Answers
a) The area of the rectangle has the following inequality: 12 ≤ 6 · x ≤ 36.
b) The value of the variable x has the following inequality: 2 ≤ x ≤ 6.
How to build and interpret an inequality associated to the area of an rectangle
The area of a rectangle (A) is described by the following formula:
A = b · h
Where:
b - Base of the rectangleh - Height of the rectanglea) If we know that b = 2 · x and h = 3, then the area of the rectangle is:
A = (2 · x) · 3
A = 6 · x
And the inequality is:
12 ≤ 6 · x ≤ 36
b) And the solutions for the values of x are represented by the following inequality:
2 ≤ x ≤ 6
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Related Questions
QuestionSolve the inequality 37v < -18 and write the solution in interval notation, using improper fractions if necessary.
Answers
Determine if the expression -y^4 is a polynomial or not. If it is a polynomial, state the
type and degree of the polynomial.
Answers
This expression -y⁴ is a polynomial and it's a type of biquadratic polynomial.
What is a polynomial?
One-variable polynomials are algebraic expressions that have terms of the form axⁿ, where n is a non-negative (i.e., positive or zero) integer and an is a real number that is known as the term's coefficient. A polynomial with one variable has its biggest exponent at its degree.
We have,
-y⁴
It has a degree of 4 and a coefficient is -1 a real number.
It is called a biquadratic equation or quartic equation. Generally, any polynomial with a degree of 4, which means the largest exponent is 4 is called a fourth-degree equation.
Hence, this expression -y⁴ is a polynomial and it's a type of biquadratic polynomial.
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3.13 Which triangle congruence postulate or theorem proves that these triangles are congruent?
Answers
The SAS triangle congruence postulate proves that these triangles are congruent .
Given,
In the figure,
There are two triangles ABC and Triangle XYZ
Now, According to the question:
Consider the triangle ABC and triangle XYZ .
we can see that
(i) angle C = angle Z .....given in the figure
(iii) side AC = side XZ .... given in the figure
(ii) side BC = side ZY ....given in the figure
From the above three statements we conclude that
ΔABC ≅ ΔXYZ
both the triangles ABC and XYZ are congruent by SAS Congruence Postulate .
Therefore , The SAS triangle congruence postulate proves that these triangles are congruent .
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Solve for w4/6 = w/9Simplify your answer as much as possible.
Answers
We want to find the value of w, so the following equation is true:
[tex]\frac{4}{6}=\frac{w}{9}[/tex]Since both sides of the equation are equal, we must do the same on both sides, so they keep equal.
We want to leave w in only one side of the equation.
Then we want to bring 9 of the division to the left side so w can be alone in the right sides.
In order to do so we multiply both sides by 9:
[tex]\begin{gathered} 9\cdot\frac{4}{6}=9\cdot\frac{w}{9} \\ \downarrow\text{right side} \\ 9\cdot\frac{w}{9}=\frac{9w}{9}=w \\ \downarrow left\text{ side} \\ 9\cdot\frac{4}{6}=\frac{36}{6}=6 \end{gathered}[/tex]Then, we have that:
[tex]\begin{gathered} 9\cdot\frac{4}{6}=9\cdot\frac{w}{9} \\ \downarrow \\ 9\cdot\frac{4}{6}=w \\ \downarrow \\ 6=w \end{gathered}[/tex]Answer: w = 6
A population of values has a normal distribution with μ = 159.8 and σ = 59.5 . If a random sample of size n = 13 is selected, Find the probability that a single randomly selected value is greater than 156.5. Round your answer to four decimals. P(X > 156.5) = Find the probability that a sample of size n = 13 is randomly selected with a mean greater than 156.5. Round your answer to four decimals. P(M > 156.5) =
Answers
In a population of values having a normal distribution with (μ = 159.8) and (σ = 59.5), if a random sample of size (n = 13) is selected, then the probability that a single randomly selected value is greater than 156.5 will be 0.52.
As per the question statement, a population of values has a normal distribution with (μ = 159.8) and (σ = 59.5) and a random sample of size (n = 13) is selected,
Then we are required to calculate the probability that a single randomly selected value is greater than 156.5.
To solve this question, let us assume that, a random variable "X" follows normal distribution with mean (μ = 159.8), standard deviation (σ = 59.5) and a sample size of (n = 13).
Then the probability that a single randomly selected value is greater than 156.5 can be calculated as follows:
P (X > 156.5) = [1 - P(X < 156.5)]
= [1 - P{(X - μ)/σ < (156.5- 159.8)/59.5}]
= [1 - P{Z < (-0.0554)}]
= (1 - 0.477885127828 )...[Using Excel Function "NORMSDIST (-0.0554)]
= 0.522114872172
≈ 0.52
Probability: Probability is the branch of mathematics that deals with the numerical descriptions on the extent to which an event is likely to occur, or how likely it is, that a proposition is true, being calculated by the ratio of the favorable cases to the total number of cases possible.To learn more about Samples and Probability, click on the link below.
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Three Albany Middle Schools raised money to buy new computers.EON raised $286.00 Hackett raised $192.84 Myers raised $113.25 more than Hackett. What is the total amount of money raised by all three schools
Answers
We have to find the amount of money raised by all three schools.
The first school: EON, raised $286.00
The second school: Hackett raised $192.84
The third school: Myers raised $113.25 more than Hackett
To calculate the amount that the third school raised, we add $113.25 to the amount that the second school raised $192.84:
[tex]192.84+113.25=306.09[/tex]Myers raised $306.09
Finally, we add the money that the three schools raised to find the total:
[tex]286.00192.84+306.09=784.93[/tex]The total amount of money raised was $784.93
Answer:
$784.93
NEED HELP!! GIVING BRAINLIEST
Several bakeries in a town were asked the price for different amounts of donuts at their shop. The scatter plot with a line of best fit was created from the data gathered.
Part A: Estimate the correlation coefficient. Explain your reasoning for the given value. (4 points)
Part B: How many positive and negative residuals are there? Explain your reasoning. (3 points)
Part C: State the point with the largest absolute value residual and interpret the point in terms of the context of the data. (3 points)
Answers
Considering the given scatter plot, it is found that:
a. The correlation coefficient is of 0.303.
b. Regarding the residuals, there are six positive and four negative.
c. The point with the largest residual is (6,2), which is the point in which the largest difference between the predicted and the actual value were found.
How to find the correlation coefficient of a scatter plot?The correlation coefficient is gotten by selecting the points (x,y) from the scatter plot, and inserting them into a calculator.
The coordinates of these points from the given plot are;
(1,2), (1,3), (2,4), (3,4), (3,5), (4,3), (4,5), (5,5), (5,6), (6,2).
Punching these points into a calculator, gives the coefficient as 0.303.
A residual is calculated as the difference that is gotten between the observed value and the predicted value. Thus;
The positive residuals are defined as the points that exists above the line and in this given plot we have six positive residuals.
The negative residuals are the points that exists below the line, and in this plot, we have four negative residuals.
Hence the largest residual, with the aid of absolute value, is at the point:
(6,2).
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This table gives a few (x,y) pairs of a line in the coordinate plane.
x y
40 -30
61 -45
74 -60
What is the x-intercept of the line?
( , )
its on khan academy
Answers
The x-intercept of the line is found to be -38 from the given table data using the slope-point form.
What exactly is the slope-point form?The equation of a straight line that is inclined at a specific angle to the x-axis and passes through a specific point may be found using the slope-point form. Only when the line's slope and a particular point are known can the point slope formula be applied. The slope-point form's equation is as follows: y - y₁ = m(x - x₁)Take a look at any two points, such as (40, -30), and (61, -45).
The line connecting them must have the following slope:
(y₂ - y₁)/(x₂ - x₁) = (-45 -(- 30))/(61 - 40) = -15/21.
Since they are on the same line, any combination of (48,30) and (74,60) will have the same answer.
The slope-point form is given as follows:
y - y₁ = m(x - x₁)
y -(- 30) = (-15/21) (x - 40)
21(y + 30) = -15(x - 40)
-15x + 21y = 570
Now, we can convert the above equation in intercept form to find x-intercept.
The intercept form is given as:
x/a + y/b = 1, where a and b are x and y intercepts.
-15x + 21y = 570
Dividing by 570 we get,
(-15x)/570 + (21y/570) = 1
x/-38 + y/27 = 1
Compare this to x/a + y/b = 1, where a and b are the x and y intercepts, respectively.
In this case, the x intercept is -38.
Therefore, the x-intercept of the line is found to be -38 from the given table data.
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I'm having a problem with logarithms I will upload a photo
Answers
SOLUTION:
Step 1 :
In this question, we are asked to solve the equation:
[tex]In\text{ ( 4 x + 4 ) = 2}[/tex]Step 2 :
Now, taking the exponents of both sides, we have that:
[tex]\begin{gathered} e^{In\text{ ( 4 x + 4 ) }}=e^2 \\ 4x+4=e^2 \\ \text{But e}^2\text{ = 7.3891 ( to 4 decimal places )} \\ 4\text{ x + 4 = 7. 3891} \\ \text{ 4 x = 7. 3891 - 4} \\ \text{4 x = 3.3891} \\ \text{Divide both sides by 4 , we have that:} \\ x\text{ = }\frac{3.3891}{4} \\ x\text{ = 0.847275} \\ \text{x = 0.8473( to 4 decimal places)} \end{gathered}[/tex]1. If Rocco makes 18 out of 25 free throws and Graham makes 14 out of 20 free throws, who has the better free
throw record? Show why using comparable rates.
Answers
what was the initial amount of water in a barrel, in liters, if x liters remain after y liters were spilled and 6 were added?
Answers
Let's call A the initial amount of water, in liters, in that barrel.
After y liters were spilled, the amount left was
A - y
Then, after 6 liters were added, the final remaining amount was given by:
A - y + 6
Now, since x liters remain, we have:
x = A - y + 6
Therefore, if we can find the expression for the initial amount of water, in liters, by isolating A in that equation:
x = A - y + 6
x + y = A + 6
x + y - 6 = A
A = x + y - 6
Thus, the initial amount of water was (x + y - 6) liters.
write an equation in slope intercept form for the lines that passes through (-2,-8) and is parallel to y=-9x-81
Answers
The general form of an equation in slope intercept form is ;
y= mx + c where m is the gradient and c is the y-intercept
The equation given is : y = -9x-81 ------this means the slope is -9
This is determined from the general equation ;
y = m x + c
y= -9 x - 81
where -9 is the gradient
Because the two lines are parallel, it means the other equation should have a slope of -9, thus apply the formula for slope give point {-2,-8}
m= change in y-coordinates value / change in x coordinate values
-9 = y --8/x--2
-9 = y+8 /x+2
-9 {x+2} = y+8
help please, do working outs too i don’t understand it
Answers
1.) The line with the greatest slope.
The greater the slope of the line, the more upright it is. Observing the given graph, the line with the greatest slope is line a.
2.) Lines that are parallel.
Two lines are parallel if they do not have an intersection with each other at any point in the graph. We can see that line b and line d, do not intersect at any point in the graph and are thus parallel lines.
3.) Line with a negative slope
A line with a negative slope is a line that goes downwards from left to right, in the graph we can see that line e and line f goes downwards from left to right.
4.) Line that is perpendicular to the y-axis.
A line that is perpendicular to the y-axis, is a line that is parallel to the x-axis. Looking at the graph, line c is perpendicular to the y-axis.
For the point P(-24,-24) and Q(-19,-19), find the distance d(P,Q) and theof the midpoint M of the segment PQ,coordinates
Answers
Solution:
Given;
[tex]P(-24,-24),Q(-19,-19)[/tex]The distance d(P,Q) is;
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\ x_1=-24,y_1=-24,x_2=-19,y_2=-19 \\ \\ d=\sqrt{(-19-(-24))^2+(-19-(-24))^2} \\ \\ d=\sqrt{50} \\ \\ d=5\sqrt{2} \end{gathered}[/tex]Also, the midpoint, M, is;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \\ M=(\frac{-24+(-19)}{2},\frac{-24+(-19)}{2}) \\ \\ M=(-\frac{43}{2},-\frac{43}{2}) \end{gathered}[/tex]I need help with this problems please I need a huge explanation
Answers
In this case we must apply the properties of supplementary angles and opposite angles.
1 .
opposite angles
∠ 1 = 120 °
supplementary angles
∠ 1 + ∠ 2 = 180
120 + ∠ 2 = 180
∠ 2 = 180 - 120
∠ 2 = 60 °
The same properties can be applied in the other exercises to solve them.
The solution is:
∠ 1 = 120 °
∠ 2 = 60 °
I can enter the problem here so ill add a picture, sorry for the inconvenience
Answers
Given two numbers a and b
Their Arithmetic mean (A), Geometric mean (G) and Harmonic mean (H) are given below,
[tex]\begin{gathered} A=\frac{a+b}{2} \\ G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \end{gathered}[/tex]To find the formula that correctly relates H, a and b,
Relating the last two equations, i.e the geometric and harmonic mean below,
[tex]\begin{gathered} G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \\ \text{relating both equations} \\ \sqrt[]{ab}=\sqrt[]{AH} \\ \text{Square both sides } \\ (\sqrt[]{AH})^2=(\sqrt[]{ab})^2 \\ AH=ab \\ \text{Make H the subject},\text{ by dividing both sides by A} \\ \frac{AH}{A}=\frac{ab}{A} \\ H=\frac{ab}{A} \end{gathered}[/tex]Substituting for A into the above expression,
[tex]\begin{gathered} \text{recall A=}\frac{a+b}{2} \\ H=\frac{ab}{A}=\frac{ab}{\frac{a+b}{2}} \\ H=(2\times\frac{ab}{a+b})=\frac{2ab}{a+b} \\ H=\frac{2ab}{a+b} \end{gathered}[/tex]Hence, A is the correct option.
PLS ANSWER THIS FOR ME ASAP!
Answers
Answer:
D,E,F
Step-by-step explanation:
dialation causes the sides to get smaller or bigger when it’s more or less than 1
Hopes this helps please mark brainliest
Find the volume of this object.Use 3 for a.Volume of a CylinderV=Tr2hVolume of a Sphere4 cmV=-Tr36 cm8 cmV ~ [?]cm3
Answers
The figure given in the question is a composite figure, meaning that it comprises two different figures
The volume of the composite figure can be found as follow
The two figures are:
Cylinder and sphere.
To solve this, we will first find the area of a cylinder
[tex]\begin{gathered} \text{Area of a cylinder is given by:} \\ V_{\text{cylinder}}=\pi r^2h \\ \text{where} \\ \pi=3 \\ r=4 \\ h=6 \end{gathered}[/tex]So, we will have
[tex]\begin{gathered} V_{\text{cylinder}}=3\times4^2\times6 \\ V_{\text{cylinder}}=288\operatorname{cm}^3 \end{gathered}[/tex]Then, we will find the volume of the sphere
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\pi r^3 \\ \text{where} \\ \pi=3 \\ r=4 \end{gathered}[/tex]Thus, the volume of the sphere will be
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\times3\times4^3 \\ V_{\text{sphere}}=256\operatorname{cm}^3 \end{gathered}[/tex]Thus, the total volume will be
[tex]288+256=544\operatorname{cm}^3[/tex]The volume is:
[tex]544\operatorname{cm}^3[/tex]The answer is 544cm³
help please tyyyyyyyyy
Answers
Answer: 5 tadoples
Step-by-step explanation:
Please get me the Braniliest award, thanks!
Answer:
30
Step-by-step explanation:
If there are 18 swans in the ratio of 3
you divide 18 by 3 = 6
So you times 5 by 6 to get 30 as your answer
What is the measure of each interior angle of the regular polygon picture below ?if necessary, round to the nearest tenth
Answers
Our figure is a regular polygon. A polygon is regular when all angles are equal and all sides are equal. The measure of each inside angle of a regular polygon is given by the following expression
[tex]\frac{180^o\times(n-2)}{n}[/tex]Where n represents the amount of sides.
Since our polygon is a regular hexagon, we have n = 6. Using this value on the expression, we have
[tex]\frac{180^o\times(6-2)}{6}=\frac{180^o\times4}{6}=\frac{720^o}{6}=120^o[/tex]The measure of each interior angle a regular hexagon is 120º.
<1 and <2 form a linear pair. If m<1
= (18r - 1)° and m<2 = (23r + 17)°. find m<2.
Answers
The measure of angle m<2 for the given linear pair is found as 109°.
What is meant by the term linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are referred to as linear. The sum of the angles of a linear pair has always been 180°.For the given question;
<1 and <2 form a linear pair.
m<1 = (18r - 1)° and m<2 = (23r + 17)°
Thus, from the property of the linear pair;
m<1 +m<2 = 180
Put the values;
(18r - 1)° + (23r + 17)° = 180
Simplify the expression.
18r - 1 + 23r + 17 = 180
41r = 180 - 16
r = 4
m<2 = (23r + 17)°
m<2 = (23×4 + 17)°
m<2 = 109°
Thus, the measure of angle m<2 for the given linear pair is found as 109°.
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What is the maximum value of this function on the interval [-2,0]
Answers
Answer:
2,0?
Step-by-step explanation:
To do this, find your first derivative and then find where it is equal to zero. Because we are only concerned about the interval from -5 to 0, we only need to test points on that interval. (i really don't know hot to explain)
((x-j) ÷ k) + m =n what does x equal?
Answers
Explanation
[tex]\frac{x-j}{k}+m=n[/tex]
Step 1
subtract m in both sides
[tex]\begin{gathered} \frac{x-j}{k}+m=n \\ \frac{x-j}{k}+m-m=n-m \\ \frac{x-j}{k}=n-m \end{gathered}[/tex]Step 2
multiply each side by k
[tex]\begin{gathered} \frac{x-j}{k}=n-m \\ \frac{x-j}{k}\cdot k=(n-m)\cdot k \\ x-j=(n-m)\cdot k \end{gathered}[/tex]Step 3
finally, add j in both sides
[tex]\begin{gathered} x-j=(n-m)\cdot k \\ x-j=nk-mk \\ x-j+j=nk-mk+j \\ x=nk-mk+j \end{gathered}[/tex]I hope this helps you
Suppose a 95% confidence interval for the average amount of weight loss on a diet program for males is between 13. 4 and 18. 3 pounds. These results were based on a sample of 42 male participants who were deemed to be overweight at the start of the 4-month study. What is the standard error of the sample mean?.
Answers
The standard error of the sample mean is 1.213
How to calculate the standard error of the sample mean?
Given,
c = 95% = 0.95
n = 42
lower limit = 13.4
upper limit = 18.3
Since standard deviation population is unknown, we use this formula to calculate standard error.
standard error = margin of error / [tex]t_{\alpha/2,d.f.}[/tex]
First, we calculate the t distribution value
[tex]t_{\alpha/2,d.f.}[/tex] = [tex]t_{(1-c)/2,n-1}[/tex]
= [tex]t_{(1-0.95)/2,42-1}[/tex]
= [tex]t_{0.025,41}[/tex]
To find the value use t table. So, [tex]t_{0.025,41}[/tex] = 2.0195
Next, we calculate the margin of error
margin of error = (upper limit - lower limit)/2
= (18.3 - 13.4)/2
= 4.9/2
= 2.45
Now, we can calculate the standard error. So,
standard error = 2.45 / 2.0195
= 1.213
Thus, the standard error of the sample mean is 1.213
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Write 2 proportions so that the product of the means equal 27
Answers
Two proportions that has a product of 27 are
first proportion is 27 = 2/3 * 81/2second proportion is, 27 = 4/7 * 189/4What is proportion as used in math?Proportion as used in math refer to the condition when two ratios are equal.
Let the two proportions be x and y
say 2/3 * x = 27
x = 27 / 2/3
x = 81/2
4/7 * y = 27
y = 27 / 4/7
y = 189/4
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Voters in Arizona in 2020 passed Prop 207, legalizing the sale of recreational marijuana. At the time the industry estimated that the Arizona Department of Revenue would collect $135 million in taxes. In the first year, the state has generated approximately $200 million in tax revenue.State the absolute difference in the estimated amount of tax revenue generated and the actual amount received by the AZ Department of Revenue. Be sure to answer in a complete sentence.
Answers
The estimated amount of tax is 135 million
The actual amount received is 200 million
The difference means subtraction
Taking the absolution value means when we subtract, we find the positive value of the result
| estimated - actual |
| 135 million - 200 million |
| -65 million|
Taking the positive result
65 million
The absolute value of the difference in the estimate amount of the tax revenue generated and the actual amount received by the AZ department of Revenue is 65 million dollars.
Which segment is a reflection of segment AB over the line x=1? X CD O EF O GA O IJ
Answers
Since the line on which segment AB is reflected is x = 1 then the rule for this reflection will be
[tex](x,y)\rightarrow(-x+2\cdot1,y)=(-x+2,y)[/tex]Then, the coordinates of the segment that is reflections of segment AB with respect to the line x = 1 will be
[tex]\begin{gathered} A(-4,3)\rightarrow(-(-4)+2,3)=(4+2,3)=(6,3) \\ B(-1,1)\rightarrow(-(-1)+2,1)=(1+2,1)=(3,1) \end{gathered}[/tex]And the segment with these coordinates is EF
[tex]\begin{gathered} E(6,3) \\ F(3,1) \end{gathered}[/tex]Therefore, the correct answer is b. EF.
A diagram is shown, where kill and Move statements and reasons to the table to provem is a transversal.that 21 25.mReasonsStatements1. kl-K2.1. Given2. Corresponding anglesare congruent.3.253763.4. 215 254.A <10 -2 B-1u23C218 24 D-2013E-2014 F-2025 G229 26 1723324I 23:25 J24325 R-4826L_Transitive property Msymmetric propertyN Vertical angles are congruent.Straight angles form a linear pair.P Corresponding angles are congruent.Q Alternate exterior angles are congruent.
Answers
Given:- The triangle with dimensions in it.
To find:- Which triangle is congruent to triangle MNO.
Solution:-
As we know that two triangles are congruent only when they satisfy one of the given rules.
1. SSS (Side-side-side) congruency rule.
2. SAS (side-angle-side) congruency rule.
3. ASA (Angle-Side-Angle) congruency rule.
4. AAS (Angle-Angle-Side) congruency rule
5. RHS (Right angle-Hypotenuse-Side) congruency rule.
So, check one by one option.
Option A:-
One side is 4.6 cm, another side is 4.99 cm and one angle is 60 degrees.
But it does not satisfy any of the congruency rules because there are 2 sides and then one angle.
So, option A is incorrect.
Option B:-
In option B there are three angles given 70 degrees, 60 degrees and 50 degrees. But to prove that the triangle is congruent we need at least one side.
So, Option B is incorrect.
Option C:-
In option C, there are only two sides given as 4.07 cm and 4.99 cm and to prove that the triangles are congruent we need at least three measurements of the triangle.
So, option C is incorrect.
Option D:-
In option D, there is one side of 4.07 cm, then one angle of 60 degrees and then one side of 4.99 cm. And we can observe that there is an angle between the two sides.
So, it follows SAS (side-angle-side) congruency rule.
So, Option D is correct.
Final answer:-
Therefore, the answer is option D.
Principal Phillips asked 150 sixth graders to vote on their end-of-year trip. 120 sixth graders voted for a trip to the water park. What percent of sixth graders voted for a trip to the water park?
Answers
Answer:
80%
Step-by-step explanation:
Geometry! Just the first question:)
Answers
Hi your answers would be
a) 30 degrees
b) 65 degrees
c) 115 degrees
d) 85 degrees
e) 150 degrees
f) 30 degrees
Hope these answers help.
Answer:
5 round table pizza and amen and amen and amen and amen
Step-by-step explanation:
the program I think the banner side effects