Answer:
(a)The solution set is: [tex]x \in [6, \infty) \forall x \in R[/tex]
(c) [tex]6 \leq x[/tex]
Step-by-step explanation:
Given the inequality: [tex]12+\dfrac{11}{6}x\leq 5+3x[/tex]
We solve by collecting like terms
[tex]12+\dfrac{11}{6}x\leq 5+3x\\12-5\leq 3x-\dfrac{11}{6}x\\7\leq \dfrac{18x-11x}{6}\\42 \leq 7x\\$Divide both sides by 7\\6 \leq x\\$We can re-write this as:\\x\geq 6[/tex]
The solution set is therefore: [tex]x \in [6, \infty) \forall x \in R[/tex]
Help please .....................
Answer:
70
Step-by-step explanation:
well you know that angles in the same segment are equal so angle VWZ also= 38
triangle VWZ is a triangle so the sum of interior angles sums to 180
180-72-38=70
A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for π, and round your answer to the nearest hundredth. 38.47 units2 94.99 units2 153.86 units2 379.94 units2
Step-by-step explanation:
here first you have to find the perimeter of square
given that perimeter of circle is equal to perimeter of square,,,,, therefore with the perimeter of square you have to find the radius of the circle.....
now you have the radius of the circle so by applying the formula of area of circle the answer will be finded
Please follow
Answer:
38.47 units²
Step-by-step explanation:
I got it right on the test...
Simplify (10–2) 4. A) 10^-8 B)10^-6 C)-10^-6 D)-10^8
Answer:
A
Step-by-step explanation:
[tex](10^{-2})^{4}[/tex]
Apply the law of exponents.
[tex]10^{-2 \times 4}[/tex]
[tex]=10^{-8}[/tex]
Answer:
[tex] = {10}^{ - 8} \\ [/tex]
Answer A is correct.
Step-by-step explanation:
[tex] {( {10}^{ - 2}) }^{4} \\ {10}^{ - 2 \times 4} \\ = {10}^{ - 8} [/tex]
Triangle JKL is similar to triangle TUV. Find the missing side length of triangle TUV.
A. 10.6
B. 6
C. 6.2
D. 5.8
Answer:
B) 6 inches
Step-by-step explanation:
==>Given that ∆JKL ~ ∆TUV, it therefore means the ratio of proportion of the corresponding sides of ∆JKL and ∆TUV are equal.
Thus:
JK/TU = JL/TV = KL/UV
10/7.5 = 8/x = 13/9.75
Let's find x
10/7.5 = 8/x
=>Cross multiply
10*x = 8*7.5
10x = 60
Divide both sides by 10
x = 6 inches
Our answer is B) 6 inches
I’m confused. Thanks
Step-by-step explanation:
Angle XBC = 55 degrees because it is a corresponding angle with Angle AXC
and corresponding angles are equal or congruent.
Ok so angle XBC = 55 degrees and since this an isosceles triangle
XBC = XCB which means XCB = 55 degrees
Now to find angle BXC we know that all angles of a triangle add up to 180 degrees.
Angle XBC + Angle XCB + Angle BXC = 180 degrees
Let x represent angle BXC
55 + 55 + x = 180
110 + x = 180
x = 180 - 110
x = 70
∴ Angle BXC = 70 degrees
I'd greatly appreciate the help-
Answer:
The 3rd option
Step-by-step explanation:
To prove that 2 triangles are similar, we need to prove that 2 pairs of their angle measurements are congruent.
This is because all triangles have 180 degrees, so if 2 pairs are congruent, the remaining angles will also be congruent
We know that m<D=m<E
We also know that m<DCA=m<ECB because they are vertical angles.
Vertical angles are always congruent.
Therefore, the triangles are similar.
The correct similarity statement would be 1, since <D corresponds with <E.
Now let's look at the 3rd Statement. To prove that two lines are similar, we would have to prove that their alternate interior angles are congruent.
A pair of alternate interior angles would be <D and B or or <E and <A
There is no way to prove this, since we do not know any of the angle or that measurements or if the triangles are isosceles triangles.
Hence, the correct choice would be 1 only.
Simplify -{2x-[3-(4-3x)]+6x}.
Step-by-step explanation:
_2x _3x+3+64-4=
_5x+63
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) What is Miguel’s expected value from playing the game?
Answer:
The answer is "[tex]\bold{-\frac{1}{2}}[/tex]"
Step-by-step explanation:
Miguel's choose the best way to win the 2 dollars by pulling the two chips with the number 1. In total, there are four balls, so his probability of winning is:
[tex]\to \frac{2}{4} \times \frac{1}{3}= \frac{1}{6}[/tex]
The chances of losing a dollar add up to that amount, so 5/6.
Price predicted = [tex]\frac{1}{6} \times (2) + \frac{5}{6} \times (-1)[/tex]
[tex]=\frac{1}{6} \times 2 + \frac{5}{6} \times -1\\\\=\frac{1}{3} - \frac{5}{6} \\\\=\frac{2-5}{6}\\\\=\frac{-3}{6}\\\\=- \frac{1}{2}\\[/tex]
The final answer is "[tex]-\frac{1}{2}[/tex]"
The area of a room is roughly 9∗10^4 square inches. If a person needs a minimum of 2.4∗10^3 square inches of space, what is the maximum number of people who could fit in this room
Answer:
37
The maximum number of people who could fit in this room is 37
Step-by-step explanation:
Given;
The area of a room A = 9 × 10^4 square inches
Minimum Area needed per person M = 2.4×10^4 square inches
The maximum number of people who could fit in this room is;
N = The area of a room A/Minimum Area needed per person M
N = A/M
Substituting the values;
N = 9×10^4 ÷ 2.4×10^3
N = 37.5
Since we can not have a 0.5 person, the number would be approximated down to nearest lower whole number.
N = 37
The maximum number of people who could fit in this room is 37
I’m stuck on this!?!!
Answer:
[tex]x=66^\circ[/tex]
Step-by-step explanation:
[tex]x=\frac{180^\circ - 48^\circ}{2}\\\\=\frac{132^\circ}{2}\\\\=66^\circ[/tex]
Best Regards!
A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for π, and round your answer to the nearest hundredth. 38.47 units2 94.99 units2 153.86 units2 379.94 units2
Answer:
Answer choice A) About 38.47 square units
Step-by-step explanation:
Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths. The perimeter of the square and therefore the circumference of the circle is 5.5*4=22. The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is therefore:
[tex]\dfrac{22}{2\pi}\approx 3.503[/tex]
Since the area of a circle is [tex]\pi r^2[/tex], the area of this circle is:
[tex]\pi \cdot 3.503^2= 3.14\cdot 12.271\approx 38.47[/tex]
Hope this helps!
The area of a circle with a circumference that equals the perimeter of the square is about 38.47 square units
Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths.
The perimeter of the square and therefore the circumference of the circle is [tex]5.5*4=22.[/tex]
The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is, therefore
[tex]22/2\pi=3.503[/tex]
What is the area of the circle?The area of a circle is [tex]\pi r^2[/tex],
the area of this circle is:
=[tex]\pi \times 3.305^2[/tex]
[tex]=3.14(12.27)[/tex]
=38.47 unit^2
Thus, The area of a circle with a circumference that equals the perimeter of the square is about 38.47 square units.
To learn more about the circle visit:
https://brainly.com/question/24375372
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What is the area of the triangle given below? 2 and 6
Answer:
6 sq. units
Step-by-step explanation:
The area of a triangle is base times height divided by 2.
[tex]\frac{bh}{2}[/tex]
[tex]\frac{6 \times 2}{2}[/tex]
[tex]\frac{12}{2} =6[/tex]
Answer:
D. 6
Step-by-step explanation:
The formula for the area of a triangle is A=1/2bh. In this case, the base is 6 and the height is 2. The work is below:
A=1/2bh
A=1/2(6)(2)
A=1/2(12)
A=6
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Suppose a triangle has two sides of length 3 and 4 and that the angle
between these two sides is 60°. What is the length of the third side of the
triangle?
A. 5
B. 113
C. 413
D. 3
SUBMIT
What is an equation in point-slope form of the line that passes through the point (8, 5) and has slope −7?
Answer:
y - 5 = -7(x - 8)
Step-by-step explanation:
We can immediately adapt y - k = m(x - h) as follows: replace m with -7, h with 8 and k with 5, obtaining:
y - 5 = -7(x - 8)
This is the desired equation in point-slope form.
a store is having a sale on almonds and jelly beans. for 2 pounds of almonds and 3 jelly beans , the total cost is $14. for 4 pounds of almonds and 8 pounds of jelly beans, the total cost is $33. find the cost of each pound of almonds and each pound of jelly beans
Answer:
almonds cost $3.25 per pound and jelly beans $2.50
Step-by-step explanation:
system of linear equations
2a+3j=14
4a+8j=33
solution is (3.25, 2.5)
Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches. A square labeled 16 x squared minus 40 x + 25 What is the side length, in inches, of the pet shop sign?
Answer:
length of side of square = (4x - 5) inches
Step-by-step explanation:
We are given;
Area of square = 16x² – 40x + 25
Let's find the roots of this quadratic equation [-b ± √(b² - 4ac)]/2a
Thus;
x = [-(-40) ± √((-40)² - 4(16 × 25)]/(2×16)
x = [40 ± √(1600 - 1600)]/32
x = (40 ± 0)/32
x = 40/32
x = 5/4
Thus, the factors of the polynomial are;
(4x - 5)²
So,
Area = 16x² – 40x + 25 = (4x - 5)²
Since, the right hand side is (4x - 5)² and area of square is (length of side)², thus we can say that length of side of square is (4x - 5) inches
Is the following graph a linear function, a nonlinear function, and/or a relation
Answer: Option C.
Step-by-step explanation:
Ok, first, a linear function is something of the shape of:
y = a*x + b.
And the graph of those functions is a line, as the name implies, so we can discard that option.
So this must be a non-linear function, you can see that is a function because each value of x has only one value of y related to it.
Second, in a Venn diagram you will see that the set of functions is contained into the set of relationships, this means that all the functions are relationships, but not all the relationships are functions, and we know that this is a non-linear function, so this also must be a relationship.
Then the correct option is C, nonlinear, and a relationship.
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.
(A) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
Answer:
The answer is "64".
Step-by-step explanation:
Given:
8-sided fair die
output of Die = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }
if the Dice is thrown two times. so, the possible outputs are as follows:
[tex]\to 8 \times 8=64[/tex]
[tex]\texttt{ = (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),}\\ \ \ \texttt{(1,7),( 1, 8),(2,1),(2,2),(2,3),(2,4),}[/tex]
[tex]\texttt{(2,5),(2,6),(2,7),(2,8),(3,1), (3,2),}\\ \texttt{(3,3),(3,4),(3,5),(3,6),(3,7),(3,8) ,}\\\texttt{(4,1),(4,2),(4,3), (4,4),(4,5),(4,6),} \\[/tex]
[tex]\texttt{(4,6),(4,7),(4,8),(5,1),(5,2),(5,3),}\\\texttt{(5,4),(5,5),(5,6),(5,7),(5,8),(6,1),}\\\texttt{(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),}[/tex]
[tex]\texttt{(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),} \\\texttt{(7,6),(7,7),(7,8),(8,1),(8,2),(8,3),}\\ \texttt{(8,4),(8,5),(8,6),(8,7),(8,8)}[/tex]
That's why the product is 64.
Because you are working a late shift, you will get an increase in your wage. You will get and additional 10% per hour from 6:00pm to 12:00 am and additional 15% from 12:00 am to 1:00 am
CHECK THE COMPLETE QUESTION BELOW:
Supervisor: "Because you are working a late shift, you will get an increase in your wage. You will get an additional 10% per hour from 6:00 PM to 12:00 AM and additional 15% from 12:00 AM to 1:00 AM." Employee: "I am working from 2:00 PM to 12:00 AM. Between 2:00 PM and 6:00 PM, I will make $12.00 per hour. Between 6:00 PM and 12:00 AM, I will make __________ per hour
Answer:
I will make $13.2 per hour
Explanation:
It can be deducted from the question that that the money Employee gets money for Working from 2.00 PM to 6.00 PM = $12per hour
Also the Employee gets additional 10% of money for working from 6.00 PM to 12.00 AM which implies that
10% = (10/100)*$12per hour
=$1.2per hour
Again, Employee gets additional 15% of the money for working from 12.00 AM to 01.00 AM which can be calculated as:
15% = (15/100)*$12per hour
=$1.8 per hour
which means that Employee gets additional $1.8 per hour
of the money for working from 12.00 AM to 01.00 AM
Therefore, if Employee works from 2.00 PM to 12.00 AM,
Employee will gets money for Working from 2.00 PM to 6.00 PM as well as the 10\% extra wage which
= $12 + $1.2 = $13.2
= \$ 12 + \$ 1.2 = \$ 13.2
2x + 5y = 12
-2x + 3y = 4
In elimination method
The cost of each white tile was £2 the cost of each blue tile was 4 pounds work out the ratio of the total cost of the white tiles to the total of the blue tiles
Answer:
2x/4y = x/2y = x : 2y
Step-by-step explanation:
The question only gave us the cost of each white tiles and blue tiles respectively . The cost of each white tiles is £2 while the cost of each blue tiles is £4. The total cost of the blue tiles and the white tiles can only be calculated if we know the number of blue and white tiles available.
Let us assume
the number of white tiles = x
the number of blue tiles = y
total cost of white tiles = 2 × x = 2x
total cost of blue tiles = 4 × y = 4y
Therefore, the ratio of the total cost of white tiles to the total cost of the blue tiles can be expressed as follows
2x/4y = x/2y = x : 2y
If the number of white and blue tiles is known it can be replaced in the ratio to find the ratio of the total cost of the white tiles to the total cost of the blue cost.
77 POINTS PLEASE ANSWER: A b and c share 90 pound the amount a and b get is in the ratio 1:2 the amount b and c get is in the ratio 4:3 how much does A get
Answer:
Brainliest!!!
Step-by-step explanation:
A:B
1:2
B:C
4:3
B is both 4 and 2
In B:C, B is double (in ratio) than when B is in A:B
2:4:2
A:B:C
this would mean there is a total of 8
A would get 1/4 of the 90 pounds
help asap!!!!!! please
Answer:
Point B is 3/4
Step-by-step explanation:
the number line is split into fourths. Therefore, it is 3/4
25 points !!! 3 1/3 x 52
Answer:
Irrational
Step-by-step explanation:
3 1/3 × √52
= 10/3 × √52
= 20/3√13
= 24.037009
Irrational, the product cannot be written in the form p/q as a fraction.
Answer:
irrational
Step-by-step explanation:
3 1/3 * sqrt(52)
Changing to an improper fraction
10/3 * sqrt(52)
10 /3 * sqrt( 4*13)
10/3 * sqrt(4) sqrt(13)
10/3 * 2 sqrt(13)
20/3 sqrt(13)
Since sqrt(13) is irrational the product is irrational
In this picture B,D, and F are midpoints. AC=50, CE=60, and BD=35
DF=[?]
please help !!
Answer:
DF = 25
Step-by-step explanation:
We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
So,
DF = [tex]\frac{1}{2} AC[/tex]
Where AC = 50
DF = 50/2
DF = 25
A company laid off one-sixth of its workforce because of falling sales. If the number of employees after the layoff is 690, how many employees were laid off?
Answer:
138
Step-by-step explanation:
Let the number of employees before the layoff be x.
1/6 of the company's workers were laid off and the remaining workers are 690. This means that:
1/6 * x = x - 690
=> x/6 = x - 690
=> 690 = x - x/6
690 = 5x/6
=> x = (690 * 6) / 5
x = 828
There were 828 workers before the layoff. Therefore, the number of employees that were laid off is:
828 - 690 = 138 employees
The company's laying off its workforce is an illustration of proportions.
A total of 138 employees were laid off
The proportion (p) laid off is given as:
[tex]p = \frac 16[/tex]
The proportion (q) remaining in the workforce would be
[tex]q = 1 - p[/tex]
This gives
[tex]q = 1 - \frac 16[/tex]
[tex]q =\frac 56[/tex]
The workforce after 1/6 were laid off is given as 690.
So, we have:
[tex]q \times n = 690[/tex]
Where n represents the original workforce
This gives
[tex]\frac 56 \times n = 690[/tex]
Multiply both sides by 6/5
[tex]n = 828[/tex]
The number of employees that were laid off is:
[tex]Employee = 828 - 690[/tex]
[tex]Employee = 138[/tex]
Hence, 138 employees were laid off
Read more about proportions at:
https://brainly.com/question/16981404
Work out the range of these numbers : -8, 6, -5, 2.5 thanks!
Answer:
14
Step-by-step explanation:
The range of a given set of values is the lowest value deducted from the highest value.
Lowest value is -8 and highest value is 6.
Therefore,
[tex]Range = Highest value - Lowest value \\ = 6 - ( - 8) \\ = 6 + 8 \\ = 14[/tex]
Hope it helps!
can someone help asap
Answer:
1/3
Step-by-step explanation:
7/12 - 3/12= 4/12= 1/3
someone please help :rewrite 2.267 repeating 67 as a simplifed answer
Answer:
2⁵³/₁₉₈
Step-by-step explanation:
2.2676767 = 2.7676767 − 0.5
2.2676767 = 2⁷⁶/₉₉ − ½
2.2676767 = 2¹⁵²/₁₉₈ − ⁹⁹/₁₉₈
2.2676767 = 2⁵³/₁₉₈
Answer:
449/198 or 2 53/198
Step-by-step explanation:
2. 267676767 = x
10x= 22. 67676767
1000x= 2267. 676767
1000x-10x= 2267.676767- 22.676767
990x= 2245x= 2245/990x= 449*5/5*198x= 449/198 x= 2 53/198A sandwich shop is ordering apples and grapes to make chicken salad. Apples cost $2.19 per pound and grapes cost $2.60 per pound. If they ordered a total of 20 pounds of apples and grapes and paid $35.80, how many pounds of grapes did they order?
We got $19.51 but we think it is wrong.
Answer:
Less than 13 pounds of grapes,
as 14 pounds of grape exceeds $35.80,
If you order as low as zero pounds of grapes, then the price of apple pounds would be $35.80/20 =$1.79 per pound
Step-by-step explanation:
Let
Quantity of Apple and grapes=20
Cost of apple=$2.19
Cost of grape=$2.60
Total cost of apple and grape=$35.80
a+g=20
a=20-g
PaQa+PgQg=35.80
2.19(20-g)+2.60g=35.80
43.8-2.19g+2.60g=35.80
0.41g=35.80-43.8
0.41g=-8
g=-8/0.41
g= -19.51
PaQa+PgQg=35.80
2.19a+2.60(-19.51)=35.80
2.19a-50.726=35.80
2.19a=35.80+50.726
2.19a=86.526
a=86.526/2.19
=39.51
PaA+PgG=35.80
Pa(20-G)+2.60G=35.80
35.80/2.60 = 13.77 pounds of grapes, but no money will be left to buy apples, unless Pa=0
G<13.77