Solution
Step 1
Write the equation:
[tex]x^2\text{ + 6x - 4 = 0}[/tex]Step 2:
Rewrite the equation:
[tex]x^2\text{ + 6x = 4}[/tex]Step 3
[tex]\begin{gathered} Add\text{ }\frac{b^2}{4a\text{ }}\text{ to both sides to get a perfect square.} \\ \text{a = 1, b = 6} \\ \frac{b^2}{4a}\text{ = }\frac{6^2}{4\times1}\text{ = }\frac{36}{4}\text{ = 9} \end{gathered}[/tex][tex]\begin{gathered} x^2\text{ + 6x + 9 = 4 + 9} \\ Add\text{ similar terms:} \\ (x\text{ + 3\rparen}^2\text{ = 13} \end{gathered}[/tex]Final answer
[tex]d)\text{ \lparen x + 3\rparen}^2\text{ = 13}[/tex]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.
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.
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in tall, and the initial velocity of the ball is 30 ft per sec. The height s of the ball in feet isgiven by the equation s= -2.7t^2 + 30t + 6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b.a. After how many seconds is the ball 18 ft above the moon's surface?After ____ seconds the ball will be 18 ft above the moon's surface.(Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
In order to find when the ball will be 18 ft above the moon's surface, we need to equal the expression to 18
[tex]18=-2.7t^2+30t+6.5[/tex]then, solve the associated quadratic expression
[tex]\begin{gathered} 0=-2.7t^2+30t+6.5-18 \\ 0=-2.7t^2+30-11.5 \\ using\text{ }the\text{ }quadratic\text{ }formula \\ x=\frac{-30\pm\sqrt{(30)^2-4\ast(-2.7)\ast(-11.5)}}{2\ast(-2.7)} \\ x_1\cong0.40 \\ x_2\cong10.72 \end{gathered}[/tex]answer:
after 0.40 seconds the ball will be 18 ft above the surface
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.
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-5Finding 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 statement is true if the graph of the linear function passes through the points (-1, -6)and (5,6) function first if needed
The correct option is C
Explanation:We check through each of the options to see if they are true
Option A is not true
The slope of the graph is as follows:
(6 - (-6))/((5 - (-1))
= (6 + 6)/(5 + 1)
= 12/6
= 2
Option B is not true
The zero of the graph is the point on the x-axis where y = 0, this is x = 2
Option C is true
The x-intercept is the point where the graph crosses the x-axis. This is (2, 0)
Option D is not true
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.
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.
guys please help
60% of = 45
Answer:
Step-by-step explanation:
Answer: 75
Use the equation is/of = %/100
Plug in the numbers to get 45/x = 60/100
Cross Multiply and you get 60x = 4500
Divide both sides by 60
X = 75.
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.
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)
Thursday: Word Problems 1 The plant growth is proportional to time. When Tia bought the plant, it measured 2 cm. It measured 2.5 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth.
We have the next informtion
initial measure = 2 cm
after
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
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.
Create an expression that can be used to find the value of x
There are two possible expressions that can help to calculate "x"
First
[tex]\begin{gathered} \text{ cos 28 = }\frac{42}{x} \\ \text{ } \end{gathered}[/tex]Second
[tex]\text{ sec 28 = }\frac{x}{42}[/tex]Both are possible to find "x".
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.
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:
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]Help Please!!use the drawing to form the correct answers on the graph complete the function table for the given domain and plot the points on the graph
The Solution:
The given function is
[tex]f(x)=-x^2+2x+5[/tex]Step 1:
We shall complete the table.
Explanation of how the table was completed:
Substituting each value of x to obtain the corresponding value of y.
[tex]\begin{gathered} f(-1)=-(-1)^2+2(-1)+5=-1-2+5=2 \\ f(0)=-(0)^2+2(0)+5=5 \\ f(1)=-(1)^2+2(1)+5=-1+2+5=6 \\ f(2)=-(2)^2+2(2)+5=-4+4+5=5 \\ f(3)=-(3)^2+2(3)+5=-9+6+5=2 \end{gathered}[/tex]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
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)
From the graph identify the zeros of the quadratic function
The zeros of the function are the points where it crosses the x axis:
Answer: (1,0) and (3,0)
7. Let f(x) = 3x and g(x) = (x + 2)^2. Find the value of (f og)(-5)A.135B. -27 C. 169. D.27.
f(x)= 3x
g(x)= (x+2)²
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;
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]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
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.