Answer:
x = 77
Step-by-step explanation:
x and 103° are same- side interior angles and sum to 180° , then
x + 103 = 180 ( subtract 103 from both sides )
x = 77
I have to solve the equation:
[tex] |4 \sqrt{2} - 6 | + |2 \sqrt{10} - 6| [/tex]
The first thing I tried is simply removing the modules, it seemed like the most logical solution and this is the answer I got, but it wasn't any of the options:
[tex]4 \sqrt{2} + 2 \sqrt{10} + 12[/tex]
The second thing I tried is putting both equations in one module and sum the first one with the second one in parentheses like this:
[tex] |4 \sqrt{2} - 6 + (2 \sqrt{10} - 6 | = \\ = |4 \sqrt{2} - 6 + 2 \sqrt{10} + 6 | = \\ = 4 \sqrt{2} + 2 \sqrt{10}[/tex]
But this wasn't in the answers either.
After I checked, the correct answer was:
[tex]2 \sqrt{10} - 4 \sqrt{2} [/tex]
So I was wondering where does the minus come from?
It is in a module and between the modules, there's a plus and even if that plus somehow turns into a minus when it goes inside the modules, which I'm not aware of, it would still turn into a plus because it is in a module ;-; Or I'm just st*pid, I don't know.
Think back to the definition of absolute value:
• If x ≥ 0, then |x| = x.
• If x < 0, then |x| = -x.
In other words, the absolute value always returns a positive number. So if x is positive, leave it alone; but if it's negative, then you have to negate it to get a positive number back.
This means that you cannot simply reduce |x - y | to x - y because you need to consider the possibility that x - y may be negative, in which case |x - y | would reduce to -(x - y) = y - x.
In this case,
|4√2 - 6| = -(4√2 - 6) = 6 - 4√2
because 4√2 < 6, which you can determine by comparing both of these numbers as square roots:
4√2 = √16 √2 = √32
6 = √36
and √32 < √36 because 32 < 36.
Similarly,
|2√10 - 6| = 2√10 - 6
because
2√10 = √4 √10 = √40
6 = √36
So ultimately,
|4√2 - 6| + |2√10 - 6| = (6 - 4√2) + (2√10 - 6) = 2√10 - 4√2
Help with this ASAP please
Answer:
86
Step-by-step explanation:
43×2=86
bisector means halves an angle into two equal angles
4. Find the solution for the following problem. Explain your reasoning."
What is the solution to the equation below?
2(x - 3) = 2x + 5
Answer:
no solution
Step-by-step explanation:
Given
2(x - 3) = 2x + 5 ← distribute parenthesis on left side
2x - 6 = 2x + 5 ( add 6 to both sides )
2x = 2x + 11 ( subtract 2x from both sides )
0 = 11 ← not possible
This indicates the equation has no solution
Explain how to use the standard normal table to
find the probability associated with the shaded
area under the curve.
A
^
-3
-2.
0
1
2
3
0.4
1.9
The probability associated with the shaded area under the curve is 0.6267
How to determine the probabilities?From the curve, we have the following parameters:
z1 = 0.4
z2 = 1.9
Using the standard normal table, determine the p values at the respective z-scores
P(z >0.4) = 0.3446
P(z<1.9) = 0.9713
The probability is then calculated using:
P = P(z<1.9) - P(z >0.4)
Substitute the known values
P = 0.6267
Hence, the probability associated with the shaded area under the curve is 0.6267
Read more about probability at:
https://brainly.com/question/15076391
Answer:
The standard normal table gives areas under the curve to the left of z-scores.
Find the probability in the standard normal table that a value is to the left of 1.9.
Find the probability in the standard normal table that a value is to the left of 0.4.
Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.
find the measure of an interior angle of a regular decagon (10 sided polygon)
Answer:
1440°
Step-by-step explanation:
The sum of angles in a polygon is (n - 2)180 where n = number of sides.
A decagon has 10 sides, so n = 10
(10 - 2)180
8(180) = 1440°
Answer:
the answer is 144
Step-by-step explanation:
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Answer:
C = 20
Step-by-step explanation:
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Step 1
We solve for C first
6A + 4B + 5C = 390....Equation 1
6A + 4B + 5.75C = 405... Equation 2
We substract Equation 1 from Equation 2
0.75C = 15
C = 15/0.75
C = 20
The measure of 1 in the diagram below is 113º.
What is the measure of <4?
Answer: 67°
Step-by-step explanation:
From the diagram given, we can see that 1 and 4 are angles on a straight line. It should be noted that sum of angles on a straight line equals to 180°.
Therefore,
Angle 1 + Angle 4 = 180°
113° + Angle 4 = 180°
Angle 4 = 180° - 113°
Angle 4 = 67°
Therefore, the measure of <4 is 67°
Distribute 5x\left(1+3x\right).5x(1+3x)
Answer:
5x + 15x²
Step-by-step explanation:
Given the expression 5x(1+3x)
Generally, according to the distribution rule,
A(B+C) = AB + AC
A is distributed over B and C
Similarly,
5x(1+3x)
= 5x(1) + 5x(3x)
= 5x + 15x²
Hence the expression required is 5x + 15x²
In January, a bookstore sells 450 books, but in February, it sells only 300 books. What is the percent of change from January to February?
66.7%
-50%
-33.3%
50%
Answer:
-33.33%
Step-by-step explanation:
((450-300)÷450)×100
(150÷450)×100
-33.33%
the expression -7y is called what
Answer:
called "pi".
Step-by-step explanation:
quiere cercar con alambre un terreno rectangular que mide 180 m (metros) de largo por 85 m de ancho.¿cuantos metros de alambre necesita? ¿Con qué concepto matemático relacionas esta situación?
You want to wire a rectangular piece of land that is 180 m (meters) long by 85 m wide. How many meters of wire do you need? With what mathematical concept do you relate this situation?
Answer:
The wire required to fence is 530 m.
Step-by-step explanation:
Length, L = 180 m
Width, W = 85 m
The perimeter of the wire is
P = 2 (L + W)
P = 2 (180 + 85)
P = 530 m
So, the wire required to fence is 530 m.
Find the value of k if the slope of the line 2x-ky+3=0 is 5/3
Answer:
6/5
Step-by-step explanation:
2x+3=ky
ky=2x+3
y=(2x+3)/k
y=2x/k + 3/k - > equation 1
y=mx + c - >equation 2
Comparing equation 1 and 2,
2/k=m
2/k=5/3
6/5=k
k=6/5
Rewrite the following quadratic function in vertex form. Then, determine if it has a maximum or minimum and say what that value is.
y = -x 2 + 6x + 5
HELP PLEASE!!!!!!
Answer:
-(x-3)²+14
maximum
(3,14)
Step-by-step explanation:
y= -x²+6x+5
y-5= -x²+6x
y-5= -(x²-6x)
complete the square
y-14= -(x²-6x+9)
x²-6x-9= -(x-3)²
y-14= -(x-3)²
y= -(x-3)²+14
maximum because a is negative
vertex is (3,14)
A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $37,000. The anticipated profit for the end of the fourth year is $68,200. After the first year, the ratio of change in time to change in profit is constant. Let x be years and P be profit in dollars. a. Write a linear function P(x) that expresses profit as a function of time. P(x)=
Answer:
P(x) = 35,900 + 2,800(x-1)
Step-by-step explanation:
P(x)
P(1) = $35,900
P(4) = $44,300
Difference in profits
P(4) - P(1)
= P(3)
= $44,300 - $35,900
= $8,400
Rate of change per year = $8,400 / 3
= $2,800 per year
The linear equation
P(x) = 35,900 + 2,800(x-1)
Where
x = number of years
Mathematicians 4: Who is Who?
Unit: Factoring Quadratics
Factor the following quadratic equations to determine each person's name: Show your work
Answer:
a. x = -9 or x = -2
b. -5(x - 4)
c. x = -3 or x = 5
d. x = ±7
Step-by-step explanation:
a. First person;
y = x² + 11x + 18
y = x² + 9x + 2x + 18
y = x(x + 9) + 2(x + 9)
y = (x + 9)(x + 2)
y = x = -9 or x = -2
b. Second person;
y = -5x + 20
The common factor is 5.
y = -5(x - 4)
c. Third person;
y = x² - 2x - 15
y = x² - 5x + 3x - 15
y = x(x - 5) + 3(x - 5)
y = (x + 3)(x - 5)
y = x = -3 or x = 5
d. Fourth person;
y = x² - 49
Applying the difference of squares formula;
(a² - b²) = (a - b)(a + b)
y = x² - 49 = x² - 7² = (x - 7)(x + 7)
y = (x - 7)(x + 7)
y = x = ±7
Is how far from work do all the employees live a statistical question
Answer:
need more info sry
Step-by-step explanation:
I need help please! ASAP!
Answer:
Step-by-step explanation:
Each month, Kelsey donates 1/5 of her allowance to her school for supplies. 1/2 of that amount goes to the chorus class. How much of her allowance goes to supplies for the chorus class?
Please show your work.
Thank you :)
Solve for x:
2x + 5 = 12
Answer:
x = 7/2
Step-by-step explanation:
2x + 5 = 12
Subtract 5 from each side
2x + 5-5 = 12-5
2x = 7
Divide each side by 2
2x/2 = 7/2
x = 7/2
Answer:
[tex]x = \frac{7}{2} [/tex]
Step-by-step explanation:
Let's solve:
[tex]2x+5=12[/tex]
Step 1: Subtract 5 from both sides.
[tex]2x+5−5=12−5 \\
2x=7[/tex]
Step 2: Divide both sides by 2.
[tex] \frac{2x}{2} = \frac{7}{2} \\
x= \frac{7}{2} [/tex]
Ms.Jane runs a boutique in Jumeirah. She bought 50 m cloth to stitch shirts for her boutique.If one shirt requires 2m 15cm of the cloth then
Answer: 23 shirts
Step-by-step explanation:
Given
Ms. Jane bought 50 m cloth to stitch shirts
If one shirt requires 2m and 15 cm cloth i.e. [tex]2+0.15=2.15\ m[/tex]
No of shirts that can be made using 50 m cloth
[tex]\Rightarrow \dfrac{50}{2.15}=23.25\approx 23\ \text{Shirts}[/tex]
Therefore, Ms. Jane can made 23 shirts from 50 m cloth.
Write 5/8 as a sum of fractions two different ways.
Answer:
2/8 + 3/8
1/8 + 4/8
Step-by-step explanation:
I hope this is what you mean!
If this helps you, please mark brainliest!
The requried, 5/8 can be expressed in two different ways of the sum as 1 / 8 + 4 / 8 and 2/8 + 3/8.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
Here,
As mentioned in the quesiton, to determine 5/8 as a sum of fractions in two different ways.
5 / 8 = a / 8 + b / 8
5 = a + b
So the above-modeled equation, gives the required fraction, by assuming a value that satisfies the equation,
For a = 1, 2, 3, 4 , b = 4, 3, 2, 1
So different combination is given as, 1 / 8 + 4 / 8 and 2/8 + 3/8.
Thus, the requried, 5/8 can be expressed in two different ways of the sum as 1 / 8 + 4 / 8 and 2/8 + 3/8.
Learn more about fractions here:
https://brainly.com/question/10708469
#SPJ2
is x = 3 a function or not a function ?!
Answer:
x = 3 is not a function because, for one thing, its graph does not pass the vertical line test.
Use the image to complete the equation below
How do I do this ( answer please )
Answer:
I think see what circuit is connected to the light
Step-by-step explanation:
Jacob drove 450 miles at an average rate of 65 miles per hour. Rounded to the nearest tenth of an hour, how long did the trip take
Time = distance / speed
Time = 450 miles / 65 miles per hour
Time = 6.9 hours
Paula reside em uma cidade em que a densidade demográfica é igual a 5 500 hab/km2. Nessa cidade, a população está distribuída em um território de 80 km2. Qual é a população da cidade em que Paula reside? 11 078. 440 000. 880 000. 1 760 000.
Answer:
RESPOSTA:B) 440.000
Step-by-step explanation:
UMA BASICA EXPLICAÇÃO: BASTA PEGAR OS 5 500HAB/KM
E MULTIPLICAR ELE PELO TERRITORIO QUE É:80KM
5 500HAB × 80KM = 440.000
In the United States, the average public school teacher currently earns an annual salary near $55,202. Reported national average salaries for the last six decades are listed below.
Year National Average
Teachers’ Salary
1960 $4,995
1970 $8,626
1980 $15,970
1990 $31,367
2000 $41,807
2010 $55,202
Determine the average salary increase per year between the years 1980 and 1990.
$1,539.70
$8,367.80
$2,566.20
$1,004.10
A is right
Step-by-step explanation:
Obviously A is the correct answer you have already gave us hint. Btw thanks for the pts
A building casts a 21 foot shadow along the ground. A person 5 feet 3 inches casts a shadow 7 feet long.
How tall is the building?
Answer:
~28
Step-by-step explanation:
5 feet 3 inches is 5.25 feet.
We divide 7/5.25 which equals 1.3333333333333 (repeating)
That means we multiply 21 by 1.333333333333 which would round up to 28 feet. (the exact answer is 27.99999999999999999)
A group of friends wants to go to the amusement park. They have no more than $230 to spend on parking and admission. Parking is $8, and tickets cost $27.75 per person, including tax. Write and solve an inequality that can be used to determine xx, the number of people who can go to the amusement park.
Answer:
6 people
Step-by-step explanation:
$230 - $8 = $222
x · 35.75 = 222
x · 35.75 ÷ 35.75 = 222 ÷ 35.75
[tex]x=6\frac{30}{143}[/tex]
please please please help
Answer:
a S(-3) = 2(-3)(-3)+5(-3)-12
=18-15-12
=-9
b 2x2+5x-12=0
2x2+8x-3x-12=0
2x(x-4)-3(x+4)=0
(2x-3)(x+4)=0
2x-3=0
x=3/2
x=-4
sorry I couldn't answer the other question