By using function, it can be calculated that
The value of f(8, 9) is 73
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the function is
f(a, b) = ab - (a - b)
f(8, 9) = 8 [tex]\times[/tex] 9 - (8 - 9)
f(8, 9) = 72 + 1
f(8, 9) = 73
So the value of f(8, 9) is 73
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the initial number of views for a reader board was 25. the number of views is growing exponentially at a rate of 18% per week. what is the number of views expected to be four weeks from now? round to the nearest whole number.
The number of views in the four weeks round to the whole number is 48.
Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.
We have to find the number of views in the fourth week.
On the first week the increase = 25 + 25× 18%
= 25 + 25 × 18/100
= 25 + 4.5
= 29.5
The second week increase = 29.5 + 29.5 × 18%
= 29.5 + 5.31
= 34.81
The third week increase = 34.81 + 34.81 × 18%
= 34.81 + 6.2658
= 41.0758
The fourth week increase = 41.0758 + 41.0758 × 18%
= 41.0758 + 7.393644
= 48.469444
Therefore the number of views in the four weeks is 48.
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If y varies directly as x and y=8 when x=2 find when x=6
The equation is y = 4x. And the value of the function at x = 6 will be 24.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If y varies directly to x. Then the relationship between them is written as,
y ∝ x
y = kx
When y = 8 and x = 2, then the value of the constant k is given as,
8 = k (2)
k = 8 / 2
k = 4
Then the equation is written as,
y = 4x
Then the value of the function at x = 6 will be given as,
y = 4 (6)
y = 24
The equation is y = 4x. And the value of the function at x = 6 will be 24.
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Four congruent parallelograms are joined to make the shape below.
24 cm
The total shaded area is 192 cm²
Work out the value of x.
x cm
5 cm
For the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
As given in the question,
Given four congruent parallelograms
Shaded area of the parallelogram is 192cm²
As four parallelograms are congruent
Let the area of each parallelogram is A
4A = 192
⇒A = 48cm²
For two parallelogram base length = 24cm
Base length of each parallelogram = 12cm
Area of parallelogram = base × height
48 = 12 × height
⇒ height = 4cm
Value of x = 2 times of height
= 2 (4)
= 8cm
Therefore, for the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
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which statement is not a step used when constructing an inscribed equilateral triangle ?
Use the compass to join the two circles together, this statement is not a step used when constructing an inscribed equilateral triangle.
What is known as a triangle?A polygon having three vertices and three sides are called a triangle. The triangle's angles are created by joining its three sides end to end at a single point.
The triangle's construction does not include claim D, which is the case. Use the compass to join the two circles together.
It is necessary to keep the compass at a width equal to the circle's radius and to position it at the point where the circle and radius connect while building an inscribed equilateral triangle.
Additionally, it's crucial to pivot an arc the radius's length away from the circle's point. It is not a part of the steps to join the two circles using the compass.
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I need help like asap !!!
only numbers and decimal points
Answer:
a = 4.52 km
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (7.2)² = a² + (5.6)²
→ 51.84 = a² + 31.36
→ a² = 51.84 - 31.36
→ a = √20.48
→ [ a = 4.52 km ]
Hence, value of a is 4.52 km.
HELP ASAP!!! THANK YOU
To balanced hanger, adding a circle to the left and a square to the right. To both sides, add two triangles. The option 1, 2, and 5 are correct.
What is balanced hanger?
Because each side of the hanger is evenly spaced from the center and has a same amount of overall weight, they are balanced against one another. During the warm-up, students come across two real hangers—one is balanced and the other is slanted—and they observe and consider what might have caused the hangers' appearance.Adding two circles to the left side and a square to the right would adjust the hanger's balance in accordance with the lesson's emphasis on maintaining the equation in balance.
adding a circle to the left and a square to the right. To both sides, add two triangles.
Hence the option 1, 2, and 5 are correct.
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It cost Hassan $5.31 to send 59 text messages. How much does each text cost to send?
Each text will cost Hassan $0.09
What is rate ?A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.
Similarly $5.31 is the cost of 59 text messages
Therefore a text message will cost $5.31/12=$0.09
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the ratio of drummers to guitar players who tried out for a band is 10:45 .
How many times the number of drummers is the number of guitar players?
Answer:
4.5
Step-by-step explanation:
45/10=4.5
N is an integer. Work out:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
According to the integer N,
a) The smallest possible value of N is 6.5 if N >= 6.5
b) The largest possible value of N is -2 if N < - 3
c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.
Integer
Integer refers a collection of whole numbers and negative numbers.
Given,
Here we have the integer N.
And we need to find the following:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
Part a). smallest possible value of N if N >= 6.5
Here the smallest number is 6.5 because other value are greater than this one.
Part b). the largest possible of N if N < -3
The largest possible number is -2, because the other values on N are less than -2.
Part c). the possible values of N if N >= -2 and N <2.
Here the possible values between these are {-2, -1, 0, 1}.
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Evaluate the expression below without using a calculator
With the help of trignometric identities we can say that the answer is = 0.672355, nearly.
What is trignometric equation?A trigonometric equation is any equation that contains a trigonometric function. Up until now we have introduced trigonometric functions, but not fully explore them. In the lessons within this SparkNote on trigonometric equations, we'll learn exactly how to solve trigonometric equations.As mentioned in Trigonometric Identities, a trigonometric equation that holds true for any angle is called a trigonometric identity. There are other equations, though, that only are true for certain angles.They are generally known as conditional equations, but in this text we'll just call them equations. We'll learn some techniques for solving general equations, as well as how to derive an infinite number of solutions to an equation based on a single solution to that equation.acc to our question-
cos(75)= 2-√3tan(22/7)= 1+√2.sin 3π/6= √2-√√2/2Learn more about trignometric equation:
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Here is a correlation, does it also represent causation? Explain you answer.
The number of additional calories consumed and the amount of weight gained.
Yes, there is causation between the two given variables, as the weight is related at some point with the amount of calories consumed.
What does correlation and causation mean?
For two variables x and y, we say that there is causation when, if we modify one of the variables, the other changes in response.
Correlation just means that the variables are related in some way (maybe both have a causation relationship with the same other variable)
So causation implies correlation.
Correlation does not imply causation.
In this case, we have the example:
x = The number of additional calories consumed
y = amount of weight gained.
Clearly, we have causation between x and y as larger is the value of x, larger will be the value of x.-
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What is the image of the point (-7,9) after a rotation of 90 counterclockwise?
The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
Given that,
The points (-7,9).
We have to find the image of the point after a rotation of 90° counterclockwise.
Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.
Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.
(x,y)→(y,-x)
(-7,9)→(9,7)
Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
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don't need explanation just the answer
The function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statementr which best describes the graph is, the graph is streched towards the x axis by a factor of 1/3
When an object is dilated the image formed is larger or smaller, but there is a difference in the size of the shape.
the rule of function change f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8
3x = 9xk
k = 1/3
Therefore, the function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statement which best describes the graph is, the graph is streched towards the x axis by a factor of 1/3
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Given l||m and m∠1 = 60°, select all angles that are also equal to 60°. 8 2 6 7 5 4 3
Answer:
2 , 3 , 4
Step-by-step explanation:
Corresponding angles: When two parallel lines are intersected by a transversal, the angles on the same side and same position of the transversal are same.
∠3 = ∠1
Vertically opposite angles: When two lines intersect, the opposite angles are congruent.
∠2 = ∠1
∠4 = ∠3
So, ∠1 = ∠2 = ∠3 = ∠4 = 60°
Carol buys a house for £234,900
she pays a 10% deposit
work out the amount of deposit paid by carol
Answer:
£23, 490
Step-by-step explanation:
10% deposit by Carol of £234,900
10/100 *£234,900
0.1*£234,900=£23,490
3. Is this graph a function?
This is a function.
This is not a function.
This cannot be determined from this graph.
Answer:
that is a quadratic function so yes it is a function
Step-by-step explanation:
it is a function becausr you can write an equation with it. Hope I could help!
Select the ordered pair that is NOT marked on the coordinate plane.
An ordered pair that is not marked on the coordinate plane of this graph is (8, 0).
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which represent the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
What is an ordered pair?An ordered pair can be defined as a pair of two (2) data points that are commonly written in a fixed order within parentheses as (x, y), in order to represent the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
By critically observing the given graph, we can reasonably and logically deduce that data point (8, 0) is the missing ordered pair on the coordinate plane.
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carter has 24 posters in his room. if he arranges them into 6 equal rows, how many posters will be in each row?
If he arranges them into 6 equal rows, 4 posters will be in each row.
Define division.One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.
Given,
Total posters = 24
Arranging them into 6 equal rows,
Dividing:
24÷ 6
Reciprocating,
24 × 1/6
4
If he arranges them into 6 equal rows, 4 posters will be in each row.
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Indicate the distance of the segment using the given
information. Round to the nearest tenth.
5. Find AX. A(-4, 5), X (1, −2)
The distance of segment AX sis found to be 8.6 units using the distance formula.
What exactly is the distance formula?[tex]\sqrt{[x_{2}-x_{1}]^{2} + [y_{2}-y_{1}]^{2} }[/tex] is the distance formula. This works for any two points in two-dimensional space with coordinates (x₁, y₁) for the first and (x₂, y₂) for the second. You may easily remember it if you remember that it is Pythagoras' theorem, that the distance is the hypothenuse, and that the coordinate lengths are the difference between the x and y components of the points.Why do we employ the distance formula?In complex numbers, the distance formula is used to express the plane and its magnitude. Furthermore, distance formulae can be used to calculate the distance between two planes in three-dimensional or n-dimensional planes. It is also used to calculate the magnitude formula.Given: A(-4, 5), X (1, −2)
We need to find the distance of the segment AX.
Distance of AX is given as :
[tex]\sqrt{[1-(-4)]^{2} + [-2-5]^{2} } \\= \sqrt{25 + 49}\\ = \sqrt{74}\\ =8.6[/tex]
Therefore, the distance of segment AX sis found to be 8.6 units using the distance formula.
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How can 33 over 9 be expressed as a decimal?
Answer:
3.6
................................
What is the slope of the line that passes through the points (1, -9) and (4, -7)? Write your answer in the simplest form.
The slope of the line from the given points will be equal to 3/2 in the simplest form.
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given points in the question,
(1, -9) and (4, -7).
x1 = 1 and x2 = 4
y1 = -9 and y2= -7
Slope = (x2- x1)/(y2- y1)
= (4 - 1)/(-7 - (-9))
Slope = 3/2
Therefore, the slope of the line will be 3/2.
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the nth term of a gp 145800. if the fist term is 2 and the common ratio is 3. find the sum of the gp
The sum of the geometric progression with the features stated in the text is given as follows:
S = 2.62 x 10^(43).
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of a finite geometric sequence with n terms is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
In this problem, the first term and the common ratio are given as follows:
[tex]a_1 = 2, n = 3[/tex]
Hence the equation is:
[tex]a_n = 2(3)^{n - 1}[/tex]
The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:
[tex]a_n = 2(3)^{n - 1}[/tex]
[tex]1458000 = 2(3)^{n - 1}[/tex]
[tex]3^{n - 1} = 729000[/tex]
[tex]3^{n - 1} = 3^{90}[/tex]
Then:
n - 1 = 90
n = 91.
Thus the sum of the sequence is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]
S = 2.62 x 10^(43).
Typing mistakeThe problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.
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HELP ME PLEASE.
f(x) = √2x
g(x) = √50x
Find (f g)(x). Assume x ≥ 0.
A. (f.g)(x) = 10√
B. (f.g)(x) = √52x
C. (f.g)(x) = 10x
D. (f g)(x) = 50x
The representation of the composite function (fg)(x) is (fg)(x) = 10x
How to determine the possible value of the composite function?From the question, we have the following function definitions
f(x) = √2x
g(x) = √50x
The function to calculate is given as (fg)x
This can be calculated using
(fg)(x) = f(x) * g(x)
Substitute √2x for f(x) and √50x for g(x) in the above equation
So, we have
(fg)(x) = √2x * √50x
Evaluate the products
(fg)(x) = √100x²
Evaluate the exponents
(fg)(x) = 10x
Hence, the possible equation is (fg)(x) = 10x
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please help asap will give brainliest
1. The angles measures are larger than the original angle measures is a false statement.
2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.
3. The final angle measure are the same as the original angle measure is false statement.
4. The original figure and the final figure may not be congruent is true statement.
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There is no prior information about the proportion of Americans who support free
trade in 2019. If we want to estimate a 98% confidence interval for the true
proportion of Americans who support free trade in 2019 with a 0.21 margin of error,
how many randomly selected Americans must be surveyed? Answer: (Round up your
answer to nearest whole number, do not include any decimals)
31 Americans should be surveyed by Z mean.
What does critical value of Z mean?
The Z-score will show you how far a specific data point is from your sample's mean. This kind of critical value will inform you of the amount of standard deviations above or below the population mean for your sample.If the prior population proportion is unavailable then the formula to find the sample size is given by
n = 0.25[tex](\frac{z^{*} }{E} )^{2}[/tex]
where z* = Critical z-value
E = margin of error
Given, Confidence level = 98%
The critical z-value for 98% confidence interval is 2.326 ( BY z-table)
Margin of error : E= 0.21
n = 0.25 [tex](\frac{2.326}{0.21})^{2}[/tex]
n = 0.25 * ( 11 .07)²
n = 0.25 * 122.5449
n = 30.363225 ≈ 31
Hence, 31 Americans should be surveyed.
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How do I solve these?
Applying the knowledge of congruent triangles, the measures are solved as:
6. X = 14; AC = 11; T = 14; WZ = 16; WY = 60; AB = 60; m∠A = 64°; m∠Y = 64°; m∠W = 50°
7. X = 7; YZ = 28; T = 9; WZ = 10; WY = 11; AB = 28; m∠A = 31°; m∠C = m∠W = 99°
How to Solve for the Measures of Congruent Triangles?To solve for the missing measures of triangles that are congruent to each other, recall that triangles that are congruent will have corresponding sides that are equal and also corresponding angles that are equal.
6. Triangles ABC and YWZ are congruent, therefore:
m∠A = m∠Y; m∠B = m∠W; m∠C = m∠Z
AB = WY; AC = YZ; BC = WZ
Therefore:
5X - 4 = 66
Solve for X
5X = 66 + 4
5X = 70
X = 14
AC = YZ = 11
AB = WY
5T - 10 = 4T + 4
5T - 4T = 10 + 4
T = 14
BC = WZ = 16
WZ = 16
WY = 4T + 4 = 4(14) + 4
WY = 60
AB = WY = 60
AB = 60
m∠A = m∠Y
m∠A = 180 - 50 - 66
m∠A = 64°
m∠Y = 64°
m∠B = m∠W = 50°
m∠W = 50°
7. Triangles ABC and ZYW are congruent, therefore:
m∠A = m∠Z; m∠B = m∠Y; m∠C = m∠W
AB = YZ; AC = WZ; BC = WY
Therefore:
5X - 4 = 3X + 10
Solve for x
5X - 3X = 4 + 10
2X = 14
X = 7
AB = YZ
2T + 10 = 4T - 8
2T - 4T = -10 - 8
-2T = -18
T = 9
YZ = 4T - 8 = 4(9) - 8
YZ = 28
AC = WZ = 10
WZ = 10
WY = 11
AB = YZ = 28
AB = 28
m∠A = m∠Z = 3X + 10 = 3(7) + 10
m∠A = 31°
m∠C = m∠W = 180 - 31 - 50 = 99°
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monique and tara each make an ice-cream sundae. monique gets 3 scoops of cherry ice-cream and 1 scoop of mint chocolate chunk ice-cream for a total of 84g of fat. tara has 1 scoop of cherry and 3 scoops of mint chocolate chunk for a total of 60g of fat. how many grams of fat does 1 scoop of each type of ice cream have?
The amount of fat in Cherry ice-cream is 24 grams.
The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.
Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)
Multiplying equation (2) by 3 and then subtracting equation (1) from
the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12
grams C + 12*3 = 60C = 60-36 = 24
The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.
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What is the solution to this inequality? x - 1 . 5 > 2 . 5 Question 1 options: x < 4 x < 1 x > 1 x > 4
The solution to the inequality is X > 4
InequalityInequality is a set of mathematical expression which the individual side is not equal to other side
To solve for x in the inequality x - 1 . 5 > 2, we followed the step;
Step 1: Add 1.5 to both sides
x - 1.5 + 1.5 > 2 . 5 + 1.5
X > 4
Therefore, the solution to the inequality is X > 4
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The map above is being reduced by a scale factor of 1/9 and printed for the subway
station. How many square inches will the new map take up?
O 315 square inches
O 72 square inches
24 square inches
O 35 square inches
Answer:
35 square inches
Step-by-step explanation:
21x15=315
315/9=35
Therefore, the answer is 35 square inches
1/2x-7=1/3(x-12) Explain or show your reasoning.
Answer: x=18
Step-by-step explanation:
It just does ok