Answer:
[tex]x=\dfrac{-3+\sqrt{37}}{2}, \quad x=\dfrac{-3-\sqrt{37}}{2}[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]x^2+3x-7=0[/tex]
Solve by Completing the SquareStep 1
When completing the square for a quadratic equation in the form [tex]ax^2+bx+c=0[/tex] the first step is to move the constant to the right side of the equation:
[tex]\implies x^2+3x-7+7=0+7[/tex]
[tex]\implies x^2+3x=7[/tex]
Step 2
Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:
[tex]\implies x^2+3x+\left(\dfrac{3}{2}\right)^2=7+\left(\dfrac{3}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2+3x+\left(\dfrac{3^2}{2^2}\right)=7+\left(\dfrac{3^2}{2^2}\right)[/tex]
[tex]\implies x^2+3x+\dfrac{9}{4}=7+\dfrac{9}{4}[/tex]
[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{28}{4}+\dfrac{9}{4}[/tex]
[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{28+9}{4}[/tex]
[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{37}{4}[/tex]
Step 3
Factor the perfect square trinomial on the left side:
[tex]\implies \left(x+\dfrac{3}{2}\right)^2=\dfrac{37}{4}[/tex]
Step 4
Square root both sides:
[tex]\implies \sqrt{\left(x+\dfrac{3}{2}\right)^2}=\sqrt{\dfrac{37}{4}}[/tex]
[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{37}}{\sqrt{4}}[/tex]
[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{37}}{2}[/tex]
Step 5
Subtract ³/₂ from both sides:
[tex]\implies x+\dfrac{3}{2}-\dfrac{3}{2}=-\dfrac{3}{2}\pm\dfrac{\sqrt{37}}{2}[/tex]
[tex]\implies x=-\dfrac{3}{2}\pm\dfrac{\sqrt{37}}{2}[/tex]
[tex]\implies x=\dfrac{-3\pm\sqrt{37}}{2}[/tex]
SolutionsTherefore, the solutions of the given quadratic equation are:
[tex]x=\dfrac{-3+\sqrt{37}}{2}, \quad x=\dfrac{-3-\sqrt{37}}{2}[/tex]
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Answer:
i d k
Step-by-step explanation:
Can someone help me solve for
If you're talking about the lower case m, which sporadically appears before a specific angle, like m ANGLE A-B-C. The m denotes the angle ABC's "measure" (angular measure in degrees).
Here the angle m ∠UVX = [tex]52^{0}[/tex].
What is the m ∠?The measure of an angle is sometimes represented by the symbol m. Different names can be given to an angle . The same angle is known by several names. The angle might be identified by the letter of the vertex, in which case it would be called A. ABC stands for the actual physical angle and mABC for its measure. There is no distinction between the two, and any one may be used without a doubt.If you're talking about the lower case m, which sporadically appears before a specific angle, like m ANGLE A-B-C. The m denotes the angle ABC's "measure" (angular measure in degrees).To learn more about : Angular measure in degrees
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An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 18 miles per hour faster than the westbound train. After 2.5 hours, they are 280 miles apart. At what speeds are the two trains traveling?
Answer: The eastbound train is traveling at 65mph while the westbound train travels at 47mph.
Step-by-step explanation:
You would use x as the variable for the speed of the westbound train. The eastbound train would be 18+x. your equation would be 2.5(18+x+x)=280
You would find that x=47 for the westbound train. You would then add 18 to get the speed of the eastbound train which would be 65.
Victoria's car used of a gallon to travel 21 miles. At what rate doesthe car use gas, in miles per gallon?
Answer:
26 1/4 miles per gallon
Explanation:
We are told that the car travels 21 miles per 4/5 gallons. Therefore, the rate at which the car uses the gas is
[tex]\frac{21\text{ miles}}{4/5\text{ miles}}[/tex]which can also be written as (by taking the reciprocal of the denominator)
[tex][/tex]what is 5 + 2 =??? i need to know now
Answer: 5 + 2 = 7
Step-by-step explanation: its easy
What is the domain of this relation?
Answer:
(-5, -3, 1, 2, 3) .... the fourth one
Step-by-step explanation:
the domain is all the x values.
so look at your points and look at the x values ( the number on the X-axis) for those points!
A small container of paint will cover 20,000cm².
Luke wants to paint all the faces of fifty 8cm cubes.
Is one container of paint enough?
One paint container is enough to paint all the faces of fifty 8 cm cubes.
Given
The paint can cover 20,000 [tex]cm^{2}[/tex]
Side of square = 8 cm
As the Total surface area of a cube is [tex]6a^{2}[/tex],
where a is the side of the cube.
The total surface area of one cube = 6 x [tex]8^{2}[/tex]
= 384 [tex]cm^{2}[/tex]
Since there are fifty such cubes,
384 x 50
Total area to be painted = 19200 [tex]cm^{2}[/tex]
Since 19,200 [tex]cm^{2}[/tex] is less than 20,000 [tex]cm^{2}[/tex] , it is possible to paint all the cubes.
Hence one paint container is enough to paint all cubes.
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omar will run at least 28 miles this week, so far he has run 12 miles. What are the possible numbers of additional miles he will run? use t for the number of additional miles he will run white your answer as an inequality solved for t
The inequality that will define Omar's run is 12 + m ≥ 28.
An inequality in algebra is a mathematical statement that employs the inequality symbol to show how two expressions relate to one another. The phrases on either side of an inequality symbol are not equal. The phrase on the left should be larger or smaller than the expression on the right, or vice versa, according to this symbol. Relationships between two algebraic expressions that are represented by the inequality symbols are known as literal inequalities. The relationship is known as an inequality when the symbols ">", "", "", or "" are used to link two real numbers or algebraic expressions.
For this issue, it is said that Omar would run at least 28 miles this week; he may run more, but 28 miles is his minimum objective.
He had already covered 12 miles.
Afterward, the inequality symbol will be "."
The inequality is therefore 12 + m 28.
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Find the L.C.M of: 3x² + 7x + 2 and 2x² + 3x-2
Best of luck
Least Common Multiple of 3x² + 7x + 2 and 2x² + 3x-2 is (2x-1)(x+2)(3x+1)
What is lcm ?Least Common Multiple is the meaning of the abbreviation LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It can also be computed using two or more numbers. Finding the LCM of a given collection of numbers can be done in a variety of ways. Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
Given that : 3x² + 7x + 2 and 2x² + 3x-2
3x² + 7x + 2
3x² +6x +x + 2
3x(x +2)+1(x+2)
(3x+1)(x+2)
2x² + 3x-2
2x² + 4x-x -2
2x(x+2)-(x+2)
(2x-1)(x+2)
L.C.M of 3x² + 7x + 2 and 2x² + 3x-2 is
(2x-1)(x+2)(3x+1)
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1/3(2x-3/7)+1/6x=4/7 find x
If the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7.
The given equation is
1/3(2x - 3/7)+(1/6)x = 4/7
First we have to apply the distributive property of subtraction in the equation
1/3(2x - 3/7)+(1/6)x = 4/7
(3/2)x - 1/7 + (1/6)x = 4/7
Here we have to rearrange the terms and group the like terms
Move the 1/7 to right hand side of the equation
(3/2)x + (1/6)x = (4/7)+(1/7)
Addition of like terms
(5/3)x = 5/7
Move the 5/3 to the right hand side of the equation
x = 5/7 ÷ 5/3
x = 5/7 × 3/5
x = 3/7
Hence, if the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7
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Can you help me please
Which statement describes the graph?
Answer:
b
Step-by-step explanation:
i earn an annual salary of $30,572 and my commission is 5% on all sales. How much must my sales be if i want my annual salary to be $31,836?
If you want to make an annual salary of $31,836, then your sales must be $25,280
How much must my sales be to get the desired salary?
Ok, so you want to earn a total of $31,836, and he has a fixed salary of $30,572, so the missing amount is:
$31,836 - $30,572 = $1,264
Now, we know that you make a commission of the 5% of what you sell, so if X is what you sell, then to make the desired salary X must be:
X*0.05 = $1,264
Solving that linear equation for X we get:
X = $1,264/0.05 = $25,280
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A parallelogram has four angles. You know that one angle is 96. What is the other three angles
the depth of the water in a tank after t minutes is modeled by f l(t) =3+2.5t measured in inches.find the interpret f(5)
The function f(5) equals 15.5 inches
What is a function?
A function from either a set X to a set Y provides precisely one item of Y to each item of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. The Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi are credited with the first known attempt to the concept of function. Initially, functions were the idealized vision of how a variable quantity depended on another quantity. A planet's location, for example, is a function of time. Historically, the notion was developed with the infinitesimal calculus at the end of the 17th century, and the functions investigated were differentiable until the 19th century.
The function is solved as
f(5) = 3 + 2.5(5) = 3 + 12.5 = 15.5 inches
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If Andy continues descending at this rate, where will he be in relation to sea level after 6 minutes write your answer as a integer
1. The rate of the descent of Andy as a unit rate will be -4 feet per minute.
2. If Andy continues descending at this rate, the relation to sea level after 6 minutes is -24 feet.
How to illustrate the information?From the information, the following can be deduced'
1. Distance = -10 feet
Time = 2 1/2 minutes = 2.5 minutes
Speed = Distance / Time
Speed = -10 / 2.5
Speed = -4 feet per minutes
2. When Andy continues descending at this rate, the relation to sea level after 6 minutes will be:
= -4 × 6
= -24
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Andy is scuba diving. He starts at sea level and then descends 10 feet in 212 minutes. Part A How would you represent Andy's descent as a unit rate? Express your answer as an integer. Enter your answer in the box. feet per minute Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes? feet
mother ate pies in the morning, she ate one pie, while she gave half of all those left to Little Red Riding Hood who gave it to her grandmother. On the way, Little Red Riding Hood ate 2 pies and gave a third of the rest to the wolf. Little Red Riding Hood brought 8 pies to her grandmother. How many pies did mother bake?
The number of pies that Red Riding Hood's mother made is 25.
How many pies did the mother bake?Let x represent the number of pies mother baked in the morning.
Pies left after mother ate 1 = x - 1
The number of pies that Red Riding Hood takes to her grandmother: 1/2(x - 1)
0.5(x - 1)
0.5x - 0.5
Pies left after Red Riding Hood ate 2: [(0.5x - 0.5) - 2]
Pie after she gave the wolf 1/3 ; (1 - 1/3) × [(0.5x - 0.5) - 2]
2/3 × [(0.5x - 0.5) - 2] = 8
In order to determine the value of x, take the following steps:
Multiply both sides of the equation by 3/2.
[(0.5x - 0.5) - 2] = 12
Add 2 to both sides of the equation: 0.5x - 0.5 = 12 + 2
0.5x - 0.5 = 12
Add 0.5 to both sides of the equation
0.5x = 12 + 0.5
0.5x = 12.5
Divide both sides by 0.5
x = 25
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simplify 5(x+4)-2(x-3)
Answer:
3x +26
Step-by-step explanation:
The questions are at the bottom of the page. This is easy im just bad pls help
We have a translation of 3 units to the left and 4 units upwards.
How to identify the translation applied?
To find the translation, we only need to look at one of the vertices of the triangle.
We can see that the coordinates of B are (4, 1), while the coordinates of the translated point B' are (1, 5)
The translation is given by the difference:
(1, 5) - (4, 1) = (1 - 4, 5 - 1) = (-3, 4)
So the translation is defined by (-3, 4)
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i need help on this, thanks
Answer:
M∠2 = 37°
M∠3 = 143°
M∠4 = 37°
Step-by-step explanation:
∠3 is the complete opposite of ∠1
143° + 143° = 286°
there is 360° in a full circle or a repeating angle (aka the scissors)
360°-286°=74°
since ∠2 and ∠4 is opposite of each other
74°÷2=37°
Answer:
[tex]m \angle 2= \boxed{37}\;^{\circ}\\\\m \angle 3= \boxed{143}\;^{\circ}\\\\m \angle 4= \boxed{37}\;^{\circ}[/tex]
Step-by-step explanation:
Angles on a straight line sum to 180°.
⇒ m∠1 + m∠2 = 180°
⇒ 143° + m∠2 = 180°
⇒ m∠2 = 37°
Vertical Angle Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Applying the Vertical Angle Theorem:
m∠3 = m∠1 = 143°m∠4 = m∠2 = 37°Please answer this question to 1 decimal place
Answer:
To one decimal place, x = 7.7 cm
Step-by-step explanation:
Let y equal BD.
Since AD is a bisector of angle BAC, angle DAB is 17°.
tan(17°) = y/21, so y = 21 tan(17°)
tan(34°) = (x + 21 tan(17°))/21
21 tan(34°) = x + 21 tan(17°)
x = 21(tan(34°) - tan(17°)) = 7.7 cm
Add 6.2 to the difference between 4.1 and 1.9 then divide the result by 3
Difference: the outcome of subtraction.
Let's just start of with the difference between 4.1 and 1.9, because we need the result of this before we do anything else.
1. 4.1-1.9=2.2
2.2 is the difference of 4.1 and 1.9.
2. It says to add 6.2 next.
6.2+2.2= 8.4
Next we need to divide by 3.
3. 8.4/3=2.8.
4. 2.8 is the answer!!
----------------------------
i think this was simple, so good luck!! much love! <33
A reservoir has an area of about 1.8 × 104 square miles. Its volume is about 28,000 cubic miles. Find the area of the reservoir in standard form and its volume in scientific notation.
The area of the reservoir in standard form is 1.8 × 10⁴ square miles
The volume of the reservoir in scientific notation is 2.8 × 10⁴ cubic miles
Writing an expression in standard formFrom the question, we are to determine the area of the reservoir in standard form and the volume of the reservoir in scientific notation
Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form
Thus,
To write a number in standard form, we will write the number as a product of a number between 1.0 and 10.0 and a power of 10
From the given information,
The area of the reservoir is 1.8 × 10⁴ square miles.
The area of the reservoir is already written in standard form
Now,
To write the volume of the reservoir in scientific notation
NOTE: Standard form is the same as scientific notation
From the given information,
The volume of the reservoir is 28000 cubic miles
28000 = 2.8 × 10⁴
Hence, the volume in scientific notation is 2.8 × 10⁴ cubic miles
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what is the simplest form of the square root of 75
a study of how noise impacts student performance on exams is being proposed. eighty student volunteers will be randomly assigned to two groups of forty and each student will take a test on how much trivia they know. one group will take the test while construction sounds are being played and the other group will take the test without any background sounds. what will be the biggest problem with the results of this study?
The biggest problem with the results of this research study is B. Lack of realism.
What is realism about?It should be noted that when an experiment's procedures, participants, or setting are unrealistic. The ability of researchers to apply the findings of an experiment to the situations that hold the most interest may be constrained by a lack of realism.
The study is how how noise impacts student performance on exams is being proposed.
An experiment's subjects, medications, or environment might not accurately replicate the circumstances we truly wish to explore. In that circumstance, we are unable to extrapolate the experiment's findings broadly.
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The options are:
a. Lack of attention to experimental detail
b. Lack of realism
c. Placebo effect
Petra always keeps her 6 bedrooms in her house clean it takes her 15 minutes to clean a single room how many hours will it take her to clean all 6 bedrooms
Answer:
90 minutes(1hour 30 minutes)
Step-by-step explanation:
If 1 room=15 minutes
Then 6 rooms= ?
=6×15/1
=90 minutes
=1hour 30 minutes
Graph the line -3 with slope (-4,-2) passing through the point
The linear equation of the line that passes through point (-4,-2) and has a slope of -3 is y = -3x - 14.
What is the graph of the line with the given slope and point?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point ( -4, -2 )
x = -4y = -2Slope m = -3First we calculate the y-intercept 'b' using the equation of line formula.
y = mx + b
Plug in point ( -4, -2 ) and slope -3.
-2 = -3(-4) + b
-2 = 12 + b
b = -2 - 12
b = -14
Now that we have the values of slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = -3(x) + ( -14 )
y = -3x - 14
Therefore, the equation of the line is y = -3x - 14.
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HELP
What is the slope of the line?
Answer: -8/3
Step-by-step explanation:
slope is rise/run or y2-y1/x2-x1
so, the two points are (4,-4), (1,4)
-4-4/4-3= -8/3
HELP PLS DUE TOMORROW
What are the similarities and differences between these two problems?
For example:
Similar: both arithmetic/linear/common difference
Different: #1 is discrete #2 is continuous
WILL GIVE BRAIN
Answer:
Step-by-step explanation:
Similarity:Both equations are linear equations with one variable.
Difference:
Problem1: Linear equation uses discrete variable. Money can be counted.
Problem 2: Linear equation uses continuous variable. water can be measured.
Mrs. [Name] has 56 pencils and 42 erasers. If she wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers, what is the greatest number of students she can have in her class so there are none left over? How many pencils and erasers will each student have
[re post]
Answer:
there must be 14 students and each one can get 4 pencils and 3 erasers
Step-by-step explanation:
56 goes into 14 4 times. 42 goes into 14 3 times none left over
find the 1st term, 3rd term and 12th term of series whose nth term is 3n-5/4
Based on the given task content; the first term of the series whose nth term is 3n-5/4 is -1/2.
The 12th term of the series is 7.75How to find the nth term of a series?nth term = (3n - 5) /4
Where,
n = number of termsFirst term, a = (3n - 5) / 4
substitute n = 1 into the equation= (3n - 5) / 4
= {3(1) - 5} / 4
= (3 - 5) / 4
= -2/4
= -1/2
The first term of the series whose nth term is 3n-5/4 is -1/2
When n = 12(3n - 5) / 4
= {3(12) - 5} / 4
= 36 - 5 / 4
= 31/4
= 7.75
Therefore, the 12th term of the series whose nth term is 3n-5/4 is 7.75
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Write the equation in slope-intercept form:
6x−3y=−18
The equation in slope-intercept form is y = 2x + 6
How to determine the slope-intercept form of the equation?The equation is given as
6x - 3y = -18
The above equation is a linear function, and it is in its general form
To determine the slope-intercept form of the equation, we simply make y the subject of the formula in the equation
So, we have
6x - 3y = -18
Divide through the equation by -3
So, we have
-2x + y = 6
Add 2x to both sides
y = 2x + 6
Hence, the slope-intercept form of the equation is y = 2x + 6
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