Answer: [tex]5x-5 \ge 0[/tex]
This is the same as [tex]x-1 \ge 0[/tex]
========================================================
Explanation:
We have [tex]f(x) = \sqrt{5x-5}+1[/tex]
The stuff under the square root (this stuff is called the radicand) is what we'll focus on (the +1 at the end does not affect the domain at all). We want this to be 0 or larger. This is to avoid applying the square root to negative values, which leads to complications.
So 5x-5 must be 0 or larger meaning we write [tex]5x-5 \ge 0[/tex]
Optionally we can divide all three terms (5x, -5 and 0) by 5 to go from [tex]5x-5 \ge 0[/tex] to [tex]x-1 \ge 0[/tex]
If you wanted to solve for x, you would get [tex]x \ge 1[/tex] to set up the domain. Meaning that x = 1 is the smallest x value you can plug into the function. The x value can be anything larger than 1 as well.
Simplify $\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$
Let [tex]x=\sqrt[3]{3}[/tex] and [tex]x^2=\sqrt[3]{9}[/tex]. Then
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2x^2}{1+x+x^2}[/tex]
Multiply the numerator and denominator by [tex]1-x[/tex]. The motivation for this is the rule for factoring a difference of cubes:
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Doing so gives
[tex]\dfrac{2x^2(1-x)}{(1+x+x^2)(1-x)}=\dfrac{2x^2(1-x)}{1-x^3}[/tex]
so that
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2\sqrt[3]{9}(1-\sqrt[3]{3})}{1-3}=\sqrt[3]{9}(\sqrt[3]{3}-1)=3-\sqrt[3]{9}[/tex]
Find the area of the triangle.
Answer:
10.5 cm^2
Step-by-step explanation:
Since we have two sides and the angle between those sides, we can use the alternative area formula:
[tex]A=\frac{1}{2}ab\sin(C)[/tex]
a and b are the two sides while C is the angle in between the two sides.
Plug in the numbers:
[tex]A=\frac{1}{2}(7)(6)\sin(150)[/tex]
Recall the unit circle. Sin(150) is 1/2.
[tex]A=21(\frac{1}{2})[/tex]
[tex]A=21/2=10.5cm^2[/tex]
i need help with this
Answer:
Step-by-step explanation:
diameter=2×5=10 cm
32/10=3.2≈3
128/10=12.8≈12
total number of squares=12×3=36
Ans ASAP.. In pic with steps.. Plz tysm 1rst one BRAINLIEST
Answer:
The expression for the shaded region is 10x² + 12x .
Step-by-step explanation:
First, you have to find the area of both rectangles using the formula :
[tex]area = length \times height[/tex]
Small rectangle,
[tex]area = x \times (5x - 2)[/tex]
[tex]area = 5 {x}^{2} - 2x[/tex]
Large rectangle,
[tex]area = (3x + 2) \times 5x[/tex]
[tex]area = 15 {x}^{2} + 10x[/tex]
In order to find the shaded region, you have to subtract the smaller from the larger one :
[tex]area \: of \: shaded = large - small[/tex]
[tex]area = 15 {x}^{2} + 10x - 5 {x}^{2} + 2x [/tex]
[tex]area = 10 {x}^{2} + 12x[/tex]
Anita plans to cover a solid cone with construction paper for a science project. The cone has a diameter of 11 inches and a slant height of 28.5 inches. How many square inches of paper will she need to cover the entire cone? (Use 3.14 for Pi and round to the nearest hundredth. Recall the formula S A = pi r l + pi r squared.) 492.20 in.2 587.18 in.2 982.82 in.2 984..39 in.2
Answer:
587.18 in²
Step-by-step explanation:
In the above question, we are given the following values
Diameter = 11 inches
Radius = Diameter/2 = 11 inches/2 = 5.5 inches
Slant height = 28.5 inches.
We were asked to find how many square inches of paper will she need to cover the ENTIRE cone.
To solve for this, we would use formula for Total Surface Area of a Cone
Total Surface Area of a Cone = πrl + πr²
= πr(r + l)
Using 3.14 for π
Total Surface Area of a Cone
= 3.14 × 5.5( 5.5 + 28.5)
= 3.14 × 5.5 × (34)
= 587.18 in²
Therefore, Anita will need 587.18 square inches of paper to cover the entire cone.
Answer:
B
Step-by-step explanation: Just trust me bro
What the answer now hurry up and answer fast question
Answer:
927.0 cm²
Step-by-step explanation:
Step 1: find Z
m < Z = 180 - (28 + 118) (sum of ∆)
= 180 - 146
Z = 34°
Step 2: Find side XY using the law of sines
[tex] \frac{XY}{sin(34)} = \frac{42}{sin(28)} [/tex]
Cross multiply
[tex] XY*sin(28) = 42*sin(34) [/tex]
[tex]XY*0.469 = 42*0.559[/tex]
Divide both sides by 0.469
[tex]\frac{XY*0.469}{0.469} = \frac{42*0.559}{0.469}[/tex]
[tex]XY = 50.06[/tex]
XY ≈ 50 cm
Step 3: find the area.
Area of ∆ = ½*XY*YZ*sin(Y)
XY ≈ 50 cm
= ½*50*42*sin(118)
= 25*42*0.8829
Area = 927.045
Area ≈ 927.0 cm² (nearest tenth)
Will give BRAINLIEST to best answer One way to explore a career opportunity is to work as a trainee in your field of interest to gain practical experience. In this experience you would be known as a(n). A intern B. mentor C. tutor D. volunteer
Answer:
A. Intern
Step-by-step explanation:
Usually as a intern, you go around gaining experience about something. For example, if your a fresh graduate , you would first be hired as an intern to gain experience in the job you want.
Answer:
B:Mentor
Step-by-step explanation:
Translate into an algebraic expression: How much 50% sugar syrup can you make if you have x grams of sugar ?
Answer:
The algebraic expression is v = 2x
v is the volume of the sugar syrup and
x is the mass of sugar in grams.
Step-by-step explanation:
Let x be the mass of sugar in grams and v be the volume of sugar syrup.
So, mass of sugar in grams/volume of sugar syrup × 100 % = 50 %
x/v × 100 % = 50 %
x/v = 50/100
x/v = 1/2
v = 2x
So, the algebraic expression required is v = 2x where v is the volume of the sugar syrup and x is the mass of sugar in grams.
what is the measure of arc angle EG
Answer:
80 = EG
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
40 = 1/2 EG
Multiply each side by 2
80 = EG
Answer:
80 deg
Step-by-step explanation:
Theorem:
The measure of an inscribed angle is half the measure of the intercepted arc.
m<EFG = (1/2)m(arc)EG
40 deg = (1/2)m(arc)EG
m(arc)EG = 2 * 40 deg
m(arc)EG = 80 deg
11/10= x+2/5 Please Explain
Answer:
x=7/10
Step-by-step explanation:
2/5=4/10
11/10=x+4/10
11/10-4/10=x
7/10=x
Answer:
x=7/10 or 0.7
Step-by-step explanation:
I turned the fractions into decimals
so
1.1=x+0.4
subtract 0.4 from 1.1 to get 0.7
Turn it into a fraction which is 7/10
Rewrite [tex]\frac{200x - 300}{x}[/tex] as a sum of two fractions, and simplify.
Answer:
We can rewrite this as [tex]\frac{200x}{x} + \frac{-300}{x}[/tex].
[tex]\frac{200x}{x}[/tex] simplifies to 200 after eliminating x from the numerator and denominator and [tex]\frac{-300}{x}[/tex] becomes [tex]-\frac{300}{x}[/tex] so the final answer is [tex]200 - \frac{300}{x}[/tex].
Find the tangent of the angle in between the lines 2x+3y–5=0 and 5x=7y+3?
Answer:
tanФ = 2.6363636
Step-by-step explanation:
To find the tangent of the angle in-between the lines we will follow the steps below:
We are going to use the formula;
tanФ = |m₂ - m₁ / 1 + m₁m₂|
We can get the slope m₁ from the first equation
2x+3y–5=0
we will re-arrange it in the form y=mx + c
3y = -2x + 5
Divide through by 3
y = -[tex]\frac{2}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
comparing the above equation with y=mx + c
m₁ = -[tex]\frac{2}{3}[/tex]
We will proceed to find the second slope m₂ using the second equation
5x=7y+3
we will re-arrange it in the form y=mx + c
7y = 5x -3
divide through by 7
y = [tex]\frac{5}{7}[/tex] x - [tex]\frac{3}{7}[/tex]
comparing the above with y=mx + x
m₂ = [tex]\frac{5}{7}[/tex]
we can now go ahead and substitute into the formula
tanФ = |m₂ - m₁ / 1 + m₁m₂|
tanФ = | [tex]\frac{5}{7}[/tex] - (-[tex]\frac{2}{3}[/tex] ) / 1 + (-[tex]\frac{2}{3}[/tex]₁)( [tex]\frac{5}{7}[/tex])|
tanФ = | [tex]\frac{5}{7}[/tex] +[tex]\frac{2}{3}[/tex] / 1 - [tex]\frac{10}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] / [tex]\frac{11}{21}[/tex]|
tanФ = | [tex]\frac{29}{21}[/tex] × [tex]\frac{21}{11}[/tex]|
21 will cancel-out 21
tanФ =[tex]\frac{29}{11}[/tex]
tanФ = 2.636363
Sunland Mining Company purchased land on February 1, 2020, at a cost of $975,900. It estimated that a total of 57,600 tons of mineral was available for mining. After it has removed all the natural resources, the company will be required to restore the property to its previous state because of strict environmental protection laws. It estimates the fair value of this restoration obligation at $110,700. It believes it will be able to sell the property afterwards for $123,000. It incurred developmental costs of $246,000 before it was able to do any mining. In 2020, resources removed totaled 28,800 tons. The company sold 21,120 tons.
Sunland Mining Company purchased land on February 1, 2020, at a cost of $975,900. It estimated that a total of 57,600 tons of mineral was available for mining. After it has removed all the natural resources, the company will be required to restore the property to its previous state because of strict environmental protection laws. It estimates the fair value of this restoration obligation at $110,700. It believes it will be able to sell the property afterwards for $123,000. It incurred developmental costs of $246,000 before it was able to do any mining. In 2020, resources removed totaled 28,800 tons. The company sold 21,120 tons.
Calculate :
a. Per unit mineral cost.
b. Total material cost of December 31, 2020, inventory
c. Total materials cost in cost of goods sold at December 31, 2014.
Answer:
a. Per unit mineral cost is $21
b. Total material Cost of ending inventory is $161280
c. Total materials cost in cost of goods sold is $443520
Step-by-step explanation:
The Per unit mineral cost can be computed as follows:
Details Amount ($)
Cost of land 975900
Add: Restoration obligation 110700
Add: Development cost 246000
1332600
Less: Resale value of property 123000
Total cost of land 1209600
Divide:Total estimated cost 57600
of minerals
Per unit mineral cost 21
b. The ending inventory cost on December 31, 2020 can be calculated as follows:
Ending inventory = Total mined tons - sold tons
Ending inventory = 28800 - 21120
Ending inventory = 7680
Cost per ton= $21
Cost of ending inventory = 7680 × $21
Cost of ending inventory = $161280
c.To calculate the cost of goods sold in December 2020; we have:
Cost per ton = $21
Total units sold = 21120
Cost of goods sold = 21120 × $21
Cost of goods sold = $443520
Henry purchased 3 items during a sale. He received a 20 percent discount on the regular price of the most expensive of the 3 items and a 10 percent discount on the regular price of each of the other two items. What was the total amount of the 3 discounts
Answer:
Combining statement 1 and statement 2 is sufficient
Step-by-step explanation:
There are 3 items purchased
Most expensive item=20% discount
The other two items=10% discount each
Statement 1: The average (arithmetic mean) of the regular prices of the 3 items was $30.
Assume:
The 3 items cost: $40, $30 and $20 respectively,
Total discount =20% of $40 + 10% of $30 + 10% of $20
=$8 + $3 + $2
= $13
Assume
The 3 items cost: $50, $30 and $10 respectively,
Total discount = 20% of $50 +10% of $30 + 10% of $10
=$10 + $3 + $1
= $14
Therefore, statement 1 is INSUFFICIENT
Statement 2: The most expensive item was $50
The discount for the most expensive item at $50 = 20% of $50
= 0.2*$50
=$10
But we don't know the price of the other 2 items, so we can't determine the discounts.
Therefore, Statement 2 is also INSUFFICIENT
Combining statement 1 and 2
1) The average (arithmetic mean) of the regular prices of the 3 items was $30.
So, the SUM of the 3 items = $90
2) The most expensive item is $50
So the OTHER 2 items sum up to $40
$50 item gets 20% discount and the other two items ($40) each get 10% discount
The discount = 20% of $50 + 10% of $40
=0.20*50 + 0.1*40
=$10 + $4
=$14
Combining the two statements is sufficient
If you flip a coin three times in the air, what is the probability that tails lands up all three times? A. 1/2 B. 1/8 C. 1/4 D. 1/6
Answer: A) 1/2
Step-by-step explanation:
Answer:
If you flip a coin three times in the air, what is the probability that tails lands up all three times?
Step-by-step explanation:
1/2
Which is the mean for this data? 1,2,5,5,6,6,7,8
Answer:
5
Step-by-step explanation:
First you need to add all the digits so 1 +2+5+5+6+6+7+8 = 40
Then, divide that by the number of digits which is 8.
Therefore, 40/8 = 5, which is the answer.
I hope this helped!
PLs answer ASAP will make you brainlist
Answer:
[tex]\boxed{\sf A. \ 36}[/tex]
Step-by-step explanation:
The triangles are congruent. The sides are proportional.
Let x be the length of FQ.
[tex]\frac{24}{18} =\frac{x}{27}[/tex]
[tex]\sf Multiply \ both \ sides \ by \ 27.[/tex]
[tex]\frac{24}{18}(27)=\frac{x}{27}(27)[/tex]
[tex]36=x[/tex]
given that sin x equals to a over b then what is tan x
Answer:
Hey there!
Sine is equal to opposite/hypotenuse
Tangent is equal to opposite/adjacent
opposite=a
hypotenuse=b
adjacent=c
Thus, tangent x= a/c.
Hope this helps :)
Answer:
tan x = a/sqrt(b^2 - a^2)
Step-by-step explanation:
sin x = a/b = opp/hyp
tan x = opp/adj
adj^2 + opp^2 = hyp^2
adj^2 + a^2 = b^2
adj = sqrt(b^2 - a^2)
tan x = a/sqrt(b^2 - a^2)
Please help me with this question. refer to the image first.
5. The diagram below shows three circles. Circle A has a radius of 2 cm and circle B has a
radius of 1 cm.
PQ is a common tangent and all circles touch one another. Find the radius of the smallest
circle. PL5
Answer: The radius of the small circle is about 0.85 cm - 0.95 cm
Explanation: I am not completely sure but I drew the same figure with the same lengths as given and between both circles there is almost a gam of 2.5 - 3 cm and when we draw a circle between them the diameter is about 1.7 - 1.9 so dividing the diameter by 2 to get the radius we get 0.85 cm - 0.95 cm.
Answer:
o.85 to 0.95
Step-by-step explanation:
I got to go so I don' have time to explain!
Write an equation to represent the following statement. k divided by 1 is 7. Solve for k. k=
Answer:
[tex]\boxed{k = 7 }[/tex]
Step-by-step explanation:
Given Condition is:
[tex]\frac{k}{1} = 7[/tex]
Multiplying both sides by 1
k = 7*1
k = 7
I need the answer and maybe someone can tell me how to do it? Please and Thanks!! :))
Answer:
83
Step-by-step explanation:
The 126 angle is an exterior angle of the triangle.
The 43 and x angles are the two remote interior angles of the 126 angle.
Theorem:
The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.
x + 43 = 126
x = 83
Answer:
x = 83
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
126 = x+43
Subtract 43 from each side
126-43 = x+43-43
83 = x
Volume of a Triangular Prism
Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Answer:
348 km³
Step-by-step explanation:
The volume of the triangular prism can be calculated using the formula, Volume = base area of the prism*the length of the prism
Base area of the prism = area of triangle = ½*base of the triangle*height of the triangle
Base of the triangle = 12 km
Height of the traingle = 5.8
Therefore,
Base area = ½*12*5.8
= 6*5.8
Base area = 34.8 km²
Length of prism = 10 km
Volume of prism = base area*prism length
= 34.8*10
Volume of triangular prism = 348 km³
Which triangle’s area can be calculated using the trigonometric area formula?
Answer:
Triangle klm
Step-by-step explanation:
edg 2020
what is the value of 24% of 800?
Question of mathematics
Answer:
[tex] \huge \boxed{192}[/tex]Step-by-step explanation:
[tex]24\% \: of \: 800[/tex]
By definition of p% = p/100
[tex] = \frac{24}{100} \times 800[/tex]
Reduce the numbers with Greatest Common Factor 100
[tex] = 24 \times 8[/tex]
Multiply the numbers
[tex] = 192[/tex]
Hope I helped!
Best regards!!
A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of pi
Answer:
288π
Step-by-step explanation:
V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.
Si tienes 24 tubos de 6 metros de longitud cada uno para unir dos puntos que conducen agua , si los tubos fueran de 8 metros ¿ cuantos tubos se necesitarían?
Answer:
Se necesitarían:
18 tubos
Step-by-step explanation:
La longitud total de la tubería con 24 tubos de 6 metros cada uno es:
24*6 = 144 metros
si los tubos fuesen de 8 metros:
144/8 = 18
Se necesitarían:
18 tubos
Sketch the graph of y = (x - 3)2 - 16, then select the graph that corresponds
to your sketch.
10
-20
20
-5
5
. 10
10
20
A. Graph A
B. Graph B
C. Graph C
Ο Ο
D. Graph D
Answer:
Please look at the attached graph and select the appropriate answer.
Step-by-step explanation:
Make sure that the graph shows a parabola with branches up, and the vertex situated at the point (3, -16) which corresponds to the double root x = 3, and the vertical shift that lowers that vertex 16 units below the x-axis.
Please look at the attached picture.
Answer: Graph B
Step-by-step explanation:
Classify the following triangle. Check all that apply.
A. Obtuse
B. Isosceles
C. Scalene
D. Equilateral
E. Acute
F. Right
Answer:
isosceles
Step-by-step explanation:
Allison accumulated $7,000 in credit card debt. If the interest rate is 15% per year and she does not make any payments for 3 years, how much will she owe on this debt in 3 years for quarterly compounding? Round your answer to two decimal places.
Answer:
Allison will owe $10,888.50 in 3 years
Step-by-step explanation:
FV=PV(1+r/n)^nt
Where,
PV=$7000
r=15%=0.15
n=quarterly=4
t=3 years
FV=PV(1+r/n)^nt
=7000(1+0.15/4)^4*3
=7000(1+0.0375)^12
=7000(1.0375)^12
=7000(1.5555)
=10,888.50
To 2 decimal places=$10,888.50
Allison will owe $10,888.50 in 3 years
Answer:
$10,888.20
Step-by-step explanation:
Order of Operations: BPEMDAS
Compounded Interest Rate Formula: A = P(1 + r/a)ᵃᵇ
A = Final Amount
P = Initial Amount
r = rate
a = Compounded number
b = time
Step 1: Define
P = 7000
r = 15% = 0.15
a = 4
b = 3 years
Step 2: Solve for A
Substitute: A = 7000(1 + 0.15/4)⁴⁽³⁾Parenthesis: A = 7000(1.0375)⁴⁽³⁾Exponents: A = 7000(1.0375)¹²Exponents: A = 7000(1.55545)Multiplication: A = 10888.20At the end of the 3 years that elapsed, Allison will have to pay a final debt of $10,888.20.
Suppose there is a bond in ABC Company that that pays coupons of 8.5%, and suppose that these coupons are paid annually.
Suppose the face value of the ABC bond is $1000 and the maturity is 11 years.
a) If the appropriate discount rate for this bond is 6%, what would you be willing to pay for ABC’s bond?
b) If a comparable company, XYZ, has a 7.0% coupon bond with a maturity of 9 years and a face value of 1000, and that bond is trading in the market for $994.50, what would you be willing to pay for ABC’s bond?
c) Suppose you find that the true fair value for ABC bond is $1200.00, but you see that the bond trading for $1051.00, what would you recommend?
Answer:
$1197.17185
Step-by-step explanation:
ABC bond :
Par value of bond (FV) = 1000
Period (n) = 11 years
Coupon rate (r) = 8.5% annually
Discount rate (r) = 6% = 0.06
The coupon price = 8.5% of par value
Coupon price (C) = 0.085 * 1000 = 85
Current price of bond can be computed using the relation:
= C * [1 - 1 / (1 + r)^n] / r + (FV / (1 + r)^n)
85 * [1 - 1/(1+0.06)^11]/0.06 + 1000/(1 + 0.06)^11
85 * 7.8868745 + 526.78752
670.38433 + 526.78752 = $1197.17185