Answer:
1)he maximum height your feet will be above the ground is 12
2)Will you be able to dunk the ball= yes
Step-by-step explanation:
Given:
In order to dunk the basket ball, height needed to jump= 2.5 feet
The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12
1) the maximum height your feet will be above the ground=?
Given function of height,h(x)=-16t^2+12
finding maximum of the above function
The maximum of any function written in form of ax^2+bx+c is given by
max= c - (b2 / 4a)
Putting values c=12, b=0 and a=16, we get
max= 12-(0^2/4(-16))
= 12 -0
=12 feet
he maximum height your feet will be above the ground is 12 feet.
2) Will you be able to dunk the ball=?
As the maximum height the feet will be above the ground is 12 feet which is greater than the height needed to jump in the air to dunk the ball 2.5 feet i.e.
12>2.25
hence yes you will not be able to dunk the ball !
Please help I am confused
A. 10% of n is q; n = 10q
B. 25% of x is 320; x = 1280
C. 15% of y is q; y = 6.666....7q
Answer:
a = 90
b = 7.81
c = 60
What is the square root of 114 to the nearest tenth
Answer:
10.7
Step-by-step explanation:
√114 = 10.7 <----to the nearest tenth
Answer:
10.7 to the nearest tenth.
Step-by-step explanation:
It will be between 10 and 11 because 10^2 = 100 and 11^2 = 121.
Using a calculator. It is 10.67707825.
The price of a ring was increased by 8% to £486. What was the price before the increase?
Step-by-step explanation:
price before increased be x
After it is increased by 8% it becomes1.08x
equal to 486
so 1 .08x=486
x=£450
The price of the ring before the increase was £450.
What is the Selling Price?
This refers to the value given to a product when sold to consumers from the retailers or wholesalers.
Hence,
Given that the price before the increase is X
If increased by 8%,
It becomes 1.08x=486
Collect like terms
x= £450
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Last year Golden State Warriors won 80% of the first 15 matches. Then they won the rest of the three matches. What percent of all matches did they win?
Answer:
83.33%
Step-by-step explanation:
We first need to evaluate 80% of the first 15 matches in order to determine the number of watches out of 15 which they won.
80 % of 15 = 80/100 * 15 = 12
12 matches out of the first 15 were won.
Since the team won the rest of the 3 remaining matches, the total number of matches won becomes;
12 + 3 = 15
The team thus won 15 matches out of a total of 15 + 3 =18 matches .
The percent of all matches won is ;
15/18 * 100 = 83.33%
a square painting has an area of 81x^2-90x-25. A second square painting has an area of 25x^2+30x+9. What is an expression that represent the difference of the area of the paintings? show two ways to find the solution
Answer:
The answer in the procedure
Step-by-step explanation:
Let
A1 ------> the area of the first square painting
A2 ----> the area of the second square painting
D -----> the difference of the areas
we have
[tex]A1=81x^{2}-90x-25[/tex]
[tex]A2=25x^{2}+30x+9[/tex]
case 1) The area of the second square painting is greater than the area of the first square painting
The difference of the area of the paintings is equal to subtract the area of the first square painting from the area of the second square painting
D=A2-A1
[tex]D=(25x^{2}+30x+9)-(81x^{2}-90x-25)[/tex]
[tex]D=(-56x^{2}+120x+34)[/tex]
case 2) The area of the first square painting is greater than the area of the second square painting
The difference of the area of the paintings is equal to subtract the area of the second square painting from the area of the first square painting
D=A1-A2
[tex]D=(81x^{2}-90x-25)-(25x^{2}+30x+9)[/tex]
[tex]D=(56x^{2}-120x-34)[/tex]
Final answer:
To find the difference between the areas of two square paintings, subtract the second area from the first to get an expression. By direct subtraction and using the distributive property, both methods yield the expression[tex]56x^2 - 120x - 34[/tex].
Explanation:
To find an expression that represents the difference between the areas of two square paintings, we simply subtract the area of the second painting from the area of the first painting.
The area of the first painting is [tex]81x^2 - 90x - 25,[/tex] and the area of the second painting is [tex]25x^2 + 30x + 9.[/tex]To find the difference, calculate [tex](81x^2 - 90x - 25) - (25x^2 + 30x + 9).[/tex]
Here's the direct subtraction method:
Subtract the [tex]x^2[/tex] terms: [tex]81x^2 - 25x^2 = 56x^2[/tex].
Subtract the x terms: -90x - 30x = -120x.
Subtract the constant terms: -25 - 9 = -34.
Combining these, we get the expression representing the difference in areas:[tex]56x^2 - 120x - 34.[/tex]
Another way to find the solution is using the distributive property to first factor out a negative from the second polynomial, making it easier to subtract:
Rewrite as[tex]: (81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9).[/tex]
Distribute the negative sign:: [tex](81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9)..[/tex]
Now proceed as in the direct subtraction method above.
The final result is the same: [tex]56x^2 - 120x - 34.[/tex]
Simplify (x + y + 3)(x + y - 4)
Answer:
x²+2xy-x+y²-y-12
Step-by-step explanation:
(x+y+3)(x+y-4)
= x(x+y-4)+y(x+y-4)+3(x+y-4)
= x²+xy-4x+xy+y²-4y+3x+3y-12
= x²+2xy-x+y²-y-12
The answer is:
The simplified expression is:
[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Why?To solve the problem, we need to remember how to use the distributive property and how to add like terms.
The distributive property can be defined as follow:
[tex](a+b)(c+d)=ab+ad+bc+bd[/tex]
The like terms are the terms that share the same variable and the same exponent, for example:
[tex]3x+x+ x^{2}=x^{2} +4x[/tex]
We were able to add the first and the second term because they share the same variable and the same exponent.
Now, we are given the expression:
[tex](x+y+3)(x+y-4)[/tex]
So, simplifying we have:
[tex](x + y + 3)(x + y - 4)=(x*x)+(x*y)-(4*x)+(y*x)+(y*y)-(4*y)+(3*x)+(3*y)-(3*4)\\\\(x + y + 3)(x + y - 4)=x^{2} +xy-4x+xy+y^{2}-4y+3x+3y-12\\\\(x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Hence, we have that the simplified expression is:
[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Have a nice day!
Is Frieda’s work correct? Explain how she can check her solution.
z + 22 = 64
z + 22 – 22 = 64 – 22
z = 42
Answer:
by substitution
Step-by-step explanation:
To check if the solution to an equation is valid
Substitute the solution into the equation and if both sides agree then the solution is correct.
left side = z + 22 = 42 + 22 = 64 = right side
Hence z = 42 is the correct solution
The equation is given as:
[tex]z+22=64[/tex]
⇒[tex]z+22-22=64-22[/tex]
⇒[tex]z=42[/tex]
So, we have to put the value of z in the 1st equation then we can say whether Frieda's work is correct or not.
⇒[tex]42+22=64[/tex]
[tex]=RHS[/tex]
Hence, Frieda's work is correct.
What's an equation in math?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in maths when you do not know the exact number in a calculation.
What is an equation example?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
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Tasty Treats Baking Company asked a random sample of 100 students in the senior class at Ridgemont High School the question, “Do you prefer chocolate or butterscotch Tasty Treats?” Everyone surveyed had to pick one of the two answers, and 42%, percent said they preferred chocolate.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
A) About 42%, percent of all students at Ridgemont High prefer chocolate.
B)About 42%, percent of all students in the senior class at Ridgemont High prefer chocolate.
C)42%, percent of this sample preferred chocolate, but we cannot conclude anything about the population.
Answer:B!!
Step-by-step explanation:
Answer a is incorrect because only the seniors were questioned and answer c is incorrect because nothing was mentioned in the question about only testing males.
Your answer is B
Solve for x
|4x - 3| = 20
Answer: [tex]x=\frac{23}{4}[/tex] and [tex]x=-\frac{17}{4}[/tex]
Step-by-step explanation:
Given the equation [tex]|4x - 3| = 20[/tex], you can set up two cases:
Case 1: [tex]4x-3>0[/tex]
[tex]4x-3=20[/tex]
Solve for the variable "x", therefore you get:
[tex]4x=20+3\\\\x=\frac{23}{4}[/tex]
Case 2: [tex]4x-3<0[/tex]
[tex]-4x+3=20[/tex]
Solve for the variable "x". Then, you get:
[tex]-4x=20-3\\\\x=\frac{17}{-4}\\\\x=-\frac{17}{4}[/tex]
Therefore, the solution is:
[tex]x=\frac{23}{4}[/tex] and [tex]x=-\frac{17}{4}[/tex]
Jay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
10.50+4.50x=46.50
This is the fuction to use to solve the problem.
The function that can be used to find the number of rides he went on is
46.50 = 4.5x + 10.50
What is linear equation?A linear equation is a mathematical expression involving variables raised to the first power only.
It takes the form ax+b=0, where
a and b are constants, and x is the variable.
Represent the number of rides he went on by x
the total amount on rides will be
4.5x
The entrance fee = $10.50
Total amount = 45x + 10.50
Therefore, the equation that represents the number of rides he went on is
46.50 = 45x + 10.50.
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The lateral area of a right cone which has a base diameter of four units and a height of 10 units is:
since it has a diameter of 4, then its radius is half that, or 2.
[tex]\bf \textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=2\\ h=10 \end{cases}\implies LA=\pi (2)\sqrt{2^2+10^2} \\\\\\ LA=2\pi \sqrt{104}\implies LA\approx 64.076[/tex]
Answer:[tex]A = 64.076\ units^2[/tex]
Step-by-step explanation:
The lateral area of right cone is calculated by the following formula
[tex]A = \pi r *\sqrt{r^2 +h^2}[/tex]
Where r is the radius of the cone and h is the height
In this case we know that the diameter d of the base is:
[tex]d=2r[/tex]
So the radius is:
[tex]r=\frac{d}{2}\\\\r=\frac{4}{2}\\\\r=2\ units[/tex]
and
[tex]h=10\ units[/tex]
So the area is:
[tex]A = \pi*2 *\sqrt{2^2 +10^2}[/tex]
[tex]A = 64.076\ units^2[/tex]
Factorisation of ax^2 + bx + c
Answer:
-5(t+3)(t-6)
Step-by-step explanation:
-5²+15+90
= -5(t²-3t-18)
= -5(t+3)(t-6)
If P varies inversely as M2, and P= 8, while M=2, find M2 when P=10
Answer:
[tex]M^{2}=3.2[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
In this problem we have
[tex]P*M^{2}=k[/tex]
step 1
Find the value of k
For P=8, M=2
substitute
[tex]k=(8)(2)^{2}=32[/tex]
The equation is equal to
[tex]P*M^{2}=32[/tex]
step 2
Find the value of M²
when P=10
substitute the value of P in the equation
[tex]10*M^{2}=32[/tex]
[tex]M^{2}=3.2[/tex]
triangleABC is a right triangle. if AC=15 and BC=17, what is AB
Answer:
The answer in the procedure
Step-by-step explanation:
I will analyze two cases
see the attached figure to better understand the problem
case a) applying the Pythagoras Theorem
I assume that the hypotenuse is BC
[tex]AB^{2}=BC^{2}-AC^{2}[/tex]
substitute the given values
[tex]AB^{2}=17^{2}-15^{2}[/tex]
[tex]AB^{2}=64[/tex]
[tex]AB=8\ units[/tex]
case b) applying the Pythagoras Theorem
I assume that the hypotenuse is AB
[tex]AB^{2}=BC^{2}+AC^{2}[/tex]
substitute the given values
[tex]AB^{2}=17^{2}+15^{2}[/tex]
[tex]AB^{2}=514[/tex]
[tex]AB=\sqrt{514}=22.67\ units[/tex]
which sequences are arithmetic?check all that apply.
ANSWER
Option C and E
EXPLANATION
An arithmetic sequence has a constant difference among the consecutive terms.
The sequence
[tex]18,5.5,-7,-19.5,-32,...[/tex]
has a constant difference of -12.5
[tex]d = 5.5 - 18 = - 7 - 5.5 = - 19.5 - - 7 = - 32 - - 19.5 = - 12.5[/tex]
The sequence
[tex]16,32,48,64,80,...[/tex]
also has a common difference of 16
[tex]d = 32 - 16 = 48 - 32 = 64 - 48 =80 -64 = 16[/tex]
Therefore correct answers are C and E
Answer:
Step-by-step explanation:
An arithmetic sequence has a constant difference among the consecutive terms.
The sequence has a constant difference of -12.5
The sequence also has a common difference of 16
Therefore correct answers are C and E
use the formula a=p(1+r/n)nt to find the compound interest account . zakk deposited $5600.0in an account which compounded 1.9%quarterly and left there for ten years. what was the amount in the account at the end of ten years,?
Answer:
[tex]A=\$6,768.75[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$5,600\\ r=0.019\\n=4[/tex]
substitute in the formula above
[tex]A=\$5,600(1+\frac{0.019}{4})^{4*10}[/tex]
[tex]A=\$5,600(1.00475)^{40}=\$6,768.75[/tex]
Find the volume of the sphere.
Either enter an exact answer in terms of Find the volume of π or use 3.14 for Find the volume of the sphere.
Either enter an exact answer in terms π or use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
1436.03 units³
Step-by-step explanation:
The formula for the volume of a sphere of radius r is
V = (4/3)πr³. We'll use 3.14 for π.
Then:
V = (4/3)(3.14)(7 units)³. To the nearest hundredth: 1436.03 units³
Answer:
Step-by-step explanation:
Given
r = 7
pi = 3.14
Formula
V = (4/3) pi * r^3
Solution
V = (4/3) * pi * 343
V = (1.3333) * 3.14 * 343
V = 1435.99 You are going to get a lot of variation in this question: Everything depends on what value you use for 4/3. I used 1.3333 but it does go on. I would try this yourself. Whatever you get, enter it.
You are better off using 3.14 than using pi. You are still going to have to problem of how to represent 4/3
The mean absolute deviation is a measure of . This value represents the average distance each value is from the .
Previous
Answer:
I am not sure i am sorry if i was smart i would know but ya sorry
Step-by-step explanation:
::::::::::::::
PLEASE HELP RIGHT AWAY
Answer:
95
Step-by-step explanation:
Week Number of Beetles
0 16
1 16 + (16/4) = 20
2 20 + (20/4 ) = 20 + 5 = 25
3 25 + (25/4 ) = 25 + 6.25 ≈ 31
4 31 + (31/4) = 31 + 7.75 ≈ 31+8 ≈ 39
5 39 + (39/4) = 39 + 9.75 ≈ 39 + 10 ≈ 49
6 49 + (49/4) = 49+ 12.25 ≈ 49+12 ≈ 61
7 61 + (61/4) = 61 + 15.25 ≈ 61 + 15 ≈ 76
8 76 + (76/4) = 76 + 19 = 95
Hence there will be approximately 95 beetles by 8th week
56. Mikayla is filling a glass sphere with water.
If the diameter of the sphere is 12 inches,
what is the minimum amount of water she
needs to completely fill the sphere?
The minimum amount of water she needs to completely fill the sphere is; 904.32 inches³
How to find the Volume of a Sphere?
The formula for Volume of a Sphere is given as;
V = ⁴/₃πr³
We are given;
Diameter; d = 12 inches
Thus;
Radius; r = 12/2 = 6
To get the minimum amount of water she needs to completely fill the sphere, we just plug in the relevant values into the volume equation to get;
V = ⁴/₃π(6)³
V = 904.32 inches³
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Plz answer right away
Answer:
1 whole and 1 over 12
Step-by-step explanation:
Answer:
Step-by-step explanation:
7
12
+
3
6
=
7
12
+
3
6
=
7
12
+
1
2
=
7
12
+
6
12
=
7+6
12
=
13
12
(Decimal: 1.083333)
What is the scale factor of this dilation?
A) 1/2
B) 1/3
C) 2
D) 3
Answer:
2
Step-by-step explanation:
From X to the black dot it is 2 and from the black dot to Y it is 3
From X' to the black dot it is 4 and from the black dot to Y' it is 6
The lengths are getting twice as bigger
Answer:
2
Step-by-step explanation:
U can use this formula
Image 1/image 2
.......Help Please......
Answer:
(7,5) is the vertex
Step-by-step explanation:
I'm not sure understanding this at ALLLLL
Answer:
17. Scale Factor is 3:1
18. Scale Factor is 1:3
Step-by-step explanation:
Scale Factor: In two similar shapes, the ratio of their corresponding sides is called scale factor.
17. Give the scale factor of Figure A to Figure B
Figure A has sides:
Hypotenuse = 15
Perpendicular = 12
Base = 9
Figure B has sides:
Hypotenuse = 5
Perpendicular = 4
Base = 3
So, if we divide all sides of figure A by 3 we get Figure B
So, Figure A : Figure B
3:1
18. Give the scale factor of Figure B to Figure A
Figure B has sides:
Hypotenuse = 5
Perpendicular = 4
Base = 3
Figure A has sides:
Hypotenuse = 15
Perpendicular = 12
Base = 9
If we multiply 3 with the sides of Figure B we can get the sides of Figure A.
So scale factor is 3.
So, Figure B : Figure A
1:3
Answer:
17) 3 : 1
18: 1 : 3
Step-by-step explanation:
Figure A and Figure B are similar triangle.
Scale Factor of A : B
= 9 : 3
= 3 : 1
Scale Factor of B : A
= 3 : 9
= 1 : 3
Solve for r.
12 - - = 2r +1
r=
Answer:
r=5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Fiona’s school has three hallways that make up three sides of a triangular building design. In the morning, Fiona walks 90 yards through the first hallway to get to the next. In the afternoon, she walks 60 yards through a second hallway to exit the building. What are the possible lengths of the third hallway that she did not walk through? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
Answer:
"between 30 yards and 150 yards"
Step-by-step explanation:
Let one side of a triangle be x and another side be y. To find the possible lengths of the third side, it is given by:
Possible length of 3rd side would be between "x - y" and "x + y"
Here, given x = 90 and y = 60, so the possible length of 3rd side would be:
90 - 60 = 30,
90 + 60 = 150
Hence, in between 30 and 150
Answer:
its D between 30 and 150 just took test on ed got a 100
Step-by-step explanation:
Write an equation of an ellipse in standard form with the center at the origin and a height of 12 units and width of 19 units.
The equation of an ellipse with a center at origin, a height of 12 units, and a width of 19 units is x^2/(9.5^2) + y^2/(6^2) = 1.
Explanation:The student is asking for an equation of an ellipse. An ellipse has a standard form equation given by x^2/a^2 + y^2/b^2 = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis. The semi-major axis and the semi-minor axis are half of the major axis (width) and minor axis (height) respectively. Here, the width or major diameter of the ellipse is given as 19 units and the height or minor diameter as 12 units.
Thus, the semi-major axis is 19/2 = 9.5 and the semi-minor axis is 12/2 = 6. As the ellipse's center is at the origin, the equation of the ellipse is given by: x^2/(9.5^2) + y^2/(6^2) = 1.
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The equation of the ellipse in standard form with a center at the origin, a height of 12 units, and a width of 19 units is x²/(19/2)² + y²/(6)² = 1.
Explanation:The equation of an ellipse in standard form with the center at the origin is given by x²/a² + y²/b² = 1, where a is the semimajor axis (half the width) and b is the semiminor axis (half the height).
Given a width of 19 units and a height of 12 units, the semimajor axis will be half of the width and the semiminor axis will be half of the height. So, the equation of the ellipse will be x²/(19/2)² + y²/(12/2)² = 1.
Simplifying, x²/(19/2)² + y²/(6)² = 1. This is the equation of the ellipse in standard form with a height of 12 units and a width of 19 units.
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There are 12 inches in 1 foot. Convert 3 feet to inches.
A) 4 inches
B) 9 inches
C) 12 inches
D) 36 inches
Answer: D) 36 Inches
Step-by-step explanation:
Answer:
D)36 inches
Step-by-step explanation:
3 feet × (12 inches/1 feet) = 36 inches
the diameter of a circle is 4 feet. what is the circumference
Answer:
C=12.57 ft
Step-by-step explanation:
Answer: 12.56 feet.
Step-by-step explanation:
The independent variable in the relationship is the and should be placed on the . The dependent variable in the relationship is the and should be placed on the .
The independent variable is manipulated or controlled by the experimenter and is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable and is usually placed on the vertical axis of a graph.
Explanation:In a scientific study, the independent variable is the variable that is manipulated or controlled by the experimenter, and it is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable, and it is usually placed on the vertical axis of a graph.
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