If there is a y-intercept, we can find it by plugging a zero for x and evaluating the function. If this produces an undefined value, then there is no y-intercept. To find the x-intercept, set y to zero and solve for x.
Now, According to the question:
Logarithmic functions will always have an x-intercept, but they may not have a y-intercept. Let's look at a simple example:
y = [tex]log_1_0x[/tex]
A y-intercept would be located at the y value we get by plugging in a zero for x. The problem is that the function does not have zero as a part of its domain. It is not defined there, so there is no y-intercept. The x-intercept is the x value that causes y to be zero. For a basic logarithmic function like this, that is always x equals 1.
0 = [tex]log_1_0x[/tex]
[tex]10^0[/tex] = x
1 = x
Now we can shift, stretch, and reflect this model to change these results, but the basic idea is still the same. For example, let's consider this model:
y = [tex]log_1_0[/tex] (x + 100) + 2
As always, we look for a y-intercept by plugging in a zero for x. In this case, we do get an answer. This is because of the 100 that is added to the argument of the logarithm.
y = [tex]log_1_0[/tex] (0 + 100) + 2
y = 2 + 2 = 4
As always, to find the x-intercept, we set y to zero and solve for x
y = [tex]log_1_0[/tex] (x + 100) + 2
-2 = [tex]log_1_0[/tex] (x + 100)
[tex]10^-^2[/tex] = x + 100 [By taking antilog on both sides ]
0.01 = x + 100
x = -99.99
So, no matter what the logarithmic function is, we can find the intercepts in this way. If there is a y-intercept, we can find it by plugging a zero for x and evaluating the function. If this produces an undefined value, then there is no y-intercept. To find the x-intercept, set y to zero and solve for x.
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What must be true about the triangle?
Answer:
All three angles must add up to 180 degrees
Step-by-step explanation:
When Deema begins her drive, she is 400 mi from home. She drives at an average rate of 50 mph until she gets home. Draw a graph to represent this situation?
The linear function to model the problem is written in slope-intercept form as y = -50x + 400
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b
m = slope of lineb = y-interceptIn the question given, we can model a linear function to represent this.
Let x represent the distance covered.
The function can be written as;
f(x) = -50x + 400
This function represents the distance left till she gets home
Plotting this on a graph, we would have a straight line intercpeting the x-axis at (8, 0) and the y- axis at (0, 400)
Kindly find attached graph below.
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Hazel and Tom travel the same 18 km route.
Hazel starts at 9. 00 am and walks at a constant speed of 4. 8 km/h
Tom starts at 9. 39 am and runs at a constant speed.
Tom overtakes Hazel at 10. 15 am
At what time does Tom finish the route?
Answer:
11:27 am.
Step-by-step explanation:
The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked
1.25 * 4.8
= 6 km.
So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes
= 0.6 hrs.
So, Tom's speed is 6/0.6 = 10 km/hr.
,
and Tom will take 18/10 = 1.8 hours to finish the route,
= 1 hr 48 minutes
So he finishes the route at
9:39 + 1:48
= 11:27 am.
Franklin Middle School's spring concert is next week. The music teacher chose students from the choir and the orchestra to perform solos. There are 25 choir students, and 5 of them have a solo. There are 20 orchestra students, and 4 of them have a solo. Do the two groups have the same ratio of students with a solo to total students?
For the choir, the ratio is 1/5 and for the orchestra, the ratio is also 1/5, then yes, the two groups have the same ratio
Do the two groups have the same ratio?
Here we just need to compute the two ratios, to do that, we need to take the quotient between the number of students with a solo and the total number of students.
For the choir, there are 25 students and 5 with a solo, so the ratio is:
5/25 = 1/5
For the orchestra, there are 20 students and 4 of them have a solo, so the ratio is:
4/20 = 1/5
So yes, both groups have the same ratio of students with a solo to total students.
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Work out the length of AB.
Give your answer to 3 significant figures.
A (-1, 6)
B (5, 3)
Answer:
AB = 6.71
Step-by-step explanation:
See the attached worksheet.
Find the lengths of the two sides of the right triangle:
CB = (5 - (-1)) = 6
CA = (6-3) = 3
Use the Phythagorean Theorem to find AB.
6^2 + 3^2 = AB^2
AB^2 = 45
AB = 6.71
a tile store charges $747.50 to install 115 square feet of tile. assuming they charge the same rate per square foot regardless of the amount of tile installed, how much would they charge to install 970 square feet of tile?
With the help of simple mathematical operations, we know that the cost of installing 970 ft² will be $6,305.
What are mathematical operations?A method of calculation: The most popular ones are (+, −, ×, ÷) for add, subtract, multiply, and divide.
However, there are many more, like square roots, logarithms, and squares.
It is most likely an operation if it isn't a number.
Example: The operation in 25 + 6 = 31 is added.
So, we know that:
The store charges $747.50 to install 115 ft² of tiles.
Then, the amount that will come to install 970 ft² tiles:?
Cost of installing 1 ft² of tiles:
747.50/115
$6.5
So, the cost of installing 1 ft² of tiles: is $6.5.
Now, the cost of installing 970 ft² tiles will be:
6.5 × 970
$6,305
Therefore, with the help of simple mathematical operations, we know that the cost of installing 970 ft² will be $6,305.
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What are the 4 types of transformations and how do we describe them?
Four types of transformations are as follow:
1. Rotation : It is based on about any point.
2. Reflection : It is based on over any line.
3. Translation : It is based on a given vector.
4. Dilation : It is based on size.
As given in the question,
Four types of transformations is given by :
1. Rotation : It represent the same image but the image is rotated about a fixed point by certain degree of its preimage.
2. Reflection: It is mirror image of the given image along the line after flipping.
3. Translation: Change in the position of the image without change in the given image.
4. Dilation: In this case size of the image get enlarged or shrink as per given condition.
Therefore, the four types of transformation is given by :
1. Rotation : It is based on about any point.
2. Reflection : It is based on over any line.
3. Translation : It is based on a given vector without change in the image.
4. Dilation : It is based on size.
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After researching many different shoes, chris narrows down his choice to these two. Which shoes are the best deal?.
Based on the information provided, it appears that the Air Slammers might be the best deal for Chris if his primary concern is getting the best price.
If Chris' primary concern is getting the best price, then the Air Slammers might be the best deal for him based on the information provided. It is important to note, however, that other factors might also be important in the decision-making process, such as the durability of the shoes and any preferences or personal preferences Chris might have.
It is also possible that the Hyper-Dunks might offer other benefits, such as better performance or more comfort, that could make them a more attractive option for Chris even if they are more expensive. Ultimately, the best deal depends on what is most important to Chris and how he weighs the different factors in the decision-making process.
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The sides of a triangle are given by
(3x2 − y2);(4x2−7xy+4y)and (−3x+7xy+8y2)
3x2 − y2;4x2−7xy+4yand (−3x+7xy+8y2)
.
Find its perimeter.
Answer:
Here is the answer
Step-by-step explanation:
To find the perimeter of a triangle, we need to add up the lengths of all three sides. In this case, the sides of the triangle are given by the expressions 3x2 - y2, 4x2 - 7xy + 4y, and -3x + 7xy + 8y2.
To find the perimeter, we can simply add up these three expressions:
Perimeter = 3x2 - y2 + 4x2 - 7xy + 4y - 3x + 7xy + 8y2
= 7x2 - 3xy + 12y
This is the perimeter of the triangle. Note that the perimeter is a scalar quantity, not a vector, so it does not have a direction associated with it.
New customers with Verizon pay a flat rate installation fee plus $45.00 per month for the
service. If after nine months, Mr. Burns paid $565, write and solve a linear equation to determine
how much he would pay after one year.
He would pay $160 after one year if the installation fee per month is $45.
What is meant by installation fee?The cost of installing something. charge - the cost of a good or service; "the admittance charge" Based on the Farlex clipart collection and WordNet 3.0. Installation can be divided into two major categories: physical and virtual. While a virtual installation relates to the installation of software, a physical installation concerns the installation of tangible items like computer hard drives, wires, modems, and so on.
Simple installation entails unpacking and plugging the appliance into the main electrical outlet. This excludes mounting on brackets, reinstalling in fixed units, or connecting to the gas or water.
Installment fee per month=$45
For 9 months,
9×45=405
Total fees=Installation+405
Installation+405=$565
Let the installation be x then,
x+405=565
x=565-405
x=$160
Therefore, he would pay $160 after one year if the installation fee per month is $45.
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Choose an equivalent system of equations to the following system: (1 point) fx + gy = h qx + ry = s.
5Fx+5Gy=5H Qx +Ry=S is a system of equations that is equivalent to the following system.
An equivalent system of equations is a system of equations that has the same solutions as the original system, but the coefficients of the variables may be different.
To determine which of the given systems is equivalent to the original system, you need to solve each system and see if they have the same solutions.
The original system is:
Fx + Gy = H
Qx + Ry = S
The solution to this system can be found by either graphing the equations or using substitution or elimination methods.
If we solve each of the other systems in the same way, we find that the system that is equivalent to the original system is:
C. 5Fx + 5Gy = 5H
Qx + Ry = S
This is because all of the other systems have different coefficients for the variables, and therefore will not have the same solutions as the original system.
The complete question is;-
Choose an equivalent system of equations to the following system:
Fx + Gy = H
Qx + Ry = S
A. 5Fx + 5Gy = 5H
Qx − Ry = S
B. 5Fx + Gy = 5H
Qx + 5Ry = S
C.5Fx + 5Gy = 5H
Qx + Ry = S
D. Fx + 5Gy = 5H
Qx + Ry = S
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what's a double integral that we can't do as an iterated integral? what's an iterated integral that isn't a double integral?
What is the factor of x² 11x 18?
On solving the provided question we can say that, - the factors of the given equations [tex]x^2 -11x +18[/tex] are - x= 2 and x = 9
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
[tex]x^2 -11x +18[/tex]
(x-2)(x-9)
x= 2 and x = 9
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What are the roots of x^3 −2=2x^2 −x?
Answer:
The roots of x^3 −2=2x^2 −x can be found by using the cubic formula to solve this polynomial equation. The roots are -2, 1, and 2/3.
Step-by-step explanation:
How can I grow my height?
It is estimated that around 80% of the final height is determined by hereditary factors. Several environmental factors, also including nutrition and exercise, frequently account for the remaining portion.
Explain the meaning of the term height?A variety of factors affect your overall height.
1. Consume a diet rich in fresh, fruits, and vegetables.
proteins from whole grains.
2. Use caution when using supplements:
Few situations call for the use of supplements to help children grow taller and elderly persons stop shrinking.
3. Get the appropriate amount of rest:
On occasion skipping sleep won't have a long-term impact on your height. However, issues could arise if you consistently clock less than the advised amount during adolescence.
4. Keep moving:
Regular exercise has a lot of advantages. It aids you in maintaining a healthy weight, strengthens the muscles and bones, and encourages the synthesis of HGH.
5. Take care of your posture:
You could appear shorter than they actually are if you have poor posture.
Additionally, slouching or slumping over time might change your actual height.
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What is the end behavior of function h
Answer:
Function to be graphed is,
h(x) = 2(x - 3)²
Function 'h' is a quadratic function.
Since, the coefficient of the leading term (term with the highest power) is positive, parabola will open upwards.
Both the ends of the parabola will be upwards (towards positive infinity).
As x approaches to negative infinity, h(x) approaches to positive infinity.
As x approaches to positive infinity, h(x) approaches to positive infinity.
Step-by-step explanation:
Please give the brainliest.
What property of congruence is illustrated in the statement if ∠A ≅ ∠B then ∠B ≅ ∠A?
The property of congruence illustrated in the statement is the transitive property.
The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.
In the statement "If AB ≅ DE, EF ≅ DE then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.
The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.
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The question is -
What property of congruence is illustrated in the statement? If AB ≅ DE, EF ≅ DE then AB ≅ EF.
a. Symmetric
c. Reflexive
b. Transitive
d. Multiplication
What is the equation of the line that passes through (2, -1) and is perpendicular to the line 1 whose equation is y=-1/2
x+4?
Answer:
Step-by-step explanation:
The point-slope form of the equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
So, the equation for this problem, let
[tex](x_1,y_1)=(2,-1)[/tex]
then,
[tex]y-(-1)=m(x-2)\\y+1=m(x-2)[/tex]
If line (a) is perpendicular to line (b), then [tex]m_b[/tex] is equal to [tex]-\frac{1}{m_a}[/tex]. For this problem, let
[tex]m_a=-\frac{1}{2}[/tex] and [tex]m_b=2[/tex]
So,
[tex]y+1=(2)(x-2)\\y+1=2x-4\\(y+1)-1=(2x-4)-1\\y=2x-5[/tex]
Work out the area of this shape.
3cm
4cm
7cm
6cm
Answer: the area of the shape=25.5 cm²
Step-by-step explanation:
This shape is composed of a rectangle and a trapezoid
The area of the rectangle= 3(4)
The area of the rectangle= 12 cm²
[tex]\displaystyle\\The\ area\ of\ the\ trapezoid=\frac{3+6}{2} (7-4)\\\\The\ area\ of\ the\ trapezoid=\frac{9}{2} (3)\\\\The\ area\ of\ the\ trapezoid=4.5(3)\\\\The\ area\ of\ the\ trapezoid=13.5 \ cm^2[/tex]
The area of the shape=12+13.5
The area of the shape=25.5 cm²
How can you use a square root to relate the side length and area?
Therefore , we can calculate the side of the length of the square by finding the square root of the given area.
The square root of an integer, which is the outcome of multiplication alone, gives the initial number. Squares and square roots are a few of examples of exponents. Think about the number 36. Furthermore, this can be written as 6x6.
Here,
The base length times the height of any quadrilateral yields the area of that shape.
Since the shape is square, we can be certain that all of its sides are equal in length.
Using this information, we can work backwards to determine the length of one side by taking the square root of the area.
For example : Square having area of 25
We can find its length by taking square root of 25
Which comes out to be √25 = 5
Thus , 5 is a length of the side of the square.
Therefore , we can calculate the side of the length of the square by finding the square root of the given area.
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The graph of which equation is parallel to the graph of 4x - 3 = 12?
The graph of the equation that is parallel to 4x – 3y = –12 is determined as: A. y = 4/3x - 3/2.
What is the Equation of Parallel Lines?If two lines are parallel to each other, their graph will have the same slope value, m. This means if their equations are expressed as y = mx + b in slope-intercept form, they will both have the same value of m.
Given the equation of a graph as 4x - 3y = -12, rewrite it in slope-intercept form to determine the slope value:
4x - 3y = -12
-3y = -4x - 12
-3y/-3 = -4x/-3 - 12/-3
y = 4/3x + 4
This means the slope, m is 4/3. The slope of the graph that is parallel to it will also have a slope of 4/3.
The slope of y = 4/3x - 3/2 is also 4/3, therefore, the answer is: A. y = 4/3x - 3/2.
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Complete Question:
The graph of which of the following will be parallel to the graph of 4x – 3y = –12?
A. y = 4/3x - 3/2
B. 6x - 4y = -8
C. y = 3/4x +1
D. 4x – 2y = –12
What is the x and y intercepts of -4x+5y=20 and is (5,8) a solution?
Answer: Yes, (5,8) is a solution.
x=-5, y=4
x-intercept (-5,0)
y-intercept (0,4)
Step-by-step explanation:
To find the x-intercept, make y equal to 0 and solve
-4x+5(0)=20
-4x=20
x=-5
To find the y-intercept, make x equal to 0 and solve
-4(0)+5y=20
5y=20
y=4
To see if 5,8 is a solution, sub in and solve
-4(5)+5(8)=20
-20+40=20
20=20
Yes, (5,8) is a solution.
What is a multiple of 32?
32, 64, 96,...... are the multiples of the 32.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given term is 32,
To find the multiple of 32,
Multiply 32 which natural numbers 1, 2, 3, 4, 5.....
32 x 1 = 32.
32 x 2 = 64
32 x 3 = 96
and so on...
Since, there are infinite multiples of 32.
So, 32, 64, 96,.... are the multiples of 32.
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What is discontinuity example?
Example of discontinuity in mathematical function is given by :
f(x) = ( x - 1 )/ ( x - 2) at x = 2.
Discontinuous function is defined as:
A function is said to be discontinuous if its left hand side limit is not equal to right hand side limit.It does not show the continuity of a function.Example of discontinuous function is given by :f(x) = ( x - 1 ) / ( x - 2 )
When x = 2 function does not defined .
Hence it is not continuous at x = 2.
Therefore, the example of the discontinuity in mathematics function is f(x) = ( x - 1 )/ ( x - 2) at x = 2.
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What is the graph of the equation x =- 4?
The graph of the equation x = -4 is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
By critically observing the graph (see attachment), we can reasonably infer and logically deduce that the x-intercept is equal to -4.
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Is 2x² 7x 0 is quadratic equation?
Yes, the given equation is a quadratic equation.
What is a quadratic equation?The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Given is an equation, 2x²-7x = 0
As we know that, a quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
On comparing equation 2x²−7x=0 with standard form of quadratic equation
ax ²+bx+c=0:
We get, a=2,b=−7,c=0
Hence, the equation 2x²−7x=0 is a quadratic equation.
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The graph of the equation y = x^2 − x − 6 is shown below
For what value or values of x is y=0?
x=−2 and x=3
x=2 and x=−3
x=−6 only
x=−2 only
For the equation y=0, there is much less math involved. This is because, no matter what, for any value of x, y must always be equal to zero.
What does y-intercept 0 mean?This is so because the y-intercept occurs at x = 0. X = 0, mx = 0, and Y = B at this point. When y = 0, we solve the equation for x to determine the x-intercept. The line crosses the x-axis at y=0,
Is the Y axis at Y = 0?You can mistakenly think of the line y = 0 as the y-axis, be aware of this. It's not right. Simply put, the line y=0 indicates that the y coordinate is always 0 for all locations (x, y) in the x-y plane, indicating that the line y=0 represents the x-axis.
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13a ^2+14-17a-12a ^2+12a+6a-a^ 2
(A) a-14
(B) a+14
(C) -9a^2+14
(D) -9a^2-5a-14.
Answer:
B
Step-by-step explanation:
13a ^2+14-17a-12a ^2+12a+6a-a^ 2
=14-17a+12a+6a
=14+a or a+14
13 more than four times a number is -93
Answer:
13
Step-by-step explanation:
(x+13) find its fourth root
which will be......
x⁴+28561=-93
x⁴=-28654
x=13.01
Hi can someone fully answer the question down below
Answer:
x= -10
Step-by-step explanation:
since its > not ≥, your only answer would be -10.
at the point -6, it would be =
when x= -10,
[tex]\frac{-10+3}{6}[/tex]>[tex]\frac{-10}{4}[/tex]+1
-7/6>-3/2
which is correct