Answer:
x = 1/2 and
x = -15/2
Step-by-step explanation:
First, get the absolute value alone on one side if the equation.
2 |2x + 7 | = 16
Divide both sides by 2.
| 2x + 7 | = 8
Once the absolute value sign is by itself, you will separate the equation into two separate equations.
2x+7=8 and 2x+7=-8
Solve these two equations separately and get two solutions.
2x + 7 = 8
Subtract 7.
2x = 1
Divide by 2.
x = 1/2 Here is one solution.
2x + 7 = -8
Subtract 7.
2x = -15
Divide by 2.
x = -15/2 Here is a second solution.
Answer:
x = - [tex]\frac{15}{2}[/tex] , x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
2 | 2x + 7 | = 16 ( divide both sides by 2 )
| 2x + 7 | = 8
the absolute value function always gives a positive result, but the expression inside can be positive or negative , that is
2x + 7 = 8 ( subtract 7 from both sides )
2x = 1 ( divide both sides by 2 )
x = [tex]\frac{1}{2}[/tex]
or
- (2x + 7) = 8
- 2x - 7 = 8 ( add 7 to both sides )
- 2x = 15 ( divide both sides by - 2 )
x = - [tex]\frac{15}{2}[/tex]
As a check
substitute these values into the left side and if equal to the right side then they are a solution
x = [tex]\frac{1}{2}[/tex]
2 | 2([tex]\frac{1}{2}[/tex] ) + 7 | = 2 | 1 + 7 | = 2 | 8 | = 16 = right side
x = - [tex]\frac{15}{2}[/tex]
2 | 2(- [tex]\frac{15}{2}[/tex] ) + 7 | = 2 | - 15 + 7 | = 2 | - 8 | = 2 | 8 | = 16 = right side
then x = - [tex]\frac{15}{2}[/tex] and x = [tex]\frac{1}{2}[/tex] are the solutions
How do I solve x for 2x+8=3x+10
To solve for x in: [tex]2x + 8 = 3x + 10[/tex]
Collect like terms
[tex]→8 - 10 = 3x - 2x \\ - 2 = x[/tex]
Therefore:
[tex]x = - 2[/tex]
a unicorn is tethered by a 20-foot silver rope to the base of a magician's cylindrical tower whose radius is 8 feet. the rope is attached to the tower at ground level and to the unicorn at a height of 4 feet. the unicorn has pulled the rope taut, the end of the rope is 4 feet from the nearest point on the tower, and the length of the rope that is touching the tower is $\frac{a - \sqrt{b}}{c}$ feet, where $a$, $b$, and $c$ are positive integers, and $c$ is prime. find $a b c$.
The values of a=60, b=750, c=3, a+b+c= 813 as determined by Pythagorean Theorem..
What is Pythagorean Theorem?
A geometric theorem states that the square of a right triangle's hypotenuse equals the sum of the squares of its other two sides.
Call the circle's center O, the unicorn's tether point A, and the final spot where the rope reaches tower B. Triangle OAB is a right triangle since BA is a tangent line at point B and OB is a radius. We determine the horizontal component of AB has length [tex]4\sqrt{5}[/tex] using the Pythagorean Theorem.
The cylinder is "unrolled" to become a flat surface. Let C be the rope's bottom tether, D the point below A on the ground, and E the point directly beneath B. Triangles CDA and CEB share characteristics of right triangles. The Pythagorean Theorem states that CD=8cdotsqrt6.
Let x represent the size of CB.[tex]CD=8\cdot\sqrt{6}[/tex]
[tex]\[\frac{CA}{CD}=\frac{CB}{CE}\implies \frac{20}{8\sqrt{6}}=\frac{x}{8\sqrt{6}-4\sqrt{5}}\implies x=\frac{60-\sqrt{750}}{3}\][/tex]
Therefore,
a=60, b=750, c=3,a+b+c= 813 as determined by Pythagorean Theorem.
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6 1/2 to quarts to cups
Answer:
26 cups
Step-by-step explanation:
1 quart = 4 cups
6 quarts x 4 cups = 24 cups
1/2 a quart = 2 cups
24+2= 26Answer:
12
Step-by-step explanation:
a data set includes the following numbers: nineteen over 4, two and one fifth, 85%, and 3.24. part a: what is the order of the numbers from least to greatest?
The order of the numbers from least to greatest is:
85% < Two and one fifth < 3.24 < Nineteen over 4
The given data set of numbers are: nineteen over 4, two and one fifth, 85%, and 3.24
In order to compare these numbers, we will change all of them into float (decimal) format.
nineteen over 4 = 19/4 = 4.75
two and one fifth = 2 [tex]\frac{1}{5}[/tex] = 11/5 = 2.2
85% = 85/100 = 0.85
And 3.24 are the numbers set.
Now the order of numbers from least to greatest is clear.
Since 0.85 < 2.2 < 3.24 < 4.75, we can conclude
85% < 2 [tex]\frac{1}{5}[/tex] < 3.24 < 19/4
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can u pls help me with my ixl :)
the stock maeket fell 60 points over a period of four days. What was the average change in the stock market each day
Answer:
15 points
Step-by-step explanation:
It's 60 points over 4 days. We can divide 60 by 4, which is
15
la tarifa de un recorrido de taxi es de 7.25 de cargo fijo y de 7 por cada km recorrido determina la ecuación si p corresponde al valor del pago por x km recorridos
The equation that illustrates the amount to be paid for the number of kilometers will be 7.25 + 7x.
How to illustrate the information?Fixed rate for taxi = 7.25
Additional charges per kilometers = 7
Number of kilometers = x
Therefore, the equation that illustrates the amount to be paid for the number of kilometers will be:
= 7.25 + (7 × x)
= 7.25 + 7x
Therefore, the equation is 7.25 + 7x.
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not even an actual assignment question, just wanted to ask, how are you?
Answer:
Im sleepy. How are you?
Answer:
oh thx im good how are you
Step-by-step explanation:
−5(−x−1)+4x−1= 49 solve for x
If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth. (1 point)
A
Hence , the difference in length between segments AB and AD is 1.17 units .
Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate angle of a triangle. It means the connection between the angles and sides of a triangle area unit given by these trig functions. the essential pure mathematics functions area unit circular function, cosine, tangent, cotangent, secant and trigonometric functionThe angles of circular function, cosine, and tangent area unit the first classification of functions of trig. and also the 3 functions that area unit cotan, secant and trigonometric function will be derived from the first functions. Basically, the opposite 3 functions area unit usually used as compared to the first pure mathematics functions.
The diagram of the given question is given below .
Applying sin rule in triangle ABC , we get
sin(x°) = AC/AB
sin(45°) = 4 / AB
1 /√2 = 4 / AB
AB = 4√2
AB ≈ 5.657
Similarly, apply sin rule in triangle ACD, we get
sin(y°) = AC /CD
sin(63°) = 4 / CD
AD = 4.489
Now distinction in lengths of AB and AD = 5.657 - 4.489
= 1.168
≈ 1.17
Therefore, distinction within the lengths of AB and AD are going to be 1.17 units.
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Round off 28.964 to the nearest tenths
Answer:
Its 29.000Step-by-step explanation:Since we need to Round the Nearest Tenths, First we need to find what is the thenths.
So the order of numbers are
Hundreds - Tens - Ones - . - Tenths - hundreths
So tenths is the digit after the decimal Dot
When we convert .964 to the nearest tens
since there is .064, the number will be greater than .964
so the rounded number will be 1.000
we did this with only .964m but when we add 28.964 then the answer will be
28.000 = 1.000 - 29.000
Hope U will be clear
Pls Mark BrainliestThe gardening store sells clay flower pots, which hold 8 litres of dirt, and ceramic flower pots, which hold 9 litres. Billy bought 8 flower pots, which will hold a total of 67 litres of dirt. How many of each type of flower pot did he buy?
According to the given statement;
Billy bought 8 flower pots, which will hold a total of 67 litres of dirt. The flower pot Billy bought his flower pot is x=5.
What is one variable equation?The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
What is a linear equation in math?A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.According to given value ;
Let x = number of clay pots. Since Billy bought 8 pots in total , the number of ceramic pots Billy bought is 8-x
67 =(8 litre )*(x clay pots)+(9 litres)*(8-x);
By solving one variable equation;67=8x+72-9x
67=(-x)+72
-x =(-72+67)
( -x) = -5
x =5
Hence 8 litre of dirt clay pots is 5 then 9 litres of ceramic flower pot is is 3.
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What is the equation of the line that passes through the point (-3, 1) and has a slope
of -1/3?
Answer:
y=-1/3x+1
Step-by-step explanation:
Slope-Intercept Form: y=mx+b
m is the slope
b is the y-intercept
In the given statement it tells us the point is (-3,1).
-3 is the x-intercept while 1 is the y-intercept
In the given statement it tells us the slope is -1/3
Plug in the m for -1/3 and the b for 1
y=-1/3x+1
Hope this helps.
7) In the given figure, PQR is an equilateral triangle with coordinates of Q and
R as (-2, 0) and (2, 0) respectively. Find the coordinates of the vertex P.
The coordinates of the vertex P is calculated as (0,2√3).
What is defined as the distance formula?The distances among two points as a characteristic of their coordinates are given by an algebraic expression (like coordinate system).
The Pythagorean theorem is used to derive distance formulae for points in rectangular coordinates in 2- and three-dimensional Euclidean space.Because it has a starting and ending point, a line segment can be graphed in both two-dimensional and three-dimensional coordinate planes.Because of the two-dimensional coordinate plane, the starting and stopping points can also be marked as two-dimensional coordinates (x₁, y₁) and (x₂, y₂), culminating in the distance formula as: d = √(x₂ - x₁)² + (y₂ - y₁)².Now, according to the given question;
The coordinates of the points Q and R is given as;
Q and R as (-2, 0) and (2, 0).
Now, as the all three points P,Q and R forms the equilateral triangle. Then, the distance of each side or the distance between two consecutive points are equal.
Calculate the distances between the points;
Distance between Q and R;QR = √(2 + 2)² + (0 - 0)²
QR = 4
Distance between Q and P;Let the coordinated of P be (x, y);
Then,
QP = √(x + 2)² + (y + 0)²
QP = QR = 4
4 = √(x + 2)² + (y)² ........(equation 1)
Distance between R and P;RP = √(x - 2)² + (y + 0)²
RP = QR = 4
4 = √(x - 2)² + (y)² ........(equation 2)
Equating equation 1 and 2.
√(x + 2)² + (y)² = √(x - 2)² + (y)²
Squaring both side;
(x + 2)² + (y)² = (x - 2)² + (y)²
x² + 4 - 4x + y² = x² + 4 - 4x + y²
Simplifying the equation;
x = 0.
Put the value of x in equation 1;
4 = √(x + 2)² + (y)²
y = 2√3.
Therefore, the coordinates of the point P are found to be (0, 2√3).
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solve the equation for x if 2 to the power x = 8
Answer:
x=3Step-by-step explanation:
solve the equation for x if 2 to the power x = 8
2^x = 8
log(2x)=log(8)
x*log(2)=log(8)
x=((log(8))/((log(2))
x=3
----------------------------
check
2^3 = 8
2 * 2 * 2 = 8
8 = 8
the answer is good
If h(x)= -5/6x + 7/8 find the following values. Simplify your answer.
H(3)=
H(4)=
H(-1/2)=
If [tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex] then the value of h(3) = -13/8 , h(4) = -59/24 , h(-1/2) = 31/24 .
In the question , the equation is given as
[tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex] ....(i)
Part(a)
To find the value of h(3)
we substitute the value of x=3 .
On substituting the value of x=3 in equation (i),
we get ,
h(3) = (-5/6)3+7/8
= -15/6+7/8
taking LCM of 6 and 8 as 24, we get
= -60/24 + 21/24
= (-60+21)/24
= -39/24
Writing in the simplest form we get
= -13/8
so, the value of h(3)= -13/8 .
Part(b)
for h(4) ,we substitute the value of x=4 .
On substituting the value of x=4 in equation (i) ,
we get ,
h(4) = (-5/6)4+7/8
= -20/6+7/8
taking LCM of 6 and 8 as 24, we get
= -80/24 + 21/24
= (-80+21)/24
= -59/24
so , the value of h(4)= -59/24 .
Part(c)
for h(-1/2) ,we substitute the value of x as -1/2 .
On substituting the value of x = -1/2 in equation (i) ,
we get ,
[tex]h(\frac{-1}{2} )=\frac{-5}{6} *\frac{-1}{2} +\frac{7}{8}[/tex]
= 5/12 +7/8
taking LCM of 12 and 8 as 24, we get
= 10/24 + 21/24
= (10+21)/24
= 31/24
so , the value of h(-1/2)= 31/24 .
Therefore , if h(x) = (-5/6)x+7/8 the the value of h(3)= -13/8 , h(4)= -59/24 and h(-1/2)= 31/24 .
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A sequence is ____ while a series is ______. A series is definite if_________, it is infinite if ________.
Answer: A sequence is a enumerated collection of objects in which repetitions are allowed/order matters while a series is a infinite series. A series is definite if its based on the concept of sequences.
A series could be finite or infinite because its mainly often represented in compact form which is also known as a sigma notation(∑)to indicate the summation involved. infinite series is the sum of an infinite sequence.
Step-by-step explanation:
pls help u with these to
Answer:
5 acute
6 acute
3 obtuse
4 obtuse
Step-by-step explanation:
Hope this helps
D - 8 over -2 = 12 solve for D
Answer: D = -6
Step-by-step explanation:
[tex]\frac{D-8}{-2} =12[/tex]
1) Divide both sides by -2
[tex]D - 8=-6[/tex]
2) Add 8 to both sides
[tex]D=-6[/tex]
In any circle the ratio of circumference to diameter is constant and is approximately equal to 22:7. what is the circumference of a circle if its diameter is 60 in?
Answer:
188.57 in
Step-by-step explanation:
Circumference = 2πr = 2πd/2 = πd
[tex] = \frac{22}{7} \times 60 \: in[/tex]
= 188.57 in ( approx.)
ALMN is an isosceles triangle with LM = LN, LM LN, LM = 3x - 2, LN = 2x+1, and MN = 5x - 2. Find the length of MN.
Answer:
x = 3
Step-by-step explanation:
TR= 3x + 5, and RA = x + 17. Find the value of x.
Greetings from Brasil...
The small green lines on the line segments indicate that TR = RA, as well as the small red lines indicate that MR = RH, then
TR = RA
3X + 5 = X + 17
X = 6
What is the quotient of 204 decided by 34
Answer:
204 ÷ 34 = 6
Step-by-step explanation:
204 ÷ 34 = 6
Check:
34
x 6
------
204
hope this helps :)
Answer : 6
Explanation :
34 + 34
68
68 + 34
102
102 + 34
136
136 + 34
170
170 + 34
204
OR just simply use Multiplication
34 x 6
Which statement is true when comparing how a student would complete the solution for the linear equation -2x + 3 = 6 to how the student would complete the solution for the linear inequality -2x + 3 < 6?
Completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case.
Completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case.
Completing the solution for the equation is the same as completing the solution for the inequality. The student would multiply both sides by -2 in either case.
Completing the solution for the equation is the same as completing the solution for the inequality. The student would multiply both sides by -2 in either case.
Completing the solution for the equation is not the same as completing the solution for the inequality. The student would divide by -2 to complete the solution for the equation and would divide by -2 and change the less than sign for the inequality to greater than.
Completing the solution for the equation is not the same as completing the solution for the inequality. The student would divide by -2 to complete the solution for the equation and would divide by -2 and change the less than sign for the inequality to greater than.
Completing the solution for the equation is not the same as completing the solution for the inequality. The student would multiply by -2 to complete the solution for the equation and would multiply by -2 and change the less than sign for the inequality to greater than.
The statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A
How to determine the statementFrom the information given, we have that;
The linear equation is ;
-2x + 3 = 6
Let's solve for x
First, collect like terms
-2x = 6 - 3
-2x = 3
Divide both sides by - 2
x = 3/ -2
The linear inequality is;
-2x + 3 < 6
collect like terms
-2x < 6 - 3
Make 'x' the subject by dividing both sides by -2
-2x/ -2 = 3/ -2
x = 3/ -2
We can see that the linear equation and the linear inequality have the same solution and steps.
Thus, the statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A
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(-4,5) is translated by the vector (-1/10). What coordinate would it be at?
The coordinates of the image of the point (- 4, 5) is (- 5, 15).
What is the image of a coordinate by using a translation?
In this question we find the coordinates of the original point and the translation vector. Please notice that translations are examples of rigid transformations, meaning that Euclidean distance is conserved in the resulting image. A translation can be done by the following formula:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointT(x, y) - Translation vectorP'(x, y) - Resulting pointIf we know that P(x, y) = (- 4, 5) and T(x, y) = (- 1, 10), then the resulting point is:
P'(x, y) = (- 4, 5) + (- 1, 10)
P'(x, y) = (- 5, 15)
RemarkThere is a typing mistake in the statement. Correct form is shown below:
(- 4, 5) is translated by the vector (- 1, 10). What coordinate would it be at?
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Marsha pays $30 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 8 months of having the membership?
|−30| − 8 = $22
−8|30| = −$240
8|−30| = $240
|−30| − |8| = $22
Marsha pay $30 each month for a car wash membership.
In one month Marsha pay $30
In eight month Marsha pay 8*$30 = $240
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Answer:
A. |-30| - 8 = $22
Step-by-step explanation:
You are told to subtract 30 and 8, and the 30 is represented as |-30| - 8 = $22
(if this is incorrect am sorry ;-;)
Please help quickly!!!!
-3/5 - (-2/5) =
Write the answer as a fraction
Answer:
-1/5
Step-by-step explanation:
Minus a negative is plus.
-3/5 - (-2/5) =
= -3/5 + 2/5
= -1/5
Explain the properties used to solve inequalities and how they are different from properties of equality
The major difference between inequality and equality is that equality represents a particular value(s) while inequality represents a range of values that are in a specific direction.
What are the properties that are used to solve inequalities?This must be noted when solving questions on equality and inequality.
For example:
x = a means that the value of x is a. It represents a particular value which is a
x < a represents all the values that are less than a.
x ≤ a represents values from a and below.
x > a represents all the values that are greater than a
x ≥ a means that the values of x are greater than or equal to a.
From the examples given above, it is obvious that a change in the direction of the inequality sign changes the values of the data represented by the inequality.
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Need the answer asap
Pls answer it correctly
Answer:
I will be your human calculator! top to bottom!
1. (+1) 5. (+28) 9. (+8)
2. (+4) 6. (+3) 10. (-5)
3. (+14) 7. (+24) 11. (+6)
4. (-3) 8. (-3) 12. (+1)! Good Luck!
25 points plus brainliest
Answer:
I believe it's B
4x - 5y = 16
Step-by-step explanation:
First you divide the whole term by -1 to get rid of negative in front of equation and then you add the c term (-16) to both sides to get the final answer.
I hope you get this right.