[tex] \sqrt{12} + 1 - \sqrt{5} \\ = \sqrt{4} \times \sqrt{3} + 1 - \sqrt{5} \\ = 2 \sqrt{3} + 1 - \sqrt{5} [/tex]
The graph of a linear function f passes through
the point (1,4) and has a slope of -2.
What is the zero of f?
Answer:
x = -1
Step-by-step explanation:
(x1,y1) = (1,4) and m = 2
(y-y1)/(x-x1) = m
derive the linear function first before finding the zero.
(y-4)/(x-1) = 2
cross multiply
y-4 = 2(x-1)
y-4= 2x - 2
y = 2x - 2+4
y. = 2x + 2 is the linear equation
at y = 0 gives the zero
2x + 2 = 0
2x = -2
x = -2/2
x = -1 is the zero
Write an equation for the line that is parallel to the given line that passes through the given point.
y = -6x + 2; (-1,2)
Answer:
The correct answer is y = -6x - 4
Step-by-step explanation:
The given equation of the line : y = -6x + 2
Now, the general equation of the line in the slope-intercept form is given by : y = mx + c
Now, comparing the given equation with the general form, We get slope, m = -6
We need to find the equation of the line which is parallel to the given line and since the slope of two parallel lines are equal so the slope of the required line will also be -6
And it passes through the point (-1, 2)
The required equation will be :
⇒ y - 2 = -6 × (x + 1)
⇒ y - 2 = -6x - 6
⇒ y = -6x - 4
Therefore, The required equation is y = -6x -4
Hence, The correct answer is. y = -6x - 4
Brainlist?????
a number, n is multiplied by -5/8 the product is -0.4 how would you set this up to solve
The value of n in the mathematical statement is 0.64
How to solve the equation?The statement is given as:
n multiplied by -5/8 equals -0.4
Rewrite properly as:
n * -5/8 = -0.4
Multiply both sides by -1
n * 5/8 = 0.4
Multiply both sides by 8/5
n = 0.64
Hence, the value of n in the mathematical statement is 0.64
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Jacob bought a deluxe computer system for his home business. The system cost
$2,395. The value of the computer system will depreciate at a rate of 12% a year.
What will be the cash value of the computer system in 3 years? Round your answer to
the nearest dollar.
O $287
O $2108
O $1632
O $2682
The cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632
DepreciationFrom the question, we are to determine the cash value of the computer system in 3 years
From the given information,
The computer system cost $2,395 and it will depreciate at a rate of 12% a year
After the first year, the worth of the computer system will be
$2,395 - (12% of $2,395)
$2,395 - (0.12 × $2,395)
= $2,395 - $287.4
= $2107.6
After the second year, the worth of the computer system will be
$2107.6 - (12% of $2107.6)
$2107.6 - (0.12 × $2107.6)
= $2107.6 - $252.912
= $1854.688
After the third year, the worth of the computer system will be
$1854.688 - (12% of $1854.688)
$1854.688 - (0.12 × $1854.688)
= $1854.688 - $222.56256
= $1632.12544
≅ $1632
Hence, the cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632
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Please help see picture
Answer:
688 cm²
Explanation:
Area of triangular prism = Base × Height + Length × (perimeter of base)
Here given:
Base: 6 cmHeight: 12 cmLength: 20 cmPerimeter of Base: (6 + 12.4 + 12.4) = 30.8 cm============================================
Surface Area = 6 × 12 + 20 × (30.8) = 688 cm²
If a company reports operating profit of $70 million, earns net income of $50 million in year 8, has 20 million shares of common stock outstanding, pays a dividend of $1. 50 per share, and has annual interest costs of $15 million--all in year 8, then
The company's EPS for Year 8 would be $2.50 and its retained earnings for Year 8 would be $20 million
How do we calculate EPS and retained earnings?Note: The options for the questions are as follows:
A. the company's total earnings for Year 8 would be $10 million (net income of $50 million less interest costs of $10 million less dividend payments of $30 million = $10 million).
B. the company's EPS for Year 8 would be $2.50 and its retained earnings for Year 8 would be $20 million (net income of $50 million less dividend payments of $30 million).
C. the company's credit rating would be no less than an A because operating profit is seven times higher than annual interest costs.
D. the company's EPS for Year 8 would be $5.50 and its retained earnings for Year 8 would be $10million (net income of $50 million less interest costs of $10 million less dividend payments of $30million).
E. the company's EPS for Year 8 would be $1.50 (operating profit of $70 million less interest costs of$10 million, less dividend payments of $30 million= $30 million divided by 20 million shares).
The question can now be answered as follows:
From the question, we can calculate the following:
EPS = Net income / Number of shares of common stock outstanding = $50 million / 20 million = $2.50
Dividend payments = Number of shares of common stock outstanding * Dividend per share = 20 million * $1. 50 = $30 million
Retained earnings = Net income - Dividend payments = $50 million - $30 million = $20million
Therefore, the correct option is B. the company's EPS for Year 8 would be $2.50 and its retained earnings for Year 8 would be $20 million (net income of $50 million less dividend payments of $30 million).
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One evening, the candy counter at the Cineplex sold 532 buckets
of popcorn for $1,489.50. A large bucket sells for $2.25 and a
jumbo bucket sells for $3.75. How many jumbo buckets of
popcorn were sold?
Please help!!
Answer:
337 large buckets and 195 jumbo buckets were sold.
Step-by-step explanation:
x = the number of large buckets sold
y = the number of jumbo buckets sold
x + y = 532
(2.25x + 3.75y = 1489.50) x100 = 225x + 375y =148950
(x + y = 532) x -225 = -225x - 225y = -119700
+ 225x + 375y =148950
150y = 29250
y = 195
x + 195 = 532
x = 337
What are the values of a and b? O a 14, b=6 O a=14, b = 8 O a=17, b = 6 O a = 17, b = 8
The value of a is 17 and the value of b is 6. The correct option is third option a = 17, b = 6
Calculating the length of the sides of a kiteFrom the question, we are to determine the values of a and b
From the given kite diagram, we can conclude that
/FG/ = /HG/
Thus,
30 = 2a - 4
∴ 2a - 4 = 30
2a = 30 + 4
2a = 34
a = 34 / 2
a = 17
Also,
/FJ/ = /HJ/
3b + 6 = 24
3b = 24 - 6
3b = 18
b = 18/3
b = 6
Hence, the value of a is 17 and the value of b is 6. The correct option is third option a = 17, b = 6
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1.
Which of these is equivalent to
A. 2-19
1
B.
27
1
C.
2
23
D.
(2-4)²x2-5
2-6
-?
The solution to the given indices are 1/2^7, 11^4 and -1/64
Indices expressionGive the following indices expression
[tex]\frac{(2^{-4})^2\times 2^{-5}}{2^{-6}} \\[/tex]
This can be further simplified according to the law of indices as:
[tex]\frac{(2^{-4})^2\times 2^{-5}}{2^{-6}} =\frac{2^{-8-5}}{2^{-6}}[/tex]
Determine the result
[tex]\frac{2^{-8-5}}{2^{-6}} = 2^{-7} = 1/2^7[/tex]
For the indices expression
[tex]11^{-4}\times 11^{8} = 11^{-4+8}=11^4[/tex]
For the indices expression
[tex]-4^4\times4^{-7}\\=-(4^{4-7})\\= -4^{-3}\\=-1/4^3\\=-1/64[/tex]
Hence the solution to the given indices are 1/2^7, 11^4 and -1/64
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Which set of ordered pairs represents a function
Answer:
C: is a function because each input (x) has exactly one output( y).
Step-by-step explanation:
A function is when one input (x) has exactly one output (y).
A: is not a function because -4 is paired with two different y values.
B: is not a function because -4 is paired with two different y values.
C: is a function because each input (x) has exactly one output( y).
D: is not a function because -1 is paired with two different y values.
Regress smoker on cubic polynomials of age, using a linear probability model. What is the p-value for testing the hypothesis that the probability model is linear in age? (two decimal places)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is probit regression?A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
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A computer randomly picks a number from the group 20, 21, 22, 23, 24, 25, 26, 27. What is the probability the number is greater than 24 or less than 21?
Answer:
The answer you're looking for is .5
Step-by-step explanation:
Cause 20 is less than 21, and 25, 26, and 27 is larger than 24, and that's 4 numbers. There's 8 numbers in total, so your answer is 4/8. Divide that by 4, and you get 1/2. That's 50%, if you're thinking out of "1" then it would be ".5"
Answer: 0.5 or 50%
Numbers-Set {20, 21, 22, 23, 24, 25, 26, 27}
Total outcomes: 8
numbers greater than 24 are 25, 26, 27 - 3 numbers
number less than 21 is 20 - 1 number
Total favorable outcomes: 3 + 1 = 4
Probability = favorable outcomes/total outcomes = 4/8 = 0.5
Given the parent function of f(x) = x³, what is the value of k in the translated graph of f(x - h) + k?
int)
k=-3
k=-2
k=2
k=3
The value of k in the translated graph of f(x - h) + k is; k = 2
How to carry out Translations on Graphs?We are given the parent function of f(x) = x³.
Now, the point (0, 0) in the graph of f(x) is the point (3, 2) in the translated graph. Thus;
The rule of translation is;
(x, y) → (x + 3, y + 2)
That means;
The translation is 3 units to the right and 2 units up
The equation of the translated graph is equal to;
f(x) = (x - 3)³ + 2
Thus;
The value of k is equal to 2.
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A right square pyramid and its dimensions are shown below.
Answer:
C) 8 m²
Step-by-step explanation:
Volume of a square pyramid :
V = 1/3BhV = 1/3 x (2.5)² x 4V = 1/3 x 25V = 25/3V = 8.3 ≈ 8 m²8). Triangle A'B'C' is formed when Triangle ABC is
translated right by 4 and up by 2. Which statement is
true?
Choose all that apply:
1.The angles of Triangle ABC and Triangle A'B'C' are the
same
2.Triangle A'B'C' is congruent to the original triangle.
3.The perimeter of Triangle ABC and Triangle A'B'C' are
the same.
Answer:
Answer 2 is correct because triangle ABC is the same as the original just that the position has changed
A jeweler wants to combine a 60% gold alloy with a 20% gold alloy to make 1000 grams of 50% gold alloy. How many grams of 60% alloy should be used?
Answer:
750 grams of 60% alloy
Step-by-step explanation:
Define x = amount of 60% alloy and y = amount of 20% alloy
Equating the amounts of gold:
0.6x+0.2y = 1000(0.5)
Since there must be 1000 grams total:
x+y = 1000
Writing the 2 resulting equations together:
0.6x + 0.2y = 500
x + y = 1000
Multiply the first equation by 5:
3x + y = 2500
x + y = 1000
Subtracting the 2nd equation from the 1st:
2x = 1500
x = 750
Answer: 750 grams of 60% alloy
Carlos has at most $40 to spend on food for a barbeque. He wants to buy hot dogs and hamburgers and then
Alls for each. Carlos has already spent $31.50 on the hot dogs and hamburgers. Let r represent the amount of
noney that Carlos can spend on the rolls.
Write and solve an inequality.
Answer:
$8.50
Step-by-step explanation:
I don't know what Alls are, but if Carlos insists, we can calculate how much he can spend on Alls with the expression:
($31.50) + r [tex]\leq[/tex] $40
This says the sum of what Carlos has already spent (hot dogs and hamburgers) plus the amount he spends on Alls (rolls?), r, must be equal to or less than the $40 he has allowed himself to spend.
($31.50) + r [tex]\leq[/tex] $40
r [tex]\leq[/tex] $40 - $31.50
r [tex]\leq[/tex] $8.50
In the following diagram, BC is parallel to DE.
What is the measure of a?
Angles are not necessarily drawn to scale.
B
W
103
D
F
4* =
42°
E
Answer: 35
Step-by-step explanation:
Angles in a triangle add to 180 degrees, so in triangle ABC, [tex]m\angle C=180-103-42=35^{\circ}[/tex].
Sp, by the corresponding angles theorem, x=35
Define a quadrilateral.
please explain and help me pls
Answer:
A Quadrilateral is a 4 sided figure. In other words any shape that has 4 sides is a quadrilateral for example square, rectangle, trapezium etc
Step-by-step explanation:
I need the answer please!!!!
Answer:
53712.4
Step-by-step explanation:
10^3 = 1000
To multiply a decimal by 1000, move the decimal point in the multiplicand by three places to the right.
so, 53.7124 becomes 53712.4
hope this helps :)
Can somebody help me solve this inequality
Answer:
108 cm²
Step-by-step explanation:
The composite shape can be divided as shown into a trapezoid and a triangle. The area of the shape is the sum of the areas of those parts.
__
trapezoidThe top portion of the shape is marked as a trapezoid with bases 12 cm and 6 cm, and height 6 cm. Its area is given by ...
A = 1/2(b1 +b2)h
A = 1/2(12 cm +6 cm)(6 cm) = 1/2(18 cm)(6 cm) = 54 cm²
__
triangleThe bottom portion of the shape is marked as a triangle. The triangle has a base of 12 cm and a height of (15 cm -6 cm) = 9 cm. Its area is ...
A = 1/2bh
A = 1/2(12 cm)(9 cm) = 54 cm²
__
total areaThe area of the composite figure is the sum of the areas of its parts:
total area = trapezoid area + triangle area
total area = 54 cm² +54 cm² = 108 cm²
The area of the logo is 108 cm².
7/12 - 1/6 in simplest form
Answer:
5/12
Step-by-step explanation:
1/6 can be turned into 2/12
7/12-2/12=5/12
Find the slope of the line through the each pair of points
(16, 14), (-2, 0)
Answer:
[tex]\text{Slope} = \dfrac{7}9[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1) = (16,14)~ \text{and}~ (x_2,y_2) = (-2,0)\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 -x_1}\\\\\\~~~~~~~~~~~~=\dfrac{0-14}{-2-16}\\\\\\~~~~~~~~~~~~=\dfrac{-14}{-18}\\\\\\~~~~~~~~~~~~=\dfrac{7}9[/tex]
Answer:
m = 7/9
m = 7/9m ≈ 0.80
Step-by-step explanation:
Given two points:
(16, 14), (-2, 0)
To find:
The slope
Solution:
We know that,
[tex] \rm Slope(m) = \cfrac{ y_2 - y_1}{x_2 - x_1} [/tex]
According to the question,
y_2 = 0y_1 = 14x_2 = -2x_1 = 16Note:[The underscore refers to that the numbers after the underscore is a subscript]
So Substitute them on the formulae:
[tex] \implies \rm \: m = \cfrac{0 - 14}{ - 2 - 16} [/tex]
Simplify it.
[tex] \implies \rm \: m = \cfrac{ \cancel{- 14} \: {}^{7} }{ \cancel{- 18} \: {}^{9} } [/tex]
[tex] \implies \boxed{ \rm \: m = \cfrac{7}{9} }[/tex]
[tex] \implies \rm \boxed{ \rm m \approx0.80}[/tex]
Thus,the slope is 7/9 in fraction and 0.80 (Nearest tenth) in decimal.
Find the mean of the following set of numbers. 4,10,12,8,6
Answer:
Mean = 8
Step-by-step explanation:
The mean is another way of describing the average. To find the mean, you need to (1) add all of the numbers together and (2) divide by the amount of numbers added.
(Step 1)
4 + 10 + 12 + 8 + 6
= 40
(Step 2)
4, 10, 12, 8, 6 -----> There are 5 numbers
40 / 5
= 8
The perimeter of a semicircle is 81.212 yards. what is the semicircle's diameter?
[tex]\textit{circumference of a semicircle}\\\\ C=\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=81.212 \end{cases}\implies 81.212=\pi r\implies \cfrac{81.212}{\pi }=r \\\\\\ \stackrel{\textit{its diameter is}}{2r\implies 2\left( \cfrac{81.212}{\pi } \right)} ~~ \approx ~~ 51.7[/tex]
please help me!!!!!!!! will mark brainliest
Answer:
i) 0.5
ii) 0.76
Step-by-step explanation:
i) 0.5
ii) 0.76
true or false? The sum of the difference is not always zero for any distribution consisting of n observations
Answer:
i believe the answer is false !
Step-by-step explanation:
Vera is looking for vegetables for dinner. She purchases 2 5/8 pounds of baby potatoes and 1 1/2 pounds of green beans. If she uses a $10 bill to pay, what will her change be?
Baby potatoes=$1.62 per pound and green beans=2.54 per pound
Answer:
6.5 $
Therefore she needs 6.5 $ is she doesn't rwk
Roger works part-time as a waiter at a pizza joint. He earns $9 per hour. How much does he earn for 20 hours of work?
Answer:
180
Step-by-step explanation:
well 9×12=180 roger only works 20 hours he gets plaid $9 per hour he's working so yes the answer is 180
Answer:
180
Step-by-step explanation:
10×9=90, so 90+90= 180
Please help i been asking since yesterday
Calculate the perimeter of the triangle for problems
B. Calculate the area of the triangle for problems
Answer:
To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.
Answer:
1) 21.24cm
2)19.8ft
3)22.84mm [2.284cm]
Step-by-step explanation:
To calculate the perimeter of a triangle, add the length of its sides.
1) perimeter = 5.4+8.84+7
=> 5.4+8.84+7 = 21.24,
21.24cm
2) perimeter = 6.6 + 6.6 + 6.6 i.e 6.6* 3
=> 6.6 x 3 = 19.8
19.8ft
3) perimeter = 8.3 + 4.9 + 9.64
=> 8.3 + 4.9 + 9.64 = 22.84
22.84mm or 2.284cm
AREA
1) it's a right triangle,
=> Area of a right triangle = 1/2 × base × height.
=> here, base is a and height is b
=> a = 7, b = 5.4
=> now we multiply it,
=> 7*5.4 = 37.8
=> now multiply it with 1/2,
=> 1/2 x 37.8 = 37.8/2
=> 37.8/2 = 18.9
2) it's an equilateral triangle,
18.8620
the formula is √3 a^2/ 4
=> √3* 6.6^2/ 4
=> 75.4481/4 = 18.8620
3) 20.335
base = a = 8.3
height = b = 4.9
=> 8.3 * 4.9 = 40.68
=> 40.68/2 = 20.335
hope this helps:)