The values of a and b are;
⇒ a = 3
⇒ b = 3
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
An exponential function is,
⇒ f (x) = a bˣ
And, It passes through the points (0, 3) and (3, 81).
Now,
Since, It passes through the points (0, 3) and (3, 81).
Hence, Substitute x = 0 , f(x) = 3 in the function,
⇒ f (x) = a bˣ
⇒ 3 = a b⁰
⇒ a = 3
And, Substitute x = 3 , f(x) = 81 and a = 3 in the function,
⇒ f (x) = a bˣ
⇒ 81 = 3 b³
⇒ b³ = 27
⇒ b = 3
Thus, The values of a and b are;
⇒ a = 3
⇒ b = 3
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How do I divide 16.64 by 6.40?
Answer: 2.6
Step-by-step explanation:
Use long division:
16.64 over 6.4
First multiply the numerator by 10 to get 166.4 over 64
Then divide 166.4 by 64 (using long division)
At the end you'll get 2.6
How do you find the equidistant point of a triangle?
The equidistant point of the triangle is point O , which is shown below.
In the question ,
we have to find the equidistant point in the triangle ,
We know that the equidistant point from the vertices of the triangle is the circumcenter ,
let the circumcenter be point O .
The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .
We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .
So ,we draw OA ,OB and OC .
we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.
that means , OA = OC and OC = OB .
which means OA = OB .
we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.
So, we can say that point O is on the perpendicular bisector of AB .
and
Since OA = OB = OC , the point O is equidistant from A , B and C .
Therefore , the equidistant point of the triangle is the circumcenter (point O) .
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if y varies jointly with x and z and y=-60 when x=-5 and z=4, find y when x=4 and z=-3
The value y is -36.
What is proportionality?Proportionality is the property of two variables being in a multiplicative relation to a constant.
Given that, y varies jointly with x and z and y=-60 when x=-5 and z=4,
y ∝ xz
Let k be the Proportionality constant,
y = kxz
-60 = k*4*-5
k = 3
When x = 4 and z = -3
y = 3*4*-3
y = -36
Hence, The value y is -36.
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Represent the following statement on a number line: I have anywhere from $5 to $8 in my pocket.
The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Translating the statement, we have the following inequality:
Let the variable x represent the amount of money in pocket.
From $5 to $8 in my pocket = 5 ≤ x ≤ 8.
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Pedro vive cerca del bosque, el terreno de su propiedad ocupa 15 metros en total, su casa ocupa sólo 6 metros, tiene un huerto el cual ocupa 4 metros y el resto es un espacio donde puede disfrutar de la naturaleza ahí encuentra algunas clases de musgos que le dan un aspecto maravilloso al bosque.” ● Representa con fracciones el espacio que ocupa la casa, el espacio que ocupa el huerto y deduce qué fracción representa el resto del terreno, a lado de cada fracción realiza la representación gráfica de cada una, usando las herramientas como tablas o insertar formas en PowerPoint.
El espacio que ocupa la casa sería 6/15, el espacio que ocupa el huerto sería 4/15 y el espacio restante del terreno sería 5/15.
¿Cómo representar las fracciones del terreno?Para representar en forma de fracciones el área de los diferentes espacios del terreno de Pedro debemos tener en cuenta que el total tiene 15 metros. Adicionalmente, cuando representamos una fracción estamos informando cuántas unidades de un número x de unidades estamos utilizando. Por ejemplo, en este caso del total (15 metros) del terreno que tiene Pedro, él esta utilizando 6 metros para su casa. Esta fracción se representaría así:
6 / 15
Por otra parte, la fracción para representar el área del huerto de Pedro debe seguir los mismos lineamientos que la anterior, es decir en el numerador (número de la parte de arriba) ponemos el número de unidades que utilizamos y en el denominador (número de la parte de abajo) ponemos el número total de unidades disponibles. Entonces la fracción del huerto sería:
4 / 15
Por ultimo, para saber cuántas unidades quedan disponibles del terreno de Pedro, debemos restarle al total de terreno la cantidad de espacio que usamos:
15 - 4 - 6 = 5
De acuerdo con lo anterior, el espacio disponible serían 5 metros, que expresado en fraccionarios sería:
5 / 15
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Fathi has $ 1.10 in his printing account. Each sheet of paper he uses reduces his printing account balance by $0.25 Fathi wants to print out a PDF document that is 47 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet. After Fathi prints, what will be the balance in his printing account?
As described in the algebra the balancing amount is - 1.8375
what is algebra?
Mathematics has several different subfields, including algebra. Algebra, broadly stated, is the study of mathematical symbols and the guidelines for using these symbols in formulas.
Solution;
Balance of account = account amount - account used
= 1.10 - 0.25 * ( 47/2)
= 1.10 - 0.25* 11.75
= 1.10 - 2.9375
Balance of account = - 1.8375
Hence, by algebra the balancing amount of account is - 1.8375
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5. Julia is playing a computer game. To enter a new quest she has
to pay a "tax" of 2.5 points, but she expects to gain 75 points.
For each quest, how many points can she gain overall?
The number of points gained overall by Julia playing the game is 30 point
How to determine the number of points gained overall?From the question, we have the following parameters that can be used in our computation:
Tax paid for a new quest = 2.5 points
Total points gained playing the game = 75 points
The above parameters can be represented as
The number of points gained overall = Total points gained playing the game/Tax paid for a new quest
Substitute the known values in the above equation, so, we have the following representation
The number of points gained overall = 75/2.5
Express as a correct fraction
So, we have the following representation
The number of points gained overall = 750/25
Evaluate the quotients
So, we have the following representation
The number of points gained overall = 30
Hence, the number of points gained overall =is30
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NO LINKS!! Express the statement as an inequality. Part 5
Answer:
[tex]\textsf{(d)} \quad \sf \dfrac{1}{5} < c < \dfrac{1}{3}[/tex]
(e) p ≤ -5
(f) -m ≥ -9
Step-by-step explanation:
Symbol notation
< means "less than".> means "greater than".≤ means "less than or equal to".≥ means "greater than or equal to".= means "equals".A negative real number is any real number that is less than zero.
A positive real number is any real number that is greater than zero.
Zero is neither positive nor negative.
Part (d)[tex]\textsf{c is between $\dfrac{1}{5}$ and $\dfrac{1}{3}$}.[/tex]
If c is between 1/5 and 1/3, it is greater than 1/5 and less than 1/3 (as 1/5 < 1/3), but not equal to either number:
[tex]\sf \dfrac{1}{5} < c < \dfrac{1}{3}[/tex]Part (e)If p is not greater than -5, then it is less than or equal to -5:
p ≤ -5Part (f)If the negative of m is not less than -9, then it is greater than or equal to -9:
-m ≥ -9A rectangular paperboard measuring 21 in long and 16 in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the paperboard remaining after a semicircle is cut out of it is 235.52 in².
What is area?The area is the amount of space within the perimeter of a 2D shape.
To calculate the area of the rectangular board that remain, we use the formula below.
Formula:
A' = lw-[πr²/2]............. Equation 1Where:
A' = Area of the paperboard leftl = Length of the paperboardw = width of the paperboardr = Radius of the semi circleFrom the question,
Given:
l = 21 inw = 16 inr = 16/2 in = 8 inπ = 3.14Substitute these values into equation 1
A' = (21×16)-(3.14×8²/2)A' = 336-100.48A' = 235.52 in²Hence, the area of the paperbaord left is 235.52 in².
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What is the value of t??
1.4t - 0.4 ( t - 3.1 ) = 5.8
Please explain step by step on how I could get this answer!
1.4t - 0.4(t-3.1)=5.8
Combine terms in paratheses
1.4t - 0.4t + 1.24 = 5.8
Combine t's
(1)t + 1.24 = 5.8
Subtract 1.24 over
t = 4.54Without using a calculator, find the value of sin^2(55) + cos^2(55) - sin(60)/cos(30)
Answer:2 minus the square root of 3 divided by 2
Step-by-step explanation:
8+[8+(−1⋅(−3)−4)]÷(−7)
Answer:
8 + [8 + (-1*(-3)-4)]÷(-7) = 7/1 = 7
Hope this helped answer your question!
Answer:
7
Step by Step Explanation:
The rectangular prism below is labeled with its measured dimensions. Taking measurement error into account, what are the minimum and maximum possible volumes?
Minimum possible volume =
ft³
Maximum possible volume =
ft³
The minimum possible volume of this rectangular prism is 176.78 ft³.
The maximum possible volume of this rectangular prism is 131.11 ft³.
How to determine the minimum and maximum possible volumes?Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume = L × W × H
Where:
L represents the length of a rectangular prism.H represents the height of a rectangular prism.W represents the width of a rectangular prism.In order to determine the minimum possible volume of this rectangular prism, we would add the greatest possible error to each measurement and then multiply as follows:
Vmin = (3.5 + 0.25) × (8.4 + 0.25) × (5.2 + 0.25)
Vmin = 3.75 × 8.65 × 5.45
Minimum possible volume, Vmin = 176.78 ft³.
In order to determine the maximum possible volume of this rectangular prism, we would subtract the greatest possible error from each measurement and then multiply as follows:
Vmax = (3.5 - 0.25) × (8.4 - 0.25) × (5.2 - 0.25)
Vmax = 3.25 × 8.15 × 4.95
Maximum possible volume, Vmax = 131.11 ft³.
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Is centroid and Circumcentre same?
No, the centroid and Circumcentre are not same but it is same in equilateral triangle.
The intersection of a triangle's perpendicular bisectors is called the circumcenter.A triangle's circumcenter is a location that is equally spaced from each of its vertices.The centroid of a triangle is the location where its medians connect.
Triangle's centroid is always within it. The centroid of a triangle is its center of gravity in physical terms. If the triangle is evenly distributed around the plane's surface and you want to balance it by supporting it at only one point, you must do it near the center of gravity.Are the circumcenter and centroid at the same location? In the case of an equilateral triangle, they will both be.
Therefore, the centroid and Circumcentre are not same but it is same in equilateral triangle.
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How do you write a equivalent?
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number.
Given,
Equivalent;
Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2.
Here,
When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.
That is,
The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.
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27.5 percent of what is 13.75
Answer:
50Step-by-step explanation:
27.5 percent of what is 13.75
13.75 : 27.5 * 100 =
(13.75 * 100) : 27.5 =
1375 : 27.5 = 50
A water line enters a house 2.0m below ground. A smaller diameter pipe carries water to a faucet in the house. Water flows at 2.0m in the main line and 7.0m out of the second-floor faucet. Take the density of water to be 1.0 ×10^-3 ^3 If the pressure in the line is 2.00 × 10^5 and the pressure at the faucet is 1.40 × 10^5 , how far above ground is the faucet?
The difference in pressure between the main line and the second floor is 91,100 Pa.
How to calculate difference in pressure between main line and second floor ?Bernoulli's theorem states that a drop in fluid pressure is connected with an increase in fluid velocity if the fluid flows horizontally so that there is no change in gravitational potential energy.
On the basis of the idea of energy conservation, Bernoulli's principle is explained. According to this law, the total amount of mechanical energy in a fluid travelling along a streamline will be the same at every point along that streamline in a steady flow.
Given ,
The settings provided;
The main line's water speed is 2.0 m/s,
The second floor's water speed is 7.0 m/s,
The water's density is 1.0 x 103 kg/m3.
The following formula can be used to compute the pressure difference between the main line and the second level using Bernoulli's equation:
[tex]p_1+1/2pv2/1+pgh1+ = p2+1/2pv2/2+pgh_2[/tex]
[tex]p1- p2 = 1/2pv2/2 - 1/2pv2/1 + pgh2 - pgh1[/tex]
[tex]p1 - p2 = 1/2p(v2/2 - v 2/1) + pg (h2- h1)[/tex]
p1 - p2 = 1/2(1000)(7² - 2²) + (1000 ×9.8)(5 - (-2))
p1 - p2 = 91100 pa
Thus, the difference in pressure between the main line and the second floor is 91,100 Pa.
The complete question is : A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 × 103 kg/m 3 . The difference in pressure between the main line and the second floor is _______.
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The box-and-whisker plots below (sometimes called boxplots) summarize the noon temperatures for each city.
Use the box-and-whisker plots to answer the questions.
Comparing the box-and-whisker plots for both data of each city, we have:
a. City B had more noon temperatures above 76°F
b. Both had the same interquartile range.
c. City B had a larger median noon temperature
d. City A had the largest noon temperature.
How to Analyze a Box-and-whisker Plot?The box-and-whisker plot has the following values it displays about a data distribution:
Minimum value: This is the value at the beginning of the left whisker.Lower quartile (Q1): This is indicated by the beginning of the edge of the box, 25% of the data are below this point.Median value: the line that divides the box is the median value which is 50% of the data.Upper quartile (Q3): This is indicated by the end of the edge of the box, 75% of the data are below this point.Maximum value: This is the largest data point and is located at the end of the right whisker.Interquartile range = Q3 - Q1
Analyzing the box-and-whisker plots given above, we have the following to conclude:
a. City B had more noon temperatures above 76°F because about more than 50% of the data are above 76°F.
b. Interquartile range for City A = Q3 - Q1 = 75 - 68 = 7
Interquartile range for City B = Q3 - Q1 = 80 - 73 = 7
Both had the same interquartile range.
c. Median for City A = 70
Median for City B = 78
City B had a larger median noon temperature
d. City A had the largest noon temperature of 85.
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What property describes the number sentence of 6 0 6?
The property that defines the number sentence 6 + 0 = 6 is Additive Identity Property.
Given,
6 + 0 = 6
We have to find the property that defines the number sentence;
Additive Identity Property;
Additive identity property says that if zero is added to any real number, the resultant would be the same real number.
Here,
6 + 0 = 6
In this instance, we have added 0 to a real number (6) and have received back the same real number (6).
That is,
Additive Identity Property is the property that defines the number sentence 6 + 0 = 6
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The graph of F is shown below evaluate each integral by interpreting it in terms of area
The answer to this question is after solving definite integration 0,1,-4,-10
What is Definite integration?
It is just basically Simple Integration with limits. In other words it is completely same as area under curve
Solution:
We will proceed by finding area under curve
Here we have to consider the area above x axis as positive and area under x axis as negative area
In First part +ve area and -ve area cancels each other hence answer is 0
In second part after cancellation only 1 square block above x axis remains whose area is 1 hence answer is 1
remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative
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A person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken. If the distance driven, in kilometers, is represented by d and the time taken, in hours, is represented by t, which equation could represent the relationship between d and t?
The equation that could represent the relationship between [d] and [t] is d = 60t.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken.
We can write the equation that could represent the relationship between [d] and [t] with the help of the equation of a straight line.
y = mx + c
for c = 0
y = mx
m = 120/2
m = 60
So -
y = 60t
or
d = 60t
Therefore, the equation that could represent the relationship between [d] and [t] is d = 60t.
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What is the length of 1 ton AC?
The length of 1 on AC is 54.6 cm.
Given:
Let x be the length
we know that,
AC dimensions = 54.6 * 175.7 * 85.6 cm
It is the volume = l * b * h
Volume :
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Length :
Length is defined as the measurement or extent of something from end to end.
Breadth :
The breadth of something is the distance between its two sides.
On comparing both
Length l = 54.6 cm
Breadth b = 175.7 cm
Height h = 85.6 cm
Therefore the length of 1 on AC is 54.6 cm.
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PLSSSSSSS HELPPPPPPPPP
Answer:
undefined
Step-by-step explanation:
since all the x are zero it’s undefined and when all y is zero it’s 0
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How do you rewrite equivalent expressions?
To rewrite equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
We know that,
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
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The numerator of a fraction is 2 less than its denominator. When both the numerator and denominator are increased by 3, the fraction is increased by 3/20. Find the original fraction.
Using the given information, the original fraction is 3/5
Determining the numerator and the denominator of a fractionFrom the question, we are to determine the original fraction.
Let the numerator of the fraction be x and the denominator be y.
From the given information,
"The numerator of a fraction is 2 less than its denominator"
That is,
x = y - 2 ----------- (1)
and
"When both the numerator and denominator are increased by 3, the fraction is increased by 3/20"
That is,
(x + 3)/(y + 3) = x/y + 3/20
Then,
(x + 3)/(y + 3) = (20x + 3y)/20y
(x +3)(20y) = (y + 3)(20x + 3y) ---------- (2)
Substitute the value of x into equation (2)
((y - 2) +3)(20y) = (y + 3)(20(y - 2) + 3y)
(y - 2 +3)(20y) = (y + 3)(20y - 40 + 3y)
(y +1)(20y) = (y + 3)(23y - 40)
20y² + 20y = 23y² - 40y + 69y - 120
23y² - 20y² - 40y + 69y - 20y - 120 = 0
3y² + 9y -120 = 0
Divide through by 3
y² + 3y - 40 = 0
y² + 8y - 5y - 40 = 0
y(y + 8) -5(y + 8) = 0
(y - 5)(y + 8) = 0
y - 5 = 0 OR y + 8 = 0
y = 5 OR y = -8
Substitute the values of into equation (1)
x = y - 2
When y = 5
x = 5 - 2
x = 3
When y = -8
x = -8 - 2
x = -10
Ignoring the negative values, the fraction is 3/5
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graph the system of equations below on a piece of paper. what is the solution y=x-1 y=3x+1
The intersection of these lines is the answer to the given system of equations. → (-1, -2)
Given the system of equations,
y = x - 1
y = 3x + 1
Now, equating both the given equations,
x - 1 = 3x + 1
3x - x = -2
2x = -2
x = -1
From, y = x - 1
y = -1 - 1
y = -2
The answer to the given system of equations is located at the intersection of these lines.
⇒ (-1, -2)
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Find the area of the shaded region as a simplified expression 5x + 3 * 2x
Answer:11x
Step-by-step explanation:
The cost of a cheese pizza is $11.99 plus $0.45 for each additional topping, t. Write an inequality that can be used to represent the cost of a pizza that is at most $16. What is the most number of toppings that a pizza can have and still be at most $16?
Answer: 11.99 + 0.45t ≤ 16 The most toppings you can have is 8
Step-by-step explanation:
11.99 + 0.45 is a basic cheese pizza plus one topping
11.99 + 0.45t represents a pizza plus an undefined amount of toppings
11.99 + 0.45t ≤ 16 The cost of the pizza has to be 16$ or less
Subtract 11.99 from each side
0.45t ≤ 4.01
Divide both sides by 0.45
t ≤ 8.9111
You can't have a partial number of toppings, and 9 is too much, so we round down to 8.
Find the volume of the silo if the radius of the hemispherical top is 20 feet. Use 3.14
for pi. The volume of the silo, rounded to the nearest thousand, is about ____ feet.
Answer:
Step-by-step explanation:
V = 16755.1608 m3
Which function represents a function with direct variation?
Functions of the form f(x)=kx represents direct variation.
The table of values that appears a constant proportion between two variables speaks to a direct variation function. In the event that there's at slightest one pair of values that features a different proportion, at that point the function isn't a direct proportion. the equation applies to each corresponding value between the two variables. Functions of form f(x)=kx, where k is the constant, are as they were functions that can speak to a direct variation. Typically since direct proportion is spoken to by the direct variation formula that's given by. Functions of the form, there may be a constant, are the as it were functions that can speak to a direct variety. Typically since coordinate proportion is spoken to by the coordinate variation formula that's given by y=kx.
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