hello
to solve this question, we proceed to apply the formula given
initial velocity v0 =
[tex]\begin{gathered} v_0=10\text{ m/s} \\ s=660m \end{gathered}[/tex]next we proceed to substitute the values into the equation
[tex]\begin{gathered} s=4.9t^2+v_0t \\ 600=4.9t^2+10t \\ 4.9t^2+10t-600=0 \end{gathered}[/tex]we'll proceed to solve this quadratic equation to find the time it took the ball to hit the ground
there are several methods to solve a quadratic equation and for the purpose of this session, i'll make use of quadratic formula
[tex]t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]in our equation, we have
[tex]\begin{gathered} a=4.9 \\ b=10 \\ c=-600 \end{gathered}[/tex]let's substitute the values into the equation
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-10\pm\sqrt[]{10^2-4\times(4.9\times-600)}}{2\times4.9} \\ t=\frac{-10\pm\sqrt[]{100+11760}}{9} \\ t=\frac{-10\pm\sqrt[]{11860}}{9} \\ t=\frac{-10\pm108.9}{9} \\ t=\frac{98.9}{9}\text{ or t}=\frac{-118.9}{9} \\ t=10.99\text{ ot t}=-13.21 \end{gathered}[/tex]but since time can't have a negative value, the answer is approximately 10.99.
the time taken for the object to hit the ground is approximately 10.99s
b.
how far will it fall in 3s
to find the distance the object travelled in 3s, let's substitute the value of time in the original equation
[tex]\begin{gathered} s=4.9t^2+v_0t \\ t=3 \\ v_0=10\text{ m/s} \\ s=4.9(3)^2+10\times3 \\ s=4.9\times9+30 \\ s=44.1+30 \\ s=74.1m \end{gathered}[/tex]in 3s, the ball travelled a distance of 74.1m
it f (x) = √ which equation describes the graphed function? y = f(-x+4)
y = -f(x+4)
y= -f(x-4) y=f(-x-4)
For the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
As given in the question,
Given equation is equal to :
f(x) = √x
Equation which help us to defined the graphed function is as follow:
From the graph we have different values of x we get,
When x = 4, x=3 x=2
a. y = f(-x +4) y = f(-x+4) y = f(-x+4)
= √-x +4 = √-3+4 = √-2+4
= √-4 +4 = 1 = 1.414
= 0
Correct. Correct Correct
b. y = -f(x+4)
= -√x+4
= -√4+4
≠ 0
Incorrect.
c. y = -f(x-4) y = -f(x-4)
= -√x-4 = -√3-4
= -√4-4 = -√-1
= 0
Correct Incorrect
d. y = f(-x-4)
= √-x-4
=√-4-4
≠0
Incorrect
Therefore, for the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
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Carol Wynne bought a silver tray that originally cost $150 and was advertised at 30% off. What was the sale price of the tray?The sale price was $(Type an integer or a decimal.)
The original price was $150
the discount was 30%
therefore, the final price is the following:
[tex]\begin{gathered} P_{final}=150*(1-0.3) \\ =150*0.7 \\ =105 \end{gathered}[/tex]Thus, the final price of the tray was $105
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 timesBrooke's age. How old is Darius now?
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 times
Brooke's age. How old is Darius now?
Let
x ------> darius's age
y -----> Brooke's age
we know that
x+y=78 ------> equation A
(x-7)=3(y-7) -----> equation B
solve the sytem of equations
isolate the variable x in the equation A
x=78-y -------> equation C
substitute equation C in equation B
78-y-7=3(y-7)
slve for y
71-y=3y-21
3y+y=71+21
4y=92
y=23
Find the value of x
x=78-y
x=78-23=55
therefore
Darius now is 55 year old
The polynomial P(x) = 5x^3 + 2x^2- 42 has ___ local maxima and minima
SOLUTION:
Case: Local maxima and local minima
Given:
[tex]P(x)=5x^3+2x^2-42^{}[/tex]Required: To find the local maxima and minima
Method:
[tex]\begin{gathered} P(x)=5x^3+2x^2-42^{} \\ \text{ } \end{gathered}[/tex]First the find the first derivative:
[tex]\begin{gathered} P^{\prime}(x)=15x^2+4x \\ we\text{ make P'(x) = 0} \\ 15x^2+4x=\text{ 0} \\ x(15x+4)=0_{} \\ x=0\text{ or 15x+4 =0} \\ x=\text{ 0 or x= }\frac{-4}{15} \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = 0. The points are {-1, 1}.
[tex]\begin{gathered} \text{when x=-1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(-1)=15(-1)^2+4(-1) \\ P^{\prime}(-1)=15(1)^2-4 \\ P^{\prime}(-1)=15^{}-4 \\ P^{\prime}(-1)=11 \\ \text{when x= 1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(1)=15(1)^2+4(1) \\ P^{\prime}(1)=15^{}+4 \\ P^{\prime}(1)=19 \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = -4/15. The points are {-1, 0}
[tex]\begin{gathered} \text{when x= 0} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(0)=15(0)^2+4(0) \\ P^{\prime}(0)=0^{}+0 \\ P^{\prime}(0)=0^{} \end{gathered}[/tex]Final answer:
The local minima is at x= 0 while the local maxima is at x= -4/15
What is the exact volume of the figure?5 om12 cm(The figure is not to scale.)cm3V=(Type an exact answer in terms of A.)
Explanation
The volume of a cone is one third the area of the base multiplied by the height of the cone:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]This cone has a radius of 5cm and a height of 12cm. The volume is
[tex]\begin{gathered} V=\frac{1}{3}\pi(5\operatorname{cm})^2(12\operatorname{cm}) \\ V=\frac{1}{3}\cdot\pi\cdot5^2\cdot12\cdot cm^{2}cm \\ V=\pi\cdot\frac{1}{3}\cdot25\cdot12\operatorname{cm}^{3} \\ V=\pi\cdot\frac{300}{3}cm^{3} \end{gathered}[/tex]Answer
The volume of the figure is:
[tex]V=100\pi cm^{3}[/tex]Find the values of A, B, and C in the table.Intervalfa) for a in Relation ofinterval fa) to x-axis(0, 1)f(-2)= -12below(-1, A)f(0)=Babove(A, 2)f (1.5) -0.6(2,)f(3) = 8above
From the first line of the table, it shows
[tex]f(-2)=-12[/tex]This means that
when x = -2, y = -12,
so
[tex]a=-2[/tex]Now,
Madison says that 579.8 x 0.001 is the same as 579.8 : 10? Is she correct? Explain your answer in 3-5 sentences
Step 1:
First, write the expression for each value
[tex]\begin{gathered} 579.8\text{ }\times\text{ 0.001 = 0.5798} \\ \\ 579.8\text{ }\times\text{ 10 = 5798} \end{gathered}[/tex]Final answer
The two are not the same because the value of 579.8 x 0.001 is less than the value of 579.8 x 10.
Drag each tile to the correct box.Arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the function thateventually has the greatest value.3x + 8+4+3x² + 63x4*
To answer the question we are going to graph the functions given:
From the graph we notice that the order will be:
[tex]\begin{gathered} 3x \\ 3x+8 \\ x^2 \\ x^2+6 \\ 4^x \\ 4^x+3 \end{gathered}[/tex]it take Sarah to 1/2 AJ to make a birdhouse how much of the birdhouse will be built after 2/5 day choose the model that correctly illustrates the problem 2/5 ÷ 1/2
After 2/5 days Sarah can build 4/5 of a birdhouse.
It is given that Sarah can build birdhouses at the rate of 1/2 day per birdhouse.
Now let us use unitary method to calculate the number of birdhouses she can make in the given amount of time in a day.
Sarah takes 1/2 day to make 1 birdhouse
Sarah takes 1 day to make 1 ÷(1/2) birdhouse
Sarah takes 2/5 day to make 1÷ 1/2 × 2/5 birdhouse
Hence Sarah will make
= 1 ÷ 1/2 × 2/5
= 4/5 birdhouse
The unitary approach is a technique for solving problems that requires first figuring out how much one unit costs, then multiplying that amount to get the answer.
Therefore Sarah will take 2/5 days to make 4/5 of a birdhouse.
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if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<14=?
According to the diagram, angles 10 and 14 are supplementary, so they sum 180°.
[tex]\begin{gathered} m\angle10+m\angle14=180 \\ 77+m\angle14=180 \\ m\angle14=180-77 \\ m\angle14=103 \end{gathered}[/tex]Hence, angle 14 measures 103°.Which of the following expressions is equal to5 - 2(x + 2)?O -2x+1O 3x+6O -2x+2O 3x+2
Given:
an expression is given as 5 - 2(x + 2)
Find:
we have to simplify the expression and find correct expression from the options, which is equal to the given expression.
Explanation:
Now
5 - 2(x + 2) = 5 - 2x - 4 = - 2x + 1
Therefore, 5 - 2(x + 2) = - 2x + 1
Do these coordinate pairs represent a function?: *{(2, 4), (2,5), (3,6), (3, 7) }
Given,
The coordinate pairs are
{(2, 4), (2,5), (3,6), (3, 7) }
Here the argument 2 returns to both 4 and 5 while 3 returns to both 6 and 7.
This violates the defination of function.
Thus the coordinate pairs doesnot represent a function.
The answer is No.
whstbis the area in square inches of the shaded part of the retangle below
The shaded area is trapezium with parallel sides as a = 10, b = 5 and height of trapezium is h = 18 in.
The formula for the area of trapezium is,
[tex]A=\frac{1}{2}\cdot(a+b)\cdot h[/tex]Determine the area of the tapezium.
[tex]\begin{gathered} A=\frac{1}{2}\cdot(10+5)\cdot18 \\ =15\cdot9 \\ =135 \end{gathered}[/tex]So area of shaded region is 135 square inch.
2. The sum of the perimeters of similar quadrilaterals is 22.5 dm. Find the perimeters of the quadrilaterals if the similarity coefficient k = 1.25.
Given:
The sum of the perimeters of similar quadrilaterals is 22.5 dm. The similarity coefficient k = 1.25.
Required:
To find the perimeters of the quadrilaterals.
Explanation:
The quadrilaterals are similar and the similarity coefficient is k = 1.25.
If the quadrilateral is similar then the ratio of their corresponding sides is equal.
Let the perimeter of the one quadrilateral is x then the perimeter of the other quadrilateral will be 1.25x
Now
[tex]\begin{gathered} x+1.25x=22.5 \\ x(1+1.25)=22.5 \\ 2.25x=22.5 \\ x=\frac{22.5}{2.25} \\ x=10 \end{gathered}[/tex]Thus the perimeter of the one quadrilateral is 10dm.
The perimeter of the other quadrilateral = 1.25 x 10 = 12.5 dm
Final Answer:
Thus the perimeter of the quadrilaterals is 10dm and 12.5 dm.
Find the shape, or rate of change, from the following table?
ANSWER
C. -6
EXPLANATION
The rate of change is the change in the dependent variable when the independent variable changes 1 unit. In this case, all columns in the table have a change in the x variable of 1, so the difference between each column in the y-row is the rate of change,
[tex]m=-9-(-3)=-15-(-9)=-21-(-15)=-6[/tex]Hence, the rate of change is -6.
What would be the equation for this line? 80 60 40 20 time in minutes 2 3 4 5 6 7 8 9 X distance in miles
the equation of the line is given as follows,
first we take points on this line
A(2,20)
and
B (4,40)
so, the equation of the line is,
[tex]y-20=\frac{40-20}{4-2}(x-2)[/tex][tex]\begin{gathered} y-20=\frac{20}{2}(x-2) \\ y-20=10x-20 \\ y=10x \end{gathered}[/tex]thus, the equation of the line is
y = 10x
What is the measure of ZBDC?What is the measure of arc length BC?
SOLUTION
Step 1:
To find the measure of
Step 2:
The angle subtended by an arc at the centre is twice the angle subtended at the circumference. More simply, the angle at the centre is double the angle at the circumference.
Step 3:
Dividing both sides by 2, we have;
[tex]\begin{gathered} <\text{BDC = }\frac{BOC}{2}\text{ = }\frac{138}{2} \\ \\Step 4:
We are to find the measure of arc length BC;
Angle BOC is given as 138
[tex]\begin{gathered} \frac{\theta}{360}\text{ x 2 }\pi\text{ r} \\ \\ \frac{138}{360}\text{ x 2 x 3.14 x r } \\ \\ 2.407r \end{gathered}[/tex]Note: Since the value of the radius was not given so we need to express our answer in term of r.
The measure of arc length BC is 2.407r, where r is the radius.
The angle of elevation to the top of a 10-story skyscraper ismeasured to be 3° from a point on the ground 2000 feet fromthe building. What is the height of the skyscraper to thenearest hundredth of a foot?
ANSWER :
The height is 104.82 feet
EXPLANATION :
The angle of elevation to the top of the building is 3 degrees from a point that is 2000 feet away from the building.
Using tangent function :
[tex]\tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}[/tex]The opposide side to the angle is H and the adjacent side is 2000 feet.
Then :
[tex]\begin{gathered} \tan3=\frac{H}{2000} \\ \\ H=2000\tan3 \\ H=104.816\sim104.82\text{ }ft \end{gathered}[/tex]A fuelling vehicle finished filling a plane with 12.40 tons of fuelat 10:35. If the fuelling rate is 0.20 ton of fuel per min, at whattime did the fuelling start? Give your answer in a 12-hour clockformat, such as 9:00.9:33xHmm, that wasn't the right answer. Let's give it one more try.
A teacher receivesa monthly salary of $2800.00 What isheraunnual salary?
The year has 12 months, since the teacher receives a monthly salary of $2800, then his annual salary is:
[tex]2800\times12=33600[/tex]Answer:
$33600
"A quadrilateral is a square if and only if it has fourright angles."Which of the following terms provides acounterexample for why the biconditional statement is
Given statement: A quadrilateral is a square if and only if it has four right angles
Counterexample: A quadrilateral with four right angles can be also a rectangle. Then, not all quadrilaterals with four right angles are squares.
Answer: Rectangle
What is the value of x in the triangle?a right triangle with a short leg of length x and hypotenuse of length 3 times the square root of 2A. B. C. D. E.
Solution:
Given the right triangle below:
To solve for x, we use the trigonometric ratio.
In the above triangle, the angles at A and B are equal.
Thus, we have
[tex]\begin{gathered} \angle A+\angle B+\angle C=180(su\text{m of angles in a triangle\rparen} \\ \angle A=\angle B \\ thus, \\ 2\angle\text{B+90=180} \\ \Rightarrow2\angle\text{B=180-90} \\ 2\angle\text{B=90} \\ \Rightarrow\angle\text{B=45} \end{gathered}[/tex]From trigonometric ratio,
[tex]\sin\theta\text{=}\frac{opposite}{hypotenuse}[/tex]In this case, θ is the angle at B, which is 45; opposite is AC, and hypotenuse is AB.
Thus,
[tex]\begin{gathered} \sin45=\frac{x}{3\sqrt{2}} \\ \Rightarrow x=3\sqrt{2}\times\sin45 \\ =3\sqrt{2}\times\frac{1}{\sqrt{2}} \\ =3 \end{gathered}[/tex]Hence, the value of x is
[tex]3[/tex]The correct option is B
Finding the multiplier to give a final amount after a percentage increase or decrease
(a) The function with which the new price can be found in terms of the original price is; New price = 0.86 × Original price
(b) New price: $34, 056
What is a function in mathematics?A function is a relationship that maps the elements of a set A to the elements of another set B, such that each element of A is mapped to only one element of the set B.
The original price of the car = $39,600
The percentage by which the price of the car is decreased = 14%
The equation that can be used to find the new price in terms of the original price is therefore;
New price = (1 - 0.14) × Original price = 0.86 × Original price
Therefore;
New price = 0.86 × Original price(b) The value of the new price is obtained by plugging in the value of the original price in the equation above, as follows;
New price = 0.86 × 39,600 = 34,056
The new price is; $34,056
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Hero and Lisa are photographers they take pictures of seniors for high school yearbooks they charge a standard fee for taking the pictures there’s also a charge for each set of prints ordered so the number sets of prints determine the total cost S stand for the sets of prints ordered right the rule that describes the students total cost
Given:
We get the points (0,30), (1,31),(2,32), and (3,33) from the table.
Required:
We need to find the total cost.
Explanation:
From the point(0,30).
There is an initial cost of $30 for print.
Let s be the number of sets of prints ordered.
Let k be the additional cost for each number of sets of print
The equation of the given model is
[tex]Total\text{ cost =ks+30}[/tex]Consider the point (1,31).
Substitute total cost =31 and s=1 in the equation.
[tex]31\text{=k\lparen1\rparen+30}[/tex][tex]31\text{=k+30}[/tex]Subtract 30 from both sides.
[tex]31-30\text{=k+30-30}[/tex][tex]1\text{=k}[/tex]Substitute k =1 in the equation.
[tex]Total\text{ cost =s+30}[/tex]Consider the point (2,32).
Substitute total cost =32 and s =2 in the equation.
[tex]32\text{ =2+30}[/tex]It is true, so the equation satisfies the values in the table,
Final answer:
[tex]Total\text{ cost =s+30}[/tex]Commercial agents earn 5% of the cost of each product they sell. If an agent earsn $2000 for selling a product, what was the cost of the product?
Answer: 40,000
Step-by-step explanation: 5 (the earnings) times twenty is 100 (the total cost) and if we substitute 5 for 2000, the total is 40,000.
Answer: 40,000
Step-by-step explanation:
just because
Factor out the greatest common factor. Simplify the factors, if possible.6x4 - 42x3 + 12x2Select the correct choice below and fill in any answer boxes in your choice.O A. 6x4 - 42x3 + 12x2 =(Type your answer in factored form.)OB. There is no common factor other than 1.ih
You have to find the greatest common factor first.
To do so, do as follows:
[tex]6x^4-42x^3+12x^2[/tex]Factors of 6 are: 1, 2, 3, 6
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The greates common factor is the greatest common factor shared by all values, in this case is 6
Now to factor it out you have to divide each term of the equation by it.
[tex](\frac{6x^4}{6})=x^4[/tex][tex](\frac{42x^3}{6})=7x^3[/tex][tex](\frac{12x^2}{6})=2x^2[/tex]The expression with the GCF factorized is then:
[tex]6(x^4-7x^3+2x^2)[/tex]Answer To this question so that we can move on to the next question so we can get all this homework done
Can you please help and Copy the pictures and put the answers
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
Explanation:We trace each point on the x-axis to the corresponding point on the y-axis to have the following
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
Ever NL OP N 2 PN, and is the midst of MO. PALUN APON STATEMENTS REASONS: 2. Nisthe MO 1. Gren Given the following proof, what is the 5th reason? 2 MZ - OP 2. Given 3. IN EN 3. Given 2 MIN ON 4. Definition of midpoint 5 5. ALMN 2 APON SAS CPCTC SSS ASA
In this case, we have to use the SSS Postulate for the congruency of the triangles, that is, if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.
We have that all reasons are given congruent sides. The midpoint divides the segment into two equal parts, then the angles are congruent because of the reason: SSS ( SSS Postulate for congruency of triangles).
y^(3)-27=9y^(2)-27y. could you please show steps
The solution to the algebraic expression is y =3
Algebraic expressionThis algebraic expression contain variable and constant along with unknow variables.
y^(3)-27=9y^(2)-27y
Add 27y to both sides
y^(3)-27 +27y =9y^(2)-27y +27y
Simplify
y^3-27 +27y =9y^2
Subtract 9y^2 from both sides
y^3-27 +27y-9y^2 =9y^2- 9y^2
y^3-27 +27y-9y^2= 0
Simplify
y^3 - 9y^2 + 27y - 27 =0
Factor by grouping y^3 - 9y^2 + 27y - 27 ; (y-3)^3
(y -3) (-y^2 + 6y -9) = 0
(y-3)^3 =0
Using the zero factor principle if ab = then a = 0 or b= 0
y-3= 0
Add 3 to both sides
y =3
Therefore, solution to the algebraic expression is y =3
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