[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
Let's solve ~ ☂
⧠ Here, I'm using middle term split method :
[tex] \qquad\rightarrowtail \sf {x}^{2} + 6x + 8[/tex]
[tex] \qquad\rightarrowtail \sf {x}^{2} + 4x + 2x+ 8[/tex]
[tex] \qquad\rightarrowtail \sf {x(x}^{} + 4) + 2(x+ 4)[/tex]
[tex] \qquad\rightarrowtail \sf (x + 2)(x+ 4)[/tex]
[tex]\\ \rm\rightarrowtail x^2+6x+8[/tex]
[tex]\\ \rm\rightarrowtail x^2+4x+2x+8[/tex]
[tex]\\ \rm\rightarrowtail x(x+4)+2(x+4)[/tex]
[tex]\\ \rm\rightarrowtail (x+2)(x+4)[/tex]
Done!
Evaluate the following expression: (2,3)-3(1,1). Enter your answer as a vector
Answer:
Step-by-step explanation:
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The given expression can be solved as shown below.
(2,3) - 3(1,1)
Multiply 3 in the second vector,
= (2,3) - (3,3)
Subtracting vectors
= (2-3, 3-3)
= (-1, 0)
Hence, the value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).
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What value of c makes x2 6x c a perfect square trinomial? c = If x2 6x c = (x d)2, then d =.
[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}[/tex]
c=9 makes the given expression a perfect square trinomial.
The given expression is:
[tex]x^{2} +6x+c[/tex]
We can rewrite it as:
[tex]x^{2} +2*x*3 + c[/tex].....(1)
What is the expansion of [tex](a+b)^2[/tex]?The expansion of [tex](a+b)^2[/tex] is [tex]a^{2} +2ab+b^{2}[/tex]
Comparing (1) with [tex]a^{2} +2ab+b^{2}[/tex]
We get
a=x
b=3
c=b²
So, c=3² =9.
So, c=9 makes the given expression a perfect square trinomial.
Hence, c=9 makes the given expression a perfect square trinomial.
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Roald's annual salary is $100 482. If Roald gets paid monthly, calculate his monthly income.
/1
James has a job that pays him $24 per hour. Assume a working week of 38 hours. Assume
5. The dot plot shows a random sample
of the number of migrating geese
flocks observed by 25 participants
during a two-day hike.
Day 1
Day 2
IN
+ +
+ + + + +
2 3 4 5 6 7 2 3 4 5 6 7
Number of Flocks Observed Number of Flocks Observed
Use the mean value of each data set to
make an inference about the number
of flocks observed each day.
Using the dot plot, the inference is that the number of flocks observed on the second day was less than in the first.
What does a dot plot show?The dot plot shows the number of times each measure appears in the data-set.
Hence, the mean of the data-set corresponding to day 1 is given by:
M1 = (4 x 4 + 7 x 5 + 7 x 6 + 7 x 7)/25 = 5.68
And the mean of the data-set corresponding to day 2 is given by:
M2 = (2 x 8 + 3 x 7 + 4 x 6 + 5 x 4)/25 = 3.24.
M1 > M2, hence, the inference is that the number of flocks observed on the second day was less than in the first.
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What is the value of c
Answer:
x = 49º
Step-by-step explanation:
This is right angle, and right angle's are always a 90º angle. 90º - 41º is 49.
So the basic answer is 49, but it's properly written as "49º".
Hope this helps!!
The value of x: 49 degrees
Note: All the angles in a triangle add up to 180 degrees
What we're given:
41 degrees, A right angle, and x.
A right angle is 90 degrees.
Equation:
41 + 90 + x = 180
131 + x = 180
x = 49 degrees
3 is 9 greater than an unknown number
find unknown number
-6
Step-by-step explanation:
First we see 3 is greater than the subject so 3<x 3-9 = -6
in each diagram line p is parallel ANSWER FAST Pls
Answer:
choice A is correct
Step-by-step explanation:
the value of x should be 75
Answer the question with true or false:
True:
Area of trapezoid = [tex]\frac{1}{2}(b1 + b2) * h[/tex]
Hope that helps!
A circular concrete patio has a circumference of about 53 yards. The patio has a diameter of d yards. Which expression best represents the value of ?.
Applying the expression for the circumference of circle, we found the diameter as 16.86 yards
Mensuration of Flat shapeGiven Data
Circumference = 53 yardsDiameter = d yardsLet us apply the expression for the circumference of a circle
Circumference = 2πr----------1
But r = d/2
hence put r = d/2 in the expression above
Circumference = 2πd/2----------2
Circumference = πd
Substitute our given data
53 = 3.142*d
Make d the subject of formula we have
d = 53/3.142
d = 16.86 yards
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If the m<4 = 15, find the measure of <2
Answer: 75 Degrees
Step-by-step explanation: 1. Due to the law of opposite adjacent angles, we can determine angle 1 is congruent to angle 4 and therefore is 15 degrees 2. Angle 3 is shown to be a right angle (90 degrees) 3. Since angles 1,2, and 3 are on a flat line, the sum of all 3 is 180 4. 15+90 is 105 5. 180-105 is 75 which is the measure of angle 2
Jess makes and sells cube-shaped jewelry boxes. She designs the jewelry boxes in different sizes and with different patterns. Jess wants to include the volume of each box on her price list.
s = length (in.) of one side of the jewelry box
Options:
s
6s
s^2
s^3
(It’s middle school I-Ready)
Answer:
Step-by-step explanation:
s to the 3rd power so S3
I hope this works
Answer:Part two is (s+2)3
Step-by-step explanation:
I got it right I hope it helps
(5.04×10^12)÷(6.3×10^9) in scientific notation
Answer:
i think the answer will be = 8 × 10^2
Is the length of the hypotenuse of a right triangle with legs that mea-
sure 5 cm and 6 cm a rational number or an irrational number? Justify
your answer. Answer in complete sentences and indude all relevant calculations
image below ill give branliest
Answer:
E= -4,5
F=3,-2
Step-by-step explanation:
i think that's correct sorry if not
How do you solve for n and what is the rule?
Answer:
Looking at the first two given ordered pairs (3, 5) and (4, 7), it appears that for every increase of 1 unit of x, there is an increase of 2 units of y.
Let's check by writing the next ordered pairs using this rule:
(5, 9) (6, 11) (7, 13) (8, 15)
As the the ordered pair (8, 15) is in the table, then we can confirm that this is the rule.
Writing the rule as an equation:
y = 2x - 1
Therefore, n = 6
Answer:
y = 2x - 1
n = 6
Step-by-step explanation:
Hello!
This is an arithmetic sequence.
An Arithmetic sequence, also known as an arithmetic progression, is a string of numbers that follow a pattern where the difference between two terms is always the same (constant).
An Arithmetic sequence is modeled by the explicit function:[tex]\bold{t(n) = (CD)n + t(0)}[/tex]
t(n) = output (y - value)CD = common difference (slope)n = input ( x-value)t(0) = starting value (y-intercept)Let's go step by step to solve these equations:
Step 1: Common Difference
The common difference of a sequence is similar to the slope of a line. The slope formula is given as [tex]\bold{\frac{y_2 - y_1}{x_2-x_1}}[/tex].
We can input values of x and y to find the common difference
[tex]\frac{y_2 - y_1}{x_2-x_1}[/tex][tex]\frac{7 - 5}{4 - 3}[/tex][tex]\frac21 = 2[/tex]We have the CD, 2!
Step 2: Starting Value
The starting value can be shown as the y-intercept of the line or the origin point of the sequence.
To find the starting value or t(0), we can input an x and y value for "n" and "t(n)"
t(n) = (CD)n + t(0)5 = 2(3) + t(0)5 = 6 + t(0)-1 = t(0)We know have the starting value, -1!
Step 3: The Equation
We now have all the values for our equation. let's bring our attention back to the input and output variables. Since we know that "t(n)" is the same as "y" and "n" is the same as "x", we can plug that instead of t(n) and n.
t(n) = (CD)n + t(0)t(n) = 2n -1y = 2x - 1Solve for n:
With our equation, we can plug in 11 as the output and solve for n.
y = 2x - 111 = 2x - 112 = 2x6 = xn = 6
_______________________________________________________
Another way to solve this is to find the Recursive Equation
The Recursive Equation is only meant to find the next term, it doesn't do so well in finding the terms in the long run.
The basic form of a recursive equation is t(n + 1) = t(n) + (CD); where t(0) is ____
I'm not going to go in-depth with this, but you can see the values that we solved above can be implemented here.
Our recursive equation is t(n + 1) = t(n) + 2; where t(0) is -1
The port outside of the semi-colon represents where the sequence starts. If only t(n+1) = t(n) + 2 is given, we could start at 5, and go as 5, 7, 9...etc.
We would start by finding t(1) by doing:
t(0 + 1) = t(0) + 2; where t(0) = -1t(1) = -1 + 2t(1) = 1We can confirm this using our explicit rule: y = 2x - 1
y = 2(1) - 1y = 2 - 1y = 1Please help me solve this
Answer:
The length of river D is 2550
length of river C is 2550+500=3050
Step-by-step explanation:
Let the river D be 'x'
and the river C is (x+500)
x + x + 500 = 5600
2x + 500 = 5600
2x = 5600 - 500
2x = 5100
x = 5100/2
x = 2550
The length of river D is 2550
length of river C is 2550+500=3050
Find the value of d that makes line m ll n
Answer:
x = 45.
Step-by-step explanation:
The angle between the shorter line and line n is 90 degrees, so
2x must be 90 degrees for m and n to be parallel.
x = 45.
Please help on this
Answer:
5.025m
Step-by-step explanation:
The clothesline also creates an upside-down triangle with two sides being 5m, 0.5m, and the hypotenuse being the clothesline.
We can use the pythagorean theorem to find the length of the clothesline.
5 squared +.5 squared= the length of the clothesline squared
25+.25= the square root of 25.25
= 5.025
Answer:
Your answer would be:
5.025m
Step-by-step explanation:
5 sq + 0.5sq = the length of the clothesline sq
25 + 0.25= the square root of 25.25
= 5.025m
Have a great rest of your day
#TheWizzer
6.005= as what percent
Answer:
[tex]\displaystyle 600\frac{1}{2}\%[/tex]
Explanation:
Just move the decimal mark twise to the right and you will arrive at your result.
I am joyous to assist you at any time.
Write an equation for the hyperbola that satisfies the given set of conditions.
Vertices (20,0) and (-20,0) conjugate axis of length 18 units.
The vertices of the hyperbola are the x-intercepts of the hyperbola
The equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]
How to determine the equation of the hyperbola?The equation of a hyperbola is represented as:
[tex]\frac{(y - k)^2}{a^2} -\frac{(x - h)^2}{b^2} = 1[/tex]
The vertices are (20,0) and (-20,0).
So, the center of the hyperbola is:
(h,k) = (0,0).
Also, we have:
a = 20
This gives
[tex]\frac{(y - 0)^2}{a^2} -\frac{(x - 0)^2}{b^2} = 1[/tex]
Evaluate
[tex]\frac{y^2}{a^2} -\frac{x^2}{b^2} = 1[/tex]
Substitute 20 for a
[tex]\frac{y^2}{20^2} -\frac{x^2}{b^2} = 1[/tex]
[tex]\frac{y^2}{400} -\frac{x^2}{b^2} = 1[/tex]
The length of the conjugate axis is:
l = 18 units
So, we have:
[tex]b = \frac{18}2 = 9[/tex]
The equation becomes:
[tex]\frac{y^2}{400} -\frac{x^2}{9^2} = 1[/tex]
[tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]
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Mr. endres wants to put fencing around his rectangular shaped backyard. the width of the backyard is 42 feet and the length is two times the width. how many feet of fencing does mr. endres need?
The the number of feet needed for the fence of the rectangular garden = its perimeter = 252 ft.
What is the Perimeter of a Rectangle?Perimeter = 2(length + width).
The number of feet needed for the fence around the rectangular garden = perimeter of teh rectangular garden.
Given the following:
Width = 42 ft.Length = 2(42) = 84 ft.Plug the values into Perimeter = 2(length + width):
Perimeter of the rectangular garden = 2(42 + 84)
Perimeter of the rectangular garden = 252 ft
Therefore, the the number of feet needed for the fence of the rectangular garden = its perimeter = 252 ft.
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where can u buy a ruler that is 3 feet long
Answer:
A yard sale.
Step-by-step explanation:
lol
What is this question really about? Could you perhaps dive a little bit more into detail please? Ty
The lengths of all sides are different in which type of triangle?.
Answer: Scalene Triangle
Step-by-step explanation:
Answer:
Scalene Triangle
Step-by-step explanation:
Scalene Triangle: All sides are different
Isosceles Triangle: 2 sides are the same
Equilateral Triangle: All sides are the same.
In what year did the nfl vote to create a $430 million pool of money, funded by the top 15 clubs by revenue to be distributed to the bottom 15 clubs?.
The year in which the NFL voted to create a $430 million fund to help the bottom 15 clubs was 2007.
When did the NFL vote to implement this fund?The NFL voted by a margin of 30-2 in 2007 to create a pool of funds over 3 years that would amount to $430 million.
This money would then be used to help the bottom 15 clubs who might be struggling financially. The hope was that this would make things more competitive in the NFL.
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Someone please help me asap! Easy questions!!
Answer:
a. 12 inches for the shorter side
b. 1050 bushels apples
c. 7/8 cups
Step-by-step explanation:
You can solve these all by the butterfly method(aka cross multiplication)
State whether each equation is in standard form.
A.) 3x + y = 8
B.) x - y = 15z
C.) x(to the second power) + y = 11
D.) 3xy + y(to the second power) = 4
E.) x + 4y = 12
F.) 5x + 24y = 544
Please help, I'll give Brainliest!
Answer:
Step-by-step explanation:
Standard form: Ax + By = C
State whether each equation is in standard form.
A.) 3x + y = 8 (in standard form)
B.) x - y = 15z (not in standard form, because it has a variable(15z))
C.) x^2 + y = 11 (not in standard form, this is not a linear equation)
D.) 3xy + y^2 = 4 (not in standard form, this is not a linear equation)
E.) x + 4y = 12 (in standard form)
F.) 5x + 24y = 544 (in standard form)
Hope this helps!
help me solve for x and y .
Answer:
Step-by-step explanation:
Answer:
x = 20y = 114°Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the remote interior angles.
(3x +6)° = 31° +35°
3x +6 = 66 . . . . . . . . . . divide by °, collect terms
3x = 60 . . . . . . . . subtract 6
x = 20 . . . . . . . divide by 3
The value of y is the supplement of (3x+6)°, and of the sum (31 +35)°.
y = 180° -66° = 114°
The values of x and y are 20 and 114°, respectively.
Y^2-9y+2. Y=6 evaluat the expression
[tex] \huge\mathbb\orange{ANSWER} [/tex]
[tex] \mathsf\green{y = 6}[/tex]
[tex] \mathsf \purple{{y}^{2} - 9y + 2}[/tex]
[tex] \mathsf \pink{ {6}^{2} - 9(6) + 2}[/tex]
[tex] \mathsf \purple{36 - 54 + 2}[/tex]
[tex] \mathsf \pink{ - 16}[/tex]
[tex] \mathbb\green{Hope\:It\:Helps} [/tex]
A machine that assembels a car is an example of a
Answer:
Mechanical
Step-by-step explanation:
Those ttype of machines build epic cars
Please Help! Will Give Brainlest!
Answer:
period = 2π
Step-by-step explanation:
the period is the distance from one point on the waveform to the corresponding point on the next wave.
there is a maximum at 2π and a corresponding maximum at 4π
period = 4π - 2π = 2π