Answers
Answer:
[tex]\textsf{1.} \quad x=-6, \quad x=6[/tex]
[tex]\textsf{2.} \quad x=-5, \quad x=2[/tex]
[tex]\textsf{3.} \quad x=-3, \quad x=7[/tex]
[tex]\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
[tex]\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
Step-by-step explanation:
Question 1Method: Extracting the Square Root
[tex]\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}[/tex]
Question 2Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}[/tex]
Question 3Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}[/tex]
Question 4Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x-4=-2x^2[/tex]
Rearrange into standard form by adding 2x² to both sides:
[tex]\implies 2x^2+5x-4=0[/tex]
Therefore:
[tex]a=2, \quad b=5, \quad c=-4[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{57} }{4}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
Question 5Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x^2-7x-13=0[/tex]
Therefore:
[tex]a=5, \quad b=-7, \quad c=-13[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{309} }{10}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
Related Questions
Debra bought 1.025 pounds of ham and 1.143 pounds of turkey. Each pound of ham and turkey costs $5.00. How much did Debra spend?
Answers
Answer:
10.84
Step-by-step explanation:
1.025*5+1.143*5=10.84
Brainliest, 30 pts, thanks, 5 star guarantee.
Answers
The triangle ΔXYZ is congruent to the triangle ΔX'Y'Z'. And the intersection of ZZ' and AB form a right angle.
What is a transformation of a shape?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.
The reflection does not change the shape and size of the geometry. But flipped the image.
The triangle ΔXYZ is reflected across the line AB to get the tringle ΔX'Y'Z'.
The diagram is given below.
A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersects the line of reflection at a right angle.
Thus, the triangle ΔXYZ is congruent to the triangle ΔX'Y'Z'. And the intersection of ZZ' and AB form a right angle.
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3-11-(-6) subtract this and thank youuuuuu
Answers
Answer:
3-11-(-6)
the answer will be
-2
Jan is saving money to buy a bike. The bike costs $255. She has $120 saved and each week she adds $15 to her savings. Write and solve an equation to find how long will it take her to save enough money to buy the bike.
Answers
Step by step
We can use the y intercept formula
y = mx + b
The cost of the bike is “y” $255
The starting point is “b” $120 saved
The rate is “m” $15 per week
Our unknown amount of weeks is x
$255 = $15x + $120
Solve for x
Subtract 120 from both sides to isolate x
255 - 120 = 15x + 120 - 120
135 = 15x
Divide both sides by 15 to solve for x
135 /15 = 15/15 x
9 = x
9 = amount of weeks
We can check our work by substituting 9 in place of x in our equation
255 = (15)(9) + 120
255 = 135 + 120
255 = 255
if x² = √16 = x
true or false?
Answers
Step-by-step explanation:
it is true
the square root of 16 is 4
The lowest form of this fraction 49/100
Answers
The lowest form of this fraction 49/100 is still 49/100.
How to compute the value?It should be noted that a fraction can only be reduced to its lowest term if it has a common factor.
In this case, there is no common factor between 49 and 100.
Therefore, the lowest form of this fraction 49/100 is still 49/100
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i need this answer asap please
Answers
Answer:
a. y + 3 = 0
Step-by-step explanation:
x-axis has slope of 0 so any lines parallel to x-axis has slope of 0
With m = 0 , x = -4, y = -3
y = mx + b
-3 = (0)(-4) + b
b = -3
so y = -3
or y + 3 = 0
Please solve. NO EXPLAINATION NEEDED. I NEED ANSWER FAST
Answers
Answer: x=28/3
Step-by-step explanation:
6/8=7/x
3/4=7/x
3x/4=7
3x=28
x=28/3
Answer: the answer is 9 or 9.333333
Monday
Ms. Paulsen had 80 paper clips in her desk drawer. She used 39 of them on
papers.
How
many paper clips does Ms. Paulsen have in her desk drawer now?
Answers
S = 2πr(r + h)
Find the total surface area of a cylinder with radius 3 and height 5.
Enter an exact answer in terms of pie
Answers
Answer:
Step-by-step explanation:
We would substitute in 3 for r and 5 for h
s = 2[tex]\pi[/tex](3 + 5)
s = 2[tex]\pi[/tex]8
2 = 16[tex]\pi[/tex]
Calculate the distance between Point A (-8,-2) and Point B(6,-1) Leave the answer in radical form.
Answers
the distance between Point A (-8,-2) and Point B(6,-1) in Radical form= [tex]\sqrt{197}[/tex]
Distance formula:
The distance between two points formula uses the coordinates of two points in space. In coordinate geometry, the distance between two points can be calculated using the distance formula, present in a two-dimensional or three-dimensional space. The distance formula for two points is also an application of the Pythagoras theorem
the distance formula is used to find the distance between any two points when we already know the coordinates. The points could be present alone on the x-axis or y-axis or on both axes.
Let us consider, that there are two points say A and B in an XY plane. The coordinates of point A are (x1,y1), and of B are (x2,y2). Then the formula to find the distance between two points PQ is given by:
AB=[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
Note: If the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:
PQ = |x2 – x1|
the distance between point origin O(0,0) and P(x,y) is given by:
OP = √((x2 – 0)² + (y2 – 0)²)
OP = √((x2)² + (y2)²)
or simply,
OP = √(x² + y²)
Solution :
where x and y are coordinates of points other than the origin.
Given :
(x1,y1) = (-8,-2)
(x2,y2)= (6,-1)
Solution:
[tex]d=\sqrt{x^{2} +y^{2} } \\d=\sqrt{(6+8)^{2} +(-1+2)^{2} } \\d=\sqrt{14^{2}+1^{2} } \\[/tex]
[tex]d=\sqrt({197)[/tex]
Radical form= [tex]\sqrt{197}[/tex]
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How are the graphs of the functions f(x) = StartRoot 16 EndRoot Superscript x and g(x) = RootIndex 3 StartRoot 64 EndRoot Superscript xrelated?
The functions f(x) and g(x) are equivalent.
The function g(x) increases at a faster rate.
The function g(x) has a greater initial value.
The function g(x) decreases at a faster rate.
Answers
The function g(x) increases at a faster rate and has a greater initial value.
Simplify f(x).[tex]f(x) = \left(\sqrt{16}\right)^{x}[/tex][tex]f(x) =\left(\sqrt{4^{2}}\right)^{x}[/tex][tex]f(x) = \left(4\right)^{x}[/tex]Simplify g(x).[tex]g(x)=3\left(\sqrt{64}\right)^{x}[/tex][tex]g(x)=3\left(\sqrt{8^{2}}\right)^{x}[/tex][tex]g(x)=3\left(8\right)^{x}[/tex]Compare the functions f(x) and g(x).f(x) and g(x) are not equivalent as the bases of the exponents are different.We will find the initial value for both our functions (value of functions when x is 0).For x=0,[tex]f(0)=\left(4\right)^{0} = 1[/tex][tex]g(0)=3\left(8\right)^{0}=3*1=3[/tex]The initial value of g(x) is greater than the initial value of f(x).In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.With the help of a graphing tool, the two functions were plotted.The function g(x) increases at a faster rate than the function f(x)(see the attached figure).That means that the value of g(x) is greater than the value of f(x) for the same value of x.Thus,The function g(x) increases at a faster rate and has a greater initial value.To learn more about graph, visit :
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190 g = _____________ kg
Answers
A case of 8 items costs $9.44 at Costco. What is the price of each item?
Answers
Answer: $1.18 per item
Step-by-step explanation:
9.44/8=$1.18 per item
solve for x. 2/2+x=1/x+5
Answers
Answer:
Step-by-step explanation:
its 8 duh jk its your mom XD
Two more than the quotient of a number and 9 equals 5
Answers
In linear equation , the quotient of a number n= 27
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.2 + N/9 = 5
N/9 = 5 - 2
N/9 = 3
N = 9*3
N=27
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write an equation of the line through the two points -1,-6 and 3,-14
Answers
Answer: an equation of the line in slope-intercept form (y=mx+b) is
y = -2x - 8
A rectangular block has a mass of 1088g. The dimensions of the block are 8cm by 5cm by 4cm. What is the density of the block?
Answers
Answer:
277g / 40cm³
Step-by-step explanation:
Density = mass / volume
In this case:
volume = 8cm*5cm*4cm = 160cm³
then:
Density = 1088g / 160cm³ = 544g/80cm³ = 277g/40cm³
Guys I need help pls tell me the remainder too
Answers
Answer:
0.12245454545 (Quotient = 0 Remainder = 2.694)
Step-by-step explanation:
Divide 2.694 by 22. The quotient is 0 with a remainder of 2.694
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Chris is studying a type of coral that grows at a constant rate. They measured the age and height of 3
pieces of the coral. Here's what they found:
Answers
The equation is; y = 7/2x
What is the equation?We know that we could be able to obtain the equation by the use of the equation is a straight line. The general form of the equation of a straight line is given as y = mx +c
The first thing that we must do is to obtain the slope of the graph from;
m = y2 - y1/x2 x1
m = 45 - 15/6 - 2
m = 7/2
The graph begins at origin hence c = 0
y = 7/2x
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d + 9 = 35 6th grade
Answers
Answer:
D = 26
Step-by-step explanation:
All you have to do is subtract 35 by 9, which is 26.
So,
26 + 9 = 35
What is the solution to this equation
2(40-5y)=10y+5(1-y)
Answers
Answer:
The Answer is y=5.
Step-by-step explanation:
Firstly, multiply what is outside of the parentheses into the parentheses.
2(40-5y)=10y+5(1-y) --> 80-10y=10y+5-5y
Combine like terms
80-10y=5y+5
Add 10y
80=15y+5
Subtract 5
75=15y
Divide by 15
y=5
The solution to the equation is 5.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
2(40-5y)=10y+5(1-y)
Now, solving
80 - 10y = 10y + 5 - 5y
80 - 5 = 10y - 5y + 10y
75 = 20y- 5y
75 = 15y
y= 75/15
y= 5
Hence, the solution is 5.
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Determine the value of c in the diagram. C 50°
Answers
Answer: 10
Step-by-step explanation:
The value of C is 10, because if 50° was in half, it would been 10 and 5.
How do I factor 7.2x2y - 0.9xy2
Answers
Answer:
[tex]xy\left(7.2x-0.9y\right)[/tex]
Step-by-step explanation:
[tex]Rule: a^{b+c}=a^ba^c\\(x^2y=xxy,\:xy^2=xyy)\\=7.2x(xy)-0.9xyy\\=xy\left(7.2x-0.9y\right)[/tex]
For the following equation, find three ordered pair solutions by completing the table. Then use the ordered pairs to graph the equation.
y = - 4x + 8
Answers
The graph of the linear equation can be seen in the image below.
How to complete the table?
Here we have the linear equation:
y = -4x + 8
And we want to find 3 ordered pairs, to do so, we need to evaluate x in different values.
if x = 0 then:
y = -4*0 + 8 = 8
So we have the ordered pair (0, 8).
if x = 1 then:
y = -4*1 + 8 = 4
Then we have the ordered pair (1, 4)
If x = 2 then:
y = -4*2 + 8 = 0
Then we have the ordered pair (2, 0).
Now that we have these 3 ordered pairs, we can graph them in a coordinate axis and then connect them with a line, we will get something like the graph below.
That is the graph of our linear equation:
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A movie company spent $12,000,000 making a feature film. If tickets to see the movie cost $8.00 each, determine the number of tickets that must be sold in order for the company to break even
Answers
Answer:
1500000
Step-by-step explanation:
Molly is making strawberry infused water. For each ounce of strawberry juice, she uses two times as many ounces of water. How many ounces of strawberry juice and how many ounces of water does she need to make 39 ounces of strawberry infused water?
Answers
Answer: 39 ounces of strawberry juice, 78 ounces of water.
Step-by-step explanation:
Since Molly uses "each ounce" meaning 1 per strawberry juice, 39 ounces of strawberry infused water would mean she uses 39 ounces of strawberry juice. Then, it says she uses two times as many as those 39 ounces of strawberry juice for water. This means you multiply 39 by 2 which means you get 78 ounces.
Molly uses 39 ounces of strawberry juice and 78 ounces of water to get 39 ounces of Strawberry Infused Water.
Can someone tell me the answer to the domain and range please
Answers
Answer:
1)
D) -4<x≤-1
R) 4>y≥2
2)
D) 3≤x<5
R) 0≥y>-3
Step-by-step explanation:
(only in 7th so might be wrong)
1)
D) -4<x≤-1
R) 4>y≥2
2)
D) 3≤x<5
R) 0≥y>-3
Just find the range of how far the function goes (both how high; y, and how far; x)
can someone help me with this?
Answers
The value of the function f(-4) = 16.
What is termed as the function?A function is categorized as a relationship between a set of inputs that each have one output.
A function is an association between inputs in which each input is connected to exactly one output. Each function has a domain as well as a co domain, as well as a range. In general, a function is denoted by f(x), where x is really the input.For the given function in the question;
f(x) = x ² , if x < 0.
f(x) = 0 , if x = 0.
f(x) = 2x + 1 , if x > 0
Now, estimate the values;
(a) f(-4)
As, the value of the x to be substitute is negative, the function used will be.
f(x) = x ² ,for x < 0.
Put the value x = -4
f(-4) = (-4)²
f(-4) = 16
The value of f(-4) = 16.
(b) f(0)
As the value of function is zero.
Then,
f(x) = 0 , if x = 0.
Put x = 0 in function we will get.
f(x) = 0.
(c) f(2)
As the value to be substituted is positive, the function used is;
f(x) = 2x + 1 , if x > 0
Put x = 2
f(2) = 4 + 1
f(2) = 5
Thus, the value of f(2) is 5.
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You save $15 each month to buy a tablet that
Cost $184.99. Describe the number of monins
gou need to save to buy the tablet.
Answers
Answer:
13
Step-by-step explanation:
........................
