Answer:
300 SF
Step-by-step explanation:
just took the test
Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Answer:
9 m
Step-by-step explanation:
Given that
Width of rectangular flower garden, w = 4 m
Perimeter of rectangular flower garden, p = 26 m
To find:
Length of Lisa's flower garden = ?
Solution:
First of all, let us understand perimeter, length and width of a rectangle.
Let ABCD be a rectangle. Please refer to the attached image.
Opposite sides of a rectangle are equal to each other.
AB = CD = Length
Let the length be [tex]l[/tex] m.
BC = DA = Width = 4 m
Perimeter of a closed image is equal to the sum of all the sides of the image.
So, perimeter of ABCD:
[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]
[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]
The algebraic expression for the product of five and the cube of a number decreased by 40
Answer:
5a³ - 40
Step-by-step:
The algebraic expression is:
5a³ - 40
Evaluate the expresión 6c-d when c=2 and d=10 I need help?
Answer:
the answer is 18
Step-by-step explanation:
8 is the answer
Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy
Answer:
Charlie: 5 + xDanny: x - 8Eric: x × 3Calculate, correct to one decimal plice
the acute angle between the lines
3x - 4y + 5 = 0 and 2x + 3y -1 = 0
A. 70.69
B. 50.2
C. 39.8
D. 19.4
Answer:
A. 70.69 is the correct answer.
Step-by-step explanation:
Given:
Two lines:
[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]
To find:
Angle between the two lines = ?
Solution:
Acute Angle between two lines can be found by using the below formula:
[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]
Where [tex]\theta[/tex] is the acute angle between two lines.
[tex]m_1, m_2[/tex] are the slopes of two lines.
Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:
[tex]m = -\dfrac{a}{b }[/tex]
So,
[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]
[tex]m_2 = -\dfrac{2}{ 3}[/tex]
Putting the values in the formula:
[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]
So, correct answer is A. 70.69
cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 6 instead, she subtracted 6 and then divided the result by 3 giving an answer of 25 what would her answer have been if she had worked the problem correctly?
Answer:
13
Step-by-step explanation:
let the number be x
how Cindy worked it out :
(x -6) ÷ 3 = 25
x -6 = 75
x = 81
How she should have worked it out:
(x - 3) ÷ 6
(81 - 3) ÷ 6
78 ÷ 6 = 13
Please help me with this question
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...
-x^2 +10x ≥ 0
x(10 -x) ≥ 0
The two factors in this product will both be positive only for values ...
0 ≤ x ≤ 10 . . . . the domain of f(x)
Given the graph, find an equation for the parabola.
Answer:
[tex]\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
When the parabola equation is like
[tex]y=a(x-h)^2+k[/tex]
The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))
As the vertex is (3,-2) we can say that h = 3 and k = -2.
We need to find a.
The focus is (3,2) so we can say.
[tex]2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}[/tex]
So an equation for the parabola is.
[tex]\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A project has an initial cost of $40,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to the nearest cent.
Answer:
50k
Step-by-step explanation:
if pentagon OPQRS is dilated by a scale factor or ?
from the origin to create O'P'Q'R'S: what is the ordered pair of point S'?
Answer:
Option (D) : (3.5, 8.75)
Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13).
Oy= -27 - 3)' +5
Oy=2(x + 3) - 5
Oy=2(0 - 3)' + 5
Oy= -3(2 – 3) + 5
PLEASE HELP ME!!
Answer:
y = 2(x - 3)² + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 5), thus
y = a(x - 3)² + 5
To find a substitute (1, 13) into the equation
13 = a(1 - 3)² + 5 ( subtract 5 from both sides )
8 = 4a ( divide both sides by 4 )
a = 2, then
y = 2(x - 3)² + 5 ← equation of parabola in vertex form
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework?
Answer:
Step-by-step explanation:
½ of 5¼
½×(21/4)
=21/8
=2⅝ hours
Answer:
2 5/8
Step-by-step explanation:
you would divide 5 1/4 by 2 :
5 divided by 2 =2 1/2
1/4 divided by 2=1/8
then make the numbers have the same denomanator
1/2, 2/4, 4/8
1/8,
then you add
2 4/8+1/8=2 5/8
michaela has h hair ties. michaela's sister has triple the number of hair ties that michaela has. choose the expression that shows how many hair bows michaela's sister has
Answer:
[tex]S = 3 h[/tex]
Step-by-step explanation:
Let M represent Michaela hair tier and S represents Michaela sister's
Given
M = h
S = Triple of M
Required
Determine an expression for S
From the given parameters, we have that;
S = Triple of M
Mathematically, this implies;
[tex]S = 3 * M[/tex]
Substitute h for M
[tex]S = 3 * h[/tex]
[tex]S = 3 h[/tex]
Hence, the expression for Michaela sister' is [tex]S = 3 h[/tex]
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2]
Answer:
Yes , it satisfies the hypothesis and we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
Step-by-step explanation:
Given that:
[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]
which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]
Differentiating the function with respect to x is;
f(x) = 8x - 3
Using the Mean value theorem to see if the function satisfies it, we have:
[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]
since the polynomial function is differentiated in [0,2]
[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]
[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]
[tex]8c -3 = \dfrac{10}{2}[/tex]
8c -3 = 5
8c = 5+3
8c = 8
c = 8/8
c = 1
Therefore, we can conclude that c = 1 is an element of [0,2]
c = 1 ∈ [0,2]
find the value of X?
Answer:
x = 58
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
90 = 32+x
Subtract 32 from each side
90-32 = x
58 =x
let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship
Answer:
d = s x t
Step-by-step explanation:
The formula for distance.
Which expression is equivalent to 5y^3/(5y)^-2
Answer:
5^3 y^5
125 y^5
Step-by-step explanation:
5y^3/(5y)^-2
Distribute the exponent in the denominator
5y^3/(5 ^-2 y^-2)
A negative exponent in the denominator brings it to the numerator
5y^3 5 ^2 y^2
Combine like terms
5 * 5^2 * y^3 5^2
We know that a^b * a^c = a^(b+c)
5^(1+2) * y^( 3+2)
5^3 y^5
125 y^5
Write an equation showing the relationship between the lengths of the three sides of a right triangle.
Answer:
Below
Step-by-step explanation:
First triangle)
This triangle is a right one so we will apply the pythagorian theorem.
● 25 is the hypotenus
● 25^2 = b^2 + 24^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Seconde triangle)
Again it's a right triangle
x is the hypotenus.
● x^2 = 12^2 +5^2
● 12^2 = x^2-5^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
This is a right triangle
AC is the hypotenus.
● AC^2 = BC^2 + BA^2
Notice that: BC = BE+EC and BA=BD+DA
● AC^2 = (BE+EC)^2 + (BD+DA)^2
Answer: 2) b = 7 3) x = [tex]\sqrt{119}[/tex]
Step-by-step explanation:
Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²
2) b² + 24² = 25²
b² + 576 = 625
b² = 49
[tex]\sqrt{b^2}=\sqrt{49}[/tex]
b = 7
3) 5² + x² = 12²
25 + x² = 144
x² = 119
[tex]\sqrt{x^2}=\sqrt{119}[/tex]
[tex]x=\sqrt{119}[/tex]
According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters. What is the estimate of this value rounded to the nearest tenth of a millimeter?
Answer:
42.7 mm
Step-by-step explanation:
To the nearest tenth of a mm, 42.67 mm would be 42.7 mm.
After estimate of this value rounded to the nearest tenth of a millimeter,
⇒ 42.67 ≈ 42.7
We have to given that,
According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters.
Hence, After estimate of this value rounded to the nearest tenth of a millimeter, we get;
⇒ 42.67
As, 7 is grater than 5, so we can add 1 to the tenth place.
⇒ 42.67 ≈ 42.7
Therefore, After estimate of this value rounded to the nearest tenth of a millimeter,
⇒ 42.67 ≈ 42.7
Learn more about the rounding number visit:
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Cases Prudence has a special (cubic) die. The values on its face are the integers from 1 to 6, but they are not arranged ae in a normal die. When Prudence first tosses the die, the sum of the values on the four side faces is 15. In her second toss, the sum of these values is 12. Find what value appears in the face opposite 6 on Prudence’s special die. (Hint: what are possible values for the top and bottom face when the sum of the side faces is 12).
Answer: 3
Step-by-step explanation:
first, we know that:
1 + 2 + 3 + 4 +5 +6 = 21
Now, which two numbers we should take out in order to have 15?
we can remove the 2 and the 4, or the 1 and the 5.
so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)
in the other arrange, we have that removing two numbers we should get 12.
in order to reach 12, we should remove two numbers that add 9 together.
those can be 4 and 5, or 6 and 3.
Now, notice that in the first restriction we have that:
Or 2 and 4 are opposite,
or 1 and 5 are opposite.
So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.
Then we can affirm that the value that appears in the face opposite to the 6, is the 3.
Best Buy is currently selling the latest model of the iPad
Pro for $549.99. Since you are an employee there, you
receive a 5% discount. How much will the iPad Pro cost
you if you use your employee discount (before taxes).
Answer:
$522.49
Step-by-step explanation: 549.99*.05=27.50 (discount)
549.99-27.50=$522.49
Answer:
$522.49
Step-by-step explanation:
First, find the discount amount. You can do this by multiplying the original cost by the discount amount. A little trick for remembering to multiply instead of divide is to think "five percent of the original amount"
5% = 0.05
549.99 ⋅ 0.05 = 27.4995
That means the discount amount is $27.50
Subtract the discount amount from the original price
$549.99 - $27.50 = $522.49
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently conducted a survey to gauge support for each of the two candidates. The results of the poll are shown in the two-way frequency table below.
Answer:
3 only
Step-by-step explanation:
Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.
Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.
Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.
Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.
Therefore, the true statement is III only.
More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Data given in the table shows the data of elections between two candidates among the different cities.
What is Statistic?
Statistics is the study of mathematics that deals with relations between comprehensive data.
I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.
II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false
III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.
IV. Overall, more residents support candidate A than candidate B. it is also false.
Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Learn more about Statistics here:
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A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
how many meters are in 250 centimeters
Answer:
2.5 meters
Step-by-step explanation:
A triangle has vertices at (-4,-6),(3,3),(7,2). Rounded to two decimal places, which of the following is closest aporoximation of the perimeter of the triangle
Answer:
Perimeter= 29.12 unit
Step-by-step explanation:
Perimeter of the triangle is the length of the three sides if the triangle summef up together
Let's calculate the length of each side.
For (-4,-6),(3,3)
Length= √((3+4)²+(3+6)²)
Length= √((7)²+(9)²)
Length= √(49+81)
Length= √130
Length= 11.40
For (-4,-6),(7,2)
Length= √((7+4)²+(2+6)²)
Length= √((11)²+(8)²)
Length= √(121+64)
Length= √185
Length= 13.60
For (3,3),(7,2)
Length=√( (7-3)²+(2-3)²)
Length= √((4)²+(-1)²)
Length= √(16+1)
Length= √17
Length= 4.12
Perimeter= 4.12+13.60+11.40
Perimeter= 29.12 unit
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
1256 i think
Step-by-step explanation:
If f is a function that f(f(x)) = 2x² + 1, which is the value of f(f(f(f(3)))? Please help!
[tex]f(f(3))=2\cdot3^2+1=19\\f(f(f(f(3))))=2\cdot19^2+1=723[/tex]
please help me out! <3
Answer:
[tex]-1 \frac{3}{4}[/tex]
Step-by-step explanation:
Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)
Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from [tex]\frac{3}{4}[/tex].
To subtract this, we can break up [tex]2\frac{1}{2}[/tex] into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)
We land up at [tex]-1 \frac{3}{4}[/tex].
Hope this helped!
An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm, how many of these components should she consider to be 90% sure of knowing the mean will be within ± 0.1 ±0.1 mm?
Answer:
She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Step-by-step explanation:
We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.
And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.
As we know that the margin of error is given by the following formula;
The margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm
n = sample size of components
[tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%
[tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%
Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.1 mm = [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]
[tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]
[tex]\sqrt{n}[/tex] = 59.22
n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.
Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
