definition of trapezoid=
A trapezoid is a convex quadrilateral with two parallel sides of opposite length and two unequal sides. Dive into the world of learning and understanding the properties of trapezoids. People usually rely on different shapes to build, create, or measure something. One of the most common shapes is the trapezoid. A two-dimensional shape that represents a table drawn on paper. Trapezoidal patterns can be found on water glasses, table lamps, flower pots, boats, etc. after question
given data,
The measurement of the angle ∠B is
65° + 65° + 115° + ∠B = 360°
∠B = 115°
In that case, the correct choice is D.
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Write an inequality that represents the solutions on the number lines below.
Answer:
just use the number line
-3<x<4
and
x<3
Solve for Side QP. Image attached below.
The length of line QP is [tex]\sqrt{14}[/tex]
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
ΔPOR and ΔPNO are similar since line ON and line QR are parallel.
for similar triangles, the ratio of corresponding lengths is equal.
So that,
QR/ON = QP/NP = PR/OP
but ON = QP
since QR/ON = QP/NP
then
QR/QP = QP/NP
by cross multiplying we have
QP^2 = NP x RQ
but QR =2 and NP = 7
QP^2 = 2 x 7
QP^2 = 14
QP = [tex]\sqrt{14}[/tex]
In conclusion, QP = [tex]\sqrt{14}[/tex]
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1. Mike's age is 5 more than 3 times Sam's age. The sum of their ages is 72. How old
are Mike and Same?
2. The difference between two numbers is 12. Find the two numbers if the larger
number is 5 times the smaller number.
3. Sue and Tom collect baseball cards.
Sue has 8 more than 4 times as many cards as
Tom. The total number of cards they both have is 276. How many cards do they
each have?
Age of Mike is 56 and Sam is 17 years according to given equation.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.
Main body:
Let the age of mike be x and age of sam be y .
According to question :
Mike's age is 5 more than 3 times Sam's age , which means
x = 3y+5 -------(1)
The sum of their ages is 73.
x +y = 73 -------(2)
using eqn 1 in 2,
3y +5 +y = 73
4y = 68
y = 17
x = 3*17 +5
x = 56
hence , age of mike is 56 and sam is 17 years.
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Select the correct answer from each drop-down menu. the expression equivalent to sin 3x sin x is . the expression equivalent to sin 3x− sin x is .
The simplified trigonometric expression in this problem is defined as follows:
sin(3x)/sin²(x) = 3csc(x) - 4sin(x).
How to simplify the trigonometric expression?The trigonometric expression in this problem is defined as follows:
sin(3x)/sin²(x).
The equivalent expression for the sine of 3x is given as follows:
sin(3x) = 3sin(x) - 4 sin³(x).
Then the expression can be written as follows:
(3sin(x) - 4 sin³(x))/sin²(x)
The subtraction is in the numerator, hence the expression can be simplified as follows:
3sin(x)/sin²(x) - 4sin³(x)/sin²(x)
3/sin(x) - 4sin(x)
One divided by the sine is equivalent to the cossecant, hence:
3/sin(x) - 4sin(x) = 3csc(x) - 4sin(x).
Meaning that the first option among those given on the image at the end of the answer is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Lee always uses the y-axis as her vertical line when testing whether a graph represents a function. Why is this strategy flawed? A The y-axis is a horizontal line. B The y-axis is infinitely long. C The y-axis is exempted from the vertical line test. D The y-axis only tests whether x = 0 has been mapped to more than one y coordinate
Answer:
D) The y-axis only tests whether x = 0 has been mapped to more than one y coordinate.
Step-by-step explanation:
The y-axis is a vertical line and intersects the x-axis (horizontal line) at the origin (0, 0) when both x and y are zero.
Vertical line test
A graph represents a function if and only if all vertical lines intersect the graph at most once.
Therefore, the strategy of using only the y-axis as the vertical line in the vertical line test is flawed because the y-axis only tests whether x = 0 has been mapped to more than one y-coordinate.
A submarine is searching for underwater features. It is accompanied by a small aircraft and an underwater robotic vehicle.
At one time the aircraft is 200 m above the surface, the submarine is 55 m below the surface, and the underwater robotic vehicle is 227 m below the surface.
a. What is the difference in height between the submarine and the aircraft?
The difference in height between the submarine and the aircraft is 255m.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, At one time the aircraft is 200 m above the surface, the submarine is 55 m below the surface.
We know length can not be a negative value hence the difference between
the submarine and the aircraft is |200| + |-55|.
= 200 + 55.
= 255m.
Therefore, there is a 255-meter height difference between an aircraft and a submarine.
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Solve the inequality. Enter the answer as an inequality that shows the value of
the variable; for example f> 7, or 6 < w. Where necessary, use <= to write <
and use >= to write 2.
v-(-5) <-9
Solve the inequality. v - (-5) < -9 the solution for the inequality is
v < -14What is inequality?Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
How to solve the inequalityThe given algebraic expression is v - (-5) < -9
This is solved as follows
v - (-5) < -9
v + 5 < -9
v < -9 - 5
v < -14
The value of v is -14
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Just Part C because I already did the other two parts
The equation of g(x) after the transformation is given as follows:
g(x) = 192x^5 - 36x² + 12.
How to obtain the equation of g(x)?The equation for function g(x) is obtained applying the rules for each transformation to the parent function f(x).
The parent function f(x) in this problem is defined as follows:
f(x) = 2x^5 - 3x² + 4.
The first transformation is an horizontal shrink by a factor of 1/2, hence the rule for this transformation is described as follows:
g(x) = f(2x).
Thus:
g(x) = 2(2x)^5 - 3(2x)² + 4
g(x) = 64x^5 - 12x² + 4.
The vertical stretch by a factor of 3 means that all these coefficients are multiplied by 3, that is:
g(x) = 3(64x^5 - 12x² + 4).
Applying the distributive property, we have that:
g(x) = 192x^5 - 36x² + 12.
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help pls braonly to best one
Answer:
m∠1 = 62º
m∠2 = 45º
m∠3 = 24º
Step-by-step explanation:
Angle 1 is supplementary to 118º, so we can solve for its measure by subtracting 118º from 180º.
m∠1 = 180º - 118º = 62º
The interior angles of a triangle are supplementary, so we can solve for it by summing the small triangle's interior angle measures to 180º.
m∠1 + m∠2 + 73º = 180º
62º + m∠2 + 73º = 180º
m∠2 = 45º
Do the same thing as you did for angle 2 for angle 3.
(45º + m∠3) + 62º + 49º = 180º
m∠3 = 24º
Find the inverse of function f.
f(x) = 9x + 7
O A.
OB.
f¹(x) =
O c.
f¹(x) =
O D. f¹(x) =
f¹(x) =
x - 7
7x + 9
-9x - 7
x -
Reset
Next
The Inverse of the Function f(x) = 9x + 7 is (y - 7)/9 = x
What is Inverse of Function?
An inverse in mathematics is a function that helps to "undo" another function. That example, if f(x) generates y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f(-1).
We are given with the function f(x) = 9x + 7
and we wknow that f(x) = y
so, y = 9x + 7
to get the inverse of a function we need to brng the equation in terms of y
y - 7 = 9x
(y - 7)/9 = x
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(a) find the area of r. (b) region r is the base of a solid. for the solid, each cross section perpendicular to the x-axis is a square. write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. (c) the horizontal line y k divides r into two regions of equal area. write, but do not solve, an equation involving one or more integrals whose solution gives the value of k
The area of region R is given by the integral ∫[0,5] (x^2+2) dx = 41.6667,The volume of the solid is given by the integral ∫[0,5] (x^2+2)^2 dx and the equation to find the value of k is given by the equation ∫[0,k] (x^2+2) dx = ∫[k,5] (x^2+2) dx.
a) We must integrate the function (x2+2) over the range [0,5] in order to determine the area of region R. The ensuing integral provides this information:
∫[0,5] (x^2+2) dx = 41.6667
b) To get the solid's volume, we must integrate the function (x2+2)2 over the range [0,5]. The ensuing integral provides this information:
∫[0,5] (x^2+2)^2 dx \sc) We must construct an equation that asserts that the area of the region below the line y=k is equal to the area of the region above the line y=k in order to get the value of k. The following equation yields this:
∫[0,k] (x^2+2) dx = (x2 + x2)[k,5] dx
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in a school walking club, a teacher awards t-shirts to those students who complete their goal of walking 50 miles during a semester. the act of awarding t-shirts to the students is an example of a(n) .
The given statement "a teacher awards t-shirts to those students who complete their goal of walking 50 miles during a semester " is the example for tangible reinforcers.
Tangibles serve as a visual reminder for employees to keep an eye out for desired behaviours and then provide specific positive feedback. . This aided you in completing your assignment quickly and correctly. "You have earned a Tiger Ticket because you followed directions," can improve the student-teacher relationship. You can give the student positive specific feedback without using a tangible (ticket, token, etc.), but a tangible must always be accompanied by positive specific feedback.
Hence, the given statement is an example of tangible reinforcers
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Find the zero of the function f(x)= 4x+8
Answer:
x = -2
Step-by-step explanation:
Solve for x:
4 x + 8 = 0
Subtract 8 from both sides:
4 x + (8 - 8) = -8
8 - 8 = 0:
4 x = -8
Divide both sides of 4 x = -8 by 4:
(4 x)/4 = (-8)/4
4/4 = 1:
x = (-8)/4
8/4 = (4×2)/4 = 2:
Answer: x = -2
Answer:
The zero of the function is at x = -2
Step-by-step explanation:
The graph of the parent function f(x) = x3 is transformed such that g(x) = f(-2x³). How does the graph of g(x) compare
to the graph of f(x)?
The transformation from the parent function are (a) g(x) is horizontally stretch by 1/2 and reflected across the y-axis
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x³
g(x) = (-2x)³
First, we have the transformation to be:
From f(x) = x³ to f'(x) = (−x)³
This means the function is reflected across the y-axis
So, we have the following representation
f'(x) = f(-x)
Next, we have:
From f'(x) = (−x)³ to g(x) = (−2x)³
This means the function is horizontally stretched by a factor of 1/2
Hence, the transformation is reflection across the y-axis and horizontally stretch by 1/2
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What is the value of cose in the diagram below?
R
Y
37
2
Z
2
r=1
(0.6, 0.8)
0
x
The required value of cos( θ ) = 3/5 in the shown figure which is the correct option would be an option (A).
To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) :
x = r × cos( θ ) ....(i)
y = r × sin( θ ) ....(ii)
As per the given question, we have
x = 0.6 and r = 1
Substitute the values of x = 0.6 and r = 1 in the equation (i), and solve for cos( θ )
0.6 = 1 × cos( θ )
0.6 = cos( θ )
cos( θ ) = 0.6
cos( θ ) = 6/10
cos( θ ) = 3/5
Therefore, the required value of cos( θ ) = 3/5.
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A pair of linear equations is shown: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1. On a graph, find the point of intersection of two lines; the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2. On a graph, find the point of intersection of two lines; the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1. On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2
The solution to this pair of equations is the point (2, -1).
Which of the above phrases best describes the stages involved in solving the two equations graphically?On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.To solve these equations graphically, plot both lines on the same graph. For the first equation, plot the y-intercept at (0, 3) and plot each additional point using the slope of -5. For the second equation, plot the y-intercept at (0, -1) and plot each additional point using the slope of -2.Connect the points of each line to create two lines. The point of intersection of the lines is the solution to the pair of equations. The solution to this pair of equations is the point (2, -1).To learn more about linear equations graphically refer to:
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Help solve now please
1. 16%
8/50 = .16 x 100% = 16%
2. 135 x .16 = $21.6
you want to use the summarize() and mean() functions to find the mean rating for your data. add the code chunk that lets you find the mean value for the variable rating. 1 reset what is the mean rating? 1 point 4.230765 3.995445 3.185933 4.701337
You want to use the summarize() and mean() functions to find the mean rating for your data. add the code chunk that lets you find the mean value for the variable rating. 1 reset. the mean rating is 3.185933
How to find the mean rating?To determine the mean value for the variable Rating, you must add the code snippet summarize(mean(Rating)). Trimmed flavors df%>% summarize(mean(Rating)) is the right code. In this section of code:
You can display summary statistics using the summarize() method. To generate specific statistics, you can combine the summarize() method with others like mean(), sd(), and max().
In this instance, you compute the mean value for the variable Rating using the mean() function.
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if you want to know the probability that it is a defective bolt (event c), which formula would you use?
The given probability is based on conditions of two events, hence it is called as conditional probability and it's formula according to the events is option.a [tex]p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(C)}{p(A)}[/tex]
Bayes' rule is a mathematical theorem that allows you to modify probability statements in response to new information. With this rule, you can reverse the conditional probability statement and find the probability of the first event occurring given the probability of the second event occurring by using the probability of the second event occurring given the probability of the first event occurring.The first event in this case is that the bolt is defective (event C). The second occurrence is that it was selected from the first machine (event A). As a result, given that the bolt is from the first machine, we can state the conditional probability that it is defective.
Hence, the formula is [tex]p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(C)}{p(A)}[/tex].
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Your question is incomplete , here is the complete question
In a factory that manufactures bolts, the first machine manufactures 70% of the bolts and a second machine manufactures the remaining 20%. The percentage of defective bolts is 3% and 5%, respectively.An employee picks a bolt off a shelf at random and it is from the first machine (event A).If you want to know the probability that it is a defective bolt (event C), which formula would you use?
[tex]a.\ p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(C)}{p(A)}\\\\b.\ p(\frac{A}{C})=\frac{p(\frac{A}{C}).p(A)}{p(C)}\\\\c.\ p(\frac{C}{A})=\frac{p(\frac{A}{C}).p(A)}{p(C)}\\\\d.\ p(\frac{A}{C})=\frac{p(\frac{C}{A}).p(A)}{p(C)}[/tex]
Question
Solve for x.
3/5(x−7/10)=−314
Enter your answer as a mixed number in simplest form in the box.
x =
Answer:
x = -522 19/30
Step-by-step explanation:
To solve for x, distribute the 3/5. This gives us 3/5x - 21/50 = -314. Add over 21/50 to the other side, allowing for 3/5x to equal -313 29/50. Divide by 3/5 on both sides and we get x equal to -522 19/30. This is the final answer as a mixed number and is also in simplest form.
numbers 6 and 7 please
Answer:
Perimeter WXY = 48
a = 9.75 b = 16.5 c = 21.75
Step-by-step explanation:
13/a = 4/3
a = 9.75
29/c = 4/3
c = 21.75
22/b = 4/3
b = 16.5
Perimeter = 9.75 + 21.75 + 16.5 = 48
A square rug has an area 66 ft2. Write the side length as a square root. Then decide if the side length is a rational number.
Answer:
sqrt66
Step-by-step explanation:
Area of a square is
A = s^2
Here, the area is 66.
66 = s^2
Squareroot both sides to solve.
sqrt66 = s
The side of the square is sqrt66 ft.
This number, sqrt66 is not a rational number because 66 is not a perfect square. Sqrt64 is 8, sqrt81 is 9. But sqrt66 is 8.1240384046 (continuing, neverending, never repeating decimal)
That is not rational.
forty percent (40%) of consumers believe that cash will be obsolete in the next twenty years. assume that 8 consumers are randomly selected. find the probability that:
The probability that less than three of the chosen consumers think that currency won't be used in 20 years is 0.293.
According to the statement, 40% of consumers think cash will be unnecessary in 20 years. Let us assume that eight consumers are chosen at random.
We need to determine the likelihood that fewer than three of the chosen consumers think currency will be obsolete in 20 years.
We will use the properties of probability distribution in the given scenario.
We know that for randomly selected variable the properties of combination are used.
P(X=1) + P(X=2) = C¹₈ × 40 × 60⁷ + C²₈ × 40² × 60⁶
P(X=1) + P(X=2) = 0.293
Therefore, there is a 0.293 percent chance that fewer than 3 of the chosen customers think that cash will be obsolete in 20 years.
The ratio of likely outcomes to all scenarios that are feasible, to all possible outcomes is called probability.
Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.
This claim asserts that under certain conditions, the average of many samples (observations) of a random variable without finite mean and variance is itself a random variable, whose distribution converging to either a normal distribution as the number of samples increases.
Disclaimer: The complete question is :
40% of consumers believe that cash will be obsolete in the next 20 years. Assume that only 8 consumers are randomly selected. Find the probability that less than 3 of the selected consumers believe that cash will be obsolete in the next 20 years .
(Round to three decimal places as needed.)
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A 30" stainless steel smooth-top electric range is on
sale for $479.99, a savings of 20% off the regular price. Find the
regular price.
$600 is the regular price of the stainless steel
How to determine the regular price?Percentage simply means the number or ratio that can be expressed as a fraction of 100. In this case, when we have to calculate percent of a number, we then divide the number by the whole and multiply by 100.
Given: Sales price with discount = $479.99, savings = 20% off. This implies there is a 20% discount.
Let P represent the regular price. Thus, we can write:
P - (20% of P) = $479.99
P - 0.2P = 479.99
0.8P = 479.99
P = 479.99 / 0.8
P = $599.9875 ≈ $600
Thus, the regular price of the stainless steel is $600
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Determine the distance between the points (-5, -3) and (-10, -8).
O√7 units
O √48 units
O√50 units
O√250 units
The distance between points ( -5 , -3 ) and ( -10 , -8 ) is AB = [tex]5\sqrt{2}[/tex] Units
What is Distance Formula ?The Pythagorean theorem is used to calculate the distance between two points using the distance formula. Rewriting the Pythagorean theorem as d = [tex]\sqrt{(x_{1} - x_{2}) ^{2} + (y_{1}-y_{2} ) ^{2} }[/tex] to calculate the separation between any two locations.
According to the given information
Let one point be [tex](x_{1},y_{1})[/tex] = ( -5 , -3 )
Let second point be [tex](x_{2} , y_{2})[/tex] = ( -10 , -8 )
According to the distance formula
AB = [tex]\sqrt{(x_{1} - x_{2}) ^{2} + (y_{1}-y_{2} ) ^{2} }[/tex]
AB = [tex]\sqrt{(-5 + 10) ^{2} + (-3+8 ) ^{2} }[/tex]
AB = [tex]\sqrt{5^{2}+5^{2} }[/tex]
AB = [tex]\sqrt{50}[/tex]
AB = [tex]5\sqrt{2}[/tex] Units
The distance between points ( -5 , -3 ) and ( -10 , -8 ) is AB = [tex]5\sqrt{2}[/tex] Units
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Solve for x.
72x-6-1,154
round to three places
Helppp
The value of 'x' in the expression 72x - 6 - 1154 = 0 is 16.666 rounded to three decimal places.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 72x - 6 - 1154 = 0 and we have to solve for 'x' or find the value of 'x'.
Now,
72x - 6 - 1154 = 0.
72x - 1200 = 0.
72x = 1200.
x = 1200/72.
x = 16.666 rounded to three decimal places.
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Which of these expressions equal 15 when x = and y = 3?
*There is more than correct answer.
ry+3+201
4 (2y-4r) -1
04r²+2y-10
04 (2²+1) + 2x + 3y
0-14r2
The given are the expressions that are equivalent to 15 for [x] = 1/2 and [y] = 3 :
4(2y - 4x) - 1 4(x² + 1) + 2x + 3yxy + 3[tex]\frac{1}{2}[/tex] + 20xWhat is expression in mathematics?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.
Given are the expressions as shown in the image attached.
Let us check the expressions for an equivalent value of 15.
Expression [1] :
4(2y - 4x) - 1
4(2 x 3 - 4 x 1/2) - 1
4(6 - 2) - 1
4 x 4 - 1
16 - 1
15
Expression [2] :
4(x² + 1) + 2x + 3y
4(1/4 + 1) + 2 x (1/2) + 3 x 3
4(5/4) + 1 + 9
5 + 10
15
Expression [3] :
xy + 3[tex]\frac{1}{2}[/tex] + 20x
1/2 x 3 + 7/2 + 20 x 1/2
3/2 + 7/2 + 10
1.5 + 3.5 + 10
15
Therefore, the expressions that are equivalent to 15 when [x] = 1/2 and [y] = 3 are
4(2y - 4x) - 1 4(x² + 1) + 2x + 3yxy + 3[tex]\frac{1}{2}[/tex] + 20xTo solve more questions on functions and expressions, visit the link -
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3 ft
5 ft
4 ft
5 ft
Find the area of this figure.
Round your answer to the
nearest hundredth. Use
3.14 to approximate ™.
A = [?] ft²
Answer:
26.14 ft²
Step-by-step explanation:
The area of the two triangles is 2*(1/2*3*4) = 12 ft².
The area of the semicircle is 1/2*π*3² ≈ 14.14 ft².
The total area is 12 + 14.14 = 26.14 ft².
I’m GIVING BRANILYIST HELPPPP apple seed=1
Apple seeds Johnny planted
at each location
Charleston Louisville Richmond
Location
What is the range of apple seeds planted?
apple seeds
Springfiel
Answer: range is 4.
Step-by-step explanation:
highest apples: 6 at springfield.
lowest apples: 2 at charleston.
subtract.
6-2=4.
One angle measures 130°, and another angle measures (8k + 58)°. If the angles are vertical angles, determine the value of k.
Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure, the value of k is 9.
How to find value of k ?Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure. They are formed when two lines intersect, and they are always congruent, or equal in measure.
That if one angle measures 130°, the measure of its vertical angle must also be 130°.
If the other angle has a measure of (8k + 58)°, and it is a vertical angle to the angle that measures 130°, then it must also have a measure of 130°.
We can set up the equation 130 = 8k + 58 and solve for k to find the value of k.
Subtracting 58 from both sides gives us 72 = 8k. Dividing both sides by 8 gives us k = 9.
Therefore, the value of k is 9.
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