find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. x^2+10x+n
Answers
From the problem, we have :
[tex]x^2+10x+n[/tex]To make it a perfect square trinomial, we will use the formula :
[tex]n=(\frac{b}{2a})^2[/tex]and we can factor the trinomial as :
[tex](x+\frac{b}{2a})^2^{}[/tex]a = 1 and b = 10
so n will be :
[tex](\frac{b}{2a})^2=(\frac{10}{2\times1})^2=5^2=25[/tex]The value of n is n = 25
and the factor of the trinomial will be (x + 5)^2
Answer: the answer is (x + 5)^2
Step-by-step explanation:
Related Questions
A box has s snack bags in it. Each snack bag contains c carrot sticks.Which equation can be used to find b , the number of carrot sticks in one box?Ab = s/cB b = scCb = s+c Db = c/s
Answers
Solution
For this case we have s snacks and each snack with c carrot sticks
So then if we want to find the total of carrot sticks in one box we can do the following operation:
B. b = sc
Convert from degrees-minutes-seconds to decimal degrees.Round your answer to the nearest thousandth.
Answers
Given:
[tex]25\degree46^{\prime}11^{\prime}^{\prime}[/tex]Required:
To convert the given degrees-minutes-seconds to decimal degrees.
Explanation:
Consider
[tex]25\degree46^{\prime}11^{\prime}^{\prime}[/tex]Now
[tex]\begin{gathered} 11\div3600=0.00305 \\ \\ 46\div60=0.76666 \\ \\ 25\div1=25 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} =25+0.76666+0.00305 \\ =25.76971\degree \end{gathered}[/tex]Final Answer:
[tex][/tex]A file that is 284 megabytes is being downloaded. If the download Is 17.5% complete, how many megabytes have been downloaded? Round your answer to thenearest tenth.megabytesх5?
Answers
We are given the size of a file to download is 284 megabytes. If 17.5% has complete,
We want to find the megabytes that has been downloaded
Solution
We have
[tex]284mb[/tex]The 17.5% of 284mb will be
[tex]\begin{gathered} \frac{17.5}{100}\times284 \\ =\frac{497}{10} \\ =49.7mb \end{gathered}[/tex]Therefore, the megabytes that have been downloaded is 49.7mb (to the nearest tenth)
Find the number of degrees in the acute angle formed by the intersection of walnut street and elm street
Answers
Given two parallel lines and a transversal
So, the angles (2x + 33) and ( 5x - 15 ) are congruent because they are corresponding angles
So, 5x - 15 = 2x + 33
Solve to find x
[tex]5x-15=2x+33[/tex]Combine like terms:
[tex]\begin{gathered} 5x-2x=33+15 \\ 3x=48 \\ x=\frac{48}{3}=16 \end{gathered}[/tex]So, the required angle = 2x + 33 = 2 * 16 + 33 = 32 + 33 = 65
So, the angle is 65
• An ice cube is slowly melting, losing 3cm^3 of water each hour. If it is always a perfect cube, (V=s^3), what is the rate of change of its side length when it has 8 cm^3 of ice left?
Answers
Given:
The volume is decreasing at the rate of 3 cm^3 per hour.
The volume of the left ice is 8 cm^3.
Aim:
We need to find the rate of change of the side of the cube.
Explanation:
Let the length of the cube is denoted as s.
Consider the volume of the cube.
[tex]V=s^3[/tex]Since the volume is decreasing at the rate of 3 cm^3 per hour. we can write,
[tex]\frac{dV}{dt}=-3cm^3\/h[/tex]where t represents time and the negative sign represents decreasing.
Differentiate the volume with respect to s.
[tex]\frac{dV}{ds}=\frac{d}{ds}(s^3)=3s^2[/tex]To find the rate of change of the side length, we use the chain rule.
[tex]\frac{dV}{dt}=\frac{dV}{ds}\frac{ds}{dt}[/tex][tex]\text{ Substitute }\frac{dV}{dt}=-3\text{ and }\frac{dV}{ds}=3s^2\text{ in the equation.}[/tex][tex]-3=\frac{ds}{dt}(3s^2)[/tex][tex]-\frac{3}{3s^2}=\frac{ds}{dt}[/tex][tex]-\frac{1}{s^2}=\frac{ds}{dt}[/tex]Since the left ice is 8 cm ^3.
[tex]V=(s)^3=8[/tex][tex]s^3=2^3[/tex][tex]s=2cm[/tex][tex]Substitute\text{ s =2 in the equation}-\frac{1}{s^2}=\frac{ds}{dt}.[/tex][tex]-\frac{1}{2^2}=\frac{ds}{dt}.[/tex][tex]\frac{ds}{dt}=-\frac{1}{4}[/tex][tex]\frac{ds}{dt}=-0.25cm\text{ per hour}[/tex]Verification:
Let s =2 cm, then the volume is 8cm^3.
Let s =1.75cm, the volume is
Find the solution of the system of equations. 5x + 10y = -5 -5x - y = 32
Answers
5x + 10y = -5 ------------------------------(1)
-5x - y = 32 -------------------------------(2)
Add equation(1) and equation (2)
9y = 27
Divide both-side of the equation by 9
y = 3
Substitute y = 3 into equation (1) and solve for x
5x + 10(3) = -5
5x + 30 = -5
substract 30 from both-side of the equation
5x = -5 - 30
5x = -35
Divide both-side of the equation by 5
x = -7
The solution is (-7, 3)
i got question A &B i just can’t get C
Answers
Step 1
The domain refers to all values that go into a function. The range refers to all the values that come out.
Step 2
Find the domain
[tex]D=\mleft\lbrace2007,2008,2009\mright\rbrace[/tex]Step 3
Find the range
[tex]R=\mleft\lbrace234300,213200,\text{ 212,200}\mright\rbrace[/tex]At his new job, Manuel expects to make about $37,850 per year. He is paid bi-weekly. 15% of his gross pay will be withheld for federal income tax, 4% for state income tax and 7.65% for Social Security and Medicare taxes. Calculate his net pay, and how much he will pay in taxes each paycheck. a. Convert the Annual Pay to Biweekly Pay b. How much money will he pay in taxes each paycheck? c. What is the Net Pay (take-home pay)?
Answers
Answer:
(a)$1455.77
(b)$387.97
(c)$1067.80
Explanation:
(a)Manuel's proposed annual income = $37,850
There are 52 weeks in a year, this means that if he is paid bi-weekly (every two weeks), he will receive his salary 26 times a year.
His Biweekly pay will be:
[tex]\begin{gathered} =\frac{37,850}{26} \\ =\$1455.77 \end{gathered}[/tex](b)
Federal Income Tax = 15% of his gross pay
[tex]\begin{gathered} =\frac{15}{100}\times1455.77 \\ Federal\; Income\; Tax=\$218.37 \end{gathered}[/tex]State Income Tax = 4% of his gross pay
[tex]\begin{gathered} =\frac{4}{100}\times1455.77 \\ State\; Income\; Tax=\$58.23 \end{gathered}[/tex]Social Security and Medicare taxes = 7.65% of his gross pay
[tex]\begin{gathered} =\frac{7.65}{100}\times1455.77 \\ =\$111.37 \end{gathered}[/tex]The total taxes paid will be:
[tex]\begin{gathered} Taxes=218.37+58.23+111.37 \\ =\$387.97 \end{gathered}[/tex](c)
Therefore, his net pay (take-home pay) will be:
[tex]\begin{gathered} \text{Net Pay==}1455.77-387.97 \\ =\$1067.80 \end{gathered}[/tex]
Hi I need help with these problems only 1 and 3 since my teacher told us to do even number and if I don't know what to do at all
Answers
Since we are dealing with a right triangle, we can use the following trigonometric identities
[tex]\sin \theta=\frac{O}{H},\cos \theta=\frac{A}{H}[/tex]Where θ is an inner angle (different than 90°) of the triangle, O is the opposite side to θ, A is the adjacent side to θ, and H is the hypotenuse.
a) In our case,
[tex]\begin{gathered} \theta=30\text{degre}e \\ H=14,A=m,O=n \\ \Rightarrow\sin (30degree)=\frac{n}{14} \\ \Rightarrow n=14\cdot\sin (30degree)=14\cdot0.5=7 \\ \Rightarrow n=7 \end{gathered}[/tex]and
[tex]\begin{gathered} \Rightarrow\cos (30degree)=\frac{m}{14} \\ \Rightarrow m=14(\cos (30degree))=14\cdot\frac{\sqrt[]{3}}{2}=7\sqrt[]{3} \\ \Rightarrow m=7\sqrt[]{3} \end{gathered}[/tex]The answers are n=7 and m=7sqrt(3).
3) In a diagram, the problem states
Using the same trigonometric identities mentioned in part 1) (plus the tangent function), we get
[tex]\begin{gathered} \sin (30degree)=\frac{18}{H},\tan (30degree)=\frac{18}{A} \\ \Rightarrow H=\frac{18}{\sin(30degree)},A=\frac{18}{\tan(30degree)}=\frac{18}{\frac{1}{\sqrt[]{3}}}=18\sqrt[]{3} \\ \Rightarrow H=\frac{18}{0.5}=36,A=18\sqrt[]{3} \\ \Rightarrow H=36,A=18\sqrt[]{3} \end{gathered}[/tex]The hypotenuse is equal to 36 ft, and the other leg is equal to 18sqrt(3) ft
The graph in the figure shows the Smith family's driving plan for their vacation. If they want to stop and eat lunch after they've driven for 4 hours, how far will they have driven by lunchtime?Question 17 options:A) 120 milesB) 90 milesC) 60 milesD) 180 miles
Answers
ANSWER:
A) 120 miles
STEP-BY-STEP EXPLANATION:
We can determine at a distance through the graph, just like this:
This means that at 4 hours they have driven 120 miles.
Therefore, the correct answer is: A) 120 miles
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 6 and AD = 2, what is the length of AC? (Note: the figure is not drawn to scale.) B 6 2 D Answer: Submit Answer
Answers
The first step is to make a sketch of the triangle
The altitude (h= BD) of the triangle divides it into two similar right triangles and the hypothenuse, AC, into two line segments n= AD and m= DC.
The relationship between the altitude and the parts of the hypothenuse follows the ratios:
[tex]\frac{n}{h}=\frac{h}{m}[/tex]So, the first step is to determine the altitude of the triangle. To do so, you have to work with ΔABD, "h" is one of the sides of the triangle. Using the Pythagorean theorem you can determine the measure of the missing side:
[tex]a^2+b^2=c^2[/tex]Write the expression for the missing side:
[tex]\begin{gathered} b^2=c^2-a^2 \\ \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]Replace c=6 and a=2
[tex]\begin{gathered} h=\sqrt[]{6^2-2^2} \\ h=\sqrt[]{36-4} \\ h=\sqrt[]{32} \\ h=4\sqrt[]{2} \end{gathered}[/tex]Now that we have determined the value of the altitude, we can calculate the value of m
[tex]\frac{n}{h}=\frac{h}{m}[/tex]Write the expression for m:
-Multiply both sides by m to take it from the denominators place:
[tex]\begin{gathered} m\cdot\frac{n}{h}=m\cdot\frac{h}{m} \\ m\cdot\frac{n}{h}=h \end{gathered}[/tex]-Multiply both sides of the equal sign by the reciprocal of n/h
[tex]\begin{gathered} m(\frac{n}{h}\cdot\frac{h}{n})=h\cdot\frac{h}{n} \\ m=\frac{h\cdot h}{n} \\ m=\frac{h^2}{n} \end{gathered}[/tex]Replace the expression with h=4√2 and n=2 and calculate the value of m
[tex]\begin{gathered} m=\frac{h^2}{n} \\ m=\frac{(4\sqrt[]{2})^2}{2} \\ m=\frac{32}{2} \\ m=16 \end{gathered}[/tex]So DC=m= 16cm and AD=n= 2cm, now you can determine the measure of the hypothenuse:
[tex]\begin{gathered} AC=AD+DC \\ AC=2+16 \\ AC=18 \end{gathered}[/tex]The hypothenuse is AC=18cm
A quadrilateral is formed by the points A(1,-1), B(0,3), C(5,5), and D(6, 1). Plot the points and use the distance formula to find the lengths of all 4 sides. What type of quadrilateral is this?
Answers
If we have the given points on a cartesian point, the result would be:
It is not difficult to see that these points will form a rhombus. In this case, we do expect that the opposite sides have the same size. To verify it, we will use the following formula to calculate the distance among the given points:
[tex]d_{P1-P2}=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Substituting each pair, we have:
AB
[tex]\begin{gathered} d_{AB}=\sqrt[]{(1-0)^2+(-1-3)^2}=\sqrt[]{1^2+(-4)^2}=\sqrt[]{1+16}_{} \\ d_{AB}=\sqrt[]{17} \end{gathered}[/tex]BC
[tex]undefined[/tex]Given f(x) f(x) = (- x2 + 7), what is the value of f(4)?
Answers
Given the below function;
[tex]f(x)=(-x^2+7)[/tex]At Orangefield Junior High 40% ofthe seventh graders participate in extra-curricular activities a such as athletics, band, and drama. If there are 80 seventh graders participating in extra-curricular activities how many seventh graders are in the class.
Answers
Answer:
200
Explanation:
To know the total number of graders, we will use the rule of three. Where we know that 40% is equivalent to 80 graders and we want to know how many graders are equivalent to 100%. Then:
40% -------- 80 seventh graders
100% -------- x
Where x is the number of seventh graders in the class.
So, solving for x, we get:
[tex]x=\frac{100\text{ \% }\cdot\text{ 80}}{40\text{ \%}}=200\text{ seventh graders}[/tex]Then, there are 200 seventh graders in the class.
7.4.PS-13 Question Help David drew this diagram of a picture frame he is going to make. Each square represents 1 square inch. What is the area of the picture frame? 12- 10- 0 2 4 6 8 10 12 14 16 18 The area is Enter your answer in the answer box and then click Check Answer. Clear All Check Ans All parts showing of 10 Next → Back Question 7 Review progress
Answers
52
1) In this question, since we need to calculate the shaded region or the frame. We'll calculate the whole picture, and then subtract the white rectangle from it.
2) Examining the picture, we can see that the whole larger shape has a width of
14 -4 = 10 units Horizontal (width)
7-1 = 6 units Vertical (height)
3) Let`s use now the formula for the Rectangle Area
[tex]\begin{gathered} A_{\text{Whole Rectangle}}=w\cdot l \\ A_{\text{Whole Rectangle}}=6\times10=60units^2 \\ A_{\text{White Rectangle}}=2\times4=8u^2 \\ A_{\text{FRAME}}=60-8=52units^2 \end{gathered}[/tex]Hence the area of the frame is 52 square units.
What does y equal? -y=5y-6
Answers
Subtract 5y from both sides of the equation:
[tex]-y-5y=5y-5y-6[/tex][tex]-6y=-6[/tex]Divide both sides by -6
[tex]-\frac{6y}{-6}=-\frac{6}{-6}[/tex][tex]y=1[/tex]Which shows the graph of x - 4y=-4?5O1 2 3 4 5 x433-2+4-5-4-3-2-12-لنا -343-51543212-A
Answers
Explanation
Using a graphing calculator, the graph of x-4y =-4 can be seen below.
Find the circumference with a diameter of 10 feet long. I missed the notes for this section, so I don't know what I'm doing.
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We need to find the circumference using the diameter.
The equation for the circumference is given by:
[tex]C=\pi d[/tex]Where d represents the diameter.
Replace d=10 ft
[tex]\begin{gathered} C=\pi10ft \\ \text{Then, the circumference is:} \\ C=10\pi\text{ }ft \end{gathered}[/tex]Let n =2. Evaluate the following (nn)n
Answers
We have the following:
[tex](nn)n[/tex]n=2
[tex]2\cdot2\cdot2=8[/tex]What is the solution to the equation?3+√3x- 5 = x A. -2 and -7B.2 and 7C. -2D. 7
Answers
Given the equation:
[tex]3+\sqrt[\placeholder{⬚}]{3x-5}=x[/tex]Isolating the square root:
[tex][/tex]Find the equation of a line that contains the point (-2, -6) is perpendicular to the line
Answers
Answer:
answer Is y= 5x+4......
-1/4÷ (x/y) = -1/2what is the missing fraction
Answers
-1/4 / (x/y) = -1/2
Cross fractions
-1/4 / (-1/2) = x/y
-1/4 (-2/1) = x/y
2/4 = x/y
1/2 = x/y
How do I relation in amplitude compared to parent function of sine?How do I describe the relation in period compared to parent function of sine?
Answers
Hello I just need the answer for “What is the inverse for the equation y=x^2+16”
Answers
Given:
The given equation is
[tex]y=x^2+16[/tex]Required:
We need to find the inverse for the equation.
Explanation:
[tex]\text{ Let y=f\lparen x\rparen and }x=f^{-1}(y)\text{ and substitute }x=f^{-1}(y)\text{ in the given equation.}[/tex][tex]y=(f^{-1}(y))^2+16[/tex]Substract 16 from both sides of the equation.
[tex]y-16=(f^{-1}(y))^2+16-16[/tex][tex]y-16=(f^{-1}(y))^2[/tex]Take square root on both sides of the equation.
[tex]\pm\sqrt{(y-16)}=f^{-1}(y)[/tex][tex]f^{-1}(y)=\pm\sqrt{(y-16)}[/tex]Replace y=x in the equation.
[tex]f^{-1}(x)=\pm\sqrt{x-16}[/tex]Final answer:
[tex]f^{-1}(x)=\pm\sqrt{x-16}[/tex]how do you identify sets of real numbers?
Answers
The set of number that best describe each situation is shown below:
[tex]\begin{gathered} \text{Whole numbers: These are natural counting positve numbers. e.g 1,2,3,4,5,etc} \\ \text{Integers: These are whole numbers that are positive, negative and zero. e.g 0,1,-1,2,-2,etc} \\ Rational\text{ numbers: These are numbers that can be expressed in the form of }\frac{a}{b},\text{ where b}\ne0,1.\text{ e.g 1/2, 3/5 etc} \\ \text{Irrational numbers: These are numbers that can be expressed in the form of }\sqrt[]{p}\text{ wh}ere\text{ p is prime. e.g }\sqrt[]{2,}\text{ }\sqrt[]{3}\text{ etc} \end{gathered}[/tex]Real numbers in general are majorly sub-divided into two(2) and they are Rational and Irrational numbers.
I need help in math can you please help me please
Answers
Trigonometric Equations
Solve:
[tex]9\tan ^3x=3\tan x[/tex]In the interval [0,2pi)
We have to find all the values of x that make equality stand. First, divide by 3:
[tex]3\tan ^3x=\tan x[/tex]Subtract tan x
[tex]3\tan ^3x-\tan x=0[/tex]Factor tan x out:
[tex]\tan x(3\tan ^2x-1)=0[/tex]One solution comes immediately:
tan x = 0
There are two angles whose tangent is 0:
[tex]x=0\text{ , x=}\pi[/tex]The other solutions come when equating:
[tex]3\tan ^2x-1=0[/tex]Adding 1, and dividing by 3:
[tex]\tan ^2x=\frac{1}{3}[/tex]Taking the square root:
[tex]\tan x=\sqrt[\square]{\frac{1}{3}}=\pm\frac{\sqrt[]{3}}{3}[/tex]The positive answer gives us two solutions:
[tex]\tan x=\frac{\sqrt[]{3}}{3}[/tex]x=pi/6 and x=7pi/6
The negative answer also gives us two solutions:
[tex]\tan x=-\frac{\sqrt[]{3}}{3}[/tex]x=5pi/6, 11pi/6
Summarizing the solutions are:
{
Determine if the shape is a polyhedron using Eulers formula choices: 8, 12, 3, 5,9, 2, 18
Answers
Given:
The given shape is a polyhedron.
Required:
We need to use Euler's formula for the given shape.
Explanation:
Consider Euler's formula.
[tex]V-E+F=2[/tex]where V is the number of vertices, E is the number of edges and F is the number of faces.
Recall that a vertex is a corner.
The number of corners in the given shape is 12.
[tex]V=12[/tex]Recall that an edge is a line segment between faces and a face is a single flat surface.
The number of edges in the given shape is 18.
[tex]E=18[/tex]The number of faces in the given shape is 8.
[tex]F=8[/tex][tex]V-E+F=12-18+8[/tex][tex]V-E+F=2[/tex]The given shape satisfied Euler's formula.
So it is a polyhedron.
Final answer:
[tex]V=12[/tex]
[tex]E=18[/tex]
[tex]F=8[/tex]
[tex]V-E+F=2[/tex]
The given shape is a polyhedron.
What is the constant of proportionality of the tablex 5 8 11y 35 56 77
Answers
y =kx
Where:
k = Constant of proportionality
If x = 5, y = 35
35 = k5
Solving for k:
k = 35/5 = 7
Verify the answer:
If x = 8 , y = 56
y = kx = 7*8 = 56
The constant of proportionality is 7
Reflection over the y-axis Example 2 Original Point Coordinates Image Point Coordinates A (-8,2) A B (-4,9) B C (-3,2) C'
Answers
We have to reflect the 3 points shown over the y-axis.
The simple rule for reflecting over y-axis:
• keep y coordinate same
,• negate the x coordinate
So,
(x,y) would become (-x,y)
Now, let's reflect the 3 points:
A(-8,2) would become A'(8,2)
B(-4,9) would become B'(4,9)
C(-3,2) would become C'(3,2)
a student's can sit at 1 cafeteria table about how many tables are needed for 231 students explain
Answers
We can solve this question by means of the rule of three:
[tex]\begin{gathered} 1\text{ student ------- 1 table} \\ 231\text{ students ------ x} \end{gathered}[/tex]then, x is given by
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