The solutions are:
[tex]x=-5.372\ and\ x=0.372[/tex]
Step-by-step explanation:The equation is given by:
[tex]2x(x+5)=4[/tex]
on using the distributive property of multiplication in the left hand side of the equation we have:
[tex]2x\times x+2x\times 5=4\\\\i.e.\\\\2x^2+10x=4\\\\i.e.\\\\2x^2+10x-4=0\\\\i.e.\\\\2(x^2+5x-2)=0\\\\i.e.\\\\x^2+5x-2=0[/tex]
Now, we know that the solution of the quadratic equation:
[tex]ax^2+bx+c=0[/tex] is given by:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
[tex]a=1,\ b=5\ and\ c=-2[/tex]
Hence, the solution is:
[tex]x=\dfrac{-5\pm \sqrt{5^2-4\times 1\times (-2)}}{2\times 1}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{25+8}}{2}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{33}}{2}\\\\x=\dfrac{-5+\sqrt{33}}{2},\ x=\dfrac{-5-\sqrt{33}}{2}[/tex]
Hence, in decimal for the solution is:
[tex]x=-5.372\ and\ x=0.372[/tex]
Write a short paragraph to answer the following question.
How are these four types of transformation similar to each other? How do they differ? In particular, what is one major difference between dilations and the other three types of transformations?
Final answer:
Geometric transformations include translations, rotations, reflections, and dilations; while the first three preserve figure size and shape, dilations change the size of the figure by a scale factor.
Explanation:
Geometric transformations include translations, rotations, reflections, and dilations, all of which change a figure's position and/or size on the plane while maintaining the straightness of lines and parallelism where applicable. These transformations are similar in that they can be applied to geometric figures to alter their position or size within a coordinate system. A major difference between dilations and the other transformations is that dilations change the size of the figure but do not preserve angles and lengths in the same way as the others. A dilation either enlarges or shrinks a figure by a scale factor from a central point, while translations, rotations, and reflections do not alter the size of the figure, only its position or orientation.
Question 15 please
Please show work and Thank you for your time
Write 3.35 as a mixed number
Identify a sequence of transformation that maps triangle ABC onto A"B"C" in the image below.
A. Clockwise 270 degrees rotation; reflection over the X-axis
B. Counterclockwise 90 degrees rotation; reduction
C. Counterclockwise 270 degrees rotation; reflection over the Y-axis
D. Enlargement; clockwise 90 degrees rotation
What are the domain and range of the function on the graph
Find the volume of each cone please help me with number 20 please
A candidate to the presidency wants to know what percentage of the registered voters in the country would vote for him. So, he gives that task to one of his aides and tells him he has 3 days to come up with the results. Describe a method the aide should use to complete the task in time and which provides meaningful data. Use size of the sample, population of interest, and method of selection to complete your answer.
Answer:
Since the aide has only 3 days to come up with the results So, firstly he will collect the data of those people only who has the right to vote which is called the population of interest.
The size of the sample will depend on the population of the country.
Finally, for method of selection, a random and wide range of people must be surveyed. Ideally, he would want people from different professions, age groups, political parties, and geographical locations.
Since the aide has only 3 days, the most practical decision may be to use online surveys spread around varying interest groups to collect the information in the given short period of time. Because it is very difficult to collect this information in a very short period of time.
Sylvia has 3/4 of a yad of paper to wrap candles. It takes 1/8 of a yard of paper to wrap each candle. How many candles can Sylvia Wrap?
Sylvia can wrap 6 candles.
To find out how many candles Sylvia can wrap with 3/4 of a yard of paper, we need to divide the total paper by the paper needed for each candle. Since it takes 1/8 of a yard to wrap one candle, we can find the number of candles by dividing 3/4 by 1/8:
3/4 ÷ 1/8 = 3/4 x 8/1 = 6 candles
Therefore, Sylvia can wrap 6 candles with the available paper.
What is the area of this figure ?
Using the relation in Part B, what is the value of x if f(x) = 99?
If i=Square root of -1, what is the value of i^3?
A.-1
B.i
C.1
D.-i
An app developer projects that he will earn $22.00 for every 8 apps downloaded. Write an equation to represent the proportional relationship between the number of apps and the total earnings.
Answer:
y = ($2.750 / app) . x
Step-by-step explanation:
Let's call
x = number of appsy = earned moneyThere is a linear relation between x and y, that follows the general form:
y = a . x + b
where
a is the slope
b is the y-intercept
The slope is:
Δy / Δx = $22.00 / 8 app = $2.750 / app
The, we have
y = ($2.750 / app) . x + b
When x = 0 (no app has been sold), y = 0 (no money has been earned).
0 = ($2.750 / app) . 0 + b
b = 0
The equation representing the proportionality between x and y is:
y = ($2.750 / app) . x
A paper cup is dropped and its landing position is recorded. The cup can land on the side, on the open end, or on the closed end. The results of 20 trials are shown in the table below: A chart shows tally marks. Main title for the chart is Paper Cup Experiment. The title for the second column is Number of times occurred. The tally mark corresponding to open shows a set of 4 vertical lines cut by a slanting line and a set of 3 vertical lines. The tally mark corresponding to closed shows a set of 4 vertical lines. The tally mark corresponding to side shows a set of 4 vertical lines cut by a slanting line and a set of 3 vertical lines. Based on the table, which of the following best compares the experimental probability of the cup landing on its open end with the experimental probability of the cup landing on its closed end?
Order the following sets of numbers from least to greatest 2.1 notation bar,-2.1,2 1/11,-2
Calculate the resistance of a piece of aluminum wire with a diameter of 100 mils and a length of two miles, at 68°F. Hint: Be sure to first convert mils to cmils and use the K value for aluminum found in the reference. (Round the FINAL answer to two decimal places.)
The resistance of the aluminum wire with a diameter of 100 mils and a length of two miles is 0.20 ohms.
Explanation:To calculate the resistance of a piece of aluminum wire, we first need to convert the diameter from mils to cmils. 1 mil is equal to 1000 cmils. So, a diameter of 100 mils is equal to 100,000 cmils. Next, we need to use the K value for aluminum, which is 1.82 ohms * cmil/ft. We convert the length of the wire from miles to feet, which gives us 10560 feet. Now, we can calculate the resistance using the formula:
Resistance = (K * Length) / Area
Where K is the conductivity of aluminum, Length is the length of the wire in feet, and Area is the cross-sectional area of the wire in cmils. Plugging in the values, we get:
Resistance = (1.82 * 10560) / 100000 = 0.1957 ohms
Therefore, the resistance of the aluminum wire is 0.20 ohms.
The resistance of the aluminum wire with a diameter of 100 mils and a length of two miles, at 68°F, is 0.0002784 ohms.
To calculate the resistance of the aluminum wire, we need to convert the diameter from mils to cmils. 1 mil is equal to 1000 cmils.
So, the diameter of the wire in cmils would be 100 * 1000 = 100,000 cmils.
Next, we need to use the K value for aluminum, which is 2.65 micro-ohm cmil/foot. We need to convert the length of the wire from miles to feet. 1 mile is equal to 5280 feet.
So, the length of the wire in feet would be 2 * 5280 = 10,560 feet.
Now, we can calculate the resistance using the formula R = (K * L) / A, where R is the resistance, K is the K value for aluminum, L is the length of the wire in feet, and A is the cross-sectional area of the wire in cmils.
Plugging in the values, we get R = (2.65 * 10^(-6) * 10560) / 100000 = 0.0002784 ohms.
Write 4.4 as a reduced mixed number
What is the range of the function represented by the table?
A {2, 4, 6, 8, 10}
B {2.5, 5.0, 7.5, 10.0, 12.5}
C {2, 2.5, 4, 5.0, 6, 7.5, 8, 10, 12.5}
D {0.0, 0.5}
Answer:
{2.5, 5.0, 7.5, 10.0, 12.5}
Step-by-step explanation:
xfinity cable charges $60 set up fee and $80 a month for cable. direct tv has. a $160 equipment fee and $79 a month for cable services. How many months will it take before the cost is the same? What is that cost?
The correct answer is 100 months, 8060$,
To solve this problem, we need to find the point where the total cost of Xfinity cable and Direct TV cable services become equal, and then calculate the corresponding cost at that point.
Given:
- Xfinity cable charges a [tex]$60[/tex] setup fee and [tex]$80[/tex] per month.
- Direct TV charges a [tex]$160[/tex] equipment fee and [tex]$79[/tex] per month.
Let's define the total cost functions for both cable services:
Xfinity cable total cost ([tex]C_x[/tex]) after x months:
[tex]C_x = 60 + 80x[/tex]
Direct TV total cost ([tex]C_d[/tex]) after x months:
[tex]C_d = 160 + 79x[/tex]
To find the point where the total costs are equal, we set the two equations equal to each other and solve for x:
[tex]60 + 80x = 160 + 79x[/tex]
[tex]x = 100[/tex]
Substituting x = 100 into either equation, we can find the total cost at that point:
[tex]C_x = 60 + 80(100) = 8060[/tex]
[tex]C_d = 160 + 79(100) = 8060[/tex]
Therefore, after 100 months, the total cost of both cable services will be the same at [tex]$8060[/tex].
What is 7.3 x 10^2 = !????
Help!?
Kim rode her bicycle 135 miles in 9 weeks riding the same distance each week. Eric rode his bicycle 102 miles in 6 weeks, riding the same distance each week. Which statement correctly compares the number of miles per week they rode?
A.) Eric rode 2 more miles per week than Kim rode
B.)Kim rode 3 more miles per week than Erick rode
C.) Kim rode 11 more miles per week than Erick rode
D.) Eric rode 17 more miles per week than Kim rode
Answer:
The answer is the option A
Eric rode [tex]2[/tex] more miles per week than Kim rode
Step-by-step explanation:
Step 1
Find the number of miles that Kim rode per week
Divide the total miles by the total weeks
so
[tex]\frac{135}{9}\frac{miles}{weeks}= 15\frac{miles}{week}[/tex]
Step 2
Find the number of miles that Eric rode per week
Divide the total miles by the total weeks
so
[tex]\frac{102}{6}\frac{miles}{weeks}= 17\frac{miles}{week}[/tex]
Step 3
Compare the unit rates
Kim [tex]15\frac{miles}{week}[/tex]
Eric [tex]17\frac{miles}{week}[/tex]
[tex]17\frac{miles}{week}-15\frac{miles}{week}=2\frac{miles}{week}[/tex]
so
Eric rode [tex]2[/tex] more miles per week than Kim rode
HELP EASY I just have a lot more work i need to do, i need 9, 11-14, and 18 show work, please
Describe a real-world situation that the graph could represent
(80 POINTS)
For each pair of shapes, decide whether they are congruent, similar, or neither. Choose the best answer.
The first figure is congruent by SSS congruency.
The second figure is congruent by ASA congruency.
The third figure is congruent by SAS congruency.
The fourth figure is Similar.
The fifth figure is congruent by ASA congruency.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
By first figure,
In both triangles, All sides are equal to each other.
Hence, The first figure is congruent by SSS congruency.
By second figure,
In both triangles, One side and two angles are equal to each other.
Hence, The second figure is congruent by ASA congruency.
By third figure,
In both triangles, Two sides and One angle are equal to each other.
Hence, The third figure is congruent by SAS congruency.
By fourth figure,
In both triangles, Ratio of there corresponding sides are equal as;
⇒ 2 : 4 = 5 : 10
⇒ 1 : 2 = 1 : 2
Thus, The fourth figure is Similar.
By fifth figure,
In both triangles, Two angles and One side are equal to each other.
Hence, The fifth figure is congruent by ASA congruency.
Learn more about the triangle visit:
https://brainly.com/question/17335144
#SPJ2
In which quadrant is the point (0,7) located? Explain your answer.
Mr. Lopez wrote the equation 32g+8g-10g=150 on the board. Four students explained how to solve for g. Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.” Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.” Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is ” Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.” Which student’s work is correct?
Answer:
Wilhem
Step-by-step explanation:
The given equation is
[tex]32g+8g-10g=150[/tex]
Step 1 : Add 32g and 8g.
[tex](32g+8g)-10g=150[/tex]
[tex](32+8)g-10g=150[/tex]
[tex]40g-10g=150[/tex]
Step 2: Subtract 10 from 40.
[tex](40-10)g=150[/tex]
[tex]30g=150[/tex]
Step 3: Divide both sides by 30, find the value of g.
[tex]\frac{30g}{30}=\frac{150}{30}[/tex]
[tex]g=5[/tex]
The value of g is 5.
Therefore, Wilhem is correct.
Answer: D
Wilhem
Step-by-step explanation:
Edge2020
Which statements are correct steps in finding the linear equation of a line that passes through the points (−1, 7) and (2, 4) using the point-slope form method? Select all that apply.
Answer:
y – 4 = –1 (x – 2)
y – 7 = –1 (x – (–1))
y = –x + 6
Step-by-step explanation:
To find the linear equation using the point-slope form method, determine the slope and substitute the coordinates into the formula.
Explanation:To find the linear equation of a line that passes through the points (-1, 7) and (2, 4) using the point-slope form method, follow these steps:
Determine the slope using the formula: slope = (y2 - y1) / (x2 - x1)Choose one of the given points and substitute the coordinates into the point-slope formula: y - y1 = m(x - x1)Simplify the equation to get the linear equation in point-slope formUsing these steps, the correct options are:
a. Find the slope using the formula: m = (4 - 7) / (2 - (-1))
b. Substitute the coordinates (2, 4) into the point-slope formula: y - 4 = m(x - 2)
https://brainly.com/question/32634451
#SPJ2
Which percents would be close to 7%? 4.8% 5.2%. 6.8%. 5.5%
Choosing a graph to fit a narrative ^^
Please help and explain why, so that I understand.
Should the number of people in different cities be represented on a graph as one-dimensional, two-dimensional, or three-dimensional?
A. one-dimensional
B. two-dimensional
C. three-dimensional
Which of the following graphs shows the value of the antique clock, y, in dollars, after x years?