Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.
what is equations ?Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either contingent equations or identities are categories for equations. An identity holds true for whatever value of the variables.
given
x+y=7
2x-y=-1
8x=20
x= 5/2
-4y = -8
y = 2
Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.
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figure A is reduced of figure B.
a). what is the scale factor?
b). if A has area 15cm2. find the area of B.
Part A
Answer: 3/5Reason:
Divide the side lengths of B over A to get B/A = 3/5. The order is important. The fraction 3/5 is smaller than 1 to indicate a size reduction. There are no units involved with the scale factor.
=========================================
Part B
Answer: 5.4 square cmReason:
The linear scale factor is 3/5. The area scale factor is (3/5)^2 = 9/25. It means if figure A had area 25, then figure B would have area 9.
Let's use that idea to set up the following:
(area of figure B)/(area of figure A) = 9/25
B/A = 9/25
x/15 = 9/25
25x = 15*9
25x = 135
x = 135/25
x = 5.4 represents the area of figure B
you plan to mark up your taco prices by 15%, of your original prices are 4.50, 2.25, and 3.00 what would be the new prices?
Answer:
Step-by-step explanation:
$4.50 + $4.50(0.15) = $5.18
$2.25 + $2.25(0.15) = $2.59
$3.00 + $3.00(0.15) = $3.45
Predict a ranking for the speed of sound in four different substances: steel, 25°C air, 50°C air, and water. Use the kinetic theory of matter to defend your predictions.
Based on the principles of kinetic theory, the speed of sound in matter is determined by the mean free paths of the molecules that make up the matter and the properties of the material itself.
What is speed?Velocity is the speed at which an object moves or changes position over a period of time. It is usually measured in units such as meters/second, miles/hour, kilometers/hour. It is an important factor in the movement of objects and the movement of sound, light and other forms of energy. Speed is also an important factor in transport safety, as it affects how long it takes a vehicle to stop and how far it must travel to stop safely.
Predict the ranking of sound speeds for four different materials.
Steel, 25°C air, 50°C air and water. Use the theory of motion of matter to protect your predictions.
Therefore, the speed of sound varies greatly depending on the material. Below is the ranking of the speed of sound for the four substances listed. From fastest to slowest:
1. 25°C Air: The speed of sound in warm air at 25°C is the fastest of the four substances, and because air is made up of both light and heavy molecules, it can travel quickly. The speed of sound in warm air at 25 °C is about 343 m/s.
2. 50°C air: The speed of sound in air at 50°C is slower than in air at 25°C. This is because molecules in warm air spread out more and move more slowly. The speed of sound in air at 50 °C is approximately 331 m/s.
3. Water: Water molecules are denser and move slower, so the speed of sound in water is slower than in air. The speed of sound in water is approximately 1,482 m/s.
4. Steel: The speed of sound in steel is the slowest of the four substances. This is because steel is composed of heavier molecules that move slower than those in air and water.
Overall, the order of sound velocities for the four materials is air at 25°C, air at 50°C, water, and steel. This classification is based on the principle of kinetics that the speed of sound in a material is determined by the mean free paths of the molecules that make up the material and the properties of the material itself.
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Without looking, you get to choose twice. You will not put them back
each time, because that would be gross.
A) What kind of event is this (independent or dependent)?
B) What is the probability that you would draw 2 reds?
show your work and answer
A) This is an independent event.
B) The probability that you would draw 2 reds is 0.017
What is probability?The likelihood of an event occurring is known as probability. You can determine how likely something is by asking someone what the probability of something happening is.
When people purchase lottery tickets, the likelihood of winning is typically stated, and it occasionally may be as low as 1/10,000,000. (or even worse). This informs you that there is a low likelihood that you will succeed.
There are 4 reds out 0f 30 colours
The probability of drawing red the first time is 4/30 = 2/15
The probability of drawing red on the 2nd time is 4/30 = 2/15
The probability of drawing red on the both draw is = 2/15 × 2/15
= 4/225
= 0.0170
Thus, The probability of drawing red on the both draw is 0.0170.
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A construction company is building a fence that is 1 1/3 miles long. They can building the fence 1/6 Mile every hr. How long to build the fence?
The time to build the fence will be 10 hours.
How to calculate the time?The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since construction company is building a fence that is 1 1/3 miles long and they can building the fence 1/6 Mile every hr.
The time to build the fence will be:
= 1 1/3 ÷ 1/6
= 5/3 × 6/1
= 30 / 3
= 10 hours.
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A family buys a studio apartment for $140,000 They pay a down payment of $35,000
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $7,000 down payment be?
Answer:
a. Their down payment is 25% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$35,000 ÷ $140,000 = 0.25 = 25%
b. A $7,000 down payment would be 5% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$7,000 ÷ $140,000 = 0.05 = 5%
question 12 to find the shaded portion
12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.
9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,
= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].
= [8×8 - 4×4] cm².
= 64 - 16 cm².
= 48 cm².
10. Similarly the figure in (10) is twice the area of the two trapezoids.
11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.
12. The total area is the sum of the areas of the trapezoid and the parallelogram.
13. The larger figure is a rectangle with a right-angle triangle on top.
We have to subtract two rectangles from this to obtain the area of the shaded region.
14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.
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Proving Triangles congruent by ASA and AAS
Answer: Congruent by AAS
Step-by-step explanation:
FG and EH are congruent because they are given.
EH is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.
FG is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.
Angle G is congruent to Angle E because they are both right angles, and right angles are congruent.
Angle EIH and Angle FIG are congruent because of the vertical angles theorem.
Triangle EHI and Triangle GFI are congruent by the Angle-Angle-Side Theorem, or AAS.
Jen has some buttons. She gets
23 more buttons from her mom.
Now she has 65 buttons.
How many buttons did
Jen have to begin with?
Answer:
x + 23 = 65
x = 42
She had 42 buttons to begin with.
the chef mixes 12 tablespoons of flour to 8 tablespoons of sugar what fraction of the mixture is sugar.
Answer:
2/5
Step-by-step explanation:
To find the fraction that is sugar,
part sugar/ total
The total is sugar + flour = 8+12 = 20
8/20
We can simplify
Divide the top and bottom by 4
8/4 =2
20/4 = 5
The fraction is 2/5
Answer:
[tex]\sf\frac{8}{20}[/tex]
Step-by-step explanation:
First let us find the total.
Total = Flour + Sugar
Total = 12 + 8
Total = 20
Now we know that, there are 8 tablespoons of sugar in the whole mixture.
So, write it as a fraction, you have to divide the number of tablespoons of sugar by the total.
Sugar = 8/20
Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
Answer: [tex]\frac{c}{d} = \frac{a}{b}[/tex]
Step-by-step explanation:
By the given figure, the triangle's sides appear congruent. By the Segment Addition Postulate:
RT + TQ = RQ and
RU + US = RS
Substitute this with the given variables.
c + d = RQ
a + b = RS
From this, we can create the following proportion:
[tex]\frac{c}{d} = \frac{a}{b}[/tex]
Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 140. The comet follows a parabolic path with directrix x = 100 and vertex at (85, 0). Part A: Write the equation of the planet's orbit in standard form. Show your work. (2 points) Part B: Write the equation of the comet's path in standard form. Show your work. (4 points) Part C: Identify all points where the planet's orbit intersects the path of the comet. Show your work and round answers to the hundredths place. (4 points)
Answer:
Part A: The equation of the planet's orbit is simply the equation of a circle with radius 70 (half the diameter) and center at the origin. The standard form equation of a circle with radius r and center at (h,k) is (x-h)^2 + (y-k)^2 = r^2. In this case, h and k are both 0, so the equation of the planet's orbit is simply x^2 + y^2 = 70^2.
Part B: The equation of the comet's path is a parabola with directrix x=100 and vertex at (85, 0). The standard form equation of a parabola with directrix x=p, vertex at (h,k), and focus at (h,k+f) is y = (4f/p^2)(x-h)^2 + k. In this case, p=100, h=85, k=0, and f is the distance from the vertex to the focus. We can find f by using the equation f = sqrt(p^2+4ah), where a is the distance from the vertex to the directrix. In this case, a=50, so f = sqrt(100^2+45085) = 50. Plugging this value into the equation for the parabola, we get y = (4*50/100^2)(x-85)^2 + 0. Simplifying this gives us y = (2/25)(x-85)^2.
Part C: To find the points where the planet's orbit intersects the path of the comet, we need to find the points where the x and y coordinates of the two equations are equal. Setting the two equations equal to each other gives us (2/25)(x-85)^2 = x^2 + y^2 - 70^2. Expanding the left side and rearranging the terms gives us x^2 - 170x + 15129 = 0. We can use the quadratic formula to find the solutions for x: x = (170 +/- sqrt(170^2 - 4115129))/2. This simplifies to x = 85 +/- sqrt(40900). Therefore, the points of intersection are (85 + sqrt(40900), 0) and (85 - sqrt(40900), 0). Rounding these values to the hundredths place gives us (92.84, 0) and (77.16, 0).
write a x 10^n where 10>a<100
On solving the provided question, we can say that - the value the exponent [tex]10^n\\[/tex] will be 100000
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
from the given exponents we have
[tex]10^n[/tex]
where n = 5
so [tex]10^5 = 100000[/tex]
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(16,1), (17,7) find the slope of line through each pair of points
The slope of the line through each pair of points (16,1), (17,7) is 6.
A line's slope serves as a gauge for its steepness. Between any two locations on the line, it is the ratio of the vertical change to the horizontal change.
The slope of a line can be positive, negative, zero, or undefined.
In algebraic equations, the letter "m" frequently stands in for slope. In slope-intercept form, a line's equation is written as y = mx + b, where m denotes the line's slope and b its y-intercept.
To find the slope of the line that passes through two points (x1, y1) and (x2, y2), you can use the following formula
m = (y2 - y1) ÷ (x2 - x1)
where m is the slope of the line and (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the slope of the line through the points (16,1) and (17,7) is:
m = (7 - 1) ÷ (17 - 16) = 6 ÷ 1 = 6
So the slope of the line is 6.
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Yoga Common Core Performance Assessment_ Regina takes yoga classes 2 days a week at the community center. The cost for the classes is $72, and Regina pays an additional one-time fee of $12 to rent the yoga equipment used in class. The classes run for 6 weeks. The local gym offers the same yoga program, including equipment, for $8 a class. Is Regina paying more or less than what the local gym charges for yoga classes?
On solving the provided question, we can say that - by the help of unitary method the value of 9 units will be
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
cost for the 12 classes = $72
cost of 1 unit = $6
cost of 9 units = $54
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-15 POINTS-
How many sides does a regular polygon have if one interior angle measures 144°
Answer: 10 sides
Step-by-step explanation:
You can always use the given formula to calculate but I (personally) find it much easier to calculate the number of sides using the exterior angle.
To calculate the exterior angle, it is 180 - the interior angle.
In this example, the exterior angle would be 180-144 = 36°
Because it is a regular polygon, we know that all the angles in the shape are the same.
In all polygons, the exterior angles always add up to 360 degrees.
So divide 360 by 36 (the size of each exterior angle), and you get 10.
360/36 = 10
Discussion Topic
How did the United States' entry into World War I change the culture and
international political policies of the country?
The United States' entry into World War I led to a rise in nationalism and patriotism, as well as a shift towards a more interventionist foreign policy. This had a lasting impact on the culture and international political policies of the country.
Explanation:The United States' entry into World War I marked a significant shift in the culture of the country. Prior to the war, the United States had maintained a policy of isolationism, with a focus on avoiding involvement in foreign conflicts. However, the country's entry into the war marked a shift towards a more interventionist foreign policy, as the United States began to take a more active role in international affairs.
HOPE IT HELPS!If a circle has a radius of 7/4 cm, what is the diameter?
Responses
a) 3 1/2 cm
b) 7/8 cm
c) 1 3/4 cm
d) 2 1/4 cm
Answer:
Step-by-step explanation:
Answer:
Option A) [tex]3\frac {1}{2}[/tex]
Step-by-step explanation:
In order to find the diameter you need to multiply the radius x 2
Over here the radius is given as 7/4cm
But the diameter is
[tex]\frac{7}{4} X\frac{2}{1}[/tex] = [tex]\frac{7}{2}[/tex]
And when we simply the mixed fractions we only get one possible answer
which is [tex]3\frac{1}{2} = \frac{7}{2}[/tex] Option A)
Help ASAP PLSSS!! I’d really appreciate it! Thank youuu!
How many 2/3 Tablespoons are in a half Tablespoon
Therefore , the solution of the given question of equation come out to be
x = 1/3 tablespoon .
Define equation.Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.
Here,
Given : 2/3 cup Tablespoons
We have to find the half Tablespoons
So,
In order to find the half Tablespoons
Thus,
=> 1 Tablespoon = 2/3Tablespoons + x
where x is the half Tablespoons
=> x = 1/3 tablespoon
Therefore , the solution of the given question of equation come out to be
x = 1/3 tablespoon .
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What is -6 - t/4 = -1
Answer: t=-20
Step-by-step explanation:
Prove that limx→2 x/1+x= 1/2 using the definition of limit
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 140 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?
New York City is 2.727272.% of the United States' population. NYC's population is 9 million people. What is the population of the United Sates?
The population of US is 330 million approx.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.
Given
population of new york = 2.727272% population of US
population of new york = 9 million
population of US = 1/2.727272% of new york
population of US = 36.6666 x 90,00,000
population of US = 33,00,00,087.9 = 330 million approx
Hence population of US is approx 330 million.
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Timothy bought a house for $360,000. He paid 20% down, and agreed to pay $1,375.69 per month for 30 years. His payment of $1,375.69 does not include property tax and insurance. How much interest will Timothy pay in 30 years?
INTREST-300000
Step-by-step explanation:
36000000
Explain what the ratio 15:73 represents
Therefore , the solution of the given problem of ratio comes out to be 15:73 ratio simplified is 15/73.
What is ratio?A ratio or fraction in math displays how many times one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3 or decimal 1.333).
Here,
To simplify the ratio 15:73, we find the greatest common divisor of 15 and 73, and then we divide 15 and 73 by the greatest common divisor.
The greatest common divisor that you can use to simplify 15:73 is 1. Which means the answer to ratio 15:73 simplified is:
Here is the math to illustrate better:
15/1 = 15 and 73/1 = 73
Thus, 15:73 ratio simplified is 15/73
Therefore , the solution of the given problem of ratio comes out to be 15:73 ratio simplified is 15/73.
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A pipe has 9/16" that is threaded, but you need to trim 4/32" off of the threaded part. How long will the threaded be after the trim? a. 17/32, b. 7/8, c. 7/16, d/ 15/32
two equivalent ratios for 17:5?
Answer:
34/10 is equivalent to 17/5 because 17 x 2 = 34 and 5 x 2 = 1051/15 is equivalent to 17/5 because 17 x 3 = 51 and 5 x 3 = 1568/20 is equivalent to 17/5 because 17 x 3 = 68 and 5 x 3 = 20
Step-by-step explanation:
hii, how are you
How many tens do u need to make 280
Answer:
28
Step-by-step explanation:
280 divided by 10 = 28
1. choices : never. always. sometimes
2. choices: never. always. sometimes
3.choices: variables. coefficient. exponents
4:choices: variables. coefficient. exponents
5. choices: not closed. closed
please help
The product of f(x) and g(x) is always a polynomial. By the definition of
polynomials the product of polynomials is always a polynomial because
the coefficient are real numbers and the exponents are whole
numbers. Real numbers and whole numbers are closed under addition
and subtraction.
What is Polynomial?A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.
Here f(x) and g(x) are two given polynomial,
let f(x) = x+1 ang g(x) = x-1
f(x).g(x) = (x+1)(x-1).
f(x).g(x) = x²-1.
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