Answer:
Step-by-step explanation:
Answer:
The width is 8 units
Step-by-step explanation:
This is a variation problem we are to work with.
Length is inversely proportional to width, let length be l and width be w
modeling the statement mathematically, we have lw = k where k is the proportionality constant
Now let’s get k from l = 12 and w = 6
k = 12 * 6 = 72
Now for the second rectangle also;
lw = k given l = 9
9w = 72
w = 72/9
w = 8
does this represents apolynomial?and if it does is it amonomial,binomial,trinonial,ornoneand what's the degree if it is
The algebriac expression is a polynomial, if all the exponents of expression is non negative.
if 1/4 of the class is girls and one half of the girls in the class are wearing dresses what fraction of the class are girls with dresses one eighth 1/6 1/5 1/4
Given that one-fourth of the class are girls;
[tex]f(G)=\frac{1}{4}[/tex]And one half of the girls in the class are wearing dresses;
[tex]f(D)=\frac{1}{2}[/tex]The fraction of the class that are girls with dresses is;
[tex]\begin{gathered} f(G\cap D)=\frac{1}{4}\times\frac{1}{2} \\ f(G\cap D)=\frac{1}{8} \end{gathered}[/tex]Therefore, the fraction of the
с C' B' A B D' D The distance from A to B is 10 and the distance from A to B'is 2. What is the scale factor? 1/5 4 5 1/4
In this problem, we have that
the center of the dilation is pointed A ----> because the intersection segments c
so
the scale factor is equal to
scale factor=AB'/AB
substitute given values
scale=2/10
scale =1/5Can I please get some help with this equation? Evaluate and simplify log of csc(5pi/6) multiplied by csc(pi/4). Explain your work.
1) Considering that the 1st property of Logarithms tells us:
[tex]\log _ab\text{ =c}\Leftrightarrow a^c=b[/tex]2) Let's evaluate that:
[tex]\begin{gathered} \log _{\csc (\frac{5\pi}{6})}(\frac{\csc \pi}{4})=x\Rightarrow\csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \\ \csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \log \csc (\frac{5\pi}{6})^x=\log \csc (\frac{\pi}{4}) \\ \text{x}\log \csc (\frac{5\pi}{6})^{}=\log (\sqrt[]{2}) \\ x\log (2)=\text{ log(}\sqrt[]{2}) \\ x=\frac{\log\sqrt[]{2}}{\log\text{ 2}} \\ x=\frac{1}{2} \end{gathered}[/tex]• Notice that we've descended that exponent x, to become a factor (3rd line).
,• Then divided both log with a common base, in this case, base 10.
3) Hence that equation yields 1/2 as its result.
What is eight times the square root of two square root of two
Given expression is
[tex]8\sqrt[]{2\sqrt[]{2}}[/tex]Now, solving it as:
[tex]8\sqrt[]{2\sqrt[]{2}}=8\cdot2^{\frac{3}{4}}[/tex]So,
[tex]8\cdot2^{\frac{3}{4}}[/tex]is the required solution.
Put the steps in order to find the distance between these
Answer:
See attachedStep-by-step explanation:
The distance between the points is found using the given coordinates and the distance formula.
The distance formula is based on right triangle and Pythagorean theorem and is the calculation of the hypotenuse provided the legs are known.
So the right order of operations is attached for you below.
You have found most of it, just small correction is needed.
Answer:
1., 2., 4., 5., 6., 3., 7.
Step-by-step explanation:
1. Draw a right triangle by dropping a vertical side and a horizontal side. (See attachment).
2. Determine the vertical side (2 units) and horizontal side (6 units) lengths by counting on the grid (be careful of the scale), or using the vertical coordinated (3 to 1) and horizontal coordinate (-2 to 4).
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Therefore:
a = 2b = 64. Use the Pythagorean Theorem for right triangles to determine the diagonal length:
[tex]\implies \sf 2^2+6^2=c^2[/tex]
[tex]\sf 5.\quad 4 + 36 = c^2[/tex]
[tex]\sf 6. \quad 40 = c^2[/tex]
[tex]\sf 3.\quad \sqrt{40}=\sqrt{c^2}[/tex]
7. √40 is between √36 and √49, so between 6 and 7 - closer to 6, so about 6.3 units.
What is the total cost for fixing a drain that takes 6 hours?If the plumber charged a total of 364$ how many hours did she spend fixing the drain?
a) Recall that to evaluate a function at a given value, we substitute the variable by the given value.
Therefore, evaluating C(h) at h=6 we get:
[tex]C(6)=76+24\cdot6.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} C(6)=76+144 \\ =220. \end{gathered}[/tex]b) Setting C(h)=364 we get:
[tex]76+24h=364.[/tex]Subtracting 76 from the above equation we get:
[tex]\begin{gathered} 76+24h-76=364-76, \\ 24h=288. \end{gathered}[/tex]Dividing the above equation by 24 we get:
[tex]\begin{gathered} \frac{24h}{24}=\frac{288}{24}, \\ h=12. \end{gathered}[/tex]Answer:
(a) $220.
(b) 12.
here is my question:simplify 10p4
The value of 10P4 is 5040
Permutations and combinations are defined as the various ways in which objects from a set may be selected, generally without replacement, to form subsets.
Given 10P4
we have to evaluate the value of 10P4
10P4 is in the form of npr
Formula for npr = n!/(n-r)!
Here n =10 and r=4
Now substitute the values in the formula
(10! )/(10-4)!
= (10! )/6!
=(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(6 x 5 x 4 x 3 x 2 x1)
= 10 x 9 x 8 x 7
= 5040
Therefore the value of 10P4 is 5040
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Answer:
The value of 10P4 is 5040
Permutations and combinations are defined as the various ways in which objects from a set may be selected, generally without replacement, to form subsets.
Given 10P4
we have to evaluate the value of 10P4
10P4 is in the form of npr
Formula for npr = n!/(n-r)!
Here n =10 and r=4
Now substitute the values in the formula
(10! )/(10-4)!
= (10! )/6!
=(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(6 x 5 x 4 x 3 x 2 x1)
= 10 x 9 x 8 x 7= 5040
Step-by-step explanation:
For which equation would x = 12 NOT be a solution?Options:X\1=12x\4=2x\3=4x\2=6
Given:
[tex]x=12[/tex]is given.
Required:
Which option is not appropriate.
Explanation:
Now we check all the option for this
[tex]\begin{gathered} \frac{x}{1}=12 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{4}=2 \\ x=8 \end{gathered}[/tex]which is not appropriate
[tex]\begin{gathered} \frac{x}{3}=4 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{2}=6 \\ x=12 \end{gathered}[/tex]which is appropriate
Final answer:
I keep overthinking and confusing myself can you help me please
We are asked to prove that triangles △PQR and △TSR are congruent.
Let us write the statements and reasons to prove that the given triangles are congruent.
[tex]\begin{gathered} 1.\: Statement\colon\: \bar{PQ}\cong\bar{TS} \\ 1.Reason\colon Given \end{gathered}[/tex]We are given that R is the midpoint of QS and PT
This means that QR ≅ SR and also PR ≅ TR by the property of "Definition of midpoint"
[tex]\begin{gathered} 2.\: Statement\colon\: \bar{QR}\cong\bar{SR} \\ 2.\: Reason\colon\: \text{Definition of midpoint} \end{gathered}[/tex][tex]\begin{gathered} 3.\: Statement\colon\: \bar{PR}\cong\bar{TR} \\ 3.\: Reason\colon\: \text{Definition of midpoint} \end{gathered}[/tex]So, now we have 3 equal sides in both triangles
Therefore, by the property of "Side-Side-Side" (SSS) the given triangles are congruent.
[tex]\begin{gathered} 4.\: Statement\colon\: \triangle PQR\cong\triangle TSR \\ 4.\: Reason\colon\: \text{Side}-\text{Side}-\text{Side theorem of triangle congruence } \end{gathered}[/tex]V = πr (R²-r²)
make r the subject of the formula
The subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]
Given,
V = πr (R²-r²)
then to find r in terms of the other values divide both the sides by the multiplier of r.
r is multiplied by πr²
Now divide both sides by V
[tex]\frac{V}{\pi r } = \frac{\pi r(R^{2}- r^{2})}{\pi r}[/tex]
[tex]\frac{V}{\pi r } = {(R^{2}- r^{2})}[/tex]
[tex]{\pi r } = \frac{{(R^{2}- r^{2})}}{V} \\\\\pi r^{2} = {r(R^{2}- r^{2})}[/tex]
Hence the answer is the subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]
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Matilda covers the interior faces of a kitchen drawer with shelf paper. The height of the drawer is 3/4 its width and the depth front to back is 7/4 its width. if the exact amount of shelf paper needed is 846 square inches what is the depth of the drawer? help me I need help
To know the depth of the drawer you need to know that the shelf paper is the area of the interior faces of the drawer, then:
A = 846sq in
the area is equal to:
[tex]A=A_b+A_l[/tex]Where:
Ab is the area of the base of the drawer
Al is the area of the laterals of the drawer
The Area of the base is:
[tex]A_b=\frac{7}{4}x\cdot x=\frac{7}{4}x^2[/tex]And the area of the laterals is the sum of the area of every lateral:
[tex]A_l=2\lbrack(\frac{3}{4}x)\cdot(\frac{7}{4}x)\rbrack+2\lbrack(\frac{3}{4}x)\cdot(x)\rbrack[/tex][tex]A_l=\frac{21}{8}x^2+\frac{3}{2}x^2=\frac{33}{8}x^2[/tex]Then:
[tex]846=\frac{7}{4}x^2+\frac{33}{8}x^2[/tex][tex]846=\frac{188}{32}x^2=\frac{47}{8}x^2=5.87x^2[/tex]The we clear the x:
[tex]\frac{846}{5.87}=x^2[/tex][tex]\sqrt[]{144.12}=x[/tex][tex]x=12.004in[/tex]The depth of the drawer is x= 12,004 inchesIf ABCDE is reflected over the x-axis and then translated 3units left, what are the new coordinates B?E..ADO A. (1, -2)O B. (7,-2)C. (4, -2)D. (-7,2)CBX
Recall that the rule of transformation for a point (x,y) reflected over the x-axis is:
[tex](x,y)\rightarrow(x,-y),[/tex]and the rule of transformation for a point translataled n units to the left is:
[tex](x,y)\rightarrow(x-n,y).[/tex]Therefore, point B(4,2) reflected over the x-axis:
[tex](4,2)\rightarrow(4,-2),[/tex]and then translated 3 units to the left has as image the following point:
[tex](4,-2)\rightarrow(4-3,-2)=(1,-2).[/tex]Answer:[tex]\begin{equation*} (1,-2). \end{equation*}[/tex]1.5 part 1 question 18 Determine whether the table represents functions or not assume that the input is in the left column or top row (explain your answer)
A function is a relation in which each element of the input is associated with exactly one element of the output. For example:
In this case, we have:
As we can see, the table does not represent a function because there is a value in the input set that is associated with two values in the output set.
Graph each pair of inequalities and indicate the solution set of the system with Cross hatching or shading. The cross hatching or shading, if extended would cover a set of three letters.
Given:
[tex]\begin{gathered} y4 \end{gathered}[/tex]To graph each pair of inequalities and indicate the solution set with cross hatching or shading
Solution
Determine the x and y intrcept of each of the given ineqiualities
[tex]\begin{gathered} y4 \\ 3x+2y=4 \\ y-intercept,make,x=0 \\ 3(0)+2y=4 \\ 2y=4 \\ y=\frac{4}{2}=2 \\ Coordinateof\text{ the y-intercept}:(0,2) \\ x-intercept,make,y=0 \\ 3x+2(0)=4 \\ 3x=4 \\ x=\frac{4}{3} \\ Coordinate\text{ of the x-intercept}:(\frac{4}{3},0) \end{gathered}[/tex]Plot the graph as shown below
It can be observed that the solution set is unbounded, as shown by the cross hatching
a researcher wants to determine the number of televisions in a household.he conducts a survey of 40 random select house and I obtains data in accompying tabe. what is the relative frequency distribution of the data
The relative frequency (RF) can be calculated as follows:
[tex]RF=\frac{F}{\sum ^{}_{}F}[/tex]where RF is the relative frequency, F is the value of the frequency, and ∑F represents the sum of all frequencies.
Using a spreadsheet, we can get the following table:
Based on this table, we can see that ∑F = 40. Thus, we have to divide each frequency by 40 to get the relative frequency. As an example, using the first, second, and third row:
[tex]RF_1=\frac{1}{40}=0.025[/tex][tex]RF_2=\frac{15}{40}=0.375[/tex][tex]RF_3=\frac{13}{40}=0.325[/tex]Answer:
find the circumstance of each circle. use your calculator's value of pi. round your answer to the nearest tenth.
The area of the circle is given by:
[tex]\pi\cdot r^2[/tex]where r is the radius of the circle
Given area = 615.8 yd^2
so, we will calculate the radius of the circle as follows:
[tex]\begin{gathered} \pi\cdot r^2=615.8 \\ r^2=\frac{615.8}{\pi}=196.015 \\ \\ r=\sqrt[]{196.015}\approx14yd \end{gathered}[/tex]So, the radius of the circle = r = 14 yd
The circumference of the circle =
[tex]2\cdot\pi\cdot r=2\cdot\pi\cdot14=87.9646[/tex]rounding the answer to the nearest tenth
So, the circumference = 88 yd
All points from which of the following patterns would be contained on the given graph?321-6-5-4-3 -2 -1 0123 4 5 6-1-2-3OA. -1.-3.-5.-7....OB. -3, -7, -11, -15....OC. -2,-5.-8.-11.....OD. 3,5,7.9....Ht
To determine which pattern could represent points on the graph, we notice that the following points are on the graph:
[tex](1,-1),(2,-3),(3,-5).[/tex]We can infer that the point
[tex](4,-7)[/tex]is also on the line.
Therefore, the pattern that could be contained in the graph is:
[tex]-1,-3,-5,-7...[/tex]Answer: Option A.
Answer each part. If necessary round to the nearest hundredth
If 85 pounds of seed are needed to plant a 10-acre field, then each pound can cover
[tex]\frac{10}{85}\text{acres per pound.}[/tex]Computing the above division, we get:
[tex]0.12\text{ acres per pound.}[/tex]Now, in the second problem, the rent for 3 hours is $10, therefore, the cost per hour is:
[tex]\frac{10}{3}\text{dollars per hour.}[/tex]The decimal form of the above solution is:
[tex]3.33\text{ dollars per hour.}[/tex]Answer:
a)
[tex]0.12\text{ acres.}[/tex]b)
[tex]3.33\text{ dollars per hour.}[/tex]Question 5 Cameron put his dog Buddy in a kennel while he went on a long business trip. The equation y = 15x + 25 shows the total charge y that Cameron will pay to put Buddy in a kennel for x days. Which statement is true? The kennel charges $15 for the first day and $25 per day after the first day. The kennel charges an initial fee of $25 and $15 per day. The kennel charges $25 per day with an initial fee of $15. The kennel charges $25 for the first day and $15 per day after the first day. SUBMI
The true statement regarding the expression is that D. The kennel charges $25 for the first day and $15 per day after the first day.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Cameron put his dog Buddy in a kennel while he went on a long business trip and the equation y = 15x + 25 shows the total charge y that Cameron will pay to put Buddy in a kennel for x days.
Therefore, option D illustrate this.
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What is y=3x2-1 linear or not linear
Answer:
it would be linear i gotcha bro
Write an inequality for the word problem and answer the question about the inequality. The faculty team scored less than half as many points as the varsity team. A total of 100 points was scorered. If x represents the number of points that the varsity team scored Could x = 60
From the exercise we can indentify the following
• x, = number of points that the varsity team scored
,• y ,= number of points that the faculty team scored
[tex]\begin{gathered} x+y=100\to(1) \\ y<\frac{1}{2}x\to(2) \end{gathered}[/tex]Let's clear y in (1) to be able to replace in (2)
[tex]\begin{gathered} y=100-x\to(1) \\ 100-x<\frac{1}{2}x\to(1)\text{ in (2)} \\ \frac{1}{2}x+x>100 \\ \frac{3}{2}x>100 \\ x>\frac{100\cdot2}{3} \\ x>\frac{200}{3} \\ x>66.6666 \\ x>67 \end{gathered}[/tex]The answer is x cannot be equal to 60 because they have to be at least 67 points to comply with the inequalityAn animal shelter has 12 cats and 9 dogs. If 1 cat and 1 dog adopted, would the ratio of cats to dog remain the same? Explain.
At the beggining the ratio of cats to dogs is
[tex]\frac{12}{9}=\frac{4}{3}[/tex]because ratio indicates a fraction (12 cats divided by 9 dogs)
After the adoption there were 11 cats and 8 dogs, then the ratio is
[tex]\frac{11}{8}[/tex]Since
[tex]\frac{4}{3}\ne\frac{11}{8}[/tex]Answer: the ratio of cats to dog does not remain the sameWhat is the slope of y= -4
Hello!
We have the equation of the line y = -4.
Let's put this equation in a cartesian plane:
Notice that this equation will be always constant. So, as we just have a straight line with no inclination, the slope is 0.
is 0.56>0.056 yes or no
The question is asking you to compare to decimal numbers:
0.56 and 0.056 and decide which one
III m 40 ft 65 ft What is the area of this trapezoid? square feet
remember that the area of a trapezoid can be expressed as
[tex]\begin{gathered} A=\frac{(B+b)\cdot h}{2} \\ \end{gathered}[/tex]Replace in the formula taking into account that B is the greater base, b is the smallest base and h is the height of the trapezoid.
[tex]\begin{gathered} A=\frac{(95+65)\cdot40}{2} \\ A=\frac{160}{2}\cdot40 \\ A=80\cdot40 \\ A=3200 \end{gathered}[/tex]The area of the trapezoid is 3,200 sqft.
Kelly bought a cup of coffee and drank 5/8 of it. Write an addition equation to represent how much coffee is remaining.Enter your answer as an addition equation, formatted like this: 42+(-53)=-11
Step 1
Given; Kelly bought a cup of coffee and drank 5/8 of it. Write an addition equation to represent how much coffee is remaining.
Step 2
[tex]\begin{gathered} The\text{ total fraction representing the cup=1} \\ Let\text{ the fraction left be x} \\ Thus; \\ x+\frac{5}{8}=1 \end{gathered}[/tex]The addition equation representing how much coffee is remaining is;
[tex]\begin{gathered} x=1+(-\frac{5}{8}) \\ x=\frac{3}{8} \\ Thus \\ 1+(-\frac{5}{8})=\frac{3}{8} \\ \end{gathered}[/tex]Answer;
[tex]1+(-\frac{5}{8})=\frac{3}{8}[/tex]Can you solve this ? Solve the x And get Angle 1 :And Angle 2 :Question 17
SOLUTION
Solve for the value of x using supplementary angles
If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together.
[tex]\begin{gathered} <1=4x-5 \\ <2=x \end{gathered}[/tex]To solve using the supplementary angle rule
Add the two angles together
[tex]\begin{gathered} <1+<2=180^0 \\ 4x-5+x=180 \\ collect\text{ like terms} \\ 4x+x=180+5 \\ 5x=185 \end{gathered}[/tex]Divide both side by 5
[tex]\begin{gathered} 5x=185 \\ \frac{5x}{5}=\frac{185}{5} \\ x=37 \end{gathered}[/tex]Hence the value of x = 37 degree
The measure of Angle 1 = <1 = 4x-5 = 4(37) - 5 = 143 degree
The measure of Angle 2 = <2 = x = 37 degree
find dy/
dx
Find where y = csc^-1(1/9x+5)
Answer:
csc(9x)
Step-by-step explanation:
A Snap Cube PrismA rectangular prism is 3 units high, 2 units wide, and 5 units long. What is its surfacearea in square units? Explain or show your reasoning (work).
62 u² (square units)
1) A rectangular prism is made up of 6 rectangles. So we can write them out:
2 rectangles (3 x 2)
2 rectangles ( 5 x 2)
2 rectangles ( 5 x 3)
2) Therefore the Total Surface Area of that prism can be found by applying the formula for the area of each rectangle times 2. Like this:
[tex]\begin{gathered} \text{TSA}=\text{ 2(3}\times2\text{ +5}\times2+5\times3) \\ \text{TSA}=\text{ 2(6 +10+15)} \\ \text{TSA}=\text{ 2(31)} \\ \text{TSA}=62 \end{gathered}[/tex]3) Hence the answer is 62 u² (square units)