what is the equation of x2 + 6x + 8 + 0 algebraically
Answer:
x = - 4 , x = - 2
Step-by-step explanation:
x² + 6x + 8 = 0
consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 6)
the factors are + 4 and + 2 , since
4 × 2 = 8 and 4 + 2 = 6 , then
(x + 4)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x + 2 = 0 ⇒ x = - 2
The list price of a commodity is RM420 and the percentage profit is 40%. If the commodity is sold at a discount of 10%, the profit is____.
Answer:
56
Step-by-step explanation:
you first had to get the marked price so t you can get the profit.
just as illustrated in the picture above.
What is the volume of a cylinder, in cubic feet, with a height of 13 feet and a base
diameter of 4 feet? Round to the nearest tenths place.
Answer:
163.3
Step-by-step explanation:
3.14*r^2*h
h=13
4/2 = 2
r=2
2^2 = 4
3.14*4 = 12.56
12.56*13 = 163.28
Rounded = 163.3
I believe the answer is 163.3
Damek has five number cards lying on the table. There are two number cards with digit 1, two number cards with digit 2 and one number card with 0. How many different three-digit numbers can Damek form? (Number cannot being with 0).
(P.S. Is there a way to find the answer without listing all the possibilities?)
Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.
There are five number cards on the table.
2- digit 1 card
1- digit 0 card
2- digit 2 card
There is a possibility of putting 1 or 2 in the hundredth place.
If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2
If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place
If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place
If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.
So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.
Similarly, there will be 7 possibilities that the hundredth place is filled by 2.
Hence, there are 14 possibilities as required by the problem.
So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.
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Each car on the lot at a car dealership has 4 tires and 2 headlights. Which pair correctly describes tires and headlights?
Answer: 4 : 2
Step-by-step explanation:
I am going to assume you want a ratio between number of tires to headlights which is
4 : 2
Two-thirds of the tokens in the box are red and 2/5 of the remaining tokens are blue.
If the remaining 24 tokens are green, how many tokens are there in the box?
Answer:
After solving this question I got and 120 tokens
Find the slope of the line that passes
through these two points.
Point 1
(4,0)
Point 2
(6,2)
Answer:
1
Step-by-step explanation:
(2-0) / (6-4)
2/2
xxxxxxxx
Answer:
1
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
The given inequality is -3(2x - 5) < 5(2 - x)
We need to simplify the inequality.
What is inequality?In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)
⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]
Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)
⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]
Now, - 6x + 15 < 10 - 5x
By subtracting 15 from both sides, we get
- 6x < -5 - 5x
By adding 5x to both sides, we get - x < - 5
The coefficient of x is -1. So, divide both sides by -1
Then we get x > 5
Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
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which graph correctly represents 3x+y > 7
Answer:
What graph? add a photo?
Martin uses of a gallon of paint to cover of a wall. What is the unit rate at which Martin paints in walls per gallon?
The unit rate at which Martin paints in walls per gallon is 1 7/25 walls per gallon
Unit rateUnit rate of paint per gallon = Quantity of wall / gallon of paint
= 4/5 ÷ 5/8
= 4/5 × 8/5
= (4 × 8) / (5 × 5)
= 32/25
= 1 7/25 walls per gallon
Complete question:
Martin uses 5/8 of a gallon of paint to cover4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon
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Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y)
Answer:
20 + 4y
Step-by-step explanation:
To have to fewest symbols possible, we must simplify the expression by multiplying 4 into the numbers within the parenthesis. Doing so we get:
[tex]4(5+y) = 4 * 5 + 4 * y = 20 + 4y[/tex]
Answer: 20+4y
Step-by-step explanation:
Hi, let me help you.
What we should do to simplify this expression is to "distribute" 4.
The parentheses around 5+y tell us to multiply 4 times both 5 and y. This is shown below.
[tex]\multimap\quad \tt 4\cdot5+4\cdot y[/tex]
[tex]\multimap\quad\tt 20+4y[/tex] is what we obtain upon multiplying
________________
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Reach far. Aim high. Dream big.
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The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)
2
+1 . Below is the explanation
Step-by-step explanation:
Given:
The graph of f(x)=x^{2}x
2
To find:
The equation of the transformed graph g(x).
The red graph f(x) is moved right 3 units and up 1 unit to get g(x).
When graph is moved right 3 units , 3 should be subtracted with x.
When graph is moved up 1 unit, 1 is added at the end.
So, our g(x)=(x-3)^{2} +1(x−3)
2
+1
The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)
2
+1
Carl is making a garden that is twice as long as it is wide. he wants to cover 271
square feet with the garden. which equation best represents the situation if x
represents the length of the garden?
The equation which best represents the scenario is, x²/2=271
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
Perimeter is a length of the boundary surrounding the area
Area of rectangle=length x Breadth
Perimeter=2(length+breadth)
length=x
breadth=x/2
Area=271ft²
Area=length x breadth
So, using the given value we can write
271=x²/2
⇒x=√542
=23.28ft
Therefore, the equation which best represents the scenario is, x²/2=271
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A test is worth of 150 points and contains 70 questions. Some questions are worth 2 points, and some are worth 4 points
2x + 4y = 150
Answer:
65 2 point questions, 5 4 point questions
Step-by-step explanation:
write a system of equations:
let x be the number of 2 point questions and y be the number of 4 point questions
2x + 4y = 150
x + y = 70 (since there are 70 total questions)
x + y = 70
subtract x from both sides
y = -x + 70
substitute y = -x + 70 into 2x + 4y = 150
2x + 4(-x + 70) = 150
2x - 4x + 280 = 150
-2x = -130
x = 65
substitute x = 65 into x + y = 70
65 + y = 70
subtract 65 from both sides
y = 5
What are the first 10 digits after the decimal point (technically the hexadecimal point...) when the fraction frac17 is written in base 16?
We happen to have
[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]
which is to say, the base-8 representation of 1/7 is
[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]
This follows from the well-known result on geometric series,
[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]
if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have
[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]
Uniformly multiplying each term on the right by an appropriate power of 2, we have
[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]
Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.
[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]
That is,
[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]
[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]
[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]
etc. so that
[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]
and thus the base-16 representation of 1/7 is
[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]
and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.
how to say i like chees burgers without saying that like how to say im not gonna date you while i still will im just dum what is 1+1
Answer:
2
I believe that the answer my friend
I need help explanation if possible
Step-by-step explanation:
tan x = sin x / cos x
[tex]tan \: x \: = \frac{ \frac{7}{15} }{ \frac{4 \sqrt{11} }{15} } = \frac{7}{4 \sqrt{11} } [/tex]
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation.
A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B.
umm.. i fr don’t know how to do this … help pls
Answer:
2 solutions: ( -4,0 )
( -6,0 )
2 Non solution: ( 2,0 )
( 4,0 )
Answers:
Refer to the graph below
Two solution points are (-5,-4) and (-4,-3)
Non solution points are (0,3) and (1,4)
=========================================================
Explanation:
The boundary line for [tex]y \ge 3x+3[/tex] is [tex]y = 3x+3[/tex]
This linear equation has a y intercept of (0,3) and another point on the line is (1,6). Plot these two points and draw a straight line through them. This line is a solid boundary line because of the "or equal to" as part of the inequality sign. This means points on the boundary adjacent to the shaded region area part of the solution set.
Because of the "greater than" portion, we'll shade above the solid boundary line. This only works because y is isolated.
Keep in mind that we're also told that [tex]y < -2[/tex] which means we'll also shade the region below the boundary line [tex]y = -2[/tex]. This is a dashed line through -2 on the y axis. A dashed line does not include points on the boundary as part of the solution.
---------------
To summarize: We shade above y = 3x+3 (solid) but below y = -2 (dashed).
Refer to the diagram below to see what's going on.
The entire southwest region is shaded.
That blue shaded region represents all (x,y) points that make the system true.
For example, the point (-5,-4) is in the blue region.
Notice how plugging the coordinates into the first inequality gets us...
[tex]y \ge 3x+3\\\\-4 \ge 3(-5)+3\\\\-4 \ge -15+3\\\\-4 \ge -12\\\\[/tex]
which is a true statement. If you plugged y = -4 into [tex]y < -2[/tex], you would also get another true statement.
Both inequalities are true for (x,y) = (-5,-4) which confirms it to be a solution point.
You should also find that a point like (-4,-3) is another solution in the blue region following similar steps. There are infinitely many solution points to pick from. Feel free to choose others.
Non-solution points are such that they aren't in the shaded region. We could also pick points on the dashed boundary line as non-solutions.
Side note: you can pick points on the solid boundary as solution points, but those points must be adjacent to the shaded region. The point (0,3) is NOT a solution even though it's on the solid boundary line.
Look at pictures attached for question and answer choices
The answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have a rhombus shown in the picture.
The intersection point is P
From the definition of the rhombus: JK ≅ KM
According to the SAS congruency postulate, two triangles are congruent if a triangle has two sides and an included angle that are congruent to the two sides and an included angle of another triangle.
Thus, the answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.
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On a number line, 2.5 would be located ______. Choose all answers that make a true statement.
2.5
《----|----|----|----|----|----|----|----|----|----|----》
A. to the right of 2.52
B. between 2.45 and 2.55
C. to the left of 2.3
D. between of 2.4 and 2.6
Answer:
It is both answers B and D
if the unit rate is 30 miles per hour , then how much miles is traveled in 9 hours
Answer:
270 miles
Step-by-step explanation:
Since the unit rate is 30 miles per hour, the miles on 9 hours will be:
= 30 × 9
= 270 miles.
The price of a computer at an electronics store is $1200. If the store gives an "End of the year Sale"
discount of 20%, how much Mark needs to pay to buy the computer?
Answer:
$960
Step-by-step explanation:
The discount is 20%, so we need to find 80% of the original price:
[tex].80 \times 1200 = 960[/tex]
find area of shape below to 1 dp
The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
The figure is divided into two parts one is a rectangle and the second is a semicircle.
Area of figure = Area of rectangle + Area of a semicircle
Area of figure = L × B + (πr²/2)
A = 10 cm × 15 cm + (3.14 ×(5)^2/2)
A= 189.25 cm²
Hence the area of the shape will be 189.25 cm²
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In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys
Answer:
Step-by-step explanation:
Conditions
Let the girls = g
Let the boys = b
Equations
g + b = 1280
g = b + 70
Solution
Put the value for the girls (second equation) into the first equation.
b + 70 + b = 1280 Subtract 70 from both sides
b + 70 - 70 + b = 1280 -70 Combine
2b = 1210 Divide both sides by 2
2b/2 = 1210/2
b = 605 Substitute this value into the top equation
g + 605 = 1280 Subtract 605 from both sides
g + 605 - 605 = 1280 - 605
g = 675
Answer
# boys = 605
# girls = 675
Can you solve this question and explain it for me? Thank you
Answer:
This is the answer to your question
]Which statements are true? Check all that apply.
The equation |–x – 4| = 8 will have two solutions.
The equation 3.4|0.5x – 42.1| = –20.6 will have one solution.
The equation StartAbsoluteValue StartFraction one-half EndFraction x minus StartFraction 3 Over 4 EndFraction EndAbsoluteValue equals 0. = 0 will have no solutions.
The equation |2x – 10| = –20 will have two solutions.
The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.
The equation StartAbsoluteValue StartFraction 1 Over 8 EndFraction x minus 1. EndAbsoluteValue equals 5. = 5 will have infinitely many solutions.
The correct answers are:
1. The equation |-x -4| = 8 will have two solutions. (True)
5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)
What is Equation?
An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.
1. The equation |-x -4| = 8 will have two solutions. (True)
|-x - 4| = 8
-x -4 = ±8
-x -4 = 8 and -x -4 = -8
-x = 8 + 4 and -x = -8 + 4
-x = 12 and -x = -4
x = -12 and x = 4
Therefore, it has two solutions x ∈ {-12, 4}
2. The equation 3.4|0.5x - 42.1| = -20.6 will have one solution. (False)
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)
|(1/2)x - 3/4| = 0
(1/2)x - 3/4 = ±0
Since ±0 is the same
(1/2)x = 3/4
x = 2X3/4
x = 3/2
Therefore, it has one solution x = 3/2
4. The equation |2x – 10| = –20 will have two solutions. (False)
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)
|0.5x – 0.75| + 4.6 = 0.25
|0.5x – 0.75| = 0.25 - 4.6
|0.5x – 0.75| = -4.35
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
6. The equation |(1/8)x - 1| = 5 will have infinitely many solutions. (False)
|(1/8)x - 1| = 5
(1/8)x - 1 = ±5
(1/8)x - 1 = 5 and (1/8)x - 1 = -5
(1/8)x = 5 + 1 and (1/8)x = -5 + 1
(1/8)x = 6 and (1/8)x = -4
x = 6X8 and x = -4X8
x = 48 and x = -32
Thus, it has two solutions x ∈ {48, -32}
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Write an equation of the line that passes through the point P (2,-2) and is parallel to the line
-2x+y=-3
Step-by-step explanation:
Solution:
The slope of the line -2x+y = -3 is m1 =
- coefficient of x ÷ coefficient of y
= -(-2) ÷1
=2
Then, according to the question ;
It is stated that the lines are parallel
i.e.
m1=m2
or, 2 = m2
Hence, m2 =2
Again,
The required equation of the line passing through the point P(2,-2) = (x1,y1) is
y-y1 = m2(x- x1)
or, y-(-2) = 2(x-2)
or, y+2 = 2x-4
or, 2+4 = 2x-y
or, 2x-y = 6
Therefore; 2x-y = 6.
Larry likes skeet shooting. a clay disc is shot into the air and the participant tries to shoot it. he rarely misses, because he knows that the flight of the disc can be modeled by a quadratic function. the discs are released from a firing mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120m. the average maximum vertical height that the disc reaches is 40 m.
a)The functions that represent the flight of the clay disc in Factored Form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
b)The function in its standard form is,[tex]\rm y =- \frac{1}{90} x^3 + \frac{4}{3} x[/tex].
c) The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
The given points represent on the graph is;
x = 0 , y = 0
x = 120 , y = 0
x = 60 , y = 40
The standard equation is;
[tex]\rm y = a(x-h)^2 +k \\\\ y = a(x-60)^2 +40 \\\\ 0 = sA(120-60) +40\\\\ 0= a \times 3600 + 40 \\\\ 3600 a = -40 \\\\ a = - \farc{1}{90}[/tex]
Substitute the value as;
[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
b)
The above equation in the standard form is found as;
[tex]\rm y = \frac{-1}{90}(x^2 +3600 -120 x )+40 \\\\ y =- \frac{1}{90}(x^2 -40 + \frac{4}{3}x +40 \\\\ y = \frac{-1}{90} x^2 + \frac{4}{3}x[/tex]
c)The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.
Hence, the functions that represent the flight of the clay disc in the factored form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
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