If Eric prunes 7 trees, he would earn $85.
To write an equation that relates the number of trees pruned (x) to the amount Eric earns (y), we can use the given data points to determine the pattern or relationship.
From the table, we observe that Eric's pay increases as the number of trees pruned increases, except for the case where he prunes 8 trees.
Based on the data, we can construct a piecewise equation:
For x = 2, 4, and 6:
y = 30 * x
For x = 8:
y = 80
However, we need to consider the case when x = 7. Since this data point is missing from the table, we can assume that the pay is proportional to the number of trees pruned. Therefore, we can interpolate using the given data points for x = 6 and x = 8:
Using the formula for linear interpolation:
y = y1 + (y2 - y1) * ((x - x1) / (x2 - x1))
Substituting the values, we have:
y = 90 + (80 - 90) * ((7 - 6) / (8 - 6))
y = 90 + (-10) * (1 / 2)
y = 90 - 5
y = 85
Thus, if Eric prunes 7 trees, he would earn $85.
It's important to note that the equation and solution are based on the given data points and the assumption of a linear relationship.
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I really need help doing this. please help me.
The bisector angle is angle PQT which is equal to angle RQT.
What is angle bisector?Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.
The bisected angle can be obtained using a pair of compass and a pencil attached to it.
To bisect the given angle RQP; we will take the following steps;
place the compass on exactly point Qexpand the radius of the compass such that the pencil attached to the compass will be in between R and P.strike an arc with the pencil clock wisestrike another arc with the pencil anti clock wise such that the two arc intersects.draw a line from point Q to intersect the two arcs.label the point of intersection of the two arcs Tangle PQT is equal to angle RQTLearn more about bisector angles here: https://brainly.com/question/24334771
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un edificio de 5 metros proyecta una sombra de 4 metros determina la altura que tiene una casa que proyecta una sombra 2 metros
The height of a house that has a shadow projection of 2 meters is given as follows:
2.5 meters.
How to obtain the height of the house?The height of a house that has a shadow projection of 2 meters is obtained applying the proportions in the context of the problem.
The proportional relationship between the height of the building and the height of the shadow is given as follows:
5/4 = x/2
Hence we apply cross multiplication to obtain the height of the house, as follows:
4x = 10
x = 10/4
x = 2.5.
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please help! thank uu ~ :)
Answer:
Unlikely.
Step-by-step explanation:
Possibility Formula: [tex]\frac{Desired Outcome}{Total Possible Outcoes}[/tex]
We want to roll a 5. On a standard six-sided die, then the odds of that happening is [tex]\frac{1}{6}[/tex]
[tex]\frac{1}{6}[/tex] is unlikely.
PLEASE HELP
Which of the following graphs shows an angle that would have an equivalent cosine ratio to the graph shown?
Answer: 150 deg
Step-by-step explanation:
cosine is negative in quadrants 2 and 3. the current angle, 210, is in quad 3. It will have an equal cosine value in quad 2.
that angle will be -210 degrees. in positive terms that is 360-210 = 150 degrees.
thus the answer which shows 150 degrees is correct.
in general:
[tex]cos(x) = cos(-x)[/tex]
Please help. Any unnecessary answers will be reported.
If n! = (2^8)(3^4)(5^2)(7), then what is n? Note that n! = n × (n - 1) × (n - 2) × ... × 1.
Answer:
n = 10
Step-by-step explanation:
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Therefore, n! represents the product of all positive integers from 1 to n.
[tex]\boxed{n!=n \times(n-1) \times(n-2) \times ... \times 1}[/tex]
Given expression:
[tex]n! = (2^8)(3^4)(5^2)(7)[/tex]
The expression for n! has been given as the product of prime factors.
As n! represents the product of all positive integers from 1 to n, begin by writing out the positive integers from 1 in ascending order as the product of primes (using exponents where possible):
[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-14}\vphantom{\dfrac12}n&1&2&3&4&5&6&7&8&9&10&11&12&13\\\cline{1-14}\vphantom{\dfrac12}\sf Product\;of\;primes&1&2&3&2^2&5&3\cdot 2&7&2^3&3^2&5 \cdot 2&11&2^2\cdot 3&13\\\cline{1-14}\end{aligned}\;\;\sf etc.[/tex]
If we examine the prime products of the given expression, we can see that largest prime number 7 appears only once. Therefore, n must be less than 14, since the next time 7 appears as a prime factor is when 2 · 7 = 14.
The prime number 5 appears twice in the given expression.
From the above table, we can see that the first two times the number 5 is present is (1) on its own, and (2) as a factor of 10. Therefore, n must be equal to or more than 10.
The prime number 3 appears four times in the given expression.
From the above table, we can see that the first four times the number 3 is present is (1) on its own, (2) as a factor of 6, (3) & (4) as both factors of 9.
The 5th time prime number 3 is present is as a prime factor of 12. Therefore, n must be less than 12, else 2⁵ would be a factor of n!.
Therefore, we have determined that 10 ≤ n < 12.
As 11 is a prime number and does not appear in the given expression for n!, we can conclude that n = 10.
We can check this by calculating the given expression and 10!:
[tex]\begin{aligned}n! &= (2^8)(3^4)(5^2)(7)\\&=256 \cdot 81\cdot25\cdot7\\&=20738\cdot25\cdot7\\&=518400\cdot7\\&=3628800\end{aligned}[/tex]
[tex]\begin{aligned}10!&=10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=604800 \cdot 3 \cdot 2 \cdot 1\\&=1814400 \cdot 2 \cdot 1\\&=3628800 \cdot 1\\&=3628800\end{aligned}[/tex]
Therefore, this proves that n = 10.
Solve for X
20x+30
28x-10
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
Statement:Corresponding angles are equal.Solution:20x + 30 = 28x - 10 (Corresponding angles)
Add 10 to both sides20x + 30 + 10 = 28x
20x + 40 = 28x
Subtract 20x from both sides40 = 28x - 20x
40 = 8x
Divide both sides by 85 = x
OR
x = 5[tex]\rule[225]{225}{2}[/tex]
sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answer:
sin(3pi/4 ) = -√2/2
So, B.
Name the quadrant in which angle 0 must lie for the following to be true.
Answer:
d
Step-by-step explanation:
PLEASE HELPPP IM CONFUSEDDDD
Answer: C: (-4,-3)
Step-by-step explanation:
You have the correct answer selected!
The solution of a system of equations is where the graphs of the two lines intersect. we can read that point to be (-4,-3), so thats the answer :)
NO LINKS!!!
answer all 4!!!
WILL GIVE BRAINLIEST!!
Answer:
tan T = 12/5
sin A = 12/13
sec Z = 97/65
m<H = 54.5°
Step-by-step explanation:
In general:
sin A = opp/hyp
cos A = adj/hyp
tan A = opp/adj
sec A = 1/cos A = hyp/adj
tan T = 48/20
tan T = 12/5
AB = √(100 + 576)
AB = 26
sin A = 24/26
sin A = 12/13
XZ = √(72² + 65²)
XZ = 97
sec Z = 97/65
tan H = 7/5
H = tan^-1 7/5
m<H = 54.5°
i need help can everyone please help me
Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;
Statement Reason
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
∠BCA ≅ ∠DCA Congruent angles of a triangle (SAS).
AC ≅ AC Reflexive property
ΔABC ≅ ΔADC AAS postulate
What is an angle bisector?In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
By applying the angle bisector theorem to the given triangle, we have the following statements and justifications:
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can reasonably infer and logically deduce that ∠BCA is congruent to ∠DCA i.e ∠BCA ≅ ∠DCA.
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Find the equation of the line.
Use exact numbers.
Answer:
y = 3x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line
1.The volume of a triangular prism is 204cm3 . If its height is 17cm, then find the area of its base.
Answer:
12 cm ^2
Step-by-step explanation:
Using the formula
V=ABh
Solving forAB
AB=V
h=204
17=12cm²
An isosceles right triangle has a third side measurement of 25 inches and a perimeter of 85 inches. The leg of the dilated triangle measures 6 inches. What is the perimeter of the dilated triangle?
How do you find the length of an arc expressed in terms of pi?
The Question is in the Picture, use the Pythagorean theorem to solve and show your work please
Answer:
y=8
Step-by-step explanation:
I need help can someone help me
The two figures are congruent because a reflection and a translation are used to map Figure 1 onto Figure 2.
The angle corresponding to angle M is given as follows: <S.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Lateral or vertical movements.Reflections: A reflection is either over one of the axis on the graph or over a line.Rotations: A rotation is over a degree measure, either clockwise or counterclockwise.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.For this problem, the two transformations are:
Reflection, as the orientation changed.Translation, as the position changed.These two are rigid motions, keeping the side lengths constant, hence the figures are congruent.
Angle S is corresponding to angle M, as they are the angles at the "pointed" vertex of the figure.
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If tanA = 60/11 and sinB = 45/53 and angles A and B are in Quadrant I, find the value of tan(A-B)
Based on the information, it should be noted that the value of tan(A-B) is 234/583.
How to calculate the valueGiven:
tanA = 60/11
sinB = 45/53
A and B are in Quadrant I
We can use the following identity to find tan(A-B):
tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)
Substituting the given values, we get:
tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))
= (15/53)/(295/583)
= 234/583
Therefore, the value of tan(A-B) is 234/583.
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Quentin deposited $1,264 into a savings account that earns 2.75% simple interest annually. What will Quentin’s account balance be at the end of 2.5 years? Assume he makes no additional deposits during that time period.
Answer:
I love math
Step-by-step explanation:
The formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal amount
r = interest rate (as a decimal)
t = time (in years)
In this case, we know that:
P = $1,264
r = 2.75% = 0.0275 (as a decimal)
t = 2.5 years
So, we can plug in these values and solve for I:
I = 1,264 * 0.0275 * 2.5 = $87.55
Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:
Ending balance = $1,264 + $87.55 = $1,351.55
So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.
p: 10 > 7 q: 10 > 5
p →q
F F → T
T F → F
F T → T
T T → T
Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).
Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:
If p and q are both False (F), then p → q is True (T).
If p is True (T) and q is False (F), then p → q is False (F).
If p is False (F) and q is True (T), then p → q is True (T).
If p and q are both True (T), then p → q is True (T).
Given your propositions:
P: 10 > 7
Q: 10 > 5
P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.
Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.
Please do #1 and show work
The solution to the integration of the function given, ∫√(5x - 1) dx, is:
[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]
Understanding IntegrationTo solve the integral of:
√(5x - 1) dx
we can use a u-substitution.
Let u = 5x - 1, then:
du = 5 dx
dx = du/5
Now we can rewrite the integral in terms of u:
∫√(5x - 1) dx = ∫√u * (du/5)
Simplifying the integral:
(1/5) ∫√u du
Integrating √u:
(1/5) * (2/3) * u^(3/2) + C
Where C is the constant of integration
Substituting back u = 5x - 1:
(2/15) * (5x - 1)^(3/2) + C
Therefore, the solution to the integral of √(5x - 1) dx is:
[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]
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The accompanying diagram shows a revolving door with three panels, each of which is 4 feet long. What is the width, w, of the opening between x and y, to the nearest tenth of a foot?
The width, w, of the opening between x and y, is 6.9 ft.
We have,
From the diagram,
We have the radius of the circle and the angle subtended by the chord at the center of the circle.
So,
We can also use the formula.
= 2 x radius x sin(angle/2)
This is the length of the chord.
Now,
radius = 4 ft
angle = 360/3 = 120
Substituting the values.
= 2 x radius x sin(angle/2)
= 2 x 4 x sin (120/2)
= 2 x 4 x sin 60
= 2 x 4 x √3/2
= 4 x √3
= 4 x 1.732
= 6.928
Rounding to the nearest tenth.
= 6.9 ft
Thus,
The width, w, of the opening between x and y, is 6.9 ft.
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f+90+42=180 what is the answer of this
Answer:
hello
the answer is:
f = 180 - 42 - 90 = 48
I WILL GIVE BRAINLIEST, square root of x, find the domain of x
The domain for the square root function is the set of all whole numbers
Calculating the domain of the square root functionFrom the question, we have the following parameters that can be used in our computation:
Function type = square root function
Equation: square root of x
This means that
f(x) = √x
The domain for x in the function is the set of input values the function can take
In this case, the square root function can take any whole number as its input
This means that the domain for f(x) is the set of all whole number
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Which of the following is not a condition for a geometric setting?
The trials are independent
The probability of success is the same for each trial
There are a fixed number of trials
The variable of interest is the number of trials required to reach the first success
There are only 2 outcomes for each trial
There are a fixed number of trials is not a condition for a geometric setting
In a geometric setting, we are dealing with a sequence of independent trials, where each trial can result in either a success or a failure.
The key concept in a geometric setting is the number of trials needed until the first success occurs.
The trials are independent is essential in a geometric setting.
It means that the outcome of one trial does not affect the outcome of subsequent trials.
The probability of success is the same for each trial is also crucial in a geometric setting.
It implies that the probability of achieving a success does not change from trial to trial.
There are a fixed number of trials is not specific to a geometric setting.
The variable of interest is the number of trials required to reach the first success is fundamental to a geometric setting.
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In ΔWXY, w = 320 inches, y = 740 inches and ∠Y=169°. Find all possible values of ∠W, to the nearest 10th of a degree.
Write the equation of the hyperbola
Using the center and distance between co-vertex and center, the equation of the hyperbola is written below
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
What is the equation of hyperbolaA hyperbola, in analytic geometry, is a conic section that is formed when a plane intersects a double right circular cone at an angle such that both halves of the cone are intersected.
The equation of hyperbola is given as;
[tex]\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1[/tex]
where (h,k) is the center of the hyperbola, a is the distance between a vertex and the center, and b is the distance between a co-vertex and the center.
In this case, the center is (10,−3), a=7, and b=12. Therefore, the equation of the hyperbola is
The equation of the hyperbola is;
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
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Complete the square to put
y=3x²-24x + 56 in vertex form.
a) y = 3(x-8)² +4
b) y=3(x-7)² +5
c) y = 3(x-6)² +6
d) y = 3(x - 5)² +7
e) y = 3(x-4)² +8
subtract these polynomials
(3x^-2x+5)-(x+3=
2x² -2x+2 is the polynomial we obtained after subtraction
The given polynomials are (3x²-2x+5)-(x²+3)
Three times of x square minus two times of x plus five minus x square plus three
We have to subtract the polynomials
3x²-2x+5 -x² - 3
Combine the like terms
2x² -2x+2
Hence, the polynomial we obtained after subtraction is 2x² -2x+2
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Ratios are often represented by the symbol. For example, 5 : 4 might mean 5 eggs are needed for every 4 batches of cookies. Select all of the ratios that are equivalent to the ratio 12:3. 6:1 1:4 4:1 246 15:6 120 : 30
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
We have,
To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.
The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.
Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.
Now let's check the given options:
6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.
4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.
246 - This is not a ratio and cannot be compared to the original ratio 12:3.
15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.
Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.
Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.
Thus,
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
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