Dinner would cost $123 at either restaurant if Betty's lobster weighed 36 pounds.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.In the context of this problem, the slope and the intercept are defined as follows:
Slope: cost of each pound of lobster.Intercept: cost of the meal.Hence the functions for each restaurant are given as follows:
y1(x) = 51 + 2x.y2(x) = 15 + 3x.The costs are the same when:
y1(x) = y2(x)
51 + 2x = 15 + 3x
x = 36.
The cost is of:
y = 15 + 3 x 36
y = $123.
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what is the value of the y-intercept of the graph of f(x)= 57(3.2)x
The y-intercept of the graph of a function is the point at which the graph intersects the y-axis. In other words, it's the value of the function when x=0.
So to find the y-intercept of f(x) = 57(3.2)x, we can substitute x=0 into the function:
f(0) = 57(3.2)(0)
f(0) = 0
So the y-intercept of this function is (0,0).
Solve for y
x-3/2y=-12
The equation x-3/ 2y=-12 when solved for the variable y is y = x-3/-24
How to solve for the variableWe have to make 'y' the subject from the equation, we have;
x-3/2y=-12
By solving for the variable, we need to work it out.
Also, we have to make it stand alone on one end of the equality sign.
cross multiply the values
x - 3(1) = -12(2y)
multiply the values
x-3 = -24y
Make 'y' the subject by dividing both sides by the coefficient of y
y = x-3/-24
Hence, the equation is y = x-3/-24
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solve the system of equations, with a complete solution
Answer: Solutions for x - 4,4,-5 and for y - 3,-3, 0
Step-by-step explanation: I wrote the solutions in order. To solve this question I combined both equations to eliminate the y variable to solve for x. It looked like this : [tex]x^2+x=20[/tex]. I brought the 20 to the other side and got [tex]x^2+x-20=0[/tex]. Then I factored and got [tex](x+5)(x-4)[/tex] which means x = -5 and x = 4. Finally I plugged in these values into the equation to find the possible y values.
1.) distinguish between the null hypothesis and the research hypothesis. when does the researcher decide to reject the null hypothesis?
A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.
The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.
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Grace was born on January 1, 2020. Thomas was born on December 31, 2018. How many days older is Thomas than Grace?
Answer:
I think it’s 730 days
Step-by-step explanation:
Step-by-step explanation: 2 years = 730 + the 10 months+ 740
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
None
SSS
AAS
ASA
SAS
With given features we can definably say that Both triangles are congruent under ASA Criteria.
What is a congruent triangle?A triangle is a closed polygon made up of three line segments that intersect at three different angles.
If the sides and angles of two triangles are the same length, the triangles are said to be congruent. As a result, two triangles can be superimposed side by side and angle by angle. Congruence is the term used to describe the relationship between an object and its mirror image. When two objects or shapes superimpose on one another, they are said to be congruent. They are identical in terms of shape and size. Line segments of the same length and angles of the same measure are congruent in the context of geometric figures.
Given far opposites angle are same = 25°
Given intersected line makes equal line
Intersecting angles are equal due to vertically opposite angle theorem.
Then we have,
Angle = Angle
Side = Side
Angle = Angle
With this features we can definably say that Both triangles are congruent under ASA Criteria.
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8. Gianna is making bows for her cheerleading squad. She has 4 yards of ribbon to make the
bows. If each bow requires 1/5 a yard of ribbon, will she have enough ribbon to make 18 bows?
Using the concept of proportion, Gianna will have enough yards to make 18 bows
Will she have enough ribbon to make 18 bowsTo solve this problem, we need to apply the concept of proportions.
In order to make 1 bow, she needs 1/5 yard of ribbon
Representing this in an equation form will be;
1 bow = 1/5 yard
18 bow = x yard
cross multiply both sides and solve for x
x * 1 = 18 * (1/5)
x = 3.6 yards
From the above, there will be enough yards to make 18 bows.
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What is the value of x?
first to answer brainliest
Answer:
99
Step-by-step explanation:
We can set up and solve this equation:
X + X - 50 = X + 49
X = 99
I don’t understand this can someone help
Answer:
f(-2) = 2
Step-by-step explanation:
Using the graph, we can determine the y value when x = -2.
When x = -2, the y value is 2.
f(-2) = 2
i need help with pleaseee
The points are plotted on the graph below.
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given a coordinate plane.
We have to plot the points given.
(0, 1/2) is a point on the Y axis, since the x coordinate is zero. y coordinate will be in the middle of 0 and 1.
(1, 1 1/2) is a point at a distance of 1 to the right from the origin and at a distance of 1 1/2 to the up from the origin.
(2, 2 1/2) is a point at a distance of 2 to the right from the origin and at a distance of 2 1/2 to the up from the origin.
These points are plotted in the graph below.
Hence the graph is shown below.
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Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn. Each station runs for an equal amount of time. If it takes 49 minutes for the first 7 stations to water, how long does it take to water all parts of her lawn?
The amount of time it require to water all the parts of her lawn is, 63 minutes
What is division?Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.
We denote division by '÷' this symbol.
Given that,
Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn.
Each station runs for an equal amount of time
it takes 49 minutes for the first 7 stations to water
The amount of time it require to water stations = ?
First, we need to calculate time required to water 1 station,
t = Total time taken / Total station watered
= 49 / 7
= 7 minutes/station
So
Time for water all parts = 7 x 9
= 63 minutes
Hence, the required time is 63 minutes
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What value of n makes the equation true? 7^7 multiplied by 7^5 equals (7^n)^4 over 7^4
From power rules, the value of n is 4.
Power Rules
The main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents. Division with the same base: you should repeat the base and subtract the exponents. Power. For this rule, you should repeat the base and multiply the exponents. Exponent negative - For this rule, you should write the reciprocal number with the exponent positive. Zero Exponent. When you have an exponent equal to zero, the result must be 1.For solving this question, you should convert the given text into a math expression. See below.
7^7 multiplied by 7^5 equals (7^n)^4 over 7^4 = [tex]7^7 * 7^5 =\frac{ (7^n)^4 }{7^4}[/tex]
After that, you should apply the power rules. Using the rule for the multiplication with the same base, you have: [tex]7^{12} =\frac{ (7^n)^4 }{7^4}[/tex].
Next step, you should apply the rule Power, then: [tex]7^{12} =\frac{ (7^{4n})}{7^4}[/tex]. One more time, you should apply the rule for the multiplication with the same base, and you will have:
[tex]7^{12} =\frac{ (7^{4n})}{7^4}\\ \\ 7^{16}=7^{4n}[/tex]
Thus,
16=4n
n=16/4
n=4
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What is BD?
please help!!
The length of BD in the triangle is 24 units.
How to find the side of a triangle?The triangles are similar by angle bisector theorem. The angle bisector theorem states that the angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
Therefore, let's find BD.
Hence, using the proportion,
12 / 20 = x / x + 6
cross multiply
12(x + 6) = 20x
12x + 72 = 20x
72 = 20x - 12x
72 = 8x
divide both sides by 8
x = 72 /8
x = 9
Therefore,
BD = x + x + 6 = 2x + 6
BD = 2(9) + 6
BD = 18 + 6
BD = 24 units
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what is the meaning of square?
Answer:
Step-by-step explanation:
A square is a 4 sided polygon in which all of its side lengths are equal and the diagonals are also be
For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]A =1 2 11 1 1
We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix
Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.
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an army regiment with 400 soldiers has provision for 80 days. if 80 soldiers moved out of the regiment, how long would the food last at the same rate?
Answer: If the army regiment had 400 soldiers with provisions for 80 days, the food would last each soldier for 80 days / 400 soldiers = 0.2 days per soldier.
If 80 soldiers moved out, the number of soldiers remaining in the regiment would be 400 soldiers - 80 soldiers = 320 soldiers.
Since the amount of provisions has not changed, the food would last for 80 days / 320 soldiers = 0.25 days per soldier.
Therefore, the food would last the 320 soldiers for 0.25 days * 320 soldiers = 80 days.
Step-by-step explanation:
Mr. Herman compare his students score for two class periods for a social studies final
Based on the information in the graph, it can be stated that the median test score of period 2 was less than the median test score of period 1.
How to identify the median?The median is identified by locating the value that lies in the middle, in the case of a whisker plot, the median corresponds to the value shown by the vertical line.
The median for period 1: 84
The median for period 2: 82
Based on this information, it can be stated that the median test score of period 2 was less than the median test score of period 1.
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What would you pay for 2 1/2 kg of tomatoes at 1. 50 each per kg
Answer: To find out how much you would pay for 2.5 kg of tomatoes at $1.50 per kg, we need to multiply the weight of the tomatoes by the price per kg:
Cost = 2.5 kg x $1.50/kg
= $3.75/kg x 2.5 kg
= $9.38
So, you would pay $9.38 for 2.5 kg of tomatoes at $1.50 per kg.
Step-by-step explanation:
What is the number 9.88 x 10-5 in standard notation?
SOMEBODY PLEASE LOOK AT THE PICTURE AND HELP MEEEE
The equation that represent the graph is C = 1.5m + 200.
How to represent linear equation?A moving company charges a one time fee and cost per miles of it service. Therefore, the relationship is between the total cost and the number of miles.
Therefore, let's use equation to represent the relationship between the total cost C and number of miles travelled, m.
Hence, using slope intercept form
y = mx + b
where
m = slopeb = y-interceptHence,
using (0, 200) (200, 500)
m = 500 - 200 / 200 - 0
m = 300 / 200
m = 1.5
Hence,
y-intercept = 200
Therefore, the equation is C = 1.5m + 200
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solve the equation abbc for​ a, assuming that​ a, b, and c are square matrices and b is invertible.
Considering AB=BC, the matrices A, B, and C are square matrices such that matrix B is invertible.
Now, post-multiply both sides of
[tex]AB=BC by {B}^{−1} [/tex]
[tex] {ABB}^{−1} = {BCB}^{−1} [/tex]
Solving the obtained equation for A by using the properties
[tex]AI= {BCB}^{−1} \\ A= {BCB}^{−1} [/tex]
Therefore, the required matrix A is BCB−1
A matrix, also known as matrices, is a rectangular array or table of letters, numbers, or other symbols arranged in rows and columns that is used to represent a mathematical object or a characteristic of one.
In linear algebra, matrices represent linear maps and enable explicit computations. Since most properties and operations of abstract linear algebra can be expressed in terms of matrices, the study of matrices constitutes a significant portion of linear algebra.
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Write as an algebraic expression: five times the difference between six less than a number
The algebraic expression is,
⇒ 5 (6 - n)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ five times the difference between six less than a number.
Now, Let a number = n
Hence, We can formulate;
⇒ 5 (6 - n)
Thus, The value of expression is,
⇒ 5 (6 - n)
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consider the equation 4(10^-3x)=18, solve the equation for x. Express the solution as a logarithm in base-10.
The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
[tex]\rm 4 \times (10^{-3x})=18[/tex]
Simplify the equation, then we have
[tex]\begin{aligned} \rm 4 \times (10^{-3x}) &=18\\\\\rm (10^{-3x}) &=4.5 \end{aligned}[/tex]
Take a log with base 10 on both sides, then we have
- 3x log₁₀ 10 = log₁₀ 4.5
- 3x = 0.6532
x = -0.2177
The solution of the exponent equation [tex]\rm 4 \times (10^{-3x})=18[/tex] will be negative 0.2177.
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PLS HELP ASAP!
in ABC, mC=90, mA=50, and AB=35. find the length of the altitude CH
Answer:
Step-by-step explanation:
no idea sorry :/
The length of the altitude CH is 17.234.
What is Altitude of a Triangle?Altitude of a triangle is defined as the perpendicular line segment joining the vertex to the opposite side.
The figure for the triangle is given below.
Here the area of a triangle can be found in two ways.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
Consider the triangle ABC given below.
Area of the triangle when considered base as BC and altitude as AC is,
Area, A = [tex]\frac{1}{2}[/tex] × BC × AC
BC = AB Sin (50) = 35 sin(50)
AC = AB Sin (40) = 35 sin(40)
A = [tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40))
Area of the triangle when considered base as AB and altitude as CH is,
Area, A = [tex]\frac{1}{2}[/tex] × AB × CH
A = [tex]\frac{1}{2}[/tex] × 35 × CH
Area of the same triangle will be equal when find in different ways.
[tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40)) = [tex]\frac{1}{2}[/tex] × 35 × CH
Cancelling the terms which are on both sides,
CH = 35 sin(50) sin(40)
CH = 35 × 0.766 × 0.643
CH = 17.234
Hence the length of the altitude is 17.234.
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W^2+2+48 divided by 28
Key: w=5
X=3
Y=4
Z=8
Step by step?
The solution to the algebraic expression w² + 2 + 48 ÷ 28 is 2.68
How to solve algebra?w² + 2 + 48 ÷ 28
Where,
w=5
X=3
Y=4
Z=8
w² + 2 + 48 ÷ 28
substitute w = 5 into the expression
= 5² + 2 + 48 ÷ 28
= 25 + 2 + 48 ÷ 28
Add
= 75 ÷ 28
divide
= 2.678571428571428
Approximately,
2.68
In conclusion, 2.68 is the solution to the given expression.
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what is the number of times a variable appears in a data set?
The number of times a variable appears in a data set is Known as Frequency.
Frequency
The frequency of a particular data is the number of times the data value appears. Denote the frequency of a data value by f. For example, if 5 students got an A in science, the frequency of an A score is considered to be 5.
Frequency distributions are used to tabulate the collected data. Data can be scores given by students, temperatures in different cities, scores scored in volleyball matches, and so on. After data is collected, it needs to be presented in a meaningful way for better understanding. Organize your data so that all characteristics are summarized in a table. This is called a frequency distribution.
Types of Frequency distribution:
1. Group frequency distribution: Use group frequency distribution tables to organize large numbers of observations or data. By doing so, we create class intervals to calculate the frequency of data belonging to a particular class interval.
2. Ungrouped Frequency Distribution: In an ungrouped frequency distribution table, we record the exact frequency of individual data without classifying them.
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Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R^3 that does not contain the origin.
x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1
x = -1, y = 6, z = 1 is the solution.
Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]
the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]
we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.
operating R₂→R₂-R₁ , R₃→R₃-R₁
[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]
operating, R₃→R₃-3R₃
~ [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]
which is the row echelon, form of the matrix [A:B]
we have rank of [A:B] = the number of the non zero rows in echelon form = 2
also by the same elementary transformation we get,
A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]
∴ rank of A = 2
since rank A = rank [A:B] = 2 < number of unknowns
therefore, the given equation are consistent and will have an infinite number of solutions.
We see that the given system of equations is equivalent to the matrix equation
[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]
which gives the equations x + y + z = 6 ........(1)
and y + 2z = 8 .......(2)
from (2), y = 8 - 2z, putting the value of y in (1) we get,
x = 6 - y - z = 6 (8 - 2z) z = z - 2
taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,
if k = 1
x = -1, y = 6, z = 1 is the solution.
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Acellus
Find the equation of the axis of
symmetry for this function.
f(x) = 4x² - 8x + 5
-b
Hint: To find the axis of symmetry, use the equation: x =
2a
Simplify your answer completely. Enter
the number that belongs in the green box.
x = [?]
Answer:Rewrite the equation in vertex form.
Tap for more steps...
y
=
4
(
x
−
1
)
2
−
9
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
4
h
=
1
k
=
−
9
Since the value of
a
is positive, the parabola opens up.
Opens Up
Find the vertex
(
h
,
k
)
.
(
1
,
−
9
)
Find
p
, the distance from the vertex to the focus.
Tap for more steps...
1
16
Find the focus.
Tap for more steps...
(
1
,
−
143
16
)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x
=
1
Step-by-step explanation:
y=3x+2
-4x+2y=8
elimination method
Answer:
Step-by-step explanation:
Lauren and Aidan left their offices at 6:15 P.M. and drove to meet at a restaurant the same
distance away from their offices for dinner. Lauren drove at a constant speed of 39 miles
per hour. Aidan drove at a constant speed of 42 miles per hour. Aidan reached the restaurant
away was Lauren from the restaurant when Aidan reached?
at 6:35 P.M. How far away
Lauren was 13 miles away from the restaurant when Aidan reached it.
What is travel?
Travel refers to the act of moving from one place to another, often over a distance or by means of transportation.
Lauren and Aidan both left their offices at 6:15 P.M. and traveled for 20 minutes (from 6:15 P.M. to 6:35 P.M.) before Aidan arrived at the restaurant. During this time, Lauren traveled at a speed of 39 miles per hour, so she covered a distance of:
distance = speed x time
distance = 39 miles/hour x (20 minutes / 60 minutes/hour) = 13 miles
After 20 minutes, Aidan arrived at the restaurant, having traveled for 20 minutes at a speed of 42 miles per hour. The distance he covered during this time is:
distance = speed x time
distance = 42 miles/hour x (20 minutes / 60 minutes/hour) = 14 miles
Since they both traveled the same distance to the restaurant, but Aidan arrived there first, Lauren must have been 1 mile behind him when he arrived at the restaurant.
Therefore, Lauren was 14 - 1 = 13 miles away from the restaurant when Aidan reached it.
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