The most appropriate choice of slope of a curve will be given by
Slope of the curve at x = 1.2 = -25
First option is correct
What is slope of a curve?
Slope of curve at a point is the tan of the angle that the tangent to the curve at that point makes with the positive direction of x axis.
Here,
f(x) = [tex]\frac{1}{x - 1}[/tex]
[tex]f^{'}(x) = \frac{d}{dx} (\frac{1}{x-1})[/tex]
= [tex]-(x -1)^{-2}[/tex]
= [tex]-\frac{1}{(x-1)^2}[/tex]
At x = 1.2,
Slope = [tex]f^{'}(1.2) = -\frac{1}{(1.2 - 1)^2}[/tex]
= -[tex]\frac{1}{0.04}[/tex]
= -25
First option is correct
To learn more about slope of a curve refer to the link:
https://brainly.com/question/27958086
#SPJ13
How to simplify the 6th root of y^21
The simplified expression is [tex]y^{\frac{7}{2} }[/tex]
How is the given expression simplified?
[tex]6\sqrt{y^{21} } \\\\= [(y)^{21} ]^{\frac{1}{6} } \\\\[/tex]
By applying power rule of exponents ,
[tex]6\sqrt{y^{21} } =[/tex] [tex]y^{\frac{7}{2} }[/tex]
What is power rule of exponents?
The exponent power rule is [tex](a^{m} )^{n} = a^{mn}[/tex]Exponent times power is how you raise a number with an exponent to a power.When a base is raised to a power and then the entire expression is raised to another power.An algebraic expression can be made simpler by using the power of a power rule in exponents.To learn more about power rule, refer:
https://brainly.com/question/819893
#SPJ9
The abbreviated form is
How is the expression that is given simplified?
by using the exponents' power rule.
What is the exponents power rule?
Exponent power rule states that
You increase a number with an exponent to a power by multiplying the exponent by the power.when the expression as a whole is raised to a higher power after raising a base to that powerThe power of a power rule in exponents can be used to simplify an algebraic expression.To learn more about power rule refer to:
brainly.com/question/819893
#SPJ9
The prism below is made of cubes which measure 3 of a centimeter on one side. What is the volume? NORSKEREN OA. LICO cubic cm OB. 8 cubic cm oc. i cubic cm 8 OD cubic cm 27
Recall that for a cube of this form
where the side is of length a, then the volume is calculated by the expression
[tex]a^3[/tex]So, to define the volume of the given cube, we should calculate the side's length of the bigger cube, based on the small cube
If we take a look at the front side of the cube we would look something like this
So, we want to determine the length's side of this square. We can see that in this case the length side corresponds to adding twice the length of one of the small cube. So the side's length of the new cube is
[tex]\frac{1}{3}+\frac{1}{3}=\frac{2}{3}[/tex]So, the volume of the bigger cube is
[tex](\frac{2}{3})^3^{}=\frac{2^3}{3^3}=\frac{8}{27}[/tex]So the volume of the bigger cube is 8/27 cubic centimeters
prove that the sum of the lengths of the diagonals of a quadrilateral is less than the perimeter but greater than the half of the perimeter of this quadrilateral
Let us consider a quadrilateral ABCD (as shown in the figure below) such that AC and BD are the two diagonals of ABCD.
Now, in triangle ABC and triangle ADC, by using the properties of triangle inequality we have-
AB +BC > AC .... (1)
and AD + CD >AC .... (2)
adding equations (1) and (2) we get-
AB+ BC+CD+AD > 2AC .... (3)
Similarly for diagonal BD we get-
AB+BC+CD+AD > 2BD .... (4)
Adding equations (3) and (4) we get-
2(AB+BC+CD+AD) > 2(AC+BD)
⇒ (AB+BC+CD+AD) > AC+BD
here (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence, we have proven that the sum of the length of the diagonals of a quadrilateral is less than the perimeter.
Now the 2 diagonals divide the quadrilateral into 4 quadrilaterals
Therefore, AO+OD > AD
OD+OC > CD
OC+OB > BC
and OA+OB > AB
Adding all these equations-
2(AC+BD)>AB+BC+CD+AD
⇒AC+BD > 1/2(AB+BC+CD+AD)
Hence, we've proven that the sum of the length of the diagonals is greater than the half of the perimeter of this quadrilateral.
Learn more about quadrilaterals here-
https://brainly.com/question/26690979
#SPJ1
the circumference of the circle is 76 cm. what is the area? using 3.14 for pi round to the nearest square cm
The circumference of a circle is gotten using the formula below;
[tex]\begin{gathered} C=2\pi r \\ \text{Where r is the radius of the circle} \end{gathered}[/tex]Step 1: Let's find the value of the radius;
[tex]\begin{gathered} C=2\pi r \\ r=\frac{C}{2\pi} \\ r=\frac{76}{2\times3.14} \\ r=\frac{76}{6.28} \\ r=12.10\operatorname{cm} \end{gathered}[/tex]Step 2: The area of the circle is given as;
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius of the circle} \\ A=3.14\times(12.10)^2 \\ A=459.73 \\ A=460\operatorname{cm}^2 \end{gathered}[/tex]Hence, the area of the circle is 460 square centimeters.
Find an equation for the line that bisects QII and QIV. Write your answer in general form.
Consider the equation y= mx+b
he line bisects two Quadrants II and IV,It passes through the origin.
the y intercept is =0
thus, the equation will be y=x
but the line is from the II to IV quadrants
the equation is y=-x.
Identify all the sets to which the number belongs. Choose from rational number, irrational number, whole number, and itenger. 0.62478916532
0.62478916532 is an irrational number
This is because it cannot be expressed as a rational number except in surd form which is also known to be irrational. it is neither a whole number nor an integer too
ANSWER => Option B
I don’t know how to do 4 - 6mod6
Modulus (mod) symbol is a symbol that is used to find the remainder of the quotient of two integers
6mod6 means we need to find the result of the remainder if 6 is divided by 6.
Take the ratio of the integers
6/6 = 1.0
Multiply the result by the denominator
1.0 * 6 = 6
Take the difference of the result and the denominator
Remainder = 6 - 6
Remainder = 0
This shows that 6mod6 = 0
Substitute into the original expression
[tex]4-6mod6=4-0=4[/tex]A pizza parlor offers a choice of 12 different toppings. How many 2-topping pizzas are possible? (no double-orders of toppings are allowed)
==========================================================
Explanation:
There are 12 choices for the first topping and 11 for the next topping. The decrease is to account for the fact we cannot select a repeat topping.
That gives 12*11 = 132 permutations. If order of toppings mattered, then this would be our final answer.
However, the topping order doesn't matter. So we need to divide by 2 to correct for the double counting.
There are 132/2 = 66 combinations.
------------
Alternative Method:
n = 12 toppings are available and r = 2 selections are allowed
Order doesn't matter so we use the nCr combination formula
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\12 C 2 = \frac{12!}{2!*(12-2)!}\\\\12 C 2 = \frac{12!}{2!*10!}\\\\12 C 2 = \frac{12*11*10!}{2!*10!}\\\\ 12 C 2 = \frac{12*11}{2!}\\\\ 12 C 2 = \frac{12*11}{2*1}\\\\ 12 C 2 = \frac{132}{2}\\\\ 12 C 2 = 66\\\\[/tex]
There are 66 combinations
Notice the 2nd to last step involves 132/2 which was mentioned in the previous section.
What is type of angle is it vertical complementary supplementary or none of the above I will reward you greatly if you answer
In the given figure,
∠a and ∠b are complementary angles.
This is because ∠CXB + ∠a + ∠b = 180° .........(as they form linear pairs)
∠CXB = 90° ..........(given)
Hence,
∠a + ∠b = 90°
What are Complementary Angles?Two angles whose total is 90 degrees are referred to as complementary angles in geometry. To put it another way, complimentary angles are two angles whose sums equal 90 degrees. 60° and 30°, for illustration. By adding up the two angles' measurements, one can determine the complement and supplement of the two angles. Complementary angles are those where the sum of the two angles equals the measurement of a right angle. They are referred to as adjacent complementary angles if they share a vertex and an arm. It is referred to as non-adjacent complementary angles when two complementary angles are NOT contiguous.To learn more about Complementary angles, refer to:
https://brainly.com/question/5708372
#SPJ13
(x*y)a=xa*ya illustrates which property of exponents
Consider the given equation,
[tex](x\cdot y)^a=x^a\cdot y^a[/tex]This equation represents the Product Rule of the exponents.
The properties of exponents are the general rules and laws, followed by the exponents. These are used very frequently, so it is better to memorize these standard properties.
Susan works as a Hostess where she makes $8.75 per hour she also babysitting earns $10 per hour last week she made $165 if she works 6 hours more as a Hostess than she did babysitting how many hours did she babysit last week?
6 hours as babysitter last week
1) Gathering the data
Hostess
8.75h
Babysitting
10h
2) Based on that, we can write out the following equation, considering that Susan worked 6 hours more:
8.75(h+6) +10h= 165 Distribute the factor 8.75
8.75h +52.5 +10h = 165 Combine like terms
18.75h = 165 -52.5 Subtract from both sides 52.5
18.75h = 112.5 Divide both sides by 18.75
h =6
3) Hence, we can conclude that Susan worked as a hostess for 12 hours and as a baby sitter 6 hours last week
The Massive Chemical Corporation starts an annuity to pay for the huge government penalties they expect in 11 years when a pending case finally gets litigated.Their lead attorney informs them that they can expect a $4,000,000 fine. An investment house offers 11.5% interest on annuities of that size, compoundedsemiannually. What will the semiannual payment be on this annuity? Round to the nearest cent.
To solve this problem we can use the formula for compound interes so the equation is:
[tex]Y=P_o(1+I)^t[/tex]Show where the expression in number 8 would be on a unit circle
Solution
Step 1:
Write the expression
[tex]cos270\text{ }[/tex]Step 2
[tex]\begin{gathered} cos270\text{ = 0} \\ sin270\text{ = -1} \\ (0,\text{ -1\rparen} \end{gathered}[/tex]Question 8 Second part
[tex]\begin{gathered} sin(\frac{16\pi}{3})\text{ = sin960 = sin\lparen960 - 2}\times360)\text{ = sin240} \\ sin(\frac{16\pi}{3})\text{ = }\frac{-\sqrt{3}}{2} \\ cos(\frac{16\pi}{3})\text{ = }\frac{-1}{2} \end{gathered}[/tex][tex](\frac{-1}{2},\text{ }\frac{-\sqrt{3}}{2})[/tex]Which of the following values are solutions to th I. 2 II. – 6 None O I only Submit Ang O II only O III only I and II I and III O II and III I, II and III
ok, but the inequality is not complete in the picture
[tex]\begin{gathered} \text{ 1 }\leq\text{ 1 - 2x} \\ \text{ 1 - 1 }\leq\text{ -2x} \\ \text{ 0 }\leq\text{ -2x} \\ \text{ 0/-2 }\ge\text{x} \\ \text{ 0 }\ge\text{ x} \end{gathered}[/tex]Sam takes 4 hours to peel 32 potatoes, while Josh takes 5 hours to peel 30 potatoes. How mnay potatoes will they peel together in 12 hours
To determine the amount of potato peeled in 12 hours:
Sam takes 4 hours to peel 32 potatoes
Sam take 1 hour to peel 32 / 4 potato
[tex]\begin{gathered} 4\text{ hour }\Rightarrow\text{ 32 potato} \\ 1\text{ hour }\Rightarrow\text{ }\frac{32}{4} \\ 1\text{ hour }\Rightarrow\text{ 8 potato} \\ \end{gathered}[/tex]Josh takes 5 hours to peel 30 potatoes
Josh takes 1 hour to peel 30 / 5 potato
[tex]\begin{gathered} 5\text{ hour }\Rightarrow\text{ 30 potato} \\ 1\text{ hour }\Rightarrow\text{ }\frac{30}{5} \\ 1\text{ hour }\Rightarrow\text{ 6 potato} \end{gathered}[/tex]Sam peels 8 potato
They will peel hepotatoeel together in 12 hours
Answer:
168
Step-by-step explanation:
Two rows of fluorescent lamps are installed in an office on the same branch circuit, with each row drawing 12.5 amperes. The source voltage is 277 volts, and the line resistance is 0.5 Ω. The wire used has a constant (k) of 12.6. The voltage drop will be within the recommendation of the NEC.
Farmer Anders' pumpkin patch is shown below.
19 yards ,
11 yards ,
48 yards and
22 yards.
He purchases fertilizer that costs $2.68 per square foot of coverage, but he has a coupon for half off.
How much will he spent to apply fertilizer to the entire patch.
Please help me answer!
If the cost of fertilizer is $2.68 per square foot of coverage then the farmer need to spend an amount of $5085.3 to apply fertilizer to the entire patch.
Given that the farmer Anders' pumpkin patches are such that they are in rectangle and the lengths are 19 yards and 48 yards and the breadths are 11 yards and 22 yards.
We are required to find the amount of money that the farmer need to spend to apply the fertilizer to the entire patch.
Area which is covering the entire patch=11*19+22*48
=209+1056
=1265 square yards
We know that 1 yard=3 foot
Area in foot=1265*3
=3795 square foot
Amount for fertilizer=3795*3
=$10170.6
Since 1/2 is off so it will be $5085.3 ($10170.6/2).
Hence if the cost of fertilizer is $2.68 per square foot of coverage then the farmer need to spend $5085.3 to apply fertilizer to the entire patch.
Learn more about area at https://brainly.com/question/25292087
#SPJ1
On a number line, the coordinates of X, Y, Z, and W are -7, -3, 1, and 5, respectively. Find the lengths of the two segments below. Then tell whether they are congruentXY and ZWThe length of XY isThe length of ZW is(Type an integer or a decimal.)(Type an integer or a decimal.)
The Solution:
Given:
[tex]\begin{gathered} X=-7 \\ Y=-3 \\ Z=1 \\ W=5 \end{gathered}[/tex]Required:
Determine whether segment XY is congruent to segment ZW.
Step 1:
Find the length of segment XY.
[tex]XY=-3-(-7)=-3+7=4[/tex]Step 2:
Find the length of segment ZW.
[tex]ZW=5-1=4[/tex]Since:
[tex]\begin{gathered} XY=ZW=4 \\ It\text{ follows that XTY and ZW are congruent.} \end{gathered}[/tex]Answer:
XY = 4
ZW = 4
They are congruent.
Solve using the quadratic formula
Kennedy's car used 16 gallons to travel 288 miles. How many miles can the car go for
each gallon of gas?
Answer:
18 miles
Step-by-step explanation:
The car needs 16 gallons to travel 288 miles. We can divide by 16, kind of like dividing on both sides of an equation, to get that with 1 gallon, the car can travel 288/16=18 miles.
What is the volume of a cone with height of 80 km and diameter 21 km?
The volume of a cone with height of 80 km and diameter 21 km is 9240km³.
How to determine the volume of a cone?Volume of a cone=R^2H/3
Diameter=21
To get the radius is half of diameter,:
Radius(R)= Diameter/2= 21/2=10.5kM
Height=80km
Volume=22/7×10.5^2×80/3
The volume of the Cone= 9240km^3
Read more about Cone
https://brainly.com/question/29224025
#SPJ1
To "double" a number means to multiply by two. It is often useful to be able to estimate the double of a number using mental math (without a calculator).
For example, a shirt costs $59. Estimate the cost to buy 2 shirts (disregard the tax).
Double the number $59 is $118 after applying the mental math, the answer is $118.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that:
To "double" a number means to multiply by two.
From the definition of the arithmetic operation, the operation in which we do the addition of numbers, subtraction, multiplication, and division.
Using mental math it can be easy to determine the double a number.
The number is $59
To double:
= 59 + 59
= 50 + 9 + 50 + 9
= 100 + 18
= $118
Thus, double the number $59 is $118 after applying the mental math, the answer is $118.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ1
how to write the standard equation for the hyperbola that is on the graph
The standard form of the hyperbola:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}\text{ = }1[/tex]The center of the hyperbola is at (h, k) = The point where the lines intersect
(h, k) = (0, 0)
For hyperbola:
c² = a² + b²
b is gotten by tracing the value of a to the intersecting line. Trace 3 down to the x axis. you get 5.
[tex]\begin{gathered} a\text{ = distance from center to vertex} \\ \text{the hyperbola coordinate = (0, a) = }(0,\text{ 3)} \\ \text{the other one = (0, -a) = (0, -3)} \\ \text{Hence, a = 3} \end{gathered}[/tex][tex]\begin{gathered} c\text{ = distance from the center to the focus point} \\ b\text{ = 5 and -b = 5} \\ c^2=3^2+5^2 \end{gathered}[/tex][tex]\begin{gathered} c^2\text{ = 9+25 = 34} \\ c\text{ = }\sqrt[]{34} \\ c\text{ = 5.83} \end{gathered}[/tex]The equation becomes:
[tex]\begin{gathered} \frac{(y-k)^2}{5^2}-\frac{(x-h)^2}{3^2}=\text{ }\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{3^2} \\ =\text{ }\frac{y^2}{25}-\frac{x^2}{9} \end{gathered}[/tex]A student has 30 dimes and nickels. Their total value is $2.70. If d = number of dimes and n = number of nickels, this system of equations represents the situation:
d + n = 30
0.10d + 0.05n = 2.70
How many of each type of coin are there? Solve the system to answer the question.
A.
24 dimes and 6 nickels
B.
20 dimes and 10 nickels
C.
10 dimes and 20 nickels
D.
6 dimes and 24 nickels
Taking into account the definition of a system of linear equations, a student has 24 dimes and 6 nickels.
System of linear equationsA system of equations is a set of equations in which there are two or more variables, the goal of which is to find all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.
In other words, a system of linear equations is a set of two or more first degree equations that relate two or more unknowns, in which it is desired to find the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, a system of linear equations must be proposed taking into account that:
d = number of dimes.n = number of nickels.You know that:
A student has 30 dimes and nickels. The total value is $2.70.The system of equations to be solved is
d + n = 30
0.10d + 0.05n = 2.70
It is decided to solve it using the substitution method. This method consists of isolate one of the variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "d" from the first equation:
d= 30 -n
Replacing the expression in the second equation:
0.10×(30 - n) + 0.05n = 2.70
Solving:
0.10×30 - 0.10n + 0.05n = 2.70
3- 0.10n + 0.05n = 2.70
- 0.10n + 0.05n = 2.70 -3
-0.05n= -0.3
n= (-0.3)÷ (-0.05)
n= 6
Remembering that d=30 -n you get:
d= 30 - 6
d= 24
There are 24 dimes and 6 nickels.
Learn more about system of equations:
brainly.com/question/2172700
brainly.com/question/14323743
brainly.com/question/1365672
brainly.com/question/20533585
#SPJ1
the cost price of 24 articles is the selling price of 15 articles find the gain percentage
Answer:
Step-By step explanation:
A jewelry store sells a necklace at $365 that was original purchased at $240, what is the markup? Round your answer to the nearest whole percent.
We are given a selling price of $365 and a purchase cost of $240, we are asked to find the markup. The formula for calculating the mark up is the following:
[tex]\text{markup}=\frac{sale\text{ price-cost}}{\cos t}[/tex]we have that the sale price is 365 and the cost is 240. Replacing in the formula:
[tex]\text{markup}=\frac{365-240}{240}[/tex]solving the operations we get:
[tex]\text{markup}=\frac{125}{240}=0.52[/tex]This can be expressed as a percentage like this:
[tex]\text{markup}=52\text{ percent}[/tex]the markup is 52%
PLEASE HELP FOR 20 POINT! The area model shows 3 and one-fourth. What is 3 times 3 and one-fourth?
An area model has 4 shaded rectangles. An area model has 4 shaded rectangles. An area model has 4 shaded rectangles .An area model has 1 shaded rectangle and 3 unshaded rectangles.
3 and one-fourth
3 and three-fourths
9 and one-fourth
9 and three-fourths
The multiplication of the mixed number 3 1/4 by 3 has a result given as follows:
9 and three-fourths.
Mixed numbersA mixed number is modeled as follows:
a b/c.
In which the integer and the fractional parts are given as follows:
a is the integer part of the number.b/c is the fractional part of the number.To apply multiplication involving mixed numbers, we convert these numbers to fractions, as follows:
a b/c = (ac + b)/c
In this problem, the mixed number is given as follows:
3 1/4.
Hence the fraction is given as follows:
(3 x 4 + 1)/4 = 13/4
The multiplication by 3 is given as follows:
3 x 13/4 = 39/4.
The division of 39 by 4 has a quotient of 9 and a remainder of 3, hence the mixed number that represents the division is:
9 and three-fourths.
Learn more about mixed numbers at brainly.com/question/21610929
#SPJ1
Find two points on the line.4y + 2x = 7
Given the equation of a line:
4y +2x = 7
It's required to find two points on the line.
Solving for y:
[tex]y=\frac{7-2x}{4}[/tex]We give x any value and calculate the corresponding value of y.
For example, for x = 1:
[tex]y=\frac{7-2(1)}{4}=\frac{5}{4}[/tex]The point is (1, 5/4)
Now for x = -4:
[tex]y=\frac{7-2(-4)}{4}=\frac{15}{4}[/tex]The point is (-4, 15/4)
do you think you'd be able to help me out here
1) Let's make a graph for that round trip with stops.
2) Continuing the graph, on the way back
Considering that every time the plane stops, its altitude goes down to 0, i.e. a point in the x-axis, then we can count 4 stops, 1 in the Chicago-NY and 3 on the way back. Considering that the graph touches the x-axis when it lands then the graph touches 6 times
A jellybean company produces 1,680 jellybeans per second. One box of jellybeans contains 50 jellybeans. What is this company’s production rate, in boxes of jellybeans per minute?
Answer:
2016
Step-by-step explanation:
1680:50=33.6
33.6x60=2016
