The equation of the line that passes through the point (5, 4) and is perpendicular to the line whose equation 2x + y = 3 is y = 1/2x + 3/2
The given equation of the line is
2x + y = 3
y = 3 - 2x
y = -2x + 3
The slope of the line is -2
The slope of the original line will be negative inverse of -2
= - 1/-2
= 1/2
The line is passing through the point (5, 4)
The slope intercept form is
y = mx + b
Substitute the values in the equation
4 = 1/2(5) + b
4 = 5/2 + b
b = 4 - (5/2)
b = 3/2
Therefore, the equation of the line is y = 1/2x + 3/2
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Noah is going to invest in an account paying an interest rate of 7% compounded continuously. How much would Noah need to invest, to the nearest hundred dollars, for the value of the account to reach $12,900 in 10 years?
The amount of money that Noah needs to invest would be = $ 6,558
What is interest rate?An interest rate is defined as the rate at which an individual receives an interest on an invested funds over a stipulated period of time.
The interest rate (R) = 7% = 0.07 (decimal form)
The time for the investment (T) = 10 years.
The present value of the account (A) = $12,900
n compounding frequency = 1
Using the formula;
A = P (1 +r/n) ^nt
12,900 = P ( 1 + 0.07) ^ 10
12,900 = P (1.07) ^10
12,900 =P 1.96715
P = 12,900/1.96715
P =$ 6,558
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Question is attached
Answer:
D) None of the above------------------------------------
Let the numbers be:
1, x, y, z, 81Geometric means give us:
y² = 1*81 ⇒ y = 9Then:
y² = xz ⇒ xz = 81Given options give us:
A) 3*21 = 63 ≠ 81;B) 3*18 = 54 ≠ 81;C) Same as option A (must be a typo);Since all the above options are false, the answer is option D.
To qualify for the next marathon, a runner's time must be less than 314 hours. Indicate whether or not each runner will qualify for the next marathon.
who will qualify?
Answer:
(It's weird how I answered this question for someone else 12 minutes ago.)
There was no data provided but due to simple research i have conducted the following data
Qualifiers are in bold, italics and underlined.
Step-by-step explanations:
Chio- 3 1/5
Kevin- 3.2
Ojas- 3 8/30
Sydney- 3 13/60
Qualifiers: Chico, Kevin
let me know if this is incorrect data
help pleaseee dlkwekemmwnd right now
By using the property of congruency of triangles,
[tex]\angle[/tex]Y [tex]\cong[/tex] [tex]\angle[/tex]X has been proved
What is congruency of triangles?
Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.
There are different axioms of congruency. They are
SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom
Z is the midpoint of XY [Given]
WZ [tex]\perp[/tex] XY [Given]
[tex]\angle[/tex]WZX [tex]\cong \angle[/tex]WZY [90° each]
XZ [tex]\cong[/tex] YZ [Z is the midpoint of XY]
WZ [tex]\cong[/tex] WZ [Reflexive property of congruency]
[tex]\Delta[/tex] WXZ [tex]\cong \Delta[/tex] WYZ [SAS axiom]
[tex]\angle[/tex]Y [tex]\cong[/tex] [tex]\angle[/tex]X [Corrosponding parts of congruent triangles are congruent]
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1 For 7-8, given two sides of a triangle, find a range of possible lengths for the third side 7. 4 cm, 17 cm 8. 24 ft , 52 ft
The range of possible lengths for the third side is [16.52,17.46] for 1st part and [46.13,57.27] for 2nd.
What is pythagoras theorem?
The Pythagorean theorem or Pythagoras' theorem could be a elementary relation in parabolic geometry between the 3 sides of a trigon.
Main Body:
To find range of possible lengths for the third side , we will use Pythagoras theorem : a²+b² = c²
7. 4 cm, 17 cm
4²+17²=c²
16+289=c²
305=c²
To undo the square you have to square root so
√ 305 =17.46
OR
17² = 4²+b²
289 -16 =b²
b = √273 = 16.52
range of possible lengths for the third side is [16.52,17.46]
8. 24 ft , 52 ft
24² =576
52² =2704
2704+576=3280
√3280 =57.27
OR
52² = 24²+b²
b²= 2704-576
b=√2128
b = 46.13
range of possible lengths for the third side is [46.13,57.27]
Hence the range of third side is found out.
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At a local restaurant, Tony earns $12.50 per hour with a 13% deduction for taxes and social security. His
overall earnings are modeled by the expression, 12.5-0.13(12.5x), where a represents the number of
hours Tony worked.
Tony deposits 38% of his overall wages into his savings account. How many hours will he need to work to save
$1,000?
The total number of hours Tony will he need to work to save amount $1,000 is 242 hours.
Explain the term deductions on salary?Payroll deductions are sums of money taken out of an employee's overall pay to cover taxes, garnishments, and perks like health insurance. Income tax may be one of these with holdings, which make up the difference in gross pay or net pay. tax on social security.The given data for the question is-
Tony makes $12.50 per hour at a nearby restaurant after a 13% tax and social security deduction.The equation 12.5x - 0.13(12.5x), where an is the total number of hours Tony worked, is used to model his overall earnings.38% of Tony's total pay goes into the savings account.Thus,
38%(12.5x - 0.13(12.5x)) = 1000
0.38(10.875x) = 1000
x = 2631.57/10.875
x = 241.98
x = 242
Thus, total number of hours Tony will he need to work to save
$1,000 is 242 hours.
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Graph the line that has a slope of
1
6
and includes the point (0,0).
Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].
What is the slope of line?
The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.
Here given thaat the line that has a slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex].
Then,
[tex]y=mx+c\\\\y=\frac{x}{5}+c\\\\x=0,y=0\\\\0=0+c\\\\c=0[/tex]
Thus,
[tex]y=\frac{x}{5}+c\\\\c=0[/tex]
Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].
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What transformations were applied to the parent function k(x)=x| to obtain f(x)= -1/2|x+3/-1.
Answer:
The transformations applied to the parent function k(x)=x| to obtain f(x)= -1/2|x+3/-1 are reflection in the y-axis, vertical stretching by a factor of 1/2, and a horizontal shift of 3 units to the right.
Step-by-step explanation:
To obtain f(x) from k(x), we first reflect k(x) in the y-axis, which changes the sign of the function and flips it over the x-axis. This gives us -k(x). Next, we vertically stretch the graph of -k(x) by a factor of 1/2. This makes the graph of -k(x) taller and narrower. Finally, we shift the graph of -k(x) 3 units to the right. This moves the entire graph 3 units to the right on the x-axis. The resulting function is f(x)=-1/2|x+3/-1.To understand why these transformations were applied, it's helpful to consider the effect of each transformation on the graph of k(x)=x|. Reflecting in the y-axis flips the graph over the x-axis and changes the sign of the function, so it becomes -k(x). Vertical stretching by a factor of 1/2 makes the graph of -k(x) taller and narrower. Finally, shifting the graph of -k(x) 3 units to the right moves the entire graph 3 units to the right on the x-axis. This results in the graph of f(x)=-1/2|x+3/-1.
Answer:
(Assuming it is k(x) = |x| and f(x) = -1/2|x+3| -1
Scale vertically by a factor of -1/2
Shift left 3
Shift down 1
Step-by-step explanation:
The -1/2 is multiplied by everything, so it scales the graph vertically by -1/2. The -1 is again, everything(as opposed to just modifying the x), so it shifts the graph down by 1.
The + 3 is a little more confusing. Basically, x would have to be x-3(which is shifting the graph left) in order to retain the same x-value(to make the equation true) for the same value. This is the same for y, but we usually isolate y so it doesn't come up as often. If we add 1 to both sides, we get [tex]f(x) + 1= -1/2|x+3|[/tex], and for the same reasoning the graph would shift down 1 even though it is f(x) + 1, because for the same x-value the y-value would need to be 1 less to make the equation to hold true.
Feel free to message me/comment on this answer if you would like more clarification/why it is "backwards" or anything else about my answer.
I hope this helps!
If f(x)=2x+1 and g(x)=x−5, find f(x)+g(x) to complete the polynomial
Answer:
[tex]\huge\boxed{\sf 3x -4}[/tex]
Step-by-step explanation:
Given functions:f(x) = 2x + 1g(x) = x - 5Add both equations.
f(x) + g(x):= 2x + 1 + x - 5
Combine like terms
= 2x + x + 1 - 5
= 3x - 4[tex]\rule[225]{225}{2}[/tex]
Answer:
f(x) + g(x) = 3x - 4
Step-by-step explanation:
The problem is,
→ f(x) + g(x)
Let's solve the problem,
→ f(x) + g(x)
→ (2x + 1) + (x - 5)
→ 2x + 1 + x - 5
→ (2x + x) + (1 - 5)
→ 3x +(-4)
→ 3x - 4
Hence, answer is 3x - 4.
A furniture maker buys foam rubber x times per year. The delivery charge is a flat rate of $400 dollars per purchase regardless of how much is bought. The annual cost of storage is figured as $10,000/x, because the more frequent the purchase, the less it costs for storage. The annual cost is: C = 400x+10,000/x
A. Graph the function.
B. Find the number of purchases per year that minimizes the annual cost of delivery and storage.
Answer:
Should be B
Step-by-step explanation:
Mackenzie ha ome red, yellow and blue marble. She ha 3200 more red marble than yellow marble. She ha 3840 more blue than yellow. She give 1490 blue marble away. How many more red marble than blue marble doe he have left?
We know that there are 850 more red marbles left than blue marbles by solving equations.
What are equations?The equals sign is used in mathematical equations to indicate that two expressions are equal.
An equation is a claim that demonstrates the equality of two mathematical expressions, according to algebra.
For instance, the word "equal" separates the formulas 3x + 5 and 14, which together form the equation 3x + 5 = 14.
So, a number of red marbles more than blue marbles is:
Mackenzie has 3200 more red than yellow marbles.
y + 3200 = r
Additionally, she has 3840 more blue than yellow marbles.
y + 3840 = b
Assume Mackenzie has one yellow marble, then.
1 + 3200 = 3201 red marbles
1 +3840 = 3841 blue marbles
She will have left over 2351 blue marbles after giving away 1490
3841 - 1490 = 2351
She now has 3201 red marbles and 2351 blue marbles.
r - b =?
3201 - 2351 = 850
Therefore, we know that there are 850 more red marbles left than blue marbles by solving equations.
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A science club has 13 members. The club bought b bumper stickers to split among its members. Write an expression that shows how many bumper stickers each member will get.
Answer: b/13
Step-by-step explanation:
Divide b by 13 to get b/13
suppose we have trained 10 different models on the exact same training data, and magically, they all achieve 95% precision. is there any possibility these models could all be combined to achieve better performance? if so, how? if not, why?
If you train 10 distinct models on the same training data, try integrating them into a voting ensemble, which will eventually produce better results.
what is voting ensemble ?Voting is an ensemble technique for making predictions by combining the results of various models. The predictive performance of an ensemble is better than that of a single predictive model in a predictive modeling issue. This is accomplished by the model adding bias, which lowers the variance component of the prediction error
calculation
Voting ensembles frequently produce even better results, so try combining them.
The models should differ greatly for it to operate. 95 percent accuracy.
We will therefore get better results if we combine them.
If you train 10 distinct models on the same training data, try integrating them into a voting ensemble, which will eventually produce better results.
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suppose there are 6 roads connecting town a to town b and 4 roads connecting town b to town c. in how many ways can a person travel from a to c via b?
Number of ways can a person travels from A to C via B = 24 ways
How it can be calculated that a person can travel in no. of ways?
To calculate the likelihood of an event occurring, we will apply the equation number of favourable outcomes divided by total number of outcomes. We sometimes need to apply a permutation to calculate the overall number of outcomes. A permutation is a method for calculating the number of events that occur when order is important.
Given,
Connection of roads from a = 6
Connection of roads from a = 4
Number of roads from a to b =6
Number of roads from b to c =4
Number of ways can a person travels from a to c via b
= 6*4
= 24 ways
The number of ways a person can go from A to C via B is 24.
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What is an angle that is supplementary to BGD
Answer:
DGE and BGA
Step-by-step explanation:
Supplementary angles are two angles whose measures add up to 180°
so BGD + DGE = 180 or BGD + BGA = 180
so both DGE and BGA are supplementary to BGD
Which decimal is equivalent to 2/27
Answer:
0.07407407
Step-by-step explanation:
divide 2 by 27
Answer:
0.0740
Step-by-step explanation:
just divide 2 by 27
In the following expression, both A and B are variables that can take positive values.
(A+7)*2^B
Which of these actions will cause the expression's value to increase?
Choose 2 answers:
Answer:
its 3/5 and 9/5
Step-by-step explanation:
HOPE IT HELP :D
Do the expressions (-2)(3) and (2)(-3) have the same value? Show your thinking .
1/5(4x-2.5)=5(0.4+10)+3 1/3
The Value of x is 69.78 per given equation.
1/5(4x-2.5) = 5(0.4+10)+3 1/3
0.2(4x-2.5) = 5(0.4+10)+3.33
0.2(4x-2.5) = 5(10.4)+3.33
0.2(4x-2.5) = 52 + 3.33
0.2(4x-2.5)=55.33
4x-2.5 = 276.33
4x = 276.33+2.5
4x = 279.15
x = 69.78
So, the value of x is 69.78
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I am very confused on what to do.Can someone help me?
Answer:
739 m²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Equation}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
The given scenario can be modelled as an exponential equation.
Let y be the area the fire covers (in meters squared).
Let x by the time (in hours).
If the fire currently covers an area of 32 m² then the initial value, a, is 32.
If the area covered by the fire increases by 17% each hour, then the growth factor, b, is 1.17 (since an increase of 17% is 117% of the previous amount).
Therefore:
a = 32b = 1.17Substitute the values of a and b into the exponential formula:
[tex]y=32(1.17)^x[/tex]
To find the area that the first covers in 20 hours' time, simply substitute x=20 into the equation:
[tex]\implies y=32(1.17)^{20}[/tex]
[tex]\implies y=32(23.1055991...)[/tex]
[tex]\implies y=739.37917...[/tex]
Therefore, the area the fire will cover in 20 hours' time is 739 m² (nearest 1 m²).
What is the value of 9+21(13+5)? 287 395 387 540
The answer is C. 387
Step-by-step explanation:
9+21(13+5)
First do what is in parentheses:
9+21(13+5)
=9+21(18)
Next do 21(18) or 21 x 18:
9+21(18)
=9+378
The last step is to add:
9+378=387
The answer is C. 387
Select all of the following that are quadratic functions.
x=3y²-6y+5
y+3=-2x2+5
y=2x2−8x+6
y=-7x-4
y-3x=4x³-x² +9
y = 5 x(x +9)-8
y-2x²=3x-2x²+4
DONE
Step-by-step explanation:
For this select the function with the leading term with the power of 2
1 and 6 are the only quadratic function ( BECAUSE THEY ONLY HAVE FUNCTION WITH GREATEST POWER OF 2)
HELP ANYONE PLEASE IT'S DUE TODAY I WAS STUCK ON THIS QUESTION
A line that goes through (0, 0) and (3.6, 14.4).
Wewant a description of the line that describes the same proportional relationship as the points given in the table:
(x, y) = (3.6, 14.4), (12.2, 48.8), (2.1, 8.4)
What is Proportional relation ?The graph of the relation will be a straight line through points with (x, y) values from the table. A graph of a proportional relation also goes through the point (0, 0).
Of the points listed in the answer choices, only (3.6, 14.4) and (12.2, 48.8) are ones that are given in the table. This eliminates all of the answer choices except the correct one:
A line that goes through (0, 0) and (3.6, 14.4).
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HELP
Q1: e + -10.67 + 553⅝² - e × 8⅘⁴
Q2: 95⅚⁵ + -8⅚ + 1⅜
Q3: e⁸ + ⅓² × π × π³
Q4: φ⁸ ÷ 80 - 1⅗ + -108⅔
Answer:
Step-by-step explanation:
3
10 post hole that are 3 feet deep and 1 foot across with a pipe down the center that is 3 inches in diameter
The total volume of all 10 holes and pipes is about 24.135 cubic feet.
What is Volume?Generally, To calculate the volume of the holes, you can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
In this case, the radius of the hole is 0.5 feet (since the hole is 1 foot across and the diameter of the pipe is 3 inches, which is 0.25 feet), and the height is 3 feet. Plugging these values into the formula, we get:
Volume = π * 0.5^2 * 3 = 0.785 * 3 = 2.355 cubic feet
So each hole has a volume of about 2.355 cubic feet. To find the total volume of all 10 holes, you can simply multiply this number by 10:
Total volume = 2.355 * 10 = 23.55 cubic feet
This is the volume of the holes themselves, not including the volume of the pipes. To find the volume of the pipes, you can use the same formula, but with the radius of the pipe (which is 1.5 inches, or 0.125 feet) and the length of the pipe (which is 3 feet).
Volume = π * 0.125^2 * 3 = 0.0195 * 3 = 0.0585 cubic feet
So the volume of one pipe is about 0.0585 cubic feet. To find the total volume of all 10 pipes, you can multiply this number by 10:
Total volume = 0.0585 * 10 = 0.585 cubic feet
23.55 + 0.585 = 24.135 cubic feet.
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CQ not found
Name the slope and one point or
y-1=2(x+3)
Q
(__)
=_
m=
Answer: M=2
y-intercept = (0,7)
x-intercept = (-7/2,0)
Step-by-step explanation:
The slope is already given in the equation, which is 2
M=2
y-intercept = (0,7)
x-intercept = (-7/2,0)
27. Solve and graph
-2n-5≥1 or 5n + 7 > 2
28. S
The solution to the inequality expression -2n - 5 ≥ 1 or 5n + 7 > 2 is -1 > n ≥ -3
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
-2n-5≥1 or 5n + 7 > 2
So, we have
-2n - 5 ≥ 1 or 5n + 7 > 2
Evaluate the like terms
So, we have the following representation
-2n ≥ 6 or 5n > -5
Divide both sides by the coefficient of n
This gives
n ≤ -3 or n > -1
Combine the expression
-1 > n ≥ -3
Hence. the solution is -1 > n ≥ -3
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Two similar triangles have perimeters in the ratio of 2:7. The smaller
triangle has sides measuring 6 inches, 7 inches, and 8 inches. How long, in
inches, is the longest side of the larger triangle?
A) 18
B) 21
C) 28
D) 56
E) 74
Miles is shopping for a new computer. He finds a computer with an original price of $325. 00 but finds that it is 15% off. After paying a 7% sales tax, how much does miles spend on his new computer?.
Miles has to spend $295.3375 on his new computer.
Sales tax is applied to the price after the discount is applied because discounts are typically provided directly by the retailer and lower both the sales price and the money the retailer receives.
So Original price of Computer is $325.00
Discount with computer is 15% off.
15% of $325 is (325*15)/100 = $48.75.
Price of computer after discount = 325-48.75 =$276.25
Now sales tax will be applied on this price.
7% sales tax = 0.07
amount of sales tax = 276.25*0.07 = 19.3375
Price of Computer after sales tax = 276+19.3375 = 295.3375.
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Are the polygons similar? If they are, write a similarity statement and give the scale factor.
The image consists of two quadrilaterals PQSN and AGKD. The lengths of the sides PQ = 10, QS = 7.5, SN = 15, NP = 15, AG = 12, GK = 12, KD = 8 and DA = 6. Angle P is congruent to angle K. Angle S is congruent to angle A. Angle N and G are right angles.
A. no
B. yes; POSN ~ KDAG, scale factor: 5 : 4
C. yes; POSN ~ KDAG, scale factor: 4 : 5
The polygons (quadrilaterals) are similar by the congruency of three interior angles and the equal ratios (5 : 4) of a pair of adjacent sides. The correct option is therefore
B. Yes; PQSN ~ AGKD, scale factor; 5 : 4
What are similar polygons?Similar polygons are polygons that have the same interior angle, and proportional dimensions.
The specified parameters indicate that we have;
Polygon PQSN and AGKD are quadrilaterals
Length of sides of polygon PQSN
Length of side PQ = 10, QS = 7.5, SN = 15, NP = 15
Length of sides of polygon AGKD
AG = 12, GK = 12, KD = 8, DA = 6
The measure of the angles are;
∠K ≅∠S
∠S ≅ ∠A
∠N = ∠G = 90°
The angle sum property of a quadrilateral indicates that the measure of the fourth angle of both quadrilateral are congruent
The ratio of two adjacent sides of the quadrilaterals are;
7.5/6 and 10/8
7.5/6 = 1.25
10/8 = 1.25
Therefore;
[tex]\dfrac{7.5}{6} =\dfrac{10}{8} =1.25[/tex]
The ratio of two adjacent sides of the quadrilaterals PQSN and AGKD are therefore the same.
The three interior angles of quadrilateral PQSN are congruent to three interior angles of quadrilateral AGKD, and the ratio of two adjacent sides from each quadrilateral are the same, therefore, quadrilaterals are PQSN is similar to quadrilateral AGKD
The scale factor of dilation from quadrilateral PQSN to AGKD is 7.5 : 6 = 15 : 12 = 5 : 4
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