The correct answer is the addition property of equality
Here, we want to select the property demonstrated by the example
The correct answer is the addition property of equality
What this is saying is that if we have two numbers, in this case represented by the variables a= c
If we add an equal number to both sides, then the results on both sides still stay the same regardless since it is the same number that we added on both ends
A student solved the equation sin2x/cos x and found an answer of pi/2 Describe the student's error
To find:
To determine whether the x = pi/2 is the answer of the equation
[tex]\frac{\sin2x}{\cos x}=2[/tex]Solution:
The solution of the equation is as follows:
[tex]\begin{gathered} \frac{\sin2x}{\cos x}=2 \\ \frac{2\sin x\cos x}{\cos x}=2 \\ \sin x=1 \\ x=\frac{\pi}{2} \end{gathered}[/tex]But at x = pi/2, the denominator of the function is zero, so, the function is not defined at x = pi/2.
Thus, the answer is "The function is not defined at x = pi/2. So, it is not the answer to the equation."
Nathan is taking an SAT prep class at the community center in Princeton. The community center is 4 centimeters away from Nathan's house on a city map. The scale of the map is 1 centimeter : 1 kilometer. In real life, what is the distance between Nathan's house and the community center?
we know that
The scale of the map is 1 centimeter: 1 kilometer
Applying proportion
1/1=x/4
x=4*1
x=4 km
the answer is 4 kilometersDemonstrate your understanding of segment edition postulate by writing an example of a using the picture below.
hello
segment addition postulate implies given two points and a third point between them, the sum of the first two point equals the distance of ot the third point.
i'll explain better using the question given
[tex]\begin{gathered} DN=DO+OW+WN \\ we\text{ can also say} \\ DW=DO+OW \\ ON=OW+WN \end{gathered}[/tex]given a line DN with segment O and W, the sum of DO + OW + WN = DN
Can you please help me answer the question?
We have the equation:
[tex]48h-6=426[/tex]Then solve for h:
[tex]\begin{gathered} 48h-6+6=426+6 \\ 48h=432 \\ \frac{48h}{48}=\frac{432}{48} \\ h=9 \end{gathered}[/tex]Answer: B. 9 feet
Farmer Ed has 2,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
500,000cm²
Explanations:
The formula for calculating the perimeter of the fence is expressed as:
[tex]P=2(l+w)[/tex]where:
• L is the ,length, of the fencing
,• W is the ,width ,of the fencing
If Farmer Ed does not fence the side along the river, the perimeter of the river will become;
[tex]\begin{gathered} P=l+2w \\ 2000=l+2w \\ l=2000-2w \end{gathered}[/tex]The area of the rectangular plot will be expressed as:
[tex]A=lw[/tex]Substitute the expression for the length into the area to have:
[tex]\begin{gathered} A=w(2000-2w) \\ A=2000w-2w^2 \end{gathered}[/tex]If the area of the plot is maximized, then dA/dw = 0. Taking the derivative will give:
[tex]\begin{gathered} \frac{dA}{dw}=0 \\ 2000-4w=0 \\ 4w=2000 \\ w=\frac{2000}{4} \\ w=500m \end{gathered}[/tex]Calculate the length of the plot. Recall that:
[tex]\begin{gathered} l=2000-2w \\ l=2000-2(500) \\ l=2000-1000 \\ l=1000m \end{gathered}[/tex]Determine the largest area that can be enclosed
[tex]\begin{gathered} A=lw \\ A=500m\times1000m \\ A=500,000m^2 \end{gathered}[/tex]Hence the largest area that can be enclosed is 500,000cm²
1 Х 15 8 sin-1 8 =mZT 15 T 17 U
Given:
In a right angled traingle with hypotenuse 17.
The other two length of the sides are 15 and 8.
The objective is to find the correct way of finding the angle T.
While solving a trigonometric ratio, the hypotenuse always present opposite to angle. 90 degree.
The opposite side of the triangle depends on the angle which we have to find out.
In this case, the objective is to find the measure of angle T.
So, the side opposite to angle T will be named as opposite side of right angled triangle and the reminig side will be named as adjacent side of the right angled triangle.
Since, the formula of sin is,
[tex]\sin \theta=\frac{opposite\text{ }}{hypotenuse}[/tex]If T is the angle, then opposite side is 8 and the hypotenuse is 17.
So the correct formula will be,
[tex]\begin{gathered} \sin \angle T=\frac{8}{17} \\ \angle T=\sin ^{-1}\frac{8}{17} \\ \angle T=\sin ^{-1}0.47058 \\ \angle T=28.07 \end{gathered}[/tex]Hence, the correct correct value is sin^-1 (8/17) and the measure of angle T is 28.07.
Suppose that three geological study areas are set up on a map at points please check photo
So we must find the center of the earthquake. We have three points and we know the distances from each of these points to the earthquake. In order to find the center we just need to make three circles, each centered in one of the three points and its radius must be the distance to the center of the earthquake. If we do this correctly then the three circles will meet in a given point D which is the center of the earthquake.
In order to draw a circle using the tool given by the question you'll need its center and a point in the circumference. So let's construct each of the circles:
First we have point A=(-15,2) which is at a distance of 13mi from the earthquake. So we must construct a circle centered around A with a radius of 13 units. Any point at a distance of 13 units from A will be useful, for example a point that has a horizontal distance of 13 units from A. We'll name this point E and we have:
[tex]E=(-15+13,2)=(-2,2)[/tex]So the first circle is the one that passes through (-2,2) and is centered around (-15,2).
Now we repeat this process with the other circles. We have B=(-11,1) and its distance to the earthquake is 10 miles so we can add 10 to its x-value to find a point that is at a distance of 10 units from it:
[tex]F=(-11+10,1)=(-1,1)[/tex]So this circle is centered around (-11,1) and it passes through (-1,1).
For the third circle we have C=(-6,3) and its distance to the earthquake is 5 miles. Then a point located at 5 miles from C could be:
[tex]G=(-6+5,3)=(-1,3)[/tex]So the third circle is centered around (-6,3) and passes through (-1,3).
With all this information we can graph the three circles:
As you can see these three circles intercept each other at (-3,7). Then the earth quake is located at (-3,7).
AnswerThe graphs are displayed in the picture above. The center of the earthquake is located at (-3,7).
What is the slope of the line that passes through points (0, 7) and (−3, 0)?A.–7/3B.7/3C.–3/7D.3/7
Given:
Two points are (0,7) and (-3,0).
To find the slope of the line:
Using the slope formula,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{0-7}{-3-0} \\ =\frac{-7}{-3} \\ =\frac{7}{3} \end{gathered}[/tex]Hence, the slope is,
[tex]m=\frac{7}{3}[/tex]Therefore, the correct option is B.
2) y = x + 3 + 3 A) Domain: x 2-3 Range: y = 3 B) Domain: x 2-3 Range: y s3 C) Domain: x 2 3 Range: y 2-3 D) Domain: x 2-3 Range: y 2-3
Domain : Domain of a function is the set of input values for which the function is real and defined.
Given function is :
[tex]y=\sqrt[]{x+3}+3[/tex]Since if x less than - 3 then the square root will be into the form of complex number i,
So x ≥ -3
So Domain will be : x ≥ -3
Interval notation : [ -3, infinity)
Range : Range is the set of all the output values of the function :
The range of the funtion is:
[tex]f(x)\ge3[/tex]Intervale notation : [3, infinity)
Domain = x ≥ -3, [-3, inifinity)
Range : f(x)≥3, Interval notation [ 3, infinity)
Answer : A)
Domain x ≥- 3
Range y ≥ 3
The accompanying data give the heights of 18 male college students and their fathers, in inches. Use these data to complete parts (a) through (e) below.R Click the icon to view the father and son height data.
Given:
The set of data of Capital of prisons.
1, 126, 8, 2, 746, 2, 82, 9, 33, 0 ,0.
Aim:
We need to find the median of the given data set.
Explanation:
Rewrite the given data set in terms from least to greatest numbers.
0,0, 1, 2,2,8,9,33, 82, 126, 746.
There are 11 terms in this data set.
The middle term is the 6th term.
We know that median = the middle term.
[tex]Median\text{ = 6th term.}[/tex]6 th term is 8.
[tex]Median\text{ =8.}[/tex]Median is middle term so some wedern states must have fewer than 8.
For example, Wyoming has 1 capital prisoner.
The first option is wrong.
50 % of western states have fewer than 8 capital prisoners is true since 8 is the middle of the data set.
Final answer:
D. The median is 8 capital prisoners. This means that 50% of these western states have fewer than this many capital prisoners.
What is the major axis for the equation+= 1? Type h for horizontal or v for vertical.
Consider the given equation,
[tex]\begin{gathered} \frac{x^2}{49}+\frac{y^2}{7}=1 \\ \frac{x^2}{(7)^2}+\frac{y^2}{(\sqrt{7})^2}=1 \end{gathered}[/tex]This is a standard equation of a horizontal ellipse, whose semi-major axisis given as,
[tex]a=7[/tex]So the length of major axis will be,
[tex]2a=2(7)=14[/tex]Thus, the length of major axis of the given equation is 14 units.
Bev got six dollars from her mom and four from her dad. she wants to buy a game that cost 18 dollars how many more she needs
Answer
Bev needs 8 dollars more to buy her game.
Explanation
Let the amount of dollars that Bev needs be x dollars
She needs 18 dollars
She gets 6 dollars from her mom
And 4 dollars from her dad
Mathematically,
(Amount that she has currently) + (Amount that she needs) = 18
Amount that she has currently = 6 + 4 = 10 dollars
Amount that she needs = x dollars
(Amount that she has currently) + (Amount that she needs) = 18
10 + x = 18
Subtract 10 from both sides
10 + x - 10 = 18 - 10
x = 8 dollars
Hope this Helps!!!
2 numbers whose product is -84 and whose sum is -17
Solution
- We are asked to find two numbers with a product of -84 and a sum of -17.
- Let the two numbers be x and y.
- We can form equations using the above statement. These equations are formed below
[tex]\begin{gathered} x\times y=-84 \\ xy=-84\text{ (Equation 1)} \\ \\ x+y=-17\text{ (Equation 2)} \end{gathered}[/tex]- Now that we have the two equations, we can proceed to solve them simultaneously.
- This is done using substitution as shown below
[tex]undefined[/tex]Solve the system of equations by any method. -2x + 8y = 14 x – 4y= -7
-2x+8y = 14 (a)
x-4y = -7 (b)
Multiply (b) by 2 and add both equations:
-2x + 8y = 14
2x -8y = -14
___________
0 = 0
Since both variables were eliminated there is an infinite number of solutions.
The table shows coffee preference from a survey. …If a person is chosen at random in the survey what is P (regular or creamer)?
The formula we will use to calculate the probability is given to be:
[tex]P(A\text{ or }B)=P(A)+P(B)-P(A\cap B)[/tex]Let A represent regular and B represent creamer.
We have the following parameters:
[tex]\begin{gathered} P(A)=0.78 \\ P(B)=0.41 \\ P(A\cap B)=0.32 \end{gathered}[/tex]Therefore, we can calculate the probability to be:
[tex]\begin{gathered} P(A\text{ or }B)=0.78+0.41-0.32 \\ P(A\text{ or }B)=0.87 \end{gathered}[/tex]The FOURTH OPTION is correct.
Which graph shows a function with a range of all real numbers greater than or equal to -1?55444-3+3+3+2-2-2+14 4-5-4-3-2-1₁ 1 2 3 4 5 x-5-4-3-111 2 3 4 5 x--5--3-2-11 1 2 3 4 5 x-2+-24-3+-3-3--4<-4O-5-4-3-2-1₁. 12-2-11-4 5 X543214+3YO
Answer:
The graph that has a range of all real numbers greater than or equal to -1 is the graph below (top middle graph).
Explanation:
Since the range or the y-values of the graph must be greater than or equal to -1, then the graph must be increasing starting from y = -1.
Out of the 4 graphs, only the two graphs in the middle shows a graph that is increasing.
The graph at the top part is increasing starting from y = -1 while the graph at the bottom part is increasing starting from y = 1 hence, the answer is the graph at the top middle part.
1/2×-8=9 and ×-8=18 are not equivalent because
By definition, you know that two equations are equivalent when they have the same solution. So, solving the first equation you have
[tex]\begin{gathered} \frac{1}{2}x-8=9 \\ \text{ Add 8 }to\text{ both sides of the equation} \\ \frac{1}{2}x-8+8=9+8 \\ \frac{1}{2}x=17 \\ \text{Multiply by 2 }on\text{ both sides of the equation} \\ 2\cdot\frac{1}{2}x=17\cdot2 \\ x=34 \end{gathered}[/tex]Now, solving the second equation you have
[tex]\begin{gathered} x-8=18 \\ \text{ Add 8 to both sides of the equation} \\ x-8+8=18+8 \\ x=26 \end{gathered}[/tex]Since the equations do not have the same solution then these equations are not equivalent.
At a coffee shop, the first 100customers' orders were as follows.SmallMediumLargeHot54822Cold8125What is the probability that a customerordered a small given that he or sheordered a hot drink?P(Small | Hot ) = [?]Round to the nearest hundredth.
Explanation
The probability of P(Small | Hot ) is easily observable from the table. This is given as
[tex]\begin{gathered} P(Small|Hot)=\frac{5}{5+48+22}= \\ =\frac{5}{75} \\ =0.07 \end{gathered}[/tex]The final answer is 0.07
Simplify the expression, if possible. Write the answer without negative exponents. (If the solution is not a real number, enter NOT REAL.)(-216) 1/3
The simplified expression without using negative exponents is -6 .
The given expression is of the form [tex](-216)^{\frac{1}{3}}[/tex] .
this can be written using the radical sign as ∛(-216)
Now we know that the cube root of a negative number is always a negative number .
using the properties of exponents we can write
∛(-216) = ∛(-1) × ∛216
now we know that ∛(-1) = -1 as -1³ = -1 and ∛216 = 6
Exponents are a way to show sudden increases in power. So to speak, the exponent is the amount of times a number has been multiplied by itself.
The exponent determines how many times a number is multiplied by itself, as was shown above. The mathematical notion known as the power serves as an example of the recurring multiple of the same integer or factor.
Therefore the simplified expression is -6.
To learn more about exponents visit:
https://brainly.com/question/15993626
#SPJ9
Identify the diameter of⊙Q, given that A=169π2please help
Solution:
Given that the area of circle Q is;
[tex]A=169\pi in^2[/tex]Also, the general formula is;
[tex]\begin{gathered} A=\pi r^2 \\ \\ \text{ Where }r=radius \end{gathered}[/tex]Thus, the radius, r, of the circle is;
[tex]\begin{gathered} 169\pi=\pi r^2 \\ \\ r^2=169 \\ \\ r=\sqrt{169} \\ \\ r=13in \end{gathered}[/tex]Thus, the diameter, d, is;
[tex]\begin{gathered} d=2r \\ \\ d=2(13in) \\ \\ d=26in \end{gathered}[/tex]ANSWER: The diameter of the circle is 26in
i wasn’t sure what the real answer was i did l x w and got 168
Solution
The area of the parallelogram is
[tex]\begin{gathered} A=bh \\ A=21\times8 \\ A=168in^2 \end{gathered}[/tex]Therefore the area of the figure = 168in²
Reason that y=f(x+a) is a horizontal translation by -a and not +a
Solution:
Given:
[tex]y=f(x+a)[/tex]y = f(x + a) is a horizontal translation left by a units.
Hence, the coordinate is transformed as shown;
[tex](x,y)\rightarrow(x-a,y)[/tex]Hence, since it is a horizontal translation to the left, it is translated by -a units from the original x-coordinate given.
1.y = 6xSolve:(4x + y = 72.y = 3xsolve: { x + 2y + 703Which equation, together with y = -1.5x + 3, makes a system with one solution?Ay = -1.5x + 6B.y = -1.5xC.2y = -3x + 6D.2y + 3x = 6IE.y = -2x + 34.The system x - 6y = 4, 3x - 18y = 4 has no solution.a.Change one constant or coefficient to make a new system with one solution.b.Change one constant or coefficient to make a new system with an infinite number ofsolutions5.Match each graph to its equation.Im
The system of equations:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]This comes from the fact that if we multiply the first equation by 3 then we have:
[tex]3x-18y=12[/tex]But this clearly contradicts the second one. Then the system has no solutions.
a.
To find a system with one solution we only have to change one of the coefficients of the equation. If we change the first x coefficient from 1 to 2. then we have the system:
[tex]\begin{gathered} 2x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]which has one solution.
b.
To find a system with an infinite number of solutions we can change the constant of the second equation to 12, then:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=12 \end{gathered}[/tex]then if we multiply the first by 3 then we have the second one, therefore the equations are the same and the system will have and infinite number os solutions.
What polynomial must be added to x² - 2x + 6 so that the sum is 3x^2 + 7x ? A. 4x^2 + 5x + 6 B. 3x² + 9x + 6 C. 3x² + 9x - 6 D. 2x² + 9x - 6 E. 2x^2 – 5x + 6
Answer:
The polynomial that must be added is;
[tex]2x^2+9x-6[/tex]Explanation:
Given the polynomial;
[tex]x^2-2x+6[/tex]We want to find the polynomial that must be added to it to give the polynomial;
[tex]3x^2+7x[/tex]To get that we will subtract the polynomial from the sum;
[tex]\begin{gathered} 3x^2+7x-(x^2-2x+6) \\ =3x^2+7x-x^2+2x-6) \\ \text{rearranging;} \\ =3x^2-x^2+7x+2x-6 \\ \text{simplifying;} \\ =2x^2+9x-6 \end{gathered}[/tex]Therefore, the polynomial that must be added is;
[tex]2x^2+9x-6[/tex]Suppose some government bonds are paying 5.8% simple interest. How much should you invest in the bonds if you want them to be worth $5,000 in 9 years? Round your final answer to two decimal places.
The simple interest formula is given by:
[tex]FV=PV(1+in)[/tex]FV: future value
PV: present value
i: interest rate
n: interest periods
We have from the question:
FV: $5000
PV: ?
i: 5.8%
n: 9.
Then:
[tex]5000=PV(1+(0.058\cdot9))[/tex]Thus
[tex]PV=\frac{5000}{1.522}\Rightarrow PV=3285.15[/tex]Then, we should invest in $3285.15 to have $5000 in 9 years.
Here are the ages (in years) of 10 professors at a college. , 44,38,45,34,28,56,54,28,61,48.what is the percentage of these professors who is younger than 47
Solution:
Given:
The ages in years of the 10 professors at a college to be;
44,38,45,34,28,56,54,28,61,48
Professors who are younger than 47 = 44,38,45,34,28,28
Number of Professors who are younger than 47 = 6
The percentage of these professors who is younger than 47 =
[tex]\begin{gathered} =\frac{6}{10}\text{ x 100} \\ =60\text{ \%} \end{gathered}[/tex]Therefore, the percentage of professors who is younger than 47 is 60%
Given the rectangle above, what is a possible representation of the area?
The area of a rectangle is it's width multiplied by it's length.
For this rectangle, it's lenght is:
[tex]L=x+5[/tex]And it's width is
[tex]W=x[/tex]When you multiply both of them you get the area A:
[tex]A=L\cdot W=(x+5)\cdot x[/tex]It can also be writen as:
[tex]A=x^2+5x[/tex]Simplify the expression. (W6) (w^8)^3=
We must simplify the following expression:
[tex](w^8)^3.[/tex]To simplify this expression, we must take into account the following property:
[tex](x^a)^b=x^{a\cdot b}.[/tex]Using the property above, we have:
[tex](w^8)^3=w^{8\cdot3}=w^{24}\text{.}[/tex]Answer
[tex](w^8)^3=w^{24}[/tex]Need help with #3, also might not respond very quick. Please don’t end session if I don’t!!
from the question,
if it takes the rate of 2 seats in 11 minutes
then we will we will set up a proportion to show how many minutes it will take at the rate of 1 seat.
so if,
so lets make the munites to make 1 seat be x
2 seats = 11 minutes
1 seat = x
lets cross multiply
2 X x = 11 X 1
2x = 11
divide both sides by 2
2x/2 = 11/2
x = 5.5 minutes
so i will take 5.5 minutes to make 1 seat.
*16. What is the leading coefficient of the polynomial function f(x) = 9-2x + 6x² + 5x³?A. 9 B. 3 C. 5 D. 4
ANSWER :
C. 5
EXPLANATION :
The Leading coefficient is the coefficient of the leading term.
The leading term is the term with the highest degree.
From the problem, we have the polynomial :
[tex]f(x)=9-2x+6x^2+5x^3[/tex]The term with the highest degree is 5x^3
Therefore, the leading coefficient is 5