Answer:
2
Step-by-step explanation: 2 can be divided by 644532
Which of the following shows the division problem down below
Question:
Solution:
Synthetic division is a quick method of dividing polynomials; it can be used when the divisor is of the form x-c. In synthetic division, we write only the essential parts of the long division. Notice that the long division of the given problem is written as:
thus, the synthetic division of the given problem would be:
Writing 6 instead of -6 allows us to add instead of subtracting. We can conclude that the correct answer is:
A.
The graph shows the first four ordered pairs formed by the corresponding terms of two patterns. Which ordered pair would be the fifth point on this graph? (4,12) (12,4) (12,8) (10, 4) Q1 6 7 8 9 10 11 12
As shown in the graph:
There are four points:
(0,0) , (3, 1) , ( 6, 2) and ( 9, 3)
The points represent a proportion relation between x and y
The relation will be:
[tex]y=\frac{1}{3}x[/tex]So, the fifth point will be: ( 12, 4)
determine the missing angle measures in each triangle
ANSWER:
50°
STEP-BY-STEP EXPLANATION:
We can calculate the value of the missing angle, since there is a right angle (that is, 90°) and the other is 40 °, we apply the property that says that the sum of all the internal angles of a triangle is equal to 180°, Thus:
[tex]180=90+40+x[/tex]Solving for x:
[tex]\begin{gathered} x=180-90-40 \\ x=50\text{\degree} \end{gathered}[/tex]Please help me solve this math problemRewrite in exponential form Ln3=y
1) Let's rewrite it as a logarithmic expression of the following exponential one. Let's do it step by step.
[tex]\begin{gathered} e^6=x \\ \ln e^6=\ln x \\ \ln(x)=6 \end{gathered}[/tex]Note that when we apply the natural log on both sides, we use one of those properties that tell us that we can eliminate the log since the base of a natural log is "e", as well as, "e" is the base of that power.
2) To rewrite in the exponential form we can do the following:
[tex]\ln(3)=y\Leftrightarrow e^y=3[/tex]Note that in this case, we have used the definition of logarithms.
Hi, can you help me answer this question please, thank you!
Let x be a random variable representing the blood pressures of adults in the USA. Since it is normally distributed, we would apply the formula for determining z score which is expressed as
z = (mean - population mean)/standard deviation
From the information given,
population mean = 121
Standard deviation = 16
For stage 2 high blood pressure, the probability is
P(x greater than or equal to 160). It is also equal to 1 - P(x < 160)
Thus, for x = 160, we have
z = (160 - 121)/16 = 2.4375
From the standard normal distribution table, the probability value corresponding to a z score of 2.4375 is 0.9927
P(x < 160) = 0.9927
P(x greater than or equal to 160) = 1 - 0.9927 = 0.0073
Converting to percentage, it is 0.0073 * 100 = 0.73%
b) If 2000 peaople were sampled, the number of people with stage 2 high blood pressure would be
0.73/100 * 2000 14.6
To the nearest person, it is 15 people
c) For stage 1, the probability is
P(140 < x < 160)
For x = 140,
z = (140 - 121)/16 = 1.1875
From the standard normal distribution table, the probability value corresponding to a z score of 1.1875 is 0.883
Recall, for x = 160, the probaility is 0.9927
Thus,
P(140 < x < 160) = 0.9927 - 0.883 = 0.1097
Converting to percentage, it is
0.1097 * 100 = 10.97%
d) The 30th percentile refers to all values of blood pressure below k, where k is the 30th percentile. This means that we would find
P(x < k) = 0.3
The z score corresponding to a probability value of 0.3 is - 0.52
Thus,
(k - 121)/16 = - 0.52
k - 121 = - 0.52 * 16 = - 8.32
k = - 8.32 + 121
k = 112.68
The pressure for the 30th percentile is 112.68
Find the distance and the midpoint for each set of points given
Given,
The coordinates of the points are (2,6) and (7, 2).
Required:
The distance between the points and the midpoint of the points.
The distance between two points is calculated as,
[tex]\begin{gathered} Distance\text{ =}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt{(7-2)^2+(2-6)^2} \\ =\sqrt{5^2+4^2} \\ =\sqrt{25+16} \\ =\sqrt{41} \\ =6.4 \end{gathered}[/tex]Hence, the distance between the points is 6.4
The midpoint is calculated as,
[tex]\begin{gathered} Midpoint=(\frac{2+7}{2},\frac{6+2}{2}) \\ =\frac{9}{2},\frac{8}{2} \\ =(4.5,4) \end{gathered}[/tex]Hence, the midpoint is (4.5,4).
I need you to make a problem and solve it on the side and explain how explain it I’m making a practice test and I can show you examples of how I did the others This are the topics you can choose fromTopic 1: is the relation a function- domain and range Topic 2: zero is of a function
For topic (1), we have the following question:
Which of the following is a function: y=x² or x=y²?
Identify domain and range of each equation.
We can identify a given relation if it is a function or not by identifying the number of possible values of y.
The equations below are both relations.
[tex]y=x^2\text{ and }x=y^2[/tex]However, only one of them is a function.
For the first equation, note that for each value of x, there is only one value of y. Some of the points on the equation are as follows.
[tex]\begin{gathered} x=-2 \\ y=x^2^{} \\ y=(-2)^2=4 \\ \\ x=0 \\ y=x^2 \\ y=0^2=0 \\ \\ x=2 \\ y=x^2 \\ y=2^2 \\ y=4 \end{gathered}[/tex]Thus, the equation passes through the following points.
[tex](-2,4),(0,0),(2,4)[/tex]Notice that no value of x is repeated. Therefore, the given relation is a function.
We can also determine it using graphs. The image below is the graph of the first equation.
If we test it using the vertical line test, no vertical line can pass through the graph twice. Therefore, it shows that the equation is a function.
On the otherhand, the other equation is not a function. This is because when we substitute -2 and 2 to the value of y, we will have the same value of x, which is equal to 4.
[tex]\begin{gathered} y=-2^{} \\ x=y^2 \\ x=(-2)^2=4 \\ \\ y=2 \\ x=y^2^{} \\ x=2^2=4 \end{gathered}[/tex]Since there are two values of y for only one value of x, the equation must not be a function.
To illustrate this using its graph, we can notice that the vertical line below passes through two points on the graph when x=4.
Therefore, the second equation is not a function.
As for the domain and range, we can obtain it from both graphs.
The domain the set of all possible values of x. Thus, for the first equation, since it extends indefinitely to the left and right, the domain must be from negative infinity to positive infinity.
[tex]D_1\colon(-\infty,\infty)[/tex]On the otherhand, since the second equation extends indefinitely to the right from 0, the domain must be from 0 to positive infinity, inclusive.
[tex]D_2\colon\lbrack0,\infty)[/tex]As for the range, it is the set of all possible values of y.
Thus, for the first equation, since the graph extends indefinitely upwards from 0, the range must be from 0 to positive infinity, inclusive.
[tex]R_1\colon\lbrack0,\infty)[/tex]On the otherhand, the graph of the second equation extends indefinitely upwards and downwards. Thus, its range must be from negative infinity to positive infinity.
[tex]R_2\colon(-\infty,\infty)[/tex]To summarize, here are the questions and the answers for each question.
Which of the following is a function: y=x² or x=y²?
Answer: y=x²
Identify domain and range of each equation.
Answer:
For y=x²:
[tex]\begin{gathered} D\colon\text{ (-}\infty,\infty\text{)} \\ R\colon\lbrack0,\infty) \end{gathered}[/tex]For x=y²:
[tex]\begin{gathered} D\colon\lbrack0,\infty) \\ R\colon(-\infty,\infty) \end{gathered}[/tex]what is x^4 − 14x2 + 45 as factored
Answer: B=3
Step-by-step explanation:
Some airlines charge a fee for each checked luggage item that weighs more than 21,000 grams. How many kilograms is this?
The value of 21,000 grams to kilograms is 21 kilograms
How to convert kilograms to grams ?1000 grams = 1kg
The first step is to convert 21,000 grams to kilograms
It can be calculated as follows;
= 21000/1000
= 21
Hence the value of 21,000 grams in kilograms is 21 kilograms
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make a conjecture about each value or geometric relationship.
The relationship between the angles of a triangle with all sides congruent.
Congruence of all sides implies congruence of all angles. All of the angles line up.
What is geometric conjecture?
According to Thurston's geometrization conjecture in mathematics, each of a select group of three-dimensional topological spaces has a distinctive geometric structure that can be connected to it.
How do the angles of a triangle with congruent sides relate to one another?
We refer to a triangle as being equilateral when its three sides are congruent. We add a slash mark to the sides that are congruent. An equilateral triangle always has 60° angles.Learn more about congruent
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The diameter of a circle is 6 ft. Find its circumference in terms of \piπ.
The circumference of circle with diameter 6 feet will be 6π feet.
According to the question,
We have the following information:
Diameter of the circle = 6 feet
Now, we will find the radius of the circle. We know that the radius of the circle is half that of its diameter.
Radius of the circle = Diameter/2
Radius of the circle = 6/2 feet
Radius of the circle = 3 feet
We know that the following formula is used to find the circumference of the circle:
Circumference of the circle = 2πr
Circumference of the circle = 2π*3
Circumference of the circle = 6π feet
Hence, the circumference of the circle is 6π feet.
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Natural Logs Propertydo not include any spaces when trying to type in your answer if you have an exponent use ^
Given:
[tex]ln\mleft(e^{2x}\mright)+ln\mleft(e^x\mright)[/tex]To simplify:
Applying the log rule,
[tex]\log _c\mleft(a\mright)+\log _c\mleft(b\mright)=\log _c\mleft(ab\mright)[/tex]We get,
[tex]\begin{gathered} ln(e^{2x})+ln(e^x)=\ln (e^{2x}\cdot e^x) \\ =\ln (e^{3x}) \\ =3x(\ln e) \\ =3x(1) \\ =3x \end{gathered}[/tex]Hence, the answer is 3x.
If f(x) = 8x2 - 18x + 5, find when f(x) = -4
Setting the given equation equals -4 we get:
[tex]\begin{gathered} 8x^2-18x+5=-4 \\ 8x^2-18x+5+4=0 \\ 8x^2-18x+9=0 \end{gathered}[/tex]Notice that:
[tex]8x^2-18x+9=8(x^2-\frac{9}{4}x+\frac{9}{8})=8(x-\frac{3}{2})(x-\frac{3}{4})[/tex]Therefore, f(x)=-4 when x=3/2 or x=3/4.
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 35 N acts on a certain object, the acceleration of the object is 5 m/s^2. If the force is changed to 49 N what will be the acceleration of the object?
Answer:The acceleration that an objects gains is given by the mass of the object.
If the acceleration of the object becomes 5 m/s² the force is 15 N.
Reason:
The given parameters are;
The acting force ∝ The acceleration of the object.
The acceleration given by an amount of force, F, of 18 N = 6 m/s²
Required:
The force acting on the object acceleration, a, is 5 m/s².
Solution:
According to Newton's Second Law of motion, we have;
F = m·a
Where;
m = The mass of the object
Therefore, we have;
From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the
given object is given as follows;
The force acting when the the acceleration, a = 5 m/s², is therefore;
F = 3 kg × 5 m/s² = 15 N
If the acceleration of the object becomes 5 m/s² the force is 15 N.
Step-by-step explanation:
Describe the two different methods shown for writing the complex expression in standard form. Which method do you prefer? Explain
The first method simlpy executes the distributive property of multiplication over addition, and the definition of the imaginary number, i.
The second method factored out 4i first then perform the operation on the terms left inside the parenthesis , then executes the distributive property of multiplication over addition and the definition of the imaginary number, i.
I prefer the first method . It's simple and straight forward,
24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas Choose the correct letter
Since 24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas
These are 2 equal ratios, then
They will be 2 equal fractions
[tex]\frac{24\text{ miles}}{1\text{ gallon}}=\frac{60\text{ miles}}{2.5\text{ gallons}}[/tex]The correct answer is D
A sporting goods store charges $22.00 for a football before tax. The store holds a sale that marks all prices down by 20% before tax. If the sales tax is 5%, what is the cost of the discounted football after tax?
The cost of the discounted football after applying the tax is $18.48
Discount:
Discount refers the difference between the price paid for and it's par value. Discount is a sort of reduction or deduction in the cost price of a product.
Given,
A sporting goods store charges $22.00 for a football before tax. The store holds a sale that marks all prices down by 20% before tax.
Here we need to calculate the cost of the discounted football after the tax of 5%.
We know that the cost of the football is $22.00 before tax.
So, if we apply the discount of 20% on it , then the cost of the foot ball is,
Discount = 22 x 20/100
Discount = 4.4
So, the cost of the foot ball after discount is,
=> 22 - 4.4
=> 17.6
Now, we have to apply the tax 5% on it, then we get,
=> 17.6 x 5/100
=> 17.6 x 0.05
=> 0.88
Therefore, the cost of the discounted football after the tax of 5% is.
=> 17.6 +0.88
=> 18.48
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1. Which scatter plot could have a trend line whose equation is y - 3x + 10 (A) 60 60 40 40 20 20 0 y M 10 20 0 10 20 D . 12 60 8 40 4 29 0 10 220 0 10 10 20
Explanation
Given the trend line equation that defines a scatter plot
We will have to substitute the values of x = 2.5,5,7.5,10,15,20 and check the graphs
So, when x =2.5
[tex]\begin{gathered} y=3(2.5)+10=7.5+10=17.5 \\ y=17.5 \end{gathered}[/tex]when x=5
[tex]\begin{gathered} y=3(5)+10=15+10 \\ y=25 \end{gathered}[/tex]When x= 7.5
[tex]y=3(7.5)+10=32.5[/tex]When x =10
[tex]\begin{gathered} y=3(10)+10=40 \\ y=40 \end{gathered}[/tex]If we check all the values obtained to the graph, we will discover that the best option will be
Option B is more correct
Because most of the points conform to the trend line equation
A saw blade is rotating at 2700 revolutions per minute. Find theangular speed in radians per second.
The rule of the angular speed is
[tex]\omega=No\text{ of revolution per min }\times\frac{2\pi}{60}[/tex]Since the number of revolutions is 2700 per min, then
[tex]\begin{gathered} \omega=2700\times\frac{2\pi}{60} \\ \\ \omega=90\pi\text{ rad per sec} \end{gathered}[/tex]The answer is 90pi rad per second
The answer is the 3rd answer
need two column proof I'm not understanding how the process with a midpoint and difference with a bisect
we have that
GJ=JL -------> given
so
1) HJ=JK ------> by GL bisects HK
2) m by vertical angles
3) triangle GJH is congruent with triangle LJK ------> by SAS theorem
find the x value (6x+9)° (4x-19)°
In this problem m and n are parallel lines, and the first angle is an exteriar angle an the secon is a interior angle.
this two condition give us that the two angles are complementary anlges so the sum of them should be 180 so:
[tex]6x+9+4x-19=180[/tex]and we can solve for x so:
[tex]\begin{gathered} 10x-10=180 \\ 10x=180+10 \\ x=\frac{190}{10} \\ x=19 \end{gathered}[/tex]The number of microbes in a tissue sample is given by the functionN (t) = 34.8 + In(1 + 1.2t)where N(t) is the number of microbes (in thousands) in the sample after thours.a.) How many microbes are present initially?b.) How fast are the microbes increasing after 10 hours?
Explanation
[tex]N(t)=34.8+\ln (1+1.2t)[/tex]we have a function where the number of microbes ( N) depends on the time(t)
hence
Step 1
a.) How many microbes are present initially?
to know this, we need replace time I= t = zero, because it was "initially"
so
when t=0
replace.
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(0)=34.8+\ln (1+1.2\cdot0) \\ N(0)=34.8+\ln (1) \\ N(0)=34.8+0 \\ N(0)=34.8 \end{gathered}[/tex]so, initially there were 34.8 microbes
Step 2
b)How fast are the microbes increasing after 10 hours?
to know this, let t=10
so
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(10)=34.8+\ln (1+1.2\cdot10) \\ N(10)=34.8+\ln (1+12) \\ N(10)=34.8+\ln (13) \\ N(10)=34.8+2.56 \\ N(10)=37.36 \end{gathered}[/tex]therefore , after 10 hours the number of microbes is 37.36
I hope this helps you
While waiting for the school bus, Michiko records the colors, of all cars passing through an intersection. Thetable shows the results, Estimate the probability that the next car through the intersection will be red. Exgressyour answer as a percent. If necessary, round your anewer to the nearest tenth
Given the following question:
Estimate the probability that the next car will be red.
11, 24, 16, 9
[tex]\begin{gathered} 11\text{ + 24}=35 \\ 35\text{ + 16 = 51} \\ 51\text{ + 9 = }60 \\ 60=100\text{per} \end{gathered}[/tex][tex]p=\frac{11}{60}[/tex][tex]\frac{11}{60}\times100=18.333333[/tex][tex]\begin{gathered} 18.333333 \\ 3\text{ < 5} \\ 18.3 \end{gathered}[/tex]18.3% or the first option.
15.) In the accompanying diagram, ABC is a straight line and BE bisects 4DBC. If m4ABD = 2x and m4DBE = 2x + 15, find m&ABD.
Using bisection, the measure of angle ABD is of m<ABD = 50º.
What is the bisection of an angle?The bisection of an angle is when the angle is divided into two angles of equal measure.
In the context of this problem, we have that the angle BE bisects the angle DBC, hence the measures of these angles are given as follows:
mDBE = mEBC = 2x + 15.
As shown in the diagram, the entire line forms a ray, meaning that the sum of the measures of the angles is of 180º, hence we can solve for x as follows:
2x + 2(2x + 15) = 180º
2x + 4x + 30 = 180º
6x = 150º
x = 150º/6
x = 25º.
Then the measure of angle ABD is found as follows:
m<ABD = 2x = 2(25) = 50º.
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Which of the following are solutions to the inequality below? Select all that apply.
The first step to solving this problem is to put the variable on one side. Thus, you must move 7 to the right side to make [tex]\frac{f}{25} \leq -3[/tex]
Next, you must multiply the 25 to the right side to isolate the variable
You get [tex]f \leq -75[/tex]
With this explained, the answer would be the second option (f=-75)
Hope this helped :)
solve 2x^2+5x-3>0 quadratic inequalities
The solution set of the inequality 2 · x² + 5 · x - 3 > 0 is (- ∞, - 3) ∪ (1 / 2, + ∞).
How to solve a quadratic inequality
Herein we find a quadratic inequality, whose solution set can be found by factoring the expression and determine the interval where the expression is greater than zero. Initially, we use the quadratic formula to determine the roots of the quadratic function:
2 · x² + 5 · x - 3 = 0
x₁₂ = [- 5 ± √[5² - 4 · 2 · (- 3)]] / (2 · 2)
x₁₂ = (- 5 ± 7) / 4
x₁ = 1 / 2, x₂ = - 3
Then, the factored form of the inequality is:
(x - 1 / 2) · (x + 3) > 0
In accordance with the law of signs, we must look for that intervals such that: (i) (x - 1 / 2) > 0, (ii) (x + 3) > 0, (ii) (x - 1 / 2) < 0, (x + 3) < 0. Then, the solution set of the quadratic inequality is:
Inequality form - x > 1 / 2 ∨ x < - 3
Interval form - (- ∞, - 3) ∪ (1 / 2, + ∞)
The solution set of the inequality is (- ∞, - 3) ∪ (1 / 2, + ∞).
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how do I solve (4w+3x+5)-(4w-3x+2)
Answer:
6x + 3
Explanation:
To solve the initial expression, we need to write it without the parenthesis as:
( 4w + 3x + 5 ) - ( 4w - 3x + 2)
4w + 3x + 5 - 4w + 3x - 2
Then, we need to identify the like terms as:
4w and -4w are like terms
3x and 3x are like terms
5 and -2 are like terms
Now, we can organize the terms as:
4w - 4w + 3x + 3x + 5 - 2
Adding like terms, we get:
(4w - 4w) + (3x + 3x) + (5 - 2)
0 + 6x + 3
6x + 3
Therefore, the answer is 6x + 3
Gary has read 30 pages of his book. Each day he wants to read 15 pages until he finishes the book which has a total of 180 pages. Write an equation to represent the situation
ANSWER
30 + 15x = 180
EXPLANATION
We have that Gary has read 30 pages of his book.
He wants to read 15 pages every day till he finishes the 180 pages.
Let the number of days it will take him be x.
This means that after reading 15 pages for x days, he will have read:
15 * x = 15x
Therefore, the total number of pages he will have read (180) will be:
30 + 15x = 180
That is the equation that represents the situation.
Find the rate of change of each linear function 1. y = x - 7
Rate of change = 1
Explanations:The given linear function is:
y = x - 7
The rate of change of the function is gotten by finding the derivative (dy/dx) of the function
dy/dx = 1
The rate of change = 1
if the slope of a line and a point on the line are known the equation of the line can be found using the slope intercept form y=mx+b. to do so substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. using the above technique find the equation of the line containing the points (-8,13) and (4,-2).
The general equation of a line is;
[tex]y\text{ = mx + b}[/tex]m is the slope and b is the y-intercept
To find the slope, we use the equation of the slope as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (-8,13)} \\ (x_2,y_2)\text{ = (4,-2)} \\ \\ m\text{ = }\frac{-2-13}{4-(-8)}\text{ = }\frac{-15}{12}\text{ = }\frac{-5}{4} \end{gathered}[/tex]We have the partial equation as;
[tex]\begin{gathered} y\text{ = }\frac{-5}{4}x\text{ + b} \\ \\ \text{Substitute the point (-8,13)} \\ \text{x = -8 and y = 13} \\ \\ 13\text{ = }\frac{-5}{4}(-8)\text{ + b} \\ \\ 13\text{ = 10 + b} \\ b\text{ = 13-10 = 3} \end{gathered}[/tex]We have the complete equation as;
[tex]y\text{ =}\frac{-5}{4}x\text{ + 3}[/tex]