Answer:
1: The tower is around 93 meters tall. 2: The object hit the ground at 6 seconds. 3: 3 seconds to get to about 93 meters up.
Step-by-step explanation:
1: The tower is around 93 meters tall.
2: The object hit the ground at 6 seconds.
3: the time it took to reach that height is 3 seconds to get to about 93 meters up.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Linear function is a function whose graph is a straight line
1. Since the shot was made from the top of the tower, the starting height of the object (time zero) is equal to the height of the tower.
It represent in the graph by the y-intercept of the function, that is, the value of y when x=0.
The y-intercept is at (0,10) which shows that the height of the tower is 10m
2. The point where the object hit the ground, the height is zero meters, thus
The coordinates of the x-intercept are (6,0)
This shows that the object hit the ground 6 seconds after being shot.
3.The y-coordinate of the vertex shows the highest point of the object, which is 93 meters.
The x-coordinate of the vertex shows the time it took the object to reach said height, which is 2.8 seconds
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Jonah uses 1/2 of a cup of vinegar in his salad dressing recipe. How much vinegar would
Jonah use to make 1/2 of a recipe?
Write your answer as a fraction or as a whole or mixed number.
cups
Answer:
1/4 cup
Step-by-step explanation:
Assuming that the recipe makes 1 cup of dressing, Jonah would need 1/4 cup of vinegar. Half of 1/2 is 1/4.
Triangle H J K is cut by line segment A B. Line segment A B goes from side H J to side H K. The length of H A is 5. 25 inches, the length of H B is 3 inches, and the length of B K is 5 inches. What is the length of Line segment A J if Line segment A B is parallel to lines segment J K? 8 in. 8. 75 in. 10. 25 in. 14 in.
The segments on triangle HJK are illustrations of equivalent ratios
The length of line AJ is 8.75 inches
The given parameters are:
[tex]H A = 5.25[/tex]
[tex]HB = 3[/tex]
[tex]BK = 5[/tex]
Because lines AB and JK are parallel lines, then we have the following equivalent ratios
[tex]HA:HB = AJ:BK[/tex]
Substitute values for length HA, HB and BK.
[tex]5.25:3 = AJ:5[/tex]
Express both ratios as fractions
[tex]\frac{5.25}{3} = \frac{AJ}5[/tex]
Multiply both sides by 5
[tex]\frac{5.25}{3} \times 5= AJ[/tex]
[tex]8.75= AJ[/tex]
Rewrite as:
[tex]AJ = 8.75[/tex]
Hence, the length of line AJ is 8.75 inches
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A colony of bacteria is growing at a rate of 50% per hour.
If this rate of growth remains the same and the colony starts with 100 bacteria, approximately how many bacteria will there be after 6 hours?
1139 bacteria
Answer:
1139
Step-by-step explanation:
The exponential growth rate formula is as follows:
F = A(1+r)^t, with F representing the final amount, a representing the initial amount, r representing rate, and t representing time. Here, we have
A = 100, r = 50% = 0.5 (divide 50% by 100 to convert it to a decimal), and t = 6. Plugging these in, we get
F = 100(1+0.5)^6 = 1139
find three consecutive numbers if their sum is 3n
Answer:
n-1,n,n+1
Step-by-step explanation:
let the numbers be x,x+1,x+2
x+x+1+x+2=3n
3x+3=3n
3x=3n-3
x=1/3 (3n-3)=n-1
so mumbers are n-1,n,n+1
The three consecutive numbers are n-1, n, and n+1.
We have to determine, the three consecutive numbers if their sum is 3n.
According to the question,
The consecutive number series can be even as well as odd depending on the first term of the series and the difference between the numbers.
Let, the three consecutive numbers be x, x+1, and x+2.
The sum of three consecutive numbers is equal to 33.
[tex]\rm x + x+1+x+2=3n\\\\3x+3 = 3n \\\\Divided \ by \ 3 \ on \ both \ the \ sides \\\\x +1 = n\\\\x = n-1[/tex]
Therefore,
The first consecutive number is,
[tex]\rm x = n-1[/tex]
The second consecutive number is,
[tex]\rm x+1 = n-1+1 = n\\[/tex]
The third consecutive number is,
[tex]\rm x+2= n-1+2 = n+1\\[/tex]
Hence, The three consecutive numbers are n-1, n, and n+1.
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what's the difference between (F(x))^2 and F^2(x) ?
Answer:
f^2(x) means f(f(x)). [f(x)]^2 means the square of the function.
Step-by-step explanation:
I am sorry to say so, but the other answer is rubbish.
there is no difference.
both mean the same thing : f(x) × f(x).
f(f(x)) is exactly what that expresses (f of f(x)).
another way of writing for this would be (f○f)(x).
but never ever f²(x).
please ignore the other answer.
I need help with this. 2 to the 6 power, +2 to the 3 power, raised to the 3 power. Please tell me the steps you took to get the answer. and happy. Christmas Eve
Answer: 576
Step-by-step explanation:
(I just know the powers of smaller numbers by memory so...)
2^6(2x2x2x2x2x2) = 64
You can simplify the second part( 2^3^3) by just multiplying the powers, 3x3 = 9 and 2^9 = 512
Final answer = 512 + 64 = 576
[tex]\\ \sf\Rrightarrow 2^6+(2^3)^3[/tex]
[tex]\\ \sf\Rrightarrow 2^6+2^9[/tex]
[tex]\\ \sf\Rrightarrow 64+512[/tex]
[tex]\\ \sf\Rrightarrow 576[/tex]
Option A is correct
Find the area of the figures
4 cm
T
4 cm
12 cm
8 cm
The area is
square centimeters
Answer:
120 [cm²].
Step-by-step explanation:
1) the required area is A=Area(ABCEFD)=Area(ABCD)+Area(CEFD);
2) Area of ABCD: Area(ABCD)=AB*BC=12*8=96 [cm²];
3) Area of CEFD: Area(CEFD)=0.5(CD+EF)*HD=0.5*(8+4)*4=24 [cm²];
4) finally, the required area is: A=96+24=120 [cm²].
all the details are provided in the attachment.
If sine theta almost-equals 0.3090 , what is the approximate value of csc Theta?
0.5559
1.3090
3.2362
10.4733
Step-by-step explanation:
csc(Theta) = 1/sin(Theta) = 3.2362
Answer:
C. 3.2362
Explanation:
Evaluate 46.32 You may complete your work offline to show your thinking.
Answer:
you want me to round it I will edit it and show you
Step-by-step explanation:
There are 120 apartments on 15 floors. Find the unit rate.
Which of the following lists of ordered pairs is a function?
Answer:
Option D.
Step-by-step explanation:
A function is a relation in which one input (x-value) is assigned to exactly one output (y-value).
Since option D's x-values do not repeat, then it is a function.
Hope this helps.
Can someone help me with this question
Answer:
what is the lesson? abot?
Step-by-step explanation:
Solve the following compound inequality. Graph the solutions. x <2 and x> -1 Solve the compound inequality. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solutions are enter your response here. (Simplify your answer. Type an inequality or a compound inequality.) B. The solutions are all real numbers. C. There is no solution.
please help :(
Evaluate the expression when a=-2 and x=7.
-2a+x
Step-by-step explanation:
-2a + x
Putting values of a = - 2 and x = 7
-2(-2) + 7
4 + 7
= 11
The diameter of a cylindrical construction pipe is 6 ft. If the pipe is 26 ft long, what is its volume?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
First find the area of the circular base. The diameter is 6, so the radius is 3.
A circle is pi r square, so it is 3.14 x 3^2, = 28.26
Multiply that by the length 28.26 x 26 = 734.76, which rounds to 735 cubic feet.
If the sum of the roots of the equation 3x² + kx + 1 = 0 is 7. then what the value of k
Answer:
The value of k is -21
Step-by-step explanation:
ax² + bx + c = 0
Sum of the roots = -b/a
3x² + kx + 1 = 0
= sum of the roots = -k/3
-k/3 = 7
Now, Multiply both side by (-3) we get,
(-3)-k/3 = 7(-3)
k = -21
Thus, The value of k is -21
-TheUnknownScientist 72
After 10 seconds on a zip line tour, you travel 50 feet. After 25 seconds, you travel 125 feet. Find the slope in feet per second
Answer:
5 feet per second
Step-by-step explanation:
Use the formula y2-y1/x2-x1. (10,50) is x1 and y1. 25 seconds and 125 feet is x2 and y2.
(125-50)/(25-10) = 75/15
We need to solve for the feet per (or 1) second, so we have to divide it by 15.
75/15= 5
So, the slope is 5 feet per second.
Help Please !! I Need To Have This Turned In By The Next Hour , Anybody Know It !?
Answer:
no
Step-by-step explanation:
Step-by-step explanation:
Because lines are parallel you can use certain rules to determine the relationship of angle 1 & 2.
(A1 & A2 for short)
With the C shape within the parallel lines we can guarantee that the sum of A1 and A2 is equal to 180.
We can also assume A2 is less than 90° as the lines are parallel and the opposing, non parallel line is acute. With this knowledge and the C shape rule, A1 is therefore more than 90°.
Hope this helps
Two what expression must 5a²-4a+3 be added to make the sum zero?
Dolly is measuring the angles of a triangle. He measures the first two angles of a triangle and gets 30 and 100. How could he find the measure of the third angle?
Answer:
the third angle is 50 degress
Step-by-step explanation:
the angle sum property states that the sum of all the interior angles of a triangle is 180.
therefore : 30 + 100 + x = 180
x = 180 - 130
x = 50
What value of x satisfies the equation 3x – 2 = 2x + 4?
Answer:
x = 6
Step-by-step explanation:
3x - 2 = 2x + 4
First, we need only 1 set of x, so I'll subtract the smallest x from the other.
-2x both sides.
x - 2 = 4
Next, add +2 to both sides. (In these types of questions always do the inverse!)
And so your answer is:
x = 6
Answer:
x = 6
Step-by-step explanation:
1. Add 2 to both sides of the equation
3x - 2 = 2x + 4
3x - 2 + 2 = 2x + 4 + 2
2. Simplify
3x = 2x + 6
3. Subtract 2x from both sides of the Equation
3x - 2x = 2x + 6 - 2x
4. Simplify
x = 6
Elissa got a manicure and pedicure for $40. If she wants to give a 20% tip, how much would the tip be?
Answer:
$8.01
Step-by-step explanation:
a group of 3 people are sharing chocolates each person wants 8 chocolates and each box has 4 chocolates
Answer: not sure
Step-by-step explanation: uhhh this ain't clear. how many boxes are there?
Which option is an example of a survey?
A. Asking students in a school how much time they spend exercising
B. Flipping a coin 50 times and counting the number of heads
C. Measuring the heights of the players on the basketball team
D. Testing the effectiveness of a new reading program by allowing a
classroom to use it and comparing the results with another
classroom that doesn't use it
Answer:
I think the answer is A
Step-by-step explanation:
The example of a survey are; A. Testing the effectiveness of a new reading program by allowing a classroom to use it and comparing the results with another classroom that doesn't use it
What is an survey?An survey is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before.
Since Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.
The survey asks participants to quantify their trust in politicians while a numerical scale, with 1 being the least amount of trust.
Example of a survey;
Testing the effectiveness of a new reading program by allowing a classroom to use it and comparing the results with another classroom that doesn't use it
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PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT
Answer:
c = 13
m∡A = 60°
m∡B = 30°
Step-by-step explanation:
This is a 5-12-13 triangle. However, to make sure, I will put the steps.
Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:
a² + b² = c²
Plug in the corresponding numbers to the corresponding variables:
5² + 12² = c²
Simplify. First, solve the exponents, and then add:
(5²) = 5 * 5 = 25
(12²) = 12 * 12 = 144
25 + 144 = c²
c² = 169
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:
√c² = √169
c = √169 = √(13 * 13) = 13
c = 13
13 is your answer for c.
Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).
Columbus would have taken some live animals aboard for food sources. If there were one hundred forty one animals, of which seventy two were rabbits and the rest were chickens,what percentage of animals were chickens? Round your answer to the nearest percent.
Answer:
49
Step-by-step explanation:
hope it will help I think 49 is the answer
Evaluate the expression when c=−4 and y=2
-y+4c
Answer:
-2 - 16 = -18
Step-by-step explanation:
-y+4c
You take the values for c and y and substitute them in the original equation.
It would then look like:
-(2) + 4(-4)
Solving that would be -2 -16 = -18
Answer:
-18
Step-by-step explanation:
-(2)+4(-4) Plug in the values of y and c.
-2+(-16) Simplify.
-2-16
-18
Hope this helps you out!! Have an amazing day <3
W
Enter the value of x-21.
(x - 21)
71
What is the smallest integer $k>2000$ such that both $\dfrac{17k}{66}$ and $\dfrac{13k}{105}$ are terminating decimals?.
The smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals is 2079.
GivenK is greater than 2000.
[tex]k> 2000\\[/tex].
Given fractions are
[tex]\dfrac{17k}{66} \ and \ \dfrac{13k}{105}[/tex].
How to find the smallest integer greater than 2000 for the fractions to be terminating decimals?In order for the decimal equivalents to be terminating, the only factors that can remain in the denominators are 2 and 5.
Here, the given denominators are 66 and 105 respectively.
Now factors of 66 will be 2,3,11.
And the factors of 105 will be 3,5,7.
So, the value of k must be multiples of 3, 7, and 11. The LCM of these numbers will be,
[tex]3\times 7\times 11=231[/tex]
Now the value of K must be greater than 2000, so the multiple of 231 which is greater than 2000 is its [tex]9^{th}[/tex] multiple,
[tex]231\times9=2079[/tex]
Hence 2079 is the smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals.
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Use exponents to write each expression. Then evaluate the expression. 3x3x3x3x3
Step-by-step explanation:
3 to the power of 5
3^5
= 3x3x3x3x3
= 243
Answer:
243
Step-by-step explanation:
3^5=243