We can do the following steps to solve the given expression for r.
Step 1: We divide by πh from both sides.
[tex]\begin{gathered} v=\pi r^2h \\ \frac{v}{\pi h}=\frac{\pi r^2h}{\pi h} \\ \frac{v}{\pi h}=r^2 \end{gathered}[/tex]Step 2: We apply square root to both sides of the equation.
[tex]\begin{gathered} \sqrt{\frac{v}{\pi h}}=\sqrt{r^2} \\ \sqrt{\frac{v}{\pi h}}=r \end{gathered}[/tex]Answer[tex]r=\sqrt{\frac{v}{\pi h}}[/tex]Use synthetic division to divide.
(-4x3 - 22x2 - 12x - 10) ÷ (x + 5)
Answer:
-4x² - 2x - 2
Step-by-step explanation:
(-4x3 - 22x2 - 12x - 10) ÷ (x + 5)
-5 | -4 -22 -12 -10
↓ 20 10 10
-----------------------------------
-4 -2 -2 0
-4x² - 2x - 2
I hope this helps!
Use the connect line tool to draw your path so that it meets the requirements. Then drag water fountains to the map and place them along the path based on the requirements. Diagonal lines may not be used.
1 mile is equivalent to 5280 feet which is equivalent to 5280/440 in = 12 in
Hence, a path of 2miles is equivalent to 24 in on the graph
The connect line is as shown in the image from the School to the Park and it is colored red and 24 in long.
The position of the water fountains are marked in pink on the graph,
The first is 1/3 of the way from the School which is 8 in from the school.
The second is 2/3 of the way from the School which is 16 in from the school.
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The amount of coffee imported into the country in the year 1997 is approximately 1.344 million pounds.
The amount of coffee imported into the country in the year 2002 is approximately 39.3176 million pounds.
The amount of coffee imported into the country in the year 2007 is approximately 85.8966 million pounds.
What is a polynomial function?A polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:
Multiplication (product)AdditionSubtractionNext, we would determine the amount of coffee imported into the country by using the given polynomial function as follows:
At 1997, we have the following:
x = 0
P(x) = 0.7166x² + 6.627x + 1.344
P(0) = 0.7166(0)² + 6.627(0) + 1.344
P(0) = 1.344 million pounds.
At 2002, we have the following:
x = 4
P(x) = 0.7166x² + 6.627x + 1.344
P(4) = 0.7166(4)² + 6.627(4) + 1.344
P(4) = 0.7166(16) + 26.508 + 1.344
P(4) = 11.4656 + 26.508 + 1.344
P(4) = 39.3176 million pounds.
At 2002, we have the following:
x = 9
P(x) = 0.7166x² + 6.627x + 1.344
P(9) = 0.7166(9)² + 6.627(9) + 1.344
P(9) = 0.7166(81) + 59.643 + 1.344
P(9) = 58.0446 + 26.508 + 1.344
P(9) = 85.8966 million pounds.
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Identify two similar triangles in the figure below, and complete the explanation of why they are similar. Then find AB. B А C 21 D ZA = (select) and ZABD = (select), so ABD - ACB by the (select)y Triangle Similarity Theorem. AB =
Answer:
∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.
AB = 10
Explanation:
An angle is congruent to itself, so ∠A ≅ ∠A
On the other hand, taking into account the representation of the angles, we can say that: ∠ABD ≅ ∠ACB
Then, the triangles ABD and ACB are congruent by the AA (Angle-Angle) triangle similarity theorem because we have two congruent angles:
∠A ≅ ∠A
∠ABD ≅ ∠ACB
Now, if two triangles are similar their corresponding sides are proportional.
So, we can formulate the following equation:
[tex]\frac{AB}{AC}=\frac{AD}{AB}[/tex]Then, replacing AC by (21 + 4), AD by 4, and solving for AB, we get:
[tex]\begin{gathered} \frac{AB}{21+4}=\frac{4}{AB} \\ AB\times AB=4(21+4) \\ AB^2=4(25) \\ AB^2=100 \\ AB=\sqrt[]{100} \\ AB=10 \end{gathered}[/tex]Therefore, the answers are:
∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.
AB = 10
Perform the indicated operation. 22 6/11 x 1 1/2
Answer:
[tex]1\frac{1}{2}[/tex] <2<2 [tex]\frac{6}{11}[/tex]
Step-by-step explanation:
[tex]1\frac{1}{2}[/tex] is less than 2 is less than 2 [tex]\frac{6}{11}[/tex]
[tex]\frac{33}{22} < \frac{44}{22} < \frac{56}{22}[/tex]
A cylindrical vase has a circumference of about 62.8 centimeters and a height of 33 centimeters. To the nearest cubic centimeter, how much water will the vase hold?
The volume of water that the cylindrical vase can hold is 10362 cm³.
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
The circumference of a cylindrical vase is 62.8 centimeters.
The height of the cylindrical vase is 33 centimeters.
Let r be the radius of the cylinder.
The circumference of the cylinder is given as:
C = 2πr
62.8 cm = 2 × 3.14 × r
r = 10 cm
The volume of a cylinder is given as:
V = πr²h where r is the radius and h is the height of the cylinder
Then,
V = 3.14 × ( 10 )² × 33
V = 10362 cm³
Hence, the cylindrical vase can hold 10362 cm³ of water.
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Answer: Bro above is wrong it's 10,367 cm3 PLATO
Step-by-step explanation: mad maths skills
Question 20 of 25If AABC is similar to ADEF, the sides of AABC must be congruent to thecorresponding sides of ADEF.OA. TrueOB. False
Given: If triangle ABC is similar to triangle DEF, the sides of triangle ABC must be congruent to the corresponding sides of triangle DEF.
Required: To determine if the given statement is true or false.
Explanation: If two triangles are similar, then their corresponding sides are in equal proportion. So, if triangle ABC is similar to triangle DEF then
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]Final Answer: Option B, False is correct.
Solve the following equations for x and y. Any method can be used.
This is a 2 x 2 equation system: (First, let's put all variables on one side)
[tex]2x-3y=13x-4y\Rightarrow2x-13x=-4y+3y\Rightarrow-11x=-y[/tex][tex]\begin{gathered} y=11x \\ y=\frac{-3}{2}x \end{gathered}[/tex]So, to solve this problem is to find the point (xo,yo) that satisfies both equations, this means a point that intersects those two lines. In this case, we are going to use a visual help:
As you can see, the lines are intersected in the point (0,0). lines are intersected in the point (0,0). Finally, the answer is x=0, y = 0
$Write the following phrase as an algebraic expression. Use y for theunknown."A number times 9"
Given the following phrase:
[tex]\text{A number times 9}[/tex]Let the number = y
The word times means to use the product process
So, the algebraic expression will be as follows:
[tex]9y[/tex](6.8 x 10^4)+(2.3 x 10^4) as a scientific notation?
We have the fortune that the power of ten is equal in both adding up. So
[tex]6.8\cdot10^4+2.3\cdot10^4=9.1\cdot10^4[/tex]Because the integer before the dot is less than 10, we need not do modifications and our answer is 9.1x10^4.
PLEASE HURRY ILL GIVE BRAINALIEST!!!
Almost 7 over 16 of the total water supplied to a household is wasted because of leaky faucets. Determine the decimal equivalent of 7 over 16 .
Use words to explain if the decimal terminates or repeats.
Answer:
0.4375
Step-by-step explanation:
Fractions, when the numerator is divided by the denominator, will give the decimal form. Therefore, 7 divided by 16 is 0.4375. It is not a repeating number because the equation doesn't give a repeating number as an answer.
Answer:
0.4375
Step-by-step explanation:
observe
7/16=(((7/2)/2)/2)/2
=((3.5)/2)/2)/2
=(1.75/2)/2
=0.875/2
=0.4375
8. 500 Vanessa is in charge of organizing volunteers to make sandwiches to feed the homeless during the Memorial Day weekend. She needs to have 500 sandwiches made so she will want to get the help of as many volunteers as possible to assist her and the 3 other paid staff who will also be making the sandwiches. Use the function s(v) = to determine s(v), the number of sandwiches each person will have to make based on v, the number of volunteers working.
ANSWER
EXPLANATION
In this problem, we have to complete the table by replacing v with each value from 0 to 6 in the table, and compute the corresponding value of s(v) based on the equation,
[tex]s(v)=\frac{500}{v+4}[/tex]Find the values for the table,
[tex]v=0;s(0)=\frac{500}{0+4}=\frac{500}{4}=125[/tex][tex]v=1;s(1)=\frac{500}{1+4}=\frac{500}{5}=100[/tex][tex]v=2;s(2)=\frac{500}{2+4}=\frac{500}{6}\approx83.3[/tex][tex]v=3;s(3)=\frac{500}{3+4}=\frac{500}{7}\approx71.4[/tex][tex]v=4;s(4)=\frac{500}{4+4}=\frac{500}{8}=62.5[/tex][tex]v=5;s(5)=\frac{500}{5+4}=\frac{500}{9}\approx55.6[/tex][tex]v=6;s(6)=\frac{500}{6+4}=\frac{500}{10}=50[/tex]Ed has a total of 92 coins in his collection.This is 8 more than three times the number of dimes in his collection. How many dimes does Ed have in his collection ? write and solve and equation
Let x represent the number of dimes Ed has in its collection.
The total of coins in the collection is 8 more than three times the number of dimes.
The number of coins is 92.
3 times the number of dimes can be symbolized as: 3x
"8 more" is symbolized as +8
So the total number of coins equals:
92=3x+8
From this expression you can determine the number of dimes by solving the equation for x:
[tex]\begin{gathered} 92=3x+8 \\ 92-8=3x \\ 84=3x \\ \frac{84}{3}=\frac{3x}{3} \\ 28=x \end{gathered}[/tex]x=28 → Ed has 28 dimes in his collection.
Let f(x) = 2x-1, g(x) = 1
Find (gof) (-3)
The value of gof(-3) is 1.
How are composite functions defined and what are they?
When two functions, f and g, are combined to produce a new function, h, such that h(x) = g(f(x)), this is known as composition in mathematics. In this instance, the function of x is being applied to the function of g. So, in essence, a function is an application of the result of another function.
Mathematically, the composition of g and h indicated by hog: A→C provided by hog(x) = h(g(x)) for every x ∈ A; let g: A→B and h: B→C signify two functions.
Given, f(x) = 2x - 1 and g(x) = 1
Thus, following the available literature,
gof(x) = g(f(x)) = g(2x - 1) = 1
Therefore, gof(-3) = 1 (∵ No variable is present in gof(x))
Therefore, the required value of gof(-3) is gof(-3)=1
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Peaches cost $4 for a 7-pound bag. If grapes cost 15% less per pound and oranges cost 35% more per pound than peaches, which of the following could be the price per pound of grapes and oranges?
A. Grapes are $0.43 per pound and oranges are $0.82 per pound
B. Grapes are $0.48 per pound and oranges are $0.77 per pound
C. Grapes are $0.57 per pound and oranges are $0.77 per pound
D. Grapes are $0.38 per pound and oranges are $0.87 per pound
C. Grapes are $0.48 per pound and oranges are $0.77 per pound.
The cost of grapes and oranges are 0.48 and 0.77 respectively.
Cost word problem
Evaluating cost of solution is simple: You determine the time and money you need to develop and implement it. You're looking at the resources needed. Cost of problem, however, equals the price of doing nothing. That is, for what I know, an important economic principle known from cost-benefit analyses.
Given that Peaches cost $4 for a 7-pound bag, grapes cost 15% less per pound than peaches, oranges cost 35% more per pound than peaches.
Cost of 7 pounds of peaches = 4
Therefore cost of 1 pound of peaches = 4/7 = 0.57
Cost of one pound of grapes = 0.57 - 15% of 0.57
= 0.57 - 0.0855
= 0.4845
= 0.48
Cost of one pound of oranges = 0.57 + 35% of 0.57
= 0.57 + 0.1995
= 0.7695
= 0.77
Therefore Grapes are $0.48 per pound and oranges are $0.77 per pound.
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Which are correct representations of the inequality 6x >= 3+ 4(2x - 1)?
First we get rid of the parenthesis on the right side by using the distributive property:
[tex]4\cdot(2x-1)=4\cdot2x-4\cdot1=8x-4[/tex]then, we would have the following equivalent expression:
[tex]\begin{gathered} 6x\ge3+4\cdot(2x-1) \\ \equiv6x\ge3+8x-4 \end{gathered}[/tex]Now we solve for x. First we get all the terms with an 'x' to one side of the inequaility. In this case, we will pass the 8x to the other side with its sign changed:
[tex]\begin{gathered} 6x\ge3+8x-4 \\ \Rightarrow6x-8x\ge3-4 \\ \Rightarrow-2x\ge-1 \end{gathered}[/tex]Since the -2 is multiplying the x, we have to pass it to the other side dividing the -1 but since it's negative, the inequality sign will change:
[tex]\begin{gathered} -2x\ge-1 \\ \Rightarrow x\leq\frac{-1}{-2}=\frac{1}{2} \\ x\leq\frac{1}{2} \end{gathered}[/tex]We have that x <= 1/2, then, the correct representation of the inequality is:
signed numbers pls help !1) 15-(-2) a) -15+2 b) 15-2 c) 15+22) -18+(-4) a) -18-4 b) -18+4 c) 18-43) -7-(-12) a) -7 - 12 b) -7+12 c) 7+124) -8 - (+15) a) -8+15 b) 8-15 c) -8 -155) 9+(-16) a) 9-16 b) 9+16 c) -9+16
Solution:
Given:
Signed numbers consist of negative numbers and positive numbers.
Rules of multiplication in signed numbers.
If the signs are the same the result is positive. If the signs are different the result is negative.
This means;
[tex]\begin{gathered} -\times-=+ \\ +\times+=+ \\ \\ -\times+=- \\ +\times-=- \end{gathered}[/tex]To solve these questions, we expand the brackets by multiplying the signs together using the rule of multiplying signed numbers.
Question 1:
[tex]\begin{gathered} 15-(-2)=15-\times-2 \\ =15+2 \end{gathered}[/tex]Therefore, the correct answer is OPTION C.
Question 2:
[tex]\begin{gathered} -18+(-4)=-18+\times-4 \\ =-18-4 \end{gathered}[/tex]Therefore, the correct answer is OPTION A.
Question 3:
[tex]\begin{gathered} -7-(-12)=-7-\times-12 \\ =-7+12 \end{gathered}[/tex]Therefore, the correct answer is OPTION B.
Question 4:
[tex]\begin{gathered} -8-(+15)=-8-\times+15 \\ =-8-15 \end{gathered}[/tex]Therefore, the correct answer is OPTION C.
Question 5:
[tex]\begin{gathered} 9+(-16)=9+\times-16 \\ =9-16 \end{gathered}[/tex]Therefore, the correct answer is OPTION A.
You deposit $4000 in an account earning 8% interest compounding monthly. How much will you have in the next 10 years
.
In this case:
[tex]\begin{gathered} P=\$4000 \\ r=8\%=0.08 \\ t=10 \\ n=12 \end{gathered}[/tex]Applying the formula, the compound interest can be calculated as follows:
[tex]\begin{gathered} A=4000(1+\frac{0.08}{12})^{(12\times10)} \\ A=8878.56 \end{gathered}[/tex]The amount in the account will be $8,878.56.
Giselle works as a carpenter and as
a
blacksmith.
She earns $20 per hour as a carpenter and $25
per hour as a blacksmith. Last week, Giselle
worked both jobs for a total of 30 hours, and
earned a total of $690.
How long did Giselle work as a carpenter
last week, and how long did she work as a
blacksmith?
Answer:
Step-by-step explanation:
$20/hr carpenter pay
$25/hr blacksmith pay
Let c = hours working carpentry
Let b = hours working as blacksmith
c + b = 30 {equation 1}
20c + 25b = 690 {equation 2}
In equation 1 solve for one variable in terms of the other.
c = 30-b
Substitute that into equation 2:
20(30-b) + 25b = 690
600 - 20b + 25b = 690
5b = 90
b = 90/5
b = 18 hours working as a blacksmith
c = 30-b = 30-18 = 12 hours as a carpenter
Answer:
she worked as a carpenter for 12 hours
And a blacksmith for 18 hours
Step-by-step explanation:
B=hours as blacksmith
C=hours as carpenter
20c+25b=690
b+c=30
c=30-b
So we substitute this into the first equation
20(30-b)+25b=690
600-20b+25b=690
5b=90
B= 18
18+c=30
C=12
The radius of a sphere is 4 inches. If the radius is doubled, how does that change the surface area of the sphere?aThe surface area is multiplied by fourbThe surface area is squaredcThe surface area is doubleddThe surface area is multiplied by eight
Solution:
Given the radius of the sphere is 4inches.
The surface area, A, of the sphere is;
[tex]\begin{gathered} A=4\pi r^2 \\ \\ A=4\pi(4^2) \\ \\ A=201.06in^2 \end{gathered}[/tex]But when the radius is doubled;
[tex]\begin{gathered} r=8in \\ \\ A=4\pi(8^2) \\ \\ A=804.25in^2 \end{gathered}[/tex]Hence, when the radius is doubled, the surface area is multiplied by four.
what else would need to be congruent to show that triangle ABC=DEF
(AAS): If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent
UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? Define your variable, Write the equation, Solution
UPS charges are:
$ 7 for the firsr pound
+ $0.20
FedEx charges are:
$ 5 for the first pound
+ $ 0.30 for each additional pound
Let x to represent the amount of additional pounds
Equation:
7 + 0.20x = 5 + 0.30x
Like terms:
0.20x - 0.30x = 5 - 7
-0.10x = -2
Dividing by -0.10
-0.10x/- 0.10 = -2/-0.10
x = 20
Interpretation
It will take 21 pounds to cost the same: (the first plus 20 additional)
A number c is no less than -1.5 and less than 5.3
Step-by-step explanation/answer:
A number c is no less than -1.5 and less than 5.3.
So -1.5<= c < 5.3
You would label your number line and have a filled in closed circle at -1.5 and an open circle at 5.3 to signify that 5.3 is not a possible value of c.
Solve this equation: 80 = 3y + 2y + 4 + 1. O A. y = ¹1/5 O B. y = 75 O C. y = 15 O D.y = -15
Answer:
C. y= 15
Step-by-step explanation:
Add 3y +2y = 5y
Add 4+1=5
Subtract 80 -5 =75
Then divide by 5y on both sides to get
y=15
#3 list the angles of each triangle in order from smallest to biggest
Statement Problem: (3)
List the angles of the triangle in order from smallest to largest.
Solution:
First, let's use the Cosine Rule to find the angle B;
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cos B \\ 2ac\cos B=a^2+c^2-b^2 \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}[/tex]Where;
[tex]\begin{gathered} a=3,b=2.9,c=3.1 \\ \cos B=\frac{3^2+3.1^2-2.9^2}{2(3)(3.1)} \\ \cos B=\frac{9+9.61-8.41}{18.6} \\ \cos B=\frac{10.2}{18.6} \\ \cos B=0.5484 \\ B=\cos ^{-1}(0.5484) \\ B=56.74 \\ B=57^o \end{gathered}[/tex]Also, let's use the Cosine Rule to find the angle A;
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ \cos A=\frac{b^2+c^2-a^2}{2bc} \end{gathered}[/tex][tex]\begin{gathered} \cos A=\frac{2.9^2+3.1^2-3^2}{2(2.9)(3.1)} \\ \cos A=\frac{8.41+9.61-9}{17.98} \\ \cos A=\frac{9.02}{17.68} \\ A=\cos ^{-1}(0.5102) \\ A=59.32 \\ A=59^o \end{gathered}[/tex]Lastly, let's use the sum of angles in a triangle theorem to get the third angle, Angle C;
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle C=180^o-59^o-57^o \\ \angle C=64^o \end{gathered}[/tex]Hence, the angles of the triangle from the smallest to the largest are;
[tex]\angle B,\angle A,\angle C[/tex]Angle B,
Angle A,
Angle C
Given vector u equals open angled bracket 8 comma negative 6 close angled bracket and vector v equals open angled bracket negative 5 comma 2 close angled bracket comma what is v − u?
Answer:
<-13, 8>
Explanation:
Given vectors u and v below:
[tex]\begin{gathered} u=\langle8,-6\rangle \\ v=\langle-5,2\rangle \end{gathered}[/tex]In order to evaluate v-u, subtract the corresponding elements as follows:
[tex]\begin{gathered} v-u=\langle-5,2\rangle-\langle8,-6\rangle \\ =\langle-5-8,2-(-6)\rangle \\ =\langle-13,2+6\rangle \\ v-u=\langle-13,8\rangle \end{gathered}[/tex]The third option is correct.
if x is a solution to the equation 2x-5=15, select all the equations that also have x as a solution
Answer:
x=10
Step-by-step explanation:
2x-5=15
+5 +5
2x=20
2x/2=20/2
x=10
Limit as x approaches infinity of 4^x
The limit as x approaches infinity of 4^x is of infinity, that is:
[tex]\lim_{x \rightarrow \infty} 4^x = \infty[/tex]
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
In this problem, the limit is given as follows:
[tex]\lim_{x \rightarrow \infty} 4^x = 4^{\infty} = \infty[/tex]
There is nothing undetermined, hence the value of limit is of infinity, as we calculated.
If an undetermined value such as 0/0 or infinity/infinity had been reached, then alternatives such as factorization or L'Hospital rule would be searched, but is not necessary in the context of this problem.
Hence, the limit is of infinity.
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Sylvia is organizing a small concert as a charity event at her school. She has done a little research and found the expression -10x + 180 represents the number of tickets that will sell at an event given that X represents the price of the ticket. Explain why the income of the event can be represented by the expression -10x^(squared) + 180x. If all the expenses add up to $150, explain why the expression -10x^ +180x-150 represents the profit. Please help. Thank you in advance and I can't make a number squares on this device so ^ is the symbol I used for squares
The income of the event is given by the product of the number of tickets and the price of a ticket.
Hence, the income of the event can be represented by
[tex]\text{ income of the event }=x(-10x+180)=-10x^2+180x[/tex]The income of the event represented by -10x² + 180x
The profit is given by
[tex]\text{ the profit }=(\text{ income of the event) - ( the expenses)}[/tex]Therefore,
[tex]\text{ the profit}=-10x^2+180x-150[/tex]The profit is given by -10x² + 180x - 150
what does it mean to subtract 4 on both sides of 76 equals 7 and 2x
