Answer:
a) about 0.7 seconds to 5.1 seconds.
b) Listed below.
Step-by-step explanation:
h - 1 = -5x^2 + 29x
h = -5x^2 + 29x + 1
a) We will find the amount of time it takes to get to 18 meters.
18 = -5x^2 + 29x + 1
-5x^2 + 29x + 1 = 18
-5x^2 + 29x - 17 = 0
We will then use the quadratic formula to find the answer.
[please ignore the A-hat; that is a bug]
[tex]\frac{-29±\sqrt{29^2 - 4 * -5 * -17} }{2 * -5}[/tex]
= [tex]\frac{-29±\sqrt{841 - 340} }{-10}[/tex]
= [tex]\frac{-29±\sqrt{501} }{-10}[/tex]
= [tex]\frac{-29 ± 22.38302929}{-10}[/tex]
= [tex]\frac{-6.616970714}{-10}[/tex] and [tex]\frac{-51.38302929}{-10}[/tex]
= 0.6616970714 and 5.138302929
So, the time period for which the baseball is higher than 18 metres ranges from about 0.7 seconds to 5.1 seconds.
b) Restrictions on the domain and range of the function are that the domain and range can never be negative, since time cannot be negative, and height cannot be negative. The height cannot exceed the vertex of the parabola, since that is the highest the ball will ever go. It cannot exceed that height since gravity will cause the ball to fall down.
Hope this helps!
find the area of triangle whose vertices are (- 8,4 )(- 6,6) and (- 3,9)
Answer:
Area of the triangle = 0
Step-by-step explanation:
We are given the vertices of a triangle as: (- 8,4 ), (- 6,6), (- 3,9)
The formula to find the Area of the triangle =
1/2[ x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
Where :
(x₁, y₁) = (- 8,4 )
(x₂, y₂) = (- 6,6)
(x₃, y₃) = (- 3,9)
Area of the triangle = 1/2[-8(6 - 9) + -6(9 - 4) + -3(4 - 6)]
= 1/2[ (-8 × -3) +( -6 × 5) +( -3× -2)]
= 1/2[ 24 - 30 + 6)
= 1/2[ 24 + 6 - 30]
= 1/2 [30 - 30]
=1/2[ 0 ]
= 0
Therefore, the area of triangle whose vertices are (- 8,4 ), (- 6,6) and (- 3,9) is ZERO( = 0 )
Wesley makes spherical fish tanks with a diameter of 30. A customer requests a smaller tank with half the volume of the tank that Wesley usually makes.
What is the approximate diameter of the smaller tank?
Round to the nearest tenth.
Answer:
23.8
Step-by-step explanation:
V = 4/3 π r³
V = 4/3 π (15)³
V = 4500 π
V = 4/3 π r³
4500 π / 2 = 4/3 π r³
1687.5 = r³
r ≈ 11.9
d ≈ 23.8
Answer:
23.8 is the diameter.
Step-by-step explanation:
4/5 (x − 20) = 8 solve it
Answer:
30
Step-by-step explanation:
4/5 (x-20)=8
4/5x-4/5*20=8
4/5x-16=8
4/5x=24
x=(24*5)/4
x=30
hope it helps..
A printer ink cartridge that can print 550 pages has already printed 127 pages. Which solution represents the correct equation and answer to the question, "How many more pages, P, can still be printed?"
P + 127 = 550 P = 423
Answer:
P = 423
P + 127 = 550
Step-by-step explanation:
1)Determine que acción realiza la función definida como: f(x) = -7x - 7 a) Multiplica la variable independiente por -7 y luego resta 7 b) Multiplica la variable independiente por 7 y luego resta 7 c) Multiplica la variable dependiente por -7 y luego resta -7 d) Multiplica la variable dependiente por -7 y luego resta -7 2)Dada la funcion F(x) = -3x + 6 el valor de F(5) es
Answer:
a) Multiplica la variable independiente por -7 y luego resta 7
Step-by-step explanation:
Sea [tex]f(x) = -7\cdot x - 7[/tex], las acciones realizadas por la función sobre la variable independiente, esto es, [tex]x[/tex], son:
1) Multiplica la variable por 7.
2) Refleja el resultado anterior con eje de simetría en el eje x. (Multiplicación por -1).
3) Traslada vertical el resultado de 2) siete unidades en la dirección -y.
Por ende, la opción correcta es a).
What is the perimeter of the rectangle?
Answer:
32
Step-by-step explanation:
P=2(l+w)
so 2(11+5)=P
2(11+5)=32
The 2 equations only pls
Payday context:
It’s the end of the month which means it is time to pay your coffee shop employees. Make sure each employee gets paid the correct amount
(write an equation for each situation and solve) identify variables when applicable
Answer:
she works 50 hours for that week
Step-by-step explanation:
She is paid $18 per hour and received a bonus of $125 per bonus for the first week . she claims her compensation for the first week should be $1025 . The number of hour she worked base on her claim can be calculated below.
Let
the number of hours she worked = a. Therefore,
18a + 125 = 1025
18a = 1025 - 125
18a = 900
divide both sides by 18
a = 900/18
a = 50
she works 50 hours for that week
A circular table top has a radius of 24 inches.
What is the area of the table top, to the nearest square inch? Use 3.14 for n.
75 in.2
151 in.
1809 in.2
7235 in.2
Answer:
(C) 1809 in.2
Step-by-step explanation:
Took the test on edg :3
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)
y = 18(1.15)x
y = 18(0.15)x
y = 20.7(1.15)x
y = 20.7(0.15)x
Answer: A) 18(1.15)x
Step-by-step explanation:
18 was the original cost, so the price will always be determined with this starting point. Sice there is an increasing value, that makes it 1.15 instead of .15. And it goes up by 15%, making it the coefficient.
Answer:
A) y = 18(1.15)x
Step-by-step explanation:
what happens to the resistance as the conductor is made thicker
Answer:
The resistance decreases.
Step-by-step explanation:
The resistance decreases as the conductor is made thicker.
First of all, resistance is like some sort of an obstacle right?
So if the conductor is made thicker it will be easy for the electrons to pass through.
And if the conductor is made thinner it won't be easy for the electrons to pass through. Which makes the resistance increase as there will be collision between the electrons.
Hope this helped ;) ❤❤❤
Help please!!!!!! Thank you
Answer:
1/4
Step-by-step explanation:
Well see how far each points are from each other.
Start at the red triangle and go up 1, go to the right 4.
Thus,
the rise/run is 1/4.
Hope this helps :)
Answer:
1/4
Step-by-step explanation:
To find the rise/run, you first need to pick two points from the line. You can pick whichever points you want, and you will get the right answer. I will pick (-8, -3) and (8, 1).
Divide the difference of the y's by the difference of the x's.
-3 - 1 = -4
-8 - 8 = -16
-4/-16 = 1/4
The rise/run is 1/4.
please help Evaluate 5 - (3/2) to the 3 power A.) 13/8 B.) 9.5 C.) 18.5 D.) 2197/8
Answer: THE ANSWER IS A
Step-by-step explanation:
5-(3/2)^3
=13/8
im a math god
Randomization in an experiment means that the experimental units or
subjects are selected as a simple random sample from the whole population
under study.
Answer:
Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of samples is important in an experiment, that is, to carry it out in a random way.
Step-by-step explanation:
For example;
If a crop at a certain time of year, for example in summer, is affected by a certain fungus, to know if it is really the time of year that affects this problem, random samples of the same crop with the same characteristics and put it to the test at another time of the year to see if the weather is really a risk factor in the spread of this fungus.
I was at the store, and saw two sizes of avocados being sold. The regular size sold for $0.84 each. For what prices would the larger avocado be a better deal?
Answer:
The bigger avocado will be a better deal if the ratio of the sizes of the bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.
Step-by-step explanation:
Given that two sizea of avocados are being sold, since the regular size is being sold for $0.84 each, let the price for the bigger avocado be $x.
Then note the following:
1. How bigger than the smaller avocado is the bigger one?
This would determine if the price for the bigger one is a bargain, or a mistake.
If for instance, the bigger avocado is double the size of the smaller one, then for any price, $x less that $1.68 (twice of $0.84), it is a bargain.
The bigger avocado will be a better deal if the ratio of the sizes bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.
Answer:
The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.
Step-by-step explanation:
The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.
The ratio of Ed's toy cars to Pete's toy cars was initially 5:2. After Ed gave 30 toy cars to Pete, they each had an equal number of cars. How many toy cars did they have altogether?
Answer:
140 toy cars
Step-by-step explanation:
The ratio of Ed's toy car to Pete's toy car is initially given as 5:2
Ed gave Pete a total number of 30 cars
Let x represent the greatest common factor that exists between both number
Number of Ed's car is represented as 5x
Number of Pete car is represented as 2x
Since they each have an equal number of cars which is 30 then we can solve for x as follows
5x-30=2x+30
Collect the like terms
5x-2x= 30+30
3x= 60
Divide both sides by the coefficient of x which is 3
3x/3=60/3
x=20
Ed's car is 5x, we substitute 20 for x
5(20)
= 100 cars
Pete car is 2x,we substitute 20 for x
2(20)
= 40 cars
Therefore, the total number of cars can be calculated as follows
= 100+40
= 140 toy cars
Hence they have 140 toy cars altogether
Answer:
140
Step-by-step explanation:
Find x ÷ y, if x = 3 5/6 and y = 3 3/4 .Express your answer in simplest form.
Answer:
23/30
Step-by-step explanation:
x/y
(3 5/6)/(3 3/4)
((3*6)+5/6)/((3*4)+ 3/4)
(18+5/6)/(12+3/4)
(23/6)/(15/4)
(23/6)*(4/15)
(23*3)/(6*15)
(69/90)
23/30
Answer:
1 1/45
Step-by-step explanation:
Maya decides to use the method of proportions and similar triangles to find the height of a tower. She measures the length of the tower's shadow and finds it is 20 feet long. Then she holds a 12-inch ruler perpendicular to the ground and finds that it casts a 4-inch shadow. How tall is the tower? a. 2.4 ft c. 60 ft b. 5 ft d. 240 ft
Answer: C: 60 ft
Step-by-step explanation:
Her pencil is 12 inches and its shadow is 4 inches. Her pencil is 3 times longer than its shadow, so using that logic we can conclude that the tower is 3 times longer than its shadow as well.
[tex]20*3=60[/tex]
The tower is 60 feet tall.
Efren is constructing a line parallel to EF¯¯¯¯¯ through point G. What step should be his next step? With the compass point on D, construct an arc that intersects EF¯¯¯¯¯ and GD←→ . With the compass point on G, construct an arc that intersects GD←→ . With the compass point on D, construct an arc that intersects EF¯¯¯¯¯ twice. With the compass point on G, construct an arc that intersects EF¯¯¯¯¯ .
Answer:
The correct option is;
With the compass point on G, construct an arc that intersect GD←→
Step-by-step explanation:
The steps for constructing a parallel line to a given point is as follows;
1) With the straightedge, a transversal is drawn intersecting the giving line and passing through point G
2) Copy the angle formed between the transversal and the given line and the to the point G starting by constructing an arc with the compass on point G to intersect GD←→ then with the compass opening still the same, place the compass on the point of intersection of the arc constructed from point G on GD and construct another arc to intersect the arc previous arc from G to GD
3) The line drawn from the intersection through is a parallel line to EF
Therefore, the correct option is that with the compass point on G, construct an arc that intersect GD←→.
Answer:
A. With the compass on point D , construct an arc that intersects EF¯¯¯¯¯ and GD←→.
Step-by-step explanation:
I just took the test!
Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7. m∠3 is (3x + 4)° and m∠5 is (2x + 11)°. Angles 3 and 5 are . The equation can be used to solve for x. m∠5 = °
Answer:
77 degrees
Step-by-step explanation:
The diagram is drawn and attached below.
m∠3= (3x + 4)°
m∠5 = (2x + 11)°
Angles 3 and 5 are co-interior angles and are therefore supplementary (add up to 180 degrees).
(3x + 4)°+(2x + 11)°=180°
5x+15=180
5x=180-15
5x=165
x=33
Therefore, the measure of angle 5
m∠5 = (2x + 11)°
= (2(33) + 11)°
=66+11
=77°
The measure of angle 5 is 77 degrees.
Solve =14+3 l = 14 j + 3 k for k. Select one: a. =+143 k = l + 14 j 3 b. =−143 k = l − 14 j 3 c. =3+14 k = l 3 + 14 j d. =3−14
Answer:
k= l/3 - 14/3j
Step-by-step explanation:
l = 14j + 3k
Solve for k
l = 14j + 3k
Subtract 14j from both sides
l - 14j =14j + 3k - 14j
l - 14j = 3k
Divide both sides by 3
l - 14j / 3=3k / 3
k= l/3 - 14/3j
Or
1/3(l - 14j) = k
Answer:
Which expression is equivalent to ‐10
k
‐
10
?
Step-by-step explanation:
Find the values ofx and y for the triange.
x
60°
30°
у
Answer:
X=36.4 or 36.37306696.... and Y=42
Step-by-step explanation:
So you have a 30-60-90 triangle!
Do Not Worry this is a hard subject to understand, but I will try to do my best with helping you. Right now you need to find x and y. All you have is 21. Under your 60 angle, which is pointing downward, is the 21. And 21 is initially in the spot of x or 1. so 21 is the x(But not the x on the side of 90). I am sorry if this is a bit confusing.
You are then going to take your side which is x, the side that is directly in the path of 90, and it is going to be 21[tex]\sqrt{3[/tex]. Then on the side of your y, which is in the path of your 60, it will be 2 times your x.
The general layout of this is:
x is underneath the side of 90 degrees.
then on the side where 60 degrees and 30 degrees is, is going to be x[tex]\sqrt{3[/tex].
Then the last side, where 30 degrees and 90 degrees lay, will be 2(x).
So all you have to do is plug everything in.
x=36.4 in decimal
y=42(because all you had to do was plug 21 where the x is, because that is where x is in the general layout.)
The value of x = 42 units
The value of y = 21√3 units
What is Trigonometry?The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.
As per the given diagram:
The triangle is a right angle triangle.
Using trigonometric ratios to find x and y:
tan30° = (P/B)
tan30° = (21/y)
(1/√3) = (21/y)
y = 21√3 units
sin30° = (P/H)
(1/2) = (21/x)
x = 2 × 21
x = 42 units
The value of x and y is 42 units and 21√3 units, respectively.
To learn more on Trigonometry, click:
brainly.com/question/17199821
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This table gives a few (x,y) pairs of a line in the coordinate plane.
Answer:
x-intercept → (-5, 0)
Step-by-step explanation:
Let the equation of the line having pairs given in the table is,
y - y' = m(x - x')
m = slope of the line
(x', y') is a point lying on the line.
From the given table,
Two points (33, -22) and (52, -33) lie on the line.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{-33+22}{52-33}[/tex]
m = [tex]-\frac{11}{19}[/tex]
Equation of the line passing through (33, -22) and slope = [tex]-\frac{11}{19}[/tex] will be,
y + 22 = [tex]-\frac{11}{19}(x - 33)[/tex]
For x-intercept y = 0,
0 + 22 = [tex]-\frac{11}{19}(x-33)[/tex]
-38 = x - 33
x = -38 + 33
x = -5
Therefore, x-intercept of the line is (-5, 0).
Answer:
-5,0
Step-by-step explanation:
khan academy
Please answer this in two minutes
Answer:
60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between sides of a right triangle and angles.
Tan = Opposite/Adjacent
tan(T) = SU/ST
tan(T) = (5√51)/(5√17) = √3
Now, the arctangent function is used to find the angle whose tangent is √3.
T = arctan(√3) = 60°
What is the equation of a line, in general form, that passes through points (-1, 2) and (5, 2)? A. y - 2 = 0 B. y - x - 2 = 0 C. x - 2 = 0
Answer:
y=2 or y-2=0
Step-by-step explanation:
to find the equation first find the slope m points (-1,2) and (5,2)
m=y2-y1/x2-x1 =2-2/5-(-1)=0/6=0
y=mx+b the slope is zero then y=b=2
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
X+ y = 8
x- y = 6
A. (7,1)
B. (8,2)
C. (9,3)
D. (60)
Answer:
The answer is option A.
Step-by-step explanation:
The steps are :
[tex]x + y = 8 - - - (1)[/tex]
[tex]x - y = 6 - - - (2)[/tex]
[tex](1) - (2)[/tex]
[tex]x + y - x - ( - y) = 8 - 6[/tex]
[tex]2y = 2[/tex]
[tex]y = 1[/tex]
[tex]substitute \: y = 1 \: into \: (1)[/tex]
[tex]x + 1 = 8[/tex]
[tex]x = 7[/tex]
2. Find the value of [tex]5\sqrt[3]{1728} + 100 \sqrt[4]{81} - (6\sqrt{10} )x^{2}[/tex]
(a) 1 (b) 0 (c) 8 (d) 10
Answer:
(b) 0
Step-by-step explanation:
Assuming a typo in the last term:
5 (1728)^(1/3) + 100(81)^(1/4) - ( 6(10)^(1/2) )^2
=5(12) + 100(3) -36(10)
=60+300-360
=0
Answer:
[tex]\boxed{\sf (b) \ 0}[/tex]
Step-by-step explanation:
[tex]\sf 5\sqrt[3]{1728} +100\sqrt[4]{81} -(6\sqrt{10} )^2[/tex]
[tex]\sf Evaluate.[/tex]
[tex]\sf 5(12)+100(3) -((6)^2 (\sqrt{10})^2)[/tex]
[tex]\sf 60+300 -(36(10))[/tex]
[tex]\sf 360-360[/tex]
[tex]\sf 0[/tex]
Solve the equation below for the variable (x):
2y + x = 10 + 2 x
A. x = 8y
B. x = 10 - 2y
C. x = 2y - 10
D. x = -8y
Answer:
Hope this helps. If not let me know and I'll explain it better
The world's tallest building is the Burj Khalifa in Dubai at 828 m tall. The CN Tower in Toronto is 553 m tall. Ryan wants to compare the Burj Khalifa and the CN Tower by creating rectangular prism models on a 10 cm by 10 cm square base. He has decided to represent the Burj Khalifa with a rectangular prism that has a height of 40 cm. What is the volume of each rectangular prism? Round your answer to the nearest cubic centimetre. Show your work for full marks.
Answer:
Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]
Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]
Step-by-step explanation:
Given
Height of Burj Khalifa = 828 m
Height of CN Tower in Toronto = 553 m
Base of rectangular prism is a square with sides 10 cm [tex]\times[/tex] 10 cm.
Height of Burj Khalifa prism = 40 cm
828 m is represented as 40 cm
[tex]\Rightarrow 553 m[/tex] is represented as [tex]\frac{40}{828 } \times 553 = 26.71\ cm[/tex]
So, height of rectangular prism of CN Tower = 26.71 cm
Volume of a Prism is given by the Formula:
[tex]V=Area\ of\ Base \times Height[/tex]
Base is a square, so Area of base = [tex]Side^2[/tex]
Volume of Burj Khalifa Prism:
[tex]V_B=10^2 \times 40 = 4000\ cm^2[/tex]
Volume of CN Tower Prism:
[tex]V_C=10^2 \times 26.71 = 2671\ cm^2[/tex]
So, the answer is:
Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]
Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]
Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs 36 20 56 Prefers cats 10 26 36 No preference 2 6 8 TOTAL 48 52 100 Of students in the sample, what fraction were male?
Answer:
12/25
Step-by-step explanation:
There were a total of 48 males, so 48/100 = 12/25.
+---------------+------+--------+-------+
| | Male | Female | Total |
+---------------+------+--------+-------+
| Prefers Dogs | 36 | 20 | 56 |
+---------------+------+--------+-------+
| Prefers Cats | 10 | 26 | 36 |
+---------------+------+--------+-------+
| No Preference | 2 | 6 | 8 |
+---------------+------+--------+-------+
| Total | 48 | 52 | 100 |
+---------------+------+--------+-------+
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.
When the water was 4 feet from the end of the hose, what was its height above the ground?
3.2 feet
4.8 feet
5.6 feet
6.8 feet
Answer: A) 3.2 ft
Step-by-step explanation:
f(4) = -0.3(4)² + 2(4)
= -4.8 + 8
= 3.2
Answer:
3.2 feet
Step-by-step explanation: