The two expressions 17x−13y+8 and 20x+6y can be rewritten as a difference to be -3x - 19y + 8.
Explanation:To rewrite the two expressions 17x−13y+8 and 20x+6y as a difference, you can first list them separately and then combine by subtraction.
17x - 13y + 8
and
20x + 6y
. The difference between these two expressions is obtained by performing the subtraction as follows: (17x - 13y + 8) - (20x + 6y). Now, you can simplify this by removing the parentheses and switching the sign of the terms being subtracted, which results in:
17x - 13y + 8 - 20x - 6y
. Finally, you combine like terms, x-terms with x-terms and y-terms with y-terms, ending up with:
-3x - 19y + 8
which is the simplified difference of the two expressions.
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Suppose y varies directly as x and y=21 when x=7. which is an equation relating x and y
A segment of a circle has a 120 arc and a chord of 8 square root 3 in. Find the area of the segment.
To find the area of a segment of a circle, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. By plugging in the values and following the steps, we can find that the area of the segment is 3840 - 16√3 square inches.
Explanation:To find the area of a segment of a circle, we need to know the measure of the arc and the length of the chord. In this case, the arc measure is 120 degrees and the chord length is 8√3 inches. To find the area, we can use the formula A = (r^2/2)(θ - sinθ), where r is the radius and θ is the central angle in radians.
First, we need to find the radius by using the length of the chord. The formula for the radius is r = 2c/sinθ, where c is the length of the chord and θ is the central angle in degrees. Plugging in the values, we get r = 8√3/(2sin60) = 4√3/sin60 = 4√3/(√3/2) = 8 inches. Now we can find the area using the formula A = (r^2/2)(θ - sinθ). Plugging in the values, we get A = (8^2/2)(120 - sin120) = 32(120 - √3/2) = 3840 - 16√3 square inches.
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Consider a can in the shape of a right circular cylinder. the top and bottom of the can is made of a material that costs 4 cents per square centimeter, and the side is made of a material that costs 3 cents per square centimeter. we want to find the dimensions of the can which has volume 72 π cubic centimeters, and whose cost is as small as possible. (a) find a function f(r) which gives the cost of the can in terms of radius r. be sure to specify the domain. (b) give the radius and height of the can with least cost. (c) explain how you known you have found the can of least cost.
Final answer:
To find the dimensions of the can with the least cost, we need to minimize the cost function f(r) = 8πr² + 12πrh. We can find the critical points of f(r), determine the minimum point, and verify it using the second derivative test.
Explanation:
To find the dimensions of the can with the least cost, we need to consider the cost of the top, bottom, and the side of the can. Let's denote the radius of the can as 'r' and the height as 'h'.
(a) The cost of the top and bottom of the can is given by the area of two circles, which is 2 * 4 * π * r² = 8πr² cents. The cost of the side is given by the area of a rectangle, which is 4 * π * r * h * 3 = 12πrh cents. So, the function f(r) that gives the cost of the can in terms of the radius r is f(r) = 8πr² + 12πrh.
The domain of the function f(r) is the set of all non-negative real numbers, since the radius cannot be negative.
(b) To find the radius and height of the can with the least cost, we need to minimize the function f(r). We can do this by finding the critical points of f(r), where the derivative of f(r) with respect to r is equal to zero. Solving f'(r) = 0, we can find the value of r that minimizes the function. Once we have the value of r, we can substitute it back into the function f(r) to find the minimum cost.
(c) We can determine that we have found the can of least cost by verifying that the critical point we found for the function f(r) is a minimum point. We can do this by checking the second derivative of f(r) at the critical point. If the second derivative is positive, then the critical point is a minimum point.
How do you graph the equation f(x)=10x+40??
Please HELP PLS
Select the number line that correctly shows the calculation for |−5|.
A number line from negative 5 to positive 5 with increments of 1 is drawn. A horizontal line is drawn from negative 5 to 0, and 5 is written above it.
A number line from negative 5 to positive 5 with increments of 1 is drawn. A horizontal line is drawn from negative 5 to 0, and negative 5 is written above it.
A number line from negative 5 to positive 5 with increments of 1 is drawn. A horizontal line is drawn from 0 to positive 5, and 5 is written above it.
A number line from negative 5 to positive 5 with increments of 1 is drawn. A horizontal line is drawn from 0 to positive 5, and negative 5 is written above it.
Modulus of a number always yields Positive Result.Modulus is defined is as follows
|x|=x, if x>0.
|-x|=-(-x)=x, if x<0
|x|=0, if, x=0.
→ |-5|=5
⇒The best way of representing , 5 on the number line is
Option C
A number line from negative 5 to positive 5 with increments of 1 is drawn. A horizontal line is drawn from 0 to positive 5, and 5 is written above it.
which expression is equivalent to (f+g)(4)?
Answer:
a.
Step-by-step explanation:
took quiz
what is the length of the side opposite the 30 degrees angle?
The length of the side opposite the[tex]\( 30^\circ \)[/tex] angle is 22 units.
To find the length of the side opposite the \( 30^\circ \) angle in a right triangle with a hypotenuse of 44, we can use the sine function:
1. Identify the Known Angle and Hypotenuse: We have an angle of[tex]\( 30^\circ \)[/tex] and a hypotenuse of 44.
2. Use the Sine Function: Since sine relates the opposite side and the hypotenuse in a right triangle, we use the sine function for the [tex]\( 30^\circ \)[/tex] angle.
[tex]\[ \sin(30^\circ) = \frac{\text{opposite}}{44} \][/tex]
3. Sine of 30 Degrees: The sine of [tex]\( 30^\circ \)[/tex] is a known value, which is [tex]\( \frac{1}{2} \).[/tex]
4. Calculate the Opposite Side: Use the sine value to find the opposite side:
[tex]\[ \text{opposite} = 44 \cdot \sin(30^\circ) = 44 \cdot \frac{1}{2} \][/tex]
5. Result: The length of the side opposite the[tex]\( 30^\circ \)[/tex] angle is therefore:
[tex]\[ \text{opposite} = 22 \][/tex]
What is a undo table in math
Final answer:
An undo table in mathematics refers to using inverse functions to reverse the effect of their counterpart operations, such as using the square root to undo a square, and logarithms to revert exponential calculations.
Explanation:
An undo table in math refers to a concept rather than a literal table. It encompasses mathematical operations that effectively reverse the effect of their counterparts. For example, to undo a squaring operation, we use a square root; similarly, to reverse an exponentiation, we utilize a logarithm. In essence, these operations are known as inverse functions.
Let's take the scenario of finding the side length of a right triangle. Given the triangle's side b and hypotenuse c, the Pythagorean Theorem states that a² + b² = c². To solve for side a, one would rearrange the equation to a² = c² - b². Then, to find a, we have to undo the square by taking the square root of both sides, resulting in a = √(c² - b²).
Mathematics is not about rote memorization of rules but understanding the logic and relationships between numbers. As such, when faced with the operation of squaring, we 'undo' it by understanding the core concept of square roots. Similarly, subtraction undoes addition, division undoes multiplication, and the inverse functions of trigonometric and exponential expressions undo their respective basic functions.
Therefore, the natural logarithm (ln) and the exponential function are inverses of each other and hence can undo each other as well.
Write the ratios for sin a and cos
a. sin a = 14/50, cos a = 48/50
Answer:
The ratios for sin a and cos a is [tex]\frac{7}{24}[/tex] .
Step-by-step explanation:
As given the expression in the question be as follow .
[tex]sin\ a = \frac{14}{50}[/tex]
[tex]cos\ a = \frac{48}{50}[/tex]
Thus the ratio of the sin a and cos a .
[tex]\frac{sin\ a}{cos\ a} = \frac{\frac{14}{50}}{\frac{48}{50}}[/tex]
[tex]\frac{sin\ a}{cos\ a} = \frac{14\times 50}{48\times 50}[/tex]
[tex]\frac{sin\ a}{cos\ a} = \frac{14}{48}[/tex]
Simplify the above
[tex]\frac{sin\ a}{cos\ a} = \frac{7}{24}[/tex]
Therefore the ratios for sin a and cos a is [tex]\frac{7}{24}[/tex] .
Find four smallest positive numbers theta such that cosine = 1/2
The student asked for the four smallest positive angles where cosine equals ½. By using the unit circle, the angles of 60° and 300° are identified as solutions, with their general solutions given by θ = π/3 + 2kπ and θ = 5π/3 + 2kπ. The four smallest positive answers are thus 60°, 300°, 420°, and 660°.
Explanation:The student is asking for the four smallest positive angles θ for which the cosine is equal to ½. To find these angles, it helps to recall the unit circle and the fact that the cosine of an angle corresponds to the x-coordinate of a point on the unit circle. The angles with a cosine of ½ in the first 360° (or 2π radians) are those where the corresponding points on the unit circle are at (½, √3/2) and (½, -√3/2). These points correspond to angles of 60° (or π/3 radians) and 300° (5π/3 radians) respectively. However, these are not the only solutions when considering multiple rotations around the circle.
The general solutions for cosine equaling ½ in terms of radians are given by:
θ = π/3 + 2kπ, where k is an integer.θ = 5π/3 + 2kπ, where k is an integer.The four smallest positive solutions correspond to setting k=0 and k=1 in the above equations, yielding the angles:
θ = π/3 (60°)θ = 5π/3 (300°)θ = π/3 + 2π (60° + 360° = 420°)θ = 5π/3 + 2π (300° + 360° = 660°)Note that these angles are measured in degrees for simplicity, but they can be converted to radians by using the equivalence 180° = π radians. To convert these angles to radians, simply divide by 180 and multiply by π.
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HELPPPP!!!!! GEOMETRY IS HARD CX
What is the m∠ABC?
A) m∠ABC = 45°
B)m∠ABC = 15°
C)m∠ABC = 75°
D)m∠ABC = 60°
Answer: it would be (D)
Step-by-step explanation:
Figure ABCD is a square. Prove BD ≅ AC. Statements Reasons 1. ABCD is a square 1. given 2. ∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles 2. definition of a square 3. ∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA 3. right angles are congruent 4. AB ≅ BC ≅ CD ≅ DA 4. ? 5. △BAD ≅ △ABC 5. SAS 6. BD ≅ AC 6. CPCTC What is the missing reason in the proof? all sides of a square are congruent all right angles measure 90° definition of diagonal definition of perpendicular
The missing reason in the geometric proof for step 4 is that all sides of a square are congruent. This property is part of the definition of a square and justifies the statement AB ≅ BC ≅ CD ≅ DA.
The missing reason in the proof is: "all sides of a square are congruent" Option a.
This reason is necessary to establish statement 4: "AB ≅ BC ≅ CD ≅ DA". It's a critical property of a square that all its sides are congruent to each other. Once you establish this, you can proceed with statement 5 using SAS (Side-Angle-Side) congruence to prove △BAD ≅ △ABC, and then finally, using Corresponding Parts of Congruent Triangles are Congruent to conclude BD ≅ AC.
Here is the corrected step:
ABCD is a square∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDAAB ≅ BC ≅ CD ≅ DA△BAD ≅ △ABCBD ≅ ACThe difference of twice a number and 9 is at least −15
Use the variable b for the unknown number.
PLEASE HELP!
A truck driver can travel 560 miles on 28 gallons of gas. How far can he travel on 35 gallons of gas?
Final answer:
The truck driver can travel 700 miles on 35 gallons of gas.
Explanation:
In order to determine the distance the truck driver can travel on 35 gallons of gas, we can set up a proportion using the information provided.
The truck driver can travel 560 miles on 28 gallons of gas, so we can set up the proportion:
= 560 miles / 28 gallons
= x miles / 35 gallons.
Cross-multiplying and solving for x, we find that x = 700 miles.
Therefore, the truck driver can travel 700 miles on 35 gallons of gas.
There are 5 red socks, 2 white socks and 3 blue socks in a basket. What is the probability of picking a pair of red socks?
The probability of picking a pair of red socks is 1/5.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, There are 5 red socks, 2 white socks and 3 blue socks in a basket.
So, The no. of sample space N(S) = 5 + 2 + 3 = 10.
Now pair of red socks means 2 red socks let it be N(A).
∴ The probability of picking a pair of red socks P(A) = N(A)/N(S).
P(A) = 2/10.
P(A) = 1/5.
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The table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward.
Answer:
A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.
C. The ball reaches its maximum height about 4 seconds after it is thrown
Step-by-step explanation: • The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.
• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.
• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.
• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.
• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.
Mikw earned %ll.76 per hour for working 23.5 hours last week. how much money did mike earn last week?\
Is it possible to draw a triangle whose angles measure 50°, 50°, and 80°?
Yes, it is possible to draw a triangle with the angle measures to be; 50, 50 and 80 degrees.
How are triangles discriminated based on angles?A right angled triangle is a triangle having one of its angle with measure of 90°. If all of three angles of a triangle are < 90° then triangle is acute.
If one of the angle is of 90° then the triangle is right angled triangle.
If one of the angle is > 90° then triangle is called obtuse triangle.
First of all, we need to know a quality of all interior angles of a triangle, they must be add to 180 degrees.
Total = 50 + 50 + 80 degrees
Total = 100+80
Total =180 degrees
Therefore, yes, it is possible to draw a triangle with the angle measures to be; 50, 50 and 80 degrees.
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What is the value of g(−3) when g(x)=2x−2 ?
Enter your answer in the box.
g(−3)= ____
Answer:
The answer is -8
Hope this helps :)
Identify the complete predicate in the sentence below.
"The settlers traveled west in covered wagons"
a. traveled west
b. settlers traveled
c. traveled west in covered wagons
Identify the simple subject and verb
"Soon, telegraph lines provided additional communication to the city."
a. lines provided
b. telegraph lines soon provided
c. lines provided communication
Identify the complete predicate in the sentence below.
traveled west in covered wagons.
Identify the simple subject and verb
lines provided
The correct answers are:
Complete predicate: a. "traveled west."
Simple subject and verb: a. "lines provided."
For the sentence "The settlers traveled west in covered wagons":
The complete predicate is: a. "traveled west."
Now, for the sentence "Soon, telegraph lines provided additional communication to the city":
The simple subject is "lines."
The verb is "provided."
So, the correct option is: a. "lines provided."
This simple subject and verb combination makes up the core of the sentence, indicating what the sentence is about and what action is taking place.
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For her tutoring services, Thuy charged Demi $10 per hour and $8 for books and supplies. Demi paid a total of $48.00. Which equation represents this situation?
The equation representing this situation is expressed as [tex]\[ 10h + 8 = 48 \][/tex] and
Demi received 4 hours of tutoring services.
Let's denote the number of hours Demi received tutoring services as [tex]\( h \).[/tex]
The equation representing this situation can be expressed as:
[tex]\[ 10h + 8 = 48 \][/tex]
Now, let's solve for [tex]\( h \):[/tex]
[tex]\[ 10h = 48 - 8 \][/tex]
[tex]\[ 10h = 40 \][/tex]
[tex]\[ h = \frac{40}{10} \][/tex]
[tex]\[ h = 4 \][/tex]
So, Demi received 4 hours of tutoring services.
To find the equation representing the situation, we need to consider the total cost Demi paid. She paid $10 per hour for tutoring services, so the cost for the tutoring service itself is [tex]\( 10h \),[/tex] where [tex]\( h \)[/tex] represents the number of hours of tutoring. Additionally, she paid $8 for books and supplies, which is a fixed cost regardless of the number of hours. Therefore, we add $8 to the cost equation. This gives us [tex]\( 10h + 8 = 48 \).[/tex]
Next, we solve this equation to find the value of [tex]\( h \),[/tex] which represents the number of hours of tutoring. We subtract 8 from both sides to isolate the term [tex]\( 10h \),[/tex] giving us[tex]\( 10h = 40 \)[/tex]. Then, we divide both sides by 10 to solve for [tex]\( h \),[/tex] which gives us[tex]\( h = \frac{40}{10} = 4 \).[/tex]
So, Demi received 4 hours of tutoring services.
Complete question:
For her tutoring services, Thuy charged Demi $10 per hour and $8 for books and supplies. Demi paid a total of $48.00. Which equation represents this situation?
Item 19 Question 1 A furniture store is having a sale where everything is 40% off. a. Write a function that represents the amount of discount dd on an item with a regular price pp.
To calculate the discount amount on an item with a regular price during a sale of 40% off, use the function d(p) = 0.40 x p.
The question involves creating a mathematical function to calculate the amount of discount during a sale. The store is offering a 40% discount on items, so to find the discount amount d on an item with a regular price p, we can write the function as d(p) = 0.40 * p. Here, p represents the regular price of the item, and d represents the discount amount in dollars that will be subtracted from the regular price.
Complete the following multiplication problems. a. 0.34 × 6 b. 0.11 × 4 c. 17 × 0.07 d. 28 × 0.003 e. 3.8 × 5 f. 5.931 × 7 g. 14.07 × 13 h. 3.005 × 32 i. 0.8 × 0.3 j. 0.45 × 0.05 k. 0.09 × 0.02 l. 0.074 × 0.08 m. 2.3 × 0.9 n. 7.25 × 0.3 o. 4.53 × .003 p. 53.67 × 0.056 q. 1.1 × 3.7 r. 3.76 × 18.9 s. 4.57 × 6.1 t. 24.13 × 1.48
Answer with Step-by-step explanation:
a. 0.34 × 6=2.04
b. 0.11 × 4=0.44
c. 17 × 0.07=1.19
d. 28 × 0.003= 0.084
e. 3.8 × 5=19
f. 5.931 × 7=41.517
g. 14.07 × 13=182.91
h. 3.005 × 32=96.16
i. 0.8 × 0.3=0.24
j. 0.45 × 0.05=0.0225
k. 0.09 × 0.02=0.0018
l. 0.074 × 0.08=0.00592
m. 2.3 × 0.9=2.07
n. 7.25 × 0.3=2.175
o. 4.53 × .003=0.01359
p. 53.67 × 0.056=3.00552
q. 1.1 × 3.7 =4.07
r. 3.76 × 18.9 =71.064
s. 4.57 × 6.1 =27.877
t. 24.13 × 1.48=35.7124
NEED AN ANSWER ASAP!!!!!!!!!!!
The graph of the function f(x) = x3 + 5x2 + 3x – 9 intersects the x-axis at the points (–3, 0) and (1, 0) as shown. Which expression is equivalent to x3 + 5x2 + 3x – 9?
A) (x – 3)(x – 3)(x + 1)
B) (x – 3)(x + 1)(x + 1)
C) (x – 1)(x – 1)(x + 3)
D) (x – 1)(x + 3)(x + 3)
Keira created color panels for a wall using a mix of only red and blue paints. She plotted the quantities of red and blue paints used for each mix and connected them using a line segment, as shown in the graph below:
A line graph titled Color Mix, with Quantity of Blue Paint, in millimeters, on the X axis and Quantity of Red Paint, in millimeters, on the Y axis. The X axis has a scale from 0 to 9 with an increment of 1. The Y axis has a scale of 0 to 18 in increments of 2. A straight line connecting 3, 2 and 7, 12 is drawn. Which statement best describes the domain of the function represented in the graph? (1 point)
Answer:
3 ≤ x ≤ 7
Step-by-step explanation:
Why, because i said so, and also because i got it right in the quiz
Answer:
3 ≤ x ≤ 7
Step-by-step explanation:
What are the solutions of 4 + 5t < 19?
a courier earns a fixed amount for each package she delivers and yesterday her average hourly wage was $12.50 an hour if she worked 8 hours yesterday and delivered 25 packages how much does she earn for each package delivered?
Answer: She earned $ 4 for each package delivered.
Step-by-step explanation:
Since, her total rate of earning = $ 12.50 per hours,
And, she worked for 8 hours.
⇒ She earned in 8 hours = 8 × 12.50 = $ 100
According to the question,
She delivered 25 packages in 8 hours.
⇒ 25 packages = 8 hours
⇒ 25 packages = $ 100
⇒ 1 package = $ 4
Thus, she earned 4 dollars for each package.
At Billy‘s preschool they have bicycles and tricycles with a total of 57 wheels. The number of bicycles is three less than three times the number of tricycles. How many of each are there?
20 points! Please help! a/b = c for b = ?
p: x – 5 =10 q: 4x + 1 = 61 Which is the inverse of p → q?
a- If x – 5 ≠ 10, then 4x + 1 ≠ 61.
b- If 4x + 1 ≠ 61, then x – 5 ≠ 10.
c-If x – 5 = 10, then 4x + 1 = 61.
d- If 4x + 1 = 61, then x – 5 = 10.
Answer: the correct option is
(a) If x – 5 ≠ 10, then 4x + 1 ≠ 61.
Step-by-step explanation: We are given to select the correct inverse of the conditional statement p → q if
p : x – 5 =10 and q : 4x + 1 = 61.
We know that
the inverse of a conditional statement p → q is given by "not p → not q".
Therefore, the inverse of the given statement is
not p → not q
that is, if x – 5 ≠ 10, then 4x + 1 ≠ 61.
Thus, the required inverse is " x – 5 ≠ 10, then 4x + 1 ≠ 61."
Option (a) is CORRECT.