Given:
A polynomial of the 5th degree A leading coefficient of 7A constant term of 6Problem-solving:
Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.
[tex]\boxed{ \ 7x^5 + bx^4 + cx^3 + dx^2 + ex + 6 \ }[/tex]
Now we make the first polynomial, for example:
b = 3c = -2d = 2e = -5Thus, the result is [tex]\boxed{\boxed{ \ 7x^5 + 3x^4 - 2x^3 + 2x^2 - 5x + 6 \ }}[/tex]
Then we make the second polynomial as an alternative. For example:
b = -6c = 0d = -2e = 0Thus, the polynomial is [tex]\boxed{\boxed{ \ 7x^5 - 6x^4 + 4x^2 + 6 \ }}[/tex]
Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.
Notes:
Let us rephrase the following definitions.
A monomial is an algebraic expression which comprises a single real number, or the product of a real number and one or more variables raised to whole number powers. For example, [tex]\boxed{-2} \boxed{3x^2} \boxed{4a^3b^4} \boxed{-5xy^3z^2} \boxed{\frac{3}{5}}[/tex]A coefficient is each real number preceeding the variable(s) in a monomial. In the examples above [tex]\boxed{ \ -2, 3, 4, -5, \frac{3}{5} \ }[/tex] are the coefficients.A polynomial is the sum or difference of a set of monomials. For example, [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex]Each monomial that forms a polynomial is called a term of that polynomial. For example, the term of polynomial [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex] are [tex]\boxed{ \ 2, - 3, and \ 4. \ }[/tex]The constant term is the term of polynomial that does not contain a variable.The leading coefficient is the coefficient of the term containing the variable raised to the highest power.For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]
[tex]\boxed{ \ 2x^4, - 3x^2, - 4x, and \ - 5 \ }[/tex] are the terms of polynomial.[tex]\boxed{ \ 2, - 3, - 4 \ }[/tex] are the coefficients.- 5 is the constant term.2 is the leading coefficient.A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:
[tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex] is a polynomial in standard form.[tex]\boxed{ \ - 3x^2 + 2x^4 - 5- 4x \ }[/tex] is the polynomial, but it is not in standard form.Learn moreThe remainder theorem https://brainly.com/question/950038768.32 divided by 2.8 is divisible https://brainly.com/question/5022643#Determine whether each algebraic expression is a polynomial or not https://brainly.com/question/9184197#Keywords: a polynomial of the 5th degree, a leading coefficient of 7, a constant term of 6, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer
A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 could take the form of 'f(x) = 7x^5 + 6'. The other coefficients (b, c, d, e) can be any real numbers, but for simplicity, they can be set to zero in this instance.
Explanation:The student's question relates to constructing a polynomial of the 5th degree with specific characteristics in the field of Mathematics, specifically in algebra. One can present such a polynomial with the general form:
f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f
Where the leading coefficient a is 7 and the constant term f is 6. In this case, since the only information provided is the leading coefficient and the constant term, and not any constraints on the other coefficients (b, c, d, e), they can be any real numbers, including zero. Thus, one example of a polynomial fitting these constraints is:
f(x) = 7x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 6
To simplify the algebra and make calculations easier, one can eliminate terms wherever possible, which in this example has been executed by setting the coefficients of x^4, x^3, x^2, and x to zero. After forming any polynomial, it is also important to check the answer to ensure that it matches the given criteria, which in this case it does.
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Select the correct difference. -3z 5 - (-7z 5) (A)-10z5 (B)-4z5 (C)4z5 (D)4z
Answer:
Correct choice is (C). [tex]4z^5[/tex].
Step-by-step explanation:
Given expression is [tex]-3z^5-\left(-7z^5\right)[/tex].
Now we need to simplify that then select the correct difference value from the given choices.
[tex]-3z^5-\left(-7z^5\right)[/tex]
negative times negative is positive
[tex]=-3z^5+7z^5[/tex]
Combine like terms because variable z has same exponent.
[tex]=(-3+7)z^5[/tex]
[tex]=4z^5[/tex]
Hence correct choice is (C). [tex]4z^5[/tex].
Find the quotient. Simplify your answer.
b + 3 3
Answer:
[tex]\frac{b+3}{3}[/tex]
Step-by-step explanation:
[tex]\frac{b+3}{b} \div\frac{3}{b}[/tex]
We need to solve the above equation.
We replace the division sign by multiplication and reciprocated the second term
[tex]=\frac{b+3}{b} *\frac{b}{3}[/tex]
Multiplying both fractions:
[tex]=\frac{(b+3)*b}{3b}[/tex]
Cancelling b from numerator and denominator.
[tex]=\frac{(b+3)}{3}[/tex]
So, answer is:
[tex]\frac{b+3}{3}[/tex]
ANSWER
[tex]\frac{b + 3}{3}[/tex]
EXPLANATION
The given expression is
[tex] \frac{b + 3}{b} \div \frac{3}{b} [/tex]
We multiply the first fraction by the multiplicative inverse of the second fraction.
[tex]\frac{b + 3}{b} \times \frac{b}{3}[/tex]
We now cancel out the common factors to get:
[tex]\frac{b + 3}{3} [/tex]
Therefore simplified form is:
[tex]\frac{b + 3}{3} [/tex]
Identify the equation of the circle B with center B(4,−6) and radius 7. HELP ASAP!!
Answer:
(x − 4)2 + ( y + 6)2 = 49
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is (x − h)2 + (y − k)2 = r2.
Define h, k and r using the given values. So, h = 4, k = −6 and r = 7.
Substitute the values into the equation of a circle:
(x − 4)2 + (y − (−6))2 =72
Simplify.
(x − 4)2 + (y + 6)2 = 49
Therefore, the equation of the circle B with center B(4, -6) and radius 7 is (x − 4)2 + (y + 6)2 = 49.
The equation of the circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the corrcet option is B.
What is the equation of the circle?A circle can be represented as;
[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]
Where h and k are the centers of the circle and r is the radius of the circle.
The equation of circle B with center B(4,−6) and radius 7.
Substitute all the values in the equation
[tex]\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-4)^2+(y-(-6))^2=7^2\\\\\rm (x-4)^2+(y+6)^2=49[/tex]
Hence the equation of circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the correct option is B.
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For what value of x does (the equation is in the picture)
1
3
12
no solution
the answer is.... no solution
An equation is formed of two equal expressions. For the given equation 64³ˣ=512²ˣ⁺¹² no solution for x exists.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The above equation 64³ˣ=512²ˣ⁺¹² can be solved in the following manner as stated below,
64³ˣ = 512²ˣ⁺¹²
(8²)³ˣ=(8³)²ˣ⁺¹²
8⁶ˣ = 8⁽⁶ˣ⁺³⁶⁾
6x = 6x +36
6x - 6x = 36
0 = 36
As the value of x can not be defined, it can be concluded that the equation has no solution.
Hence, for the given equation no solution for x exists.
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Please dont ignore, Need help!!! Use the law of sines/cosines to find..
Answer:
16. Angle C is approximately 13.0 degrees.
17. The length of segment BC is approximately 45.0.
18. Angle B is approximately 26.0 degrees.
15. The length of segment DF "e" is approximately 12.9.
Step-by-step explanation:
16By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.
For triangle ABC:
[tex]\sin{A} = \sin{103\textdegree{}}[/tex],The opposite side of angle A [tex]a = BC = 26[/tex], The angle C is to be found, andThe length of the side opposite to angle C [tex]c = AB = 6[/tex].[tex]\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}[/tex].
[tex]\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}[/tex].
[tex]\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}[/tex].
Note that the inverse sine function here [tex]\sin^{-1}()[/tex] is also known as arcsin.
17By the law of cosine,
[tex]c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}[/tex],
where
[tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are the lengths of sides of triangle ABC, and[tex]\cos{C}[/tex] is the cosine of angle C.For triangle ABC:
[tex]b = 21[/tex],[tex]c = 30[/tex], The length of [tex]a[/tex] (segment BC) is to be found, andThe cosine of angle A is [tex]\cos{123\textdegree}[/tex].Therefore, replace C in the equation with A, and the law of cosine will become:
[tex]a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}[/tex].
[tex]\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}[/tex].
18For triangle ABC:
[tex]a = 14[/tex],[tex]b = 9[/tex], [tex]c = 6[/tex], andAngle B is to be found.Start by finding the cosine of angle B. Apply the law of cosine.
[tex]b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}[/tex].
[tex]\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}[/tex].
[tex]\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree[/tex].
15For triangle DEF:
The length of segment DF is to be found, The length of segment EF is 9, The sine of angle E is [tex]\sin{64\textdegree}}[/tex], andThe sine of angle D is [tex]\sin{39\textdegree}[/tex].Apply the law of sine:
[tex]\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}[/tex]
[tex]\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9[/tex].
a) Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer. The equation is y=0.149x+0.89
Answer:
The predicted GPA is then y = 0.149(15) + 0.89 = 3.125
Step-by-step explanation:
Although you don't specifically say so, the equation you provide here is probably a "best fit" equation based upon data: GPA versus number of hours of study per week.
Here, y = 0.149x + 0.89 and the number of study hours of interest is 15.
The predicted GPA is then y = 0.149(15) + 0.89 = 3.125
The GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 0.149x + 0.89
Plug x = 15 hours
y = 0.149(15) + 0.89
y = 3.125
Thus, the GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89
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What is the distance between the center and edge of a circle called
Answer: The radius
Step-by-step explanation:
The radius is the distance between the center point of the circle and a edge, it is half of the diameter which is the straight line passing through the center point.
For a certain type of hay fever, Medicine H has a 30% probability of working.
In which distributions does the variable X have a binomial distribution?
Select EACH correct answer.
A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.
B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.
C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.
D. When the medicine is tried with two patients, X is the number of doses each patient needs to take.
Step-by-step explanation:
In the first three, the probability of success (or failure) is constant, so those distributions have binomial distributions.
The problem says nothing about doses, which most likely wouldn't be independent events anyways.
So the answer is indeed the first three. Good job!
Answer: A . When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.
B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.
C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.
Step-by-step explanation:
A binomial distribution is a frequency distribution of the possible number of successful outcomes in a given number of trials having same probability of success .From all the given options, option A, B and C has trials that have same probability of success for the given event X .
But option D shows event X is the number of doses each patient needs to take which varies depending on the patient.
Hence, the trials do not have same probability of success .
Please help ill give brainlist
Answer:
N⊥M
Step-by-step explanation:
If N║ P and P⊥M then N⊥M
Yvonne is a salesperson who earns a fixed amount of $1,850 per month. She also earns a commission of 4% on the amount of goods that she sells. If she wants to earn more than $2,300 in one month, how many dollars (x) in goods must she sell?
Answer:
$11,250
Step-by-step explanation:
Yvonne earns a fixed amount of $1,850 per month and want to earn $2,300. The difference is
[tex]\$2,300-\$1,850=\$450.[/tex]
This difference is her commission. If she earns the commission of 4% on the amount of goods that she sells, then
$x - 100%
$450 - 4%
Make a proportion:
[tex]\dfrac{x}{450}=\dfrac{100}{4}\Rightarrow 4x=45,000\\ \\x=\dfrac{45,000}{4}\\ \\x=\$11,250[/tex]
Yvonne must sell $11,250
Determine the fourth term of the sequence defined by the formula:
t1=2a
t2=3a−1
Tn = 2tn−1−3tn−2+1,n ≥ 3
1
−9a+2
-1
−5a+4
Answer:
B. -9a+2
Step-by-step explanation:
You are given the sequence
[tex]t_1=2a,\\ \\t_2=3a-1,\dots\\ \\t_n=2t_{n-1}-3t_{n-2}+1,\ n\ge 3[/tex]
According to the given rule, find [tex]t_3,\ n=3[/tex]
[tex]t_3=2t_2-3t_1+1=2\cdot (3a-1)-3\cdot 2a+1=6a-2-6a+1=-1[/tex]
and [tex]t_4,\ n=4[/tex]
[tex]t_4=2t_3-3t_2+1=2\cdot (-1)-3(3a-1)+1=-2-9a+3+1=-9a+2[/tex]
Measures of the angles of a triangle are in the extended ratio 4:12:14. What is the measure of the smallest angle
A. 6°
B. 24°
C. 72°
D. 84°
Answer:
24°
Step-by-step explanation:
The sum of the ratios is 30. We know that the degree measure of a triangle is 180, so if we divide 180 by 3 we get increments of 6°. That means that 4 parts algebraically can be expressed as 4(6°); 12 parts as 12(6°); 14 parts as 14(6°). That gives us angles of 24°, 72°, 84°. If we add those up we do indeed get 180°, so the smallest angle measure in that extended ratio is 24°
A number cube with the numbers 1 through 6 is rolled 159 times and shows the number four 27 times. Calculate the experimental probability of rolling a four.A number cube with the numbers 1 through 6 is rolled 159 times and shows the number four 27 times. Calculate the experimental probability of rolling a four.
Answer:
Step-by-step explanation:
answer: 27/159
The experimental probability of rolling a four is [tex]27 \div 159[/tex]
Given information:A number cube with the numbers 1 through 6 is rolled 159 times and shows the number four 27 times.
Calculation of probability:The experimental probability should be [tex]27 \div 159[/tex]
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Question 2 POST MATH
Answer:
D. x > -4 or x < -8
Step-by-step explanation:
For this case we must indicate the solution of the following inequalities:
[tex]4x> -16[/tex]
We divide both sides of the inequality by 4:
[tex]x> - \frac {16} {4}\\x> -4[/tex]
On the other hand we have:[tex]6x\leq - 48[/tex]
We divide between 6 on both sides of the inequality:
[tex]x\leq - \frac {48} {6}\\x\leq- 8[/tex]
Thus, the solution will be:
[tex]x>-4[/tex] or [tex]x\leq-8[/tex]
ANswer:
Option D
Jenna's packing company uses a machine to fill boxes of raisins. Due to a defect in the machine, the actual weight of the raisins packed differs by a maximum of 5 ounces from the desired weight of 15 ounces.
Select the correct inequality and number line that model the situation above.
Graphs in this order: B, C, D, E, A
Answer:
your answer is a
Step-by-step explanation:
The correct inequality and number line that model the situation above is:
10 ≤ weight of boxes ≤ 20
and the correct graph is: Graph A
Step-by-step explanation:The desired weight of raisins is: 15 ounces.
As the weight of the raisins packed differs by a maximum of 5 ounces.
This means that the weight of the raisins packed could either be less by 5 ounces or more by 5 ounces.
i.e. Weight of raisins could be minimum= 15-5=10 ounces.
and weight of raisins could be maximum= 15+5=20 ounces.
Hence, the inequality that will hold true is:
10 ≤ weight of boxes ≤ 20
and the graph that describe this situation is attached to the answer.
Trig help
Solve these triangles
Any or all please
Answer:
see below
Step-by-step explanation:
21) The law of sines can be used, since you have a side and its opposite angle.
sin(F)/DE = sin(D)/EF
F = arcsin(DE/EF·sin(D)) = arcsin(20/31·sin(95°)) ≈ 39.994°
E = 180° -95° -39.994° ≈ 45.006°
DF = sin(45.006°)/sin(95°)·31 ≈ 22.006
__
22) The remaining two problems can be solved using the law of cosines:
c^2 = a^2 + b^2 - 2ab·cos(C)
Of course, c is the square root of the expression on the right.
EF = √(19^2 +35^2 -2(19)(35)cos(61°)) ≈ √(941.203) ≈ 30.679
Then an angle can be found using the law of sines
E ≈ arcsin(35/30.679·sin(61°)) ≈ 86.203°
F ≈ 180° -61° -86.203° ≈ 32.797°
__
23) As in 22 …
RS = √(20^2 +28^2 -2(20)(28)cos(91°)) ≈ √(1203.547) ≈ 34.692
R ≈ arcsin(20/34.692·sin(91°)) ≈ 35.199°
S ≈ 180° -91° -35.199° ≈ 53.801°
Deanna is a dog groomer. On Monday, she groomed 12 dogs in 8 hours. On Tuesday, she groomed 9 dogs in 6 hours. On Wednesday, she groomed 6 dogs in 6 hours. Which statements are true about Deanna’s workload? Check all that apply. The Wednesday ratio was equal to the Monday ratio. The Monday ratio was equal to the Tuesday ratio. The Tuesday ratio was greater than the Wednesday ratio. The Wednesday ratio was less than the Monday ratio. The Monday ratio was twice the Wednesday ratio.
Answer:
The Monday ratio was equal to the Tuesday ratio.
The Tuesday ratio was greater than the Wednesday ratio.
The Wednesday ratio was less than the Monday ratio.
Step-by-step explanation:
Using the ratio and Proportion concept, The true statements are:
The Monday ratio was equal to the Tuesday ratio.
What is Ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, while part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, but the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the portion to the total is 5: 10, meaning that 5 out of every 10 persons enjoy reading.
What is Proportion?
Ratio and fractions are the main bases on which proportion is discussed. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a percentage. In this case, a and b can be any two numbers. Ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics.
So, According to the question:
The ratio on Monday = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]
The ratio on Tuesday = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex]
The ratio on Wednesday = [tex]\frac{6}{6}[/tex] = [tex]\frac{1}{1}[/tex]
So, from the above fraction, we can easily conclude that The Monday ratio was equal to the Tuesday ratio.
Hence, The Monday ratio was equal to the Tuesday ratio.
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The length of a rectangle is 6 1/2 inches and the width is 3 3/4 inches. What is the ratio, using whole numbers, of the length to the width?
Answer:The length is 13/2, while the width is 15/4, after combination. Ratio of length to width is then (13/2)/(15/4) = 26/15.
Planes S and R both intersect plane T .
Which statements are true based on the diagram? Check all that apply.
[A] Plane S contains points B and E.
[B] The line containing points A and B lies entirely in plane T.
[C] Line v intersects lines x and y at the same point.
[D] Line z intersects plane S at point C.
[E] Planes R and T intersect at line y.
False
As indicated in Figure A below, Plane S contains only point B (remarked in red). Point E (remarked in blue) lies on plane R.
[B] The line containing points A and B lies entirely in plane T.True
As indicated in Figure B below, the line containing points A and B lies entirely in plane T. That line has been remarked in red and it is obvious that lies on plane T.
[C] Line v intersects lines x and y at the same point.False
As indicated in Figure C below, line v intersects lines x and y, but line x in intersected at point B while line y (remarked in red) is intersected at point A (remarked in blue), and they are two different points, not the same.
[D] Line z intersects plane S at point C.True
As indicated in Figure D below, line z that has been remarked in yellow, intersects plane S at point C that has been remarked in blue.
[E] Planes R and T intersect at line y.True
As indicated in Figure E below, planes R and T intersect at line y. The line of intersection has been remarked in red.
Please Help!!!!!!!Carmela is planning a season-themed event for the residents of a town. She would like to conduct a survey of a sample of residents to determine whether people prefer summer or winter.What is the best way that the she could select the sample? A. Randomly select from residents who own a vacation home at the beach B. Randomly select from residents who skiC. Randomly select from all of the town residentsD. Randomly select from residents who own pools
C. randomly select from all residents.
Answer:
Sorry if i'm late but i think the answer is C. Randomly select from all of the town residents
im 97% sure
Someone please help??
Answer:
2
Step-by-step explanation:
It is not 7, although that looks possible. The 7 is a coefficient (in my day we called it a numerical coefficient).
The constant is not d either. That is a variable.
The constant is the 2
The surface areas of two similar figures are 64 m^2 and 169 m^2. The volume of the larger figure is 4394 m^3. What is the volume of the smaller figure?
Set up a ratio for the area.
Area is squared so find the square root of the scale
√64/169 = 0.61538
Volume is cubed so cube the scale factor:
0.61538^3 = 0.23304
Multiply that by the volume:
4394 x 0.23304 = 1024
The volume of the smaller figure is 1,024 m^3
Answer:
1024 m³Step-by-step explanation:
We know:
The ratio of the surface of two similar figures is equal to the square of the similarity scale. The ratio of the volume of two similar figures is equal to the cube of the similarity scale.
Therefore
k - similarity scale
[tex]k^2=\dfrac{64}{169}\to k=\sqrt{\dfrac{64}{169}}=\dfrac{\sqrt{64}}{\sqrt{169}}=\dfrac{8}{13}\\\\\dfrac{V}{4394}=\left(\dfrac{8}{13}\right)^3\\\\\dfrac{V}{4394}=\dfrac{512}{2197}\qquad\text{cross multiply}\\\\2197V=(512)(4394)\qquad\text{divide both sides by 2197}\\\\V=(512)(2)\\\\V=1024\ m^3[/tex]
If C is the midpoint of KN what is KC?
A. 18
B. 4.5
C. 19
D. 9
Answer:
19
Step-by-step explanation:
If C is the midpoint of KN, then KC = CN
So we can equate the expressions
[tex]KC= 2x+10[/tex]
[tex]CN= 4x+1[/tex]
KC = CN
[tex]2x+10=4x+1[/tex]
Subtract 2x on both sides
[tex]2x-2x+10=4x-2x+1[/tex]
[tex]10=2x+1[/tex]
Subtract 1 on both sides
[tex]9=2x[/tex]
Divide both sides by 2
[tex]x=4.5[/tex]
Now we find out KC
[tex]KC= 2x+10[/tex]
[tex]KC= 2(4.5)+10[/tex]
[tex]KC= 19[/tex]
22broccy-here you go g-
what is the sum of negative two squared plus one?
Answer:
The sum is equal to 5
Step-by-step explanation:
we know that
The algebraic expression of the phrase " the sum of negative two squared plus one" is equal to
[tex](-2)^{2}+1\\=4+1\\=5[/tex]
Answer:
5
Step-by-step explanation:
(-2)^2 +1
Since the quantity is squared, it becomes a positive number
4+1
5
Find cscx if sinx+cotx cosx= sqrt3
Answer:
The answer is (d) ⇒ cscx = √3
Step-by-step explanation:
∵ sinx + (cotx)(cosx) = √3
∵ sinx + (cosx/sinx)(cosx) = √3
∴ sinx + cos²x/sinx = √3
∵ cos²x = 1 - sin²x
∴ sinx + (1 - sin²x)/sinx = √3 ⇒ make L.C.M
∴ (sin²x + 1 - sin²x)/sinx = √3
∴ 1/sinx = √3
∵ 1/sinx = cscx
∴ cscx = √3
Answer:
d. [tex]\sqrt{3}[/tex]
Step-by-step explanation:
see attachment, it's correct :))
(30 points! I just need someone to correctly answer this, please.)
Graph the system of equations on graph paper to answer the question.
{y=1/3x−2 y=−3x−12
What is the solution for this system of equations?
Step-by-step explanation:
y = ⅓x − 2
y = -3x − 12
The first line has a y-intercept of -2 and a slope of ⅓.
The second line has a y-intercept of -12 and a slope of -3.
The graph looks like this: desmos.com/calculator/raouxrikbg
From the graph, we see they intersect at (-3, -3).
Draw a box-and-whisker plot for the set of data. 27, 35, 44, 51, 52, 54, 56, 69, 69, 79, 80, 100, 100 a. Please select the best answer from the choices provided A B C D
look at the picture not my text lol
Answer:
B
Step-by-step explanation:
Look at the other guys box and whisker plot
Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year. Which type of function could model the value of the car? A. Exponential B. Can't be determined C. Linear D. Quadratic
Answer:
an exponential function
Step-by-step explanation:
Use a function of the same form as the compound amount formula:
A = P(1+r)^5, where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.
The given function could model the value of the car as an exponential function.
We have given that,
Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year.
We have to determine which type of function could model the value of the car.
Use a function of the same form as the compound amount formula
A = P(1+r)^5,
where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.
Therefore the given function could model the value of the car as an exponential function.
Therefore the option A is correct
To learn more about the exponential function visit:
https://brainly.com/question/12940982
#SPJ2
Write an equation of a line in slope-intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (2, 6).
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We have the following line:
[tex]2x-3y = 12\\2x-12 = 3y\\y = \frac {2} {3} x-4[/tex]
If the line we wish to find is perpendicular to the one given, then its slope is given by:
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {\frac {2} {3}}\\m_ {2} = - \frac {3} {2}[/tex]
Then the line is:
[tex]y = - \frac {3} {2} x + b[/tex]
We substitute the point:
[tex]6 = - \frac {3} {2} (2) + b\\6 = -3 + b\\b = 6 + 3\\b = 9[/tex]
Finally, the equation is:
[tex]y = - \frac {3} {2} x + 9[/tex]
Answer:
[tex]y = - \frac {3} {2} x + 9[/tex]
Dr.Potter Provides vaccinations against polio and measles. Each polio vaccination multi-dose vial consist of 44 individual doses, and each measles vaccination multidose vial’s consist of 22 individual doses period last year, Dr.Potter used a total of 60 multi-dose vial’s that consisted of a total of 2024 individual doses. How many individual polio and measles vaccinations did Dr.potter give, respectively?