The linear inequality in open-sentence form are
2x - 7y > 10 8 + x > 5 What are open sentences?An open sentence is a mathematical statement that contains at least one blank or unknown and that becomes true or false when the blank is filled or a quantity is substituted for the unknown.
Now, since we have the expressions,
2x + 8 = 10y 2x - 7y > 10 8 + x > 5 and3 < 5First, we note that there are 3 open sentences and only two of them are inequalities.
The 3 open sentences are
2x + 8 = 10y 2x - 7y > 10 8 + x > 5The two inequalities are
2x - 7y > 10 8 + x > 5So, the linear inequality in open-sentence form are
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Need help as soon as possible!! Edge 2023
The given quadratic equation is f(x) = x³ - 3x² + 2x-1. The two solutions to the equation are x = (3x + √(9x² + 4))/2x² and x = (3x - √(9x² + 4))/2x².
What is quadratic equation?A quadratic equation is written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
To solve this equation, we will use the quadratic formula.
The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions are given by
x = [-b ± √(b² - 4ac)]/2a.
In this equation, a = x², b = -3x, and c = -1. Plugging these values into the formula, we get x = [3x ± √(9x² - 4(x²)(-1))]/2(x²). Simplifying this, we get
x = [3x ± √(9x² + 4)]/2x².
Now, we must solve for the two solutions. The first solution is x = (3x + √(9x² + 4))/2x². The second solution is
x = (3x - √(9x² + 4))/2x².
Therefore, the two solutions to the given equation are
x = (3x + √(9x² + 4))/2x² and
x = (3x - √(9x² + 4))/2x².
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Partial credit is only available if all your work is shown.
1. Express each ratio as a fraction in simplest form.
a. 26:169 b. 36 to 78
2. While walking her dog, Sylvia noticed that 32 houses had a pot of red flowers on their
front step and 24 had a pot of yellow flowers. Write the ratio of red to yellow pots of
flowers three different ways.
a. b. c.
3. Express each rate as a unit rate.
a. 32 teams in 4 divisions
b. $2.70 for 15 ounces WILL GIVE BRAINLIEST
1. The expression of each ratio as a fraction in the simplest form is as follows:
a) 26:169 = 2/13b) 36 to 78 = 6/13.2. Writing the ratio of red to yellow pots of flowers three different ways are as follows:
a) 32:24 = 4:3b) 32:24 = 57%c) 32:24 = 0.57.3. Expressing each rate as a unit rate is as follows:
a. 32 teams in 4 divisions = 8 team per divisionb. $2.70 for 15 ounces = $0.15.What is a ratio?A ratio is the unit rate, which is the quotient of one value compared to another.
The quotient of the value is the division of one quantity by another.
Expressing Ratio as a Fraction:a) 26:169 = 26/169 = 2/13
b. 36 to 78 = 36/78 = 12/26 = 6/13
Ratio of Red to Yellow Pots of Flowers:The number of houses with a pot of red flowers = 32
The number of houses with a pot of yellow flowers = 24
The ratios of red to yellow pots of flowers in three different ways = 32: 24
The sum of ratios = 56 (32 + 24)
a) 32:24 = 4:3 = 1.75:1
b) 32:24 = 57% (32/56 x 100)
c) 32:24 = 0.57 (32/56)
Expressing each rate as a unit rate:a. 32 teams in 4 divisions = 8 team per division (32/4)
b. $2.70 for 15 ounces = $0.15 ($2.70/15)
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What is 6 equations that are equivalent to 6m=48?
Answer:
3m=24
m=8
12m=96
24m=192
48m=384
96m=768
A group of collage students are going to a lake house for the weekend and plan on renting small cars(s) and large(l) cars to make the trip. Each car can hold 5 people and each large car 8 people. A total of 15 cars were rented which can hold 90 people altogether. Determine the number of large car and rental cars.
Answer:
10 small, 5 large
Step-by-step explanation:
if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l
students would need to rent 5 small cars and 8 large cars
A right triangle is drawn on a coordinate plane. Two vertices of the triangle are points A(−2,4) and B(3,−2). The third vertex of the triangle is point C, which lies in the third quadrant of the coordinate plane.
What is the distance from point A to point C?
_____________________________________
(giving brainliest to correct answer)
(reporting spams/wrong answers)
_____________________________________
Answer:
6
Step-by-step explanation:
This is a right triangle, so the point is C(-2, -2), so 2+4=6
The table below shows the cost of downloading songs from a website. Number of Songs Number of Songs Total Cost Total Cost 6 6 $ 1.80 $1.80 12 12 $ 3.60 $3.60 20 20 $ 6 $6 What is the constant of proportionality between the total cost and the number of songs?
Answer:
Step-by-step explanation:
To find the constant of proportionality, we can use the formula for a proportional relationship: y = kx, where y is the total cost, x is the number of songs, and k is the constant of proportionality.
Using the table, we can find two pairs of values for y and x:
When x = 6, y = $1.80
When x = 12, y = $3.60
We can set up a proportion:
y1 / x1 = y2 / x2
$1.80 / 6 = $3.60 / 12
Simplifying, we get:
$0.30 = $0.30
This tells us that the constant of proportionality is $0.30.
We can check this by using another pair of values:
When x = 20, y = $6
Using the formula y = kx, we get:
$6 = ($0.30)(20)
Simplifying, we get:
$6 = $6
This checks out, so we can be confident that the constant of proportionality is $0.30.
The diagonals of a square are 15 cm. Find the perimeter of the square
Answer:60
Step-by-step explanation:
6 friends share 3 apples.
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please help me i need a big help it is very cunfuseing
Answer:
the answer is C.
Step-by-step explanation:
Put both equations in the slope intercept form of the line and then graph to estimate where the lines cross.
y = mx + b
7x - y = 7 The 7x is on the wrong side of the equal sign, so subtract 7x from both sides of the equation
7x - 7x -y = -7x + 7
-y = -7x + 7 We want the equation to start y = , not -y =. so divide all the way through by -1
[tex]\frac{-1y}{-1}[/tex] = [tex]\frac{-7x}{-1}[/tex] + [tex]\frac{7}{-1}[/tex]
y = 7x - 7
x + 2y = 6 The x is on the wrong side of the equal sign. Subtract x from both sides
x -x + 2y = -x + 6
2y = -x + 6 Divide all the way through by 2
[tex]\frac{2y}{2}[/tex] = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{6}{2}[/tex]
y = [tex]\frac{-1}{2}[/tex] x + 3
You can see from the graph attached where the lines cross.
Helping in the name of Jesus.
Aaron wraps present in a store. In one hour, he wraps 8 games and one console. How much wrapping paper does Aaron use? How much wrapping paper does Aaron use? Use exercises 1-3 to answer the question.
The wrapping paper used by Aaron is 9 and 2/3 feet of paper
Finding the amount of wrapping paper used:To solve this problem, use the given information about how much wrapping paper is needed for each game and gaming console, and then multiplied by the number of games and consoles that Aaron wraps in one hour. For simple calculation convert mixed fractions into an improper fraction and solve the problem.
Here we have
Aaron wraps present in a store. In one hour, he wraps 8 games and one console.
From the given figure,
Each game takes 2/3 foot of wrapping paper
Each gaming console takes 4 1/3 feet of wrapping paper
From the data
Aaron wraps 8 games in 1 hour
The wrap is used for 8 games = 8 × [ 2/3 foot ] = 16/3 foot
He wraps one console.
The wrap used for 1 console = 4 1/3
Here 4 1/3 = 13/3 [ Converting mixed fraction to improper fraction ]
Hence,
Total amount of wrap used = 16/3 + 13/3
= [ 16 + 13]/3 = 29/3 = 9 2/3
Therefore,
The wrapping paper used by Aaron is 9 and 2/3 feet of paper
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Find the area of the figure.
(Sides meet at right angles.)
Answer: The answer is 14mm
Step-by-step explanation: Area of A= 4mm times 2mm= 8mm
Area of B= 3mm times 2mm= 6mm
8mm + 6mm= 14mm
How I got Area A or Area of A Is I divided the shape into two with an imaginary line
Answer:
See below.
Step-by-step explanation:
We are asked to find the area of the figure.
Let's first break the figure into 2 parts, where there is 2 rectangles.
Rectangle A has the dimensions of 4 mm to 2 mm.
Rectangle B has the dimensions of 3 mm to 2 mm.
For clarification what rectangle is which, Rectangle A is on its smallest side, and Rectangle B is on its longest side.
To find the area of the 2 rectangles we multiply the 2 dimensions given to us, then add their areas together.
[tex]A = L \times W[/tex]
Substitute:
[tex]8 = 4 \times 2 \ (Rectangle \ A)[/tex]
[tex]6 = 3 \times 2 \ (Rectangle \ B)[/tex]
Add:
[tex]6+8=14 \ (A \ and \ B)[/tex]
The area of the figure is 14 mm².
Use your line plot to answer the question below.
How much more white paint was on the palette with the most white paint than on the palette with the least white paint?
Write your answer as a fraction, mixed number, or whole number.
There are 3/8 more white paint on the palette of the highest than the least
What is a line plot?A line plot is a type of graph or simple data visualization tool that uses dots to represent individual data points along a numerical axis.
How to determine how much more white paint was on the paletteFrom the question, we have the following parameters that can be used in our computation:
The line plot
On the line plot, we have
Most white paint = 3/4
Least white paint = 3/8
Calculate the difference between both so, we have
Amount = 3/4 - 3/8
Evaluate
Amount = 3/8
Hence, the amount is 3/8
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Three men took part in a business. They put in N2 000, N4 000 and N1 500 as capital. The profit made was divided among them in the same proportion as the amounts put in. If the profit was N300, how much did each man get?
Answer:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
Step-by-step explanation:
Answer:
N80, N160, and N60
Step-by-step explanation:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
help me please i got 5849.82 but thats not on there
Answer: 1863[tex]\pi[/tex] cm^3 (option C)
Step-by-step explanation:
The volume is given by the equation
[tex]V=\pi r^2h[/tex]
Just placing the values:
[tex]V=\pi (9)^2(23)[/tex]
Notice the pi is left over, so just get the 9^2*23=1863
So the answer for the volume is 1863[tex]\pi[/tex] in cm^3
So your answer is just fine, 5849. Just notice the pi is not in it.
Russell can buy 6 dinners with salads for $114. What is the cost of 6 dinners without any sides?
Use the drop-down menu to show the correct answer.
The cost of one dinner without any sides is $2, and the cost of 6 dinners without any sides is 6 times that amount, which is $12. Answer: $12.
What is equation?An equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are quantities that can take on different values. The goal of solving an equation is to find the values of the variables that make the equation true.Equations can take many different forms, but some common types include linear equations, quadratic equations, polynomial equations, and exponential equations.
What is expression?An expression is a combination of numbers, variables, and mathematical operations that represents a value. Expressions can contain constants, variables, and operators, such as addition, subtraction, multiplication, and division.
In the given question,
There are different ways to approach this problem, but one possible method is to use ratios. Let's assume that the cost of a dinner without any sides is x dollars. Then, the cost of a dinner with salad is x plus some additional amount for the salad, which we don't know yet. Let's call this additional amount y dollars. Therefore, the cost of a dinner with salad is x + y dollars.
According to the problem, Russell can buy 6 dinners with salads for $114. This means that the total cost of 6 dinners with salads is $114. We can write this as an equation: 6(x + y) = 114
Simplifying this equation, we get: 6x + 6y = 114
Dividing both sides by 6, we obtain: x + y = 19
Now we need to find the cost of 6 dinners without any sides, which is 6 times the cost of a dinner without any sides. We already know that the cost of one dinner without any sides is x dollars, so the cost of 6 dinners without any sides is 6x dollars.
To find x, we can use the fact that x + y = 19, which we derived from the given information. We don't know y, but we can express it in terms of x by using the fraction of the salad price to the total price of a dinner with salad. From the long division, we have:
2x - 3
x + 1
This means that y is equal to the remainder of the division, which is -3/(x+1). Therefore, we have: y = -3/(x+1)
Now we can substitute this expression for y into the equation x + y = 19:
x - 3/(x+1) = 19
Multiplying both sides by x+1, we get: x(x+1) - 3 = 19(x+1)
Expanding the products and simplifying, we obtain a quadratic equation:
x^2 + 18x - 22 = 0
We can solve this equation by using the quadratic formula:
x = (-18 ± √(18^2 + 4122)) / (2*1)
x = (-18 ± √(400)) / 2
x = (-18 ± 20) / 2
x = -9 or x = 2
Since we are interested in the cost of a dinner without any sides, which should be a positive number, we discard the negative solution and take x = 2. Therefore, the cost of one dinner without any sides is $2, and the cost of 6 dinners without any sides is 6 times that amount, which is $12. Answer: $12.
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EASY MATH POINTS!
Answer from the screenshot.
There are initially 150 pharaoh ants in Southeast Asia, and every year the population increases by 950,000 ants.
Define the rate of change and initial value of the function.The rate of change of a function refers to how much the output of the function changes with respect to changes in its input, typically expressed as the derivative of the function.
The initial value of a function refers to the value of the function at a specific point in its domain, often denoted as f(0) or f(x_0) for some value x_0 in the domain. It is called "initial" because it is usually the starting point for analyzing the behavior of the function over a range of inputs.
The given function is y=-150x+950,000, where x represents time in years and y represents the total population of pharaoh ants in Southeast Asia.
The initial value of the function is the y-intercept, which is 950,000. This means that at the beginning of the observation period (when x=0), there are 950,000 pharaoh ants in Southeast Asia.
The rate of change of the function is the coefficient of x, which is -150. This means that every year, the population decreases by 150,000 ants. Therefore, option A is correct because it states that the population decreases every year by 150,000 ants, which is the same as -150 multiplied by 1,000.
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PLEASE HELP IM TIMED
Write equivalent fractions for 3/10 and 1/7 using the least common denominator. Type the fractions, using a slash ( / ) to separate the numerator and denominator.
3/10=
1/7=
Answer: Your welcome!
Step-by-step explanation:
The equivalent fractions for 3/10 and 1/7 using the least common denominator are 6/20 and 3/20. The least common denominator of 3/10 and 1/7 is 20, so the fractions must be multiplied by the same number to reach the denominator of 20. 3/10 multiplied by 2/2 is 6/20, and 1/7 multiplied by 3/3 is 3/20.
Q14: In the store, Lean Statks up eight cans each weighing 1 1/3 kg. What is the total weight of the cans
Answer:
10 2/3 kg
8 X 1 1/3 kg = 10 2/3 kg
Answer this please!
the solution to a system of linear equations is (0,4) one of the linear equations in the system is Y=8x+4
Curriculum which addresses learning goals across multiple subjects areas at the same time known as
A curriculum is said to as "integrated" when it simultaneously targets learning objectives across different topic areas.
Explain about the integrated curriculum?Children can pursue learning holistically with an integrated curriculum, free from the limitations frequently imposed by topic boundaries.
Early childhood programs have a strong emphasis on how all subject areas relate to one another and how they all work together to give kids fundamental learning skills. It acknowledges that reading, writing, thinking, speaking, literature, drama, world history, integrated maths ,science, health, sport science, music, and creative arts are all part of the primary school curriculum.Moreover, technology and investigative techniques are included in the curriculum. Integration recognizes and strengthens the connections that exist among the things. A curriculum that is integrated involves learning that is synthesised across conventional topic areas and learning experiences that are intended to reinforce one another.Know more about the curriculum
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If the angle 405° rotates 180° clockwise, what is the new measurement of the co-terminal angle?
___°
Answer: I believe the answer would be 130°
Step-by-step explanation:
Answer:
The angle A will remain the same irrespective of their rotation so it will be 130°.
Step-by-step explanation:
MARK ME BRAINLIST!Can someone help me figure out how to do this? What’s the answer?
The different circumferences to go from the start to the finish are 21.98, 31.4, 37.68, and 65.94.
How to calculate the circumference?One of the ways of calculating the circumference is using the diameter of a circle (distance from one side to the next one) and applying the formula circumference = diameter x [tex]\pi[/tex]. Now, let's calculate the circumference.
7 x 3.14 = 21.9810 x 3.14 = 31.412 x 3.14 = 37.6821 x 3.14 = 65.9442 x 3.14 = 131.8813 x 2 (radius to diameter ) x 3.14 = 81.647.25 x 2 (radius to diameter) x 3.14 = 45.533.4 x 3.14 = 10.67650 x 3.14 = 1572.24 x 3.14 = 7.032.1 x 2 (radius to diameter ) x 3.14 = 13.189.5x 2 (radius to diameter ) x 3.14 = 59.66FinishLearn more about the circunference in https://brainly.com/question/30023353
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The assets and liabilities of a landscaping business are listed below.
What is the net worth of the landscaping company?
A) $126,790
B) $187,205
C) $282,799
D) $470,004
The net worth of the landscaping company is given by:
$187.205.
How to calculate the net worth?
The net worth of a company or of a person is given by the sum of all assets of the person subtracted by the sum of all debts of the person.
In the context of this problem, the assets, and it's values, of the company are given as follows:
Owned Inventory: $48,760.
Cash: $126,790.
Savings account: $32,436.
Owned equipment: $20,700.
Accounts receivable: $15,640.
Property value: $225,678.
Hence the sum of the assets is given by:
Assets = 48760 + 126790 + 32426 + 20700 + 15640 + 225678 = $469,994.
The debts of the company, with it's values, are given as follows:
Small Business Loan: $76,400.
Building Mortgage: $189,429.
Other debt: $16,970.
Hence the sum of the debts is given by:
Debts = 76400 + 189429 + 16970 = $282,799.
Then the net worth of the company is:
Net worth = Assets - Debt = 469,994 - 282,799 = $187,205.
Consider the equation 5 + x = n . What must be true about any value of x if n is a negative number? Explain your answer. Include an example with numbers to support your explanation. Enter your answer, your explanation, and your example in the space provided.
Answer:
x < 5 because any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be less than 5.
p^2/4+ Q^2/9+36+pq/3+4q+6p
Answer:
The given expression is:
p^2 + 4q^2 + 9 + 36 + pq + 3 + 4q + 6p
Rearranging the terms, we get:
p^2 + 6p + 4q^2 + pq + 4q + 48
Now, we can group the first three terms and the last three terms together as follows:
(p^2 + 6p + 9) + (4q^2 + pq + 4q + 39)
The first group can be factorized as a perfect square trinomial:
(p + 3)^2
The second group can be factorized by grouping the first two terms and the last two terms:
(pq + 4q) + (4q^2 + 39)
We can factor out q from the first two terms, and 4 from the last two terms:
q(p + 4) + 4( q^2 + 9)
Now, we can factor the second group as a sum of squares:
q(p + 4) + 4(q + 3)(q - 3)
Therefore, the fully factorized form of the expression is:
(p + 3)^2 + q(p + 4) + 4(q + 3)(q - 3) + 48
Note that this expression cannot be simplified further.
Find the c and y- intercepts of the parabola y = 3x^2 -9x + 9
The y-intercept is (0, 9), and the parabola has no x-intercepts.
What are intercepts?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.
X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.
To find the y-intercept of the parabola, we set x = 0 and solve for y:
y = 3x² - 9x + 9
y = 3(0)² - 9(0) + 9
y = 9
Therefore, the y-intercept is (0, 9).
To find the x-intercepts, we set y = 0 and solve for x:
0 = 3x² - 9x + 9
0 = x² - 3x + 3
Using the quadratic formula, we get:
x = [3 ± √((-3)² - 4(1)(3))]/(2(1))
x = [3 ± √(9 - 12)]/2
x = [3 ± √(-3)]/2
The square root of a negative number is not a real number.
The parabola does not intersect the x-axis, and therefore, there are no x-intercepts.
Therefore, the y-intercept is (0, 9), and the parabola has no x-intercepts.
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prime and composite numbers hard questions reasoning questions
1-Is the sum of two prime numbers always a prime number?
Solution:
No. Here is an example.
3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.
2-Is the product of two prime numbers also a prime number?
Solution:
Never because it will have 1 and itself as factors and also the two numbers involved in the product.
Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.
3-Which is the largest 3 digit prime number?
Solution:
Start with the largest three digit number 999.
4- Which is the smallest 2 digit prime number?
Solution
Start with the smallest 2 digit number 10.
10 is not a prime number
Answer: 11 is a prime number
Nakia is an architect designing a house with a peaked roof. She is trying to decide what the limitations are on her design. If AB is 8 feet and triangle ABC will be isosceles, describe the possible lengths for AC.
The possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
How did we get the value?If triangle ABC is isosceles, then AC must be equal to BC. Let's call the length of AC "x".
Using the Pythagorean theorem, we can find the length of the diagonal line segment BD (which is also the height of the peaked roof):
BD^2 = AB^2 - (AC/2)^2
BD^2 = 8^2 - (x/2)^2
BD^2 = 64 - x^2/4
To ensure that the roof is peaked, we need BD to be less than x (otherwise, the roof would be flat). So we can set up an inequality:
BD < x
√(64 - x^2/4) < x
64 - x^2/4 < x^2
256 - x^2 < 4x^2
5x^2 > 256
x^2 > 51.2
x > √(51.2)
Therefore, the possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
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Find an equation for the line that passes through the points (4,2) and (-6,4) .
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{4}}} \implies \cfrac{ 2 }{ -10 } \implies - \cfrac{ 1 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{ 1 }{ 5 }}(x-\stackrel{x_1}{4}) \\\\\\ y-2=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}\implies y=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 5 }x+\cfrac{14}{5} \end{array}}[/tex]