The value of F (- 3 2 where F x )= 4x2 3x 72 is:
F ( -3) = - 27 and F (2) = - 62
What is function?In mathematics, function is an expression that shows a relationship between an independent variable and a dependent variable. In other words, a function creates a relation between an input to an output.
As per the given function F(x), x is the independent variable and F (x) is the dependent variables.
generally, we write F(x) = y
What is the value of F ( -3, 2) for the function given in question?given, F (x) = 4x² - 3x -72
F (x) is a function of x
for x = - 3, F ( -3) = 4(-3) ² - 3(-3) -72
F (- 3) = - 27
again, x = 2, we get F (2) = 4(2) ² - 3(2) - 72
F (2) = - 62
from the above calculation, we find (-3, 2) are domain of function F (x) and
(- 27, -62) are ranges of the above function.
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Select the correct answer. what is the height, x, of the equilateral triangle? an equilateral triangle with the angles labeled as 60 degrees and a side length of 8 inches, the height labeled as x
a. in.
b. in.
c. in.
d. in.
The height of the equilateral triangle when its side length is given as 8 inches is calculated to be 6.93 inches.
The equilateral triangle has all sides and angles equal. The angles are always equal to 60 degrees.
Given that,
Side length of the equilateral triangle = 8 inches
Angles = 60 degrees
Height = ?
Therefore, let us find the height of the triangle using the Pythagoras theorem,
c² = a² + b²
8² - 4² = b²
b² = 64 - 16
b² = 48
b = 6.93 inches
Thus, the height of the equilateral triangle is calculated to be 6.93 inches.
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Difference of functions
Joy is solving a quadratic equation of the form a2+bx+c=0 where b
and care integers.
She correctly solves the equation to get a = 3 ± √/13
Work out the values of b and c.
(3 marks)
b=
=
To find the values of b and c, we can use the quadratic formula:
[tex]x = (-b ± \sqrt{ (b^2 - 4ac)}) / 2a[/tex] which will give us the value B = -6 & C = -4
What is a quadratic equation.A quadratic equation is a second-order polynomial equation in one variable using the formula [tex]x = ax2 + bx + c = 0[/tex] and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.
So the equation that she get is [tex]x^{2} -6x-4[/tex]
this means that x=3+√13 or 3-√13
which also equals to x=3+√13 & x-3-√13=0 and
x=3-√13
x-3+√13=0
which if you try to find the quadratic equation for this. you need to do it by this
(x-3+√13)(x-3-√13)
which will get you
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Hint: your answer will be a fraction or decimal. ex: 3/5 or 0.6 *
Find the probability that a point chosen at random on the part of the number line shown will lie
between points B and C.
On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.
What is probability?A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.
Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.
Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.
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Please help me with this problem.
In the year 1582, January 1st was adopted for the new year celebration
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction. The degree of a polynomial determines it type such as linear, quadratic, cubic and so on.
The polynomial having a degree of 3 is cubic while that with a degree of 2 is quadratic and that with degree of 1 is linear
The year that January 1st was adopted as new year can be gotten using the function:
f(x) = 3x³ - 7x² - 5x + 7
f(9) gives the year that it was adopted. Substituting x = 9 gives:
f(9) = 3(9)³ - 7(9)² - 5(9) + 7
f(9) = 1582
In the year 1582, the new year was celebrated at January 1st
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A DVD player had a $108. Price tags the store gave a 25% discount. What was the amount of the discount?
Answer:
$27
Step-by-step explanation:
If we know that %25 is equal to 1/4, or 0.25, then we can use an equation that look like this:
108 × 0.25 = 27
Therefore, the amount of the discount was $27
How can you solve for percentages?Solving for percentages can be tricky, and you may need help on trying to solve a problem including one. If you need to find a percentage of a number, the easiest way to do that is to convert the percentage into a fraction or decimal and multiply the total by that number.
For ex.
What is 15% of 60?
To do this, convert the percentage into a decimal.
15% converted into a decimal is 0.15.
Now multiply 60 by 0.15.
60 ÷ 0.15 = 9
So, the answer to this example would be 9.
In ΔABC, if AB = BC and
Answer: not enough to answer
simplifying radicals worksheet algebra 2
Therefore , the solution of the given problem of expression comes out to be √14q × 2√4q = 4q√14.
Describe expression.combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.
• 3 x/2 variable is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.
Here,
The simplified expressions are 20 = 25, 56x2 = 2x14, [150x3k4] = 5xk26x, and 14q 24q = 4q14 given the facts from the question.
Simplifying the surd
A perfect square must be one of the components for a number to be written as just surds.
How to Make 20 Recall Simpler
20 = 4 × 5
Thus,
√20 = √(4 × 5)
√20 = 2√5
simple methods √(56x²)\s√(56x²) = √56 × √x²
Recall
√56 = √(4 × 14) = 2√14
√x² = x
Thus,
√(56x²) = 2√14 × x
√(56x²) = 2x√14
simple methods [150x3k4] = [150x3k4] = [150x3k4]
Recall
√150 = √(25 × 6) = 5√6
√x³ = √(x² × x) = x√x
√k⁴ = k²
Thus,
√[150x³k⁴] = 5√6 × x√x × k²
√[150x³k⁴] = 5k²x√6x
How to simplify 14q 2 4q: 14q 2 4q = 2
(14q × 4q)
√14q × 2√4q = 2 × 2q√14
√14q × 2√4q = 4q√14
Therefore , the solution of the given problem of eexpression comes out to be √14q × 2√4q = 4q√14.
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What is the graph of the linear equation 2x +3y 6 that cuts the Y-axis at the point?
The graph of the linear equation 2x + 3y = 6 is a straight line that cuts the Y-axis at the point (0,2).
A linear equation is an equation in which the highest power of the variable is 1.
The general form of a linear equation is:ax + by = c where a, b and c are constants and x and y are variables. This equation represents a straight line when plotted on a graph.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept
To find the points at which the line will intersect y-axis,
take x=0 and substitute in the linear equation 2x+3y=6
2(0) + 3y = 6
3y = 6
y = 2
So the point where the line cuts the Y-axis is (0,2)
The straight line of the linear equation 2x+3y=6 intersects the y-axis at (0,2).
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HELP ME PLEASE . THESE ARE RATIONAL NUMBERS BTW.
Answer:
15. -3 1/4
16. -4 1/2 OR -4 2/4
17. 1 1/4
18. -5 3/4
19. 1/2 OR 2/4
20. -2 1/2 OR -2 2/4
Step-by-step explanation:
Answer:
15) -3.25
16) -4.5
17)1.25
18)-5.75
19).5
20)-2.5
An office manager is planning to set up three computer workstations
and a file cabinet in a space that is 27 feet wide. The file cabinet takes up
3 feet. What is the width of the space available for each computer work
station?
PLEASE HELP
The mean height of 15-year-old boys is 175 cm and the variance is 64. For girls, the mean is 165 and the variance is 64. If 8 boys and 8 girls were sampled, what is the probability that the mean height of the sample of boys would be at least 6 cm higher than the mean height of the sample of girls
The probability of the mean height of the sample of boys being at least 6 cm higher than the mean height of the sample of girls can be calculated using a two-sample t-test. The t-test compares the means of two samples and determines whether they are different from one another. The t-test requires the assumption of equal variances and normal distribution of the data.
What does the math term "probability" mean?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given that the variances are equal, the t-test statistic can be calculated as:
t = (mean_boys - mean_girls - 6) / (sqrt(variance/n))
where n is the sample size of each group (8 in this case).
The probability of observing a t-value as extreme or more extreme than this value can be calculated using the cumulative distribution function (CDF) of a t-distribution with n1 + n2 - 2 degrees of freedom.
Because you are looking for the probability that the mean height of the sample of boys is at least 6cm higher than the mean height of the sample of girls, this is a one-tailed test. The probability of a one-tailed test can be calculated by subtracting the probability of a two-tailed test from 1.
The probability can be calculated using a t-distribution table with 14 d.f. or using software such as R or excel.
It is important to note that the sample size is very small, with 8 boys and 8 girls, which may not be representative of the population. As sample size increases the probability of getting a significant difference increases.
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find the gradient of a line passing through each of the following pair of points (0,-5) and (6,3)
Ash and her 2 friends went to dinner. If the bill was $124.72, and they left an 18% tip, how much did each person pay
Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
Which percentage is it?A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Amount of bill = $124.72
and tip they left = 18% of $124.72
total amount is =$124.72 + $124.72*18%=$147.1696
so, each person pay= $147.1696/3=$49.056
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Of the 6,960 balloons thrown in a water-ballon fight, 870 were red. At this rate, how many balloons out of 48 would be red? WRITE JUST THE ANSWER WITHOUT UNITS
At this rate, the ratio or proportion of red balloons to the total balloons, the number of red balloons out of 48 is 6.
What is proportion?Proportion describes the two or more ratios equated to each other.
Proportions are depicted as fractional values in decimals, fractions, or percentages.
In this situation, we equate the ratio or proportion of red balloons to the sample to determine the number that will likely be red.
The total number of balloons thrown in a water balloon fight = 6,960
The number of the balloons that are red = 870
The proportion of the red balloons to the total = 0.125 or 12.5% (870/6,960)
In a sample of 48 balloons, the number of red balloons will be 6 (48 x 0.125)
Thus, out of 48 balloons, there are 6 red balloons at this constant rate.
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these ar the numbers and i need the ratio
thank you!
help me please its due tomorrow !!!!!!!!!!
help please
ill get in trouble!!!!
Answer:
1:3
Step-by-step explanation:
A math club is having a bake sale. Find the area of the bake sale sign.
The Area of the sign is_ square feet
The bake sale sign has a 6 ft2 space.
What is area?
An object's area is how much space it takes up in two dimensions.
It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The word "area" refers to a free space.
A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.
But a shape's area is a two-dimensional measurement. In order to measure something in a square, it is done so using measurements like square inches (in2), square feet (ft 2), square yards (yd2), etc.
The majority of forms and things have corners and edges.
According to our question-
The opposite sides of a rectangle's quadrilateral (it has four sides and four angles) are equal and parallel.
Area of a rectangle equals length times width.
The area of the bake sale sign = length * breadth
Hence, The bake sale sign has a 6 ft2 space.
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estimate the product of 5,398 x 47 by rounding to the nearest thousand and ten.
a) 200,000
b)250,000
c)253,706
d)300,000
pls help me
Answer:
b) 250,000
Step-by-step explanation:
You want to estimate the product of 5,398 and 47 by rounding to the nearest thousand and ten.
Rounded valuesRounding 5,398 to the nearest thousand gives 5000.
Rounding 47 to the nearest ten gives 50.
Estimated productThe product of these is the estimate you want:
5000·50 = 250,000
PLS HELP :[
The graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.
A graph shows Number of Pepperoni Rolls on x-axis and Price of Pepperoni Rolls on y-axis. The x-axis scale is shown from 0 to 24 at increments of 4, and the y-axis scale is shown from 0 to 160 at increments of 20. A straight line joins the ordered pairs 4, 20 and 8, 40 and 12, 60 and 16, 80 and 20, 100 and 24, 120.
Kaiser Roll Packet
Number of Kaiser Roll Packet
Price of Kaiser Roll Packet (dollars)
4
24
8
48
12
72
16
96
How many dollars more is the price of a Kaiser roll packet than the price of a pepperoni roll at Luis's store? (1 point)
a
$1
b
$4
c
$5
d
$6
Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that the graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.
The price of a Kaiser roll packet = {C1} = (48 - 24)/(8 - 4) = 24/4 = 6
The price of a Kaiser roll = {C2} = (40 - 20)/(8 - 4) = 20/4 = 5
$6 - $5 = 1
Therefore, Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.
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What is the length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in?
The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the square of the length of the other two sides (a and b).
In this case, a = b = 9 in, so:
c2 = 92 + 92
c2 = 81 + 81
c2 = 162
c = √162
c = 12.73 in
The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in, calculated using the Pythagorean theorem.The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.
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Need answer for b)iii)
Answer:
3.23, -1.23
Step-by-step explanation:
Draw the line y=1
See where it intersects x^2-2x-3
The x coordinates of the intersections are your answer
Person A buys 10 granola bars and 6 cups of yogurt for $18. Person B buys 5 granola bars and 4 cups of yogurt for $9.50. Find the cost of each item.
Answer:
granola bar: $1.50yogurt: $0.50Step-by-step explanation:
You want the cost of each item when person A buys 10 granola bars and 6 cups of yogurt for $18, and person B buys 5 granola bars and 4 cups of yogurt for $9.50.
EquationsThe equations describing the relations can be written ...
10g +6y = 18 . . . . . . . person A's purchase
5g +4y = 9.50 . . . . . . person B's purchase
SolutionSubtracting half of the first equation from the second, we find ...
(5g +4y) -1/2(10g +6y) = (9.50) -1/2(18)
y = 0.50 . . . . . . . . . . simplify
Substituting this into the first equation gives ...
10g +6(0.50) = 18
10g = 15 . . . . . . . . . . subtract 3
g = 1.50 . . . . . . . . . divide by 10
Each granola bar costs $1.50; each cup of yogurt costs $0.50.
__
Additional comment
The attachment shows the solution found using a calculator to find the reduced row-echelon form of the augmented coefficient matrix. The variable values are in the right column of the reduced matrix. This tells us granola bars are $1.50, and yogurt cups are $0.50, as we found above.
find equation of the line passing through (4,8) and parallel to the line 3x+y=17( Please give workout)
Answer:
y = -3x +20
Step-by-step explanation:
Equation of line: y =mx + b
Where m is the slope and b is the y-intercept.
3x + y = 17
Write the above equation in y = mx +b form.
y = -3x + 17
m = -3
Parallel lines have same slope.
So, slope of the required line is (-3).
y = -3x + b
This line is passing through (4,8). Substitute in the above equation and find the value of 'b'.
8 = -3*4 + b
8 = -12 + b
8 + 12 = b
b = 20
Equation of the line:
[tex]\sf \boxed{ y = -3x + 20}[/tex]
Toss a coin 10 times and record how many times you tossed heads.
a) What is your experimental probability of tossing heads?
b) What is the theoretical probability of tossing heads?
c) Compare the two probabilities and determine if you are considered to be
"lucky" at tossing heads.
d) If you were to toss the coin 100 times, what would you expect the
experimental probability of heads to be? Defend your answer.
To solve this we must be knowing each and every concept related to probability and its calculations. Therefore, the probability of tossing heads is 0.000976.
What is probability?Probability is the branch of mathematics concerned with the outcomes of random occurrences. Probability refers to the chance or potential of an outcome. It describes the likelihood of a specific occurrence occurring.
Probability denotes the possibility of something happening. It is a statistical discipline that deals only with probability of such a random event. The number ranges from 0 to 1, with 0 being an improbable event and 1 representing a certain event.
P(getting heads on one toss) = 1/2
P(getting all heads in 10 tosses)=(1/2)¹⁰
=1/1024
=0.000976
Therefore, the probability of tossing heads is 0.000976.
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can someone please tell which congruency do you use and how?
To prove that ΔABC is isosceles.
Properties of an isosceles triangle.An isosceles triangle is a type of triangle in which the length of its two sides, and measure of its two internal angles are equal. When a bisector of an angle is drawn to one of the internal angles of the triangle, two congruent triangles of corresponding properties are produced.
To prove that ΔABC is isosceles, we have:
<CAD ≅ <BAD (definition of an angle bisector)
CD ≅ BD (definition of a midpoint)
AC ≅ AB (congruent sides of an isosceles)
<ACD ≅ <ABD (congruent internal angles of an isosceles)
<ADC ≅ <ADB (definition of right angle)
Therefore it can be concluded that;
ΔABC is an isosceles triangle (Angle-Side-Side theorem)
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What is an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35?
Answer: To find an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35, we can use the fact that two lines are parallel if and only if they have the same slope.
The slope of the line 4x−5y=35 is -4/5. Therefore, we can find an equation of the line that passes through (-5,-6) and is parallel to 4x−5y=35 by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
Substituting the values into the slope-intercept form, we get:
y = (-4/5)x + b
To find the value of b, we can substitute the coordinates of the point (-5,-6) into the equation:
-6 = (-4/5)(-5) + b
-6 = 8/5 + b
-6 - 8/5 = b
-24/5 = b
Therefore, the equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35 is:
y = (-4/5)x - 24/5
This can also be written as:
y = -4/5x - 24/5
Step-by-step explanation:
Which act of congress set the line of latitude at 36 degrees 30 minutes north, as the northernmost limit for slavery? dred scott v. sandford missouri compromise compromise of 1850 kansas-nebraska act
Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.
What did the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas" have in common?By Stephen A. Douglas's Kansas-Nebraska Act of 1854, the Missouri Compromise's prohibition on slavery in the former Louisiana Territory north of the parallel 36°30′ north had been essentially removed. Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.
The expansion of slavery into the western lands was addressed by the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas." The balance between "free" and "slave" states in the Union was a factor in each of them.
Slavery was proposed to be outlawed in the remaining Louisiana Territory above the 36° 30' latitude line in the Missouri Compromise. The Kansas-Nebraska Act of 1854 abolished this clause after it had been in effect for 34 years.
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The Missouri Compromise of 1820 established latitude 36°30′ as the northern boundary for the legalisation of slavery in the western territories.
What were the similarities between the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas"?The Missouri Compromise's ban on slavery in the former Louisiana Territory north of the parallel 36°30′ north had been largely lifted by Stephen A. Douglas's Kansas-Nebraska Act of 1854. The Missouri Compromise of 1820 established latitude 36°30′ as the northern boundary for the legalisation of slavery in the western territories.The Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas" all addressed the spread of slavery into the western areas. Each of them was influenced by the proportion of "free" and "slave" states in the Union.In the Missouri Compromise, slavery was suggested to be prohibited in the remaining Louisiana Territory above the 36° 30' latitude line. This provision was removed by the Kansas-Nebraska Act of 1854 after it had been in place for 34 years.To learn more about Bleeding Kansas, visit:
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The temperature of a city at sunset was -2°F. Overnight, the temperature decreased by 12°F. What was the lowest temperature overnight in that city?
Answer:-14°F
Step-by-step explanation:
-2°F -12°F is basically the same as 12°F+2°F which is 14°F and then you inverse it
When you see a graphed cluster of dots depicting the values and relationship of two different variables, you are seeing a visual description of relatedness called a
histogram
standard deviation distribution
percentile distribution
bar graph
scatter-plot or scatter-gram
When you see a graphed cluster of dots depicting the values and relationship of two different variables, you are seeing a visual description of relatedness called a scatter-plot or scatter-gram.
What is scatter-plot or scatter-gram?Scatter-plot: A scatter-plot is a form of mathematical diagram or plot that employs Cartesian coordinates to illustrate distinct values associated to two variables for a specific set of data. It is also known as a scatter-gram, scatter-graph, scatter-chatter, or scatter-diagram.
It is being utilized to determine how one variable influences the other.
The supplied statement in the question above represents the scatter plot.
Here,
When you observe a graphed cluster of dots reflecting the values and relationship of two separate variables, you are looking at a scatter-plot or scatter-gram, which is a visual explanation of relatedness.
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hi can someone pls help me
:)