Answers
Answer: The square root of 169 is 13, so the two solutions for x are:
x = (13 + 13) / 4 = 3.25
x = (13 - 13) / 4 = -0.25
Since the quadratic expression 2x^2 - 13x - 5 equals 0 when x is either 3.25 or -0.25, the factors of this expression are (x - 3.25)(x + 0.25).
In summary, the factors of the first quadratic expression are (x + 1.056)(x + 5.937), the factors of the second expression are (x - 0.75)(x + 3.75), and the factors of the third expression are (x - 3.25)(x + 0.25).
Step-by-step explanation: To find the factors of a quadratic expression, we can use the quadratic formula. The quadratic formula states that for a quadratic expression of the form ax^2 + bx + c = 0, the solutions for x are given by the formula x = (-b ± sqrt(b^2 - 4ac)) / (2a).
In the first equation, a is 9, b is 31, and c is 20. Plugging these values into the quadratic formula, we get:
x = (-31 ± sqrt(31^2 - 4 * 9 * 20)) / (2 * 9)
This simplifies to:
x = (-31 ± sqrt(961 - 720)) / 18
This further simplifies to:
x = (-31 ± sqrt(241)) / 18
We can find the value of the square root by using a calculator or by remembering some common square roots. The square root of 241 is approximately 15.937, so the two solutions for x are:
x = (-31 + 15.937) / 18 = -1.056
x = (-31 - 15.937) / 18 = -5.937
Since the quadratic expression 9x^2 + 31x + 20 equals 0 when x is either -1.056 or -5.937, the factors of this expression are (x + 1.056)(x + 5.937).
We can use the same approach to find the factors of the other two quadratic expressions. For the second expression 2x^2 + 7x - 4, the values of a, b, and c are 2, 7, and -4, respectively. Plugging these values into the quadratic formula, we get:
x = (-7 ± sqrt(7^2 - 4 * 2 * -4)) / (2 * 2)
This simplifies to:
x = (-7 ± sqrt(49 + 32)) / 4
This further simplifies to:
x = (-7 ± sqrt(81)) / 4
The square root of 81 is 9, so the two solutions for x are:
x = (-7 + 9) / 4 = 0.75
x = (-7 - 9) / 4 = -3.75
Since the quadratic expression 2x^2 + 7x - 4 equals 0 when x is either 0.75 or -3.75, the factors of this expression are (x - 0.75)(x + 3.75).
For the third expression 2x^2 - 13x - 5, the values of a, b, and c are 2, -13, and -5, respectively. Plugging these values into the quadratic formula, we get:
x = (13 ± sqrt(13^2 - 4 * 2 * -5)) / (2 * 2)
This simplifies to:
x = (13 ± sqrt(169 + 40)) / 4
``
Related Questions
The ratio of two numbers is 5:6. The product of these numbers is 120. What is the smaller of these two numbers?
Answers
The smaller of the two number is 10.
What are Ratios?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.
Given:
Ratio of two Positive number = 5:6
Let , the smaller number be 5x
then , the bigger number = 6x
According to the question,
product of these numbers = 120
Therefore,
[tex]5x * 6x = 120\\30x^{2} = 120\\x^{2} =4\\x = 2[/tex]
Smaller number = 5x = 5*2 = 10.
Hence, the smaller of the two number is 10.
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1. A painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until
they used all the paint. Sketch a graph to represent the start to the end of the job, assuming all paint was
used Be sure to title your graph, label your axes, and label your intercepts. This must be graphed by hand
or by using the tools in Word. a You may not use a web-based graphing program.
Answers
The equation is 55 = 5t and the graph is attached with the answer.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until they used all the paint.
The equation can be written as,
55 = 5t
Here, t is the number of hours.
The graph is attached with the answer below.
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a linear function has slope of -5/3. What does the slope tell us about the graph of the function
Answers
Answer:
Step-by-step explanation:
The slope of a linear function is a measure of the rate at which the value of the function changes as the input (x) changes. A slope of -5/3 means that for every 3 units of change in the input, the output (y) changes by -5 units.
In general, a negative slope indicates that the graph of the function is decreasing. As the input increases, the output decreases. A slope of -5/3 is a relatively steep negative slope, which means that the graph of the function will have a steep downward slope.
A slope of -5/3 also tells us that the function is not a horizontal line. A horizontal line has a slope of 0, which means that the output does not change as the input changes. A slope of -5/3 is not equal to 0, which means that the function is not a horizontal line.
Overall, the slope of a linear function tells us about the direction and steepness of the graph of the function. A slope of -5/3 indicates that the graph of the function is decreasing and relatively steep.
Which expression is equivalent to this polynomial?
15x - 24
A.3(5x-8)
B. 5(3x-8)
C. 3(5x-24)
D.3(5x - 5)
Answers
Answer: A 3(5x-8)
Step-by-step explanation: 3 times 5x is 15x and 3 times -8 is -24
1. (*) Tres amigos, Alex, Beto y Valentín, van al cine y se sientan en una fila de tres asientos contiguos vacíos. Si se sabe que:
• Alex se sienta adyacente a Beto y Valentín.
• Valentín se sienta a la derecha de Beto.
¿Cuál es el orden en que se sientan dichos amigos, empezando de izquierda a derecha?
Beto, Alex, Valentín
O Valentín, Beto, Alex
Valentín, Alex, Beto
O Alex, Valentín, Beto
Answers
By using the concept of arrangement, it can be concluded that-
The correct order is Beto, Alex, Valentin
What is arrangement?The act of arranging people and things towards a certain goal is referred to as arrangement. the arrangement or arrangement of details in a written work. Readers to whom a piece of writing is addressed; those who read or hear what you have written.
Why is writing arrangement crucial?Your reader could feel disoriented and lose interest if there is no obvious organizational structure. Your essay's organization will aid readers in making connections between the essay's body and thesis, as well as help you stay on task as you plan and compose the essay.
It is known that:
• Alex sits next to Beto and Valentin.
• Valentin sits to the right of Beto.
So the correct order is Beto, Alex, Valentin
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What is the value of x?
Answers
Answer: 71
Step-by-step explanation:
Calculate c, ∠B, and ∠A based on given b, a, and ∠C.c = √b2 + a2 - 2ba·cos(C) = 13.67386∠B = arccos(c2 + a2 - b22ca)= 1.23918 rad = 71°∠A = arccos(c2 + b2 - a22cb)= 1.23918 rad = 71°
In the diagram below, OQ = 25, PM = 9, and QN = 15. Find the length of OP.
Round your answer to the nearest tenth if necessary.
0
Answer: OP |
P
M
Q
N
Submit Answer how do I come up with the number
Answers
In the diagram, the length of OP to the nearest tenth is 5.4
How to determine the length?We are to determine the ratio of the sides of the diagram.
The ratio of the sides using the given sides is
Let the unknown side be x
The ratio of the sides is given as follows
25:34 = 15:x+15
Put into fraction we have
25/(25+9)= 15/(x+15)
Cross multiplying we have
25x+375 = 375+135
Collecting like terms
25x=510-375
Simplify further to have
25x=135
Making x the subject
x=5.4
Therefore the length OP is 5.4 units
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An airline finds that about 888 percent of the time, a person who makes an advance reservation does not keep the reservation. Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations. Based on this information, about how many of the scheduled people will not keep their reservation?.
Answers
Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.
Given,
In the question:
An airline finds that about 8 percent of the time, a person who makes an advance reservation does not keep the reservation.
Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations.
Now, According to the question:
Capacity of the airline per trip = 105 only
But company schedules = 113 people with advance reservations
Since 8% do not turn up
Out of 113 passengers who reserved in advance we can say
that 8% of 113 passengers will not keep their reservation
Based on this information, number of the scheduled people will not keep their reservation
= 8% x 113
= 0.08*113
=9.04
Hence, Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.
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Find the measure of angle f given the information below. please help !!
Answers
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
What is the relation between Angles and Parallel lines ?On a shared plane, parallel lines do not cross one another. Now, if a transversal crosses two parallel lines at two separate sites, four angles are created at each location. The characteristics of parallel lines with respect to transversals are therefore listed below.
Angles that coincide are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that alternate are equal.Exterior angles that alternate are equal.On the same side of the transversal, a pair of internal angles are additional.The pair of alternative internal angles are equal when two parallel lines are crossed by a transversal.
When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional.
In the problem angle
a = [tex]119^{o}[/tex]
e = [tex]66^{o}[/tex]
Now , c = e ( alternate angles, interior)
⇒ c = [tex]66^{o}[/tex]
a + b = [tex]180^{o}[/tex] ( as sum of angles on a straight line is [tex]180^{o}[/tex] )
b = [tex]180^{o}[/tex] - [tex]119^{o}[/tex] = [tex]61^{o}[/tex]
f + b+ c = [tex]180^{o}[/tex] [sum of angles of a Triangle is [tex]180^{o}[/tex] ]
f = [tex]180^{o}[/tex] - [tex]61^{o}[/tex] - [tex]66^{o}[/tex] = [tex]53^{o}[/tex].
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
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How many liters of a 10% salt solution must be mixed with 5 liters of a 40% salt solution
to give a 15% solution?
Answers
Please help me thank you
Answers
The slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The parallel lines have same slope
The slope of LM = the slope of NO
The slope of LM = (-1-(-5))/(4-(-2))
The slope of LM = 4/6 = 2/3
Slope of NO = 2/3
If LMNO is rectangle:
The slope of LO = -1/(slope of LM)
The slope of LO = -1(2/3)
The slope of LO = -3/2
Thus, the slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.
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let lines x and y be parallel, and let lines z and w be parallel. if angle a is the angle formed by lines y and z, and angle b is the angle formed by lines w and x, if the measure of angle a is 25 degrees, what is the measure of angle b?
Answers
155° is the measure of angle b .
What is an example of parallel lines?
Two lines that are equally spaced apart from one another and never cross each other are said to be parallel lines.
Both horizontal and vertical shapes are possible. In our daily lives, parallel lines can be seen in the form of zebra crossings, rows of notebooks, and the nearby railroad tracks.
from the figure , we understand that ∠1 and ∠3 together from a straight line.
thus, ∠1 + ∠3 = 180°
25° + ∠3 = 180°
∠3 = 155°
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Simplify the expression:
5t+
–
9+
–
8t+
–
5
Answers
The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 5t + (-9) + (-8t) + (-5)
Simplify the expression, then the value of the expression is given as,
⇒ 5t + (-9) + (-8t) + (-5)
⇒ 5t - 9 - 8t - 5
⇒ – 3t – 14
⇒ – (3t + 14)
The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).
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Write the
equation
of the line In
Slope-Intercept
Form.
Type your
answer here.
Answers
The equation of line in slope intercept form is y = -1/3 x + 1.
What is equation of a line?
The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. The slope of the line and a point on the line can be used to create the equation of a line.
The points on the line are (3,0) and (0,1).
The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of line is (1 - 0)/(0 - 3) = -1/3.
The line cuts y-axis at (0,1). Thus y-intercept of the line is 1.
The slope-intercept form of the line is
y = -1/3 x + 1
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Daryl walks 10.5 miles in 3.5 hours. How many miles does he walk per hour?
Answers
Answer: 3
Step-by-step explanation: Daryl is walking 3 miles in 1 hour. When you divide 10.5 by 3.5 you get. So 3 miles in one hour. For example if you walk 12 miles in 4 hours, you divide and get 3. That three becomes the miles in one hour.
please help on all PLEASE IM BEGGING YOU I CANT FAIL PLEASE
61=7-6x
3/2a -26=-5
4=n-10/-3
Answers
system of equations: n=2/3 ,a=14,x=−9
for each thing: x= −9 | a= 14 | n= 2/3
1. x = -9
2. a = 14
3. n = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:Here are the steps to the first question:1. Rearrange Terms
61 = 7 - 6x
61 = -6x + 7
2. Subtract 7 from both sides
61 = -6x + 7
61 - 7 = -6x + 7 - 7
3. Simplify
Subtract the numbers:
61 - 7 = -6x + 7 - 7
54 = -6x + 7 - 7
Subtract the numbers:
54 = -6x + 7 - 7
54 = -6x
4. Divide both sides by the same factor
54 = -6x
[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]
5. Simplify
Divide the numbers:
[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]
-9 = [tex]\frac{-6x}{-6}[/tex]
Cancel terms that are in both the numerator and denominator:
-9 = [tex]\frac{-6x}{-6}[/tex]
-9 = x
Move the variable to the left:
-9 = x
x = -9
Solution to Question 1:x = -9
Here are the steps to the second question:
1. Combine multiplied terms into a single fraction
[tex]\frac{3}{2}[/tex]a - 26 = -5
[tex]\frac{3a}{2}[/tex] - 26 = -5
2. Find common denominator
[tex]\frac{3a}{2}[/tex] - 26 = -5
[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5
3. Combine fractions with common denominator
[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5
[tex]\frac{3a+2(-26)}{2}[/tex] = -5
4. Multiply the numbers
[tex]\frac{3a+2(-26)}{2}[/tex] = -5
[tex]\frac{3a - 52}{2}[/tex] = -5
5. Multiply all terms by the same value to eliminate fraction denominators
[tex]\frac{3a - 52}{2}[/tex] = -5
2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)
6. Cancel multiplied terms that are in the denominator
2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)
3a - 52 = 2(-5)
7. Multiply the numbers
3a - 52 = 2(-5)
3a - 52 = -10
8. Add 52 to both sides
3a - 52 = -10
3a - 52 + 52 = -10 + 52
9. Simplify
Add the numbers:
3a - 52 + 52 = -10 + 52
3a = -10 + 52
Add the numbers:
3a = -10 + 52
3a = 42
10. Divide both sides by the same factor
3a = 42
[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]
11. Simplify
Cancel terms that are in both the numerator and denominator:
[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]
a = [tex]\frac{42}{3}[/tex]
Divide the numbers:
a = [tex]\frac{42}{3}[/tex]
a = 14
Solution to Question 2:
a = 14
Here are the steps to the third question:
1. Divide the numbers
4 = n + [tex]\frac{-10}{-3}[/tex]
4 = n + [tex]\frac{10}{3}[/tex]
2. Subtract [tex]\frac{10}{3}[/tex] from both sides
4 = n + [tex]\frac{10}{3}[/tex]
4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
3. Simplify
Subtract the numbers:
4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
[tex]\frac{2}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
Subtract the numbers:
[tex]\frac{2}{3}[/tex] = n
Move the variable to the left:
[tex]\frac{2}{3}[/tex] = n
n = [tex]\frac{2}{3}[/tex]
Solution to Question 3:n = [tex]\frac{2}{3}[/tex]
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Write an equation of the line in point plice form, through the point (4,-1) and ha a lope a 6
Answers
The equation of the line will be y = 6x - 25
Given, the point is (4, -1)
The slope is m = 6.
We have to write an equation of the line in slope-intercept form.
The standard form of equation of the line in slope-intercept form is given by
y = mx + c
Where, m is the slope.
Now, substituting the values of x, y and m in the equation,
-1 = 6(4) + c
-1 = 24 + c
c = -1 - 24
c = -25
Put the value of c in the standard equation,
y = 6x - 25
Therefore, the equation of the line is y = 6x - 25
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Evaluate f(x)=2x+5 when x=0, x=1, x=5
Answers
Answer:
f(0)=5
f(1)=7
f(5)=15
Step-by-step explanation:
f(0)=2x+5
=2(0)+5
=5
f(1)=2x+5
=2(1)+5
=2+5
=7
f(5)=2x+5
=2(5)+5
=10+5
=15
f(0) = 2(0) + 5
f(0) = 0 + 5
f(0) = 5
when x = 1
f(1) = 2(1) + 5
f(1) = 2 + 5
f(1) = 7
when x = 5
f(5) = 2(5) + 5
f(5) = 10 + 5
f(5) = 15
A shipping container is in the shape of a right rectangular prism with a length of 20 feet, a width of 8.5 feet, and a height of 8 feet. The container is filled with contents that weigh 0.25 pound per cubic foot. What is the weight of the contents in the container?
5440 pounds
1360 pounds
240 pounds
340 pounds
Answers
The weight of the contents in the container is 340 pounds
How to calculate the weight of the contents in the container ?The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units. Volume and the definition of length are related.
Given ,
volume of container = 20 x 8.5 x 8= 1360 cubic feet
weight = 0.25 pounds per cubic foot
0.25 x 1360 = 340 pounds
Therefore the weight of the contents in the container is 340 pounds
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Given vector u = ⟨−3,−2⟩ and v = ⟨1,−5⟩,determine the value of u - 2v in component form.
Answers
The component form of the linear combination of the two vectors is u - 2v = < -5, 20>
How to find the vector u - 2v?Here we have the two vectors: u = <-3, -2> and v = <1, -5> We want to determine the value of the linear combination:
u - 2v
To do that we just add the correspondent components, then we get:
u - 2v = <-3, -2> - 2*<1, -5>
= <-3, -2> - <2*1, 2*-5>
= <-3, -2> - <2, -10>
= < -3 - 2, -2 -(-10)>
= < -5, 20>
That is the component form of the linear combination.
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A pet store sells a large dog kennel 98.50 the wholesale cost o the kennel is 63.55 what is the percent of markup round to the nearest percent.
Answers
Rounded to the nearest percent, the markup is approximately 55%.
What is the percent markup?
Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus its cost to make or purchase for resale) by the cost of that unit.
To find the percent markup, you can use the following formula:
percent markup = (retail price - wholesale price) / wholesale price * 100
Plugging in the values given, we have:
percent markup = (98.50 - 63.55) / 63.55 * 100 = 34.95 / 63.55 * 100 = approximately 55%
Hence, rounded to the nearest percent, the markup is approximately 55%.
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chi-square tests are used for testing hypotheses of the association between two categorical values.
true
false
Answers
The given statement " chi-square tests are used for testing hypotheses of the association between two categorical values. " is true
The term chi square test defines if there is a significant relationship between two nominal variables.
Here we have given the statement, chi-square tests are used for testing hypotheses of the association between two categorical values.
And we need to find whether the statement is true or not.
As per the definition of chi square test, we know that the frequency of each category for one nominal variable is compared across the categories of the second nominal variable.
Here we also know that the data can be displayed in a contingency table where each row represents a category for one variable and each column represents a category for the other variable.
Therefore, based on these facts the given statement is true.
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Perpendicular lines form angles that are how many degrees at their intersection?
O a. 45 dregrees
O b. 90 degrees
O c. 135 degrees
O d. 225 degrees
Answers
Answer:
Step-by-step explanation:135 degrees
PLEASE HELP ME ASAP!!!
Answers
Answer:
$54,742.76
Step-by-step explanation:
The equation for an exponential function is [tex]f(x)=ab^x\\[/tex], where [tex]a[/tex] is the starting value, which is 40,000. This value increases by 4%, so [tex]b[/tex] is 1.04. Finally, [tex]x[/tex] is the term that the value is increasing for, which in this case is 8.
So, the equation is [tex]f(x)=40000*1.04^8[/tex]
** [tex]f(x)[/tex] can be replaced with [tex]y[/tex]
Construct a quadrilateral PQRS with PQ= 5cm, QR = 5.5cm, RS = 5.5cm, SP= 6.5cm & angle PQR = 75°.Also construct a Triangle QRM whose area is equal to quadrilateral PQRS.
Answers
The image for quadrilateral PQRS is attached below
The image for Triangle QRM is attached below
What is the construction of a quadrilateral PQRS?Generally, To construct a quadrilateral PQRS with the given dimensions, you can use a straightedge and a compass. Here is a step-by-step guide:
Start by drawing a straight line segment PQ of length 5 cm.Place the compass on point P and draw an arc with a radius of 5.5 cm.Place the compass on point Q and draw an arc with a radius of 5.5 cm. The two arcs should intersect at a point R.Place the compass on point R and draw an arc with a radius of 6.5 cm.Place the compass on point P and draw an arc with a radius of 6.5 cm. The two arcs should intersect at a point S.Connect points S and R to complete the quadrilateral PQRS.To construct a triangle QRM with an area equal to quadrilateral PQRS, you can use the same method as above. Here is a step-by-step guide:
Start by drawing a straight line segment QM of length 5 cm.Place the compass on point Q and draw an arc with a radius of 5.5 cm.Place the compass on point M and draw an arc with a radius of 5.5 cm. The two arcs should intersect at a point R.Connect points Q and R to complete the triangle QRM.To verify that the area of triangle QRM is equal to the area of quadrilateral PQRS, you can use the formula for the area of a triangle:
Area of triangle QRM = (1/2) * QM * QR * sin(angle QRM)
And the formula for the area of a quadrilateral:
Area of quadrilateral PQRS = (PQ * QR * sin(angle PQR))/2
Substituting the given values and solving for sin(angle QRM), we find that:
sin(angle QRM) = (2 * area of quadrilateral PQRS)/(QM * QR)
= (2 * (5 * 5.5 * sin(75)))/(5 * 5.5)
= sin(75)
Thus, the area of triangle QRM is equal to the area of quadrilateral PQRS, as desired.
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Write an equation of the line that passes through $\left(7,10\right)$ and is perpendicular to the line $y=\frac{1}{2}x-9$.
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The equation of the line that passes through (7, 10) and its perpendicular to the line y = (1/2)x - 9 is y = -2x + 24
The coordinates of the line passing through the point = (7, 10)
The equation of the perpendicular line
y = (1/2)x - 9
The slope of the line = 1/2
The slope of the original line = - 1 / (1/2)
= -1 × 2
= -2
The slope intercept form is
y = mx + b
Substitute the values in the equation and find the value of b
10 = -2(7) + b
10 = -14 + b
b = 10 + 14
b = 24
Substitute the value of b and m is the equation
y = -2x + 24
Therefore, the slope of the line is y = -2x + 24
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If i clap my hands 20 times in 12 seconds. How many times will i do it in 2minutes. Then 3 minutes.
Answers
If i clap my hands 20 times in 12 seconds. 200 times will i do it in 2 minutes.
The friend can clap his hands 28 times in 12 seconds, according to our knowledge. The first thing we need to know is how many times he can clap in a second:
What is clap ?
Gonorrhea is known by the slang term "the clap." Gonorrhea is also referred to as "the drip." Someone who has an may feel stigmatized and shamed by these words.
To do it, we must divide the number of seconds by the number of times he can clap his hands:
20/12 =1.6667
He can clap his hands 1.6667 times in 1 second:
Now we want to know how many times will he clap his hands in 2 minutes
We have to change 2 minutes into seconds:
1 (minute) = 60 (seconds in 1 minute)
2 (minutes) * 60 (seconds in 1 minute) = 120seconds
After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:
1.6667 times * 120 seconds = 200
200 times in 2.25 minutes
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a computer costs £2500 when new. Its value depreciates 12% compounded each year. How much does it cost after 3 years?
Answers
The computer will cost £ 33512.32
Given,
the cost of the computer = 2500
Depreciation = 12%
Cost after 3 years =?
compound interest is calculated as,
A = P(1 + r/n)nt
r = 12/100 = 0.12
So, A= P(1 + r/n)nt
A = 2500 (1+.12/1)1*3
A= 2500 (1.12)³
A= 2500 * 1.404928
A = 3512.32
So, The computer will cost £ 33512.32
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help pls
P = mgh for m
Answers
Answer:
p/gh=m
Step-by-step explanation:
divide both sides by gh to isolate m
Emma had to finish her 366-page novel by Friday. She had already read 244 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p − 244 = 366; p = 610 pages
p + 244 = 366; p = 122 pages
122p = 244; p = 2 pages
p over 244 equals 2; p = 488 pages
Answers
Answer: Its b my guy :)
Step-by-step explanation: 244 + 122 = 366
and the only answer with 366 is b! hope this helps!