Answer:
a. [tex]-3x^{5}y^{6}[/tex]
Step-by-step explanation:
We want to multiply and simplify:
[tex]-3x^2y^2\times y^4x^3[/tex]
We rearrange the product to obtain:
[tex]-3x^2\times x^3\times y^2\times y^4[/tex]
Recall that:
[tex]a^m\times a^n=a^{m+n}[/tex]
We apply this property to obtain:
[tex]-3x^{2+3}y^{2+4}[/tex]
We simplify to obtain:
[tex]-3x^{5}y^{6}[/tex]
is it posible for a system of linear equations to have exactly two solutions. true or false ?
Answer:
False
Step-by-step explanation:
If both lines are linear, they can only have 0, 1 or infinite solutions. If one was a quadratic function, they would intercept twice.
a glass cylinder has a diameter of 7 inches and a height of 1.5 inches. Glass had a density of 2.58 grams per cubic centimeter. Find the mass of the cylinder to the nearest gram.
Answer:
The mass of the cylinder is [tex]149\ g[/tex]
Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=7/2=3.5\ in[/tex] ----> the radius is half the diameter
[tex]h=1.5\ in[/tex]
assume
[tex]\pi=3.14[/tex]
substitute
[tex]V=(3.14)(3.5)^{2}(1.5)[/tex]
[tex]V=57.70\ in^{3}[/tex]
step 2
Find the mass
we know that
The density is equal to the mass divided by the volume
[tex]D=m/V[/tex]
Solve for the mass
[tex]m=D*V[/tex]
substitute the values
[tex]m=(2.58)*(57.70)=149\ g[/tex]
Answer:
2441 grams
Step-by-step explanation:
convert 7 and 1.5 inches into centimeters (2.54 centimeters per inch) so now you use half of 8.89 (7 * 2.54 = 2441) multiplied by 3.81
you find the area of the cylinder first by using [tex]\pi r^2*h[/tex] which should give you 945.97219
then plug it into the density formula, 2.58= mass/945.97219
that should give you mass=2440.61
and if you round it to the nearest gram, it's 2441
**THIS IS THE CORRECT ANSWER**
The price for a pair of sandals is $49.95 in June. In August the price is 60% less. Which expression gives the price of the sandals in August?
To calculate the new discounted price, $49.95×.60=$29.97
Answer:
The required expression is [tex]0.40\times 49.95[/tex].
Step-by-step explanation:
Consider the provided information.
The price for a pair of sandals is $49.95 in June.
In August the price is 60% less.
After getting 60% discount customer need to pay only 40% of the price.
This can be written as:
[tex]40\% \times 49.95[/tex]
[tex]\frac{40}{100}\times 49.95[/tex]
[tex]0.40\times 49.95[/tex]
Hence, the required expression is [tex]0.40\times 49.95[/tex].
Which geometric series diverges?
Answer:
1) not diverges
2)not diverges
3) diverges
4)not diverges
Step-by-step explanation:
In geometric series, If the |r|<1 then the series is convergent and if |r|>1 then the series is divergent
Where r is the ratio between the consecutive terms of series.
1) 3/5 + 3/10 +3/20 + 3/40 ......
in the above geometric series
r= (3/10) / (3/5)
= 1/2
= 0.5
As |r|= 0.5 < 1, so the series will not diverge
2) -10+4-8/5 + 16/25 -......
in the above geometric series
r= (4) / (-10)
= -2/5
= -0.4
As |r|= 0.4 < 1, so the series will not diverge
3) ∑ 2/3(-4)^(n-1)
in the above geometric series
r= -4
As |r|= |-4| = 4 > 1, so the series will diverge
4) ∑ (-12)(1/5)^(n-1)
in the above geometric series
r=1/5
= 0.2
As |r|= 0.2 < 1, so the series will not diverge !
Answer:
Its C!!!!!!!!!!
Step-by-step explanation:
Which polynomial represents the difference below (8x2+9) - (6x2+2x+2)
Answer:
2x² - 2x + 7
Step-by-step explanation:
Given
(8x² + 9) - (6x² + 2x + 2) ← distribute by - 1
= 8x² + 9 - 6x² - 2x - 2 ← collect like terms
= (8x² - 6x²) - 2x + (9 - 2)
= 2x² - 2x + 7
Answer:
2x² - 2x + 7
Step-by-step explanation:
Ape-x
An 80 kg Rottweiler needs 40 mL/kg over 12 hours. What's the flow rate per hour? A. 267 mL/hr B. 3,200 mL/hr C. 3.3 mL/hr D. 133 mL/hr
Answer:
A
Step-by-step explanation:
40ml/kg
Kg are 80 so i multiply 40×80 and I get 3200Ml, that is the amount of watet the rottwailer needs in 12 hours. But, because i need to find the amount in 1 hour i do 3200/12 and i get 266,666666 that i approximate to 267.
The flow rate per hour of the 80 Kg Rottweiler is Option(A) 267 mL/hr.
What is the flow rate per hour of the given sample ?It is given that the 80 kg Rottweiler needs 40 mL/kg over 12 hours.
Therefore, the flow rate per hour can be found out just by comparing the units and dimensions of the given sample with the required sample to found out.
The flow rate per hour is -
= ( 80 kg ) * (40 mL/kg) * (1/12 hours)
= (80 * 40) / 12 mL/Hours
= 266.6667 mL/hr
≈ 267 mL/hr .
Thus, the flow rate per hour of the 80 Kg Rottweiler is Option(A) 267 mL/hr.
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Evaluate r2h for = 3.14, r = 1 and h = 2. Round your answer to the nearest whole number and type a numerical answer in the space provided.
Answer:
The answer in the procedure
Step-by-step explanation:
we have
[tex]\pi=3.14[/tex]
[tex]r=1\ units[/tex]
[tex]h=2\ units[/tex]
case a) If the expression is
[tex]\pi r^{2} h[/tex]
then
substitute
[tex](3.14)(1)^{2} (2)=6.28\ units^{3}[/tex]
Round to the nearest whole number
[tex]6.28=6\ units^{3}[/tex]
case b) If the expression is
[tex](1/3)\pi r^{2} h[/tex]
then
substitute
[tex](1/3)(3.14)(1)^{2} (2)=2.09\ units^{3}[/tex]
Round to the nearest whole number
[tex]2.09=2\ units^{3}[/tex]
3 The Hawks soccer team played a total of 24 games. They won 6 more games than they lost, and they tied 2 games. How many games did they win?
They won 14 games. If you subtract 2 ( the ties ) you are left with 22. Subtract 6 ( games more won than loss) you get 16. Then divide by two and get 8. 8 + 6 = 14.
Answer:
14 games.
Step-by-step explanation:
Let x represent number of games lost by Hawks.
We have been given that the Hawks won 6 more games than they lost. So number of games won by Hawks would be [tex]x+6[/tex].
We have been given that they played a total of 24 games and tied in 2 games, so total game won or lost by Hawks would be [tex]24-2=22[/tex].
Now we will equate sum of games won and lost by 22 as:
[tex]x+x+6=22[/tex]
[tex]2x+6=22[/tex]
[tex]2x+6-6=22-6[/tex]
[tex]2x=16[/tex]
[tex]\frac{2x}{2}=\frac{16}{2}[/tex]
[tex]x=8[/tex]
Number of games won by Hawks would be [tex]x+6\Rightarrow 8+6=14[/tex]
Therefore, Hawks won 14 games.
David has a bank account which pays interest at the rate of 1.5% per year, compounded annually. Determine what amount David must have in the bank, given that he would like to draw an annual salary of $32,635.15 from his account at the end of each year for 30 years. Round to the nearest cent.
a.
$783,760.48
b.
$979,054.50
c.
$1,225,080.50
d.
$795,516.88
Answer:
A
Step-by-step explanation:
The amount that David must have in the bank would be $783243.6
What is annuity?An annuity is a series of payments made at equal period of time.
We need to apply the formula for determining present annuity. It is expressed as
PV = R[1 - (1 + r)^- n]r
Where, PV represents the present value of the investment.
R represents the regular payments made(could be weekly, monthly)
r = represents interest rate/number of interval payments.
n is the total number of payments made.
From the information given;
r = 1.5/100 = 0.015
n = 30 years
R = $32,635.15
Therefore,
PV = 32635.15[1 - (1 + 0.015)^- 30]/0.015
PV = 32635.15[1 - (1.015)^- 30]/0.015
PV = 32635.15[1 - 0.64]/0.015
PV = 32635.15[0.36]/0.015
PV = 32635.15 × 24
PV = $783243.6
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find the area of this figure
Check the picture below.
so we have 3 rectangles and 1 semicircle.
let's recall that the area of a circle = A = πr², so then the area of a semi-circle is πr²/2.
let's get the area of all figures, sum them up, and that's the area of the composite.
[tex]\bf \stackrel{\textit{top rectangle}}{(2\cdot 5)}+\stackrel{\textit{middle rectangle}}{(4\cdot 11)}+\stackrel{\textit{bottom rectangle}}{(9\cdot 2)}+\stackrel{\textit{semicircle}}{\cfrac{25\pi }{2}} \\\\\\ 10+44+18+12.5\pi \implies 72+12.5\pi \qquad \approx\qquad 111.27[/tex]
What is the area of a circle with a circumference of 36.68 units
Answer:
radius = circumference / (2 * PI)
radius = 5.8378033126
Circle Area = PI * radius^2
Circle Area = PI * 5.8378033126^2
Circle Area = PI * 34.0799475167
Circle Area = 107.07 square units
Step-by-step explanation:
Rewrite the expression with rational exponents as a radical expression.
Answer:
[tex]7\sqrt[3]{x^2}[/tex]
Step-by-step explanation:
The rule of exponents that dictates this to be solved is:
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]
The power of 2/3 is on "x", NOT 7, so we use this property to write it as:
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a} \\7x^{\frac{2}{3}}=7\sqrt[3]{x^2}[/tex]
third answer choice is right, [tex]7\sqrt[3]{x^2}[/tex]
Answer:
b or the second one top to botton
Step-by-step explanation:
trust
what is the range of the data set?
61
40
41
55
Answer:
40
Step-by-step explanation:
The range is the difference between the largest value and the smallest value in the data set.
minimum value = 21 and maximum value = 61
range = 61 - 21 = 40
Answer: Range of the data set would be 40.
Step-by-step explanation:
Since we have given the data set as follows:
21,23,28,28,52,54,56,56,57,60,61,61.
We need to find the range of the data set.
As we know the formula for "Range":
Range = Highest number - Lowest number
Range = 61-21
Range = 40
Hence, range of the data set would be 40.
25 points Please explain your answer, thank you!
Which expression is not a polynomial?
( ACCIDENTALLY PUT ONLY 10 POINTS ON THE LAST ONE SORRY)
A. -5x+6y
B. -3/x
C. 2p^3q^2-pq^3
D. 7-z
The answer is B.
For an expression to be a polynomial term, any variables in the expression must have whole number powers.
-3/x isn’t a polynomial term because the variable is in the denominator.
Answer:
D
Step-by-step explanation:
it only consists of one term.
Melissa’s birthday is next week and she has been receiving cards in the mail with different amounts of money. She has received 5 cards with the following amounts: $10, $20, $ 25, $30, $40. If Melissa receives one more card in the mail with $25, which of the following will happen?
Answer:
its will just add 25 to the total amount of money she got in the cards.
Step-by-step explanation:
Help?! “Find the area of each figure. Round your answer the nearest tenth”
Answer:
Check attached graph
Step-by-step explanation:
Given equation is .
Now we need to graph the given equation .
To graph that we can find two points then join them by a straight line.
We are free to plug any number for x say x=0 and x=2
plug x=0
Hence first point is (0,-2).
plug x=2
Hence first point is (2,0).
Now graph both points and joint them to get final graph as shown below.
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is the value of the first 7 ten times as great as the value of the second 7 in in 7,027
Answer:
No
Step-by-step explanation:
we have the number
[tex]7,027[/tex]
we know that
[tex]7,027=7*1,000+2*10+7*1[/tex]
so
The value of the first 7 is equal to
[tex]7*1,000=7,000[/tex]
The value of the second 7 is equal to
[tex]7*1=7[/tex]
therefore
[tex]7,000/7=1,000[/tex]
The value of the first 7 is one thousand times greater than the second 7
The answer is no
There are 45 boys and 54 girls in your school’s senior class. What is the ratio of boys to girls
Answer:
5/6
Step-by-step explanation:
The ratio is:
45 / 54
Or, reduced:
5 / 6
The ratio of boys to girls in the senior class of the school is 45:54.
Explanation:The question is asking to find the ratio of boys to girls in a senior class. Since the class has 45 boys and 54 girls, the ratio is typically written in the simplest form as 'boys: girls'. The given figures are in simplest form because they do not have a common factor other than 1. Therefore, the ratio of boys to girls in the senior class is 45:54.
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find x
x-6+9+2x-19=23
Answer:
x=13
Step-by-step explanation:
x+2x=3x
-6+9+-19=-16
3x-16=23
+16 +16
3x=39
divide by 3 on both sides.
x=13
The base of an isosceles triangle is 21 cm long. The altitude to the base is 9 cm long. What is the approximate measure of a base angle of the triangle?
Answer:
Step-by-step explanation:
tan α=9÷(21/2)=18/21=6/7
α=arc tan(6/7)≈40.6°
solve for each variable and tell how you find the value of each variable
a=180-142=38 degree
b= 180-38-88=54 degree
c=b (since the two lines are parallel to each other) therefore c=54 degree
See the attached picture:
Evaluate the expression 9 - z when z = 4
Answer:
5
Step-by-step explanation:
The expression 9 - z evaluates to 5 when z = 4. This is calculated simply by substituting 4 into the equation in place of z, and then performing the subtraction.
Explanation:The question is asking you to evaluate the expression 9 - z when z = 4. The term 'evaluate' in mathematics means to calculate the numerical value of. So this is a straightforward substitution problem. You take the value of z (which is 4) and substitute it into the equation in place of z. So, the equation becomes 9 - 4, which equals 5.
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Which number is rational?
O A. 0.7
O B. 0.31243576...
Ос. л
O D. Jo
Answer:
A. 0.7
Explanation:
B is irrational
I have no idea was c and d so that leads to A because it’s terminated
Answer:0.7
Step-by-step explanation:
A pex quiz
Given O below, the arcs AB and CD must be congruent.
Answer:
Option A true is the answer.
Step-by-step explanation:
The given circle there are two arcs AB and CD.
Angles formed by these arcs at the center arc 30°
Formula of length of arc = r × θ
where r = radius of the circle
and θ = angle formed by arc at the center.
mAB = OA × (30°) [ By formula ]
similarly mCD = DC × (30°)
Since OA = OC = r (radii of the circle )
So mAB = mCD
Therefore, statement is true.
Option A true is the answer.
Answer:true
Step-by-step explanation:
A triangular pane of glass has a height of 38 inches and an area of 304 square inches. What is the length of the base of the pane?
Answer:8 inches
Step-by-step explanation:304/38 = 8 inches
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have?
1 European euro = 1.3687 US dollars
For this case we make a rule of three to determine the initial amount of euros:
1 euro ----------------> 1.3687 dollars
x ------------------------> 250 dollars
Where "x" represents the amount of euros equivalent to 250 dollars.
[tex]x = \frac {250 * 1} {1.3687}\\x = 182.655074158[/tex]
Thus, Phelan received 182.655074158 euros.
If I spend 150 euros, we have:
[tex]182.655074158-150 = 32.655074158[/tex]
Now, we make the conversion to know the amount of dollars equivalent:
1 euro ----------------> 1.3687 dollars
32,655074158 ------------------------> y
Where "y" represents the amount of dollars:
[tex]y = \frac {32.655074158 * 1.3687} {1}\\y = 44,695[/tex]
So, Phelan has 44,695 dollars
Answer:
$ 44,695
There are 7 animals a farmer's field.
Some are cows and some are chickens.
The farmer counts 18 legs in all.
Answer:
2 cows and 5 chickens.
Step-by-step explanation:
NOTE: This will be solved using simultaneous equations.
Let x = cows and y = chickens
1. form two equations
4x + 2y = 18 ... (1)
x + y = 7 .... (2)
2. make y (or x) the subject of one equation
x + y = 7
y = 7 - x ... (3)
3. Substitute (3) into (1)
4x + 2( 7 - x) = 18
4. solve for x
4x + 14 - 2x = 18
2x = 4
x = 2
5. Now substitute x value into equation (2)
x + y = 7
2 + y = 7
y = 5
∴ cows (x) = 2
chickens (y) = 5
The number of cows is 2 and that of chickens are 5
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, There are 7 animals in a farmer's field. Some are cows and some are chickens. The farmer counts 18 legs in all.
This will be solved using system of equations.
Let x = cows and y = chickens
4x + 2y = 18 ... (1)
x + y = 7 .... (2)
x + y = 7
y = 7 - x ... (3)
4x + 2(7 - x) = 18
4x + 14 - 2x = 18
2x = 4
x = 2
2 + y = 7
y = 5
Hence, the number of cows are 2 and that of chickens are 5
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what are the solutions to the function x^2+9x+8=0
Answer:
The solutions are
[tex]x=-8\\x=-1[/tex]
Step-by-step explanation:
We must solve the equation:
[tex]x^2+9x+8=0[/tex]
To solve the equation we can use the factoring method.
To factor the expression, look for two numbers that when you add them, get the result 9 and when multiply them, get the result 8.
You can verify that the numbers that meet this requirement are: 8 and 1.
Then the polynomial factors are:
[tex](x + 8) (x + 1)[/tex]
So
[tex]x^2+9x+8=(x + 8) (x + 1) = 0[/tex]
Then
[tex]x+8= 0[/tex] or [tex]x+1 =0[/tex]
[tex]x=-8[/tex] or [tex]x= -1[/tex]
Answer:
x = -1 or x = -8
Step-by-step explanation:
It is given the function
x² + 9x + 8 = 0
To find the solution of given function
x² + 9x + 8 = 0
By using splitting method we can write,
x² + x + 8x + 8 = 0
x(x + 1) + 8 (x + 1) = 0
(x + 1)(x + 8) = 0
x+ 1 = 0 or x + 8 = 0
x = -1 or x = -8
please help ASAP! i am having issues!
i believe the answer is D.) 1 over 8
Explanation: 4 is one of the 8 numbers so it would be a 1 over 8 chance.
I will give brainlyist!!
I need the measure of angles for J B and C but C needs to be explained
Answer:
j=90 B=34 C=108
Step-by-step explanation:
if you know that the value of B=34 and the value of A= 38 and the sum of angles of the triangle =180 therefore C=180-(34+38)=108