The trigonometric expression for relation between csc A and cot A.
[tex]undefined[/tex]which situation is most likely to show a constant rate of change
A. the shoe size of a young girl compared with her age in years
B. the amount spent on grapes compared with the weight of the purchase
C. the number of people on a city bus compared with the time of day
D. the number of slices in a pizza compared with the time it takes to deliver it
Answer:
B. the amount spent on grapes compared with the weight of the purchase
The length and width of a rectangular table have a ratio of 8 to 5. The width of the table is 40 in. Find the length of the table.
Solution:
Let the length and the width of the rectangular table be represented as L and W respectively.
Given that the length and the width have a ratio of 8 to 5, this implies that
[tex]\frac{L}{W}=\frac{8}{5}[/tex]If the width of the table is 40 in, the length of the table is evaluated as
[tex]\begin{gathered} \frac{L}{40}=\frac{8}{5} \\ \text{cross multiply} \\ 5\times L=8\times40 \\ \implies5L=320 \\ \text{divide both sides by the coefficient of L, which is 5} \\ \text{thus,} \\ \frac{5L}{5}=\frac{320}{5} \\ \therefore L=64\text{ in.} \end{gathered}[/tex]Hence, the length of the table is 64 in.
Find the last term to make the trinomial into a perfect square:
x
2
+
6
x
+
When this is factored, it becomes:
The last term using factorization method to make the perfect square is 3 and the final expression is (x + 3)².
What is factorization method?
The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.
According to the question, the given quadratic equation can be solved by performing factorization as well as by adding the half of the coefficient of the x-term to the given equation.
Therefore, the expression can be written as:
x² + 6x + 3² = 0
⇒(x + 3)² = 0
Hence, the last term by using factorization method to make the perfect square is 3 and the final expression is (x + 3)².
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Choose the best estimate for the quotient.
8.23 divide by 65.29
A) 7
B) 8
C) 9
D) 10
Answer:
8
Step-by-step explanation:
65.29/8.23≈7.933
7.933 rounds to 8
(2a) Multiple Choice: Place the letter of the correct answer on the answer line to the right:
For which of the following values of k will the equation have infinite solutions?
4(4x + 1) = k(8x + 2)
(a) 4
(b) 8
(c) 2
(d) 1
(2b) Using your answer from Part (2a) replace the value you selected in the equation below. Then solve the
equation and show that it will, in fact, yield infinite solutions.
4(4x+1)=k(8x + 2)
For k=2 for infinite solutions.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
4(4x + 1) = k(8x + 2)
Now, the equation should have infinite solutions
In consider the situation then we must put value of k such that LHS part become Equal to RHS.
Now, take k=2
4(4x + 1) = k(8x + 2)
LHS: 4(4x+1)= 16x+ 4
RHS: 2(8x+ 2)= 16x+ 4
Hence, k=2 for infinite solutions.
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I call a selling books for $12 each she wants to make more than $180 in books sellers the inequality 12b>180 can be used to detain the numbers of books ,b, she must sell in order to meet her goal which number line best represents the solution of the inequality
solve for b:
Divide both sides by 12:
[tex]\begin{gathered} \frac{12}{12}b>\frac{180}{12} \\ b>15 \end{gathered}[/tex]what is the best estimate for the product 9/10 x 5/11
The best estimate for the product 9/10 x 5/11 is 1/2.
What is product?Product in Mathematics simply means a number that you get when you multiply. It is used to illustrate tye concept of multiplication
In this case, the estimate for 9/10 is 1 and the estimate of 5/11 is 1/2. Therefore, the product will be:
= 1 × 1/2
= 1/2
This shows the estimation.
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A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she dropped 37.5 feet. How many feet had she been below sea level, if she was 80.7 feet below sea level after she dropped?
Answer:1234567.00 feet
Step-by-step explanation: feet are yummy
Select the correct answer.Select how this number is read.3.7284A. three and seven thousand, two hundred eighty-four ten-thousandthsB. three and seven thousand, two hundred eighty-four hundredthsC. thirty-seven and two hundred eighty-four thousandthsD. three point seven two eight four
Given:
3.7284
The given number should be read as "three point seven two eight four.
Option D is the correct answer.
11. The distance formula is d = rt, where d is the distance, r is the rate, and t is the time.a. Rewrite the equation to isolater.r = d/tb. Brad drove from Athens to Atlanta in 1.5 hours, 72 miles away, before he flew out forKansas City. What was his rate of speed in miles per hours
B. we just replace the vlues of t=1.5 and d=72
[tex]\begin{gathered} r=\frac{72}{1.5} \\ \\ r=48\frac{m}{h} \end{gathered}[/tex]the rate of speed is 48 miles per hour
based off of this table, what would be the best guess for the domain and range of the composition?? i cant figure this out. PLEASE HELP
The composite function is:
[tex]y=\lvert-x^2\rvert[/tex]The domain (D) is:
The domain is the set of all possible x values. Since there are no limitations for the x-values, the domain is all real numbers.
D = (-∞, ∞).
The Range (R) is:
The range is the set of all possible y values (output values). As you can see in your table, there are no negative output values. So, the range is the positive real numbers and the zero.
R = [0, ∞).
Create a rational function that meets the following criteria.Vertical Asymptotes at x = 5 and x = -3Hole in the graph at x = -1Horizontal Asymptote at y = 7Leave your answer in factored form (do not multiply the factors out)
On Sunday, Christina's savings account balance was $315.12.
On Monday,
she withdraws $78.95 and $143.80. She deposits
$63.29 on Tuesday. What is her balance after the deposit?
Suppose the Rocky Mountains have 72 centimeters of snow. Warmer weather is melting the snow at a rate of
5.8 centimeters a day. If the snow continues to melt at this rate, after seven days of warm weather, how much
snow will be left?
Answer:
31.4 cm
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value when x is zero, so the initial value.
If the initial amount of snow is 72 cm, the y-intercept is 72.
The slope is the rate of change.
If the snow is melting at a rate of 5.8 cm per day, then the rate of change is -5.8.
Therefore, the equation that models the given word problem is:
[tex]\boxed{\begin{minipage}{5.4 cm}\phantom{w}\\$y=-5.8x+72$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is height of the snow in cm. \\ \phantom{ww}$\bullet$ $x$ is the time in days.\\\end{minipage}}[/tex]
To find how much snow is left after 7 days, substitute x = 7 into the found equation:
[tex]\implies y=-5.8(7)+72[/tex]
[tex]\implies y=-40.6+72[/tex]
[tex]\implies y=31.4[/tex]
Therefore, there will be 31.4 cm of snow left after seven days of warm weather.
The half-life of silicon-32 is 710 years. If 50 grams is present now, how much will be present in 700 years?(Round your answer to three decimal places.)A) OB) 25.245C) 0.054D) 46.697
In this type of question, we will use the exponential equation
[tex]y=a(b)^x[/tex]Where:
a is the initial amount
b is the factor of growth or decay
Since it is a half-life, then
b = 1/2 = 0.5
Since it is now 50 grams, then
a = 50
Since x is the number of years, then
x = 700
Substitute them in the rule above
[tex]\begin{gathered} y=50(0.5)^{700} \\ y=0 \end{gathered}[/tex]It will be representing 0 grams after 700 years
The answer is A
Write the equation of a circle given the center (2, 9) and raduis r = 3.
Answer:
[tex](x-1)^2+(y-9)^2=3^2[/tex]
Step-by-step explanation:
The standard form of the equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Where a and b are the x and y, coordinates, and r is the radius.
So, you can just substitute the a and b values for the x and y values of the center to find the equation of the circle.
Circle A has center (0, 0) and radius 3. Circle B has center (-5, 0) and radius 1. What sequence of transformations could be used to show that Circle A is similar to Circle B?
A translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) with a scale factor of 1 / 3 are necessary to transform circle A into circle B. (Correct choice: D)
What sequence of rigid transformations can be done on a circle
In this problem we must determine the sequence of transformations require to transform circle A into circle B. From analytical geometry we know that the equation of the circle in standard form is:
(x - h)² + (y - k)² = r²
Where:
(h, k) - Coordinates of the center.r - Radius of the circle.Then, we need to apply the following rigid transformations:
Translation
f(x, y) → f(x - h, y - k), where (h, k) is the translation vector.
Dilation with center at the center of the circle
r → k · r, where k is the scale factor.
The circle A is represented by x² + y² = 3, then we derive the expression for the circle B:
f(x, y) → f(x + 5, y - 2)
(x + 5)² + (y - 2)² = 9
r → k · r
(x + 5)² + (y - 2)² = (1 / 3)² · 9
(x + 5)² + (y - 2)² = 1
Then, a translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) are necessary to transform circle A into circle B.
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A math student compared the values of 17 and 60 on a number line. Which statement about the two values is true? Select one: A. The values of 17 and 60 are the same. B. The value of 17 is about 8, and the value of 60 is about 30. C. The values of both 17 and 60 are between the same two integers on a number line. D. The value of 17 is less than 5, and the value of 60 is greater than 7.
Given the two numbers, let us simplify to find the value;
[tex]\begin{gathered} \sqrt[]{17}=4.12 \\ \sqrt[]{60}=7.75 \end{gathered}[/tex]From the derived value, we can find which of the statements is true.
From the options, we can see that the only option that is entirely true is;
- The value of root 17 is less than 5, and the value of root 60 is greater than 7.
[tex]\begin{gathered} \sqrt[]{17}=4.12<5 \\ \sqrt[]{60}=7.75>7 \end{gathered}[/tex]What is the largest volume a sphere can have if it is covered by 6m2 of fabric?
The formula for determining the surface area of a sphere is expressed as
Surface area = 4 * pi * radius^2
From the information given,
surface area = 6
pi = 3.14
thus,
6 = 4 * 3.14 * radius^2
6 = 12.56radius^2
[tex]\begin{gathered} radius^2\text{ = }\frac{6}{12.56}=0.478 \\ \text{radius = }\sqrt[]{0.478} \\ \text{radius = 0.69} \end{gathered}[/tex]The formula for determining the volume of a sphere is expressed as
Volume = 4/3 * pi * radius^3
Thus,
Volume of sphere = 4/3 * 3.14 * 0.69^3
Volume of sphere = 1.38m^3
Which equation could be represented by the number line?
An equation which could be represented by the number line is: D. -5 + (-1) = -6.
What is a number line?A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to compare or determine the difference between two numbers. Additionally, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
From the number line shown above, we have:
Distance = -5 + (-1)
Distance = -5 - 1
Distance = -6.
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Recite pi - First 1000 decimal places
Pi (π) is an irrational number that can be found by dividing the radius of a circumference by its diameter.
The digits of π considering the first 1,000 digital places are:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989
what is the lcm of the rational algebraic equation 6/x+x-3/4=2
The lcm of the rational algebraic equation 6/x+x-3/4=2 be (24 -3x - 4x²) / 4x = 0.
What is LCM?The least common multiple is defined as the set of numbers with the least common multiple. The lowest positive integer with more than one factor in the set is HCF.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We must find the lcm of the rational algebraic equation.
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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1. Write the other side of this equation so that this equation is true for all values of u.2. Write the other side of this equation so that this equation is true for no values of u6(u-2)+2
SOLUTION
Given the question in the question tab, the following are the solution steps for the answer
Step 1: Write out the equation
[tex]6(u-2)+2[/tex]Step 2
A ladder 10 ft long rests against vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.7 of ft/s, now fast (in rad/s) is
the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the
angle's rate of change when the bottom of the ladder 8 ft from the wall.)
Wall
Check the picture below.
[tex]cos(\theta )=\cfrac{x}{10}\implies \stackrel{chain~rule}{-sin(\theta )\cdot \cfrac{d\theta }{dt}}=\cfrac{1}{10}\cdot \cfrac{dx}{dt} -sin(\theta )\cdot \cfrac{d\theta }{dt}=\cfrac{1}{10}(0.7)[/tex]
[tex]\cfrac{d\theta }{dt}=\cfrac{0.07}{-sin(\theta )}~\hfill \stackrel{\textit{when the ladder's bottom is 8ft, x = 8}}{sin(\theta )=\cfrac{8}{10}\implies sin(\theta )=\cfrac{4}{5}} \\\\\\ \cfrac{d\theta }{dt}=-\cfrac{0.07}{~~ \frac{4 }{5 } ~~}\implies \implies \cfrac{d\theta }{dt}=-0.07\cdot \cfrac{5}{4}\implies {\Large \begin{array}{llll} \cfrac{d\theta }{dt}=-0.0875~\frac{rad}{s} \end{array}}[/tex]
the rate is negative because the angle is decreasing as the ladder slides outwards.
tanja wants to establish an account that will supplement her retirement income beginning 10 years from now. find the lump sum she must deposit today so that $200,000 will be available at time of retirement, if the interest rate is 6%, compounded quarterly. (round to the nearest cent as needed)
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]And for this case
n= 4 compounded quarterly
t= 10 years
A= 200000
P=?
r=0.06
And we can solve for P and we got:
[tex]P=\frac{200000}{(1+\frac{0.06}{4})^{4\cdot10}}=110252.5[/tex]So then the final answer would be:
110252.5
write the next three terms of the arithmetic sequence. 4, 3 3/4, 3 1/2, 3 1/4.
In an arithmetic sequence, the consecutive terms differ by a common difference. This means that the second term minus the first term would be equal to the third term minus the second term. The pattern continues.
Looking at the sequence, the common difference is
3 3/4 - 4 = 3 1/2 - 33/4 3 1/4 - 3 1/2 = - 1/4
The next term after 3 1/4 would be 3 1/4 + - 1/4 = 3 1/4 - 1/4 = 3
The next term after 3 would be 3 + -
Choose the point which shows the correct location for the polar coordinate (3, -45°)
The argument of the polar coordinate is -45 degrees, which can be converted as,
[tex]\begin{gathered} \theta=360^{\circ}-45^{\circ} \\ =315^{\circ} \end{gathered}[/tex]Thus, the required point is D.
I dont understand the part "Would this be true if the numbers were-3, 5, -16, and -10?"
Yes, the numbers will be similar.
it will be true if the numbers were -3, 5, -16 and -10
Explanation:
The first list: -3, 5, 16 and -10
Arranging from least to greatest:
-10, -3, 5, 16
Arranging the same numbers from closest to zero to farthest to zero:
Let's use zero as our reference. Then start arranging towards the left and right side of it.
-10, -3, 0, 5, 16
Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:
-10, -3, 5, 16
The second list:
-3, 5, -16, -10
Arranging from least to greatest:
-16, -10, -3, 5
Arranging the same numbers from closest to zero to farthest to zero:
Let's use zero as our reference. Then start arranging towards the left and right side of it.
-16, -10, -3, 0, 5
Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:
-16, -10, -3, 5
Hence, fromt the above: if we arrange the same numbers from least to greatest and from closest to zero to farthest to zero, we would arrive at the same result.
What is the result when 4x3 19x2 + 19x + 13 is divided by 4x + 1? If there is a remainder, express the result in the form q(x) + 6(2):
Answer:
[tex]\frac{4x^3-19x^2+19x+13}{4x+1}=(x^2-5x+6)+7[/tex]30 locusts eats 420g of grass in a week ,how many days will 21locust take to eat 420g at the same rate .
420/30=14g
14g =2g why is 14g =2g
It will take 4.9 days for 21 locust to eat 420 grams of grass
How to determine the number of days?From the question, we have the following parameters:
Initial number of locust = 30Initial number of days = 7 days i.e. 1 weekNew number of locust = 21Given that the amount of grass is constant at 420 grams
The given parameters can be represented using the following ratio
Ratio = Locust : Days
So, we have
Locust : Days = 30 : 7
When there are a total number of 21 locust eating the grass, then we have
21 : Days = 30 : 7
Express as fraction
Days/21 = 7/30
This gives
Days = 21 * 7/30
Evaluate
Days = 4.9
Hence, the number of days is 4.9 days
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