Answer:
27 days
Step-by-step explanation:
There is a total of 90 days in the semester, and she bought lunch 30% of the total days, then the total number of days she brought the lunch is 27 days.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the information provided in the question,
Total days in the semester = 90
Margaret comes with lunch, 30% of the total days.
So, in total days, Margaret comes with lunch,
D = 90 × 30/100
D = 2700/100
D = 27 days.
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TRUE OR FALSE. if the slopes of two lines are negative reciprocals, the lines are perpendicular
Answer:
TRUE
Step-by-step explanation:
plz dont skip me help me
In which quadrant would point (12, 18) be located?
Quadrant IV
Quadrant II
Quadrant I
Quadrant III
Answer:
it's Quadrant 1 because both of he cordnates
Step-by-step explanation:
The DeMarco hotel has 500 rooms available for sale. For Monday night the hotel’s occupancy is 60%. What is the number of rooms the hotel has available to sell for Monday night? 100 200 250 300
Answer:
200 rooms are available to sell.
Step-by-step explanation:
Given,
Total number of rooms for Monday night = 500,
Occupancy percentage for Monday night = 60%,
Thus, the remaining rooms available for Monday Night
= (100-60)% of total rooms
= 40% of 500
[tex]=\frac{40\times 500}{100}[/tex]
[tex]=\frac{20000}{100}[/tex]
= 200
Therefore, there are 200 rooms available to sell for Monday night.
2)
What are the relative minimum and relative maximum values over the interval -3,3] for
the function shown in the graph? (4 points)
Minimum:
Maximum:
Answer:
minimum: -9maximum: -6Step-by-step explanation:
For a point to be a relative extreme, there must be points on both sides that are not as extreme. That is, the ends of the interval may be extreme values, but do not qualify as relative extrema, since there are not points on both sides.
In the interval [-3, 3], the relative extrema are the turning points.
The relative minimum is at y = -9 on the y-axis.
The relative maxima are at y = -6, between 1 and 2 on either side of the y-axis.
Answer:
minimum: -9
maximum: -6
Step-by-step explanation:
Point w is located at -2 and 3 on a coordinate plane point w is reflected over the x axis to create point w point w is then reflected over the y axis to create point w what ordered pair describes the location of point w
Answer:
w(2,-3)
Step-by-step explanation:
the initial coordinates of point w are w(-2,3), to differentiate the different coordinates of w we will place sub-indexes (according to the graph)
the point w is reflected over the x axis to create point w₁(-2,-3) point w is then reflected over the y axis to create point w₂(2,-3)
School D has 880 boys to 200 girls The ratio of girls to all students is 5 to 27 22/27 of all students are boys idk how to get from 880 to 27 and do a proportion
Answer:
(i)Ratio of the Number of Girls in the School to the Total Population
=5:27
(ii)Ratio of the Number of Boys in the School to the Total Population=22:27
Step-by-step explanation:
Below is the steps on how the given ratio are derived
If the school has 880 boys and 200 girls
Total Population of the School=880+200=1080
Ratio of Girls to all Student is 5:27
Now, this is derived from this:
Ratio of the Number of Girls in the School to the Total Population
=200:1080[tex]=\frac{200}{1080} =\frac{5}{27}[/tex]
Which in reduced form is 5:27
You can do likewise for boys
Ratio of the Number of Boys in the School to the Total Population=880:1080[tex]=\frac{880}{1080} =\frac{22}{27}[/tex]
Which in reduced form is 22:27
Can someone please explain this problem to me idk what I am doing wrong and can you draw the problem for me thanks
Answer:
you're not doing anything wrong
Step-by-step explanation:
In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.
__
Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.
As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.
__
This is a good one to discuss with your teacher.
George is 3 time as old as chun. Chun is 1/2 as old as elizabeth. Waneta is 4/7 as old as elizabeth. Waneta is 8 years old. How many years old is george
Answer:
21 years old.
Step-by-step explanation:
Given:
Waneta is 8 years old
Waneta is 4/7 as old as Elizabeth.
Chun is 1/2 as old as Elizabeth.
George is 3 time as old as Chun.
Question asked:
How many years old is George ?
Solution:
Let age of Elizabeth = [tex]x[/tex] years
Waneta is 4/7 as old as Elizabeth. ( given )
Age of Waneta = [tex]\frac{4}{7} \ of \ Elizabeth[/tex]
[tex]8=\frac{4}{7} \times x\\\\8=\frac{4}{7}x[/tex]
By cross multiplication:
[tex]4x=56[/tex]
By dividing both sides by 4
[tex]x=14\\[/tex]
Age of Elizabeth = [tex]x[/tex] = 14 years
Chun is 1/2 as old as Elizabeth. ( given )
Age of Chun = [tex]\frac{1}{2} \ of \ Elizabeth\\[/tex]
= [tex]\frac{1}{2} \times14= 7\ years[/tex]
George is 3 time as old as Chun. ( given )
Age of George = [tex]3\ times \ of \ Chun\\[/tex]
[tex]=3\times7=21\ years[/tex]
Therefore, George is 21 years old.
Bonita Industries sells radios for $50 per unit. The fixed costs are $645000 and the variable costs are 60% of the selling price. As a result of new automated equipment, it is anticipated that fixed costs will increase by $215000 and variable costs will be 50% of the selling price. The new break-even point in units is:
Answer:
The new break even point in units = 34400 units
Step-by-step explanation:
Fixed cost ( F ) = $ 645000
Selling price ( s )= $ 50
Variable Cost ( v ) = [tex]\frac{60}{100}[/tex] × 50 = 30
Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F}{s - v}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{50 - 30}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{20}[/tex]
⇒ [tex]x_{BEP}[/tex] = 32250 units
Now the new fixed cost ( [tex]F_{1}[/tex] ) = $ 645000 + $ 215000 = $ 860000
Selling price ( s )= $ 50
Variable Cost ( v ) = [tex]\frac{50}{100}[/tex] × 50 = $ 25
Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F_{1} }{s - v}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{860000}{50 - 25}[/tex]
⇒ [tex]x_{BEP}[/tex] = 34400 units
Therefore, The new break even point in units = 34400 units
Let f(x)=15/(1+4e^(-0.2x) )
What is the point of maximum growth rate for the logistic function f(x)? Show all work.
Round your answer to the nearest hundredth
Answer:
6.93
Step-by-step explanation:
f(x) = 15 / (1 + 4e^(-0.2x))
f(x) = 15 (1 + 4e^(-0.2x))^-1
Taking first derivative:
f'(x) = -15 (1 + 4e^(-0.2x))^-2 (-0.8e^(-0.2x))
f'(x) = 12 (1 + 4e^(-0.2x))^-2 e^(-0.2x)
f'(x) = 12 (1 + 4e^(-0.2x))^-2 (e^(0.1x))^-2
f'(x) = 12 (e^(0.1x) + 4e^(-0.1x))^-2
Taking second derivative:
f"(x) = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))
Set to 0 and solve:
0 = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))
0 = 0.1e^(0.1x) − 0.4e^(-0.1x)
0.1e^(0.1x) = 0.4e^(-0.1x)
e^(0.1x) = 4e^(-0.1x)
e^(0.2x) = 4
0.2x = ln 4
x = 5 ln 4
x ≈ 6.93
Graph: desmos.com/calculator/zwf4afzmav
The point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).
What is exponential function?Exponential function → An exponential equation is given by - y = eˣ.Graph → The graph of y = eˣ is upward-sloping, and increases faster as {x} increasesGiven is the function f(x) as follows -
f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )
The given logistic function is -
f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )
The inflection point represents the time of most rapid growth. After the inflection point, the growth rate declines, reaches the limiting value. The inflection point occurs at half of the carrying capacity. This is the level of maximum growth.The equation for a logistic model is N = {K/1 + b[tex]$e^{-rt}[/tex]}. The constant {K} is the carrying capacity. It is the limiting value of N. The inflection point occurs at N = K/2.So, we can say that at {x} = N = 15/2 = 7.5, the point of maximum growth exists. At {x} = 7.5, the value of {y} = 7.926. Refer to the graph of the function attached.
Therefore, the point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).
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Technician A says that a MAF sensor is a high-authority sensor and is responsible for determining the fuel needs of the engine based on the measured amount of air entering the engine. Technician B says that a cold wire MAF sensor uses the electronics in the sensor itself to heat a wire 20 degrees below the temperature of the air entering the engine. Who is right
Answer: Both Technicians are correct
Step-by-step explanation: Technician A talked about the functions of a MAF sensor which is to determine the fuel need of the engine based on the of air entering the engine.
Technician B talked about types of MAF sensor employed in vehicles and how they function
A line segment that has both endpoints on the circumference
Answer:
A chord
Step-by-step explanation:
By the definition of a chord, it is a line segment whose endpoints lie on the circle, (and in this case circle is meant by the set of points equidistant from a center point, or as an algebraic term: circumference)
i can't fail this class plz helppppppp
Which of the following are ordered pairs for the equation y = -1/3x - 6?
(0,-6) (3,-7) (-3,5)
(0,-6) (3,-7) (-3,-5)
(0,-6) (3,7) (-3,-5)
(0,6) (3,7) (-3,-5)
Answer:
2nd option (B)
Step-by-step explanation:
(0,-6) works
(3,-7) works
(-3,-5) works
This means the answer is B
Point M is the midpoint of AC , find the coordinates of the missing endpoint when you are given one endpoint, and the coordinates of the midpoint. M(0, 5.5) and C(-3, 6).
Step-by-step explanation:
Here, given the line segment is AC.
Let us assume the coordinates of the point A = (p,q)
The point M (0,5.5) is the mid point of line segment AC.
By Mid-Point Formula:
The coordinates of the mid point M of segment AC is given as:
[tex](0,5.5) = (\frac{p + (-3)}{2} ,\frac{q+ (6)}{2})\\\implies \frac{p + (-3)}{2} = 0 , \frac{q+ (6)}{2} = 5.5\\\implies p = 0 + 3 = 3, q = 5.5 (2) - 6 = 11-6 = 5\\\implies p = 3, q = 5[/tex]
So, the coordinates of the point A is (3,5)
Molly made 3,600 mL3{,}600 \text{ mL}3,600 mL3, comma, 600, start text, space, m, L, end text of tea for a party, and she served the tea divided equally in 12121212 cups. How many liters of tea did Molly put in each cup?
Answer:
0.3 liters
Step-by-step explanation:
Molly made 3600mL of tea for a party.
The tea was served equally in 12 cups.
We are to determine how many liters of tea Molly put in each cup.
Total Volume of Tea = 3600mL
Number of Cups=12
Volume Per Each Cup = 3600/12 = 300mL
Next, we convert our Volume Per Each Cup from mL to Liters
1000 Milliliter = 1 Liter
300 Milliliter =[tex]\frac{300}{1000}[/tex] liters =0.3 liters
Molly put 0.3 liters of tea in each cup.
Having some trouble with this...pls help (in fraction form)
Answer:
[tex]\frac{17}{6}[/tex] or [tex]2\frac{5}{6}[/tex]
Step-by-step explanation:
1.Find the Least Common Denominator (LCD)
LCD = 6
2.Make the denominators the same as the LCD.
[tex]2+\frac{1*3}{2*3} + \frac{1*2}{3*2}[/tex]
3.Simplify. Denominators are now the same
[tex]2+\frac{3}{6} + \frac{2}{6}[/tex]
4. Join the denominators
[tex]2+\frac{3+2}{6}[/tex]
5.Simplify
[tex]2\frac{5}{6}[/tex] = [tex]\frac{17}{6}[/tex]
Answer:
1 1/3
Step-by-step explanation:
Given function:
2y+xx= 1/3y= 1/2Rewrite:
2·1/2+1/3Find the solution:
[tex]2[/tex]·[tex]1/2=1[/tex] [tex]1+\frac{1}{3}=1\frac{1}{3}[/tex]Therefore, 2y+x=1 1/3..
There are twice as many flute players as there are trumpet players. If there are n flute players write an expression to find how many trumpet players there are.
Answer:
there are n flute players so that means that you have a n amount of flute players.
Step-by-step explanation:
You would need n flute players to play ou would have n trumpet players
Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water. How many fluid ounces of soap should he use? (1 cup 5 8 fl oz)
Answer: 28 fl oz
Step-by-step explanation:
84 fl oz. = 10.5 cups of water
10.5/3=3.5*8=28
why 3.5 times 8 is to get the exact amount of fluid ounces
Answer: he would need 14 fluid ounces of concentrated soap.
Step-by-step explanation:
The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water.
1 cup = 8 fluid ounces
Converting 3 cups of water to fluid ounces, it becomes
3 cups = 3 × 8 = 24 fluid ounces
Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. This means that the amount of concentrated soap that he would use is
(84 × 4)/24 = 336/24 = 14 fluid ounces of concentrated soap
A certain computer loses half of its value every two years. If the value of the computer after 3 years is 425, what was the initial value of the computer
To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases by half every two years. Let's denote the initial value of the computer as [tex]\( V_0 \)[/tex]. After the first two years, its value will be [tex]\( \frac{1}{2}V_0 \)[/tex], after another two years (total of 4 years), its value will be [tex]\( \frac{1}{4}V_0 \)[/tex], and after three years, its value will be [tex]\( \frac{1}{8}V_0 \).[/tex]
Given that after three years its value is $425, we can set up the equation:
[tex]\[ \frac{1}{8}V_0 = 425 \][/tex]
Now, let's solve for [tex]\( V_0 \):\[ V_0 = 425 \times 8 \]\[ V_0 = 3400 \][/tex]
So, the initial value of the computer was $3400.
help help help help
Which of the following is 2x(x-7)(x+3)/6x³(x+3)(x-5) simplified?
Cannot be simplified
(x-7)/3x(x-5)
2x(x-7)/6x³(x-5)
(x-7)/3x²(x-5)
Yes it can be, it will be a fraction
Answer:
[image]
Step-by-step explanation:
follow the steps provided in the picture
Factor the expression. 100k^3 – 75k^2 + 120k – 90
5(5k^2 + 6)(4k – 3)
(25k^2 – 6)(20k + 3)
5(5k^2 – 6)(4k + 3)
(5k^2 + 30)(4k – 15)
For this case we must factor the following expression:
[tex]100k ^ 3-75k ^ 2 + 120k-90[/tex]
We take common factor 5:
[tex]5 (20k ^ 3-15k ^ 2 + 24k-18) =[/tex]
We have two groups within the parentheses:
Group 1: [tex]20k ^ 3-15k ^ 2[/tex]
Group 2: [tex]24k-18[/tex]
We factor each group:
Group 1: [tex]6 (4k-3)[/tex]
Group 2: [tex]5k ^ 2 (4k-3)[/tex]
Rewriting we have:
[tex]5 (5k ^ 2 (4k-3) +6 (4k-3)) =\\5 ((5k ^ 2 + 6) (4k-3))[/tex]
Answer:
[tex]5 (5k ^ 2 + 6) (4k-3)[/tex]
An ice cream shop serves small and large scoops of ice cream. Each scoop is sphere-shaped. Each small scoop has a diameter of approximately 6 centimeters. Each large scoop has a diameter of approximately 10 centimeters What is the difference, in cubic centimeters, between a large scoop of ice cream and a small scoop of ice cream? Round your answer to the nearest tenth.
The difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.
Explanation:To find the difference in volume between a large scoop and a small scoop of ice cream, we need to calculate the volume of each scoop and then subtract the volume of the small scoop from the volume of the large scoop.
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Since the diameter of the small scoop is 6 cm, the radius is 3 cm. Plugging this into the formula, we get V = (4/3)π(3 cm)³. Evaluating this expression, we find that the volume of the small scoop is approximately 113.1 cm³.
Similarly, the diameter of the large scoop is 10 cm, so the radius is 5 cm. Using the same formula, we find that the volume of the large scoop is approximately 523.6 cm³.
To find the difference in volume, we subtract the volume of the small scoop from the volume of the large scoop: 523.6 cm³ - 113.1 cm³ = 410.5 cm³. Therefore, the difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.
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The final answer is 410.5 cubic centimeters.
1. Calculate the volume of a small scoop:
- Given the diameter of the small scoop, [tex]\( d_{\text{small}} = 6 \) cm[/tex].
- Radius of small scoop, [tex]\( r_{\text{small}} = \frac{d_{\text{small}}}{2} = \frac{6}{2} = 3 \)[/tex] cm.
- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \).[/tex]
- Substitute the radius into the volume formula: [tex]\( V_{\text{small}} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) \)[/tex].
- Calculate:
[tex]\( V_{\text{small}} = 36 \pi \)[/tex] cubic centimeters.
2. Calculate the volume of a large scoop:
- Given the diameter of the large scoop,[tex]\( d_{\text{large}} = 10 \) cm[/tex].
- Radius of large scoop, [tex]\( r_{\text{large}} = \frac{d_{\text{large}}}{2} = \frac{10}{2} = 5 \) cm[/tex].
- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].
- Substitute the radius into the volume formula:
[tex]\( V_{\text{large}} = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) \)[/tex].
- Calculate:
[tex]\( V_{\text{large}} = 166.7 \pi \)[/tex] cubic centimeters.
3. Find the difference:
- Difference in volume: [tex]\( V_{\text{large}} - V_{\text{small}} = 166.7 \pi - 36 \pi \)[/tex].
- Calculate: [tex]\( V_{\text{large}} - V_{\text{small}} = 130.7 \pi \)[/tex].
- Approximate [tex]\( \pi \)[/tex] to 3.14.
- [tex]\( 130.7 \times 3.14 = 410.498 \)[/tex].
- Rounded to the nearest tenth, the difference is approximately 410.5 cubic centimeters.
Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through (minus1,3) and is parallel to the line whose equation is y equals 2 x plus 1.
Answer:
y = 2x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 1 ← is in slope- intercept form
with slope m = 2
Parallel lines have equal slopes, thus
y = 2x + ← is the partial equation of the parallel line
To find c substitute (- 1, 3) into the partial equation
3 = - 2 + c ⇒ c = 3 + 2 = 5
y = 2x + 5 ← equation of parallel line
Please assist me with these story problems.
Answer:
4. 16
5. $88
6. $687.50
Step-by-step explanation:
4. Let n represent the number.
An expression representing the number multiplied by 0.9 and 6.3 subtracted from the product is ...
0.9n -6.3
We want that result to be 4.5, so we have the equation ...
0.9n -6.3 = 4.5
Since all of the coefficients are divisible by 0.9, we can divide by 0.9 to get ...
n -7 = 9
Adding 7 gives ...
n = 16
The number is 16.
_____
5. For a problem like this, I like to work it backward. If Craig got an extra $18, then everyone's share was $32 -18 = $14. That was the share from a 5-way split, so the amount the friends split evenly was 5×$14 = $70. The total they started with must have been $70 +18 = $88.
The amount they split unevenly was $88. The amount they split evenly, after setting aside $18 for Craig's parents, was $70.
__
It is a bit tricky to write one equation for the amount the friends started with before they did any splits. Call that amount A. Then after setting aside $18, they split (A-18) five ways. Each of those splits was then (A-18)/5. When the $18 was added to one of those, the result was the $32 that Craig got. So, we have ...
(A -18)/5 +18 = 32
and the solution process is similar to the "working backward" description above: subtract 18, multiply by 5, add back 18.
(A -18)/5 = 14
A -18 = 70
A = 88 . . . . . . . . the amount the friends split unevenly
_____
6. Let P represent the original price of the laptop. We're told the price after all of the discounts was 500, so we have ...
P -50 -(0.20P) = 500
0.80P = 550 . . . . . add 50, collect terms
P = 687.50 . . . . . . . divide by the coefficient of P
The original price was $687.50.
the area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height. What are the base and the height of the triangle
Answer: height = 10 feet
Base = 24 feet
Step-by-step explanation:
Let h represent the height of the triangular flower bed.
Let b represent the base of the triangular flower bed
The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
The area of a triangular flower bed in the park has an area of 120 square feet. This means that
1/2 × bh = 120
bh = 120 × 2
bh = 240- - - - - - - - - - - - - - - 1
The base is 4 feet longer than twice the height. This means that
b = 2h + 4
Substituting b = 2h + 4 into equation 1, it becomes
h(2h + 4) = 240
2h² + 4h = 240
2h² + 4h - 240 = 0
Dividing through by 2, it becomes
h² + 2h - 120 = 0
h² + 12h - 10h - 120 = 0
h(h + 12) - 10(h + 12) = 0
h - 10 = 0 or h + 12 = 0
h = 10 or h = - 12
Since the height cannot be negative, then h = 10
Substituting h = 10 into equation 1, it becomes
10b = 240
b = 240/10
y = 24
The answers are : (a) The height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet[/tex]. (b) The base [tex]\( b \)[/tex] of the triangular flower bed is [tex]24 \ feet[/tex]
Let's denote the height of the triangular flower bed as [tex]\( h \)[/tex] feet.
According to the problem, the base of the triangle is [tex]4\ feet[/tex] longer than twice the height. Therefore, the base [tex]\( b \)[/tex] can be expressed as:
[tex]\[ b = 2h + 4 \][/tex]
The formula for the area [tex]\( A \)[/tex] of a triangle is given by
[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Given that the area [tex]\( A \)[/tex] of the triangular flower bed is [tex]120\ square\ feet[/tex], we can write the equation:
[tex]\[ \frac{1}{2} \times b \times h = 120 \][/tex]
Substituting [tex]\( b = 2h + 4 \)[/tex] into the area equation:
[tex]\[ \frac{1}{2} \times (2h + 4) \times h = 120 \][/tex]
Now, solve for [tex]\( h \)[/tex]
[tex]\[ (2h + 4) \times h = 240 \][/tex]
[tex]\[ 2h^2 + 4h = 240 \][/tex]
[tex]\[ 2h^2 + 4h - 240 = 0 \][/tex]
Divide the entire equation by [tex]2[/tex] to simplify:
[tex]\[ h^2 + 2h - 120 = 0 \][/tex]
Now, solve this quadratic equation using the quadratic formula, [tex]h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 2 \), and \( c = -120 \)[/tex]
[tex]\[ h = \frac{-2 \pm \sqrt{(2)^2 - 4 \times 1 \times (-120)}}{2 \times 1} \][/tex]
[tex]\[ h = \frac{-2 \pm \sqrt{4 + 480}}{2} \][/tex]
[tex]\[ h = \frac{-2 \pm \sqrt{484}}{2} \][/tex]
[tex]\[ h = \frac{-2 \pm 22}{2} \][/tex]
The solutions for [tex]\( h \)[/tex] are:
[tex]\[ h = \frac{20}{2} = 10 \][/tex]
[tex]\[ h = \frac{-24}{2} = -12 \][/tex]
So, the height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet.[/tex]
Now, calculate the base [tex]\( b \)[/tex]
[tex]\[ b = 2h + 4 \][/tex]
[tex]\[ b = 2 \times 10 + 4 \][/tex]
[tex]\[ b = 20 + 4 \][/tex]
[tex]\[ b = 24 \][/tex]
The complete Question is
The area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height.
a. What is the base of the triangle ?
b. What is the height of the triangle ?
In the library at lenape elmentary school, there are 3/8 as, many fiction books as there are nonfiction books. There are 44 books in school library. How many booka are fiction books
Answer:
12 fiction books.
Step-by-step explanation:
Let b represent number of non-fiction books.
We have been given that in the library at Lenape elementary school, there are 3/8 as many fiction books as there are nonfiction books. So number of fiction books would be [tex]\frac{3}{8}x[/tex].
We are also told that there are 44 books in school library. We can represent this information in an equation as:
[tex]x+\frac{3}{8}x=44[/tex]
Let us solve for x.
[tex]\frac{8x}{8}+\frac{3}{8}x=44[/tex]
[tex]\frac{8x+3x}{8}=44[/tex]
[tex]\frac{11x}{8}=44[/tex]
[tex]\frac{11x}{8}\cdot \frac{8}{11}=44\cdot\frac{8}{11}[/tex]
[tex]x=4\cdot 8[/tex]
[tex]x=32[/tex]
Therefore, there are 32 non fiction books in the library.
Number of fiction books would be [tex]\frac{3}{8}x\Rightarrow \frac{3}{8}*32=3*4=12[/tex]
Therefore, there are 12 fiction books in the library.
Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four.
[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .
Step-by-step explanation:
We need to Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four. Which is equivalent to [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] :
[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex]
⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{44}[/tex]
⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{16(3)} - \sqrt{9(6)}[/tex]
⇒ [tex]7\sqrt{3}- 4\sqrt{6} + 4\sqrt{(3)} - 3\sqrt{(6)}[/tex]
⇒ [tex]11\sqrt{3}- 4\sqrt{6}- 3\sqrt{(6)}[/tex]
⇒ [tex]11\sqrt{3}- 7\sqrt{6}[/tex]
[tex]\sqrt{3} = 1.732 , \sqrt{6} = 2.449[/tex]
⇒ [tex]11(1.723)- 7(2.449)[/tex]
⇒ [tex]1.909[/tex]
Therefore, [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .
Answer:
11√3 - 7√6
Step-by-step explanation:
I took the test and got it right.
HL Theorem
ASA Postulate
SSS Postulate
SAS Postulate
Answer:
HL theorem.
Step-by-step explanation:
This states that if the hypotenuse (H) and one leg (L) of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
Answer:
ASA Postulate
Step-by-step explanation:
[tex] In \:\triangle QTS \:\&\:\triangle SRQ\\\\
QT || SR\\\\
\angle QTS \cong \angle SRQ... (each\: 90°)\\\\
TS \cong QR.... (given) \\\\
\angle QST \cong \angle SQR.. (alternate\:\angle s) \\\\
\therefore \triangle QTS \cong \triangle SRQ\\.. (By \: ASA \: Postulate) [/tex]
RHS Postulate can also be applied to prove both the triangles as congruent.
A plane can fly 520 miles in the same time as it takes a car to go 200 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.
Answer: the speed of the plane is 130 mph
Step-by-step explanation:
Let x represent the speed of the plane. If the car travels 80 mph slower than the plane, then the speed of the car would be (x - 80) mph.
Time = Distance/speed
plane can fly 520 miles in the same time as it takes a car to go 200 miles. This means that the time it takes the plane to fly 520 miles is
520/x
Also, the time it takes the car to drive 200 miles is
200/(x - 80)
Since the time is the same, it means that
520/x = 200/(x - 80)
Cross multiplying, it becomes
520(x - 80) = 200 × x
520x - 41600 = 200x
520x - 200x = 41600
320x = 41600
x = 41600/320
x = 130 mph
The vertex of this parabola is at (2, -4). Which of the following could be its equation?
A.y = 2(x - 2)2 + 4
B.x = 2(y + 4)2 + 2
C.x = 2(y - 4)2 + 2
D.y = 2(x - 2)2 - 4
Answer:
The answer to your question is letter B
Step-by-step explanation:
Data
Vertex = (2, -4)
Process
From the image we know that it is a horizontal parabola that opens to the right so the equation must be
(y - k)² = 4p(x - h)
Let 4p be 1
- Substitution
(y + 4)² = (x - 2)
- Solve for x
(y + 4)² = x - 2
- Result
x = (y + 4)² + 2
The answer is letter B, because of the signs.