Answers
The measure of ∠EFJ is 60°. Option B is the correct option.
What is a linear pair?
When two lines cross at one point, a linear pair of angles are created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.
∠EFG is a linear pair of angle.
This means ∠E F G = 180°
Given that ∠J F K = 90° and ∠E F J = 2∠K F G.
∠E F G is the sum of angles ∠E F J, ∠J F K and ∠K F G
∠E F G = ∠E F J + ∠J F K + ∠K F G
Now putting the value of ∠E F G, ∠J F K
180° = ∠E F J + 90° + ∠K F G
Again putting ∠K F G = 1/2∠E F J:
180° = ∠E F J + 90° + 1/2∠E F J
180° - 90° = 3/2 ∠E F J
90° = 3/2 ∠E F J
∠E F J = 90° ×(2/3)
∠E F J = 60°.
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Related Questions
Which reason completes the proof for step 6? A. Definition of slope B. Definition of midsegment C. Definition of median D. Definition of midpoint
Answers
The reason that completes the proof for step 6 is given as follows:
D. Definition of midpoint.
How to obtain the midpoint of a segment?The midpoint between two points is the halfway point between them, hence it is found obtaining the mean of the coordinates of each endpoint.
Thus the coordinates of P' are obtained as follows:
x: (2r + 0)/2 = r.y: (2s + 0)/2 = 2.(applying the mean of the coordinates of x and y for the endpoints of the segment P').
The coordinates of R' are obtained as follows:
x: (0 + 2t)/2 = t.y: (0 + 0)/2 = 0.The coordinates of Q' are obtained as follows:
x: (2r + 2t)/2 = 2(r + t)/2 = r + t.y: (2s + 0)/2 = s.Meaning that the correct option is given by option D.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Joshua drove 22 miles in 55 minutes. If he drove at a constant rate, how far did he travel in one hour?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, whole numbers, or decimals.
Answers
If Joshua drove at a constant rate, he drove 24 miles in one hour since he could drive 22 miles in 55 minutes or 0.4 miles per minute (driving speed).
What is the speed?Joshua's driving speed is the quotient of the total distance and the time.
The quotient is the result of a division operation, where a numerator (distance) is divided by the denominator (time) to obtain the unit rate or constant rate.
This constant rate (speed) is multiplied by the time (one hour), according to the distance, time, and speed formula, to obtain the distance to be covered.
The distance covered in 55 minutes = 22 miles
Constant driving speed or rate = 0.4 miles per minute (22/55)
1 hour = 60 minutes
For one hour, the distance Joshua could cover = 24 miles (60 x 0.4)
Thus, we can assert that in one hour, Joshua traveled 24 miles, given his constant driving rate.
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If i scored 88 on one test and a 93 on the other what was the average score
Answers
Explanation:
The average is calculated by adding the numbers and dividing them by the amount of numbers we have. So 88+93 and we get 181
And then we divide it by 2 (181/2)
The average score is 90.5
Step-by-step explanation:
"average" or "mean value" are calculated by adding all data points up and dividing that sum by the number of data points.
e.g. if you eat 1 popsicle today, ate 2 popsicles yesterday and 3 the day before, you have 3 data points : 3, 2, 1.
in my example you had
(3 + 2 + 1)/3 = 6/3 = 2 popsicles every day on average.
the same principle here.
you have 2 days points. and your average score is
(88 + 93)/2 = 181/2 = 90.5
HURRY AND ANWSER BRO ILL GIVE BRAINLIST AND POINT
Question 4(Multiple Choice Worth 2 points)
(Line of Fit MC)
Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 4.05 + 0.4d, where w is the weight of the kitten in ounces and d is the age of the kitten in days.
What is the w-intercept of the line of fit and its meaning in terms of the scenario?
4.05; for each additional day after the kitten is born, its weight is predicted to increase by 4.05 ounces
4.05; a kitten who is just born is predicted to weigh 4.05 ounces
0.4; for each additional day after the kitten is born, its weight is predicted to increase by 0.4 ounces
0.4; a kitten who is just born is predicted to weigh 0.4 ounces
Answers
A kitten who is just born is predicted to weigh 4.05 ounces and its weight is predicted to increase by 0.4 ounces. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Information was gathered on the weight, in ounces, of cats for the initial three months after birth. A line of fit was drawn through the dispersed plot and had the condition w = 4.05 + 0.4d, where w is the heaviness of the cat in ounces and d is the age of the little cat in days.
A kitten who is just born is predicted to weigh 4.05 ounces and its weight is predicted to increase by 0.4 ounces. Then the correct option is B.
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Let f(x)=e^x and g(x). What are the domain and range of (gxf)(x)?
domain: x > 0 range: y > 0
domain: x > 6 range: y > 0
domain: all real numbers range: y > 6
domain: all real numbers range: all real numbers
Answers
Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
What are the domain and range?
The domain and range of a function are the set of all the inputs and outputs a function can give respectively. The domain and range are important aspects of a function. The domain takes all the possible input values from the set of real numbers and the range takes all the output values of the function.
We have the functions, f(x) = eˣ and g(x) = x+6
So, their composition will be g(f(x)).
Then, g(f(x)) = g(eˣ) = eˣ+6
Thus, g(f(x)) = eˣ+6.
Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.
Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.
Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
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Find the area of the rectangle below be sure to include the correct unit in your answer
Answers
Answer:
The area is 48 feet^2
Step-by-step explanation:
The area of a triangle can be calculated with the following formula:
area=1/2(base)(height)
Substitute in the numbers and find the answer.
a=(0.5)(6)(16)=48
3
6
4
8
7
5
Select all the correct answers.
Answers
The statement 4, 6 and 7 is enough to prove that 45° + m∠AOW = 90°.
What is congruence?A harmonious relationship, agreement, or correspondence are all concepts that are denoted by the mathematical term "congruence," which is used in a variety of contexts.
The two geometric figures are said to be congruent, or to be in the relation of congruence, if they can be superimposed on one another so that their entire surfaces match. If two triangles have the same two sides and included angle, they are said to be congruent.
The idea of a "rigid body," which can be moved from one place to another without changing the internal relationships between its parts, appears to be the foundation for congruence.
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The distance from Earth to the sun is about 1.47 X 10^11 meters. The distance from Earth to the moon is 3.71 X 10^8 meters. The distance from Earth to the sun is about how many times larger than the distance from the Earth to the moon? Round your answer to the nearest whole number!
Answers
The distance from Earth to the Sun is 396 times larger than the distance from the Earth to the moon.
Scientific notation.
This is a mode of expressing large numbers of great power. Its helps in the simple expression of numbers so that some arithmetic operations can be performed as required.
In the given question, we have;
distance from Earth to the Sun = 1.47 X 10^11 meters
and
distance from Earth to moon = 3.71 X 10^8 meters
Thus,
to determine by how much is the distance between the Earth and Sun greater than that between the Earth and moon;
n = distance from Earth to the Sun/ distance from the Earth to the moon
= 1.47 X 10^11/ 3.71 X 10^8
= 3.962 x 10^2
n = 396
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Janelle bought a beach chair on sale at 60% of. The original price was 46.95. Find the the amount of discount in dollars
Answers
The amount of discount in dollars is 28.17
To find the amount of the discount, we need to multiply the original price by the percentage that was discounted.
Discount = Original Price x (Discount Percentage/100)
Discount = 46.95 x (60/100) = 28.17
So, the amount of discount in dollars is 28.17
Write the expression as a product of polynomials: p(c–d)+c–d
Answers
The simplified expression as a product of polynomials is given as follows:
(c - d)(p + 1).
How to simplify the expression?
The expression for this problem is defined as follows:
p(c - d) + c - d.
The expression can be defined as an addition in which the terms are given as follows:
p(c - d).(c - d).The common factor to both of the terms of the addition is given as follows:
(c - d).
The quotients of each term relative to the common factor are given as follows:
p(c - d)/(c - d) = p.(c - d)/(c - d) = 1.Hence the simplified expression is given as follows:
(c - d)(p + 1).
(the plus sign for p + 1 is because the expression is an addition and not a subtraction).
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PLSSS HEPP MEEE THYYY
Answers
In November 2018, the frequency tree shows us that 35 students aged 15 years old had part-time work.
That number 35 drops to 23 a year later in 2019. There are two reasons for this:
The student lost their job. They got fired or quit their job.The 15 year old student had a birthday and turned 16.Case (2) mentioned above only works if the student's birthday is before April 2019.
HELP!
The Sum of three consecutive odd integers is 93 Find the integers
Answers
Therefore, the three consecutive odd integers that add up to 93 are 33, 35, and 37.
Find the integers?The sum of three consecutive odd integers is 93. This means that the integers must be odd numbers that come after each other in order.If we look at this problem another way, we can say that the integers must add up to 93.Since odd integers only come in odd numbers, we can divide 93 by 3 to get 31.This means that the three consecutive odd integers must add up to 31 each.Starting with the first integer, we can see that it must be an odd number that is divisible by 3. The first odd integer that is divisible by 3 is 33. Now that we have the first integer, we can use this number to find the other two.To do this, we must add 2 to 33 to get 35. This is the second integer. To get the third integer, we must add 2 to 35 to get 37.To learn more about the integers refer to:
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cylinder has a volume of 2,034.72 cubic millimeters and a radius of 6 mm, whats the height?
Answers
Answer:
2,260.80 cubic millimeters
Step-by-step explanation:
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters
ANYONE GOOD AT MATH! PLEASE HELP!
Answers
Answer:
To find f(2), we substitute 2 for x in the equation of the parabola F(x) = x^2 - 2x - 3:
F(2) = 2^2 - 2(2) - 3 = 4 - 4 - 3 = -3
So f(2) = -3
To find g(-3), we substitute -3 for x in the equation of the line g(x) = x - 2:
g(-3) = -3 - 2 = -5
So g(-3) = -5
The correct solution to this question is as follows:
f(2)= -3 & g(-3)=-5
Step-by-step explanation:
[tex]f(x)=x^{2} -2x-3[/tex]
[tex]f(2)=2^{2} -2(2)-3[/tex]
[tex]f(2)=4 -4-3[/tex]
[tex]f(2)=-3[/tex]
[tex]g(x)=x-2[/tex]
[tex]g(-3)=-3-2[/tex]
[tex]g(-3)=-5[/tex]
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solve w/4+11/12=1/2-w/6
Answers
The simplified value of the equation is w = -1.
What is simplification?To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given equation w/4 + 11/12 = 1/2 - w/6
the equation is written as,
w/4 + w/6 = 1/2 - 11/12
solving by LCM
(3w + 2w)/12 = (6 - 11)/12
5w = -5
w = -5/5
w = -1
Therefore the value of w is -1.
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solve for x and 5x+2y=9
Answers
Answer:
Step-by-step explanation:
242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424 242424242424242424242424242424242424how to identify what type of shape ABCD is if A is (-3,0), B (1,5), C(-3,10) and D(-7,5) the slope of BC=-5/4 and the length of DA=6.4
Answers
The shape of the ABCD is a rhombus. The diagonals are not equal to each other.
What is the 2-dimensional shape?
A 2d shape is a two-dimensional shape with horizontal and vertical axes (x-axis and y-axis). 2D shapes are flat shapes with only length and width. These shapes have no thickness or height.
Given the vertices of ABCD are A(-3,0), B (1,5), C(-3,10) and D(-7,5).
The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4
The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4
The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10
The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8
The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of AB is (5-0)/(1-(-3))=5/4
The slope of BC is (10-5)/(-3-1)=-5/4
The slope of CD is (5-10)/(-7-(-3))=5/4
The slope of AD is (5-0)/(-7-(-3))=-5/4
The number of vertices of the quadrilateral is 4.
Thus it is either a square or rectangle or rhombus or parallelogram.
Since the length of all sides is equal thus it is either a square or rhombus.
Since the diagonals are not equal it is a rhombus.
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You go to the mall to buy some new shoes. You have a coupon for $25 off the price of a pair of
shoes. When you arrive at the store, you find out that the shoes are on sale for 25% off. If
c(x) = x - 25 represents the cost of the shoes with your coupon and s(x) = 0.75x is the cost
of shoes after the markdown, which of the following composition functions represents receiving
the sale price of the shoes and then applying the coupon?
Answers
Answer:
50%
Step-by-step explanation:
25%+25%
The composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.
Given that, c(x) = x - 25 represents the cost of the shoes with your coupon and s(x) = 0.75x is the cost of shoes after the markdown.
Here, the composition function is
c(s(x))= 0.75x-25
Therefore, the composition functions represents receiving the sale price of the shoes and then applying the coupon is c(s(x))= 0.75x-25.
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How to solve this equation -7^2-(-1)
Answers
-7^2 = 49
49-(-1) = 49+1
49+1= 50
Final answer is 50
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For problems 11 and 12, plot the points in the coordinate plane. Then find the perimeter and area of the polygon.
11. A(-2, 1), B(2, 5), C(5, 1) (round your answers to the nearest tenth.)
Perimeter:______________
Area: __________
12. A(-3, 5), B(1, 6), C(3, -2), D(-1, -3)
Perimeter:
Area:
Answers
Given vertices:
A(-2, 1), B(2, 5), C(5, 1)Plot the points (see attached).
AC is the base of the triangle:
AC = 5 - (-2) = 7 unitsAdd BD, the height. It will help to find the length of the other two sides and the area:
AD = 4 units and DC = 3 units (from the graph)BD = 5 - 1 = 4 unitsFind AB and BC using Pythagorean:
[tex]AB = \sqrt{4^2+4^2}=\sqrt{32} =5.7\ units[/tex][tex]BC=\sqrt{4^2+3^2}=\sqrt{25}=5\ units[/tex]Perimeter: 7 + 5.7 + 5 = 15.7 units
Area: 1/2*7*4 = 14 units²
Question 12Given vertices:
A(-3, 5), B(1, 6), C(3, -2), D(-1, -3)Plot the points (see attached).
As we see this is a rectangle.
Find two adjacent sides using distance equation:
[tex]AB = \sqrt{(1 - (-3))^2+(6-5)^2} =\sqrt{16+1}=\sqrt{17}=4.1\ units[/tex][tex]AD = \sqrt{(-1 - (-3))^2+(-3-5)^2} =\sqrt{4+64}=\sqrt{68}=2\sqrt{17} =8.2\ units[/tex]Perimeter: 2(4.1 + 8.2) = 2(12.3) = 24.6 units
Area: √17 * 2√17 = 2*17 = 34 units²
Answer:
11. Perimeter: 17.7 units
11. Area: 14 square units
12. Perimeter: 24.7 units
12. Area: 34 square units
Step-by-step explanation:
Question 11Given vertices of the polygon:
A = (-2, 1)B = (2, 5)C = (5, 1)Plot the given points in the coordinate plane (see attachment 1).
From inspection, we can see that the polygon is a triangle with the following dimensions:
Base = 7 unitsHeight = 4 units[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
The length of AC is 7 units.
To find the length of AB and BC, use the distance formula.
[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(2-(-2))^2+(5-1)^2}\\&=\sqrt{(4)^2+(4)^2}\\&=\sqrt{16+16}\\&=\sqrt{32}\\&=4\sqrt{2}\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(5-2)^2+(1-5)^2}\\&=\sqrt{(3)^2+(-4)^2}\\&=\sqrt{9+16}\\&=\sqrt{25}\\&=5\;\sf units\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Perimeter}&=AB+BC+AC\\&=4\sqrt{2}+5+7\\&=12+4\sqrt{2}\\&=17.6568542...\\&=17.7\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{2}\cdot 7\cdot 4\\\\&=\dfrac{7}{2} \cdot 4\\\\&=\dfrac{28}{2}\\\\&=14\;\sf square\;units\end{aligned}[/tex]
Question 12Given vertices of the polygon:
A = (-3, 5)B = (1, 6)C = (3, -2)D = (-1, -3)Plot the given points in the coordinate plane (see attachment 2).
From inspection, we can see that the polygon is a rectangle.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Since AB = DC and BC = AD, find the length of AB and BC using the distance formula.
[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-3))^2+(6-5)^2}\\&=\sqrt{(4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(3-1)^2+(-2-6)^2}\\&=\sqrt{(2)^2+(-8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\\&=2\sqrt{17}\;\sf units\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Perimeter}&=AB+BC+CD+AD\\&=2(AB+BC)\\&=2(\sqrt{17}+2\sqrt{17})\\&=2(3\sqrt{17})\\&=6\sqrt{17}\\&=24.7386337...\\&=24.7\;\sf units\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area}&=AB\cdot BC\\&=\sqrt{17} \cdot 2\sqrt{17}\\&=34\;\sf square\;units\end{aligned}[/tex]
A study was developed to evaluate effectiveness of a weight loss diet plan. An ad was placed in two towns to locate study participants who were to follow the diet. In Town A, the clinicians asked each dieter to report how much weight they had lost over the previous 6 weeks while following the diet. In Town B, the clinicians weighed each dieter at the beginning of the study and again after 6 weeks on the diet program. The weight lost was calculated as the difference between the beginning weight and the weight after 6 weeks. At the end of the study, it was determined that Town B had lost significantly less weight than Town A. a) What is the population of interest in this situation? b) Identify source(s) of bias in this study.
Answers
Answer:
a) The population of interest in this situation is individuals who are following a weight loss diet plan.
b) There are several sources of bias in this study:
Self-report bias: Town A relies on self-reported weight loss, which may not be accurate as participants may not accurately report their weight loss or may exaggerate their progress.
Measurement bias: Town B uses a different method of measuring weight loss than Town A, which could introduce a bias in the results.
Selection bias: Participants in this study are self-selected, which means that individuals who are more motivated or more likely to succeed in the diet may be more likely to sign up for the study. This can lead to a bias in the results as the sample may not be representative of the population of interest.
Hawthorne effect: Participants in Town B may have changed their behaviors simply because they knew they were being weighed, which could lead to a bias in the results.
Placebo effect: Participants in Town A may have lost weight due to the mere act of participating in a study and receiving attention, which could lead to a bias in the results.
FInd the half-life of a radioactive element, which decays according to the function A(t)= A0e^-0.0372t, where t is the time in years
Answers
Answer:
below
Step-by-step explanation:
1/2 = e^(-.0372t) ln both sides to get :
-.693147 = - .0372t then t = 18.6 yrs
HELP I NEED HELP IVE BEEN STUCK IN THIE FOR 3 HOURS STRAIGHT
Answers
Answer:
OK the so the answer is this,
A - Irregular - It is an irregular polygon as the sides and angles are unequal.
B - Neither - As circle is not a polygon.
C - Irregular - Again, it is an irregular for the same reason.
D - Regular - Sides and angles are equal
E - Regular - Equilateral triangle
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Find the area of the shaded region of the shapes below. (Label Units.)
Answers
Answer:
1) 216 units², 2) 138 units²-------------------------------------
Top figureWe know that the area of a rectangle with same dimensions is twice the area of a triangle.
The shaded area is half the area of the rectangle:
A = ab/2 = 18*24/2 = 216 units²Bottom figureYou already divided it to rectangle and triangle.
Area of rectangle:
A = ab = 10*12 = 120 units²The triangle have same base, 12 units. It height is 16 - 10 = 6 units.
Its area is:
A = bh/2 = 12*6/2 = 36 units²Area of the small rectangle in the middle:
A = 6*3 = 18 units²The shaded area is the difference of the total area and the small rectangle:
Shaded area = 120 + 36 - 18 = 138 units²The sum of an A.P. is 340, the first term is 7 and the common difference is 6.
Calculate the number of terms in the sequence
Answers
The number of terms (n) in the sequence = 10.
We know that,
S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}
Where,
S = Sum of A. P. series
n = number of terms in A. P. series
a = first term of the series
d = common difference
According to the question,
Sum of the series, S = 340
First term, a = 7
Common difference, d = 6
S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}
340 = [tex]\frac{n}{2}[/tex] {2*7 + (n-1)6}
340 = [tex]\frac{n}{2}[/tex] {14 + 6n - 6}
340*2 = n( 6n + 8)
680 = 6n^2 + 8n
6n^2 + 8n - 680 = 0
2 (3n^2 +4n - 340) = 0
3n^2 +4n - 340 = 0
3n^2 + 34n - 30n - 340 = 0
n (3n+ 34) - 10 (3n + 34) = 0
(3n + 34) (n - 10) = 0
if we take, 3n + 34 = 0
3n = - 34
n = -34/3
which is not possible, as the number of terms can not be negative
if we take, n- 10 = 0
n = 10
Hence, the number of terms in the given A. P. series is 10.
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Every week, Estella has guitar lessons.
A guitar is shown. The caption says that Guitar Lessons are thirty-five dollars per lesson.
Question 1
Part A
Complete the expression to represent the change in Estella’s account balance due to guitar lessons after 2 years.
Answers
1. The completion of the mathematical expression to represent the change in Estella's account balance due to guitar lessons after 2 years is 52 - 35x, where x is the number of years.
2. After two years, the account balance will be $-18, without reflecting interest.
What is a mathematical expression?A mathematical expression is a combination of variables, constants, numbers, and mathematical operands (addition, subtraction, division, and multiplication).
A mathematical expression may not convey any meaning since it sounds like a phrase in the English language that does not make complete sense.
The unit rate (cost per lesson) for guitar lessons = $35
Estella's account balance = $52
Let the number of years = x
Lesson period, x = 2 years
Mathematical Expression: 52 - 35x
Solution: 52 = 35(2)
= $-18
Thus, after 2 years of guitar lessons, Estella will be indebted to the bank by $18 if she does not deposit an additional amount in her account.
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Question Completion:Expression: 52 - 35
Set up and solve a proportion for the following application problem. If 3 pounds of grass seed cover 403 square feet, how many pounds are needed for 6045 square feet? HELP
Answers
The number of pounds needed for 6045 square feet will be 45.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If 3 pounds of grass seed cover 403 square feet.
The ratio of the number of pounds of seed to the area that covers the seed.
Let 'x' be the pounds needed of seed. Then the equation is given as,
x / 6045 = 3 / 403
x = 6045 × 3 / 403
x = 15 · 3
x = 45
The number of pounds needed for 6045 square feet will be 45.
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Vanessa picked 12 strawberries. She divided the strawberries and gave 1/3 to her brother. She kept the rest for herself. How many strawberries did she give her brother.
Answers
Answer: 4 strawberries
Step-by-step explanation:
First, we can change the total number of strawberries into a fraction, that way it makes the division process easier. 12 is really equivalent to 12/1 since it is a whole number. Now, we can set up an equation: (12/1) * (1/3) will solve to give us the number of strawberries the brother has. Since there is a one in both the numerator and the denominator, they will cancel, leaving us with (12/3). This is now just division, which gives us 4. Therefore, the brother will receive 4 strawberries. Hope this helps!
Hot dogs come in packages of 10. Buns come in packages of 8. What is the least number of packages of each you have to buy to have the same number of hot dogs and buns? Drag and drop an answer into each box to complete the statement. You need to buy packages of hot dogs and 1 4 5 packages of buns. 8 10 12
Answers
Therefore , the solution of purchased so that the consumer has an equal amount of each LCM if hot dogs are packaged with 10 dogs per pack .
How many hot dog buns are included in a package?"Sandwich rolls or hot dog buns are typically sold in packs of eight because the buns are baked in clusters of four in pans designed to hold eight rolls." Because hot dogs are sold by the pound and store-bought standard-sized hot dogs weigh 1.6 ounces,
Here,
purchased so that the consumer has an equal amount of
each if hot dogs are packaged with 10 dogs per pack and hot dog buns are packaged with 8 buns per pack LCM is 40.
hot dog buns are packaged with 8 buns per pack LCM is 40. 4 packages of hot dogs and 5 packages of buns are required.
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A computer and printer cost a total of $1056. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Answers
Answer:
Hope This Helps <3
Step-by-step explanation:
Printer cost 265
Computer cost 795
