The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.
What is a function?
A function is defined as a relation between a set of inputs having one output each.
We have,
f(x) = ( x + 5 ) ( x - 2 )
g(x) = ( 2x + 1 ) ( x - 2 )
To find the points of intersection between the two functions we must equal the function.
f(x) = g(x)
( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )
( x - 2 ) gets canceled
x + 5 = 2x + 1
5 - 1 = 2x - x
4 = x
x = 4
This means that at x =4 the function f(x) and g(x) intersect.
we can see that at x = 4 both the functions have the same value.
f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2
f(x) = 18
g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )
= 9 x 2
g(x) = 18
Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.
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Assuming that a personal space is 3ft squared. Estimate how many people can fit into a circular arena a diameter of 100 yards?
Answer
2617.
Step-by-step explanation
To estimate the number of people that can fit into a circular arena with a diameter of 100 yards, we first need to find the area of the arena. To do this, we can use the formula for the area of a circle, which is equal to pi times the radius squared. Since the diameter of the arena is 100 yards, the radius would be half of that, or 50 yards. Plugging this value into the formula for the area of a circle, we get:
Area = pi * 50^2
Since pi is approximately equal to 3.14, we can plug this value into the equation to get:
Area = 3.14 * 50^2
This simplifies to:
Area = 3.14 * 2500
Which gives us an area of approximately 7850 square yards.
Since one person requires a personal space of 3 square feet, we can divide the total area of the arena by 3 to find the number of people that can fit in the arena. This gives us:
7850 square yards / 3 square feet/person = 2616.666... people
Rounded to the nearest whole number, this means that approximately 2617 people could fit in the circular arena with a diameter of 100 yards.
Select all the true statements given that APQR= ASTU.
A. PO= ST
B. PQ= TU
C. mLR =mLU
D. MLP = m
E. ML0= m
The true statements that satisfy ΔPQR ≅ ΔSTU are PQ = ST, m∠R = m∠U, and m∠Q = m∠T.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Here, we have
Given
ΔPQR is congruent to ΔSTU
We have to find a true statement that satisfies the given condition.
We concluded that PQ = ST, m∠R = m∠U, and m∠Q = m∠T.
Hence, the true statements that satisfy ΔPQR ≅ ΔSTU are PQ = ST, m∠R = m∠U, and m∠Q = m∠T.
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100 POINTS!!!!! HELPPPP PLEASE, ILL GIVE BRAINLIEST IF CORRECT
The display summarizes grades on a World History exam.
A vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.
Which of the following describes the data set?
The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical
The option that best describes the data is B; The data is univariate and numerical.
What is univariate data?This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.
In this case, the one variable is World History scores exam
Since we are given vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.
A numerical data is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.
Numerical data, also known as quantitative data, that is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.
Hence, the correct one is B; The data is univariate and numerical.
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Answer:
it is univariate and numerical
Step-by-step explanation:
univariate vs bivariate thsi is univariate because it only deals with one varialbe and its numberical because it is numbers ( that parts a litle clear)
hope i helped a litle i tried to explain it bc i know how tought this class can be (this is flvs from 4.09 from lesson4.05 incase that helps)
PLEASE HELP ME WITH THIS QUESTION
Draw an example of a polynomial with
-Degree of 5
-Positive lead coefficient
-Zeros at -5, -2, 0, 3, 6
The required polynomial is x⁵ - 2x⁴ - 35x³ + 36x² + 180x.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, We have to construct a polynomial of degree 5, a positive lead
co-efficient and zeros or roots are -5, -2, 0, 3, 6.
If roots are -5, -2, 0, 3, 6 factors are (x + 5), (x + 2), (x + 0), (x - 3), (x - 6).
∴The required polynomial is (x + 5)(x + 2)(x + 0)(x - 3)(x - 6).
= x(x + 5)(x + 2)(x - 3)(x - 6).
= (x² + 5x)(x² - 3x + 2x - 6)(x - 6).
= (x² + 5x)(x² - x - 6)(x - 6).
= (x² + 5x)(x³ - 6x² - x² + 6x -6x + 36).
= (x² + 5x)(x³ - 7x²+ 36).
= x⁵ - 7x⁴ + 36x² + 5x⁴ - 35x³ + 180x.
= x⁵ - 2x⁴ - 35x³ + 36x² + 180x.
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Pronghorn Company purchased a delivery truck for $26,000 on January 12022. The truck has an expected salvage value of $1.280 and is expected to be driven 103,000 miles over its estimated useful life of 10 years. Actual miles driven were 12,700 in 2022 and 10,200 in 2023
compute the depreciation expense using
A) Striaght-line Method
B) Units Of Activity Method
C) Declining Balance method
The computation of the depreciation expense using the following methods are as follows:
2022 2023
A) Straight-line Method $2,472 $2,472
B) Units Of Activity Method $3,048 $2,448
C) Declining Balance method $5,200 $4,160
What is the depreciation expense?The depreciation expense is the periodic recognition of the cost for a long-term asset over its useful life.
The costs of long-term assets are spread over their estimated life through depreciation, depletion, or amortization.
The various depreciation methods include:
Straight-line methodUnit-of-activity methodDouble-declining-balance methodSum-of-the-years-digit methodModified accelerated recovery systems (MACRS).The cost of the delivery truck on January 1, 2022 = $26,000
Expected salvage value = $1,280
Depreciable amount = $24,720
Estimated useful life = 103,000 miles or 10 years
Depreciation Expenses:
Straight-line method = $2,472 annually ($24,720/10)
Units of activity method per mile = $0.24 ($24,720/103,000)
2022 = $3,048 (12,700 x $0.24)
2023 = $2,448 (10,200 x $0.24)
Declining-balance method rate = 20% (100/10 x 2)
2022 = $5,200 ($26,000 x 20%)
2-23 = $4,160 ($20,800 x 20%)
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Question 1 options: James is observing the population of the fish he put into a pond. He built a pond and populated it with 900 fish. The population of the fish doubles every year.
The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.
Given that,
James is keeping an eye on the fish population in the pond he created. He constructed a pond and added 900 fish to it. Every year, the fish population doubles.
We have to find the equation by using x represent the number of years and y represent the number of fish.
We know that,
We get
Number of fish at starting =900
Number of fish after 1 year =900×2=1800
Number of fish after 2 year =1800×2=3600=900×(2)²
Number of fish after 3 year =3600×2=7200=900×(2)³
So,
Here we can see that the number of fish are in Geometric progression (G.P) with a=900 and r=2
So,
Tₙ=arⁿ⁻¹
We get
y=900×(2)ˣ
Therefore, The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.
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Evan added -2 1/2+4 and got six 1/2 draw arrows on the number line to represent the problem and explains Evans error
Evan made a mistake to add. As the sign of 4 positive and the sign of [tex]2\frac{1}{2}[/tex]. The subtraction operation must be performed for this.
What is a number line?
The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever.
The given expression is
[tex]-2\frac{1}{2}[/tex] +4
It can be written as 4 [tex]-2\frac{1}{2}[/tex] .
Now perform the subtraction operation:
= 4 - 5/2
= (8-5)/2
=3/2
= [tex]1\frac{1}{2}[/tex]
The number line that represents the given operation is attached below.
Evan added 4 and [tex]2\frac{1}{2}[/tex] which is incorrect way.
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If 2^x = 32 , then x=
Using the exponent's rule we know that x = 5.
What are exponents?Exponentiation is a mathematical process that involves the base b and the exponent or power n.
It is represented as bn and is pronounced as "b to the n."
A number's exponent indicates how many times to multiply that particular number.
It appears as a little number above and to the right of the basic number.
For instance, 82 = 8 x 8 = 64.
(The exponent "2" instructs us to multiply by two and use the number eight.)
Another illustration is 53 = 5 * 5 * 5 = 125.
So, we have: 2ˣ = 32
We know that:
2 * 2 * 2 * 2 * 2 = 32
2 is multiplied 5 times which means:
2⁵ = 32
Hence, x = 5.
Therefore, using exponents we know that x = 5.
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The_______states that the part equals the percent multiplied by the whole
The percentage equation states that the part equals the percent multiplied by the whole.
What is percent?
A percentage is a number that indicates how much is 100 and can also be expressed as a decimal or fraction.
What is Percentage Equation?
Percentage equations allow you to find parts or ratios of amounts (or wholes). Percentages are specified with a % sign after the number of hundredths.
The formula for percentage equation is given below
Percent=(Part/Whole)x100
Example: 45 is 60% of what number?
Modifying the above percentage equation, we get
Whole= (Part/Percent) x 100
⇒Whole= (45/60) x 100
⇒Whole= (3/4) x 100
⇒Whole= 3 x 25
⇒Whole= 75
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What is the solution to this equation
x^2+4x-12=0
Answer:
x = 2 or –6
Step-by-step explanation:
x² + 4x –12 = 0
x² +6x –2x –12 = 0
x(x + 6) –2( x + 6) = 0
(x–2)(x+6)= 0
x–2= 0
x= 2.
x+6= 0
x= –6
x = 2 or –6
The odds on (against) your bet are 3
to 7
.
If you bet $49
and win, how much will you gain?
Answer:
No more than 10 dollars
Step-by-step explanation:
Facts!
1. Is H nonempty? 2. Is H closed under addition? If it is, enter CLOSED. If it is not enter two vectors in H whose sum is not in H. using a comma separated list and syntax such as <1,2,3>, <4,5,6>. 3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not enter a scalar in R and a vector in H whose product is not in H, using a comma separated list and syntax such as 2, <3,4,5>. 4. Is H a subspace of the vector space V? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your answers to parts 1-3.
As per the concept of vector, the subspace of the vector is < 3, 4, 5>
The term vector is defied as the geometric entity that has both magnitude and direction.
Here we have to find the given vector <1, 2 , 3> and < 3, 4, 5> subspaces by using the vector formula.
Let us consider V = R³ and let H be the subset of V of all points on the plane 7x+4y+6z=0.
By looking into the given equation, we have identified that H is a non empty set.
And here be looking into the given vector, the second one is always the subspace. Based on this, the resulting subspace is written as,
=> < 3, 4, 5>
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Twenty-five people in a survey were asked to give their current checking account balances. Use the balances shown in the following list to complete the frequency distribution table.
$220
$337
$29
$60
$201
$519
$462
$290
$131
$572
$227
$111
$124
$509
$331
$306
$439
$28
$504
$431
Fill in the missing information.
Class Intervals
Class Frequency
(Account Balances) (Number of People)
$0-$99
$431
$83
$451
$417
$341
CIP
Twenty-five people in a survey were asked to give their current checking account balances and the frequency = 4.
What is frequency and example?
The frequency of a particular data is the number of times the data value occurs. We represent the frequency of a data value by f. For example, if five students got an A in science, and then the grade A is said to have a frequency of 5.Given that;
Class intervals Class frequency
(Account Balance) (No of people)
$0 - $99 ?
Entries in this ($0 - $99) range are $29 , $60 , $28 , $83 = 4
Therefore, class frequency (no of people) = 4
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Jody takes out a 30-year mortgage for $300,000 at 3.524% APR. Her monthly payment is $1,350. She pays $186,175 in interest over those 30 years.
What is the total amount she will pay for the house?
If her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.
What is APR?The full name of APR is the annual percentage rate. It is defined as the percentage rate applied on borrowing money in the form of interest but APR is applied annually.
It is given that, Jody takes out a 30-year mortgage for $300,000 at 3.524% APR. Her monthly payment is $1,350. She pays $186,175 in interest over those 30 years.
1 year = 12 month
30 year = 360 month
We have to find the total amount she will pay for the house,
Total amount = Monthly payment × 360 + intreast over 30 years
Total amount =1,350 × 360 + 186,175
Total amount =$ 672175
Thus, if her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.
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decimals and fractions, percents and decimals, percents over 100% and less than 0%, compare and order fractions, decimals and percents
No matter how they are expressed, fractions, decimals, and percentages can all have the same value.
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
Here,
It is possible to have fractions, decimals, and percentages that have the same value regardless of how they are expressed.
These fractions, decimals, and percentages are said to be equivalent.
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The formula v(t)=14t+29 represents the cost of renting a moving van. The variable t represents the number of hours the moving van is rented for. If the cost of renting the
moving van is $439, how many hours was it rented for? Round to the nearest whole number.
Answer:
29 hrs
Step-by-step explanation:
439 = 14t + 29
439-29 = 14t
410 = 14t
t = 410/14
t= 29.28
t = 29
SDSADASDASDADASDASDA
Answer:
ong
Step-by-step explanation:
find the x and y of the graph of 3x +2y=15. State each answer as an integer or an improper fraction in simplest form.
Answer:
Step-by-step explanation: To find the x let y=0
We substitute into the equation 3x+2y=15
3x+2 *0=15
3x=15
x=15/3=5
To find the y let x=0
we substitute into the equation x =0
3*0+2y=15
2y=15
y=15/2
Cupcakes are packed six to a box Abby only buys full boxes of cupcakes give two possible numbers of cupcakes that she could buy?
Two possible numbers are 6 and 12.
6 would mean she bought one box, and 12 would mean she bought 2 boxes.
Find the slope of the line that goes through the given points
(-5-10) and (-6, -1)
Answer:
-9
Step-by-step explanation:
(y2-y1)/(x2-x1)
[tex]\frac{(-1--10)}{(-6--5)}[/tex]=-9
What is the equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2?
y=3x+7y
y=3x−5y
y=−3x+5y
y=−3x−7
The equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is y = 3x - 5.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form, point slope form, standard form and general form.
Linear equation in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x −2.
parallel lines have the same slope.
Therefore, the slope of the line is 3.
The y-intercept can be found as follows:
using (3, 4)
y = 3x + b
4 = 3(3) + b
b = 4 - 9
b = -5
Therefore, the equation in slope intercept form is y = 3x - 5.
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Water boils at a minimum temperature of 100 degrees Celsius. Which inequality represents this scenario? 100 > b 100 < b 100 ≤ b 100 ≥ b
The inequality which represents the range of temperature at which water boils is 100 ≤ b thus, option (C) is correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
Water boils at a minimum temperature of 100 degrees Celsius.
Suppose b is the temperature at which water boils.
100 ≤ b
Hence "The inequality which represents the range of temperature at which water boils is 100 ≤ b".
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1. In a triangle∆ABC, if DE is parallel to BC, AD
DB
=
3
4
and AC = 15 cm, then the length AE is:
(a) 45 (b) 23/7 (c) 1 (d) 45/7
The length of the segment AE on the triangle is 45/7
How to determine the length of AE?From the question, we have the following parameters that can be used in our computation:
DE parallel to BC,
Also, we have
AD/DB=3/4
The above parameters mean that
AD/AB = AE/AC
Also, we know that
AB = AD + DB
From the ratio values, we have
AB = 3 + 4
Evaluate the sum
AB = 7
Updating the initial ratio, we have
AE/15 = 3/7
Multiply both sides by 15
So, we have the following representation
AE = 15 * 3/7
Evaluate the products
AE = 45/7
Hence, the length of AE is 45/7
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Answer the questions below to explain what kind of function would better model the data, linear or exponential.
function would better model the data because as x increases, the
y values change . The of this function is approximately
The linear model would be a better model for the given function.
What are linear models?
A response variable can be described in terms of a linear combination of predictor variables using linear models. The response ought to be continuous and at least roughly regularly distributed. Although these models are widely used, they are unable to handle clearly discrete or skewed continuous data.
In the table, we see that as x increases, y values change in a steady manner. The slope of this function is approximately 1860.
We use straight lines to visually illustrate linear relationships. Typically, a linear model has two parameters: the slope, also known as the growth factor or rate of change, and the y-intercept, often known as the beginning value. The linear model can be expressed as a linear function, y = mx + b or y=mx+b, where m is the slope and b is the y-intercept.
So, we get the slope as 1860.
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I need help with this
Answer:
D
Step-by-step explanation:
5*1 = 5
5*2 = 10
5*3 = 15
5*4 = 20
5*5 = 25
evaluate for the value of sum and x after the following code is executed. sum is initialized to 4. x is initialized to 2.
The value of the given sum after the execution of code segment is equal to 16.
As given in the question,
Using attached code segment.
Given values are:
num1 = 6
num2 =4
num3 =10
Value of sum after execution of code segment is given by:
num1 < num2
⇒ 6< 4 which is false.
Else num3 = num2
⇒ num3 = 4
num2≥ num3
⇒4 ≥ 4
True as 4 =4
num1 = num2 + num3
= 4 + 4
= 8
Final sum = num1 + num2 + num3
= 8 + 4 + 4
= 16
Therefore, using code segment the value of the sum is equal to 16.
The given question is incomplete, I answer the question in general according to my knowledge:
What is the value of sum after the code segment is executed?
code segment is attached:
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A recipe requires 1 1/4 cups of sugar for every 1/3 of a cup of salt. What is the unit rate of salt to sugar in the recipe?
Answer:
3 3/4 cups of sugar per cup of salt
Step-by-step explanation:
To find the unit rate of salt to sugar in the recipe, we need to divide the number of cups of sugar by the number of cups of salt. In this case, the unit rate of salt to sugar is 1 1/4 cups of sugar divided by 1/3 of a cup of salt, which can be simplified to 3 3/4 cups of sugar per cup of salt.
Answer:
The unit rate of cups per teaspoon is 1 1/3
Step-by-step explanation:
-A recipe calls for 2 by 3 cup of sugar for every 1 by 2 teaspoon of vanilla.
Based on the above information, the calculation is as follows:
=(2/3)/(1/2)
=(2/3)/(1/2)
=(2/3)x(2/1)
=(2x2)/(3x1)
=(4/3)
= 1 1/3
Below are two parallel lines with a third line intersecting them.
Answer: 132 degrees
Step-by-step explanation:
Because the lines are parallel, and the line intersecting them is straight, the angle on top should be the same as the angle on the bottom.
So that makes x=132
PLEASE HLEP I WILL MARK U BRANLIEST I REALLY NEEED HELPPPP
Answer:
Step-by-step explanation:
-1<x<0
x<0
so x is negative.
Hence -x is positive.
and -1<x
or
x>-1
or
x+1>0
x+5=x+1+4>0+4
hence x+5 is positive.
x is negative .
∴x-2 is negative.
f(x)=(+)×(+)×(+)×(-)=-
B
3. Laurie uses yellow and white tiles to create a pattern.
a) Make a table of values to show the number of yellow tiles in relation to the figure number.
b) Describe the relationship between the number of yellow tiles and the figure number.
c) Develop an expression and an equation to model the number of yellow tiles. Explain what each part of the equation represents.
d) How many yellow tiles are in Figure 24?
e) Which figure number has 176 yellow tiles? Verify your answer.
f) Is it possible to have a figure with 54 yellow tiles? Show how you know.
a) Figure 1 2 3
Number of tiles 8 12 16
b) The number of tiles is 8 more than 4 times of 1 less than the number of figure.
c) The equation of model the number of yellow tiles is y = 4x + 4.
d) The number of tiles in figure 24 is 100.
e) Figure 43 has 176 yellow tiles.
f) No.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given that
the number of yellow tile in figure 1 is 8.
The number of yellow tile in figure 2 is 12.
The number of yellow tile in figure 3 is 16.
(a) The table is
Figure 1 2 3
Number of tiles 8 12 16
(b)
The number of tiles increase at a constant rate.
The rate is (12 - 8) = (16 - 12) = 4
The relation with the figure and number of tiles is
The number of tiles is = 4 + (the number of figure - 1)4
C)
Assume that y represents total number of tiles.
x = Number of figure
Rewrite "The number of tiles is = 4 + (the number of figure - 1)4" in term of x and y:
y = 8 +(x - 1)4
y = 8 + 4x -4
y = 4x + 4
d) Putting x = 24 in y = 4x + 4
y = 4×24 + 4
y = 96 + 4
y = 100
e)
Putting y = 176 in y = 4x + 4
176 = 4x + 4
Subtract 4 from both sides:
172 = 4x
Divide both sides by 4
x = 43
f)
Putting y = 54 in y = 4x + 4
54 = 4x + 4
Subtract 4 from both sides:
50 = 4x
Divide both sides by 4
x = 50/4
The value of x is not a whole number. Thus it is not possible that a figure has with 54 yellow tiles.
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