Answer:
x = 1/14
Step-by-step explanation:
You can work it as is by subtacting ln(14), then taking antilogs:
ln(x) = -ln(14)
x = 14^-1
x = 1/14
___
Or you can rewrite to a single log and then take antilogs:
ln(14x) = 0
14x = 1
x = 1/14 . . . . . divide by the coeffient of x
Antuan deposited $2590 into a 3 year CD at an interest rate of 2.3% compounded quarterly.
What is the ending balance after the three years? Show your work.
Answer:
$2774.47
Step-by-step explanation:
To find how much Antuan's ending balance will be, we can use the formula for compound interest.
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
The values that we currently have are:
P = 2590
t = 3
n = 4 quarterly
r = 2.3% or 0.023
Now we can plug these values into our formula.
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
[tex]A=2590(1+\dfrac{0.023}{4})^{4(3)}[/tex]
[tex]A=2590(1+0.00575)^{12}[/tex]
[tex]A=2590(1.00575)^{12}[/tex]
[tex]A=2774.47[/tex]
So Antuan's ending balance will be $2774.47.
Write an area word problem so that the solution is 36 square units
Answer:
Find the area of a cardboard box with a length of 9 inches and a width of 4 inches.
Step-by-step explanation:
9 in × 4 in = 36 in²
(f/h)(2)
f(x)=3x-4
h(x)=8-3x
Answer:
1
Step-by-step explanation:
find f(2)
f(2) = 3(2) - 4 = 6 - 4 = 2
Now find h(2)
h(2) = 8 - 3(2) = 8 - 6 = 2
Now find f(2)/h(2)
2/2 = 1
Help! Please!
Let x=a+bi and y=c+di
2x+3y
Answer:65
Step-by-step explanation:
Of all the books at a certain library, if you select one at random, then there is a 90% chance that it has illustrations. Of all the illustrations in all the books, if you select one at random, then there is a 90% chance that it is in color. If the library has 10,000 books, then what is the minimum number of books that must contain colored illustrations?
Final answer:
The minimum number of books that must contain colored illustrations is 8100.
Explanation:
To find the minimum number of books that must contain colored illustrations, we can use the concept of conditional probability.
The probability of a book having illustrations is 90%, and the probability of an illustration being in color is also 90%. These two probabilities are independent events.
To find the minimum number of books with colored illustrations, we can multiply the probabilities together.
Therefore, the minimum number of books that must contain colored illustrations is 90% x 90% x 10000 = 8100.
the shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent
Answer:
The statement is True
Step-by-step explanation:
Rhombus is a quadrilateral with the following characteristics;
All sides are congruent by definition.The diagonals bisect the angles.The diagonals are perpendicular bisectors of each other.Adjacent angles are supplementary.All the four sides are equal.in science class, Priscilla heats water and measures the temperature of the water every 2 minutes\or data are shown in the table.
Time in mutes 0 2 4 6 8 10
Tempt in C 25 30 35 40 45 50
What was the temperature of the water at 5 minutes?
Explain
Answer:
37.5 °C
Step-by-step explanation:
The temperature appears to be increasing linearly at the rate of 5 °C in 2 minutes, or 2.5 °C per minute.
1 minute after 4 minutes, when the temperature is 35 °C, we expect it to be 2.5 °C higher, or 37.5 °C.
Which Contacts section results from the intersection of the plane and the double nap cone shown in the figure
Answer:
your choice is correct: hyperbola
Step-by-step explanation:
When the plane intersects both naps of the cone, the result is a hyperbola. When only a single nap is intersected (and the plane is parallel to the edge of the cone), the curve is a parabola. An ellipse or circle results when the plane crosses both edges of the cone on the same nap.
Answer:
ellipse
Step-by-step explanation:
Explain why a rotation of 270∘ clockwise will result in the same transformation as a rotation of 90∘ counterclockwise
Because there is a maximum rotation of 360°, so if you rotate x° clockwise it's the same as if you rotate (360-x)° counterclockwise.
What is 1/2x=18
can you please show steps. Thank you
Answer:
x = 36
Step-by-step explanation:
Multiply both sides of the equation by the inverse of the coefficient of x.
(2/1)·(1/2)x = (2/1)·18 . . . . . . . coefficient of x is 1/2, so we multiply by 2/1
x = 36
_____
This "multiplicative inverse" is also called the reciprocal. It has the property that when multiplied by the coefficient of x, the result is 1, the multiplicative identity element. So, your equation becomes ...
1·x = 36
The property of the multiplicative identity element is that anything multiplied by it is that thing. So, 1x = x, and your equation becomes
x = 36
This is the solution you're looking for.
The answer is 36 !!!!!
The diagonals of kite KITE intersect at point P. If M
The diagonals of kite KITE intersect at point P. This would be at 44 degrees then.
Answer: 44 degrees
..._..._..._..._..._..._
appreciate
find the value of the greater root of x^2-6x+5=0
Answer:
5
Step-by-step explanation:
the roots are:
[tex]\left \{ {{x_1+x_2=6} \atop {x_1*x_2=5}} \right. \ => \ \left \{ {{x_1=1} \atop {x_2=5}} \right.[/tex]
Given four functions, which one will have the smallest y-intercept?
f(x)
g(x)
h(x)
j(x)
Answer:
g(x)
Step-by-step explanation:
y-intercept is the y cutting point, at x = 0.
1. f(x)
This will be an exponential function that starts from 6 and moves upward exponentially. So y-intercept is 6.
2. g(x)
We can see that at x = 0, the value of the function is 2, so that is the y cutting point. So y-intercept is 2.
3. h(x)
We can clearly see from the graph that the y-cutting point is at 4. So y-intercept is 4.
4. j(x)
We can plug in x = 0 into the equation to find y intercept.
[tex]j(x)=10(2)^x\\=10(2)^0\\=10(1)\\=10[/tex]
So y - intercept is 10.
Smallest y-intercept is that of g(x).
GIVING MANY POINTS!
Let p=x^999 − x^100+3x^9 − 5 and q=x + 1. Since q has degree 1, it follows that the remainder when p is divided by q is a constant function k, for some k. What is the value of k?
The polynomial remainder theorem gives an immediate answer. It says that the remainder upon dividing [tex]p(x)[/tex] by [tex]x-c[/tex] is exactly [tex]p(c)[/tex]. In this case [tex]q=x+1\implies c=-1[/tex], and we have
[tex]k=p(-1)=(-1)^{999}-(-1)^{100}+3(-1)^9-5=-1-1-3-5=-10[/tex]
f(x)=2x is transformed to g(x)=5⋅2x. How was the graph affected?
shifted up by 5 units
shifted down by 5 units
stretched by a factor of 5 units
compressed by a factor of 5 units
Answer:
vertically stretched by a factor of 5
Step-by-step explanation:
Multiplying the function value by 5 makes each vertical coordinate 5 times the value it was, so it is 5 times as far away from the x-axis. This has the appearance of stretching the graph vertically by a factor of 5.
_____
Comment on the answer choices
The stretch factor is a "pure number", a ratio of new units to old units. It is "5", not "5 units."
For example, if f(x) is 1 ft (1 unit, where the unit is a foot), then g(x) = 5 ft, the value of f(x) multiplied by 5. It is not 5 ft^2, as you would get if f(x) were multiplied by 5 units, or 5 ft.
The perimeter of a rectangle is 14.
Write the function that describes its area in terms of one of the sides
If one side is a, the formula will be S=______
To express the area of a rectangle with a perimeter of 14 in terms of one side, use the function S = 7a - a² where S is the area and a is one side length.
Explanation:To find the function that describes the area of a rectangle in terms of one of its sides with a given perimeter, we can follow these steps. Let's say one side length is a; we will then call the other side length b. The perimeter of a rectangle is given by the formula P = 2a + 2b, where P is the perimeter, and a and b are the lengths of the sides of the rectangle.
Given that the perimeter is 14, we can express b in terms of a as follows:
b = (14 - 2a) / 2
Next, to find the area (S) in terms of a, we multiply the two side lengths together.
S = a × b
Substitute b into the area formula:
S = a × ((14 - 2a) / 2)
Simplifying the formula gives us the function for the area in terms of side a:
S = (14a - 2a²) / 2
Which simplifies further to:
S = 7a - a²
Learn more about Area of a Rectangle here:https://brainly.com/question/15218510
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What is another way to write the calculation add 9 and 4, and then multiply by 3? A) (3)(9)+4 B) 3(9+4) C) 3x4+9 D) 3x9+4
Answer: B) 3(9+4)
Step-by-step explanation:
B is the correct answer because of the PEMDAS rule telling in what order to solve an expression with more than one operation. (parenthesis, exponents, multiplication, division, addition, subtraction). Therefore, with parentheses coming before multiplication in the PEMDAS rule it would be adding 9+4 and then mulriplying it by three.
plz fill the blanks
The number 72 lies between the perfect squares ----------- . So, the square root of 72 lies between the numbers ----------- , which means the square root of 72 is ------------ number.
Answer:6√2 8-9 Irrational number
Answer:
64 and 81, 8 and 9, irrational
identify whether each equation has no solution, one solution, or infinitely many solutions.
1. 4x−x=2x+x
2. 2x+1=5
3. 4x+2=5x−x+4
4. 2(x+4)=4(x+2)
Answer:
infinitely manyone solutionno solutionone solutionStep-by-step explanation:
1. 4x−x=2x+x
Simplifies to 3x = 3x, which is true for all values of x. Hence there are infinitely many solutions.
___
2. 2x+1=5
True only for x=2; one solution.
___
3. 4x+2=5x−x+4
Simplifies to ...
4x +2 = 4x +4
2 = 4 . . . . . . . not true for any value of x; no solution.
___
4. 2(x+4)=4(x+2)
Simplifies to ...
2x +8 = 4x +8
0= 2x . . . . . . . . . subtract 2x+8
True only for x=0; one solution.
The composite figure is made up of a rectangular prism and a a0 .a1
Answer:
volume of the given shape = 896 cubic centimeters.
Step-by-step explanation:
Given a composite figure is made up of a rectangular prism and a square pyramid.
Now we need to find the volume of that composite shape.
So we can find volume of each part then add both to get total volume.
Volume of rectangular prism = (length)(width)(height) = (8)(8)(13)= 832 cubic centimeter
Base area of square pyramid = (length)(width)=(8)(8)=64
Volume of square pyramid. [tex]=\frac{1}{3}\left(Base\ area\right)\left(Height\right)[/tex]
[tex]=\frac{1}{3}\left(64\right)\left(3\right)[/tex]
[tex]=64[/tex]
Then total volume of the given shape = 832+64 = 896 cubic centimeters.
Answer:
a0 - square
a1 - pyramid
Step-by-step explanation:
Which of the following describes the given graph of the function over the interval [2, 6]? A. increasing B. constant C. decreasing D. decreasing to increasing
Final answer:
To determine the function's behavior over an interval, compare the y-values as the x-values increase. It could be increasing, decreasing, constant, or changing direction. Choose the description that matches the graph's movement over the given interval.
Explanation:
To determine how the function behaves over the interval [2, 6], we must look at the description of the graph presented. If during the interval the function is always moving upwards as the x-values increase, then it is increasing. If it moves downwards, it is decreasing. If the graph stays at the same level without moving up or down, then it would be constant. If the graph changes its direction, from either increasing to decreasing or vice versa, then it would be described as decreasing to increasing or increasing to decreasing, accordingly. Given these possibilities, the student should match the behavior of the graph with one of these descriptions.
What is 27 3 over 8 minus
16 3 over 4
-6.625 or -6.63 rounded up
What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0? units
Answer:
2
Step-by-step explanation:
x²+8x+y²-6y= -21;
(x+4)²+(y-3)²-25= -21;
(x+4)²+(y-3)²=2²;
it means r²=2²; ⇒ r=2.
You are putting a fence around a square outdoor stage with an area of 289 square feet. What is the length of one side of the stage?
The length of one side of the stage is 17 feet.
To find the length of one side of a square, we take the square root of the area because the area of a square is equal to side length squared.
So, the calculation is as follows:
Area of square = side imes side
289 square feet = side imes side
Therefore, side =√289
Calculating the square root of 289 gives us the side length:
side = 17 feet
So, to determine the length of one side of a square stage with an area of 289 square feet, we calculate the square root of the area, which results in 17 feet.
Use the x-intercept method to find all real solutions of the equation x^3-6x^2+3x+10=0
Answer:
x ∈ {-1, 2, 5}
Step-by-step explanation:
The x-intercepts of the graph of the cubic are -1, 2, and 5. These are the values of x that are solutions to the equation.
Answer:
answer is D. -1, 2 , 5
Step-by-step explanation:
Which function has an inverse that is not a function?
f(x) = x^2
f(x) = 2x
f(x) = x + 2
f(x) = √x
Answer:
your choice is correct
Step-by-step explanation:
f(x) = x^2 does not pass the horizontal line test (a horizontal line intersects its graph in two places), so its inverse does not pass the vertical line test. The inverse is not a function.
_____
Comment on the graph
The original function f(x)=x^2 is shown by the red curve. Its reflection across the orange dashed line y=x gives the inverse relation, in blue. The black horizontal and vertical lines show the multiple points of intersection with the curves, indicating the inverse relation is not a function.
Answer:
A) f(x)=x^2
Step-by-step explanation:
did it on i-ready
Can you just help me with 1 of the figures in my math problem and explain how you got it please!!
Part 1: Polygons and circles
a. Help Dakota with her homework. Use diagrams of inscribed polygons to approximate the area of each circle. Assume that all of the circles have a radius of 1.
The attachment isn't working so I to try to describe it as best as I can:
The inscribed Polygon is a triangular shape B=1.73 and H= 0.5
Answer:
area of triangle: 1.2975
area of circle: π ≈ 3.1416
Step-by-step explanation:
The side length (B) is used to compute the perimeter of the triangle. For the 3-sided triangle, the perimeter is ...
P = 3B = 3·1.73 = 5.19
The "height" (H) measured from the center of the circle to the middle of one side is called the "apothem" (a). The area of the triangle (A) is the product of half that and the perimeter:
A = (1/2)aP = (1/2)·0.5·5.19 = 1.2975 . . . . . . square units
What is the value of 2g(-1)?
f(x) = 4x + 10; g(x) = 2x - 5
2g(-1) =
Answer:
-14
Step-by-step explanation:
Put -1 where x is in the definition of g(x) and do the arithmetic.
2g(-1) = 2(2·(-1) -5) = 2(-2-5) = 2(-7) = -14
Solve for x please I need help ASAP
Answer:
x > 2
Step-by-step explanation:
The inequality has constants and variables on both sides. It is convenient to find the variable term with the smallest (most negative) coefficient. Add the opposite of that term to both sides of the inequality.
2x -3 +5x > 11 -5x +5x . . . . added 5x
7x -3 > 11 . . . . . . . . . . . . . . . simplify
Now, find the constant on the side of the inequality that has the variable term. Add the opposite of that constant to both sides.
7x -3 +3 > 11 +3 . . . . . added 3
7x > 14 . . . . . . . . . . . . simplify
Finally, divide by the coefficient of x. It is positive, so we do not need to do anything to the relation symbol.
x > 14/7 . . . . . . . . . . divided by 7
x > 2 . . . . . . . . . . . . simplify . . . . This is your solution.
a snowman is made of three spherical snowballs with a diameters of 3 feet, 2 feet, and 1 foot. what is the total volume of the snowman?represent your answer in terns of pi
Answer:
The total volume of the snowman is [tex]6\pi\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
step 1
Find the volume of the spherical snowball with a diameter of 3 feet
Find the radius
[tex]r=3/2=1.5\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (1.5)^{3}[/tex]
[tex]V1=\frac{9}{2}\pi\ ft^{3}[/tex]
step 2
Find the volume of the spherical snowball with a diameter of 2 feet
Find the radius
[tex]r=2/2=1\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (1)^{3}[/tex]
[tex]V2=\frac{4}{3}\pi\ ft^{3}[/tex]
step 3
Find the volume of the spherical snowball with a diameter of 1 feet
Find the radius
[tex]r=1/2=0.5\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (0.5)^{3}[/tex]
[tex]V3=\frac{1}{6}\pi\ ft^{3}[/tex]
step 4
Find the total volume
[tex]V=V1+V2+V3[/tex]
substitute the values
[tex]V=\frac{9}{2}\pi+\frac{4}{3}\pi+\frac{1}{6}\pi=\frac{27+8+1}{6}\pi=6\pi\ ft^{3}[/tex]