Answer:
[tex]f(g(-3))=-25[/tex]
Step-by-step explanation:
[tex]g(-3)=2(-3)^2+7(-3)-3=2(9)-21-3=18-24=-6\\f(g(-3))=4(-6)-1=-24-1=-25[/tex]
What is the solution for the following set of equations 6x 2y 8 3x 7y 68?
The solution of the set of equations: 6x - 2y = 8; 3x + 7y = 68 is (4,8)
The problem can be solved using elimination - substitution method.
Set of equations:
6x - 2y = 8 .... (equation 1)
3x + 7y = 68 ..... (equation 2)
Divide equation 1 by 2
3x - y = 4 ..... (equation 3)
Eliminate x by substracting equation 3 from equation 2:
3x + 7y = 68
3x - y = 4 _
8y = 64
y = 64/8
y = 8
Substitute y = 8 into equation 3:
3x - 8 = 4
3x = 12
x = 12/3
x = 4
Hence, the solution is (4,8)
Your question is incomplete, but most probably your question was:
What is the solution for the following set of equations 6x - 2y = 8; 3x + 7y = 68 ?
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What is the degree of the polynomial 7x 2y 3z 4?
The degree of a polynomial is the highest power of each variable in the equation. In the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Therefore, the degree of this polynomial is 8.
1. Identify the highest power of each variable.
For 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z.
2. Add the highest powers of each variable.
2 + 3 + 4 = 9
3. Subtract 1 from the sum.
9 - 1 = 8
4. The degree of the polynomial is the result of the subtraction.
Therefore, the degree of the polynomial 7x2y3z4 is 8.
The degree of a polynomial is the highest power of each variable in the equation. To calculate the degree of a polynomial, you must identify the highest power of each variable and add them together. Then, subtract 1 from the sum to get the degree of the polynomial. For example, in the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Adding these powers together gives us 9. Subtracting 1 from this sum gives us 8, which is the degree of the polynomial. Therefore, the degree of the polynomial 7x2y3z4 is 8.
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tan took Lily to his friend’s restaurant on a date. The friend told the waiter to remove the $12 dessert from Stan’s bill. Stan tipped the waiter 20% on the reduced bill, which was a $15 tip. Fill in the blanks to write an equation that will determine the amount of the original bill, b.(2 points)
___(b −___) = ___
$b+$12 is the equation that will determine the amount of the original bill
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that The friend told the waiter to remove the $12 dessert from Stan’s bill.
Stan tipped the waiter 20% on the reduced bill, which was a $15 tip
We need to write an equation that will determine the amount of the original bill b.
Let us find what 20% of amount will be 15
20/100×b=15
0.2x=15
b=15/0.2=75
The reduced bill is $75.
As before $12 is removed
$b+$12=$87
$87 is the original bill and 15 is the tip.
Hence, $87 is the original bill.
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Adam is trying to spot a meteor. The probability he will see one in the next 10 minutes is 0.56. What are the odds in favor of Adam seeing a meteor in the next 10 minutes?
The odds from the probability is 14 : 11
How to determine the odds from the probability ?The value of the probability is given as
Probability in the next 10 minutes = 0.56
This means that
p = 0.56
Represent the probability as a fraction
So, we have the following representation
p = 56/100
Simplify the fraction
p = 14/25
To convert the probability to odds, we make use of the following equation
Probability = Odds/(1 + Odds)
Substitute the known values in the above equation, so, we have the following representation
14/25 = Odds/(1 + Odds)
So, we have
(1 + Odds) * 14/25 = Odds
This gives
14/25 + Odds * 14/25 = Odds
Evaluate the like terms
11/25 * Odds = 14/25
So, we have
Odds = 14/11
Express as ration
Odds = 14 : 11
Hence, the odds is 14 : 11
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Terms nd coefficients and constants of 6+n2 + 1/2d
What is the relationship between the line of reflection and the segments connecting the corresponding points?
The relationship between the line of reflection and the segments connecting the corresponding points is perpendicular bisector.
Here we have to find the relationship between the line of reflection and the segments connecting the corresponding points
In order to find the relationship we must know what is meant by line of reflection.
The term line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.
As per the definition of the term we have identified that the relationship between these two element is perpendicular to the segment and bisects it. Because the line of reflection is the perpendicular bisector of the segment joining corresponding points of the preimage and image.
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When merida divides her age by 3 and adds 5, the result is 9 which equation represents this situation where m is meridas age?
a/ 9= (m ~ 3) x 5
b/ m= (9 - 3 ) + 5
c/ m = (9~3) +5
d/ 9= (m~ 3) +5
When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5.
What is an equation?The link between two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
The definition an equation in algebra is a mathematical expression that indicates the equivalence of two mathematical terms. In equation 6x + 11 = 14, for instance, the two expressions 6x + 11 and 14 are separated by the symbol "equal."
When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5, this represents the situation where m is Merida's age.
correct option: D
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How do you write coordinates for translation?
Coordinates (x ,y ) of the given geometrical figure after translation is written as ( x + h , y + k ) where h ∈ R and k ∈ R.
As given in the question,
Let us consider the coordinates of any geometrical figure is represented by ( x, y ) in the coordinate plane.
Translation is the representation of transformation the change in the location of the given geometrical figure without change in the shape and size.
It can be translated in four ways :
Translation to the right is written as ( x + h , y )
Translation to the left is ( x - h, y)
Translation in the up is ( x, y + k )
Translation in the down is ( x , y - k ).
Therefore, the original coordinate ( x ,y ) after translation written as
( x + h , y + k ) where h ∈ R and k ∈ R.
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1. Find the measure of such angle whose supplementary angle is 35° more than twice of its complementary angle.
Answer: The measure of the angle is 35, the measure of its supplement is 145, and the measure of its complement is 55
A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days. When the researcher finished his study, the height of the flower was about 11.04 inches. What is a reasonable domain to plot the growth function
After solving, the possible domain in interval notation is (0, 7).
In the given question, a researcher is following the growth of a particular type of flower.
The equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
According to the given information,
The height of the plant is modeled by the function= f(n)
The height of the plant is approximately 11.04cm when the number of days = 7
The days are started from n > 0 and n<=7
Hence the possible domain in interval notation = (0, 7)
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The complete question is:
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm What is a reasonable domain toplot the growth function?
Part B: What does the y-intercept of the graph of the function () represent?
Part C: What is the average rate of change of the function f(n) from n = 2 ton, and what does it represent?
In a triple batch of spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.
In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.
How to create a double number line?According to question:-
How much more garlic powder than salt is in the triple batch?
Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.
How much spice mix is in the triple batch?
Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.
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Let ABC be a triangle, and
M, N, and K represent the midpoints of sides AB, BC, and AC respectively.
If area of the triangle ABC is 6.0 square feet, then what is the area of the triangle MAK?
Step-by-step explanation:
please refer to the sketch
Gregory(g) is 20 years older than his cousin Mark(m). Mark is 6 years younger than his
sister Louanne(L). Write an expression to represent the sum of their ages.
Answer:
Step-by-step explanation:
Let's make Mark x as he is in both equations.
For Gregory in Marks view = x+20
For Marks's sister Louanne = x-6
Now you just add everything!
> x+x+20+x-6
> 3x+14
The sum of their ages is 3x+14
Hope that helped!
What is a function of the form f/x LOGB X?
The function form of the given function would be [tex]f(x)=log_b(x)[/tex].
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logbx.
So the function form would be the function of x is equal to the logarithmic of x having base b.
so this can be written as
[tex]f(x)=log_b(x)[/tex]
Hence, the function form of the given function would be [tex]f(x)=log_b(x)[/tex].
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The function form of the given function would be [tex]f(x)=log_b(x)[/tex].
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logbx.
So the function form would be the function of x is equal to the logarithmic of x having base b.
so this can be written as
[tex]f(x)=log_b(x)[/tex]
Hence, the function form of the given function would be [tex]f(x)=log_b(x)[/tex].
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Based on these data, how many students received a score higher than 95?
A. At least 15
B. More than 25
C. 6 or fewer
D. Exactly 10
Bar charts display categorical variables, whereas histograms display numerical or quantitative data.
What is mean by histogram?The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.
Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.
Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values). It would be ridiculous to attempt to plot an axis that included every potential value for a continuous variable.
Therefore, the correct answer is option C. 6 or fewer.
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b) Felipe is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
Cost (in dollars)
2
10
3
9
15 45
The cost for each person is not always the same.
O The cost for each person appears to be the same.
Predicted number in group for a cost of $50:
Answer:The cost for each person is not always the same. It is not a linear relationship between number in group and cost in dollars. Since we have only 4 rows it's difficult to make an accurate prediction for cost of $50, In addition, we don't have any formula or equation that can represent this data set.
The best way to find out how many people will go to movie with $50 is by looking at the table.
So the answer is, We don't have any information that can give us a prediction of number in group for a cost of $50,
Step-by-step explanation:
the cost of kens car wash was $23.95. if he wants to givve his detailer a 15% tip,about how much of a tip should he leave
Ken should leave a $3.59 tip.
We will discuss algebra, a branch of mathematics that deals with symbols and the rules for manipulating them, in the context of algebra word problem worksheets.
They represent variables or quantities without set values. Our abilities to construct and solve equations must be combined in order to solve algebraic word problems.
It is crucial to start by converting verbal descriptions into algebraic formulas before tackling word issues.
To find the amount of tip he should give, we note that 15% is equal to 0.15 as a decimal.
23.95 * 0.15= 3.5925≈3.59 (approximately)
Therefore, Ken should leave a $3.59 tip.
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Juanita changed $20 into euros when the exchange rate was €1=$1.2685.
How many euros did she receive?
Give your answer correct to 2 decimal places.
4. Find the probability that a randomly chosen point lies inside the shaded region. 4.
Express your answer as a decimal rounded to the nearest hundredth.
0.167 or 0.17 rounded to the nearest hundredth.
How do you round off decimal to the nearest hundredth?
When rounding to the nearest hundredth, you want to look at the third decimal place, the one to the right of the hundredth place. If the value in the third decimal place is less than 5, you truncate everything to the right of the hundredth place, leaving the number unchanged.
If the value in the third decimal place is greater than or equal to 5, you add one to the number in the hundredth place.
The total area of the rectangle is 15*5 = 75 square feet.
The area of the triangle inside the rectangle is (1/2)25 = 12.5 square feet.
The shaded region is the area of the triangle, so the probability that a randomly chosen point lies inside the shaded region is
12.5/75 = 0.167 or 0.17 rounded to the nearest hundredth.
Hence, 0.167 or 0.17 is rounded to the nearest hundredth.
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Work out
m
and
c
for the line:
2
y
−
4
x
=
2
Answer:
General equation : y = mx + c
2y - 4x = 2
2y = 4x + 2
y = 2x + 1
Therefore m = 2 and c = 1.
A kite is shaped like an isosceles triangle. To the nearest tenth what is the length of the spine?
The length of the spine will be;
⇒ 48.2 cm
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
A kite is shaped like an isosceles triangle.
Now,
Since, A kite is shaped like an isosceles triangle.
Hence, Two sides of a triangle is equal to each other.
Let the length of the spine = x
So, We can formulate by the Pythagoras theorem,
⇒ Hypotenuse² = Base² + Perpendicular²
⇒ 62² = (78/2)² + x²
⇒ 3844 = 39² + x²
⇒ 3844 = 1521 + x²
⇒ 3844 - 1521 = x²
⇒ 2323 = x²
⇒ x = √2323
⇒ x = 48.2 cm
Thus, The length of the spine = 48.2 cm.
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i need help with number seven with a full explanation please
The value of x would be 32.
What are a congruent quadrilaterals?
In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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By analyzing the figure, The value of x would be 32.
What are a congruent quadrilaterals?In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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DIG DEEPER! A cube is removed from a rectangular prism. Find the surface area of the figure after removing the cube.
A rectangular prism with length 9 feet, width 8 feet, and height 5 feet. A cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet.
The surface area is ______ square feet
The surface area of the figure after a cubic hollow runs to the height of the rectangular prism is 364 square feet.
The surface area is 364 square feet.
Find the surface area of the rectangular prism.
To do this, use the formula for the surface area of a rectangular prism:
(2 x length x width) + (2 x width x height) + (2 x length x height)
In this case, the length is 9 feet, the width is 8 feet, and the height is 5 feet. Plugging these values into the formula gives:
= (2 × 9 × 5) + (2 × 8 × 5) + (2 × 9 × 8)
= 314 square feet
When a cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet, 2 cubic faces is removed and 4 cubic faces added to the surface area of the resultant solid. So
surface area = 314 - 2×5² + 4×5²
= 314 + 2×5²
= 314 + 50
= 364 square feet
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Isaac's father is 49 years old. He is four years older than three times Isaac's age. How old is Isaac
If Isaac's father is four years older than three times of Isaac's age and the age of father is 49 years old. So, Isaac age will be 15 years old.
How old is Isaac?According to online myth, there is a mathematical equation that regulates the lower bound for a possible dating partner's socially acceptable age: half your age plus 7, or, in mathematical words, if x is your age, the bottom barrier is [tex]f(x) = x/2 + 7[/tex].
Consider Isaac is L
Let us suppose L is x years old.
3 times the age of L = 3x
3 times L’s age plus 4 years = 3x + 4
Furthermore, L’s father’s age is 49 years older than L’s age.
Therefore,
[tex](3x + 4) = (49) (49)\\(3x + 4) -4 = (49) – 4\\3x = 45\\3x/3 = 45/3\\X = 15[/tex]
L’s age is 15 years since we expected L’s age = x (and x=15).
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What is the easiest way to learn linear equations class 8?
The easiest way to solve linear equations is to use the elimination method.
A linear equation is an equation that has two variables and when it is graphed it gives a straight line. Linear equations can be graphed according to their slope and y-intercept. The standard equation for a line is y = mx + b, where b is the y-intercept and m is the slope.
To solve linear equations in the easiest and simplest way use the elimination method. In this method, you either add or subtract the equations to obtain an equation in one variable. When the coefficients of one variable are opposites, you add the equations to eliminate a variable and when the coefficients of one variable are equal, you subtract the equations to eliminate a variable.
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Mason worked at the water park over the summer. He made $425 in June and $680 in July if he made twice as much money in august as he did june. What is the ratio of money earned in august to July
The ratio of money earned in August to July is 5/4.
Now, According to the question:
Let's know
What is Ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
Mason worked at the water park over the summer. He made $425 in June and $680 in July.
And if he made twice as much money In August as he did in June.
That means, he made $850 in August.
Then, The ratio will be :
= August / June
= 850/680
= 5/4
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How do you graph a parent graph?
This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.
For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola. For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
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Describe a sequence of transformation that maps DOG onto CAT
Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.
what is sequence ?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). The total, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more objects in a logical order.
given
Δ DOG AND ΔCAT
According to Chanel, the series of transformations that maps triangle ABC onto triangle DEF is as follows:
Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.
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what is 7/8 x 40 equal.
The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Find the perimeter of the rectangle.
7th grade
The perimeter of the rectangle is 13x+7 feet
What is the area of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given here: The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Therefore the perimeter of the rectangle is given by
= 2(5x-1.5+1.5x+5)
=2(6.5x+3.5)
= 13x+7
Hence, The perimeter of the rectangle is 13x+7 feet
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