Chloe draws three parallelograms. In each figure, she measures a pair of angles, as shown. What is a reasonable conjecture for Chloe to make by recognizing a pattern and using inductive reasoning?
a) In a parallelogram, consecutive angles are supplementary.
b) In a parallelogram, all angles are congruent.
c) In a parallelogram, all angles are supplementary.
d) In a parallelogram, consecutive angles are congruent.
The conjecture Chloe can make based on the given information is that in a parallelogram, consecutive angles are congruent.
Explanation:Chloe's conjecture, based on the pattern she observed, would be that in a parallelogram, consecutive angles are congruent. To support this conjecture, we can explain that a parallelogram has opposite sides that are parallel, and therefore, the opposite angles are congruent. Since the consecutive angles are adjacent to these opposite angles, they must also be congruent.
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If f(x)=2−x12 and g(x)=x2−9, what is the domain of g(x)÷f(x)?
sarah competes in a long jump competion. her first jump is 4.25m. her best jump is 12% more than this. however, her best jump is 15% lower than the winning jump. work out the of the winning jump.
The winning jump is approximately 5.60 meters.
1. We start by denoting Sarah's first jump distance as [tex]\( x \)[/tex] meters.
2. We calculate Sarah's best jump distance, which is 12% more than her first jump, giving [tex]\( 1.12x \).[/tex]
3. We know Sarah's best jump is 15% lower than the winning jump, so we set up an equation equating her best jump to 0.85 times the winning jump.
4. Solving for the winning jump, we find [tex]\( \frac{1.12x}{0.85} \).[/tex]
5. Substituting the value of Sarah's first jump [tex](\( x = 4.25 \))[/tex], we find that the winning jump is approximately 5.60 meters.
Let's denote Sarah's first jump distance as [tex]\( x \)[/tex] meters.
According to the problem:
- Sarah's best jump is 12% more than her first jump: [tex]\( 1.12x \).[/tex]
- Sarah's best jump is 15% lower than the winning jump.
Let's calculate Sarah's best jump distance:
[tex]\[ \text{Best jump} = 1.12x \][/tex]
Now, let's find the winning jump distance:
[tex]\[ \text{Best jump} = 0.85 \times \text{Winning jump} \][/tex]
Since Sarah's best jump equals 0.85 times the winning jump:
[tex]\[ 1.12x = 0.85 \times \text{Winning jump} \][/tex]
To find the winning jump distance, we'll divide Sarah's best jump by 0.85:
[tex]\[ \text{Winning jump} = \frac{1.12x}{0.85} \][/tex]
Now, let's substitute the value of Sarah's first jump:
[tex]\[ \text{Winning jump} = \frac{1.12 \times 4.25}{0.85} \][/tex]
[tex]\[ \text{Winning jump} = \frac{4.76}{0.85} \][/tex]
[tex]\[ \text{Winning jump} \approx \frac{4.76}{0.85} \][/tex]
[tex]\[ \text{Winning jump} \approx 5.60 \][/tex]
So, the winning jump is approximately 5.60 meters.
Complete question
sarah competes in a long jump competion. her first jump is 4.25m. her best jump is 12% more than this. however, her best jump is 15% lower than the winning jump. work out the of the winning jump.
The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. if a room with a perimeter of 70 feet and 8-foot walls requires 5.6 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 65 feet and 10-foot walls
Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?
Answer:
f(x) intersect the x-axis ate ( 4 , 0 ) and ( -1/3 , 0)
Step-by-step explanation:
Given function, [tex]f(x)=3x^2-11x-4[/tex]
We need to find this function cuts x-axis at what point.
let, [tex]y=3x^2-11x-4[/tex]
We know that points on x-axis has y-coordinate equal to 0.
So, we put y = 0 to find value of x.
By putting y = 0, we get
[tex]0=3x^2-11x-4[/tex]
[tex]3x^2-11x-4=0[/tex]
solving by quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-11)\pm\sqrt{(-11)^2-4\times3\times(-4)}}{2\times3}[/tex]
[tex]x=\frac{11\pm\sqrt{121+48}}{6}[/tex]
[tex]x=\frac{11\pm\sqrt{169}}{6}[/tex]
[tex]x=\frac{11\pm13}{6}[/tex]
[tex]x=\frac{11+13}{6}\:\:and\:\:x=\frac{11-13}{6}[/tex]
[tex]x=\frac{24}{6}\:\:and\:\:x=\frac{-2}{6}[/tex]
[tex]x=4\:\:and\:\:x=\frac{-1}{3}[/tex]
Therefore, f(x) intersect the x-axis ate ( 4 , 0 ) and ( -1/3 , 0)
Which of the following is the largest volume? 4.5 x 102 m3 4.5 x 107 cm3 4.5 x 104 dm3 5.0 x 108 mm3 (the 100's are actually 10^2 and other numbers)
Ryan has read 30% of the pages of his book on monday if he read 45 pages how many pages does the book have
Answer:
150
Step-by-step explanation:
30%=45
30%x3=90%
45x3=135
30%/3=10
45/3=15
10%=15
135+15=
150
Suppose a cup of coffee at the campus coffee shop is $2.50 and a cup of hot tea is $1.25. suppose a student's beverage budget is $20 per week. if you were going to write an algebraic expression of this budget line of the form coffee = a + b tea. b would be
Together, teammates pedro and ricky got 2671 base hits last season. pedro had 277 more hits than ricky. how many hits did each player have?
To find out how many hits each player had, we set up a system of equations and solve for the variables. Pedro had 2474 hits and Ricky had 1197 hits.
Explanation:To solve this problem, we need to set up a system of equations. Let's represent the number of hits Pedro had as x and the number of hits Ricky had as y. We are given that their combined hits is 2671, so we can write the equation:
x + y = 2671
Additionally, we are given that Pedro had 277 more hits than Ricky. This can be represented as:
x = y + 277
We can now substitute the second equation into the first and solve for y:
y + 277 + y = 2671
2y = 2394
y = 1197
Now we can substitute the value of y back into the first equation to solve for x:
x + 1197 = 2671
x = 2474
Therefore, Pedro had 2474 hits and Ricky had 1197 hits.
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Explain the error in each statement Three points have to be collinear
In which quadrant is θ located if cscθ is negative and tanθ is positive?
Answer:
[tex]\theta[/tex] is located in 3rd Quadrant.
Step-by-step explanation:
We are given that [tex]cos\,\theta[/tex] is negative and [tex]tan\,\theta[/tex] is positive
We have to find Quadrant in which [tex]\theta[/tex] is located.
We have 4 Quadrants.
In 1st Quadrant , All trigonometric ratios are positive.
In 2st Quadrant , sin and cosec are positive while others are negative.
In 3rd Quadrant , tan and cot are positive while others are negative.
In 4th Quadrant , cos and sec are positive while others are negative.
Therefore, According to given information [tex]\theta[/tex] located in 3rd Quadrant.
Use the square root property of equality to solve (x – 3)2 = –4
Answer:
3+2i
Step-by-step explanation:
Given triangle JKL, sin 38 degree equals
Answer:
B. [tex]\text{cos}(52^{\circ})[/tex].
Step-by-step explanation:
We have been given a right triangle. We are asked to complete our given statement.
[tex]\text{sin}(38^{\circ})[/tex] equals ___.
We will use identity [tex]\text{sin}(x)=\text{cos}(90-x)[/tex] to solve our given problem.
[tex]\text{sin}(38^{\circ})=\text{cos}(90^{\circ}-38^{\circ})[/tex]
[tex]\text{sin}(38^{\circ})=\text{cos}(52^{\circ})[/tex]
Therefore, [tex]\text{sin}(38^{\circ})[/tex] equals [tex]\text{cos}(52^{\circ})[/tex].
joy is planning to purchase a sweater that costs 30$ dollars at her local department store. The sweaters are on sale for for 20% off.
Which steps are needed to find the sale price of the sweater in words?
Answer:24
Step-by-step explanation:
A student rolls a standard number cube. What is the probability the student rolled a 4, given that the number rolled was greater than or equal to 2?
In the southern hemisphere about ________ percent of the surface is land. 55 .019 19 1.9 78
The height H(in feet) of a ball T seconds after it is hit can be modeled by the function H(t)=-16t^2+32t+7
The area of this triangle is 200ft what does x have to be height is 12 feet and base 5x feet
Answer:
x=6.67
Step-by-step explanation:
We are given that area of triangle is 200 square feet .
Height of triangle =12 feet
Base of triangle =5x feet
We have to find the value of x
We know that area of triangle with base b and height h
Area of triangle =[tex]\frac{1}{2}\times b\times h[/tex]
Substitute the values then we get
Area of triangle =[tex]\frac{1}{2}\times 5x\times 12 [/tex]
[tex]200=30 x[/tex]
[tex]x=\frac{200}{30}[/tex]
[tex]x=6.67[/tex]
Hence, x=6.67
How long will it take you to bike a distance of 108 miles at a speed of 24 miles per hour ?
one of the advantages to an employer of pay employees piece-rate or commissions is that the employees paid based solely on their performance what is one disadvantage of this type of pay
Disadvantages of the Piece-Rate Pay System:
Hindered Production -- It's virtually impossible to predict how much product can be created within a set time under this system, because the system doesn’t easily lend itself to regulating and encouraging a production line.
Sick or Injured Workers -- Working for piece-rate pay means that workers might come to work when they are ill, thereby risking the health of their coworkers. This could shut down or seriously reduce production output. Additionally, depending on the materials and equipment, if workers are working too quickly in an attempt to produce more, workers could potentially injure themselves, which could open up the company to liability.
Reduced Quality -- When the focus is on quantity, the output the quality may suffer. Such a system requires dedicated employees who are determined to learn their craft thoroughly and then to increase the output. Employees are human, however, and it can be difficult to work at a rapid pace over a long duration. This can mean that employees may continue to work at a rapid pace but that production may produce items of reduced quality.
(edge 22)
Match the inequality to the graph of its solution.
a. n/4 ≤ -1
b. -10 ≥ -100
c. 5x ≥ 20
Answer:
its B
Step-by-step explanation:
p(5)=-3+4(5) solve please
A woman 5 ft tall walks at the rate of 3.5 ft/sec away from a streetlight that is 12 ft above the ground. at what rate is the tip of her shadow moving? at what rate is her shadow lengthening? ⇒
The rate at which her shadow is lengthening is 2.5ft/sec
Triangular altitude theorem:To get the rate of her shadow lengthening, we will use the similarity theorem of a triangle.
Find the triangle attached. From the triangle;
[tex]\frac{EA}{AC} =\frac{DB}{BC}[/tex]Substitute the sides as given in the diagram:
[tex]\frac{12}{x+a} =\frac{5}{x}\\12x = 5(x+a)\\ 12x=5x+5a\\7x = 5a[/tex]
Differentiate both sides with respect to t
[tex]7\frac{dx}{dt} = 5\frac{da}{dt} \\7\frac{dx}{dt}=5(3.5)\\7\frac{dx}{dt}=17.5\\\frac{dx}{dt} = 2.5ft/sec[/tex]
The rate at which her shadow is lengthening is 2.5ft/sec
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What are the domain and range for the cube root function graphed below? Justify your answer in complete sentences.
If a television is $117.00 and was marked down by 10% then what was the original price
Jennifer spent $150 at a craft fair to rent a booth. she sells knit blankets for $25 each. how would you 1.) wright the equation(slope) 2.) how many blankets does Jennifer need to sell to break even
Answer: Jeniffer wins $25 per blanket. and she must pay $150 to renth the booth.
a) So the equation of Jennifer's profit is P(x) = $25*x - $150.
where x is the number of blankets that she sells, 25*x is positive because that is the money she wins, and the 150 is negative because is the money that she has to pay for the rent.
b) For breaking even, the profit must be equal to zero, it means that she doesn't lose or win anything. Then we do P(x) = 0 = $25*x - $150.
then 25*x = 150
x = 150/25 = 6
So she must sell 6 blankets to break even.
Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use. How much of the 15% alcohol solution should Bruce use?
The amount of 15% alcohol Bruce should use ls 20 mL
Using the equation given in the question :
0.10x + 0.15(50 - x) = 0.12(50)
0.10x + 7.5 - 0.15x = 6
Collect like terms
-0.05 = 6 - 7.5
-0.05x = - 1.5
x = 1.5 / 0.05
x = 30 mL
The amount of 15% solution to be used is related can be calculated thus :
Amount of 15% solution = 50 - x
Amount of 15% solution = 50 - 30 = 20mL
Therefore, 20mL of 15% solution is required.
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Are Abel Fields’s actions protected by the First Amendment?
According to a 2012 decision by the US Supreme Court, Abel Fields's actions are protected by the First Amendment.
In the fictitious case study scenario of Abel Fields, he claimed to have received a Purple Heart for wounds suffered in combat, when in fact he had never served in the military. He asserted his claim as a freedom of speech issue.
In a real-life decision by the US Supreme Court, United States v. Alvarez, the the Court struck down the Stolen Valor Act of 2005 (signed into law by President G.W. Bush in 2006). The law had criminalized false statements about having a military medal. By a 6-3 majority, the Supreme Court determined that the Stolen Valor Act was unconstitutional under the First Amendment's protection of free speech.
According to a 2012 decision by the US Supreme Court, Abel Fields's actions are protected by the First Amendment.
What is the value of x?
A. 25 cm
B. 7 cm
C. 29 cm
D. 35 cm
Answer:
29 cm
Step-by-step explanation:
The central triangle is isosceles, so the length if its right side (x) is the same as the length of its left side (29 cm).
x = 29 cm
I need help with proofs