnings per week
- Domain: 20 ≤ hours ≤ 25
- Range: $180 ≤ earnings ≤ $225
In this situation:
- Independent quantity: The number of hours Wendy plans to work per week
- Dependent quantity: The amount of money she earns per week
Reasonable domain and range values:
- Domain: The reasonable range of values for the number of hours Wendy works per week is between 20 and 25 hours. This is because she plans to work between 20 and 25 hours per week.
- Range: The amount of money Wendy earns per week depends on the number of hours she works. The range of values for her earnings can be calculated by multiplying the number of hours worked by her hourly rate of $9. Therefore, the range of values for her earnings per week will be between $180 (20 hours * $9) and $225 (25 hours * $9).
To summarize:
- Independent quantity: Number of hours worked per week
- Dependent quantity: Earnings per week
- Domain: 20 ≤ hours ≤ 25
- Range: $180 ≤ earnings ≤ $225
There are four cars entered into a pinewood derby race. In how many different orders can they cross the finish line?
To find out the different orders four cars can finish a race, we calculate the permutations, which is 4 factorial, resulting in 24 different orders.
The student is asking about the number of different ways that four cars can finish a pinewood derby race, which is a question of permutations in mathematics. In this case, we want to find out the number of possible arrangements for the four cars crossing the finish line. Since each car is distinct, the number of permutations of four items is given by 4! (4 factorial), which is calculated as 4 × 3 × 2 × 1.
Therefore, there are 24 different orders in which the cars can cross the finish line. Remember, factorial is a mathematical operation that involves multiplying a sequence of descending natural numbers.
Find the smallest positive angle θ in the third quadrant for which tan(θ) = 1.
...?
find the values of the variables and the measures of the angles
To find variable values and angle measures, identify knowns, use appropriate equations for unknowns, calculate vector components, use trigonometric functions and the Pythagorean theorem for the resultant vector, and ensure angles are in radians.
Explanation:To find the values of the variables and the measures of the angles, you need to follow a systematic approach. Start by making a list of known variables and inferences from the problem. Once you've identified what is given, you can solve for the unknowns using the appropriate equations. If the problem involves vectors, you would identify the x- and y-axes before finding the vector components Ax = A cos and Ay = A sin, where A is the magnitude of the vector and cos and sin are the trigonometric functions corresponding to the angles the vectors make with the x-axis. After computing these, you can use the Pythagorean theorem to find the resultant vector length.
To verify your solutions, including the measures of the angles in radians, it's important to assess whether the answers are reasonable. This may involve checking the magnitude and direction of the resultant vector and ensuring that the angles are within the possible range (0 to 2π radians for a full circle).
Find an exact value. cos 15°
The exact value of cos 15° is (√6 - √2)/4.
To find the exact value of cos 15°, we can use the trigonometric identities and special angles to determine its value.
One of the key identities that can be used is the cosine addition formula: cos (A + B) = cos A x cos B - sin A x sin B.
We can rewrite 15° as the sum of two special angles: 15° = 45° - 30°.
Using the cosine addition formula, we have:
cos 15° = cos (45° - 30°) = cos 45° x cos 30° - sin 45° x sin 30°.
Now, we know the exact values of cos 45° (which is (√2)/2), cos 30° (which is (√3)/2), sin 45° (which is (√2)/2), and sin 30° (which is 1/2).
Substituting these values into the equation, we get:
cos 15° = (√2)/2 x (√3)/2 - (√2)/2 x 1/2.
Simplifying further, we have:
cos 15° = (√6 - √2)/4.
This means that cos 15° can be expressed exactly as (√6 - √2)/4 without any decimal approximation.
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Answer:
the answer is check2+check6/4
Step-by-step explanation:
i took an exam and got it right
(i dont know what those check mark things are called or how to put the actual thing on a computer so hopefully you understand the check part)
Two angles are complementary. One contains 30' more than the other. Find both angles
A sports store sells bicycle baskets at $40.00 for two. another sports store sells bicycle baskets at $110 for five. which store sells at the better rate?
The solution is store A
The store which sells the bicycle with a better rate is store A with a price of $ 40.00 for two bicycles
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first store be represented as A
Let the second store be represented as B
Now , the equation will be
The price of 2 bicycles at store A = $ 40.00
So ,
The price of 1 bicycle at store A = price of 2 bicycles at store / 2
Substituting the values in the equation , we get
The price of 1 bicycle at store A = 40/2
The price of 1 bicycle at store A = $ 20
Now ,
The price of 5 bicycles at store B = $ 110
So ,
The price of one bicycle at store B = The price of 5 bicycles at store B / 5
Substituting the values in the equation , we get
The price of one bicycle at store B = 110/5
The price of one bicycle at store B = $ 22
And ,
The price of one bicycle at store B > The price of 1 bicycle at store A
22 > 20
Hence , the store A provides better rate for the price of one bicycle
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A chicken soup recipe calls for 15cups of chicken stock how much is this in quarts
The question's topic is about converting volume from cups to quarts. In this particular case, 15 cups of chicken stock is equal to 3.75 quarts.
Explanation:The subject of this question is the conversion of volume from cups to quarts. In this case, the chicken soup recipe calling for 15 cups of chicken stock needs to be converted into quarts. We know that 1 quart is equal to 4 cups, so we can set up the equation:
4 cups/1 quart = 15 cups/x quarts
To solve for x, we multiply 15 (cups) by 1 (quart) and then divide by 4 (the number of cups in a quart).
Therefore, x = (15*1)/4 = 3.75 quarts. So, 15 cups of chicken stock is equal to 3.75 quarts.
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Write an algebraic equation for the following. Three times the sum of a number and seven is two less than five times the number.
Question 2:
Calculate the average rate of change for the function f(x) = −x^4 + 4x^3 − 2x^2 + x + 1, from x = 0 to x = 1.
A. 0
B. 1
C. 2
D. 7
When the function is given in vertex form y=a(x-h)2+k, how is the vertex found?
Answer:
Given function is [tex]y=a(x-h)^2+k[/tex] ...........(1)
We re write the function,
transfer k to LHS,
[tex]y-k=a(x-h)^2[/tex]
Since, One variable has degree 2 and one variable has degree 1.
⇒ Function Represent the equation of Parabola.
In given Function,
Coordinates of vertex is ( h , k )
So To, find the vertex of the function.
First we rewrite the function in vertex form that is like equation (1) then we compare them and write the coordinate of the vertex.
For Example,
1. y = 2(x - 2)² + 6 then vertex of the function is ( 2 , 6 )
2. y = -3 ( x + 3 )² - 6
y = - 3 ( x - (-3) )² + ( -6) then vertex of the function is ( -3 , -6 )
If side a has a length of 3 and side b has a length of 4, use the pythagorean theorem to find the length of side
c. round the answer to the nearest tenth.
PLEASE HELP ME WITH THIS??
Homer the Hungry Hippo is munching on the lily pads in his pond. When he got to the pond,there were 30 lily pads,but he is eating 5 lily pads an hour. Henrietta the Hungry Hippo found a better pond with 38 lily pads! She eats 7 lily pads every hour. If Homer and Henrietta start eating at the same time,when will their ponds have the same number of lily pads remaining?
What fraction is greater than 1/2. 4/6 3/8 1/3 2/5?
The polynomial given below has _____ root(s).
2x2 + 5x + 2
A. two complex
B. two positive
C. two negative
D. one positive and one negative
...?
What times what equels 108
8/10 of 1 percent is equal to .008. TRUE or FALSE
You can run 3 3/5 miles in 40 minutes.
What is your unit rate?
The unit rate is calculated by dividing the distance run by the time taken. In this case, the unit rate is 5.4 miles per hour, indicating that the student runs 5.4 miles for every hour they run.
Explanation:To find the unit rate, we first convert the distance to a decimal. So, 3 3/5 miles becomes 3.6 miles. Unit rate is the ratio of the amount of a single unit of an item to its cost. In this case, your unit rate is the distance you run (in miles) per unit of time (in minutes).
Now, you should divide the total distance (3.6 miles) by the time (40 minutes). 3.6 miles / 40 minutes = 0.09 miles per minute.
If you want the unit rate per hour (commonly used), you should multiply this result by 60 (as there are 60 minutes in an hour). 0.09 miles per minute * 60 minutes/hour = 5.4 miles/hour.
So, your unit rate is 5.4 miles per hour, meaning you run 5.4 miles for every one hour of running.
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Which transformation is not isometric?
how do you get a total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator?
feel free to take a gander
What is the volume of a coffee can that is 6.5 inches high and has a diameter of 5 inches?
WHAT IS THE RECIPROCAL OF 5/8 WHOLE NUMBER OR FRACTION?
The reciprocal of the fraction 5/8 is 8/5.
We have,
Fraction:
5/8
Now,
To find the reciprocal of a fraction we write as,
x = 1/x
Now,
x = 5/8
So,
1/x
= 1/(5/8)
= 8/5
Thus,
The reciprocal of the fraction 5/8 is 8/5.
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If the sail of a ship is 10 feet long and has a diagonal length of 26 feet, what is the height of the sail in feet?
29
24
17
8
The height of the sail in feet is 24 feet.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
Look at the triangle ABC below, where we have
BC² = AB² + AC².
The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation. It should be remembered that a right-angled triangle's hypotenuse is its longest side.
Given:
Base = 10 feet
Hypotenuse = 26 feet
Using Pythagoras theorem
H² = P² + B²
P²= (24)² - (10)²
P² = 676 - 100
P² = 576
P=√576
P= 24 feet
hence, height of the sail in feet is 24 feet.
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According to a magazine, a cleaning solution of 5% bleach will remove mildew from a shower or tub. a. How many ounces of bleach do you need to make a quart of 5% bleach solution? b. Explain the method you used using complete sentences. Whats the answer?
Find the perimeter of the figure below. Notice that one side length is not given.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer
The perimeter of the figure is 58 feet if the missing side length is 10 feet.
What is perimeter?It is defined as the length of the circumference or outline of the geometry. It is the sum of the all side measures.
We have a two-dimensional geometry in the picture with dimensions.
The missing side length = 15 - 5 = 10 ft
The perimeter of the figure = 5+7+10+10+15+11
= 58 feet
Thus, the perimeter of the figure is 58 feet if the missing side length is 10 feet.
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there are 1176 students in central high school. there are 50 more girls than boys. how many boys are there.
Answer:
563
Step-by-step explanation:
Plato
1. Find the area of the given circle. Round to the nearest tenth. *theres a picture of a circle and the radius is 3.5*
A. 22.0 cm *squared* B.38.5 cm *squared* C. 11.0 cm *squared* D. 42.8 cm *squared* 2.Find the circumference of the given circle. Round to the nearest tenth.
*picture of a circle with the radius of 3.5* A. 11.0 B. 38.5 C.42.8 D. 22.0 Can you please check if I'm right? I think.. 1. B 2. D
The area and the circumference of the given circle are 38.5 cm² and 20 cm respectively.
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given that, a circle with radius 3.5 cm, we are asked to find the circumference and the area of the given circle,
Area of a circle = π × radius²
Circumference of a circle = 2π × radius
1) Area =
π × 3.5²
= 3.14 × 12.25
= 38.465
≈ 38.5 cm²
2) Circumference =
2π × 3.5
= 2 × 3.14 × 3.5
= 21.98
≈ 20 cm
Hence, the area and the circumference of the given circle are 38.5 cm² and 20 cm respectively.
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Eric bought 300 t-shirts, which were sold in packs of 12. how many packs did eric buy?
Alice had 4 1/4 pounds of walnuts at the beginning of the week. At the end of the week, she had 2 3/4 pounds. How much has she used?
A. 1 3/4
B. 1 1/2
C. 2 1/2
D. 1 1/4
Step [tex]1[/tex]
Convert mixed numbers to improper fractions
we know that
[tex]4\frac{1}{4}=\frac{4*4+1}{4}=\frac{17}{4}[/tex]
[tex]2\frac{3}{4}=\frac{2*4+3}{4}=\frac{11}{4}[/tex]
Step [tex]2[/tex]
Find the difference of the numbers
[tex]\frac{17}{4}-\frac{11}{4}=\frac{6}{4}=\frac{3}{2}[/tex]
Step [tex]3[/tex]
Convert improper fraction to mixed number
[tex]\frac{3}{2}=1.5=1+0.5=1+\frac{1}{2} =1\frac{1}{2}[/tex]
therefore
the answer is the option B
[tex]1\frac{1}{2}[/tex]
a major stadium has 45000 seats. if baseball fans have bought 5/8 of the seats for the next game, how many seats are available?