Answer:
(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180
Step-by-step explanation:
A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:
p = 2w + 2l
We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.
We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.
Plugging these values into our equation we get:
p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.
Or in the form of a quadratic equation:
p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162
=
p = 4k^2 - 24k + 180
Hope this helps!
The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.
Explanation:The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).
Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.
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Which of the following is the slope of the line y - 3x =0
Answer:
-3
Step-by-step explanation:
Answer: The slope whould be 3
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: 3
y-intercept:
(0,0)
x|y
----
0|0
1|3
the ratio of boys to girls in the sixth grade is 3 to 5 if there are 45 girls how many students are there in the 6th grade
Answer: 27 boys
Step-by-step explanation:
There is a rule in math, what you do to one side, you do to the other.
So in this case the ration is 3:5
?:45
As you can see, they multiplied 5 by 9 to get 45, remember the rule, so we do the same.
3 times 9 is 27, so 27 boys
4 times a number decreased by 2 is at most 10
What's the equation and solution?
Observing the given figure , It is a balanced balance which signifies both side should be equal, The answer is 2=-8-x and x=-10.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination method2=-8-x is the required balanced equation.
-x = 2 + 8
x= -10
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Consider the composite function g(f(x)) =x√6.
If f(x) = 3x², what is g(x)?
O g(x)=√2x
Og(x)=√x+3
Og(x)=√6x
O g(x)=√9-x
So on solving the provided question, we can say that the function g(x) is equal to g(x) = [tex]\sqrt{2x}[/tex]
A composite function is what?The mathematical procedure known as "function composition" takes two functions, f and g, and creates a function, h = g f, such that h(x) = g. This process involves applying the function g to the outcome of applying the function f to x. When the result of one function is utilized as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another function g.
f(f(x)) = [tex]\frac{x}{\sqrt{6} }[/tex]
f(x) = 3x^2
g(f(x)) = [tex]\frac{3x^2}{\sqrt{6} }[/tex]
g(x) = [tex]\sqrt{2x}[/tex]
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Mental Math In a toy store, the ratio of the number of dolls to the number of teddy bears is . If the store has 240 dolls, how many teddy bears are in the store? Use pencil and paper. Describe the mental math steps you use to solve this problem.
Answer:
Step-by-step explanation:
Dolls:240 Teddy Bears:120
120:240
Please Describe the fraction If Possible.
S= pi^2(b^2-a^2)
b=8
a=10
work out the value of S and give the answer to 3 significant figure
Answer:
S = pi^2 * (8^2 - 10^2)
= pi^2 * (-4)
= -12.57 pi^2
The value of S is approximately -12.57 * pi^2. To express this value to three significant figures, we would round it to -13 * pi^2, which is the same as -12.6 * pi^2. So the final answer is -12.6 * pi^2.
How do I solve 6,000-5,258
Answer:
742
Step-by-step explanation:
6000
-5258
742
Convert the following component vectors to a linear combination:
< 20 , 14 , -23 >
The component vectors to a linear combination is given by the equation
A = 20 i^ + 14 j^ - 23 k^
What is the product of vectors?The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by
u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃
An equivalent definition, typically used in physics, is
u ⋅ v = ∣u∣ ∣v∣ cos θ,
where θ is the angle between u and v
Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero
Given data ,
Let the component vectors be represented as A
The value of A is
< 20 , 14 , -23 > be equation (1)
On simplifying the equation to the linear combination , we get
< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^
So , the linear combination of the vectors is given by the equation ,
A = 20 i^ + 14 j^ - 23 k^
Hence , the equation is 20 i^ + 14 j^ - 23 k^
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Please help will mark Brainly
Answer:
Step-by-step explanation:
the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.
A project requires you to figure out the area of a triangular lot. You take measurements and find that the lot has a base of 32 ft., while the altitude of the triangle, or height is 24 ft. What's the area of this lot?
An odometer show that a car has traveled 40,000 miles by January 1, 2020. The car travels 16,000 miles each year. Write an equation that represents the number y of miles on the car’s odometer x years after 2020.
y = __
The equation will be [tex]y=40000+16000*x[/tex]
How do you resolve a two-variable equation?Solve one of the equations for a particular variable. After that, insert that into the other equation and find the variable there. To find the value for the other variable, enter that value into either equation.
Two variables are used in what kind of equation?Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
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Find the equivalent measures. Express as a decimal
(a) 250 cm =
The answer is 2.50. This, 250% in deciaml form is 2.50, in improper fraction form is 52 and as a mixed number it is 2 12. 2 1 2.
Write complex number in standard form.
Answer:
it's B
[tex] - \frac{9}{4} + 2i = - \frac{9}{4} - 4i[/tex]
Answer:
C
Step-by-step explanation:
please refer to the sketch
Britney bought 4 apples, 5 bananas, and 8 oranges at the grocery store.
Which is the ratio of apples to oranges written as a decimal?
A.
1.6
B.
0.4
C.
0.8
D.
0.5
Answer:
Step-by-step explanation:
The question asks for apples to oranges.
So put the number of apples as a numerator and the number of oranges as a denominator. Simply put 4 on top and 8 on the bottom:
4/8 then divide: 4 divided by 8 = .5
There is the ratio as a decimal.
0.5
Option D
What is the probability of tossing a coin and getting heads three times in a row?
What is the chance that the next toss will be heads? What is the chance that the next toss will be tails?
The probability of tossing 3 heads in a row is P = 0.125, and after that, because the events are independent, the probability of getting heads (or tails) still is p = 0.5
How to find the probability?Assuming that we have a fair coin, we assume that both outcomes have the same probability, so:
P(tails) = 0.5
P(heads) = 0.5
Then the probability of getting heads 3 times in a row, is the product of the probability of getting heads 3 times, this will be:
P(3 heads) = 0.5*0.5*0.5
P(3 heads) = 0.5^3
P(3 heads) = 0.125
Now, after this point, what is the probability of getting heads or tails?
Remember that each toss of the coin is independent of the previous one, so the probability of getting tails still is 0,5, and the same for the probability of getting heads.
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Education order reads: 24 hours after bone marrow transfusion give Neupogen 10 mcg/kg/d IV. Supply on hand. Neupogan 300 mcg/ml. Patient’s weight 115 lbs. Give __ mL
Education order reads: 24 hours after bone marrow transfusion give Neupogen 10 mcg/kg/d IV. Supply on hand. Neupogan 300 mcg/ml. Patient’s weight 115 lbs. Give 1.74 mL
What is the Neupogen calculations about?To calculate the appropriate dosage of Neupogen to give to the patient, we need to convert the patient's weight from pounds to kilograms and then use the dosage provided in the order (10 mcg/kg/d IV).
First, we have to convert the patient's weight from pounds to kilograms:
115 pounds = 52.16 kg
Now we can use the dosage provided in the order (10 mcg/kg/d IV) to calculate the appropriate dosage for the patient:
10 mcg/kg/d IV
= 10 mcg/kg/day * 52.16 kg
= 521.6 mcg/day
Then, since the Neupogen is available in a solution of 300 mcg/ml, we can use the following formula to calculate the required volume of solution to give to the patient:
Volume = Dosage / Concentration
= 521.6 mcg / 300 mcg/ml
= 1.74 ml
So, the education order reads 24 hours after bone marrow transfusion, give 1.74 mL of Neupogen at a concentration of 300 mcg/mL IV.
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A small town surveyed 250 adults,
150 of the adults who
180 of whom were parents, about whether a park should be expanded The results showed that
were parents and 40
of the adults who were not parents thought the park should be expanded.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table.
Should the park be expanded?
Yes
No
Parents
Not parents
According to the findings, 40 of the adults who were not parents and 150 of the adults who were parents believed that the park should be expanded.
The park be expanded?250 adults, 180 of whom are parents, leaving 70 adults who are not parents (250 - 180). According to the findings, 40 adults without children and 150 adults with children said the park should be expanded. Thus, 180 – 150 = 30 parents.
Parents: YES OR NO Not parents: 40 | 30 of 150
In this exercise, we must determine the values of the voters who supported expanding the parking lot, which requires that we:
In fact, parents will be 150, not 40.
Parents won't be 30 in total; they'll be 40. Instead, a park should be built to accommodate 250 persons, 180 of whom were parents.
The park should be extended, according to 40 of the people who weren't parents.
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Anthony wants to buy a CD for $400 that earns 2.5% APR and is compounded
quarterly. The CD matures in 3 years. He will be paid the interest he earns
each quarter. How much interest will Anthony have earned on this CD after
the first quarter?
A. $10.00
B. $3.25
c. $1.25
D. $2.50
Answer:i think A
Step-by-step explanation:
Please help…. The table below shows the amount of money Linda spends for a craft demonstration
to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{53}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{53}-\stackrel{y1}{32}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{8}}} \implies \cfrac{ 21 }{ 7 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{ 3}(x-\stackrel{x_1}{8}) \\\\\\ y-32=3x-24\implies {\Large \begin{array}{llll} y=3x+8 \end{array}}[/tex]
The side of a triangle are 64, 47 And 39 use the Pythagorean theorem to determine if a triangle is right acute or obtuse
Answer: obtuse
Step-by-step explanation:
64+47=111
111>39
is 3/16 greater than 1/16
Find the missing measure. Round to the nearest tenth (first decimal place)
15
26°
x
The missing measure of the given right-angled triangle is: x = 2.5
How to find the measure?Given a right-angled triangle, with one of its angle as 14° ,assume
angle y= 14°. Also given length of one of it's side is 18. Let's assume the side as z = 18.
As it is given it's a right-angled triangle,
∴ By using trigonometric formula,
tan y = opposite /adjacent
∴ tan 14° = z/x
tan 14° = 18/x
7.24 = 18/x ......( as tan 14°= 7.24)
∴ x = 2.48
∴ x ≈ 2.5
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Solve the following mentally 65% of 100
Answer: 65
Step-by-step explanation:
Add 1.8m, 77cm, 210mm and give your answer in cm
The total length is 2.077m (2177 cm).
What is length?Length is a measurement of size, distance, or duration. It can refer to physical size (length of a field, length of an object, etc.), distance (length of a journey, length of a river, etc.), or duration (length of a movie, length of a school day, etc.). Length can also refer to the duration of time it takes to complete something (length of a task, length of a process, etc.). Length is typically measured in units such as meters, feet, inches, miles, kilometers, and seconds.
The given measurements can be added together to calculate a total length. The addition of 1.8m, 77cm, and 210mm can be expressed in the form of a sum equation. The equation would be 1.8m + 77cm + 210mm = ?.
To solve this equation, the measurements need to be converted to the same unit of measurement. In this case, all measurements can be converted to cm. 1.8m is equal to 1800cm, 77cm is equal to 77cm, and 210mm is equal to 21cm.
Therefore, the sum equation becomes 1800cm + 77cm + 21cm = ?. To find the total length, the numbers can be added together.
The total length is 1977cm. However, since the measurements are expressed in decimals, the answer must also be expressed in decimals. Therefore, the total length is 2.077m (2177 cm).
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what the answer to the math question?
Someone please help me out
The figures for this problem are not scale drawings, as the ratios between the equivalent side lengths are different.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Hence, when a figure is a dilation of another figure, the two figures are scale drawings.
For this problem, the ratio between the bases of the rectangles is given as follows:
12/6 = 2.
The ratio between the height of each rectangle is given as follows:
6/2 = 3.
As the ratios are different, the two figures are not scale drawings of one another.
For them to be scale drawings, it would be needed either a ratio of 2 for the heights or a ratio of 3 for the bases.
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How many rectangular faces are in a right triangular prism?
Answer: A right triangular prism is a 3-dimensional geometric shape that has a triangular base and three rectangular faces that connect the base to the top. A rectangular prism has three pairs of rectangular faces that are congruent, these faces are perpendicular to each other and connected by edges.
So, in a right triangular prism there are 3 rectangular faces which are the lateral faces (the one that connects the base and the top)
A triangular prism also has 3 triangular faces which are the base faces
So in total, a right triangular prism has 3 rectangular faces and 3 triangular faces.
Step-by-step explanation:
I’m confused HELP pls
On solving the equation n = za the value of a is obtained as a = n/z.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
To solve for a in the equation n = za, isolate a on one side of the equation.
Do this by dividing both sides by z:
n/z = (za) / z
On the right side, the z's cancel out, leaving -
n/z = a
So the solution is -
a = n/z
Therefore, the value of a that satisfies the equation n = za is equal to n divided by z.
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Victoria needs to earn at least an 85 in College Algebra. Only exam scores are used to calculate her grade. Currently she has scored an 82, 81, and 90 this semester. All that remains is the semester exam, which counts twice (counts as two exam grades). She hopes to make an 85 or higher in the class.
She would need to make two extra grades of 86 each.
What is the average?Here we can see that the average of the scores that Victoria would need to make is an average score of 85 so as to be able to pull through. In this case, we can see that we have the scores; 82, 81, and 90
Let the scores tat we have to count twice be p each and then we have;
85 = 82 + 81 + 90 + p + p/5
85 = 253 + 2p/5
5(85) = 253 + 2p
p = 5(85) - 253/2
p = 86
Hence, the twice scores that need to be earned for Victoria are both 86.
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