The rectangle's area is growing at a rate of 170 cm per second.
Given that,
Area of Rectangle given by.
A = length x width
A = LW
L =length of Rectangle
W =width of Rectangle
Now, dA/dt = W dl/dt + l dw/dt
dA/dt is the rate of change of area of the rectangle
dl/dt is the rate of change of length of the rectangle
dw/dt is the rate of change of width of the rectangle
at L = 40cm, W= 15 cm
dw = 2 cm/s,
dl = 6 cm/s,
dA = ?
dA/dt = W dl/dt + l dw/dt
= 15x6 + 40x2
= 90 +80
=170 cm /sec
Thus, the area of the rectangle increasing at 170 cm /sec
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Marcus and jeremy both evaluated the expression −52 3. marcus said the answer was −22. jeremy said the answer was 28. who is correct? explain the error in the other student’s work.
Marcus is accurate. Jeremy is wrong because he overlooked the negative sign in the equation's initial addend. Since -25 has a greater absolute value than 3, it is obvious that the sum should be negative.
Marcus is correct; the solution is -22.
The simplified expression is given as:
= -(5²)+ 3
= -(25) + 3
= - 22
The right response is this. Marcus saw the bracket or parentheses symbol when he condensed his sentence. This has major significance.
Jeremy scored 28. He squared -5 without noting that it was in a bracket or parenthesis, therefore his response is incorrect.
Consequently, Jeremy calculated this.
= -(5²) + 3
= 25 + 3
= 28
Jeremy gave a false response. He made a computation but failed to see the bracket.
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Complete Question
Marcus and Jeremy both evaluated the expression −(5²) + 3. Marcus said the answer was −22. Jeremy said the answer was 28. Who is correct? Explain the error in the other student’s work.
Which of the following functions has a graph that is a
line
f(x) = Ixl
f(x) = x
f(x)=x²
With the help of equations we can say that function has a f(x) = x,straight line.
What is an equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions.For instance, an équation is defined as having one or more variables in French.Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables.The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfill the equality are known as the equation's solutions. Equations can be categorized as either identities or conditional equations.acc to our question-
f(x) = Ixl
f(x) = x
f(x)=x²
Hence, function f(x) = x is a line.
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Jerald i having drain iue at hi home and decide to call a plumber. The plumber charge $35 to come to hi houe and $60 for every hour they work. If the plumber charge Jerald a total of $305, how many hour did the plumber work?
Write and olve an equation to determine the number of hour worked by the plumber
The calculation for the plumber's total number of hours worked is 190 = 35 + 50x, where the result is 3.1 hours.
A linear equation is what?
It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
It follows that:
Jerald chooses to call a plumber after discovering a problem with his home's drains.
The plumber bills him $35 to visit his home and $50 per hour of work.
Suppose there are x hours in a day:
190 = 35 + 50x
50x = 155
x=3.1 hours
As a result, the answer to the question of how many hours the plumber worked is 190 = 35 + 50x, which is 3.1 hours.
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what two numbers add to "-5" and multiply to "-4"
The numbers that add to -5 and multiply to -4 are -5.7015 and 0.7015.
There are two numbers. The addition of the two numbers is -5. The multiplication of the two numbers is -4. We need to find the two numbers. Let the first number and the second number be represented by the variables x and y, respectively. Then, we can write the two following equations.
x + y = -5
x*y = -4
We will substitute the value of y from the first equation into the second equation.
x*(-5 - x) = -4
x*(x + 5) = 4
x² + 5x - 4 = 0
Now, we will use the quadratic formula.
x = [-5 ± √(5² - 4(1)(-4))]/2(1)
x = [-5 ± √(25 + 16)]/2
x = [-5 ± √41]/2
x = [-5 ± 6.403]/2
The values of x are -5.7015 and 0.7015. The corresponding values of y are 0.7015 and -5.705.
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help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Jade's Gem Shop is having its annual spring sale, when every item in the store gets marked down. During the sale, charm bracelets sell for $4 less than full price. Kristen purchases 5 identical charm bracelets: one for each of her friends. She pays a total of $45. Which equation can Kristen use to find how much money, c, each charm bracelet costs at full price?
Answer:
5(c−4)=45
5c - 20 = 45
5c = 45+20
5c = 65
c = 13
The full price of the bracelets was $13.
Step-by-step explanation:
Eva says
3
4
is equivalent to
15
20
. Check her work by completing the table of equivalent ratios.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
What is a Ratio?A ratio indicates the number of times one number contains another.
To find the equivalent ratio of 3/4 write the table of 3 in one column of the table and write the table of 4 in another column of the table.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
The above table indicates that 3/4 = 6/8 = 9/12 = 12/16 = 15/20.
Therefore, from the table, 3/4 is equivalent to 15/20.
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Answer 3,4,5,6 Thank you
B) The missing angle at the intersection point of both triangles is; x = 15°
C) The missing angle is gotten as; x = 61°
How to find the missing angles?B) In the second image given, we can see two angles;
Now, we know that sum of angles in a triangle is 180 degrees. Thus, for the interior angles, we have;
90 + 5x - 14 + y = 180
where y is the third interior angle
Now, we know that sum of angles on a straight line is equal to 180 degrees. Thus;
y = 180 - (9x + 16)
Put 180 - (9x + 16) for y into the first equation to get;
90 + 5x - 14 + 180 - (9x + 16) = 180
180 will cancel out to get;
90 + 5x - 14 - (9x + 16) = 0
4x = 90 - 14 - 16
4x = 60
x = 60/4
x = 15°
C) The missing angle of the triangle with side of 12y + 3 is an alternate angle to get;
Missing angle = 63°
Sum of angles in a triangle is 180 degrees. Thus;
56 + 63 + 3rd angle = 180
3rd angle = 180 - (56 + 63)
3rd angle = 61°
Thus, x = 61° because they are opposite angles
Also, the two given sides are equal to each other as shown. Thus;
51 = 12y + 3
12y = 51 - 3
12y = 48
y = 48/12
y = 4
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tan 30 x cos 30 in exact value
3x + 4y = 7
2x - y = 12
please help?
Answer:
x=5
y=-2
Step-by-step explanation:
even though this looks like they want you to do it elimination ima do substation cause I like that better
2x-y=12
+y. +y
2x=12+y
-12 -12
2x-12=y
Now we can fill in y
3x+4(2x-12)=7
3x+8x-48=7
11x-48=7
+48. +48
11x=55
/11. /11
x=5
fill in X to find y
2(5)-y=12
10-y=12
-10. -10
-y=2
y=-2
hopes this helps please mark brainliest
Graph the parabola
y=3x^2-x-2
A parabola is a bowl-shaped figure. Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
What is a parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface: a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. : something that is bowl-shaped.
Here the given quadratic equation is
[tex]y=3x^{2}-x-2[/tex]
The standard form of the quadratic equation is
[tex]y=ax^{2}+bx+c[/tex]
where [tex]a=3,b=-1,c=-2[/tex]
The axis of symmetry is the x-axis of the vertex
[tex]x=\frac{-b}{2a}\\x=\frac{1}{2(3)}\\x=\frac{1}{6}[/tex]
The y-value of the vertex is determined by substituting [tex]\frac{1}{6}[/tex] for [tex]x[/tex] into the equation and solving it for [tex]y[/tex].
[tex]y=3(\frac{1}{6})^{2}-\frac{1}{6}-2\\y=3(\frac{1}{36})-\frac{1}{6}-2\\y=\frac{3-6-72}{36}\\y=\frac{3-78}{36}\\y=\frac{-75}{36}[/tex]
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
Since [tex]a < 0[/tex] the vertex is the maximum point and the parabola opens downward.
X-intercept values of [tex]x[/tex] when [tex]y=0[/tex]
Substituting [tex]0[/tex] for [tex]y[/tex] and solving for [tex]x[/tex] using the quadratic formula
[tex]0=3x^{2}-x-2\\x=\frac{-b+-\sqrt{b^{2}}-{4ac}}{2a}\\x=\frac{1+-\sqrt{1}-{4(3)(-2)}}{2(3)}\\\\x=\frac{1+-\sqrt({1}+{24})}{6}\\\\\\x=\frac{1+-\sqrt(25)}{6}\\\\\\\\x=\frac{1+-5}{6}\\\\\\x=\frac{1+5}{6} , x=\frac{1-5}{6}\\\x=\frac{1+5}{6},x=\frac{1-5}{6}\\\\\x=1,x=\frac{-2}{3}[/tex]
Y-intercept values of [tex]y[/tex] when [tex]x=0[/tex]
Substituting [tex]0[/tex] for [tex]x[/tex] and solving for [tex]y[/tex] using the quadratic formula
[tex]y=3(0)^{6}-0-2\\y=-2[/tex]
Y-intercept [tex](0,1)[/tex]
Now substitute [tex]3[/tex] for [tex]x[/tex] and solve for [tex]y[/tex]
[tex]y=3(3)^{2}-3-2\\y=3(9)-5\\y=27-5\\y=22[/tex]
So the point is [tex](3,22)[/tex].
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
The parabola is of the form
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Which criterion can be used to prove ABC and ADC are congruent? select the correct answer
ΔABC and ΔADC are congruent by angle-side-angle (ASA) postulate of triangle congruence.
In this question we have been given a quadrilateral ABCD and diagonal AC.
We need to prove triangle ABC and ADC are congruent.
In ΔABC and ΔADC,
∠BAC ≅ ∠ACD ...........(Given)
AC ≅ AC ...........(Common side)
∠ACB ≅ ∠DAC ..........(Given)
ΔABC ≅ ΔADC ..........(ASA postulate of triangle congruence)
Therefore, ΔABC and ΔADC are congruent by angle-side-angle (ASA) postulate of triangle congruence.
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2. Communicate and Justify Why is the algebraic
expression x, equivalent to x ¹?
Expression x is equivalent to [tex]x^{1}[/tex] by using the exponent rule.
What do you mean by algebraic expression?
A mathematical expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are three primary categories of algebraic expressions, including:
Monomial expression
Binomial expression
Polynomial expression
An algebraic expression can be divided into two additional types in addition to the monomial, binomial, and polynomial types. These are:
Numeric Expression
Variable Expression
Numeric expression - A numeric expression consists of numbers and operations, but never include any variable.
Variable expression - A variable expression is an expression that contains variables along with numbers and operation to define an expression.
As we know, exponent form [tex]x^{n}[/tex] can be simplified as [tex]x \times x\times x\times ........n~ times[/tex]
In this way , [tex]x^{1}[/tex]can be written as x multiplied by 1 time which is equal to x
Therefore, expression x is equivalent to [tex]x^{1}[/tex].
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How many solutions does the
equation have?
3(d + 11) = 6(d + 33)
a. 0
b. 1
c. infinitely many
Answer: 1 solution
Step-by-step explanation:
3(d+11)=6(d+33)
simplifing the above equation
3d+33=6d+198
3d-6d=198-33
-3d=165
d= -165/3
d=-55
Answer:
b. 1
Step-by-step explanation:
3d + 33 = 6d + 198
3d - 6d = 198-33
-3d = 165
thus, d = -165/3
= -55
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two
different proportional relationships represented in different ways.
Will give points to first correct answer that follows all the steps right.
Answer:
I Need Help On That Too
Step-by-step explanation:
Are the ratios 3:12 and 1:4 proportional? Show your work.
Explain:
Answer:
Yes
Step-by-step explanation:
3:12 both have a common factor of 3 you divide both sides by 3 to get 1:4
how many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6? repeated digits are allowed.
There will be 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 when repeated digits are allowed by fundamental counting principle.
What is fundamental counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting simplifies the approach to selection by taking into account all of the possible choices and their combinations in order to calculate the Probability.
Here,
Since there are 6 digit given,
In first place, there are 6 ways to arrange the digits. In second place, there are 6 ways to arrange the digits. In third place, there are 6 ways to arrange the digits.
This way,
6×6×6=216 ways
When repeated digits are allowed by the fundamental counting principle, 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6.
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Tanisha and her children went into a restaurant that sells hamburgers for
$7.50 each and drinks for $1.75 each. Tanisha has $70 to spend and must buy
no less than 18 hamburgers and drinks altogether. If a represents the number
of hamburgers purchased and y represents the number of drinks purchased,
write and solve a system of inequalities graphically and determine one
possible solution.
a marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce. how many kilometers did he run? (note: 1 mi
He ran 42.1 kilometers.
Define conversion.A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet. The act or process of transforming something into a different condition or form is known as conversion. to convert a value or expression between two different forms. • Measurement: converting between different units, for as from inches to millimeters or liters to gallons. For instance, change 12 inches to millimeters. 304.8 millimeters are equal to 12 inches multiplied by the inch-to-millimeter ratio of 25.4.
Given,
A marathon is a 26.2-mile race that commemorates the run made by a greek soldier, pheidippides, that took place in 490 bce.
1 mile = 1.609
Converting miles into kilometer:
26.2 miles
= 26.2 × 1.609
= 42.1
He ran 42.1 kilometers.
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J.5 unit rates
96 kilometers in 3 hours = ?
The unit rate for 96 kilometers in 3 hours is 32 kilometer per hour.
What is unit rate?
A unit is one of a particular object. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given in the question,
96 kilometer in 3 hours,
In order to find unit rate we have to change given values in kilometers per hour.
Do, 96 kilometer = 3 hours
96/3 kilometer = 1 hour
Therefore, unit rate is 32 kilometer per hour.
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"Solve the Equation."
if the equation only has one solution, enter "NS" (No Solution) .
if the equation has Infinite Many solutions, enter "IM"
1. 6(x+5)=6x+5
2. -4x=7x-33
The equation 6(x + 5) = 6x + 5 has NS (No Solution) and the equation -4x = 7x - 33 has IM (Infinite Many solutions).
Let us take the given equation
6(x + 5) = 6x + 5
⇒ 6x + 30 = 6x + 5
⇒ 6x - 6x = 5 - 30
⇒ 0 = -25
Hence, the given equation has No Solution (NS)
Let us take the given equation
-4x = 7x - 33
-4x - 7x = -33
-11x = -33
x = 3
Hence, the given equations has Infinite Many solutions (IM)
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The mean, median and mode of the numbers below are the same,
what is the value of a?
6, 2, a, 7, 4, 9,6
Answer:
8
Step-by-step explanation:
Put the numbers in order from lowest to highest. Add all the numbers together. We will ignore a for this step. You should get 34 when adding it all together. Then if you were to add 8 to that 34 you'd get 42. Divide 42 by the amount of numbers you have which is 7. Your answer is 6. Now to make sure 8 is our value. We want to make sure the median is also 6. to find the median you need to have the numbers in order for lowest to highest and find the number in the middle. Don't forget to add your new number 8 into that order. You should get 6 as the median. Therefore our answer is 8
y = -6x - 2
12x + 2y = −6
which contours are usually drawn darker than the other contours? group of answer choices index contours largest (max) value contour contour interval smallest (min) value contour
Index contours are usually drawn darker than the other contours.
Index Contours are darker and wider than the other regular contour lines for ease of identification. They are labeled with elevation and also have their altitude value mentioned on the dark lines and these values represent the altitudes of the particular contours. Index contours appears after every fifth contours. If the number with contours will increase then its elevation will also increase and similarly if the number associated with contours starts to decrease then its elevation also decreases.
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(14x - 2) - (11x-21)
Answer:
3x+19
Step-by-step explanation:
Distribute:
14 x − 2 − ( 11 x − 21 ) 1 4 − 2 − ( 1 1 − 2 1 )
14 x − 2 − 11 x + 21 1 4 − 2 − 1 1 + 2 1
Add the numbers:
14x−2−11x+21
14−2−11+2
Combine like terms:
14x+19−11x
14 +19−113x+193+19
Solution: 3x+19
Answer:
3x + 19
Example:
None.
Gerardo and his two friends order a pizza and decide to split the cost evenly. Each person ordered a drink for $1.50. How much was the pizza if each person paid $8?
19.50 cost of pizza
Step-by-step explanation:
$8.00-$1.50 = $6.50 × 3 =19.50
Me ayudan porfavor 2 trinomios cuya diferencia sea 4x²-7x+5
Answer:
Δ = b² - 4ac
Step-by-step explanation:
do math
a store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
A retailer raised a shirt's original price by a certain percentage before lowering it by the same percentage. The price was increased and decreased by 40% as the final cost was 84% of the initial cost.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Here,
Let's say the shirt originally cost Rs 100, and we're adding t% to the price.
The new price of the shirt is therefore 100 + (t/100 * 100) = Rs. 100+t after the initial t% increase.
The price is then reduced by t%.
Cost of a new shirt: (100 + t) - (t/100)
[100+t] = (100+t)
[1-(t/100] = [(100+t)/100]
therefore, the final price is equal to 84% of Rs 100, or Rs 84.
10000 - t^2 = 84.
t^2 = 1600
t = 40
The price was thus raised and lowered by 40%.
The original price of a shirt was increased by a specific percentage before being decreased by the same percentage by the retailer. As the final price was 84% of the initial price, the price was both increased and decreased by 40%.
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an urn contains 8 white balls and 12 red balls. a sample of four balls is selected at random from the urn. what is the probability that the sample contains two white balls and two red ones? a) 0.3814 b) 0.3933 c) 0.0424 d) 0.1028 e) 0.1474 f) none of the above.
0.3814 is the probability that the sample contains two white balls and two red ones .
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Total number of balls = 8 + 12 = 20
Total number of elementary cases
= ( 20 4 )
Total number of favourable cases
= ( 8 2 ) * ( 12 2 )
Required probability
= ( 8 2 ) * ( 12 2 )/( 20 4 )
= 0.3814
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how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?
There are 100 4-digit positive integers are possible between 1000 and 9999.
Our first step is to divide the four digit number into four places: tens, hundreds, and thousands.
To solve this problem, we must start from the right-hand side and find how many even numbers should be placed where the desired answer can be obtained.
There are a total of [0, 2, 4, 6, and 8] objects
There should only be one digit on one place, since it is the only digit that makes the number divisible by five
There are 1 ways to fill the one's place, so the total number is 1.
It is possible to take any number from the given sets of even numbers in the tens place,
There are five ways to fill one place, so there are five ways to fill it.
Taking a look at the hundreds place,
All numbers can be placed in the hundreds place from the given sets, so all numbers can be taken from the hundreds place.
Therefore, there are five ways to fill the hundreds place.
Taking a look at the thousands,
It is possible to fill thousands of places with 4 numbers from a given set of even numbers.
Therefore, there are four ways to fill the thousands place
The next step is to use the concept of factorial to find the number of ways to make a 4-digit number from even numbers that are divisible by 5.
To fill the respective places, we will multiply all the ways we calculated
= 4 × 5 × 5 × 1
= 100
Hence, there 100 4-digit positive integers possible.
Question
how many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?
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