We have the next given information:
- inlet pipe fill rate = 1/20 = 1job/hour
-The drain pipe empty rate = 1/45 job/hour
- The pool is 1/3 filled, then we need to fill 2/3.
If both are open, we have the next combined rate:
Combined rate =1/20 - 1/45 = 25/(20*45) = 25/900=1/36 = 1job/hour
Now,we need yo use the next equation:
rate * time = work done
Set x for time.
Replacing:
1/36 * x = 2/3
Multiply both sides by 36:
[tex]\begin{gathered} \frac{1}{36}*x=\frac{2}{3} \\ 36\left(\frac{1}{36}\right?x=36\ast\frac{2}{3} \\ x=24 \end{gathered}[/tex]Hence, it will take 24 hours to fill the pool
Hello! I just want to confirm my answer is correct and if there’s anything I should add? Thanks for your help!
Given:
given functions are
[tex]f(x)=x^4-4x^3-2x^2-12x+9,g(x)=\sqrt{x^2-2x-3},h(x)=\frac{-x^2+1}{x^2-2x-3}[/tex]Find:
(A) we have to compare the Domain and range of the function f(x) and g(x).
(B) We have to find the relationship between the break of h(x) and zeros of f(x).
Explanation:
The domain and Range of f(x) is
[tex]\begin{gathered} Domain(f)=(-\infty,\infty) \\ Range(f)=[0,\infty) \end{gathered}[/tex]Domain and Range of g(x) is
[tex]\begin{gathered} Domain(g)=(-\infty,-1]\cup[3,\infty) \\ Range(g)=[0,\infty) \end{gathered}[/tex]Domain of h(x) is
[tex]Domain(h)=(-\infty.-1)\cup(-1,3)\cup(3,\infty)[/tex]Now zeros of the function f(x) are
[tex]\begin{gathered} x^4-4x^3-2x^2+12x+9=0 \\ (x+1)^2(x-3)^2=0 \\ x=-1,-1,3,3 \end{gathered}[/tex]Therefore, zeors of the function f(x) are -1,-1,3,3.
Now,
(A)The difference between Domain of f(x) and g(x) is of the interval (-1,3). The domain of f(x) is all Real Numbers and Domain of g(x) is all the real number except the interval (-1,3).
The Range of both f(x) and g(x) is same.
(B) The breaks in the Domain of h(x) are equal to the zeros -1, 3 of f(x).
Need Help on this problem
Answer:
Marginal Average Cost Function C'(x) = 5.7
Step-by-step explanation:
The Marginal Average Cost is just the first differential of the Cost Function
[tex]\dfrac{d}{dx} C(x) = \dfrac{d}{dx}(161) + \dfrac{d}{dx}(5.7x)\\\\\\The first differential of a constant is 0 and the first differential of ax is a \\\\So ,\\\\\dfrac{d}{dx} C(x) = 0 + 5.7 = 5.7[/tex]
This means that as x increases by 1 unit, cost increases by 5.7 units. x presumably refers to the number of units produced
The Marginal Revenue can be found the same way
[tex]\dfrac{d}{dx} R(x) = \dfrac{d}{dx}6x - \dfrac{d}{dx}(0.08x^2)\\\\\dfrac{d}{dx}6x = 6\\\\\dfrac{d}{dx}(0.08x^2) = (2)(0.08)x[/tex]
[tex]= 0.16x[/tex] since [tex]\dfrac{d}{dx} (x^2) = 2x[/tex]
Order twenty-six eighths, the cube root of 32, negative pi, and negative four and two thirds from greatest to least.
The ordering of the numbers from greatest go least will be twenty-six eighths, the cube root of 32, negative pi, and negative four and two thirds
How to order true numbers?Based on the information, we want to order twenty-six eighths, the cube root of 32, negative pi, and negative four and two thirds.
It should be noted that 26/8 = 3.25
Cube root of 32 = 3.19
Negative pi = -3.14
Negative four and two thirds = -4.67
The arrangement is given above.
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Find the following quotient:
10r³ - 2x² + 8x
2x
The quotient of the expression (10x³ - 2x² + 8x)/2x is (5x² - x + 4).
What is meant by the term factorization?A polynomial can be published as the product of the its factors with degrees below or equal to the degree of the original polynomial. Factorization of polynomials refers to the process of factoring.The basic technique for factoring polynomials is to find the greatest common factor, which simplifies the problem.The second factoring technique is known as grouping. If there is no factor common to all of the terms of the a polynomial, but there are factors common to a few of the terms, this method is used.The given expression is;
= (10x³ - 2x² + 8x)/2x
Take 2x common on the numerator.
= 2x(5x² - x + 4)/2x
Cancel 2x from the numerator and denominator part.
= 5x² - x + 4
Thus, the quotient of the expression is found as 5x² - x + 4.
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Determine which set of side measurements could be used to form a right triangle.
9, 11, 13
6, 12, 17
square root of 8, 5, square root of 17
square root of 2, square root of 7, 9
There is no set of sides used to form a right triangle.
Right triangle:
The one angle is always 90° or the right angle. The side opposite angle of 90° is the hypotenuse. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°.
Let a = height of a triangle
b = base of a triangle
c = hypotenuse of a triangle
So we have formula for right triangle:
c² = a² + b²
So from this, we have
a)a = 9, b = 11, c= 13
13² = 9² + 11²
169 = 81 + 121
169 ≠ 202
Therefore the side given is not a right triangle.
b) 6, 12, 17
17² = 6² + 12²
289 = 36 + 144
289 ≠ 180
So the side given is not of a right angle triangle.
c) 8, 5, 17
17² = 8² + 5²
289 = 64 + 25
289≠ 89
So the given side is not of a right angle triangle.
d) 2, 7, 9
9² = 2² + 7²
81 = 4 + 49
81 ≠ 53
So the given triangle is not a right angle triangle.
Therefore all the given option is not of a right angle triangle.
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If T(x, y) = (x + 5, y + 6) and Pris the image of P, what is the rule for the translation in which P is the image of P'? T(x, y) = (x – [?], y -[]) Enter the number that belongs in the green box. Enter
Answer:
The translation is;
[tex]T(x,y)=(x-5,y-6)[/tex]Explanation:
Given the translation rule;
[tex]T(x,y)=(x+5,y+6)[/tex]when P' is the image of P.
For the inverse, when P is the image of P', the Translation rule would become;
[tex]\begin{gathered} x=x^{\prime}+5 \\ x^{\prime}=x-5 \\ y=y^{\prime}+6 \\ y^{\prime}=y-6 \\ So,\text{ the translation rule becomes;} \\ T(x,y)=(x-5,y-6) \end{gathered}[/tex]The translation is;
[tex]T(x,y)=(x-5,y-6)[/tex]Evaluate each expression if r=1, s=3, 1=3, and u=10. tu-3r
Explanation:
The expression: tu - 3r
where r=1, s=3, t=3, and u=10
[tex]\begin{gathered} =\text{ 3(10) - 3(1)} \\ =\text{ 30 - 3 } \\ =\text{ 27} \\ tu\text{ -3r = 27} \end{gathered}[/tex]Suppose you’re given the following table of values for the function f(x), and you’re told that the function is off:
Odd function f(x):
f(-x) = -f(x)
Let's see what is happening for x = 0:
f(-0) = -f(0)
But -0 = 0 so: f(0) = -f(0) => 2f(0) = 0 => f(0) = 0
But, from the table: f(0) = 2
So the function can't be an odd function, D is the correct answer
This table shows a function.
(-16, -41)
(-15, -20)
(-7, -2)
(-5, 5)
(2, 1)
(13, 10)
What is the average rate of change over the interval 2 ≤ x ≤ 137
A. -11/9
B. -9/11
C. 9/11
D. 11/9
Answer: Choice C) 9/11
========================================================
Explanation:
Finding the average rate of change over the interval 2 ≤ x ≤ 13 is the exact same as finding the slope of the line through the points (2,1) and (13,10)
[tex](x_1,y_1) = (2,1) \text{ and } (x_2,y_2) = (13,10)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{10 - 1}{13 - 2}\\\\m = \frac{9}{11}\\\\[/tex]
The slope of the line through (2,1) and (13,10) is 9/11 which is also the rate of change we're looking for.
The sum of the even numbers between 77 and 535 is how much less than the sum of the odd numbers between78 and 536?
The sum of the even numbers between 77 and 535 is:
[tex]78+80+82+\ldots+530+532+534=70074[/tex]Now, the sum of the odd numbers between 78 and 536 is:
[tex]77+79+81+\cdots+531+533+535=70380[/tex]Thus, the sum of the even numbers between 77 and 535 is 306 less than the sum of the odd numbers between 78 and 536 because
[tex]70380-70074=306[/tex]Which equation shows the relationship between X, the number of minutes and y, the price
The equation that shows the price to rent a scooter for any number of minutes will be D. y=0.15x
How to compute the equation?It is illustrated that the price of the scooter rental is $0.15 per minute. Therefore, 1 minute = $0.15
Jana rented a scooter for $60 minutes. This will be:
= 0.15 × 60
= $9
To frame an equation that shows the price to rent a scooter for any number of minutes :
Let us take,
The variable 'y' = the total price.
The variable 'x' = number of minutes for rental.
Total price = price of rent per minute × any number of minutes
y = 0.15 × x
y = 0.15x
Therefore, the appropriate equation is y = 0.15x.
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City scooters charges customers by the minute to rent an electric scooter. Jana rented a scooter for $60 minutes and paid $9. Write an equation that shows the price to rent a scooter for any number of minutes
The price of the scooter rental is $0.15
A: x=9y
B: y=9x
C: x=0.15y
D: y=0.15x
Answer: y=0.15x
Step-by-step explanation:
I ready
Help with finding proofs
Answer:
Statement: ∠XYZ = ∠ABC Reasons: Below
Step-by-step explanation:
For two angles to be complementary means that the sum of the two angles is equivalent to 90°. When an angle has one of those little squares, that means the angle is a right angle, or a 90° angle. Also, since it's given that line segment AB and line segment BC are perpendicular, this means the two lines/line segments cross each other at a right angle, which also proves that line segment AB and BC have a 90° angle.
Distance travelled = rate (or speed) * time.If Julio drives 248 miles at a constant speed of 62 mph. How long will it take? (Be sure to includeunits.)
Using the given formula:
[tex]D=s\cdot t,[/tex]substituting D=248 miles and s=62 mph, we get:
[tex]248\text{miles}=62\text{mph}\cdot t\text{.}[/tex]Dividing by 62 mph we get:
[tex]\frac{248\text{miles}}{62\text{mph}}=4\text{hours.}[/tex]Therefore, it will take 4 hours.
Answer: 4 hours.
Graph for y = -x– 6.
Given the linear equation;
[tex]y=-x-6[/tex]To plot the graph of this equation we need to get the corresponding values of x and y at various points;
At x = 0;
[tex]\begin{gathered} y=-0-6 \\ y=-6 \\ (x,y)=(0,-6) \end{gathered}[/tex]At x = -6;
[tex]\begin{gathered} y=-(-6)-6 \\ y=+6-6 \\ y=0 \\ (x,y)=(-6,0) \end{gathered}[/tex]We can then locate this two points on the graph then join with a straight line since it is a linear graph.
Below is the graph of the linear equation given;
F(x-3)=x^2-1. F(0)=?
The answer is f(x−3)=x2
Which of the following could be the ratio between the lengths of the two legsof a 30-60-90 triangle?Check all that apply.A. 2:13OB. 5:15C. 2:15OD. 1 : 15E. 1 : 2UO F. 5:3
Let a, b, c be the length of sides of the triangle lying opposite to angles measuring 30, 60 and 90 degrees, respectively.
Applying the sine law,
[tex]\frac{a}{\sin30}=\frac{b}{\sin60}=\frac{c}{\sin 90}[/tex]I am not understanding this question can you help me solve this? Please I desperately need your help
Given:
[tex]\[g\left(x\right)=\left\{\begin{matrix}\sqrt[3]{x+5} \\ -{{x}^2}+11\end{matrix}\text{ }\begin{matrix}x\le-4 \\ x>-4\end{matrix}\right.\][/tex]To find:
The value of:
[tex]g(-4)[/tex]Explanation:
For x = -4, we can consider the below function,
[tex]g(x)=\sqrt[3]{x+5}[/tex]Substituting the value x = -4,
[tex]\begin{gathered} g(-4)=\sqrt[3]{-4+5} \\ =\sqrt[3]{1} \\ =1 \end{gathered}[/tex]Final answer:
Hence, the required solution is:
[tex](A)\text{ 1}[/tex]27. The figure is formed from rectangles. Find the total area. The diagram is not to scale.3 ft5 ft3 ft8 ftA. 26 ft?B. 40 ftC. 73 ft?D. 34 ft?
To find the total area, we can divide the total figure into two figures as follows:
Then, we have that the total area is the sum of both areas of the figures:
[tex]A_{\text{total}}=5ft\cdot5ft+3ft\cdot3ft=25ft^2+9ft^2=34ft^2[/tex]Therefore, the total area is equal to 34 sq. feet (option D).
6x50 hundreds= 300 hundreds
The given expression 6 x 50 hundreds = 300 hundreds is true.
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 expression is,
⇒ 6 x 50 hundreds = 300 hundreds
Now,
Solve the expression for checking the expression is true or not as;
The expression is,
⇒ 6 x 50 hundreds = 300 hundreds
Since, The value of 6 x 50 hundreds is find by multiplying the number,
⇒ 6 x 50 hundreds = 300 hundreds
Thus, The given expression 6 x 50 hundreds = 300 hundreds is true.
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please help me out quickly
An identity matrix is a square matrix with 0s everywhere else and 1s on the major diagonal.
1. The given statement exists true.
2. The given statement exists false.
What is an inverse matrix transform?A rigid body transformation is the inverse matrix. It not only conforms to the original matrix's shape, but if you translate and rotate an object, you may return it to its original location by undoing the translations and rotations.
In general, AB = BA, even if A and B exist as both squares. If AB = BA, then we express that A and B commute. For a general matrix A, we cannot express that AB = AC yields B = C. (However, if we comprehend that A exists invertible, then we can multiply both sides of the equation AB = AC to the left by A-1 and get B = C.)
2. The given statement exists false.
An identity matrix is a square matrix with 0s everywhere else and 1s on the major diagonal.
Identity matrices of orders 1, 2, and 3 are those in which all the members of a square matrix are zero and none of the diagonal elements are zero. Keep in mind that when k = 1, a scalar matrix is an identity matrix. But it is obvious that any identity matrix is a scalar matrix.
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The first statement is true but the second given statement is false .
Inverse of a matrix: What does that mean?The idea of the inverse of a matrix is a multidimensional generalization of the idea of the reciprocal of a number. Just as the product of a number and its inverse is equal to 1, that of a square matrix and its inverse is equal to the identity matrix.
Even though A and B are squares, AB Equals BA in general. We can say that A and B commute if AB = BA. We cannot state that AB = AC produces B = C for a general matrix A. (However, if we are aware that A is invertible, we can multiply both sides of the expression AB = AC to the left by A-1 to obtain B = C.)
2. The aforementioned claim is untrue.
A square matrix with 1s on the principal diagonal and 0s everywhere else is known as an identity matrix.
When all of a square matrix's members are zero and none of the diagonal elements are zero, the matrix is said to be an identity matrix of order 1, 2, or 3. Do not forget that k = 1 .
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write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a^4 and 16a^4an expression is____a^4
Given the lengths of the right triangle:
[tex]\begin{gathered} 12a^4^{} \\ \text{and } \\ 16a^4 \end{gathered}[/tex]To find the perimeter, use the formula:
[tex]P=a+b+\sqrt[]{a^2+b^2}[/tex]Thus, we have:
[tex]P=12a^4+16a^4+\sqrt[]{(12a^4)^2+(16a^4)^2}[/tex][tex]\begin{gathered} P=28a^4+\sqrt[]{144a^4+256a^4} \\ P=28a^4+\sqrt[]{400a^4} \\ P=28a^4+20a^4 \\ P=48a^4 \end{gathered}[/tex]Therefore, the expression is:
[tex]48a^4[/tex]Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by two feet. She also wants the garden’s width to exceed the width of the tomato patch by five feet.Part AMelissa wants to know how the width and length of the garden relate to the length of the square tomato patch. If each side of the tomato patch is x feet, write the functions WG(x) and LG(x) to represent the garden’s width and length, respectively.Part BWrite the function AG(x) representing the area of the garden in terms of x.Part CIf the sides of the square tomato patch are seven feet, find the area of the garden.Part DMelissa decides to reserve a patch in her vegetable garden for growing bell peppers. She wants its width to be half the width of the tomato patch, and its length must exceed the length of the tomato patch by two feet. Write the functions WB(x) and LB(x) representing the width and length, respectively, of the bell pepper patch.Part EWrite the function AB(x) representing the area of the bell pepper patch in terms of x.Part FWrite the function ATB(x) representing the combined area of the tomato patch and the bell pepper patch.Part GYou’ve written functions to represent the area of the tomato patch and the area of the bell pepper patch. Now write the function AR(x) for the remaining planting area in the garden.Part HIf Melissa wants the area of the bell pepper patch to be 31.5 square feet, find the area of the remaining space in the garden after planting tomatoes and bell peppers.
Part A
The functions would be:
[tex]\begin{gathered} WG(x)=x+5 \\ LG(x)=3x+2 \end{gathered}[/tex]Part B
[tex]\begin{gathered} AG(x)=WG(x)\cdot LG(x) \\ \rightarrow AG(x)=(x+5)(3x+2) \\ \rightarrow AG(x)=3x^2+2x+15x+10 \\ \\ \Rightarrow AG(x)=3x^2+17x+10 \end{gathered}[/tex]Part C
Let's evaluate x = 7 in AG(x)
[tex]\begin{gathered} AG(7)=3(7^2)+17(7)+10 \\ \rightarrow AG(7)=276 \end{gathered}[/tex]Thereby, the area of the garden would be 276 square feet
Part D
The functions would be:
[tex]\begin{gathered} WB(x)=\frac{x}{2} \\ LB(x)=x+2 \end{gathered}[/tex]Part E
[tex]\begin{gathered} AB(x)=WB(x)\cdot LB(x) \\ \rightarrow AB(x)=(\frac{x}{2})(x+2) \\ \\ \Rightarrow AB(x)=\frac{x^2}{2}+x \end{gathered}[/tex]Part F
[tex]\begin{gathered} ATB(x)=x^2+AB(x) \\ \rightarrow ATB(x)=x^2+\frac{x^2}{2}+x \\ \\ \Rightarrow ATB(x)=\frac{3}{2}x^2+x \end{gathered}[/tex]Part G
[tex]\begin{gathered} AR(x)=AG(x)-ATB(x) \\ \rightarrow AR(x)=3x^2+17x+10-\frac{3}{2}x^2-x \\ \\ \Rightarrow AR(x)=\frac{3}{2}x^2+16x+10 \end{gathered}[/tex]Part H
We have a function for the area of the bell pepper patch in terms of x, the measurement of the lenght and width of the tomato patch. This is:
[tex]AB(x)=\frac{x^2}{2}+x[/tex]We know the value of this area. This way, we can solve the equation for x,
[tex]31.5=\frac{x^2}{2}+x\rightarrow63=x^2+2x\rightarrow x^2+2x-63=0[/tex]Using the cuadratic formula, and ignoring non-positive results, we'll get that
[tex]x=7[/tex]Now, plugging in this value in AR(x),
[tex]\begin{gathered} AR(7)=\frac{3}{2}(7^2)+16(7)+10 \\ \Rightarrow AR=195.5 \end{gathered}[/tex]This way, we can conclude that the remaining space in the garden after planting tomatoes and bell peppers is 195.5 square feet
I don't really know what to do! could you help me!
1/36
1) Since the total number of outcomes are 36 combinations:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
2) And the question wants us to find the probability of rolling two 2s, so let's bold this combination below:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So, we can see that there is only 1 favorable outcome. Then we can write out the following quotient:
[tex]P(\text{roll) =}\frac{\text{favorable outcome}}{\text{total outcomes}}=\frac{1}{36}[/tex]3) Hence, the answer is 1/36
5. A patient must receive an injection of 2.4 grams of medication. If 1 milliliter ofliquid contains 120 milligrams of medication, how many milliliters should be injectedinto the patient?
Given:
The required medication is r = 2.4 grams.
The objective is to find the quantity in terms of milliliters to be injected into the patient.
Explanation:
Since it is given that 1 milliliter of liquid contains 120 milligrams.
Then, the required quantity can be converted into milligrams as,
[tex]\begin{gathered} 1\text{gram}=1000\text{milligrams} \\ 2.4\text{grams}=2.4\times1000\text{milligrams} \\ 2.4\text{grams}=2400\text{milligrams} \end{gathered}[/tex]Consider the unknown milliliters as x. Now, 2400 milligrams can be converted into milliliters as,
[tex]\begin{gathered} 1\text{milliliter}=120\text{milligrams . . . .(1)} \\ x\text{ milliliter=2400milligrams . . . . . . (2)} \end{gathered}[/tex]To find x:
On dividing equation (2) by equation (1),
[tex]\begin{gathered} x=\frac{2400}{120} \\ x=20\text{milliliters} \end{gathered}[/tex]Hence, the milliliters to be injected into the patient is 20 milliliters.
formulas need help will send picutre
In the formula
[tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_2}[/tex]putting in the given values of R_1, R_2, and R_3 gives
[tex]\frac{1}{R}=\frac{1}{10.0}+\frac{1}{14.0}+\frac{1}{35.0}[/tex]We add the fractions on the right-hand- side to get:
[tex]\frac{1}{R}=\frac{1\cdot7}{10.0\cdot7}+\frac{1\cdot5}{14.0\cdot5}+\frac{1\cdot2}{35.0\cdot2}[/tex][tex]\frac{1}{R}=\frac{7}{70}+\frac{5}{70}+\frac{2}{70}[/tex][tex]\frac{1}{R}=\frac{14}{70}=\frac{1}{5}[/tex]Taking the reciprocal both sides gives
[tex]R=5.0[/tex]Which is our answer!
Alison had lost some puzzle pieces. She found 3/10 of them under the coffee table and another 4/10 of them under the couch. How much is she still missing?
The fractional part that Alison is still missing is 3/10.
What is a fraction?A fraction is a part of an absolute value or number.
Fractions are always less than one.
Fractions are denoted by a numerator (upper part or dividend) less than the denominator (the lower portion known as the divisor).
There are proper and improper fractions.
The fraction found under the coffee table = 3/10
The fraction found under the couch = 4/10
The total fractional part found so far = 7/10 (3/10 + 4/10)
The fractional part that Alison misses = 3/10 (1 - 7/10)
Thus, Alison still misses 3/10, which is fractionally 30% of the puzzle pieces.
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Pls help this is geometry and its a really important test
Answer:#4:B m of angle 2=35° m of angle 3=55°
Step-by-step explanation:if line C is 180° degrees because a flat line in 180° then you see that adding the angle measure of 4 which is 35° +the right angle which is 90 degree=125° So the 180°-125°=55°=m of angle 3 and to find angle measure of 2 angle 1 is a right angle and the inside of a triangle opens to 180 degrees so you grab measure of angle 1=90° and measure of angle 3=55° add them 90°+55°=145° so 180°-145°=35°
Help I will gib brain
Answer:
x-axis: (18, 0)
y-axis: (0, 12)
quadrant I: (4.5, 10.6)
quadrant II: (-15, 21)
quadrant III: [tex](-\frac{3}{4}, -\frac{4}{9})[/tex]
quadrant IV: (3, -7)
Step-by-step explanation: (view attached screenshot)
(18, 0) is 18 units left, 0 units up. This make the point line up exactly on the x-axis
(0, 12) is 0 units left, and 12 units up. This will cause it to be in the line of y-axis.
(4.5, 10.6) both x and y values in the point are positive, this means that it's in the first quadrant
(-15, 21) x value is negative, y value is positive. This means that the point is in the second quadrant
[tex](-\frac{3}{4}, -\frac{4}{9})[/tex] both x and y values are negative. This means that the point is in the third quadrant.
(3, -7) x value is positive, y value is negative. This means that it's in the fourth quadrant.
Two candles start burning at the same time. one candle is 15 cm tall and burn and burns at a rate of 5 cm every 6 hours. The other candle is 25 cm tall at a rate of 2 1/2 cm every hour
How tall will the candles be when they first burn down to the same height?
The height of the candles when they would be the same height is 10cm.
What is the height when the two candles would be the same?The first step is to determine how much of each candle is left after one hour.
Candle left after c hours = height of the candle - rate at which the candle burns per hour x c
Rate at which the candle burns per hour = 5/6
15 - 5/6c
Candle left after c hours = 25 - 2 1/2c
When the two candles are of the same height, the two above equations would be equal
15 - 5/6c = 25 - 2 1/2c
Combine similar terms: 25 - 15 = 2 1/2 - 5/6c
Add similar terms: 10 = 1 2/3 c
Divide both sides by 3/5: 10 = 5/3c
c = 10 x 3 / 5
c = 6 hours
Height in 3 hours = 15 - 5/6(6) = 15 - 5 = 10cm
To learn more about fractions, please check: https://brainly.com/question/1114498
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A laptop computer is purchased for $3200. Each year, its value is 80% of its value the year before. After how many years will the laptop computer be worth $700 or less? (Use the calculator provided if necessary.)Write the smallest possible whole number answer.
we know that
Each year, its value is 80% of its value the year before
that is the same as
Each year the value decreases by 20%
we have an exponential decay function of the form
[tex]y=a(1-r)^x[/tex]where
y is the value of the computer laptop
x is the number of years
r is the rate
a is the initial value
so
we have
a=$3,200
r=20%=20/100=0.20
substitute
[tex]\begin{gathered} y=3,200(1-0.20)^x \\ y=3,200(0.80)^x \end{gathered}[/tex]For y=$700
substitute in the equation above
[tex]\begin{gathered} 700=3,200(0.80)^x \\ solve\text{ for x} \\ \frac{700}{3,200}=(0.80)^x \end{gathered}[/tex]Apply log on both sides
[tex]\begin{gathered} log(\frac{700}{3,200})=x*log(0.80) \\ x=6.81\text{ years} \end{gathered}[/tex]therefore
The answer is 7 years