Answer:
7+8=15 that's the total
7\15 or 8\15
Answer: that is it’s simplest form
Step-by-step explanation:
2,825 people went to a rugby
match.
Tickets were £5 each.
How much money was paid in total?
Answer:
14125
Step-by-step explanation:
2,825x5=14125
Answer:
The amount paid in total was £14125
Step-by-step explanation:
Population that went to the rugby match = 2825
Cost of 1 ticket = £5
Cost of 2825 tickets = 2825x5
= £ 14125
Hence the amount paid in total was £14125
2. A line passing through (6, a) and (9,-4) is parallel to y = 2/3x - 6. What is the value of a?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x -6 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so its slope is 2/3 hmmmm
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{a})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{a}}}{\underset{\textit{\large run}} {\underset{x_2}{9}-\underset{x_1}{6}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{2}{3}}\implies \cfrac{-4-a}{3}=\cfrac{2}{3}\implies -12-3a=6 \\\\\\ -12=6+3a\implies -18=3a\implies \cfrac{-18}{3}=a\implies -6=a[/tex]
Is base angles of isosceles triangle are equal 1?
Yes, the base angles of an isosceles triangle are equal to each other.
The base angles of an isosceles triangle are equal because of the symmetry of the triangle. In an isosceles triangle, the two sides that are opposite the congruent angles are also congruent in length. This means that the triangle has a line of symmetry, or a line that divides it into two congruent halves. Since the triangle is symmetrical, the base angles are equal in measure.
Another way to understand why the base angles of an isosceles triangle are equal is to consider the definition of an isosceles triangle. An isosceles triangle is defined as a triangle with at least two congruent sides. Since the base angles are opposite the congruent sides, they must also be congruent. Therefore, the base angles of an isosceles triangle are equal.
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yes , base angles of isosceles triangle are equal 1 because An isosceles triangle is a triangle with two sides of equal length and the base angles of the isosceles triangle are equal in length.
The sides of equal length are called the legs of the triangle, and the third side is called the base. The base angles of an isosceles triangle are the angles formed by the base and the legs of the triangle. Since the base angles are formed by the base and the legs of the triangle, which are both congruent (i.e., have the same length), the base angles must also be congruent. In other words, the base angles of an isosceles triangle are equal.
The vertex angle of an isosceles triangle is the angle formed by the two legs at the apex of the triangle. This angle is always larger than the base angles, and its measure is equal to the sum of the measures of the base angles. For example, if the base angles of an isosceles triangle have a measure of 45 degrees each, the vertex angle will have a measure of 90 degrees (45 + 45). In summary, the base angles of an isosceles triangle are congruent and equal, and the vertex angle is larger than the base angles and is equal to the sum of the measures of the base angles.
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A recipe for fruit smoothies states that of the total amount of ingredients 2/3 should be fruit. The amount of 1/2 yogurt in the recipe should be of the amount of the fruit. What fraction of the total amount of ingredients is neither fruit nor yogurt?
The fraction of the total amount of ingredients is neither fruit nor yogurt is given as follows:
0.
How to obtain the fraction?The fraction is used applying the proportions in the context of this problem, which represent a fraction of a total amount.
The total fraction of all the ingredients is given as follows:
100% = 1.
The ingredients, along with their fractions, are given as follows:
Fruits: 2/3.Yogurt: half of fruit = 2/3 x 1/2 = 2/6 = 1/3.Hence the percentage composed by fruit or yogurt is given as follows:
2/3 + 1/3 = 3/3 = 1 = 100%.
Hence 0% is composed by neither fruit nor yogurt, hence the fraction is also of zero.
(as the entirety of the recipe is composed by either fruits or yogurts, as obtained above).
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Which equation describe a linear function?
a. V= s^2
b. y=(1/6)x
c. y=(2)^x
d. A= π^2
From the given option, equation y = (1/6)x describe a linear function. So the option b is correct.
In the given question, we have to find which equation describe a linear function.
As we know that,
In a graph, a linear function is one that generates a straight line. The degree of the polynomial function is often either maximum 1 or minimum 0. Despite the fact that both calculus and linear algebra can be used to express linear functions.
A function is denoted by the notation f(a), where an is an independent variable on which the function depends. The Linear Function Graph contains a straight line with the equation or formula;
y = ax + b
We we consider the options, in option a, s has power 2, in option c 2 has power x and in option d, π has power 2. So the option a, c and d is not correct option. So, only option b is correct.
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Linear functions are equations that can be represented in the form of a straight line. They can be expressed in the form of an equation, y = mx + b, where m is the slope of the line and b is the y-intercept.
A linear function can be used to calculate the output, y, for a given input, x. For example, let us consider the equation y = 3x + 4. We can interpret this equation to mean that for every increase in x, y will increase by 3. Thus, if x = 5, then y = 3x + 4 = 19.
In order to calculate y for a given value of x, we must first substitute the value of x in the equation. For example, if x = 7, then y = 3x + 4 = 25.
We can also calculate the slope of the line using the equation y = mx + b. The slope of a line, m, is the change in y divided by the change in x. To calculate the slope of a line, we can take two points on the line and calculate the change in y and the change in x. For example, let us take the points (7,25) and (5,19). The change in y is 25 - 19 = 6 and the change in x is 7 - 5 = 2. Therefore, the slope of the line is m = 6/2 = 3.
To summarize, a linear function can be expressed in the form of an equation, y = mx + b, where m is the slope of the line and b is the y-intercept. We can calculate the output, y, for a given input, x, by substituting the value of x into the equation. We can also calculate the slope of the line by taking two points on the line and calculating the change in y and the change in x.
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Find a point-slope form for the line with slope 1/5 passing through the point (-1,-7)
Answer:
y + 7 = 1/5(x + 1)-----------------------------------------
The point-slope form:
y - y₁ = m(x - x₁), where m- is the slope, (x₁, y₁) is the point on the lineSubstitute the given values to get:
y - (-7) = 1/5(x - (-1))Simplify:
y + 7 = 1/5(x + 1)Need Help ASAP!!
Find the area of the shaded region. Round to the nearest tenth.
5cm and 60 degrees
The area of the shaded region of the circle with radius of 5 cm and sector with an angle of 60° is 76.3 cm²
What is the area of a part of a circle?The area of a part of a circle can be found by finding the difference between the area of the circle and the area of the unshaded part of the circle.
The triangle formed by the two radii of length 5 cm with an included angle of 60°, and the chord at the boundary of the shaded region is an isosceles triangle which with the vertex angle of 60°, indicates that the triangle is an equilateral triangle.
The formula for the area, A, of an equilateral triangle of side length s is; A = ((√3)/4) × s²
The side length of the equilateral triangle formed by the radii is; s = 5 cm
Therefore;
Area of the equilateral triangle in the question is; [tex]A_{\Delta}[/tex] = ((√3)/4) × 5²
Area of the minor sector formed by the two radii, [tex]A_{sector}[/tex] = (60°/360°) × π·r²
[tex]A_{sector}[/tex] = π×5²/6
The area of the shaded region = Area of the circle - [tex]A_{sector}[/tex] - [tex]A_{\Delta}[/tex]
Therefore;
Area of the shaded region = π×5² - π×5²/6 - ((√3)/4) × 5² ≈ 76.3
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Determine the value b. b^2 = 225
The value of b in the expression b² = 225 is the square root of 225 which is 15.
What is square and square rootSquares are the numbers gotten after multiplying a value by itself. While the square root of a number is a number whose square is the given number. Hence, both are vice versa methods.
We shall solve for the value of the letter b as follows;
b² = 225
by taking the square root of both sides we have;
√b² = √225
b = √(15 × 15)
b = √15²
b = 15
Therefore, the square of 15 will result to 225, and the value of the letter b is the square root of 225 which is 15.
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GEOMETRY FIND LENGTH OF THIRD SIDE
Answer:
[tex]b =\sqrt{51}[/tex]
Step-by-step explanation:
Using the Pythagorean Theorem,
[tex]a^{2} + b^{2} = c^{2} \\7^{2} + b^{2} =10 ^{2} \\b^{2} = 10^{2} - 7^{2} \\b^{2} = 100-49\\b^{2}= 51\\ b = \sqrt{51}[/tex]
Hence the length of the third side is [tex]\sqrt{51}[/tex]
Danielle just moved into a new apartment and her couch was left by the entrance. The couch has a mass of 115 kg and wood feet. The entrance into the apartment has a smooth hardwood floor while the living room is carpeted (see following chart for coeffients of friction). Danielle initially tried pushing it by herself with a force of 180 N. Then her brother, Ramone, dropped by and helped. Together they were able to push the couch where she wanted it in the living room.
The weight of the couch is 1150 N hence the 180 N can not be able to move it without assistance.
Why could she not move it?We know that the force has to do with that which is able to make an object to move. We know that the friction force is the force that tends to prevent the movement of a body.
However, in this case, the force that is applied must be greater than the frictional force that is acting on the object and as such the object can be made to move from one point to another as we can see in the question.
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Missing parts;
Danielle just moved into a new apartment and her couch was left by the entrance. The couch has a mass of 115 kg and wood feet. The entrance into the apartment has a smooth hardwood floor while the living room is carpeted (see following chart for coeffients of friction). Danielle initially tried pushing it by herself with a force of 180 N. Then her brother, Ramone, dropped by and helped. Together they were able to push the couch where she wanted it in the living room. Why could she not move the couch?
Wich of these relations is a function
Answer:
A
Step-by-step explanation:
A function is when every input has only one output so therefore A is the answer.
A mole left its burrow 4 feet underground and started digging deeper into the ground. It digs straight down at a constant rate of 3 feet per minute.
How long does it take the mole to reach 13 feet underground?
Look at the expression and example there are parentheses around 4+8 to show it is about to be evaluated first are the parentheses necessary explain?
Answer:
Step-by-step explanation:
No, the parenthesis is not important. With or without them, they will equal the same thing, which is 3.
solve the following equation
Answer:
A. [tex]x<-4[/tex]
Step-by-step explanation:
[tex]-2x-8>3x+12 \\ \\ -5x-8>12 \\ \\ -5x>20 \\ \\ x<-4[/tex]
Factor the expression using the GCF for 44-11
Answer: 11(4-0)
Step-by-step explanation: take 11 out of 44= 11(4
Take 11 out of 11= 11(4-0)
Ronnie is in a stationary boat on the lake. He is reeling in a fish at 2 feet per second. The fish is swimming away from him at 1.5 feet per second. The speed at which the fish moves toward Ronnie is:
We can conclude that the fish moves towards Ronnie at a speed of 0.5 feet per second.
What is speed?Speed indicates how quickly something or someone is moving.
If we know how far something has traveled and how long it took to get there, we can calculate its average speed.
Speed is calculated as follows: speed = distance * time.
Knowing the units for distance and time is necessary to calculate the units for speed.
So, we know that:
Ronnie reeling a fish at 2 ft per second.
Fish moving away from 1.5 ft per second.
Speed of fish coming to Ronnie:
2 - 1.5
0.5 ft per second
Therefore, we can conclude that the fish moves towards Ronnie at a speed of 0.5 feet per second.
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Two parallel lines are cut
The measure of angle ∠4 will be 76°. Then the correct option is C. The measure of angle ∠4 will be 104°. Then the correct option is D.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
Angles ∠1 and ∠2 are the supplementary angle. Then the equation is given as,
(3x + 5) + (2x + 10) = 180
5x + 15 = 180
5x = 165
x = 33
The measure of angle 1 is calculated as,
∠1 = 3(33) + 5
∠1 = 99 + 5
∠1 = 104
Then the measure of the angle 2 is given as,
104 + ∠2 = 180
∠2 = 76
Angle 4 and angle 2 are opposite angles. Then we have
∠4 = ∠2
∠4 = 76
Angle 1 and angle 3 are opposite angles. And angle 3 and angle 5 are alternate angles.
∠1 = ∠3
∠5 = ∠3
∠5 = 104
The measure of angle ∠4 will be 76°. Then the correct option is C. The measure of angle ∠4 will be 104°. Then the correct option is D.
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Use the times and corresponding closing prices of the stock to create coordinate pairs. Let x represent the number of weeks since the first data point, and let y represent the closing price at each time. So, x = 0 represents the data point from 5 years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since 5 years ago, when x = 0. Fill in the table to represent your data as coordinate pairs.
The coordinate pairs of the data can be written as follows:
(0, 12.00),(26, 14.00),(52, 15.00),(78, 13.00),(104, 17.00).
Time (x) Closing Price (y)
0 $12.00
26 $14.00
52 $15.00
78 $13.00
104 $17.00
We can represent the data as coordinate pairs. Let x represent the number of weeks since the first data point, and y represent the closing price at each time. So, x = 0 represents the data point from 5 years ago.
For example, for the first data point x = 0 and y = 12.00. This can be written as (0, 12.00). Similarly, for the second data point with x = 26 and y = 14.00, the coordinate pair is (26, 14.00).
Therefore, the coordinate pairs of the data can be written as follows:
(0, 12.00)
(26, 14.00)
(52, 15.00)
(78, 13.00)
(104, 17.00)
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Convert 750 US dollars to British pound sterling. Use 1 US dollar ≈ 0.62 British pound sterling.
Answer:
4.65 British pound sterling
Step-by-step explanation:
[tex]7.50*0.62 = 4.65[/tex]
7.5 U.S. dollars = 4.65 British pound sterling
How do I commplete this ratio of
3 17
6
9
12 68
15 85
The following ratio can be completed as;
3 17
6 34
9 51
12 68
15 85
How to solve ratio?Let
The unknown number = x
3 : 17 = 6 : x
3/17 = 6/x
cross product
3 × x = 6 × 17
3x = 102
divide both sides by 3
x = 102/3
x = 34
So,
3 : 17 = 6 : 34
6 : 34 = 9 : x
6/34 = 9/x
cross product
6 × x = 9 × 34
6x = 306
divide both sides by 6
x = 306/6
x = 51
Therefore, ratio is the comparison between two or more numbers.
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What is the equation of the line that passes through the point (5, 1) and has a
slope of 1/5
Answer:
Step-by-step explanation:
y - 1 = 1/5(x - 5)
y = 1/5x - 1 + 1
Y = 1/5x
The equation of the line is x-5y=0
The point given =(5,1)
slope of the line=1/5
The equation of a line when a point in the line and its slope is given is given by
y-y₁=m(x-x₁)
y-1=(1/5)(x-5)
5y-5=x-5
x-5y=0
The equation of the line is x-5y=0
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Which graph represents the inequality y> 1-3x?
The graph of the inequality y > 1 - 3x is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The equation of inequality is,
⇒ y > 1 - 3x
Now,
Since, The inequality is,
⇒ y > 1 - 3x
Hence, The graph of inequality y > 1 - 3x is shown in image by shaded ''red region.''
Thus, The red region of the graph is shows the graph of inequality
y > 1 - 3x.
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Is displacement a distance formula?
The distance and displacement are the same because both determine the total path traveled by the object.
It is also true that the total path length covered by a subject is equal to the displacement and as well as the distance if it has moved along in a straight line.
The distance between two places of an item in motion is known as displacement. Therefore, it relies on both the starting position and the ending position. Displacement is also the shortest distance between the initial and ultimate places.
Thus, The distance and displacement are the same because both determine the total path traveled by the object.
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No, the formula of distance and displacement is not same.
In order to find the solution, we must know that what is meant by distance and displacement.
The formula of speed distance time is mathematically given as,
=> Speed = Distance/Time
And the term displacement is referred as the change in position of an object and it is the smallest distance between two positions.
Here we have also know that it is a vector quantity and it has magnitude and direction both.
The formula to calculate the displacement is written as
=> displacement = velocity x time
While we looking into the definition, we have identified that both terms are not equal.
And the formula of each of them are also differs.
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2/5 divided by 1/4= 2/5 x 4/1 =
Answer: 8/5
Step-by-step explanation:
2/5 * 4 = (2*4)/5 = 8/5
Answer:
1/10
Step-by-step explanation:
2/5÷1/4=2/5×4/1=2/5×4/1=1/10
In the year 2007, a company made $6 million in profit. For each consecutive year after that, their profit increased by 8%. How much would the company's profit be in the year 2009, to the nearest tenth of a million dollars?
In the year 2009, the company's profit would be $6.95 million.
How to calculate the amount?It should be noted that profit simply has to do with the gain that is made from the sales of a particular commodity.
In the year 2007, a company made $6 million in profit. For each consecutive year after that, their profit increased by 8%. Based on the question, we will like to know the would the company's profit be in the year 2009, to the nearest tenth of a million dollars.
The company's profit be in the year 2009, to the nearest tenth of a million dollars will be:
In the year 2008, the company made $6 million + 8% * $6 million = $6.48 million.
In the year 2009, the company made $6.48 million + 8% * $6.48 million = $6.95 million.
So in the year 2009, the company's profit would be $6.95 million, to the nearest tenth of a million dollars.
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Would anyone solve these problems for me? I’m not quite understanding how to do it
The Functions are f(g(x)) = 3773 x⁷ and f o g⁻¹(x) = 11/ 343 * x ⁶/⁷.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range and a co-domain.
Given two function
f(x) = 11 x³
g(x) = 7 [tex]x^{7/3}[/tex]
(f g)x = f of g(x)
f(g(x)) = 11* (7 [tex]x^{7/3}[/tex])³
f(g(x)) = 3773 x⁷
g⁻¹(x) = 1/7 * x³/⁷
(f/g)x = f o g⁻¹(x)
f o g⁻¹(x) = 11/ 343 * x ⁶/⁷
for the -8 value of x
f(g(x)) = 3773 (-8)⁷
f o g⁻¹(x) = 11/ 343 * (-8 )⁶/⁷
Therefore, Functions are f(g(x)) = 3773 x⁷ and f o g⁻¹(x) = 11/ 343 * x ⁶/⁷.
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The amount of alcohol in a 1 ounce shot of 80 proof whiskey, a 5 ounce glass of wine, and a 12 ounce beer are:
A amount 1 ounce shot of whiskey contains 0.4 ounces of alcohol, a 5 ounce glass of wine has 0.75 ounces, and a 12 ounce beer has 1.5 ounces.
1 ounce shot of 80 proof whiskey:
0.4 ounces of alcohol = 40% alcohol * 1 ounce
= 0.4 ounces
5 ounce glass of wine:
0.75 ounces of alcohol = 12% alcohol * 5 ounces
= 0.6 ounces
12 ounce beer:
1.5 ounces of alcohol = 5% alcohol * 12 ounces
= 0.6 ounces
A 1 ounce shot of 80 proof whiskey contains 0.4 ounces of alcohol, which is 40% of the total volume. A 5 ounce glass of wine has 0.75 ounces of alcohol, which is 12% of the total volume. A 12 ounce beer has 1.5 ounces of alcohol, which is 5% of the total volume. Each of these drinks contains different amounts of alcohol, so it is important to know the strength of each drink in order to know how much alcohol is being consumed.
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The 1 ounce shot of 80 proof whiskey, a 5 ounce glass of wine, and a 12 ounce beer are same amount of alcohol .
There are several types of liquor such as beer, wine, whiskey.
They have things in common such as having natural products such as fruits, grains, or others. There is a determining factor that differentiates them is the percentage of alcohol present in it .
Drinks such as Whiskey have 40% alcohol. While others like beer have between 4% to 5% alcohol.
the percent of alcohol in wine is between 9 to 12% .
Therefore, In different amounts of different alcoholic beverages, we can have the same amount of alcohol.
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At a certain school, 35% of children have a tablet, and 24% have a smart phone. Given that 42% of those that have smart phones also have tablets, what percent of those that have a tablet also have a smart phone? (3 pts. - you may use any method you want, but you must show work)
The percentage of people with a tablet that also have a smart-phone is given as follows:
28.8%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the result of a previous event.
The formula is defined as follows, according to Bayes' Theorem:
[tex]P(B|A) = \frac{P(B) \times P(A|B)}{P(A)}[/tex]
In which the probabilities are defined as follows:
P(B|A) is the probability of the event B happening, given that the event A happened.P(A|B): probability of event A happening when event B has happened.P(A) is the probability of the event A happening.The events for this problem are given as follows:
Event A: has a tablet.Event B: has a smart-phone.Hence the probabilities are given as follows:
P(A) = 0.35, P(B) = 0.24, P(A|B) = 0.42.
Hence the conditional probability is of:
P(B|A) = 0.42 x 0.24/0.35 = 0.288.
Meaning that the percentage is of:
0.288 x 100% = 28.8%.
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x³-4x² - 5x=0
factor completely
Equation: x³-4x² - 5x = 0 and value of x = 0, 5, - 1. This can be solved the concept of factorization.
What is factorization?The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.
Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.
x³-4x² - 5x = 0
or, x (x² - 4x - 5) = 0
or, x (x² -5x +x - 5) = 0
or, x [x (x - 5) + 1 (x - 5)] = 0
or, x (x - 5) (x + 1) = 0
thus, value of x = 0, 5, - 1.
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Use the drop-down menus to complete the statements. 42 is 32 32. therefore, △jkl is . 52 is 32 42. applying the same method, △abc is .
Applying the same method is right. Δ ABC is right angle triangle.
the drop down menu
the statements are
[tex]4^2 \ is < 3^2 +3^2[/tex]
to prove that
the value of
[tex]4^{2}[/tex] is 16
the value of [tex]3^2[/tex] is 9
so the statement is
16 < 9+9
16 < 18
as given 16 is less than 18
therefore Δ JKL is an acute angled triangle
A triangle with acute interior angles is known as an acute angle triangle. Remember the angle is acute that is one that is less than 90 degrees.
By applying the same method
[tex]5^2 = 3^2 +4^2[/tex]
the value of 5 to the power 2 is
=> 25 = 9+16
=> 25 =25
we can say that the statement is true
at the same method Δ ABC is a right angled triangle
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we simply had to subtract the two numbers given in the statement and apply the same method to the second statement. This method allows us to easily solve problems such as these.
52 - 32 = 20; △abc = 20
First, subtract the two numbers given in the statement: 42 - 32 = 10.
Next, apply the same method to the second statement and subtract the two numbers: 52 - 32 = 20.
The answer for the first statement is then 10; △jkl = 10.
The answer for the second statement is then 20; △abc = 20.
To solve this problem, we must first subtract the two numbers given in the statement: 42 - 32 = 10. This is the answer for the first statement; △jkl = 10. We must then apply the same method to the second statement and subtract the two numbers: 52 - 32 = 20. This is the answer for the second statement; △abc = 20. Therefore, the answer to the question is that △jkl is 10 and △abc is 20. In order to determine this, we simply had to subtract the two numbers given in the statement and apply the same method to the second statement. This method allows us to easily solve problems such as these.
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