Answer:
3,136cm^2
Step-by-step explanation:
A square has 4 sides that are all equal to each other. This means the perimeter can be divided by the number of sides to find the measurement of each side.
224cm ÷ 4 = 56cm
Each side is 56cm
To find the area, we must multiply base and height. Since it is a square, it will be 56cm × 56cm.
56cm × 56cm = 3,136cm^2
Answer:
3136cm²
Explanation:
to find the area of the square, we first need to find the length of one of its sides. the perimeter is the total length of all 4 sides, so we can divide it by 4 to find the length of each side.
224 ÷ 4 = 56
now, we can square this to find the area of the square:
56² = 56 × 56 = 3136
thus, the area of the square is 3136cm².
i hope this helps! :D
find the foci of the ellipse whose major axis has endpoints $(0,0)$ and $(13,0)$ and whose minor axis has length 12.
The foci of the ellipse are (4,0) (9,0)
In order to present geometric forms in a two-dimensional plane and learn about their properties, coordinate geometry is a crucial area of mathematics.
The center of that ellipse is the midpoint of the major axis,
half way between (0,0) and (13,0) on line y=0.
The coordinates of that midpoint are the averages of the coordinates of the vertices.
The midpoint is (6.5,0) , and that is the center of the ellipse.
The distance from the center to each vertex is called the semi-major axis and represented as a .
In this case a=6.5 .
Half of the minor axis is called the semi-minor axis and is represented with b .
That is the distance from the center to each co-vertex.
In this case b= 12/2=6 .
The distance from the center to each focus is represented with c ,
and is related to a and b by a²=b²+c²
In this case 6.5²=6²+c²
Solving for c :
6.5²-6²=c²
A calculator can do that
6.5 -6
0.5*12.5=c²
c=√6.25
c=2.5 .
That is the distance from center (6.5,0) to each focus.
The foci are on the same line as the vertices, line y=0,
on either side of the center,
so the x-coordinate of one focus is 6.5-2.5=4 ,
and the x-coordinate of the other focus is 6.5+2.5=9 .
So, The foci of the ellipse are (4,0) (9,0
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The coordinates of that midpoint are the averages of the coordinates of the vertices.
The midpoint is (6.5,0) , and that is the center of the ellipse.
In this case a=6.5 .
Half of the minor axis is called the semi-minor axis and is represented with b .
That is the distance from the center to each co-vertex.
In this case b= 12/2=6 .
and is related to a and b by a²=b²+c²
In this case 6.5²=6²+c²
6.5²-6²=c²
A calculator can do that
6.5 -6
c=2.5 .
That is the distance from center (6.5,0) to each focus.
The foci are on the same line as the vertices, line y=0,
on either side of the center,
so the x-coordinate of one focus is 6.5-2.5=4 ,
and the x-coordinate of the other focus is 6.5+2.5=9 .
So, The foci of the ellipse are (4,0) (9,0)
The cafeteria at Midtown Middle School surveyed 575 students about their favorite food. Find the number of students that responded for each of the following.
salad = 20%
Which answer is correct?
20
11.5
460
115
Answer:
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
Which is not a test for similarity 1 SSS 2 SAS 3 AAA 4 Asa?
The correct option is option (4) ASA is not a test for similarity
Triangles' similarities can be described based on their features. If two triangles have corresponding sides and have the same ratio and their corresponding angles are equal, then two triangles are said to be similar. The following are the criteria that are used to determine the similarity between two triangles:
1. AAA (Angle-Angle-Angle)
2. SSS (Side-Side-Side)
3. SAS (Side-Angle-Side)
The criteria ASA does not prove the similarity between two triangles as this property does not guarantee that the rest of the sides of one triangle will be similar to those of the other triangle. Thus, ASA criteria are not used to check the similarity between two triangles.
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How is i 4 equal to 1?
The given expression is a complex expression and we can prove the given expression equal to 1 by using definition.
What is i in complex number?a+ib, often known as the generic form of complex numbers, is how complex numbers are expressed. In the complex numbers a+ib form, a represents the real component of the number, b represents the imaginary part, and i is defined as√(-1). Complex numbers can take a variety of shapes.
Write the general form of complex number.z=a+bi is the general form of complex number
As by definition
i^2=-1
So
i^4=(i^2)^2
=(-1)^2
=1
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a sponsor will donate $0.15 for every meter merissa walks in a charity event. Merissa walks 5 kilometers in the charity event. How much does the sponsor donate to merissa's walk
The sponsor will donate 750 dollars.
1 kilo is 1000 meters
5 kilos is 1 kilo x 5
1000 meters x 5 is 5000 meters
0.15 x 5000 = 750
Answer:
12345678900987654321
What is the difference between continuous function and discontinuous function?
A continuous function is a function that is defined for all values of the independent variable, and its graph has no breaks or jumps. A discontinuous function is a function that is not continuous, meaning there are values of the independent variable at which the function is undefined or has a break or jump in its graph.
A continuous function is a function that can be graphed without any breaks or jumps. This means that the graph of a continuous function is a single, unbroken curve that passes through all its points. Furthermore, a continuous function is defined for all values of the independent variable. This means that the function is defined for all points in its domain. On the other hand, a discontinuous function is a function that is not continuous, meaning there are values of the independent variable at which the function is undefined or has a break or jump in its graph. This means that the graph of a discontinuous function will have jumps or breaks. Furthermore, a discontinuous function is not defined for all values of the independent variable, meaning that there are certain points in the domain for which it is not defined. In conclusion, the main difference between continuous and discontinuous functions is that a continuous function is defined for all values of the independent variable and has no jumps or breaks in its graph, whereas a discontinuous function is not defined for all values of the independent variable and has jumps or breaks in its graph.
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Why does the midpoint partition a segment into a 1 1 ratio?
Help me please with this
The domain and the range of this function shown in the graph include the following;
Domain = -5 ≤ x < 1.Range = -4 ≤ y < 7.How to identify the domain and range of this graph?In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Note: Each interval on this graph represent 1 unit and the less than or equal to (≤) would be used because the dotted point is shaded (closed).
By critically observing the graph shown above, we can reasonably and logically deduce the following:
Domain = -5 ≤ x < 1 or [-5, 1].
Range = -4 ≤ y < 7 or [-4, 7].
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What are the vertical asymptotes of f/x 10 /( x 2 1?
Taking the function given in the question [tex]f(x) = \frac{10}{x^{2} +1}[/tex] , there are no vertical asymptotes since there no any real values for x , which makes the function undefined.
What is vertical asympotote?A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.
How to calculate vertical asymptote of a function?To calculate the vetical asymptotes of a function simply equate the denominator of the equation to zero , which when solved gives the values of x at which the function is undefined. Thus the obtained values of x are the vertical asymptotes to the given function.
In the given function f(x), let's equate the denominator to zero to find the vertical asymptotes,
[tex]x^{2} +1 =0[/tex]
Solving the above equation, we get
x = [tex]\sqrt{-1}[/tex]
which is imaginary, hence there is no vertical asymptote for the given function.
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What is the slope of 3 and 8?
The Slope of the line passing through the points (0,3) and (5,8) is 1 .
The Line is passing through the points (0,3) and (5,8) .
we know that the formula to calculate the slope of the line passing through the points(x1,y1) and (x2,y2) is denoted by ;
Slope(m) = ;
It is given that points through which line is passing is (0,3) and (5,8) .
substituting the values in the above formula ,
we get ;
Slope(m) = (8 - 3)/(5 - 0)
On simplifying further ,
we get ;
slope(m) = 5/5 = 1 .
Therefore , the slope of line is = "1" .
The given question is incomplete , the complete question is
What is the slope of the line passing through the points (0,3) and (5,8) ?
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How do you read a 4 quadrant graph?
Four areas known as quadrants are created by the coordinate axes.
What is the name of a graph with four quadrants?The four quadrants of the coordinate plane can be discussed in depth and for a very long time. Encourage your students to think of further applications for it, such as in an animation or video game.As an alternative, you may show your students a variety of graphs that you've taken from readings and other assignments and invite them to talk about what they see and wonder about. A visual approach of displaying connections between numbers is coordinate graphing.On a coordinate plane, the relationships are shown. Two perpendicular axes, or lines, that are labelled similarly to number lines make up a coordinate plane. Each axis may be extended in two directions if the number system is expanded to include negative numbers. Typically, the x-axis is used to refer to the horizontal axis. Typically, the vertical axis.To learn more about quadrant graph refers to:
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Ramon's dad is an architect. He is designing a new house for his family. Yesterday, he brought home a model of a house that they will build. In the model ½ inch represents 2 feet and Ramons room measures 2.5 inches by 4 inches. Ramon wants to purchase a rug that will take up 169 square feet of space. Provide mathematical reasoning explaining why Ramon should or should not purchase the rug. (Hint: Draw the room)
Ramon should buy the rug of 169 square feet area because the room area is 160 square feet.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in the model ½ inch represents 2 feet and Ramons room measures 2.5 inches by 4 inches. Ramon wants to purchase a rug that will take up 169 square feet of space.
1/2 inch = 2 feet
1 inch = 4 feet
2.5 inch = 10 feet
4 inch = 16 feet
Area of room = L x W
Area of room = 10 x 16
Area of room = 160 square feet
The area of the rug is 169 square feet and the area of the room is 160 square feet which will cover the whole area.
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See the similar shape below and find the length of /YZ/
Answer:
YZ = 20 cm
Step-by-step explanation:
Δ XYZ and Δ CBA are similar ( AA postulate )
The corresponding sides are then in proportion , that is
[tex]\frac{YZ}{BA}[/tex] = [tex]\frac{XY}{CB}[/tex] ( substitute values )
[tex]\frac{YZ}{8}[/tex] = [tex]\frac{25}{10}[/tex] = 2.5 ( multiply both sides by 8 )
YZ = 8 × 2.5 = 20 cm
9 apples and 6 oranges cost $33. 18 apples and 20 oranges cost $80. how much does one apple and one orange cost?
Answer:
Apple: $2.50
Orange: $1.75
Step-by-step explanation:
Let A represent apples and Y represent Orange
We have equations
9A + 6Y = $33
18A + 20 Y = $80
Let's find out the cost of oranges first. Multiply the first equation by -2
-18A - 12Y = $-66
18A + 20 Y = $80
8Y = $14
Y = $1.75
Now let's put 1.75 back in the Y to find the cost of apple
18A + 20(1.75) = $80
18A + 35 = $80
18A = $45
A = $2.50
Answer:2 50
Step-by-step explanation:
Is f x )= π a polynomial function?
Yes, f(x) = π is a Polynomial function with the highest power = 0.
Let's First understand what is a polynomial function.
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Given function f(x) = π is also a polynomial function.
Given function is known as constant polynomial function.
A function of the form f(x) = c, where c is a real number with a degree of zero at its highest, is known as a constant polynomial. Simply described, a constant polynomial is an algebraic polynomial whose output value does not change regardless of changes made to the input values.
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How do you calculate decay from half-life?
Using the formula T1/2 = 0.693/λ, we may determine decay from half-life.
What is half-life?The half-life is the amount of time needed for half of the initial population of radioactive atoms to decay.
T1/2 = 0.693/λ describes the relationship between the half-life, T1/2, and the decay constant.
A percentage is used to represent the degradation rate.
Simply decreasing the percent and dividing it by 100 yields the decimal equivalent.
The decay factor b = 1-r can therefore be calculated.
For instance, the exponential function's decay rate is 0.25, and the decay factor b = 1- 0.25 = 0.75 if the rate of decay is 25%.
Nearly all decay processes that are exponential, or nearly exponential, are referred to by the phrase "half-life".
Therefore, using the formula T1/2 = 0.693/λ, we may determine decay from half-life.
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How do you prove that two right triangles are similar?
We can prove that two right triangles are similar by:
Hypotenuse-Leg (HL) Theorem.
Leg-Acute (LA) Angle Theorem.
Hypotenuse-Acute (HA) Angle Theorem.
Leg-Leg (LL) Theorem.
Two triangles are congruent if they have the same three sides and exactly the same three angles. Two right triangles can be considered to be congruent, if they satisfy one of the following theorems.
Theorem 1 : Hypotenuse-Leg (HL) Theorem :
If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.
Theorem 2 : Leg-Acute (LA) Angle Theorem :
If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.
Theorem 3 : Hypotenuse-Acute (HA) Angle Theorem :
If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.
Theorem 4 : Leg-Leg (LL) Theorem :
If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent.
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A model airplane in Yesinia's collection is at a 1:40 scale to the actual plane. If the model is 7.5 inches long, what are the dimensions of the actual airplane in feet?
The dimension of actual plane is 300 inches.
What are ratios?
A ratio is the comparison of quantities which have same parameters or units of measurement.
Why are calculation of ratios significant?
It helps to identify how big or small a quantity is as compared to other thing having same parameter of measurement.
NOTE: Things which have different measurement cannot be compared by ratio;
Example: 1 litre of milk cannot be in ratio with 1 kg of sand, as milk is measured in volume and sand is in weight.
Solution:
Given, ratio of model of plane and actual plane = 1 : 40
x = 7.5 inches
Let, x be the dimension of model of the airplane
y be the dimension of actual airplane
Using the formula by equating the ratios,
1/40 = x/y
⇒ 1 x y = 40x
⇒ y = 40 x 7.5
⇒ y = 300 inches
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What are the possible rational roots of x³ X² 10x 8 0?
The Possible rational roots of the equation "x³- x² - 10x - 8 = 0" are x = -1 , x = -2 and x = 4 .
The Rational roots of the equation are defined as the values of the variable such that value of the entire equation becomes 0 .
the function is f(x) = x³- x² - 10x - 8 ,
By the Rational Roots Theorem , we know that is p/q is the root of the equation , then p is a factor of 8 and q is a factor of 1 .
the possible values of p are ±1 , ±2 , ±4 , ±8 , and
the possible values of q are ±1 .
So , the possible rational roots (p/q) are ±1 , ±2 , ±4 , ±8 .
So , on substituting the all the possible values of the rational roots ,
we get ;
f(1) = (1)³- (1)² - 10(1) - 8 = -18
f(-1) = (-1)³- (-1)² - 10(-1) - 8 = 0
f(2) = (2)³- (2)² - 10(2) - 8 = -24
f(-2) = (-2)³- (-2)² - 10(-2) - 8 = 0
f(4) = (4)³- (4)² - 10(4) - 8 = 0
f(-4) = (-4)³- (-4)² - 10(-4) - 8 = -48
f(8) = (8)³- (8)² - 10(8) - 8 = 360
f(-8) = (-8)³- (-8)² - 10(-8) - 8 = -446.
we get , the value as 0 at x = -1 , -2 and 4 .
Therefore , the possible rational roots are x = -1 , x = -2 and x = 4 .
The given question is incomplete , the complete question is
What are the possible rational roots of x³- x² - 10x - 8 = 0 ?
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How many terms are there in the expression 5xy² 3xyz?
The number of terms in the expression 5xy² 3xyz is 1.
What are terms in equations?Various parts of an algebraic expression , which are separated by + or – are called terms of the algebraic expression.
Calculation:
The given expression 5xy²3xyz.
Step 1: Write down the given expression
The given expression is 5xy²3xyz.
Step 2: Find number of terms in the expression
We know that Various parts of an algebric expression , which are separated by + or – are called terms of the algebric expression.
In the expressions the term is 5xy²3xyz.
Hence number of terms in the expression 5xy²3xyz is 1.
The number of terms in the expression 5xy² 3xyz is 1.
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according to us postal regulations, the perimeter of the smallest end plus the length of a parcel sent by mail may not exceed 108 inches. what is the largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail? what are the dimensions of the parcel of largest volume?
The largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail according to USPS regulation is 11664 cubic inches.
The volume of a rectangular parcel with dimensions l, w, and h is lwh. We can express the volume of the rectangular parcel in terms of one variable, say l, as lwh = l(108 - 2l)h. We want to maximize this expression subject to the constraint that l is a positive number less than 54 (the maximum value for l that still allows the parcel to fit within the 108-inch limit).
Taking the derivative of the volume with respect to l and setting it equal to zero, we find that the maximum volume occurs when:
l = (27 inches)
At this value, the dimensions of the parcel are:
l = 27 inches
w = 27 inches
h = 2(108 - 2l) = 2(72) = 144 inches
The volume of the parcel is then:
lwh = (27)(27)(144) = 11664 cubic inches
This is the largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail according to USPS regulations.
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P(x)= 1/2x^2+3x-4x^3+6x^4-1 is it polynomial? If so write in standard form, and what degree, type and leading coefficient is it?
Standard form: [tex]6x^{4}-4x^{3}+\frac{1}{2} x^{2}-1[/tex]
Degree: 4
Leading coefficient: 6
What is a standard form of polynomial?A polynomial is written in the standard form when the term with the largest power of the variables comes first, followed by the subsequent terms in decreasing order of the variable power.
Detailed Explanation:Looking at the equation the highest power of the polynomial is 4;
The leading coefficient is nothing but the coefficient of the term which is having the highest power i.e.., 6;
Now arranging terms in the descending order(according to power of term) we get [tex]6x^{4}-4x^{3}+\frac{1}{2} x^{2}-1[/tex]
Standard form: [tex]6x^{4}-4x^{3}+\frac{1}{2} x^{2}-1[/tex]
Degree: 4
Leading coefficient: 6
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Determine whether the lines are parallel, perpendicular, or neither
X+7y = -3 and y= 7x + 25
Answer:
perpendicular
Step-by-step explanation:
7y = -x - 3
y = -1/7 x - 3/7
-1/7 is the reciprocal of the opposite, so the lines are perpendicular
For each graph, select all symmetries that apply. (a) (b) (C) y 6- y 4 4. 4-1 2 2- X x 76 TC -4 6 -6 -4 -2. -2 -2- -2- -4- -4- -4 -6 -6- -67 Symmetry: Symmetry: Symmetry: X-axis X-axis Ox-axis y-axis | y-axis y-axis origin origin origin none of these none of these none of these Х s ?
The symmetries of the graphs are mentioned below -
About the origin.About the {y} - axis.About the {x} - axis}What is the axis of symmetry?The axis of symmetry is a straight line that makes the shape of the object symmetrical. The axis of symmetry creates the exact reflections on each of its sides.Given are the graphs as shown in the image.
For each graph we can discuss the symmetry below -
Graph {A} -
A graph is said to be symmetric about the origin if whenever (a, b) is on the graph then so is (- a, - b) on the graph. So, the graph {A} is symmetric about the origin.Graph {B} -
The graph {B} is symmetrical about the {y} - axis.Graph {C} -
The graph {C} is symmetrical about the {x} - axis.Therefore, the symmetries of the graphs are mentioned below -
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Mateo has a piece of fabric that is 2 1/4 yards long. He cuts it into pieces that are each 3/8 yard long. How many pieces of fabric does Mateo cut?
Answer:6
Step-by-step explanation: 2 1/4 is a mixed fraction and needs to be changed into an improper fraction:
The whole number 2 is multiplied by the denominator 4 which gives 8 and we add 1 from the numerator this gives 9 and we put this over the denominator 9/4
9/4÷3/8=
The first fraction stays the same and we flip over the second fraction and use the multiplication sign in between
9/4 x 8/3=72/12=6
The tops of the fractions are multiplied together to give 72
The bottoms of the fractions are multiplied together to give 12
How do you find the base of an isosceles triangle with legs?
We can find the base of the isosceles triangle with legs using the formula:
2 × sqrt ((hypotenuse) ^ 2 - (altitude)^2) = base
Let us assume that the leg of the isosceles triangle is 'h' and one side is 'a'. Let the base be 'x'.
As there is a leg (altitude) in the isosceles triangle, then it forms a right triangle in the isosceles triangle, such that the sides form the hypotenuse.
Therefore, by using the Pythagoras' theorem,
hypotenuse ^ 2 = (altitude)^2 + (base / 2)^2
Hence, we get the base by deriving this expression from the above formula:
2 × sqrt ((hypotenuse) ^ 2 - (altitude)^2) = base
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anja simplified the expression startfraction 10 x superscript negative 5 baseline over negative 5 x superscript 10 baseline endfraction to startfraction 15 over x superscript 15 baseline endfraction. what mistake did anja make?
The simplified form of the expression 10x⁻⁵/-5x¹⁰ is -2/x¹⁵. So Anja wrote the numerator as 15 instead of -2.
What is Exponentiation?Exponentiation is the method of writing large numbers as the number in terms of power.
Exponent indicates how much time a number is multiplied to itself.
aᵇ read as a raise to b, implies that a is multiplies to itself b times.
We have to simplify the expression 10x⁻⁵/-5x¹⁰.
[tex]\frac{10x^-5}{-5x^1^0}[/tex] = 10 × [tex]\frac{1}{-5}[/tex] × x⁻⁵ × x⁻¹⁰
= -2 x⁻¹⁵
= [tex]\frac{-2}{x^1^5}[/tex]
Hence Anja simplified the expression as [tex]\frac{15}{x^1^5}[/tex] which is not true. The correct simplified form is [tex]\frac{-2}{x^1^5}[/tex].
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Answer:
its B
Step-by-step explanation:
i did the test
Sydney pays a flat rate of $20 plus a
rate of 7 cents per minute in her phone
plan. Which function shows the cost, "C",
of Sydney's plans as a function of time
in minutes?
Answer:
The answer is C(t)=0.07t+20
Step-by-step explanation:
20 is the starting value, or y-intercept in this case. The rate of change is 7 cents, or, 0.07. If we put this in y=mx+b format, it will come out as:
C(t)=0.07t+20
What is a hole of a function?
In the graph of a function there exist a point where function is not defined is known as a hole of a function.
Hole of a function is defined as:
A point where the function does not defined.In the rational function when the common factor of the numerator and denominator get cancel with each other .Common factor of numerator and denominator represents hole.In the graph of a function hole represents it approaches to the given point but in reality does not exist.Hole exist in the rational function when we input the value and it approaches to zero.Therefore, the hole of a function is a point where function does not defined only approaches.
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someone pls help me answer this question!!!! look through the directions and give a thorough explanation. thank you!
The sailboat and the medical aid should meet at the points
(0, 7) and (5, 12).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
The intersection point between the two graphs y = - x² + 6x + 7 and y = x + 7 is the point where they meet each other.
Now, For the equation y = - x² + 6x + 7,
When x = 0, y = 7 ⇒ (0, 7).
when x = 1, y = 12 ⇒ (1, 12).
Now for y = x + 7,
when x = 1, y = 8 ⇒ (1, 8).
when x = 2, y =9 ⇒ (2, 9).
Now by taking the graph paper with each box of 1 square unit will plot these points and we obtain that at (0, 7) and (5, 12) these graphs intersect each other.
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