If we have the function
[tex]f(x)=x^2[/tex]Then
[tex]\begin{gathered} f(x)+f(x)+f(x)=x^2+x^2+x^2 \\ =3x^2 \end{gathered}[/tex]This also can be written in the form
[tex]f(x)+f(x)+f(x)=3f(x)=3x^2[/tex]We see that both answer are the same, like it should be.
Choose two consecutive points on the graph and find the rate of change. Is the slope the same or different?
Choose two consecutive points on the graph and find the rate of change.
We will start with t = 1000 and t = 1500:
[tex]P(1000)=12.643(1.0027)^{1000}=187.4412[/tex][tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex]Remember that the rate of change is found by the difference in y over the difference in x.
[tex]RATEOFCHANGE=\frac{721.7263-187.4412}{1500-1000}[/tex][tex]RATEOFCHANGE=\frac{534.2851}{500}\approx1.0686[/tex]Let's do it now for t = 1500 and t = 2000.
[tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex][tex]P(2000)=12.643(1.0027)^{2000}=2778.9454[/tex]In this case the rate of change would be:
[tex]\text{rateofchange=}\frac{2778.9454-721.7263}{2000-1500}[/tex][tex]\text{rateofchange}=\frac{2057.2191}{500}\approx4.1144[/tex]The slopes are different and due to the type of function they will always increase when taking larger values.
Find the slope, x-intercept, and y-intercept for the line 10x-7y + 7 = 0. The slope is The I-intercept is h The y-intercept is Note: Your answers must be decimals. Submit Question Jump to Answer
slope=1.43
y-intercept=1
x-intercept=-1.43
Explanation
Step 1
get the slope intercept form of the equation
[tex]y=mx+b\text{ (slope intercept equation)}[/tex]where
m is the slope and b is the y-intercept
to do this, isolate y
[tex]\begin{gathered} 10x-7y+7=0 \\ \text{subtract 10 x in both sides} \\ 10x-7y+7-10x=0-10x \\ -7y+7=-10x \\ \text{subtract 7 in both sides} \\ -7y+7-7=-10x-7 \\ -7y=-10x-7 \\ divide\text{ both sides by -7} \\ \frac{-7y}{-7}=\frac{-10x}{-7}-\frac{7}{-7} \\ y=\frac{10x}{7}+1 \end{gathered}[/tex]so,
[tex]\begin{gathered} \text{slope}=\frac{10}{7} \\ y-\text{intercept}=1 \end{gathered}[/tex]Step 2
to find the x-intercept replace the y value with zero in the equation
[tex]\begin{gathered} y=\frac{10x}{7}+1 \\ 0=\frac{10x}{7}+1 \\ \text{subtract 1in both sides} \\ 0-1=\frac{10x}{7}+1-1 \\ \frac{10x}{7}=-1 \\ \text{Multiply both sides by 7/10} \\ \frac{10x}{7}\cdot\frac{7}{10}=-1\cdot\frac{7}{10} \\ x=-\frac{7}{10} \end{gathered}[/tex]so, the x intercept is
[tex]-\frac{7}{10}[/tex]I hope this helps you
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > -2 x - 7I NEED THE CORDINATES
Given:
There are given that the set of inequality is:
[tex]\begin{gathered} y>x+2 \\ y>-2x-7 \end{gathered}[/tex]Explanation:
From the given system of inequality, we need to draw the graph and find the set of points, where both of the graphs will intersect.
Now,
The graph of the given system of inequality is shown below:
Final answer:
Hence, the set of the point from the given system of inequality is shown below:
[tex](-3,-1)[/tex]What is the net price of merchandise listing for $5,900 less a trade discount rate of 45%?
A percentage is a number or ratio that represents a fraction of 100.
If there is a trade discount of 45% on the price of the merchandise of $5900, the net price of the merchandise is $3245.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
We have,
Merchandise price = $5,900
Discount rate = 45%
45% = 45/100 = 9/20
The net price of the merchandise:
= 5900 - (45% of 5900)
= 5900 - 9/20 x 5900
= 5900 - 9 x 295
= 5900 - 2655
= 3245
Thus,
If there is a trade discount of 45% on the price of the merchandise of $5900, the net price of the merchandise is $3245.
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if your 1952 what year will you be 26?
Answer:
16 January 1952, Wednesday, 70 Years, 8 Months, 26 Days or 848 months, or 3691 weeks, or 25837 days, or 37205280 minutes, or 2232316800 seconds.
Step-by-step explanation:
Answer:
Step-by-step explanation:
answer:1978
A population of a certain city increases exponentially at a rate of 6.5%. Initially, it is 1.50 million. After how many years will the population reach 2.31 million?6.5466.643 6.1236.142
Given that
The population of a certain city is 1.50 million initially and it gets increased by 6.5% exponentially. And we have to find the number of years in which the population becomes 2.31 million.
Explanation -
The formula for the exponential growth is given as
[tex]\begin{gathered} f(x)=a(1+r)^x \\ where\text{ f\lparen x\rparen is the final amount, a = initial amount, r = rate and x = time period} \end{gathered}[/tex]Here we have f(x) = 2.31 million, a = 1.50 million , r = 6.5% and x = ?
So let the time be t.
Then, on substituting the values we have
HELP Please!!!
Bridget worked on her Math homework for 1 ½ hours. Then she worked on her Social Studies homework for ¼ hour. How many hours total did she work on her homework?
Be sure to show all of your work and steps.
Answer: 1 3/4
1/4= 15 minutes
1/2 = 30 minutes
add 1/2 to 1/4 and you get 3/4 because 1/2 is equal to 2/4 if you add the 1/4 to it
heres the actual math:
1/2 = 2/4
2/4 + 1/4 = 3/4
slap that one in front of it so its 1 3/4 and therea your answer
In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
O Yes
The probability of having female baby is 0.95
What is probability?
Probability is a discipline of mathematics that deals with statistical models of how probable an event is to exist or how likely a statement is to be true. The probability of an occurrence is a value between 0 and 1 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
The probability of having female baby is = 284/(284 + 15) = 0.95
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Here is the probability model for the blood type of a randomly chosen person in the United States:Blood Type O А B ABProbability 0.14 0.32 0.01 ?(a) This probability model isA. discrete.B. continuousC. equally likelyD. None of the above.(b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that arandomly chosen American can donate blood to Maria?A. 0.01B. 0.15C. 0.33D. None of the above.(c) What is the probability that a randomly chosen American does not have type O blood?A. 0.86B. 0.68C. 0.14D. None of the above
a) A probability distribution is called continuous if its distribution function is continuous.
• Answer a: B. continuous.,
b)
[tex]0.14+0.01=0.15[/tex]• Answer b: B. 0.15
c)
[tex]1-0.14=0.86[/tex]• Answer c: A. 0.86
3x+3=2(x+7)
What does x equal?
Answer: x = 11
Step-by-step explanation:
To solve we will isolate the variable, x.
Given:
3x+3=2(x+7)
Distribute:
3x+3=2x+14
Subtract 3 and 2x from both sides of the equation:
x = 11
The square of a negative number
is sixteen more than six times the
negative number. Find the number. The sum of two numbers is
twenty three. And The product of the
two numbers is one hundred
twenty. Find the two numbers.Help me. From: Jessie
The numbers are:
1. The value of x = 5
2. The value of x = 15 or 8 and y = 8 or 15
What is Square?
The word Square means a number multiplied by itself.
The above answers were gotten in the following way:
1. Let the unknown negative number be x
The square of the negative number: x² is
Sixteen more than six times of negative x: 6x+16
It is written as: (x)²=6x+16
Equating to zero, we have:
x²-6x-16=0
Factorizing, we have:
x²-8x+2x-16=0
x(x-8)+2(x-8)=0
x+2=0 and x-8=0
x=-2 and 8
Since the number is negative, x = -2
Therefore, the value of the negative number is -2
2. Given:
Sum of two numbers = 23
Product of two numbers = 120
Calculation:
Let the two numbers be x and y
x+y=23...............equation 1
xy=120..................equation 2
From equation 1, x=23-y
Substitute the value of x in equation 2, we have:
(23-y)y=120
Opening the brackets, we have:
23y-y²=120
Rearranging the equation, we have:
-y²+23y=120
Equating to zero, we have:
-y²+23y-120=0
Multiplying both sides by (-1), we have:
y²-23y+120 = 0
Factorizing, we have:
y²-15y-8y+120=0
y(y-15)-8(y-15)=0
(y-8)(y-15)=0
y=8 or 15
Substituting the values of y in any of the equation. Choosing equation 1, we have:
From Equation 1: x+y=23
When y=8,
x+8=23
x=23-8
x=15
When y=15
x+15=23
x=23-15
x=8
Therefore the values of the two numbers are 15 and 8
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18. A student turned in the following incorrect work. - In what line was the mistake made? - What should the correct step be? - What is the correct final answer?
Be sure to describe your answer in 4-5 sentences.
Answer:
4y³/x³
Step-by-step explanation:
Line 1 is completely correct.
Line 2 has an error.
The 4/1 from line 1 should remain as 4/1 in Line 2, but the student wrote it as 1/4 on Line 2.
To fix it, rewrite Line 2, but change the first fraction, 1/4, to 4/1.
The correct final answer is 4y³/x³
The length of a rectangular room is 12 feet more than 3 times the height of the room. The floor of the room has an area that is represented by the function below, where h is the height of the room in feet. A(R) 9h2 + 45h + 36 Which statement best describes the width of the room? A. The width is 3 feet shorter than the length. B. The width is 9 feet shorter than the length. C. The width is 9 feet longer than the height. D The width is 3 feet longer than the height.ill send a picture of the question
Okay, here we have this:
Considering the provided information, and that the area of a rectangle is the product of its length and width, we obtain the following:
[tex]\begin{gathered} Width=\frac{Area}{Length} \\ Width=\frac{9h^2+45h+36}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3\left(h+4\right)} \\ =3\mleft(h+1\mright) \\ =3h+3 \end{gathered}[/tex]Now, to know if the width is greater or less than the length, we will subtract it, then we have:
[tex]\begin{gathered} (3h+12)-(3h+3) \\ =3h+12-3h-3 \\ =12-3 \\ =9 \end{gathered}[/tex]Finally we obtain that the width is feet 9 shorter than the length, so the correct answer is the option B
Write three equations whose graphs are the same line as the equation x - 9y = 3/4
y= 1/9x
y= 1/9x +2/24
y = 1/9x + 3/36
1) To be on the same line, they must share the slope and their points
Let's rewrite that into the standard form
x -9y =3/4
-9y = 3/4 -x
9y = 3/4 +x Divide both sides by 9
y = 1/12 + x/9
y= x/9 + 1/12
2) Since we have the slope 1/9, then we can write the first equation as
y= 1/9x On the same line
y= 1/9x +2/24 2/24 is a multiple of 1/12, therefore on the same line
y = 1/9x + 3/36 3/36 is a multiple of 1/12, therefore on the same line
James spins a basketball on his finger and then passes the ball to his friend.
a. What type of transformation is used when James spins the basketball on
his finger?
b. What type of transformation is used to pass the basketball?
The types of transformations that occur as a result of the motion on the ball are;
A) Rotation
B) Translation
What is the type of transformation?Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.
Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.
Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.
Rotation is a method of transformation that involves turning a given figure at an angle about a reference point.
Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.
A) When James spins a basketball on his finger, it is clear that this transformation is rotation because it involves turning the ball at an angle about a given point.
B) When James passes the basketball, the transformation would be translation because it involves moving the ball from one point to another without changing the dimension of the ball.
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The perimeter of a triangle is 38 feet. One side of the triangle is one foot longer than the second side. The third side is four feet longer than the second side. Find the lengths of all three sides (in feet). (Enter your answers as a comma-separated list.)
The length of the three sides of the triangle are 11 feet, 12 feet and 15 feet.
How to find the length of a triangle?A triangle is a polygon with three sides.
The perimeter of a triangle is 38 feet.
The perimeter of the triangle is the sum of the whole three sides.
One side of the triangle is one foot longer than the second side.
let
the second side = x
longer side = x + 1
The third side is four feet longer than the second side.
Hence,
Third side = 4 + x
Therefore,
38 = x + x + 1 + x + 4
38 = 3x + 5
3x = 38 - 5
3x = 33
x = 33 / 3
x = 11
Therefore, the sides of the triangle are 11 ft, 12 feet and 15 ft.
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Simplify the following expression by expanding and collecting like terms.-(7x + 6) + 3(-5x – 3)Give your answer in the form ax + b.Provide your answer below:
ANSWER:
[tex]-22x-15[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]-\mleft(7x+6\mright)+3\mleft(-5x-3\mright)[/tex]We solve and reduce like terms, just like this:
[tex]\begin{gathered} -7x-6-15x-9 \\ (-7x-15x)+(-6-9) \\ (-22x)+(-15)=-22x-15 \end{gathered}[/tex]3х-7-(-2х) +9 simplify
Bruno's hourly salary is $8.75. Last week he worked only 18 hours. How much did he earn
A woman earned wages of $34,600, received $1500 in interest from a savings account, and contributed $2700 to a tax-deferred retirement plan. She was entitled to a personal
exemption of $2900 and had deductions totaling $5090. Find her gross income, adjusted gross income, and taxable income.
If She was entitled to a personal exemption of $2900 and had deductions totaling $5090. her gross income is $36,100, adjusted gross income is $33,400 , and taxable income is $25,410.
Gross incomeGross Income:
Gross Income= Wages + Interest received
Gross Income= 34,600 + $1500
Gross Income= $36,100
Adjusted Gross Income:
Adjusted Gross Income = Income - Tax Def Contribution
Adjusted Gross Income = $36,100- $2,700
Adjusted Gross Income = $33,400
Taxable Income :
Taxable Income = AGI - Deductions - Personal exemption
Taxable Income= $33,400- $5,090 - $2,900
Taxable Income= $25,410
Therefore her gross income is $36,100.
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60x-30/5=18. please help meeeeee. 10 pts worth.
Given the following sequences: I. 2,4,6,8,10... II.2,4,8,16,32... III. a,a + 2, a + 4, a + 6, a +8... Which ones are arithmetic sequences?
ANSWER
The arithmetic sequences are: I and iii
EXPLANATION
The formula for the nth term of an arithmetic sequence is:
[tex]a_n=a_1+d(n-1)[/tex]where a1 is the first term of the sequence and d is the common difference.
For the first sequence I. 2, 4, 6, 8, 10... we can find the common difference by subtracting the first term from the second:
[tex]\begin{gathered} a_2=a_1+d(2-1) \\ a_2=a_1+d \\ d=a_2-a_1 \\ d=4-2 \\ d=2 \end{gathered}[/tex]So the nth term of this sequence is:
[tex]a_n=2+2(n-1)[/tex]Each term of this sequence follows this rule. Therefore this is an arithmetic sequence.
For the second sequence II. 2, 4, 8, 16, 32... there's no common difference because between the first and second term there's a difference of 2, between the second and third there's a difference of 4, and this increases as we move through the sequence. Therefore this is not an arithmetic sequence.
For the third one, III. a, a+2, a+4, a+6, a+8... we can see that there is a common difference:
[tex]\begin{gathered} a_2_{}_{}=a_1+d(2-1) \\ d=a_2-a_1 \\ d=a+2-a \\ d=2 \end{gathered}[/tex]The rule for the nth term is:
[tex]a_n=a+2(n-1)[/tex]Let's find the first 5 terms:
[tex]\begin{gathered} a_1=a+2(1-1)=a \\ a_2=a+2(2-1)=a+2 \\ a_3=a+2(3-1)=a+4 \\ a_4=a+2(4-1)=a+6 \\ a_5=a+2(5-1)=a+8 \end{gathered}[/tex]This shows that each term follows the same rule. Therefore this is an arithmetic sequence.
A Christmas tree is supported by a wire that is 3 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 21 meters shorter than the height of the tree. What is the height of the tree?
The height of the Christmas tree is 12 meters
How to determine the height of the Christmas tree?Represent the height of the tree with h
So, we have the following parameters
Tree height = hBaseline = h - 21Anchor = h + 3The figure that illustrates the above parameters is added as an attachment
From the figure, we have the following equation by Pythagoras theorem
(h + 3)² = h² + (h - 21)²
Expand the exponents
h² + 6h + 9 = h² + h² - 42h + 441
Evaluate the like terms
6h + 9 = h² - 42h + 441
So, we have
h² - 48h + 432 = 0
Expand
h² - 36h - 12h + 432 = 0
Factorize the equation
(h - 36)(h - 12) = 0
Solve for h
h = 36 and h = 12
When h = 36, the baseline will be negative
So, we make use of h = 12
Hence, the tree has a height of 12 meters
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Discount Pricing A wool suit that was originally priced at $700 is on the 30%-off clearance rack. What is the sale price of the suit?
Answer:
Sale Price = $490
Explanation:
After 30% off, the sale price is 100% - 30% = 70% the original price.
70% of the original price is
[tex]\frac{70\%}{100\%}\times\$700=0.7\times\$700[/tex][tex]=\$490[/tex]which is our answer!
Hence, the sale price of the wool suit is $490.
Please Help With This.
The angle m∠FCD is 56°
Here the line CF is an angle bisector of ∠GCD.
By this we have,
∠GCF = ∠FCD
It is given that
∠GCF = ∠GCB - 12°
Let ∠GCB be x.
∠GCF = x - 12° = ∠FCD
BCD is a straight line which form 180°.
∠BCG + ∠GCF + ∠FCD = 180°
x + x - 12° + x - 12° = 180°
3x = 204°
x = 68°
∠FCD = x - 12°
= 68° - 12°
= 56°
Therefore m ∠FCD = 56°.
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3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.
3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.
________________________________
# of Chocolates Price Ratio (Price per chocloate)
Store A 36 pack box 54 54/ 36 = 3/2 = 1.5
Sotre B 6-pack boxes 12 12/ 6 = 2
_____________________________
Store A 1.5
______________________________
Answer
Store A offers a better deal
What is the unit rate of the graph below make sure you use answer include unit three point
Answer:
have you heard of the genger bread man
Step-by-step explanation:
Give a brief history about TRIANGLE NUMBERS, including Mathematicians that contributed for its development.
Brief history of triangle numbers
What is Triangle Number?
An equilateral triangle-shaped group of objects is counted using a triangular number or triangle number. Square and cube numbers are two further examples of figurate numbers, which also include triangle numbers.
Students are typically introduced to triangular numbers through the account of Carl Gauss, a well-known mathematician who used the concept of the triangle number formula to aid him with summing consecutive integers as a student. This tale and its applications in many situations are discussed in the article Clever Carl.
Triangular numbers were created by the Pythagoreans, who discovered connections between geometric forms and numbers, giving rise to triangular, square, pentagonal, and other numbers.
After four or five terms, students may recognize that the answer can be discovered by adding consecutive terms, according to our research. As an illustration, you may use the formulas 1+2+3+4+5 or 10 (the preceding term) + 5 to determine the fifth term. However, when students attempt to transition from this to the general formula for triangle numbers of
n(n+1)/2
Drawing triangle numbers is an exercise that could be helpful in establishing a connection between these two concepts.
The nth term and substitution into algebraic expressions can then be discussed using this formula. Sequences, notably quadratic sequences, can also be discussed.
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What's the radius of 5?
The formula for radius is
radius = diameter/2
If diameter = 5, then
radius = 5/2
radius = 2.5
use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph (without drawing the graph) a graph with 4 vertices, each of 2 degree 2