Identity equations are always true, no matter the values that the variables take.
We have to calculate for each one, and if the result gives a true statement, then the equation is an identity:
1) 3(x - 1) = x + 2(x + 1) + 1
[tex]\begin{gathered} 3\left(x-1\right)=x+2\left(x+1\right)+1 \\ 3x-3=x+2x+2+1 \\ 3x-3=3x+3 \\ 3x-3x=3+3 \\ 0=6 \end{gathered}[/tex]This is FALSE (for any value of x), so the equation is not an identity.
2) x-4(x + 1) = -3(x + 1) + 1
[tex]\begin{gathered} x-4\left(x+1\right)=-3\left(x+1\right)+1 \\ x-4x-4=-3x-3+1 \\ x(1-4+3)=-2+4 \\ 0=2 \end{gathered}[/tex]This is FALSE, so the equation is not an identity.
3) 2x + 3 = 1 (4x + 2) + 2
[tex]\begin{gathered} 2x+3=14x+2+2 \\ 3-2-2=14x-2x \\ -1=12x \\ x=\frac{-1}{12} \end{gathered}[/tex]This equation holds true only for x=-1/12, so it is not an identity.
4) (6x - 3) = 3(x + 1) – x-2
[tex]\begin{gathered} \left(6x-3\right)=3\left(x+1\right)-x-2 \\ 6x-3=3x+3-x-2 \\ 6x-3=2x+1 \\ 6x-2x=1+3 \\ 4x=4 \\ x=1 \end{gathered}[/tex]This equation holds true only for x=1, so it is not an identity.
Neither of the options is an identity.
Where would 5pi be located on a number line? Show all thoguhts.
In order to locate 5π in a number line, you consider that π = 3.141516...
When this irrational number is multiplied by 5 you obtain:
5 x π = 5 x 3.141516... = 15.70796...
Then, if you have a number line with ten subdivisions between units, the position of 5π on the number line can be as follow:
State the solution in terms of x 4^x+6 = 20
We have the question as
[tex]4^{x+6}=20[/tex]Let us introduce logarithms to base 4 to both sides of the equation:
[tex]\log _44^{x+6}=\log _420[/tex]Applying the law of logarithm that states
[tex]\log A^B=B\log A[/tex]we have
[tex](x+6)\log _44=\log _420[/tex]Applying the law that states
[tex]\log _nn=1[/tex]we have
[tex]\begin{gathered} (x+6)\times1=\log _420 \\ x+6=\log _420 \end{gathered}[/tex]Collecting like terms, we have
[tex]x=-6+\log _420[/tex]Therefore, the answer is OPTION C.
1. At first street elementary school, about 21% of the 645 students ride bicycles to school. About how many students ride bicycles to school? 2. A team of biologists captured and tagged 50 deer in a forest. Two weeks later, the biologists captured a sample of 20 deer from the same forest, and found that 5 of them were tagged. How many deer would they estimate are in the forest.
1 Given that about 21% of the 645 students ride bicycles to school
The number of students that ride bicycles to school
= 21% * 645
= 21/100 * 645
= 135.45
Hence about 135 students ride bicycles to school.
Here is a system of linear equations: Which would be more helpful for solving the system: adding the two equations or subtracting one from the other? Explain your reasoning. Solve the system without graphing. Show your work.
Okay, here we have this:
Considering the provided system we obtain the following:
The option more helpful for solving the system is add one equation to the other because in this way we can cancel the term of the "y", if we solve the system we obtain the following:
[tex]\begin{bmatrix}2x+\frac{1}{2}y=7 \\ 6x-\frac{1}{2}y=5\end{bmatrix}[/tex]Adding the equations:
[tex]\begin{gathered} 8x=12 \\ x=\frac{12}{8} \\ x=\frac{3}{2} \end{gathered}[/tex]Now, let's replacing in the first equation with x=3/2:
[tex]\begin{gathered} 2(\frac{3}{2})+\frac{1}{2}y=7 \\ 3+\frac{1}{2}y=7 \\ \frac{y}{2}=4 \\ y=8 \end{gathered}[/tex]Finally we obtain that the solution to the system is x=3/2 and y=8.
What is the perimeter of the dinning room? Perimeter is distance around the room, rounded to the nearest hundredth
To answer this question, we will use the following formula to determine the perimeter of the dining room:
[tex]P=2w+2l,[/tex]where w is the width and l is the length.
Substituting w=9 feet and l=10feet 8 inches=, we get:
[tex]P=2(9ft)+2(10ft8in)=18ft+2(10ft+\frac{8}{12}ft)\text{.}[/tex]Simplifying the above result, we get:
[tex]P=18ft+20ft+\frac{16}{12}ft=38ft+\frac{16}{12}ft=\frac{118}{3}ft\text{.}[/tex]Answer: The perimeter is 39.33ft.
Write in descending order.420t + 201 to the 3rd power -210t to the 2nd power
To answer this, we need to see the polynomial. Descending order is in a way that the first term of the polynomial will be three, the second (in descending order, two....and so on).
420t+20t3-210t2
In descending order is:
20t^3 - 210t^2 + 420t
So, the option is number two.
I have an ACT practice guide problem that I need answered and explainedIt has a list of answers to choose from I will list that belowA. 1B. -2C. 4D. The limit does not exist.
SOLUTION
The limit of a function at a point aa in its domain (if it exists) is the value that the function approaches as its argument approaches a.
The limit of a function F exist if and only if
[tex]\begin{gathered} \lim _{x\rightarrow x^+}f(x)=\lim _{x\rightarrow x^-}f(x) \\ \\ \text{The left-hand limit =The Right-hand Limit} \end{gathered}[/tex]Considering the image given, the limit of the function from the left is from the first graph
[tex]\lim _{x\rightarrow1^-}f(x)=4\Rightarrow\text{ The left hand limit}[/tex]
Similarly, the limit of f(x) from the right-hand side is on the second graph
[tex]\lim _{x\rightarrow1^+}f(x)=-2\Rightarrow The\text{ Right -hand limit}[/tex]Since
[tex]\begin{gathered} \text{Left-hand limit}\ne Right\text{ hand imit} \\ 4\ne-2 \end{gathered}[/tex]Therefore
The Limit does not exist (D)
At a restaurant, the choices for hamburger toppings are cheese, tomato, lettuce,onion, mayo, mustard, ketchup and pickles. If you choose 5 toppings, how manyways can you pick your toppings?(Hint: Is this a combination or permutation?)
at the restauant we can choose 5 topping for a hamburger,
let us solve using combination,
[tex]^5C_0+^5C_1+^5C_2+^5C_3+^5C_4+^5C_5=[/tex]we know that,
[tex]^nC_0+^nC_1+^nC_2+\ldots+^nC_5=2^n[/tex]thus,
[tex]\begin{gathered} ^5C_0+^5C_1+^5C_2+^5C_3+^5C_4+^5C_5=2^5 \\ =32 \end{gathered}[/tex]hence, there are 32 ways to pick the toppings.
Given:Circle B with tangent AD and tangent DC. Arc AC has a measure of 85. What is the relationship between m
Answer:
They are supplementary
Explanation:
If AD is tangent to circle B, then the measure of ∠BAD is 90°. In the same way, if DC is tangent to circle B, the measure of ∠DCB is 90°.
So, we can complete the graph as:
Then, the sum of the interior angles of a quadrilateral is 360°, so we can calculate the m∠ADC as:
m∠ADC = 360 - 90 - 90 - 85
m∠ADC = 95°
Now, the sum of m∠ABC and m∠ADC is equal to:
m∠ABC + m∠ADC = 85 + 95 =180
Since the sum is 180, we can say that ∠ABC and ∠ADC are supplementary angles.
differentiate y=4x√3x²-8x
Okay, here we have this:
Considering the provided function, we are going to perform the requested operation, so we obtain the following:
[tex]\begin{gathered} y=4x\sqrt{3}x^2-8x \\ \\ y=4\sqrt{3}x^3-8x \\ \\ \frac{dy}{dx}=\frac{d}{dx}(4\sqrt{3}x^3)-\frac{d}{dx}(8x) \\ \\ \frac{dy}{dx}=12\sqrt{3}x^2-8 \end{gathered}[/tex]Finally we obtain that dy/dx is equal to: 12sqrt(3)x^2-8
if a=5x-2 and b=5x-22 , what is the value of x ?
Trigonometry
We are given the following condition:
sin (a) = cos (b)
Since both angles are acute, the following relationship must apply:
a = 90° - b
Both angles must be complementary
Substituting the values for each angle:
a = 5x - 2
b = 5x - 22
We have:
5x - 2 = 90 - (5x - 22)
Removing brackets:
5x - 2 = 90 - 5x + 22
Adding 5x:
5x - 2 + 5x = 90 + 22
Adding 2:
5x + 5x = 90 + 22 + 2
Simplifying:
10x = 114
Dividing by 10:
x = 114/10
x = 11.4
Correct choice: C)
HELP PLEASE AND THANK YOU
Answer: 1/4
Step-by-step explanation:
1/4 chance
46. Identify the center and radius of a circle given the equation is (x - 2)^2 + (y + 4)^2= 36
Answer: Center: (2, –4); Radius: 6.
Explanation
The equation of a circle in standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the center and r is the radius. Thus, in our given equation:
[tex]\left(x-2\right)^2+(y+4)^2=36[/tex]• h = 2
,• k = –4 (it is negative as negative sign times negative sign equals positive sign)
,• r² = 36
Therefore, the center is (2, –4) and the radius is:
[tex]r^2=36[/tex][tex]\sqrt{r^2}=\sqrt{36}[/tex][tex]r=6[/tex]Finding zeros of the function -x^3+2x^2+5x-6
SOLUTION:
Step 1:
In this question, we are meant to find the zeros of the function:
[tex]x^3+2x^2+\text{ 5 x -6}[/tex]Step 2:
The details of the solution are as follows:
The graph solution of this function is as follows:
CONCLUSION:
The only real zero of the function:
[tex]x^3+2x+5x\text{ - 6}[/tex]is at:
[tex]x\text{ = 0. 82 ( 2 decimal places)}[/tex]Which of the following properties are being used to simplify the statement (3x + 4y) + 5x = 8x + 4y? Associative and commutative properties of addition Associative property of addition and commutative property of multiplication O O OC Associative and commutative properties of multiplication Associative property of multiplication and commutative property of addition
Answer:
Associative and commutative properties of addition
Explanation:
The one thing that the associative property of addition says that
[tex](a+b)+y=a+b+y[/tex]and the commutative property of addition says
[tex]a+b=b+a[/tex](the order of addition does not matter )
Now, the steps we take to solve our equation are the following:
[tex]\begin{gathered} \mleft(3x+4y\mright)+5x=8x+4y \\ 3x+4y+5x=8x+4y\text{ (the associative property of addition )} \end{gathered}[/tex]The second step is
[tex]\begin{gathered} 3x+4y+5x=8x+4y\text{ } \\ 3x+5x+4y=8x+4y\text{ (commutative property of addition.)} \end{gathered}[/tex]which simplifies to
[tex]\begin{gathered} 8x+4y=8x+4y \\ 4y=4y \end{gathered}[/tex]Hence, we used associative and commutative properties of addition to solve our equation.
Colton has already jarred 18 liters of jam and will jar an additional 1 liter of jam every day. How many days does Colton need to spand making jam if he wants to jar 26 liters of jam in all?
8 days more
you have a square with side length of 4 meters. how many square meters is the garden
Given:
The length of the side of a square garden is a=4 meters.
To find the area of the square garden:
Using the area formula of the square,
[tex]\begin{gathered} A=a^2 \\ =4\times4 \\ =16m^2 \end{gathered}[/tex]Thus, the area of the square garden is 16 square meters.
6x-(2x+5) need help please
we have the expression
6x-(2x+5)
remove the parenthesis
6x-2x-5
Combine like terms
4x-5
therefore
the answer is 4x-5To convert temperatures in Fahrenheit to temperatures in Celsius, take the temperature in degrees Fahrenheit, subtract 32, then divide the result by 1.8. This gives the temperature in degrees Celsius. Write an equation that shows the conversion process to Celsius using the variables c and f then convert a Celsius temperature of 10 degrees to Fahrenheit.
We will have the following:
*We are given the expression:
[tex]F=C\cdot\frac{9}{5}+32[/tex]*Now, we solve for C:
[tex]C=(F-32)\frac{5}{9}[/tex]***We convert 10 °C to Fahrenheeit:
[tex]F=(10)\frac{9}{5}+32\Rightarrow F=50[/tex]So 10°C are 50°F.
Part 1Carson is g year old Haley is 2 yrs younger than Carson. find the sum of their ages in terms of gPart 2Find some of their ages in "g" years time, in terms of g
Part 1
Carson is "g" years old.
Haley is 2 years younger than Carson, you can express her age as "g-2"
To sum their ages you have to add both expressions:
[tex]\begin{gathered} \text{AgeCarson}+\text{AgeHaley} \\ g+(g-2) \end{gathered}[/tex]To simplify the expression, you have to erase the parentheses and add the like terms, i.e., add both "g-terms"
[tex]\begin{gathered} g+g-2 \\ 2g-2 \end{gathered}[/tex]The sum of their ages in terms of g is: Age(g)=2g-2
Part 2
You need to find some of their ages, this means that you have to choose any value for "g" and determine the age of Carson and Haley
For example:
For g=10 years:
Carson's age: g= 10 years-old
Haley's age: g-2=10-2= 8 years-old
The sum of their ages is: 2g-2=(2*10)-2= 20-2= 18 years
For g=15 years:
Carson's age: g= 15 years-old
Haley's age: g-2= 15-2= 13 years-old
The sum of their ages is: 2g-2= (2*15)-2= 30-2= 28 years
you are pouring canned soda into a cylinder cylinder that is 12 cm tall and a diameter of 6.5 cm The picture is 36 cm tall and has a diameter of 20 cm how many cans of soda will the picture hold
We are going to assume that the picture of 36 tall and has a diameter of 20 cm is also a cylinder.
To answer this question, we need to know the formula to find the volume of a cylinder:
[tex]V_{\text{cylinder}}=\pi\cdot r^2\cdot h[/tex]Where
• r is the radius of the base of the cylinder.
,• h is the height of the cylinder.
,• pi = 3.14159265358979...
From the question, we have:
The dimensions of the first cylinder are:
h = 12cm
D = 6.5cm.
Since the radius of a circle is half of its diameter, then, we have that the radius of this cylinder is 6.5cm/2 = 3.25cm.
Then, r = 3.25cm.
Then, the volume of this cylinder is:
[tex]V_{\text{cylinder}}=\pi\cdot(3.25\operatorname{cm})^2\cdot12\operatorname{cm}=\pi\cdot10.5625\operatorname{cm}\cdot12\operatorname{cm}=126.75\pi cm^3[/tex]Now, we need to find the volume of the cylinder of the picture following the same procedure:
h = 36cm
D = 20cm ---> r = D/2 ---> r = 20cm/2 ---> r = 10cm
[tex]V_{\text{cylinderpicture}}=\pi\cdot(10\operatorname{cm})^2\cdot36\operatorname{cm}=\pi\cdot100\operatorname{cm}^2\cdot36\operatorname{cm}[/tex]Then, we have that the volume of the cylinder of the picture is:
[tex]V_{\text{cylinderpicture}}=3600\pi cm^3[/tex]Thus, we have that we poured a canned soda into a cylinder of 147pi cm^3. How many cans of soda will hold the cylinder of the picture? We need to divide the total volume of the cylinder of the picture by the volume of the first cylinder (the one which contains the canned soda). Then, we have:
[tex]N_{\text{cannedsoda}}=\frac{V_{\text{cylinderpicture}}}{V_{\text{cylinder}}}=\frac{3600\pi cm^3}{126.75\pi cm^3}\Rightarrow N_{cannedsoda}=28.402367[/tex]Therefore, the cylinder of the picture will hold about 28.40 canned sodas.
8 G Find the area of the shaded area. Round your answer to the nearest tenth
Answer:
47.1 units^2
Explanation:
The area of the shaded region is equal to the area of the bigger circle minus the area of the smaller circle.
Now, the area of a circle is given by
[tex]A=\pi r^2[/tex]where r is the radius of the circle.
The radius of the bigger circle is r = 8; thereofre, the area is
[tex]\begin{gathered} A=\pi(8)^2 \\ A=64\pi \end{gathered}[/tex]And the radius of the smaller circle is r = 7; therefore, the area is
[tex]A=\pi(7)^2[/tex][tex]A=49\pi[/tex]The area of the shaded region is the difference between the two areas above:
[tex]Area=64\pi-49\pi[/tex][tex]\text{Area}=15\pi[/tex][tex]\text{Area}=15(3.1415)[/tex]Rounded to the nearest tenth the answer is
[tex]\text{Area}=47.1[/tex]Barry spent 1/5 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill. If $1012 was left, what was his monthly salary?
Given:
1/5 of Barry's salary was going for his rent.
1/7 of Barry's salary was going for his utility bill.
1012 dollars was left after all the payments.
Required:
What was his monthly salary?
Explanation:
Let us assume that Barry's monthly salary is 'x'
So the sum of his payments and the balance amount will give us his total salary.
[tex]total\text{ }salary=rent\text{ }payment+utility\text{ }payment+money\text{ }left[/tex]Now Barry uses 1/5 of his salary in rent, that is
[tex]\begin{gathered} rent\text{ }payment=\frac{1}{5}\times his\text{ }total\text{ }salary \\ \\ rent\text{ }payment=\frac{1}{5}\times x \end{gathered}[/tex]Barry uses 1/7 of his salary in utility bill, that is
[tex]\begin{gathered} utility\text{ }bill=\frac{1}{7}\times his\text{ }total\text{ }salary \\ \\ utility\text{ }bill=\frac{1}{7}\times x \end{gathered}[/tex]And after all the payments the money he is left with is 1012 dollars.
[tex]money\text{ }left=1012[/tex]Now let's calculate his total salary
[tex]\begin{gathered} total\text{ }salary=rent\text{ }payment+utility\text{ }bill+money\text{ }left \\ \\ x=\frac{1}{5}\times x+\frac{1}{7}\times x+1012 \\ \\ x=\frac{x}{5}+\frac{x}{7}+1012 \\ \\ x=\frac{7x+5x}{35}+1012 \end{gathered}[/tex]Simplifying it further we get
[tex]\begin{gathered} x=\frac{12x}{35}+1012 \\ \\ x-\frac{12x}{35}=1012 \\ \\ \frac{35x-12x}{35}=1012 \\ \\ \frac{23x}{35}=1012 \end{gathered}[/tex][tex]\begin{gathered} 23x=1012\times35 \\ \\ 23x=35420 \\ \\ x=\frac{35420}{23} \\ \\ x=1540 \end{gathered}[/tex]x = 1540 dollars
Final Answer:
Barry's monthly salary is 1540 dollars.
Which is not a true equation?O A. -12 · 4 = -3O B. 100 = -25 = -4O C. -72 = -9 = 80 D. –32 - 0 = 32
In the last option:
-32 / 0 = 32
But we can not divide by 0, it is undefined in mathematics, so this is not a true equation.
Answer: Option D
graph a line that passes through (-4,1) and has a slope of -3
We are given a point with coordinates;
[tex]\begin{gathered} (x,y)=(-4,1) \\ m=-3 \end{gathered}[/tex]We begin by expressing the line in slope-intercept form as follows;
[tex]\begin{gathered} y=mx+b \\ \text{Where,} \\ (x,y)=(-4,1) \\ m=-3,\text{ we now have} \\ 1=-3(-4)+b \\ 1=12+b \\ \text{Subtract 12 from both sides;} \\ 1-12=12-12+b \\ b=-11 \\ The\text{ equation now becomes;} \\ y=mx+b \\ y=-3x+(-11) \\ y=-3x-11 \end{gathered}[/tex]The graph would now be a shown below;
I need to know if I got number 13 right
The given side lengths are 38mm, 45mm, and 82mm.
It is required to use inequalities to prove if the side lengths could form a triangle.
Recall the Triangle Inequality Theorem: The Triangle Inequality Theorem states that the sum of the measures of two sides of a triangle is greater than the measure of the third side.
Check the inequality:
[tex]\begin{gathered} 38+45>82\Rightarrow83>82-True \\ 38+82>45\Rightarrow120>45-True \\ 45+82>38\Rightarrow127>38-True \end{gathered}[/tex]Hence, the side lengths can form a triangle.
The required inequality is 38+45>82.
If each side of an equilateral triangle is 2 inches long, then what is the area of the triangle?
Solution:
The image below represents the equilateral triangle of 2 inches long
From the triangle above, the given values include
[tex]\begin{gathered} a=2in \\ b=2in \\ c=2in \end{gathered}[/tex]Concept:
To calculate the area of the triangle, we will use Heron's formula below
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where,s = semi perimter} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]Step 1:
Calculate the semi perimeter s
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{2in+2in+2in}{2} \\ s=\frac{6in}{2} \\ s=3in \end{gathered}[/tex]Step 2:
Substitute the value of s,a,b,c in the heron's formula
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{3(3-2)(3-2)(3-2)} \\ A=\sqrt[]{3\times1\times1\times1} \\ A=\sqrt[]{3} \\ A=1.73in^2 \end{gathered}[/tex]Hence,
The area of the triangle = 1.73 squared inches
Look at this diagram: AL G 3 © © 5 15 HE
Answer:
Slope = 1
y-intercept = -2
Equation: y = x
Explanation:
Given the following coordinates;
(6, 4) and (2, 0)
Get the slope
Slope = y2-y1/x2-x1
Slope = 0-4/2-6
Slope = -4/-4
Slope = 1
Get the y -intercept:
Substitute B(6,4) and m = 1 into y = mx+b
4 = 1(6) + b
4 = 6 +b
b = 4-6
b = -2
Get the required equation
Recall that y = mx+b
y = 1x + (-2)
y = x - 2
This gives the required equation
Suppose that the functions g and h are defined for all real numbers x as follows. 9g(x) = 2x ^ 2 h(x) = x - 3Write the expressions for (hg)(x) and (h + g)(x) and evaluate (h - g)(- 3) .
Given
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]To write the expressions of
[tex]\begin{gathered} (h\cdot g)(x) \\ (h+g)(x) \end{gathered}[/tex]And to evaluate,
[tex](h-g)(-3)[/tex]Explanation:
It is given that,
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (h\cdot g)(x)=h(x)\cdot g(x) \\ =\left(x-3\right)\cdot\left(2x^2\right) \\ =2x^3-6x^2 \end{gathered}[/tex]Also,
[tex]\begin{gathered} (h+g)(x)=h(x)+g(x) \\ =(x-3)+2x^2 \\ =2x^2+x-3 \end{gathered}[/tex]And,
[tex]\begin{gathered} (h-g)(-3)=h(-3)-g(-3) \\ =(-3-3)-2(-3)^2 \\ =-6-(2\times9) \\ =-6-18 \\ =-24 \end{gathered}[/tex]Hence, the answer is,
[tex]\begin{gathered} (h\cdot g)(x)=2x^3-6x^2 \\ (h+g)(x)=2x^2+x-3 \\ (h-g)(-3)=-24 \end{gathered}[/tex]Convert the following equation
into slope-intercept form.
-4x + y = 12
°y = [ ? ]x +
Enter every answer is wrong need help
Answer:
Step-by-step explanation: im in 7th grade