Statements and reasons.
1) ∠1 and ∠3 are supplementary
Reason: This is true because it is stated in the question.
2) ∠1 + ∠3 = 180º
Reason: By statement 1, ∠1 and ∠3 are supplementary, and by definition, supplementary angles sum up 180º.
3) ∠2 = ∠3
Reason: From the picture we see that ∠2 and ∠3 are opposite congruent angles, so they are equal.
4) ∠1 + ∠2 = 180º
Reason: from statement 2 we have ∠1 + ∠3 = 180º, and from statement 3 we have ∠2 = ∠3, so we have ∠1 + ∠2 = 180º.
5) ∠1 and ∠2 are supplementary
Reason: from statement 4 we have that ∠1 sum up ∠2, so by definition ∠1 and ∠2 are supplementary.
6) line m || line n
Reason: from the picture we see that ∠1 and ∠2 are internal collateral angles of the lines m and n, and from statement 5 we know that ∠1 and ∠2 are supplementary, so we have that the angle between line m and line n is 180°, and by definition, they are parallel lines.
Summary of the reasons
1) It is stated in the question
2) By statement 1 and by definition of supplementary angles.
3) Because they are opposite congruent angles, so they are equal.
4) By statement 2 and 3.
5) By statement 4, and by definition of supplementary angles.
6) By picture ∠1 and ∠2 are internal collateral angles of the lines m and n, and by statement 5 they are supplementary so they are parallel lines.
Sheila bought three books for $12.63, $9.05,
and $14.97. How much did she spend?
If the perimeter of the square is 48 m. Find the area of a
circle whose circumference is the same as the square.
The area of the circle is 201 m².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.So, the area of the circle:
The perimeter of square: 4aCircumference of the circle: 2πrWe know that 4a = 2πr, now calculate r as follows:
4a = 2πr48 = 2πrr = 48/2πr = 48/2(3.14)r = 48/6.28r = 7.64Rounding off: 8m
Area of circle:
πr²3.14(8)²3.14(64)200.96Rounding off: 201 m²
Therefore, the area of the circle is 201 m².
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Find the volume of the cylinder (rounded to the nearest tenth).9 in.3 in.
We have the next formula to calculate the volume of the cylinder
[tex]V=\pi r^2h[/tex]where
r is the radius
h is the height
in our problem
r=3in
h=9in
we substitute the values
[tex]V=\pi(3)^2(9)=254.46in^3[/tex]the volume round to the nearest tenth is V=254.5 in ^3
A table is made using the following two patterns.
Pattern x: Starting number: 3, Rule: add 3
Pattern y: Starting number: 6, Rule: add 6
Complete the table for the given patterns.
And then it asks to graph the points from 3 points
The rules of the patterns are 3 + 3x and 6 + 6y
How to complete the pattern?The patterns are given as:
Pattern x: Starting number: 3, Rule: add 3Pattern y: Starting number: 6, Rule: add 6For pattern x, we have the following highlights:
Start = 3
Rule = Add 3
This means that the nth term of pattern x is:
Pattern x = 3 + 3x
For pattern y, we have the following highlights:
Start = 6
Rule = Add 6
This means that the nth term of pattern y is:
Pattern y = 6 + 6y
The complete tableFor pattern x, set x = 0, 1, 2 and 3
So, we have
3 + 3x = 3 + 3(0) = 3
3 + 3x = 3 + 3(1) = 6
3 + 3x = 3 + 3(2) = 9
3 + 3x = 3 + 3(3) = 12
For pattern y, set y = 0, 1, 2 and 3
So, we have
6 + 6x = 6 + 6(0) = 6
6 + 6x = 6 + 6(1) = 12
6 + 6x = 6 + 6(2) = 18
6 + 6x = 6 + 6(3) = 24
Next, we plot the graphs of both patterns (see attachment) where the blue line represents pattern 1, and the other represents the second pattern
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-9^2 x 3
evaluate the experssion!!
Answer:
243
Step-by-step explanation:
-9^2 = -9 * -9 = 81
81 * 3 = 243
The length of a rectangle is eight more than twice it's width. If the length is less than 34,then what is the width?
Answer:
width < 13
Step-by-step explanation:
let width of the rectangle = x
length = 8 + 2x
according to the question,
8+2x < 34
2x < 34-8
2x < 26
x < 13
Simplify the expression ∛81x^7y^9z^5 and please show your work!
By means of algebra properties for powers and roots, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the expression [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].
How to simplify an algebraic expression involving a cubic root operator and powers
In this question we need to simplify an expression by using algebra properties, that is, to transform an expression involving three variables (x, y, z), roots and power operators into an expression with only power operators, that is, where only we see power operators, no root operators of any kind. Now we proceed the entire procedure in detail:
[tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] Given[tex](81\cdot x^{7}\cdot y^{9}\cdot z^{5})^{\frac{1}{3} }[/tex] Relationship between power and roots operators[tex]81^{\frac{1}{3}}\cdot (x^{7})^{\frac{1}{3} }\cdot (y^{9})^{\frac{1}{3} } \cdot (z^{5})^{\frac{1}{3} }[/tex] Power of a product[tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex] Definition of cubic root / Power of a power / Definitions of multiplication and division / Existence of multiplicative inverse / Commutative and associative properties /ResultIn accordance to the algebra properties related to power and radical expressions, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the power product [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].
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Write the perimeter of the triangle as a simplified polynomial. Then factor the polynomial.
Answer:
4x² + 29x + 7 = (4x + 1)(x + 7)
Step-by-step explanation:
Simplify the polynomial:Like terms are terms with same variable and same power.
Perimeter = sum of all the sides
= 3x² + 1 + 15x + 6 + x² + 14x
= 3x² + x² + 15x + 14x + 1 + 6
Combine like terms,
= 4x² + 29x + 7
Factorize:
Sum = 29
Product = 4*7 = 28
Factors = 1 , 28 {28 + 1 = 29 & 28*1 = 28}
Rewrite the middle term using the factors,
= 4x² + x + 28x + 7
= x(4x + 1) + 7(4x + 1)
= (4x + 1)(x + 7)
a certain type of aluminum screen 2 feet in width has, on the average, three flaws in a 100-foot roll. we assume flaws occur randomly so the number of flaws follow some poisson distribution. what is the probability that the first 40 feet in a roll contain no flaws?
The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
CalculationΘ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]
a ) We assume that the length until the first flaw follows an exponential distribution.
Probability density function of exponential distribution:
f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]
The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.
The probability is the integral over the corresponding interval:
the further calculation has been shown in fig. attached
since equation was not possible to write here
b) We assume that the length until the first flaw follows an exponential distribution.
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Marine biologist studies the population of seals in research area. how many Seals are in the research area?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given the frequency table, what percentage of the students that like rap are also in grades 9–10? Round to the nearest whole percent. Show work
A. 16%
B. 38%
C. 40%
The percentage of the students that like rap are also in grades 9–10 is 32%.
Determining the percentage of rap in grades 9-10Given data:
Grade 9-10 for Rap = 40
Row total for grade 9-10 = 125
Now let determine the percentage of rap in grades 9-10 using this formula
Percentage of rap in grades 9-10 = Grade 9-10 for Rap / Row total for grade 9-10
Let plug in the formula
Percentage of rap in grades 9-10 = 40 /125
Percentage of rap in grades 9-10 = 0.32 × 100
Percentage of rap in grades 9-10 = 32%
Therefore we can conclude that 32% is the percentage of rap grade 9-10.
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I NEED HELP FAST
image is the question :)
solve each linear equation 7+2x=4x-3
Answer:
Simplifying
7 + 2x = 4x + -3
Reorder the terms:
7 + 2x = -3 + 4x
Solving
7 + 2x = -3 + 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
7 + 2x + -4x = -3 + 4x + -4x
Combine like terms: 2x + -4x = -2x
7 + -2x = -3 + 4x + -4x
Combine like terms: 4x + -4x = 0
7 + -2x = -3 + 0
7 + -2x = -3
Add '-7' to each side of the equation.
7 + -7 + -2x = -3 + -7
Combine like terms: 7 + -7 = 0
0 + -2x = -3 + -7
-2x = -3 + -7
Combine like terms: -3 + -7 = -10
-2x = -10
Divide each side by '-2'.
x = 5
Simplifying
x = 5
Find the values of x and y.
Answer:
x=71 y=109
Step-by-step explanation:
explain 8 - 5 * 3 from a 7th grader
Answer:
-7
Step-by-step explanation:
5 * 3 = 15. 15 - 8 = 7; so, 8 - 15 = -7.
Garcia's bike rentals, it cost $38 to rent a bike for 9 hours. How many hours of bike use does the customer get per dollar. If necessary, round the answer to the nearest hundredth
From the question, we were told that Garcia's bike rentals cost $38 to rent bike for 9 hours.
We are to find how many hours will a customer use the bike per dollar.
This can also be likened to calculating miles per gallon.
if i can drive 300 miles on 10 gallons of gas then my miles per gallon is 300/10 = 30 mpg.
So, hours per dollar is also a division problem too.
(9 hours)/($38)
= 9/38
= 0.2368
= 0.24 hours per dollar (to the nearest hundredth)
For a project in his Geometry class, Yusuf uses a mirror on the ground to measure the
height of his school building. He walks a distance of 10.25 meters from the building,
then places a mirror flat on the ground, marked with an X at the center. He then
walks 1.65 more meters past the mirror, so that when he turns around and looks
down at the mirror, he can see the top of the school clearly marked in the X. His
partner measures the distance from his eyes to the ground to be 1.55 meters. How tall
is the school? Round your answer to the nearest hundredth of a meter.
Step-by-step explanation:
sadly we don't know anything about the size of the mirror on the ground, or if e.g. the 1.65 m from the mirror mean from the edge of the mirror or from the x at the center of the mirror.
so, we must assume the mirror as a dot without any significant lengths in the calculation.
we have 2 right-angled triangles.
1. the small one : from Yusuf's eyes to the ground at his feet to the x on the mirror on the ground.
2. the large one : from the top of the building to the bottom of the building on the ground to the x on the mirror on the ground.
the mirroring creates a dilation from the large triangle to the small triangle through the point x on the mirror.
in other words, all the angles stay the same, and there is one constant scale factor for all the lengths of one triangle to the other, making both triangles similar.
that means that the scale factor "f" of the ground distances from the small to the large triangle is
10.25 / 1.65 = 1025 / 165 = 6 35/165 = 6 7/33 =
= 6.212121212...
the scaling from Yusuf's height (well, his eye level) to the height of the school must follow the same ratio :
school height / Yusuf's eye level =
= h/1.55 = 10.25/1.65
h = 10.25 × 1.55 / 1.65 = 1025 × 155 / 16500 =
= 9.628787879... m ≈ 9.63 m
the school is approximately 9.63 m tall.
FYI : this is the same principle as with a camera. the lens (and the mirror inside if applicable) create a dilated "projection" onto a film or an array of digital light sensors, so that the captured image retains all the angles and all the length ratios of the original.
but to know from the picture e.g. how tall the original was, we need to know also the distance from which the picture was taken. otherwise this can't be answered.
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the denominator of a fraction is two more than the numerator. if both numerator and denominator are increased by ten, the simplified is 9/10. find the original fraction. (Do not simplify).
Give to each part of the fraction a variable (a letter)
Numerator: n
Denominator: d
the denominator of a fraction is two more than the numerator:
[tex]d=n+2[/tex][tex]\frac{n}{d}=\frac{n}{n+2}[/tex]both numerator and denominator are increased by ten, the simplified is 9/10:
[tex]\frac{n+10}{n+2+10}=\frac{9}{10}[/tex]Use the equation above to find the value of n:
[tex]\begin{gathered} 10(n+10)=9(n+12) \\ 10n+100=9n+108 \\ 10n-9n=108-100 \\ n=8 \end{gathered}[/tex]As n is equal to 8 find the value of d:
[tex]\begin{gathered} d=n+2 \\ d=8+2 \\ d=10 \end{gathered}[/tex]The original fraction is:
[tex]\frac{8}{10}[/tex]Can someone help me with this
Step-by-step explanation:
slope intercept form is: y = ax + b
so, 19x - 19y = 18
-19y = -19x +18
[tex]y = \frac{ - 19x}{ - 19} - \frac{18}{19} [/tex]
[tex]y = x - \frac{18}{19} [/tex]
i hope that this helps
2-3x + 4 + x = -2x + 1
Answer:
No solution
Step-by-step explanation:
2- 3x + 4 + x = -2x + 1
2 -3x + 4 + x = -2x + 1
6 -3x + x = -2x + 1
6 -3x + x = -2x + 1
6 -2x = -2x + 1
6 -2x = -2x + 1
move -2x to the right by adding 2x on both sides
6 -2x = -2x + 1
+2x +2x
6 = + 1
is 6 equal to 1?
No, so No solution
If the temperature drops 5 degrees per hour , what is the change in temperature after 4 hours
Answer: -20 degrees
Step-by-step explanation:
The temperature drops 5 degrees/hour.
Find temperature after 4 hours.
Since we are not given a starting temperature, we can only say how much the temperature has dropped after the 4 hours.
5 degrees/hour x 4 hours = 20 degrees
Temperature has dropped so your answer will be negative.
what is the Riemann Hypothesis??
Answer:
lie on a certain vertical straight line
Step-by-step explanation:
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics.
would you put a closed dot or an open dot on a number line for n > -8?
Answer:
a opened because a closed means that number ond more
Step-by-step explanation:
need help again with a question
Answer: x = 58
Step-by-step explanation:
The angles are alternating interior angles. This means that the angles are equal.
So x = 58
Task 2 given the table and graph, evaluate the following functions:
Answer:
1) -12, 2) 22, 3) 9, 4) 31, 5) 4, 6) 3, 7) 5Step-by-step explanation:
Use table for f(x) related questions and equation for g(x) related questions and both for the last one.
Q1 g(0) = 3*0 - 12 = 0 - 12 = - 12Q2f(0) = 22, the value of f(x) against the x = 0Q3g(7) = 3*7 - 12 = 21 - 12 = 9Q4f(-3) = 31, the value of f(x) against the x = -3Q5g(x) = 0 ⇒ 3x - 12 = 0 ⇒ 3x = 12 ⇒ x = 4Q6f(x) = - 3, x = 3, the value of x against the f(x) = - 3Q7f(g(6)) = f(3*6 - 12) = f(18 - 12) = f(6) = 5, the value of f(x) against x = 6a couple has four children. neither the father nor the mother is bald; one of the two sons is bald, but neither of the daughters is bald. (a) if one of the daughters marries a nonbald man and they have a son, what is the chance that the son will become bald as an adult? (b) if the couple has a daughter, what is the chance that she will become bald as an adult?
If one of the daughters marries a non-bald man and they have a son, the chance that the son will become bald as an adult is 0%
If the couple has a daughter, the chance that she will become bald as an adult is 0%
In the question, we have been given that the neither the father nor the mother is bald, and out of the four children only one son is bald, but the other son and the two daughters are not bald, now we solve the following:
Part a
A chance that the son will become bald as an adult:
If the daughter has no bald gene (XX), and she marries a non bald man then there is 0% chance that the son will become bald as an adult because neither the mom nor the dad has the baldness gene
Part b
The chance that she will become bald as an adult:
If the daughter having a bald gene ([tex]X^{b} X[/tex]) marries a non bald (XY)man then also there is a 0% chance that the daughter will be bald as an adult. As the baldness is a recessive trait, for the daughter to be bald she needs to have two baldness gene( one from father and one from mother). And since this is not the case the daughter might have baldness gene but the phenotype will be non-bald.
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Which is an equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3?
The value that will be equivalent to the expression will be 5625³.
What is an expression?It should be noted that an expression is simply used in Mathematics to illustrate or show the relationship between the variables.
The equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3 will be illustrated as:
= (3² × 5⁴)³
= (9 × 625)³
= 5625³
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Your aunt bought a new television. The television screen is a
rectangle.
The length of the television screen is 54 inches and the width is
30.4 inches.
What is the area of the television screen? What is the perimeter
of the television screen?
Use the given information to complete the worksheet.
Problem apr20 Client Version 7.7.14 Server Version 73.14
O
Length of the Television Screen
Width of the Television Screen
Perimeter of the Television Screen
Area of the Television Screen
DELL
Diagram Label
SC
CR
Area Formulas:
• Parallelogram: A = bh
• Square: A = s²
.
Value
54
30.4
168.8
Triangle: A = bh
•Trapezoid: A=h(b₁+ b₂)
Units
inches
inches
inches
square inches
©2021 Carneg
Oct 13
Answer:
area: 1641.6 square inchesperimeter: 168.8 inchesStep-by-step explanation:
You want the area and perimeter of a rectangle that is 54 inches in length and 30.4 inches in width.
AreaThe area formula is ...
A = bh
We can use the length as the "base" and the width as the "height", so we have ...
A = (54 in)(30.4 in) = 1641.6 in²
The area of the television screen is 1641.6 square inches.
PerimeterThe perimeter of a rectangle is given by the formula ...
P = 2(L +W)
Using the given length and width, the perimeter is found to be ...
P = 2(54 in + 30.4 in) = 2(84.4 in) = 168.8 in
The perimeter of the television screen is 168.8 inches.
The area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.
What is the area of a rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the product of its length and breadth. Its area is the space that the rectangle's boundary encloses.
Mathematically, area of a rectangle = length * width = l * w
What is the perimeter of a rectangle?
The perimeter is defined as the sum of all sides of the rectangle. Mathematically, perimeter of a rectangle = 2(length + width) = 2*(l + w)
Given, the length of the television screen = l = 54 inches
The width of the television screen = w = 30.4 inches
Using the formula mentioned in the literature above,
Area of the television screen = l * w = 54*30.4 = 1641.6 square inches
Also, perimeter of the television screen = l + w = 54 + 30.4 = 84.4 inches
Thus, the area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.
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How do you write 3 and 6/25 as a decimal
Answer: 1.44
Step-by-step explanation:
The fraction 3 and 6/25 is equal to 1.44 when written as a fraction.
Answer:
3.24
Step-by-step explanation:
6/25 can be read as 6 divided by 25, which is 0.24. Add that to 3 and you get 3.24.