Domain of the function is all real numbers
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider a function f(x)= x² + 2x - 3
Now let us find the value of f(x-3)
Plug in the value x as x-3
f(x-3)= (x-3)² + 2(x-3) - 3
= x² +9-6x+ 2x-6 - 3
= x² -4x
The domain of this function is all real numbers. This means that any real value can be plugged into the function and produce a real output.
Hence, domain of this function is all real numbers
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A rectangular park is 8 miles long and 6 miles wide. A jogging path divides the park diagonally in half. Find the length of the jogging path.
A. 2 mi.
B. 5 mi.
C. 10 mi.
D. 13 mi.
Answer:
Option D) 10mi
Step-by-step explanation:
A rectangle has 90 degree angles. When a line cuts it diagonally, it makes a right angle.
When there is a right angle we think about the Pythagorean theorem.
a²± b² = c²
Plug the values:
8²+6²= c²
Simplify:
64+36 = c²
Combine like terms:
100 = c²
Rooting hypotenuse we get
10 = c
The length of the path is 10 miles.
The one number is 8 less than 2 times another number. Their sums are 10
Answer:
The "one number" is equal to 4 and "another number" is equal to 6.
Step-by-step explanation:
1. We can write an equation for "one number": X = 2n - 8 (X is one number and another number is N)
2. Since their sums are 10 we can write it was X + N
3. Plug in the value of X to get: 2n - 8 + N = 10
4. Put 8 to the other side to get + 8 --> 2n + N = 10 + 8
5. Now you form the equation 3n = 18
6. N = 18 / 3 which is 6
7. To get X you do 10 - 6 which is equal to 4
8. To make sure the answer is correct plug in the values into the equation: 4 = 2(6) - 8 which simplifies to 4 = 12 - 8
Therefore, one number is equal to 4 and another number is equal to 6
In the latest published financial statements, an amount of $42,000 appears against accounts payable. During the year, goods worth $150,000 were purchased on credit.
Assuming 365 days in a year, what is the approximate accounts payable payment period (in days)?
Answer:in the latest published financial statements,an amount of $42000 appears against accounts payable.During the year,goods worthy $150000 were purchased on credit .assuming 365 days in a year ,what is the approximate accounts payable payment period.
Step-by-step explanation:
For a project in her Geometry class, Morgan uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.85 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. She then walks 4.25 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Let's call the height of the goalpost "h". We can use similar triangles to solve for h. Morgan walks a total of 13.85 and placed the mirror and walk 4.25 more, let d = 13.85.
The mirror forms a right triangle with the height of the goalpost, the distance from her eyes to the ground, and the distance d.
So, we have:
h / d = 1.15 / 4.25
Solving for h:
h = (1.15 ×13.85 ) / 4.25
h = 6371 / 1700
Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.
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The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $2 per pound to get 600 pounds of the new blend. The selling price of the new blend is to be $3.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?
225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are required to get 600 pounds of a new blend costing $3.50
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Let x represent the amount of Earl Grey tea and y represent the amount of Orange Pekoe tea.
Earl Grey tea sells for $6 per pound while Orange Pekoe tea sells for $2 per pound. Both teas were mixed to get 600 pounds of a new blend selling at $3.50. Hence:
x + y = 600 (1)
Also:
6x + 2y = 3.5(600) (2)
From both equations:
x = 225, y = 375
225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are required
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Which equation represents the graph?
a graph of a line that passes through the points 0 comma negative 3 and 5 comma negative 1
y equals negative two fifths times x plus 8
y equals negative five halves times x plus 8
y equals negative five halves times x minus 3
y equals two fifths times x minus 3
The equation that represents the given graph is: D. y = 2/5x - 3.
How to Write the Equation of a Linear Graph?The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
here, we have,
To find the equation of a line that passes through two points (x1, y1) and (x2, y2), we can use the following steps:
Find the slope (m) using the formula
m = (y2 - y1) / (x2 - x1).
Plug in the slope and one of the points into the equation
y = mx + b to find b.
So, for the line that passes through the points (0, -3) and (5, -1),
the slope is (-1 - (-3)) / (5 - 0)
= 2/5,
and the y-intercept can be found by plugging in the slope and the point (0, -3) into the equation y = mx + b:
-3 = (2/5) * 0 + b
-3 = b
Therefore, the equation of the line that passes through (0, -3) and (5, -1) is: y = (2/5)x - 3
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Can you help me? I need to do this IXL ASAP
Answer:
u=20
Step-by-step explanation:
solving joint variation
Th equaton of d in terms of W and L is d = W/LK
How to determine the joint variationFrom the information given, we have that;
The weight of the metal varies jointly as its LengthIt also varies jointly as the square of its diameterGiven that the parameters are;
Weight of the metal in kilogram is WThe length of the metal in meters is LThe diameter of the metal in mm is dThis is represented as;
W ∝ Ld
Find the constant value
W/Ld = K
Substitute the values
K = 140/4×54
find the value
k = 35/54
To determine , d, we have;
d = W/LK
Hence, the expression is d = W/LK
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How much money is 1 quarter, 6 dimes, and 7 Pennies?
Answer: $0.92
Step-by-step explanation:
Answer:
92 cents = $0.92 = 0.92 dollars
Step-by-step explanation:
1 quarter = 25 cents
1 dime = 10 cents
6 dimes = 6 × 10 cents = 60 cents
1 penny = 1 cent
7 pennies = 7 cents
1 quarter + 6 dimes + 7 pennies =
= 25 cents + 60 cents + 7 cents
= 92 cents = $0.92 = 0.92 dollars
The number of people who were expected to go for the first show of a movie was 600. But due to rain the number of people who had been to the movie was 540. What is the percentage decrease in the number of people?
Answer:
10%
Step-by-step explanation:
540/600 = 90%
so 10% decrease
Please help me figure this out
Answer:
A ≈ 5568.2 cm²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
here the diameter = 84.2 , then r = 84.2 ÷ 2 = 42.1 , then
A = π × 42.1² = π × 1772.41 ≈ 5568.2 cm² ( to 1 decimal place )
Name
Multiply Mixed Numbers
1 Health and Fitness Trail running is an exercise that
involves running on trails instead of paved roads to
reduce the impact on ankles and knees. Samantha runs
on the Lakeside Trail. She runs 2½ times around the loop
and then walks the remainder of the way. How far does
Samantha run? Write an equation to model the distance
Samantha runs.
The equation formed will be a linear equation, and it will be y=5t/2.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Given Samantha runs on the Lakeside Trail. She runs 2½ times around the loop and then walks the remainder of the way.
Let t=length of loop
then, total running distance(y)=5t/2
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BRAINLIST FOR THE RIGHT ANSWER PLEASE ANSWER THE RIGHT ANSWER also let me know how you got the answer please because I have more questions
Answer:
C
Step-by-step explanation:
when multiplying 2 matrices:
a11 a12 a13 ... a1n
a21 a22 a23 ... a2n
...
am1 am2 am3 ... amn
X
b11 b12 b13 ... b1m
b21 b22 b23 ... b2m
...
bn1 bn2 bn3 ... bnm
you have to consider that this is only possible, when A has m rows and n columns, and B has n rows and m columns.
because the rows of A are multiplied by the columns of B.
the resulting matrix C is a square matrix and looks like
c11 c12 c13 ... c1m
c21 c22 c23 ... c2m
...
cm1 cm2 cm3 ... cmm
the different terms are created
cxy = ax1×b1y + ax2×b2y + ax3×b3y ... + axn×bny
so, in our case, we have m=n=2.
therefore, we get also C as 2×2 matrix :
2×3 + 8×2 2×0 + 8×-1
0.6×3 + 3×2 0.6×0 + 3×-1
=
6 + 16 -8
1.8 + 6 -3
=
22 -8
7.8 -3
FYI
as rule of thumb always remember :
first line first column
first line second column
...
first line last column
...
second line first column
second line second column
...
second line last column
...
last line first column
last line second column
...
last line last column
Swimming Pool On a certain hot summer's day, 364 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $707.50. How many children and how many adults swam at the public pool that day?
1. There were _ children at the public pool.
2. There were _ adults at the public pool.
Step-by-step explanation:
x = number of children
y = number of adults
x + y = 364
x = 364 - y
1.75x + 2.25y = 707.5
using the first equation in the second :
1.75(364 - y) + 2.25y = 707.5
637 - 1.75y + 2.25y = 707.5
637 + 0.5y = 707.5
0.5y = 70.5
y = 70.5/0.5 = 141
x = 364 - y = 364 - 141 = 223
there were 223 children at the public pool.
there were 141 adults at the public pool.
a 1.1 kg weight starts at a height of 1.22 m. How fast will the pendulum swing at the bottom of its swing ?
The pendulum will swing at the velocity of 3.06 m/s at the bottom of the swing.
What is velocity?Velocity is the rate of change of position of an object, usually measured in meters per second (m/s). It is a vector quantity, which means it has both magnitude and direction. Velocity is an essential notion in physics since it is used to describe motion and is one of the fundamental principles of classical mechanics. It is connected to other notions such as acceleration, momentum, and force. Velocity is a measure of how rapidly an item moves in a specific direction, and it is computed by dividing the distance travelled by the time it takes for the object to traverse that distance.
The speed of the pendulum at the bottom of its swing can be calculated using the formula:
v = √(2gh)
where v = velocity, g = gravitational acceleration (9.8m/s2), h = height (1.22m)
Therefore, the speed of the pendulum at the bottom of its swing is:
v = √(2*9.8*1.22)
v = 3.06 m/s
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The table shows how far four students walked in 5 minutes. How far did they walk?
32/12 is the distance walked by the four friends.
What is Fraction?A fraction represents a part of a whole.
3/4, 1/2,2/3,3/4 is the distance travelled by the four students.
We have to find the distance they walked all together.
We have to add the all the fractions.
3/4+1/2+2/3+3/4
The LCM of 4, 2 3, and 4 is 12
9+6+8+9/12
32/12
Hence, 32/12 is the distance walked by the four friends.
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THEORY
1 a. In a class of 58 students, 35 offer Biology, 28 offer Economics and 15 offer Physics. Each student offers at least one of the three subjects. If 12 students offer both Biology and Economics , 7 students offer both Biology and Physics and 5 students offer both Economics and Physics, how many students offer all three subjects?
b. A regular polygon with (2m+1) sides has each interior angle equal to 1440 . Find the value of m.
don't spam.
Answer:
a. In a class of 58 students, 35 students offer Biology, 28 students offer Economics and 15 students offer Physics.
Using the Principle of Inclusion-Exclusion, we can calculate the number of students who offer all three subjects as follows:
The total number of students who offer at least one subject is 35 + 28 + 15 = 78
The number of students who offer Biology and Economics is 12
The number of students who offer Biology and Physics is 7
The number of students who offer Economics and Physics is 5
So the number of students who offer all three subjects is given by:
35 + 28 + 15 - (12 + 7 + 5) = 58 - 24 = 34
Therefore, 34 students offer all three subjects.
b. A regular polygon with (2m + 1) sides has each interior angle equal to 1440.
Each interior angle of a regular polygon with n sides is given by:
angle = (n-2) * 180 / n
So for a regular polygon with (2m + 1) sides, we have:
1440 = (2m + 1 - 2) * 180 / (2m + 1)
Expanding and simplifying:
1440 = 360m / (2m + 1)
Multiplying both sides by (2m + 1):
1440 * (2m + 1) = 360m
Expanding the left side:
2880 + 1440 = 360m
4320 = 360m
Finally, dividing both sides by 360:
m = 12
Therefore, the value of m is 12.
This scatter diagram shows the marks scored in class tests for English and Science.
The solution is, a) Negative linear; b) about 48
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
a) Type of correlation
The graph shows a negative linear correlation.
b) Prediction
It looks like a student who makes 60 in Science would make about 48 in English.
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Express as a trinomial
(X+1)(2x-8)
The expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (X+1)(2x-8)
Apply distributive property
(X+1)(2x-8)
x(2x-8)+1(2x-8)
2x²-8x+2x-8
Trinomial is an expression which has three terms.
2x²-6x-8
Hence, the expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8
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What are two numbers that when multiplied equal 5/9 and when added together equal -2?
The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let the two numbers be 'x' and 'y'. Then the equations are given as,
xy = 5/9 ...1
x + y = - 2 ...2
From equations 1 and 2, then we have
x + 5 / (9x) = -2
9x² + 5 = - 18x
9x² + 18x + 5 = 0
9x² + 15x + 3x + 5 = 0
3x(3x + 5) + 1(3x + 5) = 0
(3x + 1)(3x + 5) = 0
x = -1/3, -5/3
At x = - 1/3, the value of y is given as,
- 1/3 + y = -2
y = - 5/3
At x = - 5/3, the value of y is given as,
- 5/3 + y = -2
y = - 1/3
The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.
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A survey was carried out to find the favorite beverage of a particular telemarketing company having 2,000 employees. To carry out this survey, two groups of 100 employees each were randomly selected and asked to vote for their favorite beverage. The results obtained are given in the table shown below.
Beverage Group A Group B
Coffee 42 44
Green Tea 9 11
Soft Drinks 28 22
Energy Drinks 21 23
Which of the following statements about the data above is true?
A.
The estimated number of employees who would have voted for coffee is higher when based on the results of Group A rather than Group B.
B.
The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.
C.
The estimated number of employees who would have voted for green tea is higher when based on the results of Group A rather than Group B.
D.
The estimates for both groups show an equal number of employees would have voted for coffee.
If a survey was carried out to find the favorite beverage of a particular telemarketing company having 2,000 employees. The statement that is true about the data: B. The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.
How to know the correct statement?The estimated number of employees who voted for coffee from Group A is 42 out of 100 (42%).
The estimated number of employees who voted for coffee from Group B is 44 out of 100 (44%).
The higher percentage of employees who voted for coffee in Group B (44%) suggests that a higher number of employees would have voted for coffee if the entire population of 2,000 employees had been surveyed.
Therefore the correct option is B.
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Answer:b
Step-by-step explanation:
5. Find (a) the discount and (b) the proceeds for the following simple discount note. Use 360 days for a
full year.
Face Value: $9700 Discount Rate: 9.5% Time (Days): 135
The discount is $278.59 and the proceeds for the following simple discount note, using 360 days for a year is $9421.41
What do you mean by discount?Discount refers to a reduction in the price of an item or service. It can be expressed as a percentage or an absolute value, and it is usually calculated as a difference between the original price and the reduced price. In finance, discount is often used to refer to the reduction in the face value of a financial instrument, such as a bond or a bill, before it matures. The amount of the discount is usually based on the interest rate and the time to maturity. The term "discount" is also used in various other contexts, such as in retail sales, where items are sold at a lower price than their regular price to encourage customers to buy.
(a) The discount is calculated by multiplying the face value of the note by the discount rate and then dividing by the number of days in a year (360).
Discount = $9700 * 9.5% * 135/360
Discount = $9700 * 0.095 * 3/10
Discount = $9700 * 0.285/10
Discount = $278.59
(b) The proceeds are calculated by subtracting the discount from the face value of the note.
Proceeds = Face Value - Discount
Proceeds = $9700 - $278.59
Proceeds = $9421.41
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Assume that a consumer has a given budget or income of $10 and that she can buy only two goods, apples or bananas. The price of an apple is $1.00 and the price of a banana is $0.50. This means that, in order to buy four bananas, this consumer must forgo
In order to buy four bananas, then the number of apples that he bought will be 8.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Assume that a consumer has a given budget or income of $10 and that she can buy only two goods, apples or bananas. The price of an apple is $1.00 and the price of a banana is $0.50.
Let 'x' be the number of apples and 'y' be the number of bananas. Then the equation is given as,
1x + 0.50y = 10
x + 0.50y = 10
In order to buy four bananas, then the number of apples that he bought is given as,
x + 0.50 (4) = 10
x + 2 = 10
x = 8
In order to buy four bananas, then the number of apples that he bought will be 8.
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How does rewriting radicals in different forms help you communicate your answer?
We can write radicals [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] forms to help us communicate our answers.
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Suppose, We have a radical [tex]16^{\frac{1}{4}[/tex].
Now, We know 2⁴ = 16.
So, We can rewrite [tex]16^{\frac{1}{4}[/tex] as [tex](2^4)^{\frac{1}{4}[/tex] and multiply the exponents which
results to 1.
Again say we have [tex]9^{\frac{3}{2}[/tex] and we know 3² = 9, Se we can rewrite [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] , and the exponent multiplies to 3 so it is now 3³ which is 27.
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Does anyone know how to do this
well, the line y = -5 is simply a horizontal line, a perpendicular line to that will simply be a vertical one, Check the picture below.
What is the perimeter of an isosceles right triangle with side lengths of 5?
A. 10
B. 15
C. 10+5√2
D. 10 √10
E. Unable to determine with this data
Martina and her roommate are renting furniture for their apartment. The delivery and set up charge is $75. There is a monthly rental fee of $90. Which expression can be used to calculate their total cost for m months?
expression : 75+90m
the 75 is the base payment, plus 90 per month, and the variable m symbolizes the amount of months.
Hope this helped =)
-YinAhara
in order to be approved for a home loan a lending institution uses the standard 28/36 ratio. Jared's loan application is for $180,000. Jared has an annual salary of $56,400, a car
mayment of $270 per month and he has a monthly student loan payment of $90. How likely is Jared to be approved for the home loan?
O Very likely, recurring debt is considerably less than what is allowed.
O Somewhat likely, recurring debt is very close to what is allowed.
O Not likely, recurring debt is higher than what is allowed.
O There is not enough information given to determine the answer.
The likelihood of getting the loan cannot be ascertained. Hence the answer is D. There is not enough information given to determine the answer.
What is the information aboutTo determine whether Jared is likely to be approved for the home loan, it would be necessary to calculate his debt-to-income ratio, which is one of the main factors that lenders consider when evaluating loan applications. This ratio is calculated by dividing a person's total recurring monthly debt payments by their gross monthly income. If the debt-to-income ratio is higher than 28% or 36% (depending on the lender), the loan application may be declined.
Based on the information provided, it is not possible to determine Jared's debt-to-income ratio. In order to determine the ratio, it would be necessary to know Jared's gross monthly income, which is not provided. Therefore, it is not possible to say whether Jared is very likely, somewhat likely, or not likely to be approved for the home loan.
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d) y=4+x
6) Find the constant of proportionality for the table below then write an equation
Hours (x)
2
4
6
Tickets Sold (y)
24
48
72
Answer: For each hour worked, the number of tickets sold increases by 12.
Step-by-step explanation:
The constant of proportionality for the table can be found by dividing the value of y by the value of x for one of the data points. For example, when x = 2, y = 24, so the constant of proportionality k can be found as follows:
k = y/x = 24/2 = 12
So, the equation relating the number of hours worked, x, to the number of tickets sold, y, can be written as y = kx, where k is the constant of proportionality, which we found to be 12.
Thus, the equation relating the number of hours worked, x, to the number of tickets sold, y, can be written as:
y = 12x
This equation states that for each hour worked, the number of tickets sold increases by 12.
Find the surface area of the prism I-Ready
The surface area of the prism is 166 square centimetres.
What is a surface area?A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.
Given that the sides of the prism are 5 cm, 4 cm, and 7 cm. The surface area of the prism will be calculated as:-
Surface area = 2 [ ( 5x 4 ) + ( 4 x 7 ) + ( 7 x 5 ) ]
Surface area = 2 [ 20 + 28 + 35 ]
Surface area = 2 x [ 83 ]
Surface area = 166 square cm
Therefore, the surface area of the prism is 166 square cm.
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