Answer:
[tex]{x, y} = {-\frac{2}{3}, \frac{5}{3}}[/tex]
Step-by-step explanation:
7x + 4y = 2
x + y = 1
// Solve equation [2] for the variable y
[2] y = -x + 1
// Plug this in for variable y in equation [1]
[1] 7x + 4•(-x +1) = 2
[1] 3x = -2
// Solve equation [1] for the variable x
[1] 3x = - 2
[1] x = - 2/3
// By now we know this much :
x = -2/3
y = -x+1
// Use the x value to solve for y
y = -(-2/3)+1 = 5/3
Solution :
{x,y} = {-2/3,5/3}
Approximately what is the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m, as shown in the diagram opposite?
Answer:
212m
Step-by-step explanation:
The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.
Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;
Since we have the angle theta = 45° and opposite = 150m
According to SOH;
Sin theta = opposite/hypotenuse.
Sin45° = 150/hyp
hyp = 150/sin45°
hyp = 150/(1/√2)
hyp = 150×√2
hyp = 150√2 m
hyp = 212.13m
Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m
By applying trigonometry ratio, the length of the rope for the kite to sail would be: 212 m.
Recall:
Trigonometry ratios used to solve a right triangle are: SOH CAH TOAThe diagram describing the situation is attached below (see attachment).
Thus:
The reference angle [tex](\theta) = 45^{\circ}[/tex]
Let the length of the rope be x = Hypotenuse
Opposite = 150 m
To find the length of the rope (x), apply SOH
Thus:
[tex]Sin(\theta) = \frac{Opp}{Hyp}[/tex]
Substitute[tex]Sin(45) = \frac{150}{x}[/tex]
Multiply both sides by x[tex]x \times Sin(45) = \frac{150}{x} \times x\\\\x \times Sin(45) = 150[/tex]
Divide both sides by sin(45)[tex]\frac{x \times Sin(45)}{Sin(45)} = \frac{150}{ Sin(45)} \\\\\mathbf{x = 212 $ m}[/tex]
Therefore, by applying trigonometry ratio, the length of the rope for the kite to sail would be: 212 m.
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The graph shows the wolf population in
Yellowstone National Park aince 2000 A
student drew a line of beat fit to model the
Wolf Population
180
160
150
Number of Wolves
5 130
120
110
100
.
0
2 4 6 8 10 12 14
Years Since 2000
Which statement best describes the line of
best fit that the student drew?
A. The line of best fit is not a strong model
for the data, because the points are not
close to the line.
B. The line of best fit is not a strong model
for the data, because it does not pass
through any of the data points.
C. The line of best fit is a strong model for
the data, because both the line and the
data show a negative trend.
D. The line of best fit is a strong model for
the data, because about half the data
points are on each side of the line.
Answer:
I think D but im not sure
Step-by-step explanation:
A number rounded to the nearest hundred thousand is 400,00. The same number rounded to the nearest ten thousand is 350,000. What could be the number?
Answer:
the number could be between 350,000 and 354,999
Step-by-step explanation:
when calculating to the nearest hundred thousand
for instance, your number is in this format abc,def, the hundred thousand place is determined by "b".
So if the value of b is over 5, when approximating, 1 is added to a.
if the value of b is below 5, when approximating, 0 is added to a.
Therefore, 354,999 to the nearest hundred thousand is 400,000
when calculating to the nearest ten thousand
for instance, your number is in this format abc,def, the ten thousand place is determined by "c".
So if the value of c is over 5, when approximating, 1 is added to b.
if the value of c is below 5, when approximating, 0 is added to b.
Therefore, 354,999 to the nearest ten thousand is 350,000
Can the two triangles be proven congruent by SAS? Explain.
A) No, there's only one pair of congruent angles, ∠B ≅ ∠D, and one pair of congruent sides, ≅ .
B) No, because the two triangles share a side.
C) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel.
D) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel
Answer:
The correct option is;
Yes because AC ≅ AC, ∠B ≅ ∠D, and AD and BC are parallel.
Step-by-step explanation:
Based on the the given information
The number of congruent sides = One which is AC is congruent to AC which is the reflexive property
The number of given congruent angles = One which is angle ∠ABC is congruent to ∠ADC
However, where angle ∠ABC is congruent to ∠ADC, we have AD is parallel to BC, therefore, ∠BAC is congruent to ∠DCB, and BA is parallel to CD, therefore AD is congruent to BC and DC is congruent to AB
Therefore the correct option is yes because AC ≅ AC, ∠B ≅ ∠D, and AD and BC are parallel.
How do you write The product of 2 and a cube of a number
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mila has 9 buttons mia has 225 mia has how many times as many buttons as mila?
Answer:
25
Step-by-step explanation:
divide mia's buttons by mila's
225 / 9
=25
Answer:
Step-by-step explanation:
225 ÷ 9 = 25
Mia has 25 times as many buttons as Mila
Select the representations that do not change the location of the point (6, 170°). a. (-6, 350°) b. (-6, 190°) c. (-6, -10°) d. (6, -190°)
Answer:
b) (_6,198,) 1112334dccfsshh
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 982 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5. It is assumed that the two tests measure the same aptitude, but use different scales.If a student gets an SAT score that is the 20-percentile, find the actual SAT score.SAT score =What would be the equivalent ACT score for this student?ACT score =If a student gets an SAT score of 1437, find the equivalent ACT score.ACT score =
Answer:
Actual SAT Score = 815.284
Equivalent ACT Score = 15.811
The equivalent ACT Score = 29.95
Step-by-step explanation:
From the given information:
Scores on the SAT test are normally distributed with :
Mean = 982
Standard deviation = 198
If a student gets an SAT score that is the 20-percentile
Then ;
P(Z ≤ z ) = 0.20
From the standard z-score for percentile distribution.
z = -0.842
Therefore, the actual SAT Score can be computed as follows:
Actual SAT score = Mean + (z score × Standard deviation)
Actual SAT score = 982 + (- 0.842 × 198)
Actual SAT score = 982 + ( - 166.716)
Actual SAT score = 982 - 166.716
Actual SAT Score = 815.284
Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5.
Mean = 19.6
Standard deviation = 4.5
Equivalent ACT Score = 19.6 + (- 0.842 × 4.5)
Equivalent ACT Score = 19.6 + ( - 3.789)
Equivalent ACT Score = 15.811
If a student gets an SAT score of 1437, find the equivalent ACT score.
So , if the SAT Score = 1437
Then , using the z formula , we can determine the equivalent ACT Score
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z = \dfrac{1437 - 982}{198}[/tex]
[tex]z = \dfrac{455}{198}[/tex]
z =2.30
The equivalent ACT Score = 19.6 + (2.30 × 4.5)
The equivalent ACT Score = 19.6 + 10.35
The equivalent ACT Score = 29.95
the function f(x)=-(x5+)(x+1) is shown. what is the range of the function
Answer:
all real numbers less than or equals to 4
A shipping company borrows $70 million at 5% p.a. compound interest to build a new cruise ship. If it repays the debt after 3 years, how much interest will the company pay?
Answer:
about 11.03 million
Step-by-step explanation:
Use the equation I = P(1+r/100)^n - P (I is the compound interest, P is the principle, r is the rate percent, and n is the number of years):
Substitute the values given:
I = 70,000,000(1 + 5/100)^3 - 70,000,000
Use a calculator to solve and you will get ~11.03 million.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
The interest the company paid is $11 million.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $70 million
r = 5%
t = 3 years
n = 1
A = 70 ( 1 + 0.05)³
A = 70 ( 1.05)³
A = 70 x 1.05 x 1.05 x 1.05
A = $81 million
The amount of interest.
= A - P
= 81 - 70
= $11 million
Thus,.
The interest the company paid is $11 million.
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What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth
Answer:
-0.28 and -2.73
Step-by-step explanation:
4x² + 12x + 3 = 0
(-12 +/- √144-48)/8
(-12 + 9.8)/8 and (-12 - 9.8)/8
-0.28 and -2.73
A number is more than half of another number by 4. The difference of these two numbers is 2. Find these numbers.
Answer:
10,12
Step-by-step explanation:
let the two numbers be x and y
difference between x and y is 2
but y is ½x + 4
x -(½x+4) = 2
x - ½x - 4 = 2
½x = 6
x = 12
y = ½x + 4
y = 10
Which statement is true about the solutions to x^2 - 1 = 24
A. There are two distinct irrational solutions.
B. There are two distinct rational solutions
C. There is only one rational solution
D. There is only one irrational solution
Answer:
B. There are two distinct rational solutions
Step-by-step explanation:
x^2 -1 = 24
Add 1 to each side
x^2 -1+1 = 24+1
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
Answer:
B.
Step-by-step explanation:
x^2 - 1 = 24
x^2 = 25
Taking the square root of both sides:
x = -5, 5.
2 distinct rational solutions.
Please help! Question is given below in form of image!
Answer:
c
Step-by-step explanation:
Answer:
None of the choices are correct.
Step-by-step explanation:
[tex] 9x^3 + 9x^2 - 4x - 4 = 0 [/tex]
The polynomial has 4 terms and no common factors. We can try factoring by grouping.
[tex] 9x^2(x + 1) - 4(x + 1) = 0 [/tex]
[tex] (x + 1)(9x^2 - 4) = 0 [/tex]
Now we factor the difference of squares.
[tex] (x + 1)(3x + 2)(3x - 2) = 0 [/tex]
[tex] x + 1 = 0~~or~~3x + 2 = 0~~or~~3x - 2 = 0 [/tex]
[tex]x = -1~~or~~x = -\dfrac{2}{3}~~or~~x = \dfrac{2}{3}[/tex]
None of the choices are correct.
Roselyn is driving to visit her family, which live 150 150150 kilometers away. Her average speed is 60 6060 kilometers per hour. The car's tank has 20 2020 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 66 kilometers per liter. Fuel costs 0.60 0.600, point, 60 dollars per liter. How long can Roselyn drive before she runs out of fuel?
Answer:
She can go 120 km before she runs out of fuel
It will take 2 hours.
Step-by-step explanation:
150 km is the distance
60 km/ h is the speed
The gas tank is 20 liters
We can go 6 km per liter
Fuel costs .60 dollars per liter
We need to determine how far she can go on a tank of gas
20 liters * 6 km / liter = 120 km
She can go 120 km before she runs out of fuel
120 km = 60 km/ h * x hours
Divide each side by 60
120/60 = x
2 hours
Answer:
Hopes this helps!
Step-by-step explanation:
Which graph represents the solution set of this inequality?
10c + 5 < 45?
Answer:
see below
Step-by-step explanation:
10c + 5 < 45
Subtract 5 from each side
10c + 5-5 < 45-5
10c < 40
Divide by 10 on each side
10c/10 < 40/10
c < 4
Open circle at 4 and the line going to the left
What is happening to this graph when the x-values are between - 1 and 1?
A. It is decreasing.
B. It is constant
C. It is increasing
Answer:
A. It’s decreasing
Step-by-step explanation:
Hey there!
Well on the graph at points -1 and 1 we can tell the line is going down,
meaning the line is decreasing.
Hope this helps :)
Answer:it is increasing
Step-by-step explanation:
answer it answer it answer it
Answer:
22.5
Step-by-step explanation:
cause
Answer:
It is 22.5
Step-by-step explanation:
add up all they shaded parts:
22.5 x 4 = 90 degrees
as each unshaded part is three times more then you do 22.5 x 3 for one part
22.5 x 3 = 67.5 degrees
then times by four because there is four unshaded sections.
67.5 x 4 = 270 degrees
270 + 90 = 360 degrees and there is 360 degrees in a circle so 22.5 degrees is the correct answer.
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----------------------------------------------------------
1. What are the solutions for x when y is equal to 0 in the following quadratic function?
y = x^2 + 4
2. What are the solutions for x when y is equal to 0 in the following quadratic function?
y = x^2 - 81
----------------------------------------------------------
Thank you if you answered!
Answer:
see explanation
Step-by-step explanation:
(1)
x² + 4 = 0 ( subtract 4 from both sides )
x² = - 4 ( take the square root of both sides )
x = ± [tex]\sqrt{-4}[/tex] = ± 2i ← complex solutions
(2)
x² - 81 = 0 ( add 81 to both sides )
x² = 81 ( take the square root of both sides )
x = ± [tex]\sqrt{81}[/tex] = ± 9 ← real solutions
Answer:
1. -2
2. 9
Step-by-step explanation:
1. 0 = x2 + 4
-4 = x2
[tex]\sqrt{-4}[/tex] = x
x = -2
2. 0 = x2 - 81
81 = x2
[tex]\sqrt{81}[/tex] = x
x = 9
MARK IT BRAINLIEST!!!
Use the grouping method to factor x3 + x2 + 2x + 2.
[tex] x^3+x^2+2x+2[/tex]
$x^2(x+1)+2(x+1)=(x^2+2)(x+1)$
Answer:
Step-by-step explanation:
x³ + x² + 2x + 2 = x²(x + 1) + 2(x+1)
= (x + 1) (x² + 2)
We want to build a swimming pool that is 2m by 6m. On our page it measured out to be 8cm by 24cm. What is tge scale that can be used
Answer:
1:25
Step-by-step explanation:
Given
Dimensions of swimming pool:
W = 2 mL = 6 mDimensions on paper:
w = 8 cml = 24 cmScale is the ratio of same measurements:
w/W = 8 cm/2 m = 8 cm / 200 cm = 1/25So the scale is 1:25
I need help with these 2 questions. PLZZ help!!!
Answer:
Step-by-step explanation:
if x is the bill and y is the tip ten
x+y>14.50
x<2 and x≤ 2
when the sign is< then the dot has to be clear , because 2 does not count and x is less than 2 and not equal to 2
when the sign is ≤ the dot on the graph is solid which represent the equal to.
Starting at the same spot on a circular track that is 80 meters in diameter, Hillary and Eugene run in opposite directions, at 300 meters per minute and 240 meters per minute, respectively. They run for 50 minutes. What distance separates Hillary and Eugene when they finish
Answer:
143.32 m
Step-by-step explanation:
Given the following :
Diameter of circular track = 80m
Hillary's speed = 300m per minute
Eugene's speed = 240m per minute
Run time = 50 minutes
Note: they both run in opposite direction.
Calculate the Circumference(C) of the circle :
C = 2πr or πd
Where r = radius ; d = diameter
Using C = πd
C = πd
C = π * 80
C = 251.327
Eugene's distance covered = (240 * 50) = 12000
Hillary's distance covered = (300 * 50) = 15000
Number turns :
Eugene = 12000/ 251.327 = 47.746561
Hillary = 15000/251.327 = 59.683201
Therefore ;
48 - 47.746561 = 0.253439
60 - 59.683201 = 0.316799
(0.253439+0.316799) = 0.570238
Distance which separates Eugene and Hillary when they finish :
0.570238 * 251.327 = 143.32 m
ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
=================================================
Explanation:
Arcs CBH and FGH are given, while arc CDF is unknown. Let's call this y
y = measure of arc CDF
Adding the three arcs forms a full circle of 360 degrees
(arc CBH)+(arc FGH)+(arc CDF) = 360
170+64+y = 360
y+234 = 360
y = 360-234
y = 126
arc CDF = 126 degrees
Then notice how inscribed angle x cuts off arc CDF. By the inscribed angle theorem, we take half of the arc measure to get the inscribed angle measure.
inscribed angle = (arc measure)/2
x = (arc CDF)/2
x = 126/2
x = 63
Answer:
rewrite the fromula 126
Step-by-step explanation:
photo of freedom fighter quotes on white sheet.
pls send me fast
Answer:
Freedom is any case,
is only possible
by constantly
struggling for it.
Albert Einstein
Find the midpoint of the line segment whose endpoints are (2.6,5.1) and (3,4.7).
1. (0.2, 0.2)
2. (1.45, 4.9)
4. (2.8, 4.9)
Answer:
Mid point is: (2.8;4.9)
Step-by-step explanation:
To find midpoint of a line segment we can use the general equation:
[tex]Mid=\frac{x_1+x_2}{2} ;\frac{y_1+y_2}{2}[/tex]
Where the point of the line are: (x₁;y₁) and (x₂;y₂).
In the problem, x₁ = 2.6, y₁ = 5.1 and x₂ = 3 and y₂ = 4.7. Replacing in the equation:
[tex]Mid=\frac{2.6+3}{2} ;\frac{5.1+4.7}{2}[/tex]
Mid point is: (2.8;4.9)Answer:
(2.8, 4.9)
Step-by-step explanation:
Events A and B are mutually exclusive. Find the missing probability.
P(A) = 1/4 P(B) = 13/20 P(A or B) = ?
4/5
1/2
9/10
3/8
Answer:
Option C.
Step-by-step explanation:
It is given that,
[tex]P(A)=\dfrac{1}{4}[/tex]
[tex]P(B)=\dfrac{13}{20}[/tex]
It is given that events A and B are mutually exclusive. It means they have no common elements.
[tex]P(A\cap B)=0[/tex]
We know that,
[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
On substituting the values, we get
[tex]P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0[/tex]
[tex]P(A\cup B)=\dfrac{5+13}{20}[/tex]
[tex]P(A\cup B)=\dfrac{18}{20}[/tex]
[tex]P(A\cup B)=\dfrac{9}{10}[/tex]
Therefore, the correct option is C.
The P (A or B) should be [tex]\frac{9}{10}[/tex]
Given that,
P(A) = 1 by 4 P(B) = 13 by 20Based on the above information, the calculation is as follows:
[tex]= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}[/tex]
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Suppose you start at the origin, move along the x-axis a distance of 5 units in the positive direction, and then move downward along the z-axis a distance of 3 units. What are the coordinates of your position
Answer:(x,z)=(5,-3)
Step-by-step explanation:
Given
We move 5 units in x-axis
3 units in downward along z-axis
Suppose a z-axis is vertical and x -axis is horizontal as shown in fig.
So, coordinates after movement is given by the movement along x-axis and z-axis.
So, final coordinates is (5,-3) in x-z Plane .
As there is no movement in z-axis , so Y-coordinate will remain zero.
True, sometimes true, or false?
The multiple of two consecutive integers is positive
Answer: sometimes true
Step-by-step explanation: if the integers are both positive or both negative, the product will always be positive. If the integers are negative and positive, then the answer will be negatove
Please answer this question now
Answer:
200 cm³ is the volume of the pyramid
Answer:
200 cubic centimeters
Step-by-step explanation:
l = length = 10 cm
w = width = 10 cm
h = height = 6cm
V = lwh / 3
= 10 * 10 * 6 / 3
= 100 * 6 / 3
= 600 /3
= 200 cubic cm
Hope this helps! Tell me if I am incorrect!
