The answer 2x power of 2 + 3x + 1. Therefore, the answer of the equation is x = 2.
Equation:
An equation is a mathematical operator that contains two algebraic expressions on either side of an equals (=) sign. Shows the equivalence between the expression written on the left and the expression written on the right. Every equation in mathematics has L.H.S = R.H.S (left = right). We can solve an equation to find the value of an unknown variable that represents an unknown quantity. If an expression does not have an equal sign, it is not an equation. This is considered an expression.
Now,
It has been given that
[tex]\frac{2^{3x-1} +10}{7} = 6[/tex]
Cross multiplying, we get
[tex]2^{3x-1} +10 = 42[/tex]
Subtract 10 to both sides
[tex]2^{3x-1} = 32[/tex]
Write 32 in exponent form
[tex]2^{3x-1} = 2^{5}[/tex]
Since, base of both sides of the equation is 2. Hence, the exponent must be equal.
3x - 1 = 5
⇒ 3x = 6
⇒ x = 2
Learn more about Equation:
https://brainly.com/question/29657983
#SPJ4
Express sin T as a fraction in simplest terms
Solving the provided question, we can say that by Pythagoras theorem VT² = 18² + 24² = 900 => VT = [tex]\sqrt{1900} = 30[/tex]
what is Pythagorean theorem?The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.
Pythagoras theorem
VT² = 18² + 24² = 900
VT = [tex]\sqrt{1900} = 30[/tex]
To know more about Pythagorean theorem visit:
https://brainly.com/question/14930619
#SPJ1
solve for x please and thank you
Step-by-step explanation:
this is the process and figure is cointerior
PLEASE HELP (will mark as brainlest)
The solution to the monomial in standard form is 0.04b^19.
What is a standard form of a polynomial?The term "polynomials in standard form" can also refer to a polynomial written in the decreasing order of the degree of the variable.
The degree of the polynomial is significant when writing it in its standard form since the terms are written in descending order of the power of x.
Given that:
= (-0.2b^6)^3*5b
Rewrite using the commutative property of multiplication
= 5(-0.2b^6)^3b
Apply the product rule to −0.2b^6
= 5(-0.2^3)(b^6)^3b
= 5(-0.008b^18)b
= 5(-0.008^19)
= 0.04b^19
Learn more about the standard form here:
https://brainly.com/question/19169731
#SPJ1
$1.76 Red Kidney Beans 400g, Can 1. $1.89 Red Kidney Beans 420g, Can 2. $1.00, Red Kidney beans, 125 g, Can 3. $2.40, Red Kidney Beans, 500g, Can 4. Which can of red kidney beans costs the least per gram?
Answer:
Can 3. $2.40, Red Kidney Beans, 500g, Can. This can costs $0.0048 per gram.
A (4,0).B (1.5), and C(-3,-5) are three vertices of a parallelogram ABCD. What is the ordered pair for D, the fourth vertex of the parallelogram?
Answer: In a parallelogram, opposite sides are equal in length and parallel, so if we subtract the vectors AB and BC from each other, we will get the vector for CD.
Given A = (4,0), B = (1.5,0), and C = (-3,-5), we can calculate the vectors AB and BC as follows:
AB = B - A = (1.5, 0) - (4, 0) = (-2.5, 0)
BC = C - B = (-3, -5) - (1.5, 0) = (-4.5, -5)
Next, we subtract these vectors to find the vector for CD:
CD = BC - AB = (-4.5, -5) - (-2.5, 0) = (-2, -5)
Finally, we add the vector CD to vertex C to find vertex D:
D = C + CD = (-3, -5) + (-2, -5) = (-5, -10)
So, the ordered pair for vertex D is (-5, -10).
Step-by-step explanation:
Convert each rate to a unit rate. $4.25 for 64 fluid ounces 297 miles on 11 gallons of gas 124 feet in ten seconds
Answer:
$4.25 for 64 fluid ounces = $0.06640625 per fluid ounce
297 miles on 11 gallons of gas = 27 miles per gallon
124 feet in 10 seconds = 12.4 feet per second
Step-by-step explanation:
Given f(x)=4(x−2)^3+2, classify each statement about f^−1(x) as true or false.
Choose the answers which are correct or false.
1. The point of symmetry on f^−1(x) is (2,2).
2. The domain of f^−1(x) is (−∞,4).
3. The graphs of f^−1(x) and f(x) are reflections across the line y = x
4. f^−1(x) is not a function.
Answer:
1. True
2. False
3. True
4. False
Step-by-step explanation:
Given function:
[tex]f(x)=4(x-2)^3+2[/tex]
1. Point of SymmetryThe point-of-symmetry of a cubic graph is its point of inflection.
To find the x-value of the point of inflection of a cubic function, differentiate the function twice:
[tex]f'(x)=12(x-2)^2[/tex]
[tex]f''(x)=24(x-2)[/tex]
Set the second differentiated function to zero and solve for x:
[tex]\implies 24(x-2)=0[/tex]
[tex]\implies x-2=0[/tex]
[tex]\implies x=2[/tex]
Substitute the found value of x into the original function to find the y-value of the point of inflection:
[tex]\implies y=4(2-2)^3+2[/tex]
[tex]\implies y=4(0)^3+2[/tex]
[tex]\implies y=0+2[/tex]
[tex]\implies y=2[/tex]
Therefore, the point of symmetry of the cubic function is (2, 2).
The inverse of a cubic function its reflection in the line y = x.
As the point of symmetry is (2, 2), then its reflection in the line y = x is also (2, 2).
So the point of symmetry on f⁻¹(x) is (2, 2).
2. DomainThe given function has an unrestricted domain and range.
Domain of f(x): (-∞, ∞) → all real numbersRange of f(x): (-∞, ∞) → all real numbersThe domain of the inverse function is the range of the function.
The range of the inverse function is the domain of the function.
Therefore, as the domain and the range of the original function are unrestricted, so are the domain and range of the inverse function.
Domain of f⁻¹(x): (-∞, ∞) → all real numbersRange of f⁻¹(x): (-∞, ∞) → all real numbers3. Reflection across the line y = xThe inverse of a cubic function with an unrestricted domain is its reflection across the line y = x.
Therefore, the graphs of f⁻¹(x) and f(x) are reflections across the line y = x.
4. Inverse functionTo find the inverse of the given function, swap x and y:
[tex]\implies x=4(y-2)^3+2[/tex]
Rearrange to make y the subject:
[tex]\implies x-2=4(y-2)^3[/tex]
[tex]\implies \dfrac{x-2}{4}=(y-2)^3[/tex]
[tex]\implies \sqrt[3]{\dfrac{x-2}{4}}=y-2[/tex]
[tex]\implies y=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]
As we have already established, the domain and range of the inverse function are unrestricted. As each x-value has only one y-value associated with it, f⁻¹(x) is a function.
a piece of wire 22cm long is sent into an arc of a circle of radius 4cm . what angle does the wire subtend at the centre of the circle
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=22\\ r=4 \end{cases}\implies 22=\cfrac{\theta \pi (4)}{180}\implies 22=\cfrac{\theta \pi}{45} \\\\\\ (22)(45)=\theta \pi \implies \cfrac{(22)(45)}{\pi }=\theta \implies 315.13\approx \theta[/tex]
In the house, m∠ 1 = 45⁰. Find the measure of ∠ 2.
The value of measure ∠2 is, 135°.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In the house,
⇒ m ∠1 = 45°
We know that;
An exterior angle of a triangle is the sum of two opposite angle of a triangle.
Hence, We can formulate;
⇒ m ∠2 = m ∠1 + 90°
⇒ m ∠2 = 45° + 90°
⇒ m ∠2 = 135°
Thus, We get;
⇒ m ∠2 = 135°
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
Aled and Gareth went on holiday to France.
The total cost of the holiday was £660.
• Aled’s mother paid 1/3 of the total cost.
• Aled and Gareth shared the remaining cost in the ratio 1:9 .
Calculate how much each person paid towards the cost of the holiday.
Answer:
Aled's mother paid £220.
Aled paid £44.
Gareth paid £396.
Step-by-step explanation:
1-(1/3)= 2/3 [fraction of amt. Aled and Gareth paid]
£660×(2/3)= £440 [amt. Aled and Gareth paid]
total units= 1+9
= 10
10 units= £440
1 unit= £440÷10
= £44
9 units= £44×9
= £396
£660×(1/3)= £220
Read the problem.
There are 60 students in the Geneva Middle School marching band. 20% of those
students play the trombone.
Shade the grid to show the percent of students in the marching band who play the trombone.
How many students in the marching band play the trombone? You can use your model to
help.
Answer: If 20% of the 60 students in the Geneva Middle School marching band play the trombone, then 60 * 20% = 12 students play the trombone. To shade the grid to show the percent, you can shade 20 out of 100 squares on the grid, or 1/5 of the total number of squares.
Step-by-step explanation:
In investing $5,750 of a couple's money, a financial planner put some of it into a savings account paying 2% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 12% annual simple interest. The combined interest earned for the first year was $475. How much money was invested at each rate?
$2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned amount for the first year was $475.
The financial planner invested $5,750 of the couple's money. Let x be the amount of money invested in the savings account paying 2% annual simple interest and y be the amount of money invested in the riskier mini-mall development plan paying 12% annual simple interest. Since the combined interest earned for the first year was $475, we can write the equation 2x + 12y = 475. Since the total amount of money invested was $5,750, we can add the equation x + y = 5,750 to our system of equations. Solving the system of equations yields x = 2,250 and y = 3,500. Thus, $2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned for the first year was $475.
Learn more about amount here
https://brainly.com/question/8082054
#SPJ4
Sammie was babysitting and took the kids to McDonalds. She ordered 1 chicken sandwich for herself that cost $2.50 and 2 happy meals. If her total bill was $8.50, how much did each of the happy meals cost?
ASAP I NEED THIS ASAP
b. Measure the length of the side DF.
c. Measure the height of the triangle, XF.
d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.
e. Use compasses to bisect the angle D. You must leave your construction arcs in.
Based on the information in the graph, the length of DF is 3.87 cm, the length of XF is 4.89 cm. The point 2cm from E is 5cm from X and the angle of D is 60°.
How to find the side length DF?To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:
a² + b² = c²7² + b² = 8²49 + b² = 64b² = 15b = 3.87How to calculate side XF?To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:
a² + b² = c²3² + 3.87² = c²9 + 14.97 = c²23.97 = c²4.89 = cThe point 2cm from E would lie on the line EX at 2cm from E and 5cm from X.
What is the angle of D?To calculate the angle of D we can use a compass, in this case, we know that the angle of X is 90°, so the other 90° that make up the triangle are distributed between point F and D. However, we know that F has a angle less than D so we can infer that F has an angle of 30° and D has an angle of 60° which we can check with a compass.
Learn more about angles in: https://brainly.com/question/28451077
#SPJ1
Help me please i just want to get ALEKS done for school :( PLEASE HELP
The measure of the side of the partial rectangle is 7 cm
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the perimeter of the rectangular figure be represented as P
Now , the equation will be
The length of the rectangle 1 = 12 cm
The width of the rectangle 1 = 6 cm
The length of the rectangle 2 = 15 cm
The width of the rectangle 2 = 5 cm
Now , let the unknown length be represented as A
And , A = length of the rectangle 1 - width of the rectangle 2
Substituting the values in the equation , we get
The unknown length A = 12 cm - 5 cm
On simplifying the equation , we get
The unknown length A = 7 cm
Hence , the unknown length of the rectangle is A = 7 cm
To learn more about perimeter of rectangle click :
https://brainly.com/question/15725265
#SPJ1
a hand woven rectange rug measures x feet long and 2 4/5 feet wide. write an expression to represent the perimeter of the rug
Answer:
see below
Step-by-step explanation:
(x+ 2 4/5) * 2 = perimeter
so perimeter = 2x + 5.6
Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of C′ if the preimage is reflected across y = 4.
C′(−3, 6)
C′(−3, 14)
C′(−1, 6)
C′(−1, 14)
Answer:
(d) C'(-1, 14)
Step-by-step explanation:
You want the coordinates of C' after the point C(-1, -6) is reflected across the line y = 4.
ReflectionReflection across the horizontal line y=4 will not change the x-coordinate of the point, so C' has an x-coordinate of -1.
The point (-1, 4) on the line of reflection will be the midpoint of C and C', so we have ...
(C +C')/2 = (-1, 4)
C +C' = 2(-1, 4) = (-2, 8) . . . . .multiply by 2
C' = (-2, 8) -C
C' = (-2, 8) -(-1, -6) = (-1, 8+6)
C' = (-1, 14)
__
Additional comment
Effectively, the reflection across the line y=4 is the transformation ...
(x, y) ⇒ (x, 8 -y)
Answer:
C'(-1, -6).
Step-by-step explanation:
the reflection across y = 4 for point C(-1, -6).
When reflecting a point across a horizontal line like y = 4, the y-coordinate remains the same, and the x-coordinate is inverted with respect to the line of reflection.
For point C(-1, -6), the y-coordinate remains -6, and the x-coordinate is inverted across y = 4:
New x-coordinate = -1
So, the reflected image of point C across y = 4 is C'(-1, -6).
None of the provided options match this reflection, so it seems there might be an error in the given answer choices. The correct reflection of point C(-1, -6) across y = 4 is C'(-1, -6).
Brian pays £466.98 a year on his car insurance.
The insurance company increases the price by 3.2%.
How much does the insurance cost now?
Give your answer rounded to 2 DP.
Answer:
£481.02
Step-by-step explanation:
To calculate, you can multiply the original cost by the increase percentage (expressed as a decimal) and add that to the original cost:
£466.98 * 1.032 = £480.9936
£480.9936 + £466.98 = £481.02
Rounding to 2 decimal places, the answer is £481.02.
a library has 2500 books.40% of the books are fiction.How many books are not fiction books
A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.
A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
Total amount of book in library are 2500 ,
Out of that 40% are fiction so the number of the non fiction books are 60%
so 60% of 2500 will give us the value of non fiction books,
Number of non fiction = 2500 x 60%
= 2500 x 60/100
= 25 x 60
= 1500
Therefore, Number of non fiction books are 1500.
Learn more about Percentages problem:
brainly.com/question/29393986
#SPJ4
Boden's account has a principal of $600 and a simple interest rate of 3.9%. Complete the number line. How much money will be in the
Answer:
Step-by-step explanation:
If Boden's account has a principal of $600 and a simple interest rate of 3.9%, then the interest he earns each year can be calculated as follows:
Simple Interest = Principal * Rate * Time = $600 * 3.9% * 1 = $23.40
So, after one year, the amount of money in the account will be $600 + $23.40 = $623.40
This process can be repeated for multiple years to find the amount of money in the account for a specific time period.
Pedro tiene 42 años y 3 hijos. Las edades de sus hijos son divisores de su edad. Sabemos que la edad del mayor es un numero compuesto impar. La del segundo es un numero compuesto par que no es multiplo de 3 y la edad del tercero es un numero primo impar que es divisor del segundo. ¿Que edad tiene cada hijo?
Answer:
No se puede determinar la edad de cada hijo con la información proporcionada.
Step-by-step explanation:
A bouncy ball is dropped such that the height of its first bounce is 6.75 feet and each
successive bounce is 74% of the previous bounce's height. What would be the height
of the 6th bounce of the ball? Round to the nearest tenth (if necessary).
Find a formula for the tenth term in this arithmetic sequence: a1=28 a2=21 a3=14 a4=7
Answer:
an = - 7n+35
Step-by-step explanation:
In an arithmetic sequence, the difference between consecutive terms is constant. To find this difference, we can subtract the first term from the second term and the second term from the third term, etc.
a2 - a1 = 21 - 28 = -7
a3 - a2 = 14 - 21 = -7
Since the difference between consecutive terms is the same, we can conclude that the difference is -7.
The nth term in an arithmetic sequence can be found using the formula: an = a1 + (n-1)d, where d is the common difference.
For this sequence, the nth term can be found as: an = 28 + (n-1)(-7) = 28 - 7(n-1) = 28 - 7n + 7 = 35 - 7n.
So, the formula for the nth term in this arithmetic sequence is an = - 7n+35
A boat starts at point A. It travels a distance of 7 km on a bearing of 135° to point B. From B it
travels 12 km on a bearing of 250° to point C. Using a scale of 1 cm: 1 km, draw a diagram to
show these bearings and journeys.
The diagram that represent the distance and the journeys is added as an attachment
How to make the diagramFrom the question, we have the following parameters that can be used in our computation:
Initial point = ADistance of 7 km on a bearing of 135° to point B. From B it, travels 12 km on a bearing of 250° to point CUsing the above as a guide, we have the following:
Next, we create the diagram (see attachment)
The attached figure represents the required diagram
Read more about bearing distance at
https://brainly.com/question/22518031
#SPJ1
Evaluate 2 + y + 1, when y = 12
Answer:
Step-by-step explanation:
Simply substitute for y in the equation if y = 12.
2 + y + 1 -> 2 + (12) + 1 = 15
Hi can somebody please explain the second question and how you got it?
Thank you in advance!
Nice work on getting part (a) correct.
The 261% falls in the "250-300%" range, so they pay 8.5% of their yearly income toward health insurance.
8.5% of $65,500 = 0.085*65500 = 5567.50
That represents the yearly contribution. Divide that by 12 to find the monthly contribution.
5567.50/12 = 463.95833 = 463.96 approximately
Then round to the nearest dollar to get 464
Answer to part (b) is 464Laura has saved $1800 to use as a down payment on a new car. If she wants to continue saving $150 a month, which equation will determine how much money, y, Laura can save in x months?
1800 + 150x = y
150x is the money she makes a month
Y is the total
enjoy :D
Find the value of x.
5
4
3
12
X
a. 24
b. 36
c. 40
d. 45
By the 1/3 ratio, the value of x for the given figure is 33 units.
What is ratio?A ratio is an ordered pair of integers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio may be written as: 1: 3 (for every one boy, there are three girls). A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Here,
4/12=3/x1=5/x2
1/3=3/x1
x1=9 units
1/3=5/x2
x2=15 units
12+15+9=33 units
The value of x for the given figure is 33 units by the ratio of 1/3.
To know more about ratio,
https://brainly.com/question/29467965
#SPJ1
There are 13
books on a shelf. 6 of these books are new.
(a) What is the ratio of used books to all books?
(b) What is the ratio of new books to used books?
The ratio of used books to all books is 7 : 13 and the ratio of new books to used books is 6 : 7
If there are 13 books on a shelf. 6 of these books are new.
(a) The ratio of used books to all books
Number of all books = 13
Number of used books = total no. of books - no. of new books
= 13 - 6
= 7
So, ratio of used books to all books
= no. of all books : no. of total books
= 7 : 13
Thus, the ratio of used books to all books = 7 : 13
(b) The ratio of new books to used books
Number of new books = 6
Number of used books = 7
So, the ratio of new books to used books
= no. of new books : no. of used books
= 6 : 7
Thus, the ratio of new books to used books = 6 : 7
Learn more about ratio
https://brainly.com/question/29192438
a) A wall has a length of 15m and breadth 7cm. The wall also has a square shaped window of length 4m. What is the cost of coloring the wall at Rs. 15 per meter square? 11
Using the formula of area of rectangle and square, the cost of painting is Rs. 1335
What is Area of RectangleThe area of a rectangle is equal to the product of its length and width. Mathematically, it can be represented as:
Area = Length × Width
In this problem, we need to substitute the values and calculate the area of the rectangular wall and then subtract the area of the window from it.
Area of rectangle = 15 * 7 = 105m²
The area of the window is calculate by using the formula of area of square.
Area of square = 4 * 4 = 16m²
Area of wall painted = 105 - 16 = 89m²
The cost of painting one square meter = Rs. 15
1m² = Rs. 15
89m² = x
x = 15 * 89
x = Rs. 1335
The cost is Rs. 1335
Learn more on area of rectangle here;
https://brainly.com/question/25292087
#SPJ1