The base of an exponent can be simplified by multiplying it by itself as many times as the exponent indicates. If you want to simplify the base of an exponent in an expression, it would be done by raising the base to the power of the exponent using the notation aᵇ = aa...*a (b times)
THE BASE OF AN EXPONENTThe base of an exponent is the number that is being multiplied by itself a certain number of times. The exponent is the number indicating how many times the base is being multiplied by itself.
For example, in the expression 2³, the base is 2 and the exponent is 3. This means that 2 is being multiplied by itself 3 times, or 2 * 2 * 2. The simplified form of this expression is 8.
In general, if the base is 'a' and the exponent is 'b' then the simplified form of the expression is 'a' raised to the power 'b' or aᵇ = aa*...*a (b times)
It's also important to note that when the exponent is 1, the expression can't be simplified anymore. For example, 2¹ = 2, where 2 is the base and 1 is the exponent.
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A credit card company uses these rules to calculate the minimum amount owed: • For a bill of less than $100, the entire amount is due. • For a bill of at least $100 but less than $500, the minimum due is $100. • For a bill of at least $500 but less than $1,000, the minimum due is $300. • For a bill of $1,000 or more, the minimum due is $500. Which graph shows the minimum amount due for a credit amount of × (given that the credit limit is $2,000). O A. graph A O B. graph B O C. graph C O D. graph D
The graph that shows the minimum amount due for a credit amount of x given that the credit limit is $2,000 is graph B.
How to illustrate the information?Let x represent the credit amount and y represent the minimum amount due.
For a bill of less than $100, the entire amount is due. That is for 0 ≤ x < $100, y = x
For a bill of at least $100 but less than $500, the minimum due is $100. That is for $100 ≤ x < $500, y = 100
For a bill of at least $500 but less than $1,000, the minimum due is $300. That is for $500 ≤ x < $1000, y = $300
For a bill of $1,000 or more, the minimum due is $500. But the credit limit is $2000. That is For $1000 ≤ x < $2000, y = $500
The graph that shows the minimum amount due for a credit amount of x is graph B.
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Derek wants to determine the height of the top of the backbpard on the basketball goal at the playground. He places a standard 12-
inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 11 inches and
the backboard has a shadow of 7.5 feet, then about how high is the top of the backboard?
the actual height of the backboard is 8.18 feet.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given
We have been given that Derek places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.
We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.
[tex]\frac{Actual height of ruler}{Shadow of ruler} = \frac{Actual height of black board}{Shadow of black board} \\\\\frac{12}{11} =\frac{Actual height of black board}{7.5} \\\\Actual height of black board = \frac{12}{11} * 7.5 = 8.18\\[/tex]
Therefore, the actual height of the back-board is 8.18 feet.
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Step 1: Place the graph paper in landscape orientation. Measure from the top left hand corner 6 inches right and 5 inches down. This will be your starting point for
your diagram.
Step 2: Using a ruler and index card/protractor create an isosceles Right triangle. Drawing the triangles legs 1 inch straight up from the starting point and 1 inch to the
right of the starting point. Connect the endpoints of the two segments to create your right isosceles triangle.
Step 3: On a separate piece of paper, use the Pythagorean Theorem to calculate the length of the hypotenuse. You only need to do this for the first 8 if you discover a
pattern.
Step 4: Using your original Right triangle, add another leg measuring 1 inch and right angle to the hypotenuse of your original Right triangle. Connect the endpoints
to form a new hypotenuse for your new Right triangle.
Step 5: Show the calculations to find the length of the new hypotenuse.
Step 6: Continue to repeat this process of connecting and drawing new triangles with a side length of 1 inch, using the previous hypotenuse as the other side. Draw
triangles until you are able to measure the square root of 17. You must show all calculations (Step 3) on a separate piece of paper.
The right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches
How to determine the hypotenuse?Step 1 and 2: Create an isosceles right triangle
This is represented by the attached figure in (see figure 1 for this triangle)
The legs of this triangle have a length of 1 inch
Step 3: The hypotenuse
This is calculated using the following Pythagoras theorem
[tex]h^2 = 1^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 2[/tex]
Step 4: Create another isosceles right triangle
This is represented by the attached figure in (see figure 2 for this triangle)
The legs of this triangle are 1 inch and 2 inches, respectively
This hypotenuse is calculated by:
[tex]h^2 = 2^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 5[/tex]
Step 5: Create another isosceles right triangle
This is represented by the attached figure in (see figure 3 for this triangle)
The legs of this triangle are 1 inch and 3 inches, respectively
This hypotenuse is calculated by:
[tex]h^2 = 3^2 + 1^2[/tex]
This gives
[tex]h = \sqrt {10[/tex]
Step 6: Create another isosceles right triangle
This is represented by the attached figure in (see figure 4 for this triangle)
The legs of this triangle are 1 inch and 4 inches, respectively
This hypotenuse is calculated by:
[tex]h^2 = 4^2 + 1^2[/tex]
This gives
[tex]h = \sqrt{[17[/tex]
See that the hypotenuse is the square root of 17
Hence, the right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches
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Visual Description for Figure 1
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
A) Rotate by 90° counterclockwise.
B) Reflection transformation about the line y = 5.
C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.
D) Perpendicular lines are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁
F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.
G) Slope of Line ED = 1
How to carry out Transformations?A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.
B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.
C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.
D) The line segments that are perpendicular are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.
F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.
G) Slope of ED = (5 - 4)/(-10 - (-11))
Slope of ED = 1/1
Slope = 1
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What is the net force acting on the crate? 352 n to the left 176 n to the left 528 n to the right 440 n to the right
The net force acting on the crate is the sum of all the forces acting in the different directions on the crate, which is 176 N to the left.
What is net force?The net force is defined as the sum of all the forces acting on an object.
From the figure given that,
Upward force = 440 N
Downward force = - 440 N
Rightward force = 176 N
Leftward Force = - 352 N
The net vertical force acting on the crate = Upward force + Downward force
= 440 N + (-440 N)
= 0 N
The net horizontal force acting on the crate = Rightward force + Leftward force
=176 N + (- 352 N)
= - 176 N
Hence, the net force acting on the crate is - 176 N, which is 176 N to the left.
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Answer:
175N to the left
Step-by-step explanation:
A researcher reports an f-ratio with df = 3, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment?
There were 4 number of treatment conditions compared in this experiment for the given degree of freedom.
We have,
df = 3, 36
Now,
We know that,
Degree of freedom (df) = Number of treatments (t) - 1
i.e.
df = t - 1
So,
We have,
df = 3
Now,
Substituting the values,
We get,
3 = t - 1,
i.e.
t = 4
So, number of treatments conditions = 4
Hence we can say that there were 4 number of treatment conditions compared in this experiment for the given degree of freedom.
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The propeller blades on a submarine have a radius of 6 feet. At full speed, they turn at 120 revolutions per minute. What is the angular velocity, in radians per minute, at the tip of the blade? Round your answer to the nearest hundredth.
Using proportions, it is found that the angular velocity at the tip of the blade is of 753.98 radians per minute.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each revolution has [tex]2\pi[/tex] radians, hence in one minute, the 120 revolutions will have a measure in radians of:
M = 120 x 2pi = 240pi = 753.98
Hence the angular velocity is of 753.98 radians per minute.
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Find angle ABH please please
Answer: 47°
Step-by-step explanation:
If both cars in Exercise 62 are on one side of the plane and if the angle of depression to one car is 38∘ and that to the other car is 52∘, how far apart are the cars?
The two cars lying on one side of the plane are 50 meters apart.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
let us assume that the height is 100 m. Let d represent the horizontal distance. For depression of 38°, Ф = 90 - 38 = 52°, hence:
tan(52°) = d / 100
d = 128 m
For depression of 52°, Ф = 90 - 52 = 38°, hence:
tan(38°) = d / 100
d = 78 m
Distance apart = 128 - 78 = 50 m.
The two cars lying on one side of the plane are 50 meters apart.
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Use the image below to describe at least three different ratios, written in simplest form. Include at least one part-to-part ratio and one part-to-whole ratio.
8 out of 36 squares unfilled*
HELP ASAP!!!!!!!!!!!!
The different ratios are 2 : 7, 2 : 9 and 7 : 9
How to determine the ratio?The statement is given as:
8 out of 36 squares unfilled
This means that:
There are 36 squares8 are unfilled28 are filledThe part-to-part ratio is represented as:
Ratio = Unfilled : Filled
This gives
Unfilled : Filled = 8 : 28
Simplify
Unfilled : Filled = 2 : 7
The part-to-whole ratios are represented as:
Ratio = Unfilled : Total
Ratio = Filled : Total
So, we have:
Unfilled : Total = 8 : 36
Filled : Total = 28 : 36
Simplify
Unfilled : Total = 2 : 9
Filled : Total = 7 : 9
Hence, the different ratios are 2 : 7, 2 : 9 and 7 : 9
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Fill out First row is standard form
Second row is Factored Form already done for you.
Answer:
(x + 6)(x - 2) = x² + 4x - 12
(x + 2)(x - 8) = x² - 6x - 16
(x + 6)(x - 6) = x² - 36
(x - 5)(x - 1) = x² - 6x + 5
(x - 4)(x - 10) = x² - 14x + 40
(x + 2)(x + 5) = x² + 7x + 10
Step-by-step explanation:
Use FOIL.
(x + 6)(x - 2) =
F - first: x × x = x²
O - outer: -2 × x = -2x
I - inner: 6 × x = 6x
L - last: 6 × -2 = -12
(x + 6)(x - 2) = x² - 2x + 6x - 12
Now, combine like terms.
(x + 6)(x - 2) = x² + 4x - 12
(x + 2)(x - 8) = x² - 6x - 16
(x + 6)(x - 6) = x² - 36
(x - 5)(x - 1) = x² - 6x + 5
(x - 4)(x - 10) = x² - 14x + 40
(x + 2)(x + 5) = x² + 7x + 10
Triangle ABC Is shown on the coordinate plane.
What is the area of AABC?
OA 22.63 square units
OB. 24 square units
OC 48 square units
OD.
m. All rights reserved
16.97 square units
4
A(4.4)
-6
8-3,-3
6
42
A
42
4
-6-
C(3,3)
Answer: B
Step-by-step explanation:
Using the distance formula, we get the height is [tex]4\sqrt{2}[/tex].
Similarly, we get the base is [tex]6\sqrt{2}[/tex].
So, the area is [tex]\frac{1}{2}(4\sqrt{2})(6\sqrt{2})=24[/tex]
A rectangular prism measures 8 m by 4 m by 5 m. What is its volume?
Answer:
160 m³
Step-by-step explanation:
the volume of a rectangular prism is equal to :
= Base × height
= length × width × height
………………………………………
= 8 × 4 × 5
= 160
Note : the length can be 8 or 5
and the width can be 4 or 5
State all integer values of x in the interval [2,8] that satisfy the following inequality: 5x+ 4 > 19
The following integer values of x satisfy the given inequality,
4, 5, 6, 7, 8
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made using inequality.
Solving the Inequality
The given inequality is,
5x + 4 > 19
5x > 19 - 4
5x > 15
x > 15/5
x > 3
So, the required values of x must be greater than 3 in the given interval, [2,8]
Thus, the integer values of x in the the interval [2,8] that satisfy the given inequality are 4, 5, 6, 7 and 8 (∵ Square brackets of an interval denote inclusion of the terminal values).
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i need help!!!!!!!!!!!!!! how many pound are in 40 ounces. this is off or i ready. please help me!!!
Answer:
2.5 pounds
Step-by-step explanation:
What is the area of the triangle?
Enter your answer in the box.
in²
Right triangle with sides forming the right traingle labeled 25 inches and 60 inches and the side across from the right angle labeled 65 inches.
Using it's formula, the area of the right triangle is of 750 inches squared.
What is the area of a right triangle?The area of a right triangle is given by half the multiplication of the two legs, which are the two smaller sides.
In this problem, the two legs are 25 inches and 60 inches, hence the area of the triangle is:
A = 0.5 x 25 x 60 = 750 inches².
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What are the center and radius of the equation (x-2)^2 + (y-9)^2 = 36?
Answer:
center (2, 9); radius 6
Step-by-step explanation:
Standard equation of a circle:
(x - h)² + (y - k)² = r²
where the center is (h, k), and r is the radius.
You have
(x - 2)² + (y - 9)² = 36
(x - 2)² + (y - 9)² = 6²
Compare this last form to
(x - h)² + (y - k)² = r²
h = 2; k = 9; r = 9
Answer: center (2, 9); radius 6
Answer:
centre = (2, 9 ) , radius = 6
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
(x - 2)² + (y = 9)² = 36 ← is in standard form
with centre (2, 9 ) and r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6
Jorge wrote the equation negative 6 x 4 x = 8. what is the value of x? –4 –2 2 4
Option (A) - 4 is the correct answer.
The value of x for linear equation -6x + 4x = 8 is - 4.
What is linear equations in one variable?If a variable's maximum power constantly equals 1, the equation is considered linear equation. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.
The given equation is -6x + 4x = 8.
Simplifying the above equation.
-2x = 8
Now, dividing both sides by -2.
x = -4
Therefore the value of x in equation -6x + 4x = 8 is -4.
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I understand that the question you are looking for is " Jorge wrote the equation -6x + 4x = 8. What is the value of x?
(A) –4
(B) –2
(C) 2
(D) 4 "
Answer: (A): -4
Step-by-step explanation:
It's the correct option.
Help me please and thank you!
Answer: B
The main word that gives the answer away is product, which means to multiply.
Using rigid motion, which statement is true about the triangles?
O ABC is congruent to FED
O ABC is congruent to FDE.
Ο Δ ABC is congruent to DEF.
triangles are not congruent
Answer:
ABC is congruent to DEF
Step-by-step explanation:
I think its this one cause the angles are the same
Direct to Coordinates
plot the point A (2, 3) then, plot point b that is 4 right and 5 up from point A.
Plot the point C (9, 7). Then, plot another point D that is 8 left and 2 down from point C.
Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C which is at D(1, 5).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C which is at D(1, 5).
The location of point A, B, C and D is located on the graph.
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If you register a 0. 08 bac or refuse to take a breath test, your license will be automatically suspended for.
If you register a 0. 08 bac or refuse to take a breath test, your license will be automatically suspended for 12 months.
What is bac test?The amount of alcohol in your blood is determined via a blood alcohol(bac)test. The breathalyzer test, which police officers frequently administer to people they suspect of driving while intoxicated, is more widely known. While breathalyzers provide quick findings, they are not as precise as bac tests that measure alcohol in the blood.
The same 0.08 bac limit applies to adults in all 50 states who are 21 years of age or older, who are driving while intoxicated and breaching the law.
No amount of alcohol is safe when you are driving, even if your bac is below the legal limit. Don't drive after drinking, please!
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An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = -4.9t2 +19.6t + 58.8, where s is in meters. How high will the object be after 3 seconds?
A)73.5 feet
B)98.49 feet
C)333.69 feet
D)161. 7 feet
The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)
What is the height of the object after launch?
Herein we have an equation that models the height of the ball as function of time, we need to evaluate the expression for t = 3 s to find the required height:
s(3) = - 4.9 · (3 s)² + 19.6 · (3 s) + 58.8
s(3) = 73.5 m
The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)
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Please help!! is there a solution to z³ = x³ + y³ for a right triangle?
There are no solutions for z³ = x³ + y³ for a right triangle
How to determine the true statement?The equation is given as:
z³ = x³ + y³
By Pythagoras theorem, we have:
z² = x² + y²
Multiply both sides by z
z³ = zx² + zy²
By comparing z³ = zx² + zy² and z³ = x³ + y³, we have:
x³ + y³ = zx² + zy²
Factor out z
x³ + y³ = z(x² + y²)
Make z the subject
z = (x³ + y³)/(x² + y²)
There exist no solution for the above equation
Hence, there are no solutions for z³ = x³ + y³ for a right triangle
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In an arithmetic sequence the first term is 2 and the second term is 5 , find the eighth term
Answer:
23
Step-by-step explanation:
Arithmetic sequence:In arithmetic sequence, the difference between any consecutive terms is constant and the progression goes either in ascending order or in descending order.
a = first term = 2
a₂ = 5
difference = d = second term - first term
= 5 - 2
d = 3
Formula for finding nth term in arithmetic sequence:
[tex]\sf \boxed{t_n = a + (n-1)*d}[/tex]
t₈ = 2 + (8 -1) * 3
= 2 + 7 *3
= 2 + 21
t₈ = 23
7. The table below shows the soft drinks preferences of people in two age groups.
Sprite
Lemonade
20
30
50
Under 21 years of age
Between 21 and 40
Totals
25
35
60
If one of the 110 subjects is randomly selected, find the probability that:
a) A person prefers to drink sprite
b) A person is between 21 and 40 years old.
c) A person drinks lemonade given they are between 21 and 40.
d) A person drinks Sprite given they are under 21 years of age.
Totals
45
65
110?
Using it's concept, the probabilities are given as follows:
a) 0.5455 = 54.55%.
b) 0.5909 = 59.09%.
c) 0.4615 = 46.15%.
d) 0.5556 = 55.56%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
Out of 110 people, 60 prefer sprite, hence the probability is:
p = 60/110 = 0.5455 = 54.55%.
Item b:
Out of 110 people, 65 are between 21 and 40, hence the probability is:
p = 65/110 = 0.5909 = 59.09%.
Item c:
65 people are between 21 and 40, and of those, 30 drink lemonade, hence the probability is:
p = 30/65 = 0.4615 = 46.15%.
Item d:
45 people are under 21 years of age, and of those, 25 drink sprite, hence the probability is:
p = 25/45 = 0.5556 = 55.56%.
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What is the common ratio in this recursive
definition?
Answer:
r = -1.5
Step-by-step explanation:
recall that ,the recursive formula for a geometric sequence [tex]a_n[/tex] is :
[tex]a_{n} = r \times a_{n-1} \ \ \text{where r is the common ratio }[/tex]
therefore
The common ratio of the sequence:
[tex]a_{n} = -1.5 \times a_{n-1}[/tex]
is r = -1.5
Convert the rational number below to a decimal. Round to the nearest hundredth when necessary. 3/5
Answer: 0.6
Explanation: You need to divide 3 by 5 and it will give you the answer of 0.6
ƒ(1) = −16 [ƒ(1)
f(n) = -29 - f(n-1)
what is f(2)=
Answer:
f(2) = -13
Step-by-step explanation:
Evaluate the given formula with the given value of the variable.
Applicationf(1) = -16 . . . . . . . . . . given
f(n) = -29 -f(n-1) . . . . given
For n = 2, we have ...
f(2) = -29 -f(2-1) = -29 -f(1) = -29 -(-16) . . . . put 2 in place of n and evaluate
f(2) = -13
Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.
The systems of linear equations have been matched with their respective solutions as shown in the image attached below.
What is a system of linear equations?A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
In this exercise, you're required to match the systems of linear equations with their respective solutions as shown in the image attached below.
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