Note that solving an equation involves finding the value(s) of the variable(s) that make the equation true. For example, solving the equation 2x + 3 = 7 would give the solution x = 2.
On the other hand, solving an inequality involves finding the set of all values of the variable(s) that make the inequality true. For example, solving the inequality 2x + 3 > 7 would give the solution x > 1.
What is inequality in Math?An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
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a ball is thrown from the top row of seats in a stadium the function h(t)=-16t^2+80t+96 gives the height, in feet, of the ball t seconds after it is thrown. how long will it be before the ball hits the ground?
The number of seconds it takes ball to before hit the ground is 6 seconds.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
Given that, a ball is thrown from the top row of seats in a stadium the function h(t)=-16t²+80t+96 gives the height, in feet, of the ball t seconds after it is thrown.
When ball hits the ground h=0
So, -16t²+80t+96=0
-16(t²-5t-6)=0
t²-5t-6=0
By using splitting middle term method, we get
t²-6t+1t-6=0
t(t-6)+1(t-6)=0
t-6=0 or t+1=0
t=6 or t=-1
Time can not be negative integer.
Therefore, the number of seconds it takes ball to before hit the ground is 6 seconds.
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4a. Find the 120th term of the sequence: a1 = 5, d = 0.5 (3 marks) b. Find the sum of the first 120 terms of that sequence. (3 marks)
Answer:
a₁₂₀ = 64.5 , S₁₂₀ = 4170
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 5 and d = 0.5 , then
a₁₂₀ = 5 + (119 × 0.5) = 5 + 59.5 = 64.5
---------------------------------------------------------
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , then
S₁₂₀ = [tex]\frac{120}{2}[/tex] [ (2 × 5) + (119 × 0.5) ]
= 60(10 + 59.5)
= 60 × 69.5
= 4170
Set V Is all do you need three digit numbers using the digits 1,2,3,4 and 5. Which set would be considered a subset V
The set that would be considered as subset V = {1,3,5} i.e set of odd numbers
What is a subset?A set A is a subset of another set B if all elements of the set A are elements of the set B. In other words, the set A is contained inside the set B. The subset relationship is denoted as A⊂B. A set is a collection of objects or elements, grouped in the curly braces, such as {a,b,c,d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.
In the set 1,2,3,4,5 contains odd numbers and even numbers. But there are just 2 even numbers and 3 even numbers.
But the subset V of the numbers above must contain 3 numbers, this means that subset V will contain odd numbers from 1 to 5.
Therefore, This means that subset V = { 1,3,5}
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A traffic radar records the speed of cars driving through an intersection. It records these statistics:
Mean=36.2 mph
Median=28.5 mph
Mode=30.0 mph
What is the most common speed of a car driving through the intersection?
a. 31.6
b. 36.2
c. 30.0
d. 28.5
The most common speed of a car driving through the intersection is 30.0 mph which is indicated by the Mode.
What is the mode of data?A mode of data is defined as an observation with the highest frequency among the values that appear most frequently in the given data.
In the case of ungrouped data, all that is required is to find the observation that happens most frequently.
A traffic radar records the speed of cars driving through an intersection. It records these statistics:
Mean = 36.2 mph
Median = 28.5 mph
Mode = 30.0 mph
As per the question, a car driving through the intersection at 30.0 mph is the most common speed.
This is indicated by the Mode which is the value that appears most frequently in a data set.
Hence, the correct answer would be an option (C).
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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%
Joshua's cousin pledged $12 for a charity walk if Joshua walked 3 miles how much did his cousin pay per mile
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.
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?
Which phrase should be inserted on the line correctly compare the two fractions? Use the models to help.
Answer:
is greater than
Step-by-step explanation:
7/8 is bigger than 2/4
How many tens do u need to make 280
Answer:
28
Step-by-step explanation:
280 divided by 10 = 28
What is the equation of this graph in slope intercept form
The slope-intercept form of the two straight lines in the graph of the question are;
y = 4y = 3What is the slope-intercept form of the equation of a straight line?The slope-intercept form of the equation of a straight line is; y = m·x + c
Where;
m = The slope of the line
c = The y-intercept of the line
The values of the ordered pair of the points on the line are in the form (x, y)
The graph consists of two straight lines, therefore the equations that represent the graphs are found as follows;
Points on the blue line graph are (0, 4), (2, 4), and (4, 4)
The slope of the blue line graph is therefore;
m = (4 - 4)/(2 - 0) = 0
The y-intercept of the blue line graph is; c = 4
The slope-intercept form of the equation representing the blue line graph is therefore;
y = 0 × x + 4
y = 4The slope-intercept form of the equation of the blue line graph is; y = 4
Points on the red line graph are; (0, 3), (2, 3), (4, 3)
The sloped of the red line graph is therefore; m = (3 - 3)/(2 - 0) = 0
The y-intercept of the red line graph is; c = 3
The slope-intercept form of the equation of the red line graph is therefore; y = 0 × x + 3
y = 3
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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
What is -6 - t/4 = -1
Answer: t=-20
Step-by-step explanation:
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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A bicycle shop is selling $500.00 bikes at 10% off. If the sales tax is 13% how much will the
bike cost?
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).
The point (0,0) is located on a line with slope of 3/4. which point could also be located on the line?
Answer:
Below
Step-by-step explanation:
The equation of the line will be y = 3/4 x pick ANY value of 'x' to find the corresponding 'y' value
Say x = 8 then y = 6 8,6 is a point on the line
Answer:
(1 , 0.75)
(2 , 1.5)
(3 , 2.25)
(4 , 3)
(5 , 3.75)
(4 , 3)
(6 , 4.5)
(7 , 5.25)
(8 , 6)
(9 , 6.75)
(10 , 7.5)
(11 , 8.25)
(12 , 9)
Step-by-step explanation:
To find the other points we must put the given information into the slope-intercept form: [tex]y=mx+b[/tex] m = slope and b = y-intercept
[tex]y=\frac{3}{4} x+0[/tex] or [tex]y=\frac{3}{4} x[/tex]
Then just simply start inputting any numbers for x so you can solve for [tex]y=\frac{3}{4} x[/tex] to get the other points of the line.
Prove that limx→2 x/1+x= 1/2 using the definition of limit
-2 3/4, -1 3/4, -3/5 < o > -2 3/4, -3/5, -1 3/4 cual es menor?
Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.
What is fraction?An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.
Here,
Given:
2 [tex]\frac{3}{4}[/tex], -1 [tex]\frac{3}{4}[/tex], 3/5 , -2 [tex]\frac{3}{4}[/tex], -3/5, -1 , [tex]\frac{3}{4}[/tex],
Therefore , by seeing the above given numbers ,
We compare above number
and we get to know ,
The 5th number 3/5, comes out to be smallest number from the following given numbers.
Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.
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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]
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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Peter works in the Spring Roll restaurant. He earns $15.50 per hour plus tips of 15% of food sales. If Peter works 35 hours this week and has $4000 of food sales, how much does he earn in total?
Base salary =
Tips =
Total earnings =
noah has a part-time job at a coffee shop. last month he earned 160$. Noah pays an income tax rate of 10%. how much does Noah earn after tax?
Step-by-step explanation:
first of all, if he continuously earns only $160 per month (or at least in that dimension), then he will not have to pay any income tax.
but to do the exercise :
100% = $160
1% = 100%/100 = 160/100 = $1.60
10% = 1% × 10 = 1.6 × 10 = $16
he earns after tax
160 - 16 = $144
FYI :
when we combine all the calculations above into one sequence, then we know
100% - 10% = 90%
and 90% of 100% is 100% × 0.9
and so he earns after tax
160 × 0.9 = $144
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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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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-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
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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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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Find the equation of the exponential function represented by the table below
The equation of the exponential function represented by the table will be y = 4(3)ˣ.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
Take two points from the table, then the points are (0, 4) and (1, 12).
The equation passes through (0, 4), then we have
4 = a(b)⁰
a = 4
The equation passes through (1, 12), then we have
12 = 4(b)¹
b = 3
Then the equation of the exponential function represented by the table will be y = 4(3)ˣ.
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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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