When we simplify (3 + √5)(3 + √2), the result obtained is:
9 + 3√2 + 3√5 + √10
Surd operationa√b × c√d = (a × c)√(b × d)
How to simplify (3 + √5)(3 + √2)(3 + √5)(3 + √2)
Expand by clearing the bracket
3(3 + √2) + √5(3 + √2)
9 + 3√2 + 3√5 + √10
Thus,
(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10
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Gracie earns 17.25/h for a 37.5h week, plus extra for overtime. During store inventory she worked 48.5h. Her gross earnings were $1,471.88. What is Gracie’s overtime rate of pay? show work please
Gracie’s overtime rate of pay would be $635.06.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Gracie earns 17.25/h for a 37.5h week, plus extra for overtime.
For one hour she earns $17.25
For 37.5h she earns = 37.5h x 17.25
= $646.87
The total money she earns = $646.87 + overtime pay
During store inventory, she worked 48.5h. Her gross earnings were $1,471.88.
= 48.5h x 17.25
= $836.625
So, $836.625 + overtime pay = $1,471.88
overtime pay = $1,471.88 - $836.625 = $635.06
Hence, Gracie’s overtime rate of pay would be $635.06.
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How do you write a proof for this
Answer: They're equal to each other yes corresponding parts of congruent triangles are equal
Step-by-step explanation:
Find the general term for the sequence 6, 9, 12, 15, .... n + 5 3 n + 3 4 n + 2 6 n + 3
The general term for the arithmetic sequence is aₙ = 3 + 3n
How to find the general term of an arithmetic sequence?The general term of an arithmetic sequence is as follows:
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore,
a = 6
d = 9 - 6 = 3
aₙ = 6 + (n - 1)3
aₙ = 6 + 3n - 3
aₙ = 3 + 3n
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Find the slope of segment CD if C is (12, 4) and D is (6,2). (if answer is not a whole number, give a simplified fraction using "" and if the
answer is negative, put the negative sign first; for example you would write-1/2, not 1/-2) Type your answer in Blank 1
Blank 1:
Answer: 1/3 (if you have other questions like these you can use a slope calculator)
I need some help with this an explanation would be nice as well thanks
Answer:
Step-by-step explanation:
write a function rule for the table
hours worked 2,4,6,8 and pay 15,30,45,60
Answer:
f(x) = 7.5x
Step-by-step explanation:
you can find the slope by using the slope formula (y2-y1)/(x2-x1). you can use any of the values but for this example I'll be using (2, 15) and (4, 30).
(30-15)/(4-2) = 15/2 = 7.5.
now we can use one of the coordinates to find the y-intercept by plugging the known values in the equation y=mx+b where m is the slope and b is the y-intercept.
for this example I'll be using (2, 15) but you could use any of the values you gave.
15 = 7.5(2) + b
15 = 15 + b
0 = b
so now we have the function rule
f(x) = 7.5x + 0 or just f(x) = 7.5x
Consider the graph of the function f(x) = 25
-10-8-6-4-2
10
8-
6-
4
2
02 4 6 8 10
2
-4
6
-8
-10
Which statement describes a key feature of function gif 9(a) = 2f(x)?
Considering it's horizontal asymptote, the statement describes a key feature of function g(x) = 2f(x) is given by:
Horizontal asymptote at y = 0.
What are the horizontal asymptotes of a function?They are the limits of the function as x goes to negative and positive infinity, as long as these values are not infinity.
Researching this problem on the internet, the functions are given as follows:
[tex]f(x) = 2^x[/tex].[tex]g(x) = 2f(x) = 2(2)^x[/tex]The limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 2(2)^x = \frac{2}{2^{\infty}} = 0[/tex]
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 2(2)^x = 2(2)^{\infty} = \infty[/tex]
Hence, the correct statement is:
Horizontal asymptote at y = 0.
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help its TIMED
WHICH OF THE FOLLOWING MAY BE TRUE ABOUT f(x)
All three are possible.
The table tells us that for certain x and y, we have f(x) < f(y) if x < y. There's also no evidence that f(x) = f(y) for some points x ≠ y in the interval, so f(x) could easily be monontonically increasing. (I is true)
If we assume f(x) is strictly increasing (which does not contradict the given table) on the entire interval, we have f'(x) > 0. A positive function can be strictly increasing. (II is true)
A function is concave up on an interval if its derivative is increasing on that interval. This follows from statement (II) if it happens to be true. (III is true)
(E)
A club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel).
Find P(S-name U Boy)
The probability of selecting a person with a name that starts with S or a boy is [tex]\frac{5}{8}[/tex]
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Given that, a club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel)
To find P(S-name U Boy), that is the probability of selecting a person whose name starts with S or boy.
n(S-name U Boy) = 5 {2 girls (Sarah, Suzie), 3 boys( Kevin, Steve and Samuel )}
Number of favourable outcomes=5
Total number of outcomes=5+3=8
P(S-name U Boy) [tex]=\frac{Number of favourable outcomes}{Total number of outcomes}[/tex]
[tex]=\frac{5}{8}[/tex]
Therefore, the probability of selecting a person with a name that starts with S or a boy is [tex]\frac{5}{8}[/tex].
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ABD and DBC are complementary angles 43 what is the measure of x
The value of x is 60
How to determine the value of x?The complete question is added as an image
From the image, we have:
ABD = 30
DBC = x
The sum of complementary angles is 90.
So, we have:
30 + x = 90
Subtract 30 from both sides
x = 60
Hence, the value of x is 60
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Select the correct answer. A line each runs from point B through points A and C. First arc, centered at B, cuts line B A at J and line B C at K. A line runs rightward from point D. Second arc, centered at D, cuts the line at L and third arc, centered at L, cuts the line at M. What needs to be corrected in the following construction for copying ∠ABC with point D as the vertex?
In order to make point D as the vertex in the construction as triangle ABC, the third arc should cross the second arc.
What is an arc?In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.
In order to make point D as the vertex in the construction as triangle ABC, you must ensure that the third arc crosses the second arc as illustrated in image attached below.
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Answer: The third arc should cross the second arc.
Step-by-step explanation: The guy above me clearly stated it, just wanted to clear up that he is correct :)
Juan is making a fruit salad. He has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and cantaloupe. He wants his fruit salad to contain five different fruits. How many ways can he make the fruit salad if it must contain watermelon?
The number of ways that he can make the fruit salad if it must contain watermelon is 35.
What is Permutation and combination?Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.
The salad contains water melon, now we have to select 4 more fruits out of 7.
Using combination
[tex]^{n{C}_r[/tex] = n! / r! (n-r)!
[tex]^{7}C_4[/tex] = 7!/ 4! (7-4)!
= 7*6*5*4! / 4! * 3*2
= 35
Hence, number of ways that he can make the fruit salad if it must contain watermelon is 35.
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Answer: 35 on edge got it right
Step-by-step explanation:
12a-10b+6
Term:
Coefficient:
Se quieren llenar 100 botellas de agua con una capacidad de 1/4lt ¿cuantos litros de agua son necesarias?
Answer:
25
Step-by-step explanation:
Because 100 25+25+25+25 or 25/1/4
PLEASE ANSWER ASAP!!!!!!!!!
How is the product of a complex number and a real number represented on the coordinate plane?
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar and a 90° counterclockwise rotation of the complex number.
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number.
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a 90° counterclockwise rotation of the complex number.
When 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar and a 90° clockwise rotation of the complex number.
The statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number:
= 6 + 4i
Multiplied by 3:
= 18 + 12i
If we plot on the coordinate plane there will be no rotation the scalar has changed by multiplying with a real number.
Thus, the statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.
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Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by
Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by Economic needs.
What do we mean by economic needs?
By economic need Elaine is trying to get a company that would pay her more. Hence the need to go for the Unionized company.
This is given that the Unionized company is said to earn more than the other company. Hence her motivation is due to her economic needs.
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Need help
cnnbc recently reported that the mean annual cost of auto insurance is 959 dollars. assume the standard deviation is 263 dollars, and the cost is normally distributed. you take a simple random sample of 37 auto insurance policies. round your answers to 4 decimal places.
a what is the probability that one randomly selected auto insurance is more than $984?
b. a simple random sample of 37 auto insurance policies, find the probability that the average cost is more than $984.
Using the normal distribution, the probabilities are given as follows:
a. 0.4602 = 46.02%.
b. 0.281 = 28.1%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24[/tex]
Item a:
The probability is one subtracted by the p-value of Z when X = 984, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{984 - 959}{263}[/tex]
Z = 0.1
Z = 0.1 has a p-value of 0.5398.
1 - 0.5398 = 0.4602.
Item b:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{984 - 959}{43.24}[/tex]
Z = 0.58
Z = 0.58 has a p-value of 0.7190.
1 - 0.719 = 0.281.
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smone answer ASAP please.
The measure of the angle x is 117 degrees
Line geometry.To determine the value of x in the given diagram, we will use the alternate angles theorem
The value of x is expressed as shown;
p + q= x
If the value of p = 51, then;
51 + q. = x
Determine the value of. q
q = 108 - 42
q = 66
Determine the value of x
x = 66 + 51
x = 117 degrees
Hence the measure of the angle x is 117 degrees
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Two numbers are in the ratio of 2 to 3. Their sum is 30. What are the numbers? 3. Two numbers are in the ratio of 2 to 3. Their sum is 30. What are the numbers ?
Answer:
12 and 18
Step-by-step explanation:
Lets say the two numbers are A and B, with A the smaller.
We are told that A/B = 2/3 [in the ratio of 2 to 3]
We also find that A + B = 30 [Their sum is 30]
Rearrange the first equation to isolate A:
A/B = 2/3
A = 2B/3 [multiply both sides by B]
Now use this value of A in the second equation:
A + B = 30
2B/3 + B = 30
(2/3)B + (3/3)B = 30
(5/3)B = 30
B = (30)(3/5)
B = 6*3
B = 18
Since A + B = 30:
A + B = 30
A + 18 = 30
A = 12
A is 12 and B is 18
===================
Check:
Does A/B = 2/3??
(12/18) = (6/9)
(6/9) = (2/3) YES
Does A + B = 30 ???
12 + 18 = 30 YES
Which triangle would be most helpful in finding the distance between the points (–4, 3) and (1, –2) on the coordinate plane?
On a coordinate plane, a triangle has points (negative 4, 3), (1, negative 2), (5, 3).
On a coordinate plane, a triangle has points (negative 4, 2), (negative 1, 4), (1, negative 3).
On a coordinate plane, a triangle has points (negative 4, 3), (negative 4, negative 2), (1, negative 2).
The correct answer is option 3 which is the third graph showing the correct locations of the points on the coordinate plane.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph in option third is showing correct points on the x-y plane which are ( -4,3) and ( 1,-2).
-4 is along the negative x-axis and 3 is along the positive y-axis similarly to the second point positive 1 is along the x-axis and negative 2 is along the y-axis.
Therefore the correct answer is option 3 which is the third graph showing the correct locations of the points on the coordinate plane.
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Round to the nearest tenth wa hit is the perimeter of the triangle
Answer:
D. 11.8 cm
Step-by-step explanation:
This triangle is a 30°-60°-90° triangle. There is a shortcut to find the lengths of the sides of a 30°-60°-90° triangle. The longest side is the hypotenuse. The longest side is double the shortest side or, the shortest side is half the longest side. Here the longest side is 5, so the short leg (shortest side) is 2.5
The other shortcut is that the longer leg is the
short leg×sqroot3
Here, the short leg is 2.5, so the long leg is 2.5×sqroot3
Perimeter is all the sides added together.
5 + 2.5+ 2.5×sqrt3
Do the times first.
5 + 2.5 + 4.3
= 11.8
help me now !!!!!!!!!!!!!!!!
In the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
In the first diagram:
The sum of the 5k + 20 and 7k + 40 is 180
5k + 20 + 7k + 40 = 180
12k + 60 = 180
12k = 180 -60
12k = 120
k = 10
In the second diagram:
The sum of the two interior angles is equal to the exterior angle.
40 + 12k + 10 = 8k + 80
4k = 30
k = 30/4 = 15/2
Thus, in the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.
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The question is in the photo! Please help
A set of equations is given below:
Equation C: y = 7x + 12
Equation D: y = 7x + 2
How many solutions are there to the given set of equations?
O One solution
OTwo solutions
O Infinitely many solutions
No solution
Answer: No solution
Step-by-step explanation:
Ths lines are parallel (as they have the same slope but different y-intercepts), and parallel lines never intersect. Thus, the system has no solutions because the lines never intersect.
An item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup. Which expression should be used to find the amount of the markup?
48 dollars (0.55)
48 dollars (55)
48 dollars (0.55) + 48 dollars
48 dollars (55) = 48 dollars
The amount of the markup is $48 + $48 (0.55) .
Option (C) is correct .
What is Markup Price?Mark up refers to the value that a player adds to the cost price of a product. The value added is called the mark-up. The mark-up added to the cost price usually equals retail price.
As given
An item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup.
55% is written in the decimal form .
= 55/100
= 0.55
Markup price = 0.55 × wholesale price of item .
= 0.55 × $48
= $48 (0.55)
Price of item after markup = Wholesale price of item + Markup price
= $48 + $48 (0.55)
Thus, the amount of the markup is $48 + $48 (0.55) .
Option (C) is correct .
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Answer:The answer is A
Step-by-step explanation:
Edg 2022 (sometimes the verified ones are wrong)
What is the equation for the graph shown below?
Answer: D
Explanation:
Since we don't know the y-value of the vertex, let's do this an easy way: plugging in.
Let's use the y intercept since that would be the easiest. Since x=0, the terms with x cancel, and you will get a leading result of -5
A) results in 2, so eliminate it
B) results in -2, so eliminate it
C) results in 5, so eliminate it
D) results in -5, so keep it
Since D was the only one that worked, that is our correct answer.
add the following rational number7/-27 and 11/18
Answer:
19/54
Step-by-step explanation:
- 7/27 + 11/18
LCM of the 27, 18 is 54
- 7/27 * (2/2) + 11/18 * (3/3)
- 14/54 + 33/54
33 - 14/54
19/54
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Determine the measure of each indicated angle. Show all necessary steps!
The measure of the unknown angle are; a) x = 89 degrees, b) p = 92 degrees.
What is the sum of all the angles of a regular polygon?
For a regular polygon of any number of sides, the sum of its exterior angle is 360°.
We already know that a 4-sided polygon's angles add up to 360 degrees.
So to find the value of x:
69 + 118 + 84 + x = 360
x = 360 - (69 + 118 + 84)
x = 89 degrees
b)
For a 4-sided polygon, we also know that the outside angles add up to 360 degrees.
So to find the value of p:
100 + 62 + 106 + p = 360
p = 360 - (100 + 62 + 106)
p = 92 degrees
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Evaluate the expression (8×6) +(8-3)
Answer:
(8×6)+8-3
48+8-3
53
Step-by-step explanation:
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a herd of 25 horses has 12 white and some black horses what is the ratio of white to black horses
12:25 is also the same as 12/25 (in the fractional form!)
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