first, lets solve by factoring:
Let's solve your equation step-by-step.
2x2+14x−4=−x2+3x
Step 1: Subtract -x^2+3x from both sides.
2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)
3x2+11x−4=0
Step 2: Factor left side of equation.
(3x−1)(x+4)=0
Step 3: Set factors equal to 0.
3x−1=0 or x+4=0
x=
1
3
or x=−4
we can also solve using the quadratic formula:
2x2+14x−4=−x2+3x
Step 1: Subtract -x^2+3x from both sides.
2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)
3x2+11x−4=0
Step 2: Use quadratic formula with a=3, b=11, c=-4.
x=
−b±√b2−4ac
2a
x=
−(11)±√(11)2−4(3)(−4)
2(3)
x=
−11±√169
6
x=
1
3
or x=−4
lastly, we can complete the square.
2x2+14x−4=−x2+3x
Step 1: Add x^2 to both sides.
2x2+14x−4+x2=−x2+3x+x2
3x2+14x−4=3x
Step 2: Subtract 3x from both sides.
3x2+14x−4−3x=3x−3x
3x2+11x−4=0
Step 3: Add 4 to both sides.
3x2+11x−4+4=0+4
3x2+11x=4
Step 4: Since the coefficient of 3x^2 is 3, divide both sides by 3.
3x2+11x
3
=
4
3
x2+
11
3
x=
4
3
Step 5: The coefficient of 11/3x is 11/3. Let b=11/3.
Then we need to add (b/2)^2=121/36 to both sides to complete the square.
Add 121/36 to both sides.
x2+
11
3
x+
121
36
=
4
3
+
121
36
x2+
11
3
x+
121
36
=
169
36
Step 6: Factor left side.
(x+
11
6
)2=
169
36
Step 7: Take square root.
x+
11
6
=±√
169
36
Step 8: Add (-11)/6 to both sides.
x+
11
6
+
−11
6
=
−11
6
±√
169
36
x=
−11
6
±√
169
36
x=
1
3
or x=−4
Answer:
x=
1
3
or x=−4
Final answer:
The equation [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex] is a quadratic equation, which can be solved by standard methods such as factoring, completing the square, or applying the quadratic formula and then validated by substituting the solutions back into the original equation.
Explanation:
To solve the quadratic equation, [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex], first combine like terms by getting all terms on one side of the equation, resulting in [tex]3x^2 + 11x - 4[/tex] = 0. This is a standardized quadratic equation [tex]ax^2[/tex] + bx + c = 0. To find the solutions for this equation, you can either factorize it, complete the square or use the quadratic formula, (-b ± √([tex]b^2[/tex] - 4ac)) / (2a). After finding the roots (values for x), verify them by plugging them back into the original equation to ensure they satisfy it.
Graph the equation y=1/2x+5 on the coordinate plane provided below / PLS HELP!
Answer:
Step-by-step explanation:
Y/1 = 2x + 5
Y = 2x + 5
Y = 2x + 5
When x = 1
Y = 2 ×1 +5
Y = 2 + 5
Y = 7
When x =0
Y = 2 × 0 + 5
Y = 5
When x = -2
X = 2 × -2 + 5
X = 1
( Make a table in the side of the page)
X | 1 0 -2
_ _______
Y 7 5 1
The graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given equation of a line is y=1/2x+5.
Substitute x=0, 1, 2, 3, 4, 5,....in a equation y=1/2x+5, we get
When x=0, y=5
When x=1, y=5.5
When x=2, y=6
When x=3, y=6.5
When x=4, y=7
So, the coordinate points are (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7)
Therefore, the graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.
To learn more about the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ5
what is the midpoint of the verticle line segment graphed below?
Answer:
C (2, -5/2)
Step-by-step explanation:
To find the midpoint of two points
mid = (x1+x2)/2, (y1+y2)/2
= (2+2)/2, (4+-9)/2
= 4/2, -5/2
=2,-5/2
Classify the system of equations. 3x = -2- y 4+ y = -3x+1 Click on the correct answer. intersecting parallel coincident
Step-by-step explanation:
rearrange the equations first
y=-3x-2---eq(1)
y=-3x+1-4
y=-3x-3---eq(2)
In first eq slope is -3x and y-intercept is -2
In second equation, the slope is -3x and y-intercept is -3
the slopes are the same in both equations but the y-intercepts are different
so the lines are parallel. The system is inconsistent
For this case we have the following system of equations:
[tex]3x = -2-y\\4 + y = -3x + 1[/tex]
By clearing "y" from both equations we have:
Equation 1:
[tex]3x + 2 = -y\\y = -3x-2[/tex]
Equation 2:
[tex]y = -3x + 1-4\\y = -3x-3[/tex]
It is observed that the slopes of both equations are equal. Recall that the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where "m" is the slope.
If the slopes are equal, then the lines are parallel.
Answer:
Parallel
Which of the following best describes the locust of points equidistant from a given directrix and focus?
A. Parabola
B. Circle
C. Ellipse
D. Hyperbola
Answer:
A. Parabola
Step-by-step explanation:
Parabola best describes the locust of points equidistant from a given directrix and focus.
Parabola is the curve that best describes the locus of points equidistant from a given directrix and focus. This can be obtained by understanding what a parabola is.
What is a parabola?Parabola is a locus of points equidistant from a given fixed point and fixed line.The fixed point is focus and the fixed line is directrix.Standard equation of a parabola:The equation is y² = 4ax, when directrix is parallel to the y-axis, a is distance from origin to focus.
Hence parabola is the curve that best describes the locus of points equidistant from a given directrix and focus.
Learn more about parabola here:
brainly.com/question/4074088
#SPJ2
Identify the property that justifies the following statement:
If m_1= m_2, then m_2 = m_1.
The symmetric property of equality justifies the statement 'If m₁ = m₂, then m₂ = m₁'.
Property of Equality: The property that justifies the statement 'If m₁ = m₂, then m₂ = m₁' is the symmetric property of equality. This property states that if a = b, then b = a. It is a fundamental property of equality in mathematics.
A boy has 40 red and blue pencils in his pencil case. If the ratio of red to blue pencils is 0.15 to 0.35, how many blue pencils does he have?
Answer:
The boy has 28 blue pencils
Step-by-step explanation:
Given
Total pencils = 40
The ratio of red to blue= 0.15:0.35
We have to find the number of blue pencils
For that we need the sum of ratio = 0.15+0.35 = 0.5
So, the number of blue pencils = (ratio of blue/sum of ratio) * total pencils
=0.35/0.5 * 40
=0.7*40
=28 pencils
Therefore, the boy has 28 blue pencils ..
Final answer:
The ratio of red to blue pencils is 0.15 to 0.35. By converting the ratio into parts and calculating the pencils per part, we conclude that the boy has 28 blue pencils in his pencil case.
Explanation:
Calculating the Number of Blue Pencils
To find out how many blue pencils the boy has, we start by understanding the ratio of red to blue pencils, which is given as 0.15 to 0.35. This ratio can also be represented as a fraction, so for every 0.15 red pencils, there are 0.35 blue pencils. To find out the total parts the ratio represents, we add them up: 0.15 (red) + 0.35 (blue) = 0.5 parts. We then divide the total number of pencils (40) by the total parts (0.5) to find out how many pencils each part represents: 40 pencils / 0.5 parts = 80 pencils per part. Since we are looking for the number of blue pencils, we multiply the blue part (0.35) by the number of pencils per part (80): 0.35 * 80 pencils per part = 28 blue pencils.
20 Points 20 points 20 points
Answer:
-5Step-by-step explanation:
[tex]A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] \\\\\det A=\left|\begin{array}{ccc}a&b\\c&d\end{array}\right|=ad-bc[/tex]
[tex]\left\{\begin{array}{ccc}x+2y=5\\x-3y=7\end{array}\right\\\\A=\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] \\\\\det A=A=\left|\begin{array}{ccc}1&2\\1&-3\end{array}\right|=(1)(-3)-(1)(2)=-3-2=-5[/tex]
Answer:
-5
Step-by-step explanation:
can any number of lines pass through two given points
[tex]\huge{\boxed{\text{No.}}}[/tex]
Unless the points are both the same point, there is only one straight line to connect them both. Any other line would either only touch one point or touch neither of the points.
Choose the correct product of (6x + 2)2.
Answer:
36x² + 24x + 4
Step-by-step explanation:
Given
(6x + 2)² = (6x + 2)(6x + 2)
Each term in the second factor is multiplied by each term in the first factor, that is
6x(6x + 2) + 2(6x + 2) ← distribute both parenthesis
= 36x² + 12x + 12x + 4 ← collect like terms
= 36x² + 24x + 4
front section tickets are $15 more expensive than back section tickets. If 275 front section and 325 back section tickets to a country music concert were sold for a total revenue of $19,125, how much does each type of ticket cost?
HELP PLEASE
Answer:
Front section tickets: $40
Back section tickets: $25
Step-by-step explanation:
If x is the price of back section tickets, and x + 15 is the price of front section tickets, then:
275 (x + 15) + 325 x = 19125
275 x + 4125 + 325 x = 19125
600 x = 15000
x = 25
So back section tickets are $25, meaning front section tickets are $40.
if f(x)=(x+3)³+4
let g(x)=f(x+1)-2
find when g(x)=12
Answer:
[tex]x=\sqrt[3]{10}-2[/tex]
Step-by-step explanation:
The composite function (f(x+1)) is moved in the x-axis by -1, you know this by solving x+1=0.
The equivalent expresion for f(x+1) is
[tex]f(x+1)= (x-1+3)^{3}+4[/tex]
[tex]f(x+1)=(x+2)^{3}+ 4[/tex]
Eval the above expression in g(x)
[tex]g(x)=(x+2)^{3}+4-2[/tex]
We must find x that gives g(x)=12
The equation is the following
[tex]12=(x+2)^{3}+2[/tex]
Grouping terms>
[tex](x+2)^{3} =10[/tex]
To solve for x, must apply cubic root in both sides of equation:
[tex]\sqrt[3]{(x+2)^{3} } =\sqrt[3]{10}[/tex]
it then turns in the following>
[tex]x+2=\sqrt[3]{10}\\[/tex]
Giving the stated answer
mk
---, for m = 6 and k = 2
m+k
So you're asking to evaluate this equation?
mk/m+k for m = 6 and k = 2
Type the correct answer in each box.
The value of x is °, and the value of y is
°.
Answer:
x = 60°, y = 50°Step-by-step explanation:
We know: the angles measures in a triangle add up to 180°.
(look at the picture)
z + 50 + 60 = 180
z + 110 = 180 subtract 110 from both sides
z = 70°
x + 50 + 70 = 180
x + 120 = 180 subtract 120 from both sides
x = 60°
Angles x, y and z are on one side of a straight line. Therefore they add to 180°.
x + y + z = 180
60 + y + 70 = 180
y + 130 = 180 subtract 130 from both sides
y = 50°
Answer:
x = 60°, y = 50°
Step-by-step explanation:
We know: the angles measures in a triangle add up to 180°.
z + 50 + 60 = 180
z + 110 = 180 subtract 110 from both sides
z = 70°
x + 50 + 70 = 180
x + 120 = 180 subtract 120 from both sides
x = 60°
Angles x, y and z are on one side of a straight line. Therefore they add to 180°.
x + y + z = 180
60 + y + 70 = 180
y + 130 = 180 subtract 130 from both sides
y = 50°
Inverse of f(x)=3x-4
Answer:
[tex]\large\boxed{f^{-1}(x)=\dfrac{x+4}{3}=\dfrac{1}{3}x+\dfrac{4}{3}}[/tex]
Step-by-step explanation:
[tex]f(x)=3x-4\to y=3x-4\\\\\text{exchange x to y and vice versa}\\\\x=3y-4\\\\\text{solve for y}\\\\3y-4=x\qquad\text{add 4 to both sides}\\\\3y=x+4\qquad\text{divide both sides by 3}\\\\y=\dfrac{x+4}{3}[/tex]
Please help! Will mark brainlyest!
Answer: The black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.
Step-by-step explanation:
Given : The mass of black hole = [tex]6.57\times10^{36}\ kg[/tex]
The mass of Sum is approximately [tex]1.99\times10^{30}\ kg[/tex]
Now, the number of times the mass of black hole more massive than the mass of sun is given by :-
[tex]n=\dfrac{6.57\times10^{36}}{1.9\times10^{30}}[/tex]
i.e.[tex]n=\dfrac{6.57}{1.9}\times\dfrac{10^{36}}{10^{30}}[/tex]
Using the division law of exponent :-
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
[tex]=\approx3.302\times10^{36-30}}\\\\=3.302\times10^{6}[/tex]
Hence, the black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.
What is the solution
Answer:
y ≥ 14.
Step-by-step explanation:
y - 27 ≥ -13 Add 27 to both sides:
y ≥ 14 (answer).
For this case we must find the solution of the following inequality:
[tex]y-27 \geq-13[/tex]
We must add 27 to both sides of the inequality:
[tex]y \geq-13 + 27[/tex]
We know that different signs are subtracted and the sign of the major is placed.[tex]y \geq14[/tex]
So, the solution is [tex]y \geq14[/tex]
Answer:
Option C
❤️❤️☺️Hello MATHS Experts☺️❤️❤️, Solve This Problem Please
Answer:
x = 70°y = 55°z = 55°Step-by-step explanation:
Look at the picture.
We know: the sum of the angles measure in the triangle is 180°. Therefore we have the equation:
[tex]35^o+35^o+\alpha=180^o[/tex]
Solve it:
[tex]70^o+\alpha=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\\alpha=110^o[/tex]
Angle α and β = x are the supplementary angles. Supplementary angles add up to 180°. Therefore:
[tex]\alpha+\beta=180^o[/tex]
[tex]110^o+\beta=180^o\qquad\text{subtract}\ 110^o\ \text{from both sides}\\\\\beta=70^o[/tex]
[tex]\beta+\gamma+\gamma=180^o[/tex]
[tex]70^o+2\gamma=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\2\gamma=110^o\qquad\text{divide both sides by 2}\\\\\gamma=55^o[/tex]
6. Identify which of the following are sets.
I: The collection of all the days in a week.
II: The collection of all teachers in a school.
III: The collection of all integers more than -5.
A. I only
B.I, II
C.III only
D. I, II, III
Answer:
D. I, II, III
Step-by-step explanation:
Let us look at the definition of set:
A set is a collection of well-defined and distinct objects
I: The collection of all the days in a week.
The set will consist of seven elements.
II: The collection of all teachers in a school.
Also a set.
III: The collection of all integers more than -5.
This is a set.
Therefore, Option D is correct ..
what are the domain and range of the absolute value parent function
Answer:
C. The domain is all real numbers, and the range is non-negative real numbers( [tex]y\ge0[/tex])
Step-by-step explanation:
The absolute value parent function is [tex]y=|x|[/tex]
The domain of a function refers to all values of x for which the function is defined.
The parent absolute value function is defined for all values of x.
Therefore the domain is all real numbers.
The range refers to the y-values for which x is defined.
The parent has a v-shape and its vertex is at the origin.
Therefore the least y-value is 0 and there is no maximum y-value.
The range is [tex]y\ge0[/tex]
See attachment.
If the probability that a person will die in the next year is 452/1000,000, what is the probability that the person will not die in the next year?
a. 99%
b. 0.00452
c. 99548
d.0.99548
Answer: 0.999548
Step-by-step explanation:
If the probability that a person will die next year is 425/1,000,000
The the probability of them not dying is:
(1,000,000-425)/1,000,000=999548/1,000,000
Next let’s move the decimal 6 spots to the left.
The answer would be 0.999548
What is the measure of angle E, in degrees?
The answer is 84 degrees because d and f both are 48 degrees so that adds up to 96. So that means you add 84 plus 96 which is 180 so the answer is 84 degrees.
Answer. The answer is 84
Solve this radical equation (square root of x+11)-x=-1
[tex]\bf \sqrt{x+11}-x=-1\implies \sqrt{x+11}=x-1\implies \stackrel{\textit{squaring both sides}}{(\sqrt{x+11})^2=(x-1)^2} \\\\\\ x+11=\stackrel{\mathbb{F~O~I~L}}{x^2-2x+1}\implies 11=x^2-3x+1\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5\\ -2 \end{cases}[/tex]
Gives x = -5 or x = 2.
Learn how to solve radical equations step by step by isolating terms and squaring, resulting in solutions to the given equation.
To solve the equation (square root of x+11)-x=-1, follow these steps:
Isolate the square root term: square root of x+11=-1+xSquare both sides to eliminate the square root: x+11 = x^2+2x+1Rearrange the equation and solve the quadratic: x^2+x-10=0, which gives x = -5 or x = 2
please answer this.
Also if you can, please answer my other question its very simmilar
For this case we have that a percentage equivalent to[tex]\frac {1} {8}[/tex]is given by:
[tex]x = \frac {1} {8} * 100 =[/tex] 12.5%
Then, according to the steps, it is observed that Harriet made an incorrect division, deboa multiply. So, the second step is the wrong one.
Answer:
Option B
Help me on this math question
Answer: B. 36
Step-by-step explanation: Round each number.
11.72 -> 12
3.01 -> 3
Multiply the rounded numbers.
12 x 3 = 36
The answer would be 36.
(1/x)+(1/x-y)
Please solve this question. I will mark you brainliest.
Answer:
[tex]\frac{2x-y}{x(x-y)}[/tex]
Step-by-step explanation:
To express as a single fraction
multiply numerator/denominator of [tex]\frac{1}{x}[/tex] by (x - y) and
multiply numerator/ denominator of [tex]\frac{1}{x=y}[/tex] by x
= [tex]\frac{x-y}{x(x-y)}[/tex] + [tex]\frac{x}{x(x-y)}[/tex]
Add the numerators leaving the denominator
= [tex]\frac{2x-y}{x(x-y)}[/tex]
Factor this expression.
4x - 16
Hii!
__________________________________________________________
Answer:
Step-by-step explanation:
Note that both terms, 4x and -16, have something in common.
In math, this "something" is known as the greatest common factor (g.c.f.).
The g.c.f. of 4x and -16 is 4, so that's what we factor out.
First, we divide both 4x and -16 by 4.
We obtain.
x-4
Put parentheses around x-4
(x-4)
Now put 4 outside the parentheses
4(x-4)
--
Hope that this helped! Best wishes,
--
The factored form of the expression 4x - 16 is 4(x - 4).
To factor the expression 4x - 16, we can look for the greatest common factor (GCF) of the terms. In this case, both terms have a common factor of 4.
We can factor out the GCF of 4 from each term:
4x - 16 = 4(x - 4)
Therefore, the factored form of the expression 4x - 16 is 4(x - 4).
Learn more about factored form here:https://brainly.com/question/25094938
#SPJ2
What is the solution to the equation x over 3 + x over 6 = 7 over 2
Answer:
x=7
Step-by-step explanation:
The given equation is:
[tex]\frac{x}{3}+\frac{x}{6} = \frac{7}{2}[/tex]
Multiplying both sides by LCM of 3 and 6
So,
[tex]\frac{x}{3}*6+\frac{x}{6}*6 = \frac{7}{2}*6\\2x+x=7*3\\3x=21\\\frac{3x}{3} =\frac{2}{3}\\ x=7[/tex]
Hence, the solution of the equation is x=7 ..
Answer: x = 7
Step-by-step explanation:
(x/3)+(x/6)=7/2
add variables
(2x+x)/6=7/2
combine like terms
3x/6=7/2
simplify
x/2=7/2
multiply denominators by 2
x=7
The slope of a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be translated to the left or right to represent the same function d(x)? Explain your answer.
Answer:
Left 4 units
Step-by-step explanation:
h(x) is a line with slope 2. Let's say it has y-intercept b. So:
h(x) = 2x + b
d(x) is h(x) shifted up 8 units. So:
d(x) = h(x) + 8
d(x) = 2x + b + 8
We want to shift h(x) left or right to get d(x). If we say that shift is a units to the right, then:
h(x−a) = d(x)
2(x−a) + b = 2x + b + 8
2x − 2a + b = 2x + b + 8
-2a = 8
a = -4
a is negative, so the shift is to the left.
h(x) should be shifted to the left 4 units.
The h(x) should be Left 4 units
Calculation of h(x) that need to be translated:Since
h(x) represent a line with slope 2.
Let's assume it has y-intercept b.
Therefore,
h(x) = 2x + b
d(x) represent h(x) shifted up 8 units.
So,
d(x) = h(x) + 8
d(x) = 2x + b + 8
Now
h(x−a) = d(x)
2(x−a) + b = 2x + b + 8
2x − 2a + b = 2x + b + 8
-2a = 8
a = -4
Since a is negative, so the shift is to the left.
Learn more about the function here: https://brainly.com/question/16995471
Parallelogram ABCD is dilated to form parallelogram EFGH.
Side BC is proportional to side FG. which corresponding side is proportional to segment CD?
Type the answer in the box below.
Answer:
side GH is proportional to segment CD
Step-by-step explanation:
Corresponding sides are those sides that are in the same spot in two different shapes.
Since parallelogram EFGH is dilated form of Parallelogram ABCD and Side BC is proportional to side FG.
So, side GH is proportional to segment CD
The graph of a function, f(x), is plotted on the coordinate plane.
Select two of the following functions that would move the graph of the function to the right on the coordinate plane.
f(x−3)+1
f(x)+4
f(x+2)−7
f(x−5)
f(x+6)
f(x)−3
f(x-5) because when it's with the x, + indicates a translation to the left and - indicates a translation to the right.
Answer:
f(x−3)+1, f(x−5)
Step-by-step explanation:
I took the checkpoint and got it right.