please when I send u this math explain it for me I'm only 12 and stuff is kinda hard to comprehend
Answers
First, we have to get rid of the parenthesis, to do that, we just multiply signs to get
[tex]-14-42[/tex]Now, we sum these numbers since they have the same signs
[tex]-14-42=-56[/tex]Therefore, the answer to (a) is -56.
The second operation is [tex]34+(-24)[/tex]We get rid of the parenthesis
[tex]34-24[/tex]Then, we subtract these numbers since they have different signs
[tex]34-24=10[/tex]Therefore, the answer to (b) is 10.
The third operation is[tex]-7+10[/tex]We just subtract these numbers since they have different signs
[tex]-7+10=3[/tex]Therefore, the answer to (c) is 3.
The fourth operation is[tex]-50+45[/tex]We just subtract
[tex]-50+45=-5[/tex]Therefore, the answer to (d) is -5.
The last operation is[tex]8+88[/tex]We just sum
[tex]8+88=96[/tex]Therefore, the answer to (e) is 96.
Related Questions
4-10x = 3+5x subtract 4 from both sides
Answers
S={1/15}
1) Solving that expression
4-10x = 3+5x Subtract 4 from both sides
4-4-10x=3-4+5x
-10x =-1+5x Subtract 5x from both sides, to isolate x on the left side
-10x -5x = -1 +5x -5x
-15x=-1 Divide both sides by -15 to get the value of x, not -15x
x=1/15
S={1/15}
I need help with some problems on my assignment please help
Answers
The circumcenter of a triangle is the center of a circumference where the three vertex are included. So basically we must find the circumference that passes through points O, V and W. The equation of a circumference of a radius r and a central point (a,b) is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]We have three points which give us three pairs of (x,y) values that we can use to build three equations for a, b and r. Using point O=(6,5) we get:
[tex](6-a)^2+(5-b)^2=r^2[/tex]Using V=(0,13) we get:
[tex](0-a)^2+(13-b)^2=r^2[/tex]And using W=(-3,0) we get:
[tex](-3-a)^2+(0-b)^2=r^2[/tex]So we have a system of three equations and we must find three variables: a, b and r. All equations have r^2 at their right side. This means that we can take the left sides and equalize them. Let's do this with the second and third equation:
[tex]\begin{gathered} (0-a)^2+(13-b)^2=(-3-a)^2+(0-b)^2 \\ a^2+(13-b)^2=(-3-a)^2+b^2 \end{gathered}[/tex]If we develop the squared terms:
[tex]a^2+b^2-26b+169=a^2+6a+9+b^2[/tex]Then we substract a^2 and b^2 from both sides:
[tex]\begin{gathered} a^2+b^2-26b+169-a^2-b^2=a^2+6a+9+b^2-a^2-b^2 \\ -26b+169=6a+9 \end{gathered}[/tex]We substract 9 from both sides:
[tex]\begin{gathered} -26b+169-9=6a+9-9 \\ -26b+160=6a \end{gathered}[/tex]And we divide by 6:
[tex]\begin{gathered} \frac{-26b+160}{6}=\frac{6a}{6} \\ a=-\frac{13}{3}b+\frac{80}{3} \end{gathered}[/tex]Now we can replace a with this expression in the first equation:
[tex]\begin{gathered} (6-a)^2+(5-b)^2=r^2 \\ (6-(-\frac{13}{3}b+\frac{80}{3}))^2+(5-b)^2=r^2 \\ (\frac{13}{3}b-\frac{62}{3})^2+(5-b)^2=r^2 \end{gathered}[/tex]We develop the squares:
[tex]\begin{gathered} (\frac{13}{3}b-\frac{62}{3})^2+(5-b)^2=r^2 \\ \frac{169}{9}b^2-\frac{1612}{9}b+\frac{3844}{9}+b^2-10b+25=r^2 \\ \frac{178}{9}b^2-\frac{1702}{9}b+\frac{4069}{9}=r^2 \end{gathered}[/tex]So this expression is equal to r^2. This means that is equal
Sean johnson 1. The angles of a triangle are described as follows: angle A is the largest angle: its measure is twice the measure of angle B. The measure of angle C is 2 less than half the measure of angle B. Find the measures of the three angles in degrees.
Answers
Explanation
Let
angle A is the largest angle
[tex]m\measuredangle A=m\measuredangle A[/tex]its measure is twice the measure of angle B,( in other words you have to multiply angle b by 2, to get angle A)
[tex]2(m\measuredangle B)=m\measuredangle A[/tex]Find the probability of obtaining exactly seven tails when flipping seven coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Answer:
Concept:
If you flip a coin once, there are
[tex]\text{2 possiblities}[/tex]Using the binomial probability formula below, we will have
[tex]P(x)=^nC_rp^xq^{x-r}[/tex]Where
[tex]\begin{gathered} p=probability\text{ of success} \\ q=probability\text{ of failure} \end{gathered}[/tex][tex]\begin{gathered} p=\frac{1}{2} \\ q=\frac{1}{2} \\ n=7 \\ x=7 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} P(x)=^nC_rp^xq^{x-r} \\ P(x=7)=^7C_7(\frac{1}{2})^7(\frac{1}{2})^{7-7} \\ P(x=7)=(\frac{1}{2})^7 \\ P(x=7)=\frac{1}{128} \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow\frac{1}{128}[/tex]NO LINKS!! Please help me with this probability question. 4a
Answers
=====================================================
Explanation:
mu = 500 = mean
sigma = 100 = standard deviation
We'll need the z score for x = 620
z = (x - mu)/sigma
z = (620-500)/100
z = 1.20
The task of finding P(x > 620) is equivalent to P(z > 1.20)
Use a Z table or a Z calculator to find that
P(Z < 1.20) = 0.88493
which leads to
P(Z > 1.20) = 1 - P(Z < 1.20)
P(Z > 1.20) = 1 - 0.88493
P(Z > 1.20) = 0.11507
This converts to 11.507% and rounds to 11.5%
About 11.5% of the students score higher than a 620 on the SAT.
-------------------------
Another approach:
Open your favorite spreadsheet program. The command we'll be using is called NORMDIST. The template is this
NORMDIST(x, mu, sigma, 1)
x = 620 = critical valuemu = 500 = meansigma = 100 = standard deviationThe 1 at the end tells the spreadsheet to use a CDF instead of PDF. Use 0 if you want a PDF value.If you were to type in [tex]\text{=NORMDIST(620,500,100,1)}[/tex] then you'll get the area under the normal distribution to the left of x = 620
This means [tex]\text{=1-NORMDIST(620,500,100,1)}[/tex] will get us the area to the right of 620. The result of that calculation is approximately 0.11507 which leads to the same answer of 11.5% as found earlier.
When using a spreadsheet, don't forget about the equal sign up front. Otherwise, the spreadsheet will treat the input as text and won't evaluate the command.
-------------------------
Another option is to use a TI83 or TI84 calculator.
Press the button labeled "2nd" in the top left corner. Then press the VARS key. Scroll down to "normalcdf"
The template is
normalcdf(L, U, mu, sigma)
L = lower boundaryU = upper boundarymu = mean sigma = standard deviationThe mu and sigma values aren't anything new here. But the L and U are. In this case L = 620 is the lower boundary and technically there isn't an upper boundary since it's infinity. Unfortunately the calculator wants a number here, so we just pick something very large. You could go for U = 99999 as the stand in for "infinity". The key is to make sure it's more than 3 standard deviations away from the mean.
So if you were to type in [tex]\text{normalcdf(620,99999,500,100)}[/tex] then the calculator will display roughly 0.11507, which is in line with the other answers mentioned earlier.
As you can see, there are many options to pick from. Searching out "normal distribution calculator" or "z calculator" will yield many free options. Feel free to pick your favorite.
Eighth grad Checkpoint: Understand functions 6NP Which of these relations are functions? Select all that apply. X y 20 -12 12 9 17 2 2013 11 14 -7 3 6 -8 15 16 6 -18 16 15 9 20 15 -9 -5 12 -13 4 20 -18 10 17 13 2. 8 15 Submit
Answers
In a function, any x-value is related to at most 1 y-value.
In the first table, x = 20 and x = 17 are related to 2 different y-values. Then, it is not a function.
In the second table, x = 9 is related to 2 different y-values. Then, it is not a function.
The third and fourth tables are functions
How do I do this, I’m unsure how to go about it
Answers
Given:
[tex]\sqrt{\frac{6}{x}}\cdot\sqrt{\frac{x^2}{24}}[/tex]Simplify:
[tex]=\sqrt{\frac{6}{x}}\cdot\frac{\sqrt{x^2}}{\sqrt{24}}=\sqrt{\frac{6}{x}}\cdot\frac{x}{2\sqrt{6}}[/tex]Apply the properties of fractions:
[tex]=\frac{\sqrt{\frac{6}{x}}x}{2\sqrt{6}}[/tex]Simplify:
[tex]=\frac{\frac{\sqrt{6}}{\sqrt{x}}x}{2\sqrt{6}}=\frac{\sqrt{6}\sqrt{x}}{2\sqrt{6}}[/tex]Eliminate common terms:
[tex]=\frac{\sqrt{x}}{2}[/tex]Answer:
[tex]\frac{\sqrt{x}}{2}[/tex]Which answer choice below is a solution to this equation?7x + 5 – 2x = 2x – 7A. 2B. 0C. -4D. 8
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
[tex]7x\text{ + 5 - 2 x = 2 x- 7}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 7\text{ x - 5 - 2 x = 2 x - 7} \\ 5x\text{ - 5 = 2x - 7} \\ collecting\text{ like terms, we have that:} \\ 5\text{ x - 2x = - 7 - 5} \\ 3\text{ x = - 12} \\ Divide\text{ both sides by 3, we have that:} \\ x\text{ =}\frac{-12}{3} \\ x\text{ = - 4 \lparen OPTION C \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 4 \lparen OPTION C\rparen}[/tex]
In TUV, the measure of V=90°, the measure of U=58°, and TU = 38 feet. Find the length of VT to the nearest tenth of a foot.
Answers
Answer:
32.2 feet
Explanation:
The diagram given is a right angled triangle
Using the SOH CAH TOA identity
Given the following
Hypotenuse = 38
Opposite = x
Sin theta = opposite/hypotenuse
Sin 58 = x/38
x = 38sin58
x = 38(0.8480)
x = 32.23
Hence the length of VT to the nearest tenth of a foot. is 32.2feet
3/4 divided by 3/5 how do you work the problem
Answers
We copy the first number, change the division sign to multiplication, then flip the second fraction
Cancel the three's
If you want to simplify the improper fraction, divide the numerator by the denominator
5/4 = 1 1/4
Find an equation for the line that passes through the points (-2,-6) and (6,-4).
Answers
Answer:
[tex](y+6)=\frac{2}{8} (x+2)[/tex]
Step-by-step explanation:
First, find the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
-4+6=2
6+2=8
m=2/8
With the slop, you have everything you need to stick one of your points in point-slope form. I chose (-2,-6)
[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]
Really, that's all you need as it is not an equation of a line. Not the most useful form, but works as an answer.
You spin the spinner once. What is P(2 or odd)?
Answers
Answer:
P(2 or odd)=1
Explanation:
The spinner has 3 parts.
The probability of spinning a 2:
[tex]P(2)=\frac{1}{3}[/tex]The probability of spinning an odd number (1, 3):
[tex]P(\text{odd)}=\frac{2}{3}[/tex]Therefore:
[tex]\begin{gathered} P(2\text{ or odd)=}\frac{1}{3}+\frac{2}{3} \\ =\frac{3}{3} \\ =1 \end{gathered}[/tex]Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
Answers
Write an equivalent fraction with the given denominator. (Only input numerator in final answer.) 2/3 = /24
we have 2/3
Multiply by 8/8
(2/3)(8/8)=16/24
therefore
the answer is 16David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.(Not sure if I'm expressing this correctly.)c = amount spent350 - c = 235c= 115
Answers
Given:
David had $350. After shopping, he was left with $235.
Required:
If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.
Explanation:
We know c is the amount spent
So,
Available amount = Total amount - spent amount
235 = 350 - c
c= 350 - 235
c = 115
Answer:
Hence, David spent $115.
Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.10-(-3,6)(-6,3(0,3)-10(-3,0)1010
Answers
Question:
Solution:
An equation of the circle with center (h,k) and radius r is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]This is called the center-radius form of the circle equation.
Now, in this case, notice that the center of the circle is (h,k) = (-3,3) and its radius is r = 3 so that the center-radius form of the circle would be:
[tex](x+3)^2+(y-3)^2=3^2[/tex]To obtain the general form, we must solve the squares of the previous equation:
[tex](x+3)^2+(y-3)^2-3^2\text{ = 0}[/tex]this is equivalent to:
[tex](x^2+6x+3^2)+(y^2-6y+3^2)\text{ - 9 = 0}[/tex]this is equivalent to
[tex]x^2+6x+9+y^2-6y\text{ = 0}[/tex]this is equivalent to:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]so that, the general form equation of the circle would be:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]thus, the correct answer is:
CENTER - RADIUS FORM:
[tex](x+3)^2+(y-3)^2=3^2[/tex]GENERAL FORM:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]what is 12 + 0.2 + 0.006 as a decimal and word form
Answers
twelve and two hundred six thousandths
If the price of bananas goes from $0.39 per pound to $1.06 per pound, what is the likely effect of quantity demanded?
Answers
When the price of bananas goes from $0.39 per pound to $1.06 per pound, the likely effect of quantity demanded is that it will reduce.
What is demand?The quantity of a commodity or service that consumers are willing and able to acquire at a particular price within a specific time period is referred to as demand. The quantity required is the amount of an item or service that customers will purchase at a certain price and period.
Quantity desired in economics refers to the total amount of an item or service that consumers demand over a given time period. It is decided by the market price of an item or service, regardless of whether or not the market is in equilibrium.
A price increase nearly invariably leads to an increase in the quantity supplied of that commodity or service, whereas a price decrease leads to a decrease in the quantity supplied. When the price of good rises, so does the quantity requested for that good. When the price of a thing declines, the demand for that good rises.
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Help with these two questions please. Match the sentence with a word
Answers
EXPLANATION
Given that two angles form a linear pair, we can assevere that the postulate that applies is the Linear Pair Postulate.
Identity the triangle congruence postulate (SSS,SAS,ASA,AAS, or HL) that proves the triangles are congruent. I will mark brainliest!!!
Answers
SSS, or Side Side Side
SAS, or Side Angle Side
ASA, or Angle Side Side
AAS, or Angle Angle Side
HL, or Hypotenuse Leg, for right triangles only
Side Side Side Postulate
A postulate is a statement taken to be true without proof. The SSS Postulate tells us,
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Congruence of sides is shown with little hatch marks, like this: ∥. For two triangles, sides may be marked with one, two, and three hatch marks.
If △ACE has sides identical in measure to the three sides of △HUM, then the two triangles are congruent by SSS:
Side Angle Side Postulate
The SAS Postulate tells us,
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
△HUG and △LAB each have one angle measuring exactly 63°. Corresponding sides g and b are congruent. Sides h and l are congruent.
A side, an included angle, and a side on △HUG and on △LAB are congruent. So, by SAS, the two triangles are congruent.
Angle Side Angle Postulate
This postulate says,
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
We have △MAC and △CHZ, with side m congruent to side c. ∠A is congruent to ∠H, while ∠C is congruent to ∠Z. By the ASA Postulate these two triangles are congruent.
Angle Angle Side Theorem
We are given two angles and the non-included side, the side opposite one of the angles. The Angle Angle Side Theorem says,
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Here are congruent △POT and △LID, with two measured angles of 56° and 52°, and a non-included side of 13 centimeters:
[construct as described]
By the AAS Theorem, these two triangles are congruent.
HL Postulate
Exclusively for right triangles, the HL Postulate tells us,
Two right triangles that have a congruent hypotenuse and a corresponding congruent leg are congruent.
The hypotenuse of a right triangle is the longest side. The other two sides are legs. Either leg can be congruent between the two triangles.
Here are right triangles △COW and △PIG, with hypotenuses of sides w and i congruent. Legs o and g are also congruent:
[insert congruent right triangles left-facing △COW and right facing △PIG]
So, by the HL Postulate, these two triangles are congruent, even if they are facing in different directions.
Proof Using Congruence
Proving Congruent Triangles 5
Given: △MAG and △ICG
MC ≅ AI
AG ≅ GI
Prove: △MAG ≅ △ICG
Statement Reason
MC ≅ AI Given
AG ≅ GI
∠MGA ≅ ∠ IGC Vertical Angles are Congruent
△MAG ≅ △ICG Side Angle Side
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree. a. 87 ft b. 74 ft c. 65 ft d. 63 ft
Answers
Given the information on the picture, we have the following right triangle:
we can use the tangent trigonometric function to find the height of the tree:
[tex]\begin{gathered} tan(44)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{h}{90} \\ \Rightarrow\tan (44)=\frac{h}{90} \end{gathered}[/tex]solving for h, we get:
[tex]\begin{gathered} \frac{h}{90}=\tan (44) \\ \Rightarrow h=90\cdot\tan (44)=86.9\approx87 \\ h=87ft \end{gathered}[/tex]therefore, the height of the tree is 87 ft
Am I correct? I need some clarification on this practice problem solving I have attempted this problem but for some reason I feel like I may be wrong
Answers
Solution:
The modulus of a complex number;
[tex]z=a+bi[/tex]is denoted by;
[tex]|z|=|a+bi|=\sqrt[]{a^2+b^2}[/tex]Thus, given the complex number;
[tex]2-6i[/tex]The modulus is;
[tex]\begin{gathered} a=2,b=-6 \\ |2-6i|=\sqrt[]{2^2+(-6)^2} \\ |2-6i|=\sqrt[]{4+36} \\ |2-6i|=\sqrt[]{40} \\ |2-6i|=\sqrt[]{4\times10} \\ |2-6i|=\sqrt[]{4}\times\sqrt[]{10} \\ |2-6i|=2\times\sqrt[]{10} \\ |2-6i|=2\sqrt[]{10} \end{gathered}[/tex]ANSWER:
[tex]2\sqrt[]{10}[/tex]What is the slope of a line parallel to the line whose equation is 5x-3y=18
Answers
Slope and slant both refer to an incline away from a reference surface or line that is generally straight.The definition of slope is "a vertical inclination in an oblique direction"Here, the land abruptly slopes either upward or downhill.
How to Determine a Line's Slope?
slope,The inclination of a line with respect to the horizontal is measured numerically.The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). To determine how much the y coordinates have changed, find the difference.To determine how much the x coordinates have changed, find the difference.Find the slope by dividing y by x.
Y=mx+b, where m is the slope and b is the y-intercept, is the slope-intercept form.
y=mx+b
Change the formula to 3y+18=5x.
−3y+18=5x
From both sides of the equation, deduct 18.
−3y=5x−18
Simplify by multiplying each term in 3y=5x18 by 3.
Subtract 3 from each term in 3y=5x18.
−3y/−3=5x/−3+−18/−3
Make the left side simpler.
Tap to take additional steps:Y= -5X/3+-18/-3
Make the right side simpler.
Tap to take additional steps: y=5x/3+6
Write in the form y=mx+b.
Tap to take additional steps: y=5/3x+6
The slope is- 5/3 using the slope-intercept form.
.
m=−5/3
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If Lanny spins the spinner below 70 times, how many times can he expect is to land on a number divisible by 3? *
Answers
From 1 to 10, there are 3, 6, and 9 are divisible by 3
Then we have 3 choices out of 10 numbers
Since the probability = an event/outcomes
Since the event is 3
Since the outcomes are 10, then
[tex]P(\frac{no}{3})=\frac{3}{10}[/tex]This is the probability for spinning the spinner one time
But we need to spin it 70 times
We will multiply 3/10 by itself 70 times, which means make it to the power of 70
[tex]P(\frac{no}{3})=(\frac{3}{10})^{70}[/tex]The answer is (3/10)^70 OR (0.3)^70
Find the distance between the following points using the pythagorean theorem (5,10) and (10,12)
Answers
Answer:
\sqrt[29]
Explanation:
Given the coordinate (5,10) and (10, 12). The formula for calculating the distance between two points is expressed as;
[tex]D\text{ =}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]Given that;
x1 = 5
y1 = 10
x2 = 10
y2 = 12
Substitute:
[tex]\begin{gathered} D\text{ = }\sqrt[]{(10-5)^2+(12-10)^2} \\ D=\text{ }\sqrt[]{5^2+2^2} \\ D\text{ =}\sqrt[]{25+4} \\ D\text{ =}\sqrt[]{29} \end{gathered}[/tex]Hence the distance between the points is \sqrt[29]
The System of PolynomialsYou are aware of the different types of numbers: natural numbers, integers, rational numbers, and real numbers. Now you will work with a property of the number system called the closure property. A set of numbers is closed for a specific mathematical operation if you can perform the operation on any two elements in the set and always get a result that is an element of the set.Consider the set of natural numbers. When you add two natural numbers, you will always get a natural number. For example, 3 + 4 = 7. So, the set of natural numbers is said to be closed under the operation of addition.Similarly, adding two integers or two rational numbers or two real numbers always produces an integer, or rational number, or a real number, respectively. So, all the systems of numbers are closed under the operation of addition.Think of polynomials as a system. For each of the following operations, determine whether the system is closed under the operation. In each case, explain why it is closed or provide an example showing that it isn’t.1)AdditionType your response here:2)SubtractionType your response here:3)MultiplicationType your response here:4)DivisionType your response here:5)Determine whether the systems of natural numbers, integers, rational numbers, irrational numbers, and real numbers are closed or not closed for addition, subtraction, multiplication, and division.Type your response here: 6)Addition Subtraction Multiplication Division natural numbers integers rational numbers irrational numbers real numbers When a rational and an irrational number are added, is the sum rational or irrational? Explain.Type your response here:7)When a nonzero rational and an irrational number are multiplied, is the product rational or irrational? Explain.Type your response here:8)Which system of numbers is most similar to the system of polynomials?Type your response here:9)For each of the operations—addition, subtraction, multiplication, and division—determine whether the set of polynomials of order 0 or 1 is closed or not closed. Consider any two polynomials of degree 0 or 1.Type your response here:10)Polynomial 1 Polynomial 2 Operation Expression Result Degree of Resultant Polynomial Conclusion addition subtraction multiplication division What operations would the set of quadratics be closed under? For each operation, explain why it is closed or provide an example showing that it isn’t.Type your response here:11)Is there a set of expressions that would be closed under all four operations? Explain.Type your response here:
Answers
The Solution To Question Number 10:
The question says what operations would the set of quadratics be closed under.
Let the sets of quadratics be
[tex]\begin{gathered} p(x)=ax^2+bx+c \\ q(x)=mx^2+nx+k \end{gathered}[/tex]The set of two quadratics (polynomials) is closed under Addition.
Explanation:
[tex]\begin{gathered} P(x)+q(x)=(ax^2+bx+c)+(mx^2+nx+k) \\ =(a+m)x^2+(b+n)x+(c+k) \\ \text{which is still a quadratic.} \\ \text{Hence, the set of quadratics is closed under Addition.} \end{gathered}[/tex]The set of two quadratics is closed under Subtraction.
[tex]\begin{gathered} P(x)-q(x)=(ax^2+bx+c)-(mx^2+nx+k) \\ =(a-m)x^2+(b-n)x+(c-k) \\ \text{which is still a quadratic, provided both a}\ne m,\text{ b}\ne n\text{ } \\ \text{Hence, the set of quadratics is closed under Subtraction.} \end{gathered}[/tex]The set of quadratics is not closed under Multiplication.
[tex]\begin{gathered} P(x)\text{.q(x)}=(ax^2+bx+c)(mx^2+nx+k)=amx^4+(bn+ak)x^2+ck+\cdots \\ \text{Which is not a quadratic.} \\ \text{Hence, the set of quadratics is not closed under multiplication.} \end{gathered}[/tex]The set of quadratics is not closed under Division.
[tex]\begin{gathered} \text{Let the sets be f(x)=8x}^2\text{ and} \\ h(x)=2x^2-1 \\ \text{ So,} \\ \frac{f(x)}{h(x)}=\frac{8x^2}{2x^2_{}-1} \\ \text{Which is not a quadratic.} \\ \text{Hence, the set is not closed under Division.} \end{gathered}[/tex]
Find 5 number summary for data given
Answers
The 5 number summary of the data given is:
Minimum = 59
Q1 = 66.50
Median = 78
Q3 = 90
Maximum = 99
What is the 5 number summary?A stem and leaf plot is a table that is used to display a dataset. A stem and leaf plot divides a number into a stem and a leaf. The stem is the first digit in a number while the leaf is the second digit in the number.
The minimum is the smallest number in the stem and leaf plot. This is 59. Q1 is the first quartile.
Q1 = 1/4 x (n + 1)
Where n is the total number in the dataset
1/4 x 19 = 4.75 term
(64 + 69) / 2 = 66.50
Q3 is the third quartile.
Q1 = 3/4 x (n + 1)
Where n is the total number in the dataset
3/4 x 19 = 14.25 term = 90
The median is the number that is at the center of the dataset.
Median = 1/2(n + 1)
1/2 x 19 = 8.5 term
(76 + 80) / 2 = 78
The maximum is the largest number in the dataset. This number is 99.
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Express the answer in simplest formIf A die is rolled one time find the probability of
Answers
Solution
If A die is rolled one time find the probability of getting an even number
The total number in a die rolled once = 6
number of even number = 3
Probability = number of required outcome / number of possible outcome
[tex]\begin{gathered} Pr(evene\text{ number\rparen = number of even / total number} \\ Pr(even)\text{ = 3/6} \\ =\frac{1}{2} \end{gathered}[/tex]Therefore the probability of getting an even number = 1/2
help with this functions and equations question. please answer correctly
Answers
The distance D(t) Maya travels in her racecar and the times taken, given in the table indicates the average rate of change of distance over the specified times are;
(a) 30.3 meters per second
(b) 25.4 meters per second
What is the average rate of change of a function?The average rate of change of a function, over an interval, gives the rate at which the function changes per unit of the interval.
The average rate of change of the distance is given by the equation;
[tex] \displaystyle {Average \: rate \: of \: change = \frac{The \: sum \: of \: distance \: traveled }{The \: sum \: of \: the \: time taken } }[/tex]
The following values are obtained from the given table;
(a) At time t = 0 seconds, distance traveled, D(0) = 0 meters
At time t = 5 seconds, distance traveled, D(5) = 151.5 meters
Which gives the average rate of change as follows;
[tex] \displaystyle {Average \: rate \: of \: change = \frac{(151.5 - 0) \: m }{(5 - 0 ) \: s} = 30.3 \: m/s }[/tex]
The average rate of change for distance driven is 30.3 meters per second(b) The table gives that at time, t = 7 seconds, distance traveled, D(7) = 205.1 meters and that at time t = 9 seconds, distance traveled, D(9) = 255.9 meters, which gives;
[tex] \displaystyle {Average \: rate \: of \: change = \frac{(255.9 - 205.1) \: m }{(9 - 7) \: s} = 25.4 \: m/s }[/tex]
The average rate of change of distance between the points in time of 7 seconds and 9 seconds is 25.4 meters per secondLearn more about the average rate of change of a function here:
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Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P,P, in terms of x,x, representing Madeline's total pay on a day on which she sells xx computers.
I need equation
Answers
The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.
Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We can model the equation for Madeline's total pay as follows -
P = base pay + (number of sold computer) × (cost of 1 computer)
P = 80 + 20x
Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x
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Function g is defined as g(x)=f (1/2x) what is the graph of g?
Answers
Answer:
D.
Explanation
We know that g(x) = f(1/2x)
Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).
It means that f(-2) = 0 and f(2) = 0
Then, g(-4) = 0 and g(4) = 0 because
[tex]\begin{gathered} g(x)=f(\frac{1}{2}x_{}) \\ g(-4)=f(\frac{1}{2}\cdot-4)=f(-2)=0 \\ g(4)=g(\frac{1}{2}\cdot4)=f(2)=0 \end{gathered}[/tex]Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.
