h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.
What is the value of h(24)?Given,
h(x) = -0.017x² + 1.08x + 5.8
Put h = 24,
h(24) = -0.017(24)² + 1.08(24) + 5.8
h(24) = -9.792 + 25.92 + 5.8
h(24) = 21.93
The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.
What is the value of the vertical intercept?Vertical intercept, x = 0
h(0) = -0.017(0)² + 1.08(0) + 5.8
h(0) = 5.8
The height of the shot put above the ground is 5.8 feet at the start.
What is the values of the vertex coordinates?vertex coordinates,
(h,k) = [(-b/2a),-(b²- 4ac)/4a]
(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]
(h,k) = [(1.08/0.034),(1.5608)/0.068)]
(h,k) = (31.76,22.95)
The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.
How far from the start did the shot put strike the ground?Put h(x) = 0,
-0.017x² + 1.08x + 5.8 = 0
Use quadratic formula for solving x,
x = (-b±√b²- 4ac)/2a
Here a = -0.017, b=1.08, c=5.8
x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)
x = [-1.08±√1.5608]/-0.034
x = [-1.08-1.2493]/-0.034 and x = [-1.08+1.2493]/-0.034
x = 68.509 and x = - 4.98
Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²
= √73.49²
= 73.49 feet
Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.
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equivalent expressions to 7^3*7^x
The double number line shows that Toni can type 180 words in 2 minutes.
A double number line with 6 equally spaced tick marks. The line labeled Time, minutes, reads from left to right: 0, an unlabeled tick mark, 2, three unlabeled tick marks. The line labeled Words, reads from left to right: 0, an unlabeled tick mark, 180, three unlabeled tick marks.
A double number line with 6 equally spaced tick marks. The line labeled Time, minutes, reads from left to right: 0, an unlabeled tick mark, 2, three unlabeled tick marks. The line labeled Words, reads from left to right: 0, an unlabeled tick mark, 180, three unlabeled tick marks.
Based on the ratio shown in the double number line, how many words can Toni type in 3 minutes?
_words
The number of words that Toni can type in 3 minutes is 270 words per minute.
How to work with ratios?We are given 180 words in 2 minutes. This means;
Toni can type 180/2 = 90 words per minute (90wpm).
Using the above same ratio/rate, it means that in 3 minutes, Toni would be able to type:
90 * 3 = 270 words per minute.
Thus, we conclude that the number of words that Toni can type in 3 minutes is 270 words per minute.
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Shawn averages 10,142 steps every day. If there were 31 days in the month, about how many steps did he take in that month.
Answer:
314402 steps
Step-by-step explanation:
10142 x 31
graph y=1/3x+5 PLS HELP ASAP
Answer:
Graph attached.
Step-by-step explanation:
Given equation:
[tex]y=\dfrac{1}{3}x+5[/tex]
The given equation is a linear equation in slope-intercept form, where 1/3 is the slope and 5 is the y-intercept.
To graph the equation, find and plot at least two points, then draw a straight line through them.
To find the points on the line, input values of x into the equation:
[tex]x = 0 \implies y=\dfrac{1}{3}(0)+5 \implies (0,5)[/tex]
[tex]x=3 \implies y=\dfrac{1}{3}(3)+5 \implies (3,6)[/tex]
[tex]x=6 \implies y=\dfrac{1}{3}(6)+5 \implies (6,7)[/tex]
See attachment for the graph of the given equation.
Find some points
x=0
y=5x=3
y=1+5=6x=-3
y=-1+5y=4Graph attached
What The What The???
Considering a geometric sequence, the pattern is given as follows:
1, 2, 4, 8, 16, 32, 64.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The first term and common ratio are given as follows:
[tex]a_1 = 1, q = 2[/tex].
Hence the remaining terms are:
[tex]a_4 = 2^{4-1} = 8[/tex][tex]a_5 = 2^{5-1} = 16[/tex][tex]a_7 = 2^{7-1} = 64[/tex]More can be learned about geometric sequences at https://brainly.com/question/11847927
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for this graph, mark the statements that are true.
Answer:
C,D
Step-by-step explanation:
C: Range refers to the y axis and all values shown on this graph (and even beyond the graph) are greater than 0
D: The domain refers to the x-axis. The line goes on forever both to the right and the left therefore meaning all x values are used.
pls help I dont understand this
Answer:
D
Step-by-step explanation:
Here are the gold medal times for the women’s 100-meter freestyle (swimming) in every other Summer Olympics:
The least-squares regression line equation is y = -0.28x + 610.31
The scatter plot of the dataTo plot the scatter plot of the data, we represent the x-axis with year and we represent the y-axis with time
Next, we plot the scatter plot using the dataset
See attachment for the scatter plot
Describe the relationship between the variables in the graph.From the attached scatter plot, we can see that the relationship between the variables in the graph is approximately linear.
This is so because the points appear to be on a straight line
Find the correlation coefficient.To do this, we make use of a graphing calculator, with the following summary:
X Values
∑ = 21608Mean = 1964.364∑(X - Mx)2 = SSx = 10062.545Y Values
∑ = 686.41Mean = 62.401∑(Y - My)2 = SSy = 842.83X and Y Combined
N = 11∑(X - Mx)(Y - My) = -2806.684R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -2806.684 / √((10062.545)(842.83)) = -0.9638
Hence, the correlation coefficient is -0.9638
Find the least-squares regression line.To do this, we make use of a graphing calculator, with the following summary:
Sum of X = 21608Sum of Y = 686.41Mean X = 1964.3636Mean Y = 62.4009Sum of squares (SSX) = 10062.5455Sum of products (SP) = -2806.6836The least-squares regression line equation is
y = bx + a
Where
b = SP/SSX = -2806.68/10062.55 = -0.27892
a = MY - bMX = 62.4 - (-0.28*1964.36) = 610.30872
So, we have
y = -0.27892x + 610.30872
Approximate
y = -0.28x + 610.31
Hence, the least-squares regression line equation is y = -0.28x + 610.31
The estimated gold medal time for 1924 and for 1976.We have:
y = -0.28x + 610.31
Substitute 1924 and 1976 for x
y = -0.28 * 1924 + 610.31 = 71.59
y = -0.28 * 1976 + 610.31 = 57.03
Are these estimates reliable?
Yes, the estimates are reliable
Are they reasonable?
Yes, the estimates are reasonable
Why are your answers in Question 5 different than the times given in the table?The results are different because the answers in 5 are estimated from the formula while the table are the actual values
Find the estimated gold medal time for 2022 and for 2200.We have:
y = -0.28x + 610.31
Substitute 2022 and 2200 for x
y = -0.28 * 2022 + 610.31 = 44.15
y = -0.28 * 2200 + 610.31 = -5.69
Are these estimates reliable?
No, the estimates are not reliable
Are they reasonable?
The estimate in 2022 is reasonable, while the estimate in 2200 is not reasonable
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Eric's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Eric $5.50 per pound, and type B coffee costs $4.40 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $762.30. How many pounds of type A coffee were used?
115.2 pounds of type A coffee were used.
What is the solution of the equation?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
Let the number of pounds of type A coffee be x and the number of pounds of Type B coffee be y.
According to the question, the equations are,
5.50x + 4.40y = 762.30
x = 4y
So, the solution of the equation is obtained as follows:
5.50(4y) + 4.40y = 762.30
26.40y = 762.30
y = 762.30/26.40
y = 28.8 pounds
x = 4*28.8 = 115.2 pounds
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When the sum of a number and 3 is subtracted from 10 the result is 5 solve om algebraic equation?
Answer:
y = 2
Step-by-step explanation:
Algebraic Equation is an equation where alphabets are used to represent numbers.
Solving the above question,
Let the number = y
Therefore,
Sum of the number = y + 3
If it's subtracted from 10 it becomes
10 - ( y + 3 )
The result : 10 - y - 3 = 5
- y = 5 - 10 + 3
- y = -2
Therefore,
y = 2
A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?
a)0.09%
b) 6.25%
c)13%
d)52%
A single card is drawn from each of two decks of 52 cards. The probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.
Probability means possibility.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
There are 52 cards in a standard deck.
So, the total number of possible outcomes=52
We have to pick a single card from each of decks of 52 cards.
In a deck of 52 cards there are 13 heart cards and 13 diamond cards.
Therefore the probability of getting a heart from the first deck=13/52
And the probability of getting a diamond from the second deck=13/52
Hence the probability of getting a heart from the first deck and then a diamond on the second deck=(13/52)×(13/52)=6.25%
Thus, the probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.
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Answer:
6.25%
Step-by-step explanation:
I got it right on the test.
In 1996 an outbreak of a disease affected 10 people in a large community. By 1997, the number of those infected had grown to 40. Find an exponential growth function that fits the data.
Answer: The initial population is 18 and 1 year(t=1) later it is 38
Step-by-step explanation:
38 = 18 * e^(1*k), where k is the growth rate
e^(1*k) = 38/18
Take the natural log(ln) of both sides of the = k = ln(38/18) = 0.747
P(t) = 18 * e^(0.747*t), where P(t) is the population affected at time t(years since 1996)
Evaluate each expression:
I-3|=
The value of the modulus function |-3| is 3.
What is the value of modulus?'Modulus' exists a Latin word, which signifies 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value designates only the numeric value and does not contain the sign of the numeric value. The modulus of any vector quantity exists ever taken as positive and exists in its absolute value.
The absolute value (or modulus) | x | of a real number x stands as the non-negative value of x without regard to its sign.
For example, the absolute value of 5 stands at 5, and the absolute value of −5 exists also at 5. The absolute value of a number may be considered as its distance from zero along a real number line.
Therefore, the value of the modulus function |-3| is 3.
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In the figure below, the radius of the larger circle is 6,8 and the radius of the smaller circle is 4.5. Which of the following best approximates the area of the shaded region? Note: The figure is not drawn to scale. O 14.45 O 16.62 O 25.99 O 81.65 O 145.27
A circle is a figure bounded by a curved side which is referred to as circumference. Thus the area of the shaded region is option D. 81.65.
A circle is a figure bounded by a curved side which is referred to as circumference. Some of its parts are radius, diameter, sector, arc, etc.
The area of a circle can be determined by the given expression:
Area = π[tex]r^{2}[/tex]
where r is the radius of the circle and π = [tex]\frac{22}{7}[/tex]
So, the area of the shaded region can be determined as:
Area of the shaded region = area of the larger circle - area of the smaller circle
Area of the shaded region = π[tex](6.8)^{2}[/tex] - π[tex](4.5)^{2}[/tex]
= π (46.24 - 20.25)
= [tex]\frac{22}{7}[/tex] x 25.99
= [tex]\frac{571.78}{7}[/tex]
Area of the shaded region = 81.683
Thus the appropriate answer to the question is option D. 81.65.
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Three quarters of a cake was eaten at a party .how much cake is left?
Hi! ◈
Answer:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1/4 of the cake was left
Step-by-step explanation:
Since the total cake is [tex]\sf{\dfrac{4}{4}}[/tex], all we should do is subtract 3 from 4
[tex]\sf{\dfrac{4-3}{4}}=the \ cake \ that \ was \ left[/tex]
_____________________
[tex]\sf{\dfrac{1}{4} \ of \ the \ cake \ was \ left}[/tex]
Hope this made sense to you !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CalligrxphyQuestion Find the area of a trapezoid whose height is 6 ft and whose bases are 9.7 ft and 6.3 ft.
Answer:
48 Square feet
Step-by-step explanation:
A=((a+b)/2)*h,
((6.3+9.7)/2)*6=48ft^2
Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12)
Here, 12 is the mode.
Step-by-step explanation:
Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12) ?
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.
So let's talk in brief:-
First, we arrange it in ascending order.
3,3,6,6,9,9,12,12,12,12
and now as we see that we get 12 as the most repeated ones.
reference link-
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jerome wants to bake two batches of muffins. He can bake two batches of chocolate chip (C), two batches pumpkin, or one batch of each.
The situation presented can be represented using the following letters CC, CP, PC, and PP.
How many combinations are possible in this situation?The possible combinations are:
Two batches of chocolate chip or CC.Two batches of pumpkin or PP.One batch of chocolate chip and another of pumpkin of CP.One batch of pumpkin and another of chocolate chip or PC.Based on this, the option that represents the situation is:
CC, CP, PC, and PP.
Note: This question is incomplete; here is the missing section:
What is the sample space of the event described above?
Answer choices:
a. CC, CP, PC, PP
b. CC, PP
c. CC, CP, PC
d. C, P
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a x = ±5
b. x = ±5i
C. x = ±3√√5
d. x = ±3√3
e. x = ±3i√√3
f. x= ±3i√√5
1. x^2+45=0
2. x^2=-25
3. x^2-25=0
4. x^2-45=0
5. x^2=27
6. x^2+27=0
Match the items
Answer:
1f, 2b, 3a, 4c, 5d, 6e
see image
Step-by-step explanation:
Solve the equations by getting x all by itself on one side. Then, square root to get rid of the exponent.
Any problem where you square root a negative will give you an i in the answer. This is because sqrt(-1) is i. Because i^2 = -1
Also, when you are simplifying square roots for your final answer, look for a perfect square number inside of the radical. Like Sqrt45 can be broken down to
Sqrt9•sqrt5
And because 9 is a perfect square, sqrt9 simplifies to just 3. See image.
Solve for x. Round your answer to the nearest tenth if necessary. Figures are
not necessarily drawn to scale.
T
63°
72°
18
19
45
630
37
72°
W
45°
X
X
Answer:
18/19= X/37 because 18 and x are both between 72 and 45 degrees
Multiply 18 and 37 then divide by 19 to get answer
Step-by-step explanation:
suppose the equation z^2+4z+20+iz(A+1)=0 where A is constant has complex conjugate root if one of the root of this quadratic is z=B+2i where B is real constant find possible value of A ? please help me I need your help
If one of the roots is [tex]w=B+2i[/tex], then the other root is its conjugate [tex]\bar w=B-2i[/tex]. So we can factorize the quadratic to
[tex]z^2 + 4z + 20 + iz (A+1) = (z-(B+2i)) (z-(B-2i))[/tex]
Expand the right side and collect all the coefficients.
[tex]z^2 + (4+(A+1)i) z + 20 = z^2 - 2B z + B^2+4[/tex]
From the [tex]z[/tex] and constant terms, we have
[tex]\begin{cases}4 + (A+1)i = -2B \\ 20 = B^2 + 4 \end{cases}[/tex]
From the second equation we get
[tex]B^2 = 16 \implies B = \pm4[/tex]
Then
[tex]4+(A+1)i = \pm8[/tex]
[tex](A+1)i = 4 \text{ or } (A+1)i = -12[/tex]
Since [tex]\frac1i=-i[/tex], we have
[tex]-\dfrac{A+1}i = 4 \text{ or } -\dfrac{A+1}i = -12[/tex]
[tex]A+1 = -4i \text{ or } A+1 = 12i[/tex]
[tex]\boxed{A = -1 - 4i \text{ or } A = -1 + 12i}[/tex]
What is the lateral surface area of the cone?
A cone with diameter 18 centimeters, height of 12 centimeters, and slant height of 15 centimeters.
L A = pi r l
108 pi centimeters squared
135 pi centimeters squared
180 pi centimeters squared
270 pi centimeters squared
Answer:
135 pi centimeters squared
Step-by-step explanation:
Hello!
where la is lateral surface area
[tex]first \: the \: formula \: for \: the \: lateral \: surface \: are \: of \: cone \: is \\ la = \pi \times r \times l \\ where \: r = radius \\ l = slant \: height \\ therefore.first \: find \: the \: radius(r) = \frac{d}{2} \\ r = \frac{18cm}{2} = 9cm \\ so \: as \: we \: have \: the \: radius \: we \: can \: solve \: for \: the \: la \\ la = \pi \times r \times l \\ la = \pi \times (9cm) \times (15cm) \\ la = 135\pi \: cm {}^{2} [/tex]
Find cos B, sinB,tanb
Using right triangle relations, we will get:
tan(B) = 1.05sin(B) = 0.735cos(B) = 0.7How to find the value of the trigonometric equations?
We assume that bot triangles are equivalent, then the angle B will be the same as the angle Z.
Now remember the relations:
tan(θ) = (opposite cathetus)/(adjacent cathetus).sin(θ) = (opposite cathetus)/(hypotenuse)cos(θ) = (adjacent cathetus)/(hypotenuse).If we step on angle B, we have:
opposite cathetus = 29.4adjacent cathetus = 28hypotenuse = 40.6Replacing that, we get:
tan(B) = 29.4/28 = 1.05sin(B) = 29.4/40.6 = 0.735cos(B) = 28/40.6 = 0.7If you want to learn more about trigonometric functions:
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WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
The correct order of reasons that complete the proof about the rectangle and square is that D. definition of congruence, distance formula if two consecutive sides of a rectangle are congruent, then it's a square.
What is congruence?It should be noted that congruence simply means an agreement or a correspondence between shapes.
In geoemtry, it should be noted that figures are said to be congruent if it is possible to superpose one of them on another.
It should be noted that the opposite sides of a rectangle are parallel while in a square, all the sides that are given are equal.
Therefore, the correct order of reasons that complete the proof about the rectangle and square is the definition of congruence, and that if two consecutive sides of a rectangle are congruent, then it's a square.
In conclusion, the correct option is D.
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A perimeter of a movie screen is 56 meters. the area is 171 square meters what are the dimensions of the screen
Using the formula for the perimeter and area of rectangle, the dimensions are: Length = 19 m; width = 9 m.
What is the Perimeter and Area of a Rectangular Shape?Perimeter = 2(length + width)
Area = (length)(width).
Let x represent the length and y the width, therefore:
2(x + y) = 56 --> eqn. 1
xy = 171 --> eqn. 2
Rewrote eqn. 1
x + y = 56/2
x = 28 - y
Substitute x = (28 - y) into eqn. 2
171 = (28 - y)y
171 = 28y - y²
171 - 28y + y² = 0
y² - 28y + 171 = 0
Factorize
(y - 9)(y - 19)
y = 9 and y = 19
Therefore, the dimensions are: Length = 19 m; width = 9 m.
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Let m = X^2 + 3.
What is (x^2+3)^2+7x^2+21=-10 in terms of m?
OR
Let m=x^2+3m=x
2
+3m, equals, x, squared, plus, 3.
Which equation is equivalent to (x^2+3)^2+7x^2+21=-10(x
2
+3)
2
+7x
2
+21=−10left parenthesis, x, squared, plus, 3, right parenthesis, squared, plus, 7, x, squared, plus, 21, equals, minus, 10 in terms of mmm ?
The Equation in terms of m, m^2+7m+10=0
What is substituting in the equation ?
substituting means changing or replacing the values in the given equation.
Calculation:
Given equation is (x^2+3)^2+7x^2+21=-10
and m= X^2 + 3.
make the given equation in the form X^2 + 3,
now,
(x^2+3)^2+7x^2+21=-10
(x^2+3)^2+7(x^2+3)=-10
where,
X^2 + 3= m
after putting the value or replacing the values
we get, m^2+7m=-10
m^2+7m+10=0
the above equation is in the form of "m".
The Equation in terms of m, m^2+7m+10=0
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Answer:
m^2+7m+10=0
Step-by-step explanation:
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Dana believes that she needs to study for at least 14 hours to be prepared for her monthly accounting test. If she can study for 4 hours per day, what is the minimum number of days that she should allow to study for the test?
How do u solve for X?
Answer:
x = 70
Step-by-step explanation:
x and 2x - 30 are supplementary angles , sum to 180° , then
x + 2x - 30 = 180 ( add 30 to both sides )
3x = 210 ( divide both sides by 3 )
x = 70
Answer:
2x - 30 and x degrees should add up to 180 degrees
2x - 30 + x = 180
3x = 210
x = 70 degrees
The correct answer would be D
The coconut milk is in a can but he doesn’t know how much the can holds.
The can is 12 cm high and the diameter is 8 cm.
Using the formula V = π r2 h, work out how much coconut milk is in the can.
Use 3 as a value for π.
Give your answer using the correct units.
Joanne knitted a blanket that measures 174 cm by 230. Her sister asked joanne to make a matching one for her son. If joanne wants to make a similar blanket using a scale factor of 0.55, what will it,s dimensions be.
Answer:
95.7 cm by 126.5 cm
Step-by-step explanation:
To use the scale factor of 0.55, we multiply 174 and 230 by 0.55: 174*0.55 = 95.7, 230*0.55 = 126.5