The eqaution of the tangent at the point x = -1 is:
[tex]y=-12x-8[/tex]To solve this, first, we need to find the value of y when x = -1:
[tex]f(-1)=(3\cdot(-1)+1)^2=(-3+1)^2=(-2)^2=4[/tex]Then we want to find the equation of the tangent at the point (-1, 4)
The next step is to find the derivative of the equation, because the derivative thell us the slope of the tangent line at a certain point:
[tex]\begin{gathered} f(x)=(3x+1)^2 \\ f^{\prime}(x)=2(3x+1)\cdot3=6(3x+1)=18x+6 \\ \\ f^{\prime}(x)=18x+6 \end{gathered}[/tex]Now that we have the derivative, let's calculate the slope of the tangent like in the point (-1, 4). To do this, we evaluate the derivative in x = -1:
[tex]f^{\prime}(-1)=18\cdot(-1)+6=-18+6=-12[/tex]The slope of the tangent line is -12.
Now we have all the necessary things to construct the equation of a line: we have the slope (-12) and a point (-1, 4).
The slope-point form of a line is:
[tex]\begin{gathered} y=m(x-x_0)+y_0 \\ \end{gathered}[/tex]Where m is the slope and x0, y0 are the x and y coordinates of a point
Then:
[tex]\begin{gathered} \begin{cases}m=-12 \\ x_0=-1 \\ y_0=4\end{cases} \\ y=-12(x-(-1))+4=-12\mleft(x+1\mright)+4=-12x-12+4=-12x-8 \end{gathered}[/tex]And that's the equation of the line y = -12x - 8
Can u solve it please
Answer:
1. you have to write down Some nubers in the koordinatsystem
than you can read that it is(if you use only one Box) (-6|5)(6|1)
Fill out this whole column in an organized manner please
We can calculate the slope as:
[tex]S=\frac{{\Delta}Y}{\Delta X}[/tex]From this, we have: (FIRST ANSWER)
[tex]\begin{gathered} S_{ZY}=\frac{0-\mleft(-3\mright)}{1-6}=-\frac{3}{5} \\ S_{YX}=\frac{-6-(-3)}{1-6}=\frac{3}{5} \\ S_{XW}=\frac{-3-(-6)}{-4-1}=-\frac{3}{5} \\ S_{WZ}=\frac{-3-0}{-4-1}=\frac{3}{5} \end{gathered}[/tex]The length of the non-parallel sides can be measured as:
[tex]L=\sqrt[]{(\Delta Y)^2+(\Delta X)^2}[/tex]From this, we have: (SECOND ANSWER)
[tex]\begin{gathered} L_{ZW}=\sqrt[]{(1-(-4))^2+(0-(-3))^2}_{}=\sqrt[]{25+9}=\sqrt[]{34} \\ L_{ZY}=\sqrt[]{(6-1)^2+(-3-0)^2}=\sqrt[]{25+9}=\sqrt[]{34} \end{gathered}[/tex]From the figure in the beginning and the values we found, this is a Rhombus.
yaretzyΣ 21. $1,500 is deposited into a savings account that earns 2.5% simple interest for 4years. How much interest will be earned in the 4 years? *Your answer
We have the next formula to the simple interest
[tex]I=P\times r\times t[/tex]where
I= interest earn after t years
P is the initial deposit
r is the rate
t is the time
P=1500
r=2.5%
t= 4 years
then we substitute the values in the formula
[tex]I=1500(.025)(4)[/tex][tex]I=150[/tex]He will earn $150 after 4 years, his final capital will be $1650
What is debt? How does debt create financial risk and instability?
Debt can be defined as a sum of money that is owed or due.
Debt creates financial risk and instability by:
a) spreading economic pain and hardship to the country's citizens and to other countries.
b) causing Financial losses, market turmoil, and sharp slowdowns in trade and economic growth are some of the ways countries can feel the effects of a debt crisis in other countries.
c)Creating a heavy debt load that you can’t pay off, your credit score will start to go down resulting in a bad credit score and report.
d) leading to stress by limiting your ability to enjoy life. This can result in various health issues.
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. Debt is a deferred payment, or series of payments, differentiating it from an immediate purchase. It can lead to financial risk and instability for both individuals and the state at large.
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The tank of a car holds 10 gallons of gas. How many liters does the tank hold?
Given:
The tank of a car holds 10 gallons of gas.
To find the number of liters does the tank hold:
As we know,
1 gallon = 3.785 liters
So that, for 10 gallons
[tex]\begin{gathered} =10\times3.785 \\ =37.85\text{ liters} \end{gathered}[/tex]Thus, the tank can hold 37.85 liters of gas.
Given f(x), use Remainder Theorem to find f(4). f (x) = 2x^3 – 11x^2 + 7x - 5
To find f(4) you divide the given polynomial into (x-4):
To divide:
1. Divide the first term of the dividend by the highest term of the divisor:
[tex]\frac{2x^3}{x}=2x^2[/tex]2. Multiply the divisor by the result:
[tex]2x^2(x-4)=2x^3-8x^2[/tex]3. Substract the product in step 2 from the appropiat terms of the dividend (when you substract the symbols change) (then bring down the next term from the dividend)
4. Repeat previous steps:
[tex]\frac{-3x^2}{x}=-3x[/tex][tex]-3x(x-4)=-3x^2+12x[/tex][tex]\frac{-5x}{x}=-5[/tex][tex]-5(x-4)=-5x+20[/tex]As the remainder is -25:
[tex]f(4)=-25[/tex]C. 3 to 2 D. 1 to 1Will give brainliest
AS shown in the table :
The number of t-shirts and shorts = 25 + 15 = 40
The number of sunglasses = 10
So, the ratio between them =
[tex]\frac{40}{10}=\frac{4}{1}[/tex]so,the answer will be option B: 4 to 1
What do you know about the role of financial accounting standard setting in the United States? This is actually for an intermediate accounting course in college
The role of financial accounting standard setting in the United States is to establish and improve financial accounting and reporting standards to provide useful information to those who need it.
What is the Financial Accounting Standard?The Financial Accounting Standard is a term to refer to an institution established in 1973 that was created with the objective of establishing financial reporting and accounting standards for public and private companies and non-profit organizations.
What is the role of this institution?The main role of this institution is to create accounting standards focused on public companies. This process of creating accounting standards is focused on promoting financial information in the financial field for different institutions and people interested in investing.
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solve for the unknown angle measure given that f || g
use a system of equations with two variables and two equations to solve.A number is 11 more than another number.twice the sum of the two numbers is 42. find the two numbers
"A number is 11 more than another number" can be expressed as
[tex]x=y+11[/tex]"Twice the sum of the two numbers is 42" can be expressed as
[tex]2(x+y)=42[/tex]So, these two equations for a system. Let's combine them to find y in the first place
[tex]\begin{gathered} 2(x+y)=42 \\ 2(y+11+y)=42 \\ 2(2y+11)=42 \\ 2y+11=\frac{42}{2} \\ 2y+11=21 \\ 2y=21-11 \\ 2y=10 \\ y=\frac{10}{2} \\ y=5 \end{gathered}[/tex]Then, we find x
[tex]x=y+11=5+11=16[/tex]The solution is (16, 5).Lovely Landscapes has been contracted to plant some trees and bushes at a new park in Townsend. They have a budget of $1008. Each tree(x)costs $63 and each bush(y) costs $28. Write the equation that represents the situation: no spaces,no dollar signs
The equation will be
[tex]63x+28y=1008[/tex]HELP ASAP PLS PLS PLS
Jimmy earned $6840 from the gift basket sold
What is selling price ?
The selling price is how much a buyer pays for a product or service.
Given,
Number per basket for fruits = 12
Total number of fruits shipped last year = 3,420
Per basket price = $24
Now, we have to find total number of baskets
Total number of baskets = 3420 / 12
= 285
Total amount jimmy earned = 285 * 24
= $6840
Therefore, Jimmy earned $6840 from the gift basket sold.
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What is the slope of the line described by the equation y+3=-2x
Using the equation of the line, the slope of the line is -2.
How to find the slope of a line?The slope of a line is the change in y with respect to the change in x.
In other words, slope is rise over run.
Therefore, the equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptHence, we will rearrange the equation of the line to get the slope of the line.
y + 3 = - 2x
y = -2x - 3
Therefore, the slope is -2.
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Question in picture will give brainlist
The correct options are first : ∠3 + ∠4 = 180°, third : ∠1 and ∠2 are a linear pair, fourth : ∠2 = ∠4, and fifth : ∠1 = ∠3.
We are given a diagram that has two straight lines that intersect at a point.This results in the formation of four angles ∠1, ∠2, ∠3, and ∠4.The first option is ∠3 + ∠4 = 180°.It is true because ∠3 and ∠4 form a linear pair and are on the same side of the line.The second option is ∠1 = ∠2.It is false because we don't see any relationship between the two angles as such.The third option is ∠1 and ∠2 are a linear pair.It is true because ∠1 + ∠2 = 180°.The fourth option is ∠2 = ∠4.It is true because they are vertically opposite angles.The fifth option is ∠1 = ∠3.It is true because they are vertically opposite angles.To learn more about angles, visit :
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Find x to the nearest tenth.
The value of x = 42
Given : A right angled triangle with the below mentioned measures :
angles ∠ 1 = 28 °
∠ 2= 25° and the length is 600
To find : the value of x
Let us assume the rest of the length is y that is the side opposite of the angle will now be x + y
thus tan 28 ° = [tex]\frac{x+y}{600}[/tex]
tan 28 °= 0.53 thus the equation after cross multiplying becomes ;
0.53 × 600 = x + y
318 = x + y ------------------ equation 1
And tan 25° = [tex]\frac{y }{600}[/tex]
tan 25 ° = 0.46
After cross multiplying we get : 0.46 × 600 = y
=> 276 = y
Substituting this value in equation 1 we get : 318 = x + 276
=> x = 318 - 276
=> x = 42
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Enter values for alien base of the system of equation shown has one solution
we have the system of equations
y=3x+4 ----> equation 1
y=ax+b ----> equation 2
Remember that
The only condition for the system, to have only one solution is that the slopes of both lines are different
so
The values for a are all real numbers except for a=3
The values for b are all real numbers
Therefore
A solution could be
a=2 and b=4The solution is (0,4)
3. The volume of the cone is 4π dm3 and the diameter of the base is 80 cm. Calculate the cone: the area of the base.
Answer:
[tex]Area\text{ of the base = 50.24 dm}^2[/tex]Explanation:
Given:
Volume of the cone = 4π dm³
diameter of the base = 80cm
To find:
the area of the base
The base of a cone is a circle. Area of the base will be area of the circle
[tex]\begin{gathered} Area\text{ of a circle = \pi r}^2 \\ r\text{ = radius} \end{gathered}[/tex]diameter = 80cm
diameter = 2(radius)
radius = diameter/2
radius = 80/2 = 40 cm
We need to convert from cm to dm to get same units
10cm = 1 dm
40cm = 4 dm
let π = 3.14
substitute the values into the formula:
[tex]\begin{gathered} Area\text{ of the circle = 3.14 }\times\text{ 4}^2 \\ Area\text{ of the circle = 50.24} \\ \\ Area\text{ of the base = 50.24 dm}^2 \end{gathered}[/tex]please help me out quickly
[tex]A^{-1} =\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]
[tex]x =\left[\begin{array}{ccc}108\\-14\\22\end{array}\right][/tex]
Given matrix A:
[tex]\left[\begin{array}{ccc}5&-15&-44\\-1&2&6\\1&-3&-9\end{array}\right][/tex]
To find the inverse of the matrix we start by finding the determinant of the matrix.
|A| = 5(-18+18) + 15(9-6) - 44(3-2)
= 0 + 15(3) - 44 = 45 - 44 = 1
As the determinant 1 ≠ 0, hence the inverse of the matrix exists.
Now, we find the minors of each element of the matrix.
m₁₁ = [tex]\left[\begin{array}{ccc}2&6\\-3&-9\end{array}\right][/tex] = 0
m₁₂= [tex]\left[\begin{array}{ccc}-1&6\\1&-9\end{array}\right][/tex] = 3
m₁₃ = [tex]\left[\begin{array}{ccc}-1&2\\1&-3\end{array}\right][/tex] = 1
m₂₁ = [tex]\left[\begin{array}{ccc}-15&-44\\-3&-9\end{array}\right][/tex] = 3
m₂₂ = [tex]\left[\begin{array}{ccc}5&-44\\1&-9\end{array}\right][/tex] = -1
m₂₃ = [tex]\left[\begin{array}{ccc}5&-15\\1&-3\end{array}\right][/tex] = 0
m₃₁ = [tex]\left[\begin{array}{ccc}-15&-44\\2&6\end{array}\right][/tex] = -2
m₃₂ = [tex]\left[\begin{array}{ccc}5&-44\\-1&6\end{array}\right][/tex] = -14
m₃₃ = [tex]\left[\begin{array}{ccc}5&-15\\-1&2\end{array}\right][/tex] = -5
The cofactor matrix can be obtained as:
[tex]\left[\begin{array}{ccc}0&3&1\\3&-1&0\\-2&-14&-5\end{array}\right][/tex]
Now the adjoint of matrix A (written as adj A) by taking the transpose of the cofactor matrix of A is,
[tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]
To determine the inverse of a square matrix A, we use the formula:
A⁻¹ = adj(A) / |A|
Therefore, the inverse of the given matrix is:
A⁻¹ = 1/1 [tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]
It is given, Ax = b
and b = [tex]\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]
Let x be [tex]\left[\begin{array}{ccc}a\\b\\c\end{array}\right][/tex]
Putting values in Ax = b equation,
[tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right]\left[\begin{array}{ccc}a\\b\\c\end{array}\right]=\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-3b-2c\\-3a-b+14c\\a-5c\end{array}\right]=\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]
Equating the three equations with the respective values,
So, -3b - 2c = -2
-3a -b + 14c = -2
a - 5c = -2 ⇒ a+2/5 = c
Solving the above equations we obtain the values of a,b, and c as 108, -14, and 22.
So, the matrix x is
[tex]x =\left[\begin{array}{ccc}108\\-14\\22\end{array}\right][/tex]
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the student council raised 2,790 during its annual fundraiser. the money was shared equally among the events committee the sports committee and the sunshine committee. the sports committee wants to use its share of the money to purchase t shirts. if each t shirt costs $12 what is the greatest number of t shirts the sport committee purchase
The student council raised $2,790 and they have to shared equally among 3 comittees, then:
[tex]\frac{2,790}{3}=930[/tex]Each commitee has a budget of $930, then for the sports committee that wants to purchase t-shirts and each t-shirt costs $12, we can create the following expression:
Let x be the greatest number of t-shirts
[tex]\begin{gathered} 12x=930 \\ x=\frac{930}{12} \\ x=77.5 \end{gathered}[/tex]Rounding, the sport commitee can purchase 77 t-shirts.
The entire graph of the function f is shown in the figure below.
Write the domain and range of f as intervals or unions of intervals.
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
A graph of the function f.
We can see two curves on the graph.
One curve:
Domain = [1, 2]
Range = [-4, 0]
Other curve:
Domain = [-5, -2]
Range = [-3, 3]
We can combine both the curve domain and the range.
Domain = [-5. -2] U [ 1, 2 ]
Range = [-4, 3]
Thus,
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
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The inner core is solid because the inner core consists of a lot of pressure and high temperatures. And the more pressure and high temperatures the more dense the substance gets.
The inner core is solid because the inner core consists of a lot of pressure and high temperatures. This is true.
How to illustrate the information?The pressure surrounding the inner core, as well as the planet's atmosphere, keeps the iron from melting. The iron atoms cannot migrate into a liquid form due to the pressure and density, which are simply too high.
Temperature is a measure of how hot or cold something is, more particularly the average kinetic energy of the particles in an object, which is a sort of energy related with motion. Temperature is a measure of how hot or cold something is represented in terms of one of several scales, including Fahrenheit and Celsius.
Because the inner core is under intense pressure and is extremely hot, it is solid. And the stuff becomes denser as pressure and temperature increase. Therefore, the inner core's high heat and pressure are what are solidifying it since the denser the stuff is, the more solidified it becomes.
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The inner core is solid because the inner core consists of a lot of pressure and high temperatures. And the more pressure and high temperatures the more dense the substance gets. True or false?
find the area of the shaded sector in terms of Pi
Let f(x) = 9x-2 and g(x)=√√3x +7. Evaluate the following. a g (3)-g (-2) b (g (-1))² Let f(x) -f(0)/x
The given functions are f(x) = 9x-2 and g(x)=√(√3x +7) the value of f (3) and g (3) will be 25 and 3.4592.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that f(x) = 9x-2 and g(x)=√√3x +7.
We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.
We have to evaluate the values one by one putting the value of an independent variable as,
a) g (3)
g(x)=√(√3x +7)
g(3) = √(√3(3) +7)
g(3) =√(5.196 + 7 )
g(3) =√(12.196)
g(3) =3.492
b)f (3)
f(x) = 9x-2
f(3) = 9× 3 -2
f(3) = 27 - 2
f(3) = 25
Thus, the given functions are f(x) = 9x-2 and g(x)=√(√3x +7) the value of f (3) and g (3) will be 25 and 3.4592.
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Select the correct answer.Which expression has a value closest to 1? (Use 3.14 as the value of T.)OA.77V10OB. V75-V74OC. 37-V26OD3V5 V20V2
the expression has a value closest to 1 is √37 - √26 (option C)
Explanation:
To determine the expression, we need to solve each of the options.
a) 7π/√10 = 7(3.14) /√10 = 21.98/3.1623
= 6.95
b) √75 - √74 = 8.66 - 8.60
= 0.06
c) √37 - √26 = 6.083 - 5.099
= 0.984
d) (3√5 - √20)/√2 = (6.708 - 4.472)/1.414 = 2.236/1.414
= 1.58
√37 - √26 = 0.984 is closest to 1
From the above, the expression has a value closest to 1 is √37 - √26 (option C)
Please find the square root. Round your answer to the nearest thenth.√121=
Explanation
Step 1
A square root of a number is a value that, when multiplied by itself, gives the number.
hence, we need to find a value(s) that when multiplied by itself gives 121,so
[tex]\sqrt[]{121}=\pm11[/tex]because
[tex]\begin{gathered} 11\cdot11=121 \\ or \\ -11\cdot-11=121 \end{gathered}[/tex]I hope this helps you
So there's a question and it's like a parallelogram and it's for question true and it's 10' by 5' and I'm trying to find out that area
we have that
the area of a parallelogram is
A=b*h
we have
b=10 ft
h=5 ft
so
A=10*5=50 ft2
area is 50 square feeta circular garden has a diameter of 8 yards. what is the area of the garden? use 3.14 for piπ.
To calculate the area of a circle you have to use the following formula:
[tex]A=\pi r^2[/tex]Where
A is the area
π is the number pi, for this exercise you have to use up to its two first decimal values: 3.14
r is the radius.
The radius of a circle is half its diameter, so the radius of the circular garden will be
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{8}{2} \\ r=4\text{yards} \end{gathered}[/tex]Next, you can calculate the area of the circular garden as follows:
[tex]\begin{gathered} A=3.14\cdot(4^2) \\ A=3.14\cdot16 \\ A=50.24yd^2 \end{gathered}[/tex]The area of the circle is 50.24yd²
Factor. v2 + 22v - 23
we can factor this quadratic expression finding the zeros, as follows:
[tex]\begin{gathered} v_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ v_{1,2}=\frac{-22\pm\sqrt[]{22^2-4\cdot1\cdot(-23)}}{2\cdot1} \\ v_{1,2}=\frac{-22\pm\sqrt[]{484+92}}{2} \\ v_{1,2}=\frac{-22\pm\sqrt[]{576}}{2} \\ v_1=\frac{-22+24}{2}=1 \\ v_2=\frac{-22-24}{2}=-23 \end{gathered}[/tex]Then, the quadratic expression can be expressed as
[tex]\begin{gathered} a(v-v_1)(v-v_2) \\ v^2+22v-23=(v-1)(v+23) \end{gathered}[/tex]Find the zeros for:f(x)=x^5+2x^4+11x^3+22x^2+24x+48
The given polynomial
[tex]f\mleft(x\mright)=x^5+2x^4+11x^3+22x^2+24x+48[/tex]To get the zeros of the polynomial, the best way to go about it is the graphical method
Upon graphing the polynomial
we will have
The price of tuition has tripled since my parents went to school - that’s a 200% increase
in price.
The statement makes sense. This is because A 200 percentage increase in price corresponds to a price that is 300% of the original price
How to illustrate the information?You can express a fraction of something using percentages. A change in something can be described using percentages. As an illustration, the price of milk increased by 5% last month.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.
A figure or ratio stated as a fraction of 100 is called a percentage. The % sign is frequently used to indicate it. In this case, 200% of something implies that it will give 300% of the initial amount.
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The price of tuition has tripled since my parents went to school thats a 200% increase in price corresponds to a price that is 300% of the original price. Does this makes sense?
