Answer:
B.
Step-by-step explanation:
First thing to determine is how this parabola opens. Up or down? Or left or right?
*We see that the axis of symmetry is a line parallel to the y-axis; therefore, the axis of symmetry is an x = line, making this an up or down parabola. Now we need to determine how everything else all fits in.
The standard form of this type of parabola is
[tex]4p(y-k)=-(x-h)^2[/tex]
where p is the distance between the vertex and the focus. If the vertex has a y coordinate of 3, and the focus has a y coordinate of -3, the vertical distance between those 2 numbers is 6. Therefore, p = 6. Filling in then:
[tex]4(6)(y-3)=-(x-4)^2[/tex]
and [tex]24(y-3)=-(x-4)^2[/tex]
Dividing both sides by 24 gives you what you are looking for:
[tex]y-3=-\frac{1}{24}(x-4)^2[/tex]
The equation of the parabola is:
⇒ y - 3 = -(1/24)(x - 4)²
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
We can use the standard form of the equation of a parabola with vertex (h, k) and axis of symmetry parallel to the y-axis, which is given by:
(x - h)² = 4p(y - k)
where (h, k) is the vertex and p is the distance between the vertex and the focus.
In this case, the vertex is (4, 3) and the focus is (4, -3).
Therefore, We get;
p = 3 - (-3)
p = 6.
Substituting the values of h, k, and p, we get:
(x - 4)² = 4(6)(y - 3)
Simplifying, we get:
(x - 4)² = 24(y - 3)
Now, we can simplify the equation to match it with the given options:
(x - 4)² = 24y - 72
(x - 4)² + 72 = 24y
y = (1/24)(x - 4)² + 3
Therefore, the equation of the parabola is:
B.) y - 3 = -(1/24)(x - 4)²
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What is the highest point in a particular section of a graph.
Answer:
One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph.
Answer:
Step-by-step explanation:
8x+2=-2
((Please Answer with A B C or D))
A firefighter needs to rescue a person from a burning building. The person is located 50 feet up in the building. If the base of the ladder is on top of a 10 foot tall fire truck and the ladder is 105 feet long, what is the approximate angle of elevation for the rescue ladder?
A. 68°
B. 69°
C. 21°
D. 22°
The answer is:
The correct option is:
[tex]D.22\°[/tex]
Why?We can calculate the angle of elevation of the rescue ladder (formed triangle) using the following trigonometric formula:
[tex]Sin(\alpha)=\frac{y}{hypothenuse}[/tex]
Where,
y, is represented by the height where the person is located (50 feet) less the height of the top of the fire truck (10 feet)
hypothenuse, is represented by the length of the ladder (105 feet)
So, substituting and calculating we have:
[tex]Sin(\alpha)=\frac{y}{Hypothenuse}\\\\\alpha =Sin(\frac{Height}{LadderLength})^{-1}\\\\\alpha =Sin(\frac{50feet-10feet}{105feet})^{-1}=Sin(\frac{40feet}{105feet})^{-1}\\\\\alpha=Sin(\frac{40feet}{105feet})^{-1}=Sin(0.38)^{-1}=22.33\°=22\°[/tex]
Hence, we have that the correct option is:
[tex]D.22\°[/tex]
Have a nice day!
greatest common factor.
44+48
Answer:
4 is the greatest common factor
Step-by-step explanation
The factors of 44 are: 1, 2, 4, 11, 22, 44
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
please help will receive brainliest
The perimeter of the rectangle is 32 m. One side is 11 m long.
What is the length of the missing side?
Answer:
5 m
Step-by-step explanation:
The perimeter is the sum of the lengths of the four sides. Opposite sides have the same length, so it is twice the sum of the lengths of adjacent sides.
The sum of adjacent sides is (32 m)/2 = 16 m. If one of them is 11 m long, the other is ...
16 m - 11 m = 5 m
The "missing" side is 5 m long.
Threre are 25 streets in squaresville each day there 5 police officers working if all of the officers want to patrol the same number of streets each day how many streets will each officer need to patrol
Answer:
you would divide 25 by 5.
Step-by-step explanation:
each of the 5 officers would patrol 5 streets with a final of 5 x 5 = 25.
Answer:
5 streets
Step-by-step explanation:
Data:
The number of streets = 25
Number of officers = 5
Each officer will patrol = [tex]\frac{25}{5}[/tex]
= 5 streets
Triangle CAT is equilateral and centered at the origin. How many degrees will it need to be rotated counterclockwise about the origin to take point C to the initial location of point A?
Answer:
-120 degrees.
Step-by-step explanation:
This triangle has a rotational symmetry of 3 (it repeats its orientation 3 times as it makes a complete circle around the center), so the angle of rotation is 360 / 3 = 120 degrees.
As the rotation is counter clockwise strictly speaking the answer is -120 degrees.
Answer:
its A on egd
Step-by-step explanation:
i just took the test
The following figures are not drawn to scale but AB and CD are straight lines. Find x
Answer:
x=45
Step-by-step explanation:
Since AB is a straight line, it is 180 degrees
AOE + EOF + FOD + DOB = 180
15+x+2x+120-2x = 180
Combine like terms
135 +x = 180
Subtract 135 from each side
135-135 +x = 180 -135
x = 45
To find x, use the concept of similar triangles and set up a proportion. Cross multiply and simplify the equation to solve for x.
Explanation:To find x, we need to use trigonometry. Given that AB and CD are straight lines and the figures are not to scale, we can use the concept of similar triangles. We need to find the relationship between the corresponding sides of the triangles to find x.
Let's assume that the length of AB is a and the length of CD is b. From the given information, we can form a proportion:
a/b = (a+x)/a
Cross multiplying and simplifying the equation, we get:
a^2 = b(a+x)
Now we can substitute the given values to solve for x.
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If a seed is planted, it has a 65% chance of growing into a healthy plant.
If 8 seeds are planted, what is the probability that exactly 1 doesn't grow?
Chance of seed growing into healthy plant: 0.65
Chance of seed NOT growing into a healthy plant: 0.35
To answer this question, we will use the nCr button on the calculator.
In this situation, n = 8 and r = 1.
If 1 seed doesn't grow, then 7 seeds will grow. So will raise 0.65 to the 7th power and 0.35 to a power of 1
7 seeds grow, so we use the 7th power
1 seed doesn't grow, so we use power 1 :
So the answer is:
⁸C₁ × (chance of successful growth)⁷ x (chance of Unsuccessful growth)¹
= ⁸C₁ × 0.65⁷ × 0.35¹
= 0.137 (3sf)
_____________________________
Answer:
Probability that exactly one seed doesn't grow is:
0.137
To calculate the probability in this case, we make use of the Binomial Probability formula. Here, we want to find out the probability that out of the 8 seeds planted, 7 sprout successfully and 1 fails to sprout.
Explanation:The problem you're working out can be classified under the category of Binomial Probability. A binomial probability problem deals with yes-no scenarios repeated multiple times (like a seed either germinating or failing).
For this problem, we know that the probability of a seed sprouting (success) is 0.65 and therefore the probability of not sprouting (failure) is 0.35 (1 - 0.65). You have 8 seeds, and you want to find the probability that 7 succeed and 1 fails.
The formula for binomial probability is:
P(X=k) = C(n,k) * (p^k) * (q^(n-k))
Where:
P(X=k) is the probability of k successes,C(n,k) is the number of combinations of n items taken k at a time,p is the probability of success,q is the probability of failure,n is the total number of trials,k is the number of successes.
By substituting the appropriate values into the formula, we would calculate the binomial probability of exactly 1 seed not sprouting.
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Factor the expression. 49x^2-16
A. (7x + 4)(7x − 4)
B. (7x − 4)(7x − 4)
C. (4x + 7)(4x − 7)
D. (4x − 7)(4x − 7)
Answer:
The answer is :
A. (7x + 4)(7x - 4)
Answer:
The correct answer is first option
(7x + 4)(7x − 4)
Step-by-step explanation:
Points to remember
Identities
(a + b)(a - b) = a² - b²
It is given an expression,
49x² - 16
To factorize the expression 49x² - 16
We know that 7² = 49 and 4² = 16
Therefore we can write the given expression as,
49x² - 16 = (7x)² - 4²
It is in the form of the above identity,
(7x)² - 4² = (7x + 4)(7x - 4)
The correct answer is first option
Using the following triangle, what is the cosine of angle B?
Answer:
cos(B) = a/c
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Cos = Adjacent/Hypotenuse
The leg adjacent to angle B is "a". The hypotenuse is "c", so the desired cosine is ...
cos(B) = adjacent/hypotenuse = a/c
Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measured 14 inches what is the gratest possible whole number length of the unknown side
Answer:
26
Step-by-step explanation:
If the sides of a triangle are a, b, and c, the triangle inequality theorem tells us, about the sides possible to make up this NON-right triangle:
a + b > c
b + c > a and
a + c > b
Since we have 2 sides, we will call the third unknown side x. Let a = 12 and b = 14:
12 + 14 > x
14 + x > 12 and
12 + x > 14.
The first inequality, solved for x, is that x < 26.
The second inequality, solved for x, is that x > -2. We all know that the 2 things in math that will never EVER be negative are distance/length measures and time; therefore, we can safely disregard -2 as a side length of this, or ANY, triangle.
The third inequality, solved for x, is that x > 2.
We now have the solutions for the side length possibilities:
2 < x < 26
From this inequality statement, we see that the longest the side could possibly be and still make a triangle with the other 2 side lengths given, is 26
Answer:
C. 7 inches
Step-by-step explanation:
The Obtuse Triangle Inequality Theorem: c^2 > a^2 + b^2.
14^2 > 12^2 + b^2.
196 > 144 + b^2.
so b < 52. and the square root of 52 is 7.
Thank you and have a great day!
The fuel efficiency of a car decreases as tire pressure decreases. What's the independent variable in the situation? A. Tire pressure B. The price per gallon of gas C. The speed of the car D. Fuel efficiency
Hello There!
The fuel efficiency of a car decreases as tire pressure decreases. The independent variable in the situation is: Tire pressure.
Answer:
A
Step-by-step explanation:
The Price per gallon goes with the fuel efficiency and the speed of the car determines how much gas you use so the answer is A Tire Pressure
Given the following linear function identify the slope in the Y intercept of the function
Hello There!
The slope of a function is always in the form of "y=mx"
The slope for this function would be [tex]\frac{1}{6}[/tex] and the y intercept would be positive 7
Answer:
2nd answer
Step-by-step explanation:
For a linear equation in the form
f(x) or y = mx + b
m = slope
b = y - intercept
By observation, f(x) = [tex]\frac{1}{6}[/tex]x + 7
m = slope = [tex]\frac{1}{6}[/tex] (Answer)
b = y-intercept = 7 (answer)
6. Calculate the value of tan (48°19'23").
A. 0.75
B. 88.81
C. 1.12
D. 0.66
Answer:
C. 1.12
Step-by-step explanation:
There are 60' (minutes) in a degree and 60" in a minute meaning that we have (60×60) seconds in a degree.
Therefore to convert seconds to degrees we divide by 3600. and minutes to degrees we divide by 60.
The angle 48°19'23'' can be converted into a decimal as follows
48°+(19/60+23/3600)°
=48.323°
Tan 48.323= 1.12
While reviewing for exams a teacher knows that the number of topics he can cover is directly proportional to the length of time he has to review. If he can cover 9 topics in a single 45-minute period, how many topics can he cover in a 1-hour period?
A) 5
B) 7
C) 10
D) 12
Answer:
the answer is D
Step-by-step explanation: so you know that he can do 9 topics in 45 minutes. which is 1 topic every 5 minutes when you divide 45/9. if there is 60 minutes in an hour, and he does 1 topic every 5 minutes, he would do 12. hope this helps xd
A teacher can cover 12 topics in a 1-hour period. It is given that the number of topics he can cover is directly proportional to the length of the time he has to review. So, option D is correct.
How the variables are said to be directly proportional?Two variables are said to be directly proportional if one variable increases/decreases with respect to the increase/decrease in the other variable. They are related to each other by proportionality.
A ∝ B (A and B are two variables)
⇒ A2/A1 = B2/B1
How the given variables are related?The given variables are 'N - number of topics' and 'T - time period'.
It is given that they are directly proportional to each other.
So, we can write
N ∝ T
⇒ N2/N1 = T2/T1
Calculation:Given that,
A teacher can cover 9 topics in a single 45-minute period.
So, N1 = 9 topics and T1 = 45 minutes
And T2 = 1 hour
We need to find N2 =?
Thus, from the above equation
N2/N1 = T2/T1
⇒ N2/9 = (1 hour)/45 minute
1 hour = 60 minutes
⇒ N2/9 = (60/45)
⇒ N2 = 9 × 4/3
∴ N2 = 12 topics
So, he can cover 12 topics in 1 hour. Thus, option D is correct.
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18. Remove the parentheses from the following expression, and combine like terms: (a + b – c) + 3a – 2c
A. 4a + b + 3c
B. 4a + b – 3c
C. 2a – b – c
D. 2a – b + c
Combine (or subtract) like terms.
a + b – c + 3a – 2c
4a + b – 3c <-------------------Answer
So, Choice B.
For this case we have the following expression:
[tex](a + b + c) + 3a-2c[/tex]
We eliminate parentheses:
[tex]a + b-c + 3a-2c =[/tex]
We add similar terms:
[tex]a + 3a + b-c-2c =[/tex]
We have that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed, then:
[tex]4a + b-3c[/tex]
Answer:
[tex]4a + b-3c[/tex]
Option B
Segment XZ is bisected by point Y. If XY= 12x, and the measure of XZ= 18x-6, solve for x.
let's bear in mind that Y is a bisecting point, so it's really cutting XZ into two equal halves.
[tex]\bf \underset{\textit{\Large 18x-6}}{\boxed{X}\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}} Y\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}}\boxed{Z}} \\\\\\ 12x+12x = 18x-6\implies 24x=18x-6 \\\\\\ 6x=-6\implies x=\cfrac{-6}{6}\implies x=-1[/tex]
If segment XZ is bisected by point Y and XY=12x and XZ=18x-6 then the value of x=-1.
What is bisection?Bisection means division of a line segment into two equal parts by other line or line segment.
How to find length of line after bisection?We know that bisector cuts line into equal parts so 2XY=XZ
2(12x)=18x-6
24x=18x-6
6x=-6
x=-1
Hence the value of x is -1 if XZ is bisected by point Y.
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Mrs. Rosso has to travel 390 miles on a highway. She drives 130 miles in 2 hours. If she 7 hours to travel at that rate, will she arrive at her destination on time?
Step-by-step explanation:
Find the miles per hour. Divide 130 with 2
130/2 = 65
Mrs.Rosso travels 65 miles per hour. She has 7 hours to travel. Multiply 7 with 65:
65 x 7 = 455
455 > 390 ∴ If everything stays constant, Mrs.Rosso will arrive to her destination on time.
~
Answer: yes
Step-by-step explanation:
If she travels at that rate she gets 65 miles per hour. 65 multiplied by 7 is 455, so she will get there before the 7 hours is up.
GIVE ANSWER ASAP (SHOW STEPS)
Use a calculator to find an angle theta for which tan theta = 2. Round to the nearest hundredth. I don't have a graphing calculator and I don't know what to do to solve this.
Answer:
Step-by-step explanation:
Your calculator knows all. You just have to know how to unlock it.
A graphing calculator is not necessary. A simple scientific one will work. The calculator on your computer will work (a PC) and my phone has one that will solve this as well.
2nd Function
Tan-1(
2
)
=
You should get 63.43
Make sure your calculator says degrees (DEG) at the top. Good luck.
A team of runners is needed to run a 1 3 -mile relay race. If each runner must run 1 9 mile, how many runners will be needed?
Answer:
3 runners
Step-by-step explanation:
The number of runners needed is the length of the race divided by the length each runner can run:
(1/3 mi)/(1/9 mi/runner) = 9/3 runner = 3 runners
_____
There are a couple of ways you can divide fractions:
→ "invert and multiply." That is, multiply the numerator by the reciprocal of the denominator. Here, that is (1/3)(9/1) = 9/3 = 3
→ make the denominators the same and use the ratio of the numerators. Here that is (1/3)/(1/9) = (3/9)/(1/9) = 3/1 = 3
→ use a calculator (see attached)
Find the missing factor. Write your answer in exponential form.
1^9 = 1^7 • __
Answer:
Step-by-step explanation:
1^7 = 1
1^9 = 1
1= 1 x 1 or if they really want it 1^2
Need help with a math question
ANSWER
[tex]y = 8x - 26 [/tex]
EXPLANATION
The given points are (3,-2) (4,6).
The slope formula is given by:
[tex] m= \frac{y_2-y_1}{x_2-x_1} [/tex]
We use the slope formula to get:
[tex]m = \frac{6 - - 2}{4 - 3} [/tex]
The slope is
[tex]m = 8[/tex]
We use the point-slope formula to get;
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y + 2 = 8(x - 3)[/tex]
We expand to get;
[tex]y = 8x - 24 - 2[/tex]
The slope-intercept form of the equation is:
[tex]y = 8x - 26[/tex]
. The child’s physical density is being measured by the displacement method. A child of 50 pounds is placed in a tub filled with water, and the water that comes out of the tub goes into another small tub that measures 40 cm long, 30 cm wide, and 60 cm deep. The water level in the small tub is 18 cm high. Find the density of a child in gm/cm3 to the nearest hundredth. (Hint: density = mass/volume; 1 pound = 454 grams)
Answer:
1.05 g/cm³
Step-by-step explanation:
The mass of the child is ...
(50 lb)(454 g/lb) = 22,700 g
The volume displaced is ...
(40 cm)(30 cm)(18 cm) = 21,600 cm³
Then the density of the child is ...
mass/volume = 22700 g/(21600 cm³) ≈ 1.05 g/cm³
Which of the following statements are true about the graph of f(x) = 6(x + 1)² -9?
Check all of the boxes that apply.
A. The vertex is (1, -9).
B. The graph opens upward.
C. The graph is obtained by shifting the graph of f(x) = 6(x + 1)² up 9 units.
D. The graph is steeper than the graph of f(x) = x².
E. The graph is the same as the graph of f(x) = 6x² + 12x - 3.
Explain your answer?
Don't spam your answer, it's going to mark report.
If it's wrong answer and it's going to mark report as a "improper answer."
Don't copy or paste answers from other sites, if you copied and that's going let the mark as a report called "plagiarism."
Thank you!
-Charlie
Answer:
B, D, E
Step-by-step explanation:
A. The vertex is (1, -9).
False. The vertex is at (-1, -9).
B. The graph opens upward.
True. The leading coefficient 6 is positive.
C. The graph is obtained by shifting the graph of f(x) = 6(x + 1)² up 9 units.
False. It is shifted down 9 units.
D. The graph is steeper than the graph of f(x) = x².
True. The absolute value of the leading coefficient |6| is greater than 1.
E. The graph is the same as the graph of f(x) = 6x² + 12x - 3.
f(x) = 6(x² + 2x + 1) - 9
f(x) = 6x² + 12x + 6 - 9
f(x) = 6x² + 12x - 3
True.
The graph of f(x) = 6(x + 1)² -9 has its vertex at (-1,-9), opens upwards, is steeper than f(x) = x² and is not equal to f(x) = 6x² + 12x - 3. The graph is also shifted downwards by 9 units, not upwards.
Explanation:The graph of f(x) = 6(x + 1)² -9 is a parabolic function. Let's check each of the given statements:
A. The vertex is not at (1, -9). Because the general form of a parabola is f(x) = a(x-h)² + k, where (h,k) is the vertex, in this case the vertex is at (-1,-9). B. The graph does open upward. As 'a' in the equation of the parabola (considered positive when the graph opens upward) is 6, a positive number. C. This statement is false. The negative sign in front of the 9 causes the graph to be shifted down, not up. D. The graph is indeed steeper than the graph of f(x) = x². This is because of the multiplication by 6, which stretches the graph vertically. E. The graph is not equivalent to that of f(x) = 6x² + 12x - 3. Expanding the given equation will give us a different result. Learn more about Parabolic Function here:
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Please help me with this.
Answer:
Step-by-step explanation:
The range is 6 to 10 inches per month; 6 is the least amount of rain, whereas 10 is the most, for these four months.
Find the median by rearranging these four measurements in ascending order: 6 6 8 10. Since four is an even number (of measurements), we find the median by averaging the middle two measurements: (6 + 8) /2 = 7 in.
The mean is found by summing up the four measurements and dividing the result by 4:
6+6+8+10
-------------- = 30/4 = 7.5
4
Draw a histogram as two vertical bars, one of which is 3 units higher than the other. We don't yet know the total number of cats that each boy has, so your markings of your histogram have to be algebraic expressions, for example:
x + 0 for the first vertical bar and x + 3 for the second. Then, clearly, one boy has 3 more cats than does the other.
Corey has 3 more cats than Taylor. Let t represent the number of cats owned by Taylor and c the number by Corey.
Then t = c + 3 (general relationship), and so
6 = c + 3
We must isolate c to determine how many cats corey has.
Subtract 3 from both sides, which results in c = 3. Corey has 3 cats and Taylor has 6.
The figure PQRSTU represents the shape of the parking lot at a shopping mall. What is the area of the parking lot?
A.
834 square feet
B.
918 square feet
C.
984 square feet
D.
1,068 square feet
Answer:
D.
1,068 square feet
Step-by-step explanation:
Split the figure into 2 shapes: triangle and rectangle
Area of rectangle = 36 x 25 = 900 ft^2
Area of triangle = 1/2 (39-25)(36-12) = 1/2 (14)(24) = 168 ft^2
Area of the figure PQRSTU = 900 + 168 = 1068 ft^2
Answer
D.
1,068 square feet
Answer:
D. 1,068
Step-by-step explanation:
Area of rectangle PQRU = 25 x 36 = 900 sq-ft
Consider triangle RST,
Base of triangle = TR = 36 - 12 = 24 feet
Height if triangle = 39 - 25 = 14 feet
Hence area of triangle = [tex]\frac{1}{2}[/tex] x 24 x 14 = 168 sq-ft
Total area = 900 + 168 = 1068 sq-ft
Find the amount of simple interest earned for depositing the given principle in an account if $2200 is invested at 5.5 %
for 6 months
Answer: $726 in interest is accumulated over a period of 6 months
Answer:
$60.50
Step-by-step explanation:
Put the given numbers into the formula and do the arithmetic. 6 months is 1/2 year.
i = Prt . . . . i is interest earned, P is principal amount, r is annual rate, t is number of years
i = $2200×0.055×0.5 = $60.50
The amount of simple interest earned in 6 months is $60.50.
If n = 44 mm and p = 67 mm, what is the measure of angle θ?
A. 41°
B. 57°
C. 49°
D. 33°
Answer: Option C
49°
Step-by-step explanation:
By definition, the cosine of an angle is defined as:
[tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex].
The hypotenuse is always the opposite side to the 90 ° angle
The adjacent side is the one that contains the angle theta and the angles of 90 °.
In this case note that:
[tex]adjacent = n = 44\ mm\\\\hypotenuse = p = 67\ mm[/tex]
So:
[tex]cos(\theta) = \frac{44}{67}[/tex]
[tex]\theta = arcos(\frac{44}{67})[/tex]
[tex]\theta =49\°[/tex]
The answer is:
The correct option is:
C. 49°
Why?To calculate the measure of the angle, we can use the following trigonometric relation:
[tex]Cos\theta =\frac{Adjacent}{Hypothenuse}[/tex]
We are given the following information:
[tex]adjacent=n=44mm\\hypothenuse=p=44mm[/tex]
So, substituting and calculating we have:
[tex]Cos(Cos\theta)^{-1} =Cos(\frac{Adjacent}{Hypothenuse})^{-1}\\\\\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}\\\\\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}[/tex]
[tex]\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}=Cos(\frac{44}{67})^{-1}=48.95\°=49\°[/tex]
Hence, the correct option:
C. 49°
Have a nice day!
The Sullivan household wants build a patio deck in the shape of a 45-45-90 triangle in a nice corner section of their backyard . They have enough room for a triangle with a leg of 20 feet . What will the length of the hypotenuse be ?
Answer:
20√2=28.2842....
Step-by-step explanation:
special right traingles
a 45-45-90 states that the legs are congruent and the hypotenuse is leg√2
PLEASE HELP 30 PTS!!! Select ALL the correct answers. Which expressions are equivalent to the following?
30x^2-5x-10
A: (10x − 5)(3x − 5)
B: 3x(2x − 1) + 2(2x − 1)
C: 5x(6x − x − 2)
D: -5(-6x2 + x + 2)
E: 5(2x + 1)(3x − 2)
F: 5(2x − 1)(3x + 2)
Answer:
D: -5(-6x^2 + x + 2)
E: 5(2x + 1)(3x − 2)
Step-by-step explanation:
You want to identify the expressions equivalent to 30x² -5x -10.
ComparisonThe first two answer choices have incorrect constants (25 and -2 vs. -10).
Factored formsA factor of 5 is removed from the remaining answer choices, so let's remove a factor of 5 and see what we get:
30x^2 -5x -10 = 5(6x^2 -x -2)
An additional x cannot be factored from the expression, so choice C can be eliminated.
Multiplying each of these factors by -1 will make the product correspond to answer choice D.
Factoring will make it correspond to answer choice E, best verified by finding the x-term of the product of the binomial factors:
E: 2x(-2) +1(3x) = -x, as required
F: 2x(2) -1(3x) = x, wrong sign
The equivalent expressions are those of choices D and E.