The gallon of water required by Dakota to fill the pool will be given as:-
V(x) = 2x⁶ + 10x⁴.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
Given that:-
Dakota drained his 2,268 ft³ pool to clean it. The pool is a rectangle with an area that can be expressed as 2x⁴ + 10x² The depth that can be expressed as x² if a gallon of water has a volume of 1/60 x²The function which will represent the gallons of water will be:-
As it is given in the question the pool is of a rectangular shape so the volume of the pool will be calculated as:-
V = Area of the rectangular part x depth
V = ( 2x⁴ + 10x ²) ( x² )
V = 2x⁶ + 10x⁴.
Since the amount of the water will be equal to the volume of the pool so the function for the gallons will be given as;-
V (x) = 2x⁶ + 10x⁴.
Therefore gallon of water required by Dakota to fill the pool will be given as:-V(x) = 2x⁶ + 10x⁴.
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A patient is to take 7 mL of amoxicillin 250 mg/5 mL. How many milligrams?
Step-by-step explanation:
that means that in 5 ml there are 250mg.
and that means that in 1 ml there are 250/5 = 50 mg.
and now we can find out the mg in 7 ml (by multiplying everything by 7) :
7 ml = 50 × 7 = 350 mg
What is the area of triangle ABC?
A(2,1) B(4,7) C(6,3)
Answer: 10
Step-by-step explanation:
It appears that [tex]\overline{AC} \perp \overline{BC}[/tex], so to check if this is the case, we can use the slope formula.
[tex]m_{\overline{AC}}=\frac{3-1}{6-2}=\frac{1}{2}\\m_{\overline{BC}}=\frac{3-7}{6-4}=-2[/tex]
Since these slopes are negative reciprocals, we can see that this is the case. So, we can take [tex]\overline{AC}[/tex] as the base of the triangle and [tex]\overline{BC}[/tex] as the height of the triangle, and then use the formula [tex]A=\frac{1}{2}bh[/tex].
Using the distance formula,
[tex]AC=\sqrt{(6-2)^{2}+(3-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(4-6)^{2}+(7-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]
So, the area is [tex]\frac{1}{2}(2\sqrt{5})(2\sqrt{5})=\boxed{10}[/tex]
Triangle MRN is created when an equilateral triangle is folded in half.
Triangle N R M is shown. Angle N R M is a right angle. An altitude is drawn from point R to point S on side M N to form a right angle. The length of N S is 6, the length of S M is 2, the length of R M is x, the length of N R is y, and the length of R S is z.
What is the value of y?
The value of y based on the values given ib the equilateral triangle will be 4.
How to illustrate the triangle?From the information given, MN is one of the sides of the equilateral triangle. Therefore, side MR will be:
= 1/2 × 8 = 4
In the above, it should be noted that MR was calculated since it's half of the value of MN which is 8.
Here, value of y based on the values given ib the equilateral triangle will be 4.
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Answer:
Step-by-step explanation:
4
Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.
Use the diagram to complete the statements.
Angles 1 and 5 are
because they are
angles.
Angles 4 and 6 are
because they are
angles.
Using the vertically opposite angles theorem and corresponding angles theorem, we have proven that alternate exterior angles are congruent
Angle theoremsFrom the question, we are to prove that alternate exterior angles are congruent.
In the given diagram, examples of alternate exterior angles are
∠1 and ∠8
∠2 and ∠7
Now, we will prove that ∠1 = ∠8
In the diagram, we can observe that
∠1 = ∠4 (Vertically opposite angles theorem)
and
∠4 = ∠8 (Corresponding angles theorem)
Then,
By the substitution property of equality
∠1 = ∠8
Hence, alternate exterior angles are congruent
Here is the complete and correct question:
Consider parallel lines cut by a transversal. Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.
Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
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Answer:
Step-by-step explanation:
Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.
Use the diagram to complete the statements.
Angles 1 and 5 are
✔ congruent
because they are
✔ corresponding
angles.
Angles 4 and 6 are
✔ supplementary
because they are
✔ same-side interior
angles.
Carol has some dimes and quarters. If she has 19 coins worth a total of $3.10, how many of each type of coin does she have?
Answer:
Step-by-step explanation:
Equations
Let the dimes be x
Let the quarters be y
x + y = 19 (1) Multiply this equation by 0.1
0.1x + 0.25y = 3.10 (2)
0.1x + 0.1 y = 1.90 (3) Subtract 3 from 2
0.15y = 1.20 Divide by 0.15
0.15y/0.15 = 1.20/0.15
y = 8
x + y = 19
x + 8 = 19 Subtract 8 from both sides
x+8-8 = 19-8 Combine
x = 11
Answer
Carol has 8 quarters
She has 11 dimes
15+ 2x = 5 + 3x
what's the answer
Answer:
x = 10
Step-by-step explanation:
rewrite this equation with x on the left and numbers on the right
2x - 3x = 5 - 15
-x = -10
x=10
give brainliest, please!
hope this helps :)
The value of x is x = 10
To solve a first degree equation, first: we add or subtract like terms. Finally, we split the terms of both equalities.
- In this equation, we're going to subtract the like terms -- and on the other side of the equation, we're going to also subtract the real terms.
Resolution15 + 2x = 5 + 3x
2x - 3x = 5 - 10
-1x = -10
x = 10
So, the correct value is x = 10
What is the value of x?
to
x = [? ]°
Answer: 30
Step-by-step explanation:
(Assuming the line is a tangent)
6/(x^2-3x)=12/x+1/(x-3)
[tex]\\ \rm\Rrightarrow \dfrac{6}{x^2-3x}=\dfrac{12}{x}+\dfrac{1}{x-3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6}{x(x-3)}=\dfrac{12}{x}+\dfrac{1}{x-3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6}{x(x-3)}=\dfrac{12(x-3)+x}{x(x-3)}[/tex]
[tex]\\ \rm\Rrightarrow 6=12x-36+x[/tex]
[tex]\\ \rm\Rrightarrow 6=13x-36[/tex]
[tex]\\ \rm\Rrightarrow 13x=42[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{42}{13}[/tex]
Solve the quadratic equation 2x^2 + 6 = 8x by graphing.
A)
x = –3, x = 1
B)
x = –3, x = –1
C)
x = –1, x = 3
D)
x = 1, x = 3
Answer:
D is the right ans after solving eqn we get two value of x and they are 1 and 3
Help pleasee math oo
Answer:
This equation has no solutions. So your answer is the last one!
Step-by-step explanation:
Answer:
The correct answer is D. none.
Which of the following algebraic expressions is not simplified?
A. 9x³y² +5x²y³ - 2x²y² + xy
3 2
2
B. -3a²b² +4ab² +6a²b-3ab
2.3
C. 2p²q² +2p²q²³ - 2p²q² + xy
D. 8m²n² +3m³n - 3n³m +9mn
Solve 5x+7 > 17.
{x1x<2}
O {XIX> 2}
O {xIx>-2}
O {x1x < -2}
Answer:
The answer is [tex]x > 2[/tex]
Step-by-step explanation:
to solve this inequality:
[tex]5x+7 > 17[/tex]
Put "-7" on both sides
[tex]5x+10[/tex]
divide by 5 on both sides
your answer should be 2.
Which property is demonstrated in the equation 2 + 5 + 7 = 2 + 7 + 5
A teacher randomly selects one student from a group of students. Fourteen students are wearing a black shirt, six students are wearing a red shirt, and nine students are wearing a blue shirt. What is the probability that the selected student is wearing a black shirt?
Answer:
14/29
Step-by-step explanation:
14/29 is the answer
In a year, a hospital admitted 4500 patients. If of the patients had heart or lung diseases,
how many patients had heart or lung diseases?
Answer:
4500
Step-by-step explanation:
all of them were admitted.
PLEASE HELP ME ASAP!!!
Answer:
5.5
Step-by-step explanation:
The longest string length is 12 3/4 (12.75)
The two shortest string lengths are 3 and 4 1/4 (4.25)
combine the length of the tow shortest string by adding them together,
3 + 4.25 = 7.25
to find how much longer the longest string you subtract the two numbers,
12.75 - 7.25 = 5.5
100
2
4
-5-4-3-2-4 1 2345
-3-
900
4
Which function represents g(x), a reflection of f(x) = 4
across the x-axis?
O g(x) = -4(2)*
g(x) = 4(2)-*
g(x) = -4
g(x) = 4*
Using translation concepts, the function that represents g(x) is given by:
[tex]g(x) = -4\left(\frac{1}{2}\right)^x[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Function f(x) is given by:
[tex]f(x) = 4\left(\frac{1}{2}\right)^x[/tex]
Function g(x) is a reflection of g(x) over the x-axis, that is, is is multiplied by -1, hence:
[tex]g(x) = -f(x) = -4\left(\frac{1}{2}\right)^x[/tex]
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Which term could be put in the blank to create a fully simplified polynomial written in standard form?
8x3y2−_____+3xy2−4y3
x2y2
x3y3
7xy2
7x0y3
The term that could be put in the blank is x^2y^2
How to complete the polynomial?The polynomial is given as:
8x^3y^2 - ___ + 3xy^2 - 4y^3
From the above expression, we can see that each term has a decreasing power of x from x to 0.
The missing power of x in the expression is 2
So, the term that completes the expression must have x^2
Hence, the term that could be put in the blank is x^2y^2
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Answer:
its a
Step-by-step explanation:
A total of 10,800 pharmacy technicians were hired last year in particular country. This is 3% of all pharmacy technicians employed in the country. How many pharmacy technicians are employed in the country?
well, the total amount of technicians employed is 100% and that is "x" amount, now, we also know that 3% of of that is 10800, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10800& 3 \end{array} \implies \cfrac{x}{10800}~~=~~\cfrac{100}{3} \\\\\\ 3x=1080000\implies x=\cfrac{1080000}{3}\implies x=360000[/tex]
solve the inequality 2(4x-3)>-3(3)+5x
Answer:
[tex]x > -1\\[/tex]
Step by step explanation:
[tex]~~~~~2(4x-3) > -3(3)+5x\\\\\implies 8x-6 > -9+5x\\\\\implies 8x > -9+6+5x\\\\\implies 8x > -3+5x\\\\\implies 8x -5x > -3\\\\\implies 3x > -3\\\\\implies x > -\dfrac 33\\\\\implies x > -1[/tex]
Мальчик наловил пауков и жуков - всего 8 штук. У них вместе оказалось 54 ноги. Сколько пауков и сколько жуков поймал мальчик? Вспомни, что у паука 8 лап, а у жука - 6. ОТДАЮ !% ОЧКОВ!!! ПЖ РЕШИТЕ
Photosynthesis is the process by which plants use sunlight, water, and carbon dioxide to create oxygen and energy in the form of sugar.
[tex]\pink{ \rule{1pt}{90000000pt}}\color{blue}{ \rule{1pt}{90000000pt}}\color{yellow}{ \rule{1pt}{90000000pt}}\purple{ \rule{1pt}{90000000pt}} \green{\rule{1pt}{90000000pt}}
[/tex]
First draw the line on the graph. Then reflect each vertex of quadrilateral across the line to produce quadrilateral .
A four quadrant graph with a line and a quadrilateral with vertex.
Vertex Preimage Coordinates Vertex Image Coordinates
A (-3,-2) A' (-2,-3)
B (-2,-1) B' (-1,-2)
C (-1,-2) C' (-2,-1)
D (-1,-4) D' (-4,-1)
The equation of the line about which the quadrilateral is reflected will be y = x.
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection is given will be
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
First, draw the line on the graph. Then reflect each vertex of quadrilateral across the line to produce quadrilateral.
Vertex Preimage Coordinates Vertex Image Coordinates
A (-3,-2) A' (-2,-3)
B (-2,-1) B' (-1,-2)
C (-1,-2) C' (-2,-1)
D (-1,-4) D' (-4,-1)
The diagram is given below.
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how do i solve log base 5 (x+9)=log base 5 (x+5)+1 solve for x and check both solutions to see if they are true or false
Step-by-step explanation:
[tex] log_{5}(x + 9) = log_{5}(x + 5) + 1[/tex]
[tex] \frac{ log(x + 9) }{ log(5) } = \frac{ log(x + 5) }{ log(5) } + 1[/tex]
[tex] log(x + 9) = log(x + 5) + log(5) [/tex]
[tex] log(x + 9) = log(5x + 25) [/tex]
[tex]x + 9 = 5x + 25[/tex]
[tex]x = - 4[/tex]
If we plug it in, it is true
If 3x−4y=2 is a true equation, what would be the value of -4(3x-4y)
Answer:
-8
Step-by-step explanation:
If 3x-4y=2, then for any number a we also have a(3x-4y)=a(2) by multiplication property of equality.
Therefore, for a=-4 we have -4(3x-4y)=-4(2) which means the value of -4(3x-4y) is -8.
The value of equation - 4 (3x - 4y) will be;
⇒ - 4 (3x - 4y) = - 8
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The true equation is,
⇒ 3x - 4y = 2
Now,
Since, The true equation is,
⇒ 3x - 4y = 2 .. (i)
Hence, The value of equation - 4 (3x - 4y) is,
⇒ - 4 (3x - 4y)
Substitute from (i), we get;
⇒ - 4 (3x - 4y) = - 4 × 2
= - 8
Thus, The value of equation - 4 (3x - 4y) = - 8
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Help me, please! For 20 pts
Answer:
First box ⇒ 3.6 x 10^-1
Second box ⇒ 3.1 x 10^6
Third box ⇒ 5.3 x 10^-6
Fourth box ⇒ 4.2 x 10^-1
Step-by-step explanation:
I used a calculator and solved it :)
Answer:
first square = 3.6 x [tex]10^{-1}[/tex]
Step-by-step explanation:
They are all multiplying so there is no need for parenthesis
(3.8 * 10³) * (9.4 * [tex]10^{-5}[/tex])
3.8 * 10³ * 9.4 * [tex]10^{-5}[/tex]
35.72 * [tex]10^{-2}[/tex]
35.72 =~ 36
Everytime you elevate a number, it's the same as...
3 * 10² = 100 * 3 = 300
0.3 * 10³ = 1000 * 0.3 = 300
so then...
36 * [tex]10^{-2}[/tex] = 3.6 * [tex]10^{-1}[/tex]
What is the value of x in the triangle?
Answer:
D
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
2x = 4[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
x = 2[tex]\sqrt{2}[/tex]
9 less than the sum of x and y
If we need to turn this into a mathematical expression:
Answer: (x + y) - 9
Step-by-step explanation:
9 less than the sum of x and y
(the sum of x and y) - 9
(x + y) - 9
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HELP ASAP!!!!! The graph compares temperatures and numbers of cyclists. The equation of the trend line for the scatterplot is y = 4x + 10. Predict the number of cyclists when the temperature is 12°C.
So
Put x ax 12°CHence
y=4(12)+10y=48+10y=58Option A
Answer:
Option A
Step-by-step explanation:
y=4x+10
So
Put x ax 12°C
Hence
y=4(12)+10
y=48+10
y=58
A set of 48 cards are numbered from 1 to 48 if the cards are shuffled and one is chosen at random what is the probability that the number on the card is a mutiple of both 6 and 8.
[tex]|\Omega|=48\\A=\{24,48\}\\|A|=2\\\\P(A)=\dfrac{2}{48}=\dfrac{1}{24}\approx4.2\%[/tex]
6. If b>6, then 3b + 3 could be
A. 18
B. 19
C. 20
D. 21
E. 22
Answer:
E. 22
Step-by-step explanation:
Hello!
We know that b>6, and we are asked to find the possible values for 3b + 3.
Let's directly substitute 6 for b:
3(6) + 318 = 321Now, because b is greater than 6, and not equal to 6, any value greater than 21 will work.
The correct option is E. 22.