Answer:
Simple interest = $1,000(.10)(3) = $300
Compound interest =
$1,000(1.05)² - $1,000 = $102.50
What does |a|=|b| mean?
Answer:
a = ±b
Step-by-step explanation:
The vertical bars are the symbol for "absolute value", so the equation is saying, "the absolute value of 'a' is equal to the absolute value of 'b'." The absolute value is the magnitude of a number, so, for example, |-3| = 3.
If the magnitudes of two numbers are the same, they may be the same value, or they may differ in sign.
Answer:
See below.
Step-by-step explanation:
The 2 vertical lines about the letters mean ' the absolute value of' . That is if a or b have negative values then the absolute value will be the positive . For example if a = -4 then |a| = 4. The absolute value is always positive.
Therefore, for example, if a is 2 and b = -2 then |a| will be equal to |b|, because they both have a value of 2.
Students were surveyed to find out the most popular pizza topping. According to the bar graph, how many students were surveyed?
A) 42
B) 44
C) 46
D) 48
The total number of students surveyed = 44 students
The answer is option D.
What is a bar graph?
A bar graph is a graph that presents categorical data with rectangular bars. The heights are proportional to the values that they represent. The bars can be plotted vertically or horizontally.A bar graph shows comparisons among different categories.
According to the given graph, the total number of students is equal to the sum of all the students in each vertical column.
∴tota students surveyed=12+8+9+15=44 students answer.
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What is the reciprocal of 3 ?
What is the reciprocal of 11/8
Answer:
1 / 3 and 8 / 11
Step-by-step explanation:
When you find the reciprocal of something you flip the number over e.g
Find the reciprocal of 1 /2,
You ' flip it ' and it becomes 2 / 1 or 2
Answer: 1/3 and 8/11
Step-by-step explanation:
A cup of cereal can contain 480
480
milligrams of salt, which is 20%
20
%
of the recommended daily amount.
What is the recommended daily amount of salt?
480 x 5 = 2400. 2400 milligrams of salt is the recommended daily amount.
Answer:
2400 milligrams because 480 is 20% of the recommended amount
Step-by-step explanation:
20*5 = 100% so 480* 5 = 100% or recommended amount
Hope this helps!
which expression is equivalent to 6e+3(e-1)
6e + 3(e - 1)
6e + 3e - 3
9e - 3
Answer: Equivalent expression would be 9e-3.
Step-by-step explanation:
Since we have given that
[tex]6e+3(e-1)[/tex]
As we need to simplify the above expression:
First we open the brackets :
[tex]3(e-1)=3e-3[/tex]
Now, add it to 6e.
So, it becomes,
[tex]6e+3e-3\\\\=9e-3[/tex]
Hence, equivalent expression would be 9e-3.
An online company lets you download songs for 0.99 cents after you have paid a 5 dollar membership fee. Which domain would be most appropriate to calculate the cost to download songs?
1, rational numbers greater than zero
2, whole numbers greater than or equal to one
3, integers less than or equal to zero
4, whole numbers less than or equal to zero
The most appropriate domain to calculate the cost of downloading songs is whole number greater than or equal to one.
What are whole number?Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.
It is most appropriate since numbers of songs downloaded cannot be a negative or part quantity.
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The most appropriate domain for calculating the cost to download songs after paying a membership fee is whole numbers greater than or equal to one, as you cannot download fractional or negative numbers of songs.
Explanation:The most appropriate domain for calculating the cost to download songs, given the information that an online company charges a $5 membership fee and then $0.99 for each song, would be option 2, which is whole numbers greater than or equal to one. The domain is referring to the number of songs you can download after the initial membership fee. Since you cannot download a fraction of a song or a negative number of songs, whole numbers make the most sense in this context. The cost for downloading songs would be the membership fee plus the cost per song times the number of songs downloaded, which is a linear relationship.
what are expressions are equivalent to 6x-18y
Answer:
Step-by-step explanation:
6 is common to both terms, so 6x - 18y is equivalent to 6(x - 3y).
Determine which statements are true regarding the given solid. Check all that apply.
The three-dimensional solid is a hexagonal pyramid.
The three-dimensional solid is a hexagonal prism.
The solid can be created by stacking the same-size hexagons vertically.
The solid can be created by stacking dilated hexagons vertically.
Point D is the apex of the pyramid.
option A, D, and E
I just took it on edge
The true statement regarding the shape are:
The three-dimensional solid is a hexagonal pyramid.The solid can be created by stacking dilated hexagons vertically.Point D is the apex of the pyramid.Base: The bottom surface of a pyramid is a polygonal shape, such as a square, rectangle, triangle, or any other polygon. The base is typically larger in area compared to the other faces.
Faces: Pyramids have triangular faces that slope inward from the edges of the base to a single point at the apex. The number of faces depends on the number of sides of the base polygon.
Vertices: A pyramid has several vertices where the edges of the base meet the triangular faces, and one vertex where all the triangular faces converge at the apex.
Edges: The edges of a pyramid are the lines where the faces intersect. For example, a square pyramid has 8 edges (4 from the base and 4 connecting the base to the apex).
Solve the equation below algebraically for the exact value of x.
6 - 2(x + 5) = 42
Answer:
x= -19
Step-by-step explanation:
6-2(x+5)=42
6-2x-10=42
-4-2x=42
-2x=38
x= -19
The width of a rectangle is y feet long. The rectangle is 4 feet longer than it is wide. What is the area of the rectangle? Which expression represents the area?
Answer:
y²+4y
Step-by-step explanation:
y multiplies with (y+4)
y times y is y²
y times 4 is 4y
That leaves you with y²+4y
Answer: [tex]y^2+4y[/tex] expresses the area.
Step-by-step explanation:
Let the width of a rectangle be 'y' feet.
Let the length of a rectangle be 'y+4' feet.
As we know the area of rectangle :
Area of rectangle is given by
[tex]Length\times breadth\\\\=y\times (y+4)\\\\=y^2+4y[/tex]
Hence, [tex]y^2+4y[/tex] expresses the area.
What is the point slope form of a line with slope 3/2 that contains the point (-1,2) ?
The options are in the picture ... please help !
y-2=3/2 (x+1) must be first
It is asking for the standard form for the quadratic function.
well factored would be f(x)= (x+4)(x+2) and standard for would be
f(x)= x^2+6x+8
Angles A and B are complementary. Angle A has a measure of (3x +10). Angle B has a measure of (2x +5). What is the value of x?
Answer:
15
Step-by-step explanation:
Complementary angles mean the two angles add up to 90 degrees. So the step by step would look like this;
3x + 10 + 2x + 5 = 90
5x + 15 = 90
5x = 90 - 15
5x = 75
x = 75/5
x = 15 :)
If the angles A and B are complementary then the value of x is 15.
Complementary angles are two angles whose sum is 90 degrees. In this case, angle A and angle B are complementary, so we can set up an equation based on their measures:
(3x + 10) + (2x + 5) = 90
Now, combine like terms:
3x + 2x + 10 + 5 = 90
Combine the x terms and constants:
5x + 15 = 90
Next, isolate the x term:
5x = 90 - 15
5x = 75
Finally, solve for x by dividing both sides by 5:
x = 75 / 5
x = 15
Therefore, the value of x is 15.
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How will you write 7^5 as a multiplication expression?
A.
7 * 5
B.
7*7*777
C.
5 x 5 x 5 x 5 x 5 x 5 x 5
Answer:
The answer is 7*7*7*7*7
Step-by-step explanation:
The correct way to write 7^5 as a multiplication expression is by writing it as 7 multiplied by itself 5 times, which is 7 x 7 x 7 x 7 x 7.
The question asks how to write 7^5 as a multiplication expression. To correctly express 7^5, we represent it as 7 being multiplied by itself 5 times. So, the correct way to write 7^5 as a multiplication expression is 7 \u00d7 7 \u00d7 7 \u00d7 7 \u00d7 7. This clearly demonstrates the concept of an exponent, where the base (7) is multiplied by itself a certain number of times (5 times in this case), which is fundamentally different from just multiplying 7 by 5.
Which value is an output of the function?
Answer: An output is the function
Step-by-step explanation:
Lawrence got a car loan from a bank, with the car as collateral. What kind of loan did he get?
A. a secured loan
B. an unsecured loan
C. a fixed-rate loan
The answer is A. A secured loan, hope this helps!
Answer:A, a secured loan
Step-by-step explanation:
how do you plot f(x)= (x + 4) ^2
I hope this helps please tell me if it doesn’t
Draw a triangles with sides of 9 cm, 7 cm, and 5 cm. Find its perimeter
The perimeter is 21 cm.
thanks
Answer:
12 + √74 cm
Step-by-step explanation:
The perimeter (literally meaning "around measure") is the length around an area, shape, or boundary. Here, we have a right triangle, and the legs of that right triangle measure 5 cm and 7 cm. Using the Pythagorean theorem, we can find the hypotenuse (we'll call it h):
[tex]5^2+7^2=h^2\\25 + 49=h^2\\74=h^2\\\sqrt{74}=h\\[/tex]
Adding all the lengths together, we find a perimeter of
5 + 7 + √74 = 12 + √74 cm
what is the value of the expression 2 squared + 4 squared divided by 2 squared
Answer:
5
Step-by-step explanation:
2² + 4² = 4 + 16 = 20
20 ÷ 2² = 20/4 = 5
The table below represents the height of a bird above the ground during flight, with p(t) representing height in feet and t representing time in seconds
calculate the average rate of change from 3 to 9 seconds
Answer:
calculate the difference height (P) is -6 and (t) is 2.85
Δy divided by Δx = rate of change
3-9 = -6
6.23-3.41 = 2.85
then divide
2.85 / -6 = .475
Your answer will be - .475
Step-by-step explanation:
Using the table, the average rate of change from 3 to 9 seconds is of -0.475 feet per second.
The average rate of change of a function P(x) over an interval [a,b] is given by:
[tex]A = \frac{P(b) - P(a)}{b - a}[/tex]
In this problem, we want the rate from 3 to 9 seconds, hence [tex]a = 3, b = 9[/tex].
From the table, [tex]P(3) = 6.26, P(9) = 3.41[/tex], hence:[tex]A = \frac{3.41 - 6.26}{9 - 3} = -0.475[/tex]
Considering the units, the average rate of change from 3 to 9 seconds is of -0.475 feet per second.
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If you rotate the triangle so that the 6 is on the bottom, the two sides are both 6.2.
Because the two sides are equal the two angles at the bottom would also be equal. One is given as 61 degrees, so the other bottom angle is also 61 degrees.
The three inside angles of a triangle need to equal 180, so X would equal 180 minus the two bottom angles.
X = 180 - 61 - 61 = 58 degrees.
Given the function rule f(x) = x2 – 3x + 2, what is the output of f(-2)?
.
A. -8
B. 0
C. 4
D. 12
Answer:
C
Step-by-step explanation:
which number has the greatest value 4 1/2 4 1/6 or 4.85
Final answer:
Among 4 1/2, 4 1/6, and 4.85, the number 4.85 has the greatest value as it has the highest decimal portion when all numbers are expressed in decimal form.
Explanation:
To find which number has the greatest value among 4 1/2, 4 1/6, or 4.85, we need to compare them directly. The number 4 1/2 converts to 4.5 in decimal form, 4 1/6 converts to approximately 4.17, and 4.85 is already in decimal form. Comparing these three numbers, it's clear that 4.85 has the greatest value because it has the highest decimal portion.
What is the solution of square root x^2 + 49=x+5
Answer:
-44
Step-by-step explanation:
√x²+49=x+5
X+49=x+5
x-x=5-49
=-44
Answer:
x = 12/5
Step-by-step explanation:
[tex]\sqrt{x^{2}+49 } = x +5[/tex]
Square both sides: ([tex]\sqrt{x^{2} +49}[/tex])[tex]^{2}[/tex] = (x+5)[tex]^{2}[/tex]
[tex]x^{2} + 49 = (x+5)(x+5)\\[/tex]
[tex]x^{2} +49[/tex] = [tex]x^{2} + 10x + 25\\[/tex]
49 = 10x + 25
24 = 10x
[tex]\frac{12}{5}[/tex] = x
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slope-intercept form of the equation for this line?
y = x – 12
y = x – 4
y = x + 2
y = x + 6
Answer:
y = x - 4
Step-by-step explanation:
y - 4 = x - 8
y = x - 4
Answer:
slope-intercept form of the equation for this line is [tex]y=x -4[/tex]
Step-by-step explanation:
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8).
To find slope intercept form of a equation of a line we solve for y
[tex]y - 4 = (x - 8)[/tex]
We remove the parenthesis
[tex]y -4 =x - 8[/tex]
To get y alone, we need to add 4 on both sides
[tex]y -4+4=x - 8+4[/tex]
[tex]y=x -4[/tex]
slope-intercept form of the equation for this line is [tex]y=x -4[/tex]
How to round 2.06 to the amount to the nearest dollar
it would be 2.00 it’s closer to 2.00 than 3.00
2-(-8c)+24-7c simplified
Answer:
26+c
Step-by-step explanation:
The given expression 2-(-8c)+24-7c simplifies to 26 + c by removing the parenthesis, changing the sign of -8c to +8c, combining like terms, and adding the constants.
The equation 2-(-8c)+24-7c simplifies by applying the distributive property and combining like terms. We first remove the parentheses and change the sign of the term inside, which is -8c, to a positive. Then we combine the like terms, -8c and -7c. The equation simplifies to:
2 + 8c + 24 - 7c = 2 + 24 + (8c - 7c) = 26 + c
So, the given expression simplifies to 26 + c.
Please help! Need to confirm my answers.
Match the exponential functions f(x) and g(x) with their key features.
Answer:
Step-by-step explanation:
Average rate of change is Δy / Δx.
For f(x):
[ f(1) - f(0) ] / (1 - 0)
(1 - 3) / (1 - 0)
-2
For g(x):
[ g(1) - g(0) ] / (1 - 0)
(4 - 3) / (1 - 0)
1
Which basic calculation or process in mathematics relates to factors?
Final answer:
Dimensional analysis, also known as the factor-label method, is a mathematical process related to factors, specifically used for unit conversions and complex computations to ensure correct units are obtained in the results.
Explanation:
The basic calculation or process in mathematics that relates to factors is known as dimensional analysis or the factor-label method. This method is integral in solving problems involving unit conversions and more complex computations, where the orientation of factors according to their units is essential to ensure that quantities cancel out or combine correctly to give a result with the desired units.
Through the factor-label method, we can transform quantities into different units by multiplying by conversion factors, which are ratios that equal one, to achieve the intended units for the result. This approach ensures that we conduct operations on the units of the quantities in the same way we do on the numbers.
For example, if we want to convert meters into inches, we multiply the quantity in meters by a conversion factor that expresses the number of inches in a meter. This factor, being a ratio of inches to meters, aligns the units so that 'meters' cancel out, leaving only 'inches' in the result.
Which equation can be used to solve forB?
Answer:tan 30 = 5/b
Step-by-step explanation:
From the diagram line BC is opposite to the angle 30 and line AC is adjacent to that same angle
From trigonometric ratios
Tan 30 = opposite /adjacent
Answer:
The correct answer is first option
Step-by-step explanation:
Points to remember
Trigonometric ratio
Tan θ = Opposite side/Adjacent side
From the figure we can see that a right angled triangle ABC
BC = 5 cm, <A = 30° and <C = 90°
To find the correct equation
We have,
Tan θ = Opposite side/Adjacent side
Tan 30 =BC/AC
Tan 30 = 5/b
The correct answer is first option.