Answer:
3 seconds
Step-by-step explanation:
The height of the rocket when it hits the ground will be zero meters.
Therefore, set the equation to zero and solve for t by using the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Given equation:
[tex]-4.9t^2+14t+2.1=0[/tex]
Therefore:
[tex]a=-4.9, \quad b=14, \quad c=2.1[/tex]
Substitute the values into the quadratic formula:
[tex]\implies t=\dfrac{-14 \pm \sqrt{14^2-4(-4.9)(2.1)}}{2(-4.9)}[/tex]
[tex]\implies t=\dfrac{-14 \pm \sqrt{196+41.16}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-14 \pm \sqrt{237.16}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-14 \pm15.4}{-9.8}[/tex]
Therefore:
[tex]\implies t=\dfrac{-14 +15.4}{-9.8}=\dfrac{1.4}{-9.8}=-\dfrac{1}{7}[/tex]
[tex]\implies t=\dfrac{-14-15.4}{-9.8}=\dfrac{-29.4}{-9.8}=3[/tex]
As time is positive, t = 3 s only.
Therefore, it will take 3 seconds for the rocket to hit the ground.
A bag of tokens contains 5 red, 7 green, and 10 blue tokens. What is the probability that a randomly selected token is red? Enter your answer as a fraction.
SOLUTION
Notice that the total number of tokens is:
[tex]5+7+10=22[/tex]Notice that the number of red token is 5
Therefore the probability of that a selected token is red is:
[tex]P(R)=\frac{5}{22}[/tex]You and your friends plan to attend the county fair this weekend. The admission to the fair is $5 and the cost per ride is 50 cents. If your parents gave you $20, write and solve a linear equation to find how many rides you can go on.
The linear equation to find how many rides you can go on is 5 + 0.5x = 20 and there'll be 30 rides.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The linear equation will be:
Let the number of rides be x.
This will be:
5 + (0.5 × x) = 20
5 + 0.5x = 20
Collect like terms
0.5x = 20 - 5
0.5x = 15
Divide
x = 15 / 0.5
x = 30
The number of rides is 30
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There will be 30 rides, and the linear equation to determine the total number of rides is 5 + 0.5n = 20.
What are the equations?Mathematical statements which have at least two terms with equal quantities or variables are called equations.
Let n be the total number of rides.
The fair's entrance fee is $5, and each ride costs 50 cents, and parents gave $20 which is given in the question.
According to the given situation, the required equation as
⇒ 5 + 0.5 × n = 20
⇒ 5 + 0.5n = 20
⇒ 0.5n = 20 - 5
⇒ 0.5x = 15
Divide by 0.5 into both sides of the equation,
⇒ n = 15 / 0.5
⇒ n = 30
Therefore, the total number of rides will be 30.
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let P = (x,y) and Q = (1, 5). suing formula that you know for slope write an eqation in these terms of coordinates that says that the slope of line PQ is 3. show how this slope equation can be rewritten in the form y - 5 =3 (x -1).this linear eqation is said to be in point-slopr form. explain the terminology find coordinates for three diffrent points p that fit this equation
The equation of a line in point-slope form is y - 5 = 3( x - 1).
What is the equation of a line in slope intercept form?Equation of a line in slope intercept form is y = mx + b, where slope = m and y-intercept = b.The slope of a line is defined as the rate of change of the y-axis with respect to the x-axis.
We know the equation of a line in point-slope form is y - y₁ = m(x - x₁).
Given P = (x,y) and Q = (1,5) or (x₁, y₁).
∴ Equation of a line in point-slope form given (x₁,y₁) = (1,5) and slope(m) = 3 is y - 5 = 3( x - 1).
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question 2 (10 points)
Answer:
The answer is 476, so the third option is correct.
Step-by-step explanation:
Step 1: Recall the Order Of Operations
The order of operations tells us in which order we have to solve expressions, if there are different operations.
The order is (from first solved to lastly solved) Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
Step 2: Calculate the expression
As we can see, there are parentheses present, so we will solve the expression in them first:
[tex](6+4)\\=(10)[/tex]
The expression becomes:
[tex]10\cdot 49 -7\cdot 2[/tex]
Multiplication should occur first before the subtraction, so let's multiply the numbers:
[tex]10\cdot49-7\cdot2\\\\\text{Multiply the first expression:}\\=490-7\cdot 2\\\\\text{Multiply the second expression:}\\=490-14[/tex]
Now, you can subtract the numbers:
[tex]490-14\\=476[/tex]
I messed up and didn’t show this for my last question, so sorry on my part.
Evaluate the function for the following values
f(-2)=
f(0)=
f(3)=
Consider U = {x|x is a positive integer greater than 1}.
Which is an empty set?
{x|x € U andx is prime}
O {x|x E U and 2x is prime}
{x|x € U and x can be written as a fraction}
{x|x E U and 2x can be written as a fraction}
Options 3 and 4 are empty sets.
What is an empty set?Well-defined collection of objects or elements is called sets in mathematics. Set having no elements is known as empty set.
We can also define finite and infinite sets based on the number of elements in a set. An empty set is denoted by the symbol '∅' and is read as 'phi'.
Given U = {x|x is a positive integer greater than 1},
It is not an empty set ,if the set has elements such that x is prime or 2x is prime( positive integer greater than 1).
As the elements in the option 3 and 4 are fractions, therefore they are empty set as integers don't include fractions or decimals. Integer, also known as whole number, is any positive or negative number in which decimal parts or fractions is not included.
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You are creating identical candy bags using 36 chocolate bars and 81 caramel bars. what is the greatest number of bags you can fill using all the candy?
The greatest number of bags that can be filled using all the candy is 9.
The greatest number of bags that can be filled using all the candy can be determined by calculating the greatest common factor (GCF).
The greatest common factor of two or more numbers is a term used in mathematics that can be described as the greatest number among all the common factors of these numbers. If x and y are two numbers, GCF is the largest number that divides both x and y without leaving any remainder.
As there are 36 chocolate bars and 81 caramel bars, therefore we determine the GCF of 36 and 81;
The common factors of 36 and 81 are found to be: 1, 3 and 9
Hence the greatest common factor (GCF) out of these is 9.
Therefore the greatest number of bags that can be filled using all the candy is calculated to be 9
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Graph the following features:
• Y-intercept = -3
Slope = -3
●
-10 -9
-8
-5 -4 -3
10
-1
10
9
8
7
6
5
4
32
10
2
1
-1
21
-3
-4
-5
-6
-7
-8
-9
-10
1 2 3 4 5 6 7 8 9 10
x
Answer: ed3mt5i
Step-by-step explanation:
ok let me study
The Chan’s minivan requires 5 gallons of gasoline to travel 120 miles. How many gallons of gasoline will they need to travel 360 miles?
Answer:
15 gallons
Step-by-step explanation:
360 divided by 120= 3
3×5=15
At the mall you purchase 3 hot dogs and 1 soda. The cost of the soda is $2.25. Your total cost is $15.75. Write and solve an equation to find the cost of 1 hot dog.
Answer:
Bodzmkoutdoii6iriutdiudiwtyaoroyrisr
What is the expanded form of this number?
570.086
Responses
(5×100)+(7×10)+(8×1100)+(6×1100)
left parenthesis 5 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 8 times 1 over 100 right parenthesis plus left parenthesis 6 times 1 over 100 right parenthesis
(5×100)+(7×10)+(8×1100)+(6×11,000)
left parenthesis 5 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 8 times 1 over 100 right parenthesis plus left parenthesis 6 times 1 over 1000 right parenthesis
(5×100)+(7×10)+(8×110)+(6×1100)
left parenthesis 5 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 8 times 1 over 10 right parenthesis plus left parenthesis 6 times 1 over 100 right parenthesis
(5×100)+(7×10)+(8×110)+(6×11,000)
The expanded form of this number 570.086 will be (5 × 100) + (7 × 10) + (8/100) + (6/1000)
How to illustrate the information?It should be noted that expanded form simply means breaking down the number given into different units. A number can be written in expanded form by multiplying the sum of its digits.
The steps for writing a number in extended form are listed below.
Get the number in its simplest configuration.Determine its place values using the place value chart.Place value is multiplied by the number.Therefore, based on the information illustrated. This will be:
570.086 will be:
= (5 × 100) + (7 × 10) + (8/100) + (6/1000)
Note that your options aren't written well.
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Answer:
B I took semester test on k12 and got 100 Tell me if you want more answers
Step-by-step explanation:
Which is the better buy? 2-cup carton of milk for $0.56 2-quart carton of milk for $3.76
Given:
2-cup carton of milk = $0.56
2-quart carton of milk for $3.76
To find which of them is a better buy, let's calculate the price of each cup for both.
i) 2-cup carton of milk = $0.56
1 cup =
[tex]\frac{0.56}{2}\text{ = }0.28[/tex]Here, 1 cup carton of milk is $0.28
ii) 2-quart carton of milk = $3.76
Given that 1 quart = 4 cups
2 quart = 4 * 2 = 8 cups
Thus
1 cup =
[tex]\frac{3.76}{8}\text{ = }0.47[/tex]Here, a cup carton of milk is $0.47
$0.28 is less than $0.47, therefore the better buy would be 2-cup carton of milk for $0.56.
Therefore, the best buy would be 2-cup carton of milk for $0.56, because it is cheaper.
ANSWER:
2-cup carton of milk for $0.56
Describe the relationship between the 5's in the number 655,572:
The five in the 55 place is 5 times greater than the 5 in
the thousands places.
Answer:
im jus trying to get points lol
Step-by-step explanation:
It takes 2 cups of water to cook 1 cup of rice.
How much water dose it take to cook 6.5 cups of rice?
Answer:
13 cups of water.
Step-by-step explanation:
6.5 x 2 = 13
Answer = 13.
Hope this helps!
Btw, brainliest if correct, thanks!
can yall help me with
Answer:
B
Step-by-step explanation:
x(2y - 3) ← multiply each term in the parenthesis by x
= 2xy - 3x
A pet store clerk suggested 5 small fish for a 6-gallon fish tank. What size tank would be suggested to hold 40 small fish?
33-gallon tank
48-gallon tank
160-gallon tank
200-gallon tank
The size of the tank would be suggested to hold 40 small fish is 48 gallons. (Solved using ratios)
What is a ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains seven apples and six lemons, the apple-to-lemon ratio is seven to six. Similarly, the proportion of lemons to oranges is 6:7, while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio can be defined by providing both constituent integers, which are written as "a to b" or "a:b," or by providing only the value of their quotient a/b. Equal quotients result in equal ratios. A and B are frequently referred to as ratio words, with A being the antecedent and B being the consequent.
This can be solved using ratios
size of tank = 40x6/5 = 48 gallon
The size of the tank would be suggested to hold 40 small fish is 48 gallons.
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The experimental of spinning a 1 or a 3 is _?
we have that
the experimental probability of spinning a 1 is 8 times
and
the experimental probability of spinning a 3 is 9 times
so
the experimental probability of spinning a 1 or a 3 is
8+9=17
answer is 17
The remainder is what number (only type the number)
1. What is P(-2) given that P(x) = x - 3x² + 5x + 10?
The number of maps remaining at an information booth can be modeled by the function f(x)=274-32r where x is the number of hours that have
elapsed since the booth opened. Which statement is true?
O Every hour 274 maps are given away
O Every hour, 242 maps are given away
O There were 32 maps at the booth before it opened
O There were 274 maps at the booth before it opened
3) Factories A and B produced potato chips. Last year, each factor
ingredient. Factory A reported their amounts in scientific ne
their amounts in standard form.
Ingredient Factory A (amount used in lbs) Factory B
Potato
4.87 × 106
5.61×10³
2.87 × 10³
a) Which factory used more oil last year? By how much'
Oil
Salt
b) what is the total amount of salt use by both factories?
c) what is the total weight of all of the ingredients in Factory A?
Factory A uses more oil by 2.05×10⁵ lbs, total salt used is 4.805×10⁵ lbs and total ingredients used in factory A are 57.18×10⁵ lbs.
a) The oil used by Factory A = 5.61×10⁵ lbs
The oil used by Factory B = 3,56,000 lbs
The oil used by Factory B = 3.56×10⁵ lbs
Comparing the coefficient. Since 5.61 is greater than 3.56, the factory A used more oil. Difference in amount = 5.61×10⁵ - 3.56×10⁵
Difference in amount = 2.05×10⁵ lbs
b) Salt used by Factory A = 2.87×10⁵ lbs
Salt used by Factory B = 193,500 lbs
Salt used by Factory B = 1.935×10⁵ lbs
Total salt used by both the factories = 2.87×10⁵ + 1.935×10⁵ lbs
Total salt used by both the factories = 4.805×10⁵ lbs
c) Potato used by Factory A = 4.87×10⁶ lbs
Potato used by Factory A = 48.7×10⁵lbs
Oil used by Factory A = 5.61×10⁵ lbs
Salt used by Factory A = 2.87×10⁵ lbs
Total ingredients used in Factory A = 48.7×10⁵ + 5.61×10⁵ + 2.87×10⁵ lbs
Total ingredients used in Factory A = 57.18×10⁵ lbs
2.05×10⁵ lbs more oil is used by Factory A, 4.805×10⁵ lbs is the total amount of salt used and 57.18×10⁵ lbs ingredients are used in factory A.
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The complete question is attached in figure.
Write the equation of a line perpendicular to 8x-3y=-4 that passes through the point (-8,2).
Answer:
y=-8/3x-58/3
Step-by-step explanation:
8x-3y=-4 is y=8/3x+4/3
Make x negative so it is perpendicular
The plug (-8,2) so
2=8/3(-8)+b
Then
2=-64/3+b
-58/3=b plug b in to the equation so
You get
y=-8/3x-58/3
give brainliest pls
Answer:
3x + 8y = - 8
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 )
given
8x - 3y = - 4 ( subtract 8x from both sides )
- 3y = - 8x - 4 ( divide through by - 3 )
y = [tex]\frac{8}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{8}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{8}{3} }[/tex] = - [tex]\frac{3}{8}[/tex] , then
y = - [tex]\frac{3}{8}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (- 8, 2 ) into the partial equation
2 = 3 + c ⇒ c = 2 - 3 = - 1
y = - [tex]\frac{3}{8}[/tex] x - 1 ← equation of perpendicular line in slope- intercept form
multiply through by 8 to clear the fraction
8y = - 3x - 8 ( add 3x to both sides )
3x + 8y = - 8 ← equation of perpendicular line in standard form
2.56 = 2w solve for w
Answer: w=1.28
Step-by-step explanation:
swap the sides of the equation
2w=2.56
divide both sides of the equation by two
w=1.28
9. Which phrase best describes the translation from the graph y = (x - 2)2 to the graph of y=x²-3? O2 units left and 3 units up O2 units left and 3 units down O 2 units right and 3 units up O 2 units right and 3 units down
The transformation of the graph y = (x - 2)² to the graph of y=x²-3 is 2 units left and 3 units down therefore, option (B) is correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
As per the given graph y = (x - 2)²
A function will shift a unit left for x → x + a and b units down if y → y - b.
Replace x → x + 2 and y → y - 3
y = (x + 2 - 2)² - 3
y = x² - 3
Therefore, the transformation of the graph y = (x - 2)² to the graph of y=x²-3 is 2 units left and 3 units down".
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In the Honor Society at Carter Middle School, 54% of the members are girls. There are 108 girls in the Honor Society. How many members are there in total?
Answer:
46x2=92 108+92= 200 total members
Step-by-step explanation:
108/2=54% so 46%x2members = 92 members.
4) Write the coordinates of the vertices after a translation 4 units left and 2 units down.
-10 -8 -6
-4
2
>
104
8
6
72
T
2
-4
-6
IN
2
4
6
10
U
Answer:
Step-by-step explanation:
Can you write it in lines instead of like that, I can answer if you do that.
En la clase de gimnasia de Zuri, hay 27 estudiantes en total, 21 estudiantes usan anteojos. ¿Cuál es el porcentaje de estudiantes que usan anteojos?
Answer:
eme I sh na d9 si me 08 met sup Auburndale el sn ap7 42
A cup of popcorn at the movie theater sells for $0.25 per cubic inch. A medium sized popcorn is served in a cylindrical cup that is 6 inches in height and 4 inches in diameter. How much would it cost to the nearest cent?
PLEASE HELP :(!
Surface area - The cost of medium popcorn will be $473.25.
What is surface area?
The surface area of a three-dimensional object is the space taken up by its outer surface.
For instance,
The surface area of a cube is what we need to calculate the amount of paint needed to paint it. It is consistently expressed in square units.
The surface area of the cylinder with the top open = πr(r + 2h)
we are given that,
r = 2in
h = 6in
taking π as 3.14, and substituting these vales in the above equation,
surface area = π x 2 (2 x 2 x 6)
= 3.14 x 2 (2 x 2 x 6)
= 1893in²
cost = 1893 x 0.25
= $473.25
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Point Q lies in the interior of ZRST.
(1
If mZRST= 125°, mZRSQ = 4x-7, mZQST= 11x + 12, then find x.
Not sure how to find the area of this shape. Please help asap
Answer:
6.75m^2
Step-by-step explanation:
The shape is made up of a trapezoid on top and a rectangle on the bottom.
The rectangle's area is easier, so first:
Area_rectangle
= length × width
= 2.5 × .5
= 1.25 m^2
For area of a trapezoid, you need three measures: both bases and the height.
One base is 3m. The other base is the top side of the rectangle, so it is 2.5m.
The height is
2.5 - .5
because the height of the trapezoid is not including the rectangle, so take away .5
Trapezoid's height is 2.5 - .5 is 2.
Area_trapezoid
= 1/2 (base+base)height
= 1/2 (3+2.5)2
=5.5
Area_total
= Trapezoid+rectangle
= 5.5 + 1.25
=6.75m^2
The total area is 6.75square meters.
Answer:
Area = 6.75 meter square.
Step-by-step explanation:
At one time the thickness of different gauges of stainless steel were give. In fractions of an inch. Today, those thicknesses are listed as decimal numbers. Convert each of the following fractional thicknesses to decimal form.
Following are the fractions in decimal form.
What do fractional parts mean?A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
It is calculated by dividing the total number of parts by the number of equal parts that were counted (numerator) (denominator). Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.
a) 15 / 32 = 0.46875
b) 21/64 = 0.328125
c) 9/16 = 0.5625
d) 3/8 = 0.375
e) 1/80 = 0.0125
f) 11/1280 = 0.008593
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