We want to analyze the terms of the given expression.
15) second term, z/3
16) third term, 2*w
The given expression is:
1 + z/3 + 2*w
15) We want to find which part of the expression is a quotient.
A general quotient is something of the form a/b, so compared with the expression, the term that is a quotient is the second term; z/3.
Where the first number, z, is called the numerator and the second is called the denominator.
Notice that the variable z is on the numerator, so this would be a linear dependence with z.
16) We want to find which part of the expression is a product of two factors.
It is the third term, 2*w
Where the two factors are 2 and w.
Again, the variable si w, and we are multiplying it by a constant number, 2.
So we also have a linear dependence with w.
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In the expression 1 + z/3 + 2w, the quotient is z/3, where z is the numerator and 3 is the denominator. The product of two factors is 2w, with 2 and w being the factors.
Explanation:The student asked about parts of the expression 1 + z/3 + 2w.
15) Quotient in the Expression
The quotient refers to the result of division. In the expression given, the quotient is z/3. Its parts are the numerator z, which is the value being divided, and the denominator 3, which is the value by which z is divided.
16) Product of Two Factors in the Expression
The product refers to the result of multiplication. In the expression, the product is 2w. Its parts are the two factors being multiplied: the constant 2 and the variable w.
Solve for x (round to the nearest degree)
Answer:
Step-by-step explanation:
Sin x = opp/hyp
Sin x = 4/7
Sin x = 0.5714
X =sin-¹(0.5714)
X = 34.8
X = 35°
The required measure of angle x in the triangle is 35°.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
From triangle,
Sin x = perpendicular/hypotenuse
Sin x = 4/7
Sin x = 0.57
X =sin⁻¹(0.57)
X = 34.9
x = 35°
Thus, the required measure of angle x in the triangle is 35°.
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Y is 4 more than the product of 7 and x
Answer:
Let's write this out in an equation.
y = 4 + 7x
The mathematical equation 'Y is 4 more than the product of 7 and x' can be written as 'Y = 7x + 4' where Y is the dependent variable and x is the independent variable. This is a standard form linear equation.
Explanation:The subject of this question is Mathematics, and it appears to be targeted at a Middle School level. The statement 'Y is 4 more than the product of 7 and x' is a mathematical equation that can be written as Y = 7x + 4. Here, '7x' refers to the product of 7 and x, and the '+ 4' indicates that Y is 4 more than this product. It is a linear equation in variable x.
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A company has a $150 budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. The company also wants to use the entire budget. Suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. Which statement is correct?
The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r minus t = 20 and 5 r + 5 t = 150.
The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r minus t = 20 and 5 r + 5 t = 150.
The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
Mark this and return
Answer:
2. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
Step-by-step explanation:
The total lunch budget of the company = $150
Total number of employees = 20
The cost of 1 roast beef sandwich = $5
The cost of 1 tuna sandwich = $5
r represents the number of roast beef sandwiches provided.
t represents the number of tuna sandwiches provided.
Now, consider the given statements:
Here, total number of sandwiches purchased = Total number of employees
⇒ r + t = 20 .... (1)
Also, as each type of sandwich costs $5.
So, the cost of r roast beef sandwiches = r x ( Cost of 1 beef sandwich)
= r x ( $5) = 5 r
And, the cost of t tuna sandwiches = t x ( Cost of 1 tuna sandwich)
= t x ( $5) = 5 t
Total cost of (r +t) sandwiches = Total Lunch Budget
⇒ 5 r + 5 t = 150 .... (2)
Hence, from (1) and (2) the above situation can be represented as:
r + t = 20
5 r + 5 t = 150
Hence, the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
Help help help help help
5. What is the total length of the race course?
Final answer:
The total length of a race course would be the perimeter if it's a closed loop. Without specific details of the race course, the exact measurement cannot be provided, but several examples hint at how the length can be determined if more information is available.
Explanation:
The student's question pertains to the total length of a race course. To ascertain the total length, one would typically consider the perimeter of the race track if the course returns to the start line or the straight distance from start to finish if not returning. This question does not provide specific details about the dimensions or shape of the race course, which are necessary to give an exact measurement. However, if we refer to the provided information, option (a) says that the perimeter is the distance, and the shortest distance between the start and finish line is the magnitude of displacement. This suggests that the total length could be measured by the perimeter if it's a closed loop.
Some examples include a marathon which has a set length of 42.188 km, or a soccer field where the perimeter would be the sum of all sides, assuming the field was used for a running event. For an actual racecourse, you would need to know the specific dimensions or shape to calculate the total length.
Factor y2 + 5y + 6.
(y + 6)(y + 1)
(y + 2)(y + 3)
(y + 4)(y + 2)
Answer:
(y + 2)(y + 3)
Step-by-step explanation:
Type A is 8 feet tall and grows at a rate of 6 inches per year.
Type B is 2 feet tall and grows at a rate of 15 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
The required time is 8 years.Step-by-step explanation:
Let, it will take x years to be of same height for these trees.
We know that 1 ft = 12 inches.
8 ft = [tex]12\times8 = 96 inch[/tex]. 2 ft = 24 inch.
After x years, the height of type A will be (96 + 6x) inch and the height of type B will be (24 + 15x) inch.
We need find the value of x, for which 96 + 6x = 24 + 15x or, 9x = 72 or, x = 8.
The ____ of Powers property allows you to rewrite xa· xb as xa + b.
Answer:
product
Step-by-step explanation:
Answer:
The Correct Answer is product of powers
Step-by-step explanation:
Mark as BRAINLIEST if you are right
Answer:
E
Step-by-step explanation:
7+8+4=19
4/6 + 3/6 + 1/6 = 1 2/6
19 + 1 1/3
20 1/3
One leg of a right triangle is 12, and the hypotenuse is 20.
The length of the other leg is ___
We can ise Pythagorean triplet which is ( 12 , 16 , 20 )
Therefore the answer is 16.
Step-by-step explanation:
Or we can use Pythagoras theorem , stated as ;
( hyp )^2 = ( adj )^2 + ( opp )^2
hyp ( hypotenuse ) = 20
We can assume the adj ( adjacent ) = 12
By substituting the values ,
20^2 = 12^2 + ( adj )^2
400 = 144 + ( adj )^2
400 - 144 = ( adj )^2
256 = ( adj )^2
Take the square root of both sides
✓256 = adj
16 = adj
Therefore the length of the other leg which is the adjacent( adj ) side is 16.
The length of the other leg is 16
To find the length of the other leg of a right triangle, given one leg is 12 and the hypotenuse is 20, we use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).
This relationship is given by:
a² + b² = c²
1. Here, one leg (a) is 12 and the hypotenuse (c) is 20. So we can write:
12² + b² = 20²
2. Calculating the squares gives:
144 + b² = 400
3. Subtract 144 from both sides to find b²:
b² = 256
4. Finally, take the square root of both sides to find b:
b = √256 = 16
Thus, the length of the other leg is 16.
It is known that x1 and x2 are roots of the equation [tex]6x^{2} +7x+k=0[/tex]
, where [tex]2x_{1} +3x_{2} =-4[/tex]. Find k.
Answer:
[tex]k=-5[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]6x^{2} +7x+k=0[/tex]
so
[tex]a=6\\b=7\\c=k[/tex]
substitute in the formula
[tex]x=\frac{-7\pm\sqrt{7^{2}-4(6)(k)}} {2(6)}\\\\x=\frac{-7\pm\sqrt{49-24k}} {12}[/tex]
so
[tex]x_1=\frac{-7+\sqrt{49-24k}} {12}\\\\x_2=\frac{-7-\sqrt{49-24k}} {12}[/tex]
Remember that
[tex]2x_1+3x_2=-4[/tex]
substitute
[tex]2(\frac{-7+\sqrt{49-24k}} {12})+3(\frac{-7-\sqrt{49-24k}} {12})=-4\\\\(\frac{-14+2\sqrt{49-24k}} {12})+(\frac{-21-3\sqrt{49-24k}} {12})=-4[/tex]
Multiply by 12 both sides
[tex](-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48\\\\-35-\sqrt{49-24k}=-48\\\\\sqrt{49-24k}=48-35\\\\\sqrt{49-24k}=13[/tex]
squared both sides
[tex]49-24k=169\\24k=49-169\\24k=-120\\k=-5[/tex]
therefore
The equation is
[tex]6x^{2} +7x-5=0[/tex]
The roots are
[tex]x=\frac{-7\pm\sqrt{49-24(-5)}} {12}\\\\x=\frac{-7\pm\sqrt{169}} {12}\\\\x=\frac{-7\pm13} {12}\\\\x_1=\frac{-7+13} {12}=\frac{1} {2}\\\\x_2=\frac{-7-13} {12}=-\frac{5} {3}[/tex]
Darcy harvests 8\dfrac348
4
3
8, start fraction, 3, divided by, 4, end fraction acres of corn every \dfrac56
6
5
start fraction, 5, divided by, 6, end fraction of an hour. Darcy harvests corn at a constant rate
How many acres does she harvest per hour?
Answer:
[tex]10\frac{1}{2}\ \frac{acres}{hour}[/tex]
Step-by-step explanation:
The correct question is:
Darcy harvests 8 3/4 acres of corn every 5/6 of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?
we know that
To find out the corn rate harvested per hour or the unit rate, divide the number of acres of corn harvested by the total time it takes
so
[tex]8\frac{3}{4} :\frac{5}{6}[/tex]
Convert mixed number to an improper fraction
[tex]8\frac{3}{4}=8+\frac{3}{4}=\frac{8*4+3}{4}=\frac{35}{4}[/tex]
substitute
[tex]\frac{35}{4} :\frac{5}{6}=\frac{210}{20}=\frac{21}{2}\ \frac{acres}{hour}[/tex]
Convert to mixed number
[tex]\frac{21}{2}\ \frac{acres}{hour}=\frac{20}{2}+\frac{1}{2}=10\frac{1}{2}\ \frac{acres}{hour}[/tex]
Answer:
[tex]10\frac{1}{2}[/tex] or [tex]\frac{21}{2}[/tex]
18) . Are these two claims equivalent, in conflict, or not comparable because they’re talking about different things?
a. “We mark up the wholesale price by 33% to come up with the retail price”
b. “The store has a 25% profit margin”
The claims "marking up the wholesale price by 33% for retail" and "having a 25% profit margin" are not equivalent. While both involve pricing strategies, a 33% markup results in a profit margin of approximately 24.81%, demonstrating that markup and profit margin describe different aspects of pricing.
Explanation:The question asks if the claims "We mark up the wholesale price by 33% to come up with the retail price" and "The store has a 25% profit margin" are equivalent, in conflict, or not comparable. To examine this, we need to understand the definition of markup and profit margin. Markup refers to the percentage increase over the cost price to arrive at the selling price, while profit margin is the percentage of revenue that remains as profit after covering all costs.
Considering a hypothetical item with a wholesale price of $100:
A 33% markup means adding $33 to the wholesale price, making the retail price $133.To calculate profit: Retail Price - Wholesale Price = Profit, so $133 - $100 = $33.The profit margin is then calculated as (Profit / Retail Price) * 100, which is ($33 / $133) * 100 = 24.81%.Therefore, these two claims are not equivalent. A 33% markup on the wholesale price results in a profit margin of approximately 24.81%, not 25%. This slight difference indicates that while related, markup and profit margin describe different aspects of pricing strategy. They are not direct conversions of one another but are interrelated in determining the final retail price and the resulting profit from sales.
Suppose that circles R and S have a central angle measuring 125°. Additionally, circle R has a radius of
2
3
feet and the radius of circle S is
3
4
feet.
If the length of the intercepted arc for circle R is
4
9
π feet, what is the length of the intercepted arc for circle S?
Answer:
The length of the intercepted arc for circle S is (1/2)π ft
What does x equal? -5(x-1)=40
Hey!
~Set up the equation: -5(x-1)=40
~ Divide 5 on both sides: 40/-5
~ Simplify: x-1=-8
~ We want to get x by itself, so subtract +1 to both sides.
~ Simplify: x = -7
~ Therefore, x = -7.
Answer:
x = - 7
Step-by-step explanation:
-5(x - 1) = 40
-5x + 5 = 40
- 5x = 40 - 5
- 5x = 35 | x(-)
5x = - 35
x = - 35 : 5
x = - 7
The distance from Earth to the moon is 384,400 kilometers. What is this distance expressed in scientific notation?
3.844E5 kilometers
3.844 × 105 kilometers
3.844E-5 kilometers
3.844E-6 kilometers
3.844 × 106 kilometers
3.844E6 kilometers
3.844 × 10-6 kilometers
3.844 × 10-5 kilometers
Answer:
B: 3.844x10^5
E: 3.844x10^6
Step-by-step explanation:
Find the volume of a cube with the given side: 2cm
Volume is length x width x height.
A cube has the same length, width and height.
The volume of the cube is 2 x 2 x 2 = 8cm
Answer: 8 cm
Happy to help!
Answer: the answer is 8
Step-by-step explanation: The answer is 8 because the equation LxHxW and since It is a cube it is 2x2x2
goes through (0,0) and is parallel to the y=-5
Answer:
y=0
Step-by-step explanation:
Parallel lines never intersect therefore you need to find what y=-5 would look like on a graph (look at the image for reference, it is the blue line). Because it is a straight line then you just need to find what would make a straight line across the origin, therefore you would have to do y=0 (the red line on the image.)
The reason for putting y=0 or y=-5 is because the y value will ALWAYS stay the same and the x value will continue going on and on, without intersecting.
Which function has the greater rate of change?
Function 1
Function 2
Answer:
Function 1.
Step-by-step explanation:
The rate of change of Function 2 = (18.75 - 14.25)/ (5 - (-1))
= 4.5 / 6
= 3/4 or 0.75.
For Function 1 it is 5/6 or 0.83
So Function 1 has greatest rate of change.
Can someone help? pls.. (Find the range for the following set of data: 10.3, 12.8, 12.9, 15.3, 15.9, 11.5, 4.3, 7.9, 9.6, 13.6, 2.8) a. 11.5 c. 12.1 b. 13.1 d. 11
Answer:
B. 13.1
Step-by-step explanation:
To find the range of a set of data, first, order the numbers from least to greatest:
2.8, 4.3, 7.9, 9.6, 10.3, 11.5, 12.8, 12.9, 13.6, 15.3, 15.9
Next, find the least and greatest number:
2.8, 4.3, 7.9, 9.6, 10.3, 11.5, 12.8, 12.9, 13.6, 15.3, 15.9
Subtract the least number from the greatest number:
15.9 - 2.8 = 13.1
B. 13.1 is your answer.
~
If each side of the square is 7 units long, how long is the diagonal to the nearest tenth?
I NEED AN ANSWER ASAP
The diagonal of square is 9.90 units long.
Step-by-step explanation:
Given,
Length of each side of square= s = 7 units
Diagonal of square = s√2
Putting s = 7
Diagonal of square = [tex]7*\sqrt{2}[/tex]
Diagonal of square = 7 * 1.414
Diagonal of square = 9.898
Rounding off to nearest hundredth
Diagonal of square = 9.90 units
The diagonal of square is 9.90 units long.
Keywords: square, diagonal
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Answer:
d = 9.9 units
Step-by-step explanation:
The step by step explanation is in the picture below
Find the probability of rolling factors of 3
Final answer:
The probability of rolling factors of 3 on two six-sided dice is 13 out of 36 possible outcomes, which simplifies to approximately 0.361 or 36.1%.
Explanation:
Calculating the Probability of Rolling Factors of 3
To find the probability of rolling factors of 3 when tossing two dice, we must consider the combinations that result in multiplying to three or being a multiple of three. Each die has six faces, so there are a total of 6 x 6 = 36 possible outcomes when rolling two dice. The factors of 3 are 1 and 3. So we have to count the outcomes where at least one of the dice shows a 3 or both dice show 1, which are the relevant factors of 3. If we roll a 3 on one die, the other die can show any number from 1 to 6, giving us 6 outcomes. If we roll a 3 on the other die, we again have 6 different outcomes. However, this would double-count the scenario where both dice show 3, so we must subtract this outcome once.
Therefore, the number of favorable outcomes is (6 + 6 - 1 = 11). The probability can be computed as the number of favorable outcomes divided by the total number of possible outcomes, giving us a probability of 11/36.
If we want the probability of getting one 1 and one 3 in two tosses, we must add to this the probability of tossing a 3 first and a 1 second. The event of rolling a 1 and then a 3, or 3 and then a 1, each has a probability of 1/36. As there are two ways this can happen (1 then 3, or 3 then 1), the probability for this event is 1/36 + 1/36 = 2/36 or 1/18, which must be added to our initial 11/36.
Hence, the final probability of rolling factors of 3 on two dice is (11/36) + (1/18) = (11/36) + (2/36) = 13/36.
What is 34/8-16/3-14/9=
Answer:
-95/36
Step-by-step explanation: I think that's right.
Eric is a real estate agent. He makes a 5% commission on each house he sells. Last month, Eric sold three houses. The sale price of each house is shown in the table. House saleAmount House 1 $55,000 House 2$105,525 House 3 $35,200 How much did Eric earn last month? Enter your answer in the box .
Answer:
Eric earned last month US$ 9,786.25
Step-by-step explanation:
Commission of Eric on each house sold = 5% = 0.05
House 1 $55,000
55,000 * 0.05 = $ 2,750
House 2 $105,525
105,525 * 0.05 = $ 5,276.25
House 3 $35,200
35,200 * 0.05 = $ 1,760
Eric earned last month = $ 2,750 + $ 5,276.25 + $ 1,760
Eric earned last month US$ 9,786.25
Multiply. 35⋅34
A. 9/20
B. 4/10
C. 4/5
D. 5/4
Answer:
a
Step-by-step explanation:
FIND THE SLOPE
please explain me how to do it
Answer:
slope = - 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 7) and (x₂, y₂ ) = (0, 3) ← 2 ordered pairs from the table
m = [tex]\frac{3-7}{0+4}[/tex] = [tex]\frac{-4}{4}[/tex] = - 1
How many squares can you make from a square?
Answer:
more than 16 squares
Simplify square root of negative 49.
The value of the square root of negative 49 will be ± 7i.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ √(-49)
We know that √-1 = i, then we have
⇒ √(-1 x 49)
⇒ ± 7i
The value of the expression √(-49) will be ± 7i.
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Final answer:
The square root of negative 49 simplifies to 7i, where i is the imaginary unit.
Explanation:
The simplify question involves finding the square root of negative 49, which is a mathematical operation dealing with complex numbers. To simplify the square root of a negative number, we use the imaginary unit i, where i is defined as the square root of negative one. Therefore, to simplify √-49, we break it down into the product of √-1 and √49. Since √-1 equals i, and √49 equals 7, the simplification results in 7i.
Graph the inequality. x + 2y > 4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]x+2y > 4[/tex]
Isolate the variable y
subtract x both sides
[tex]2y > -x+4[/tex]
Divide by 2 both sides
[tex]y > -\frac{1}{2}x+2[/tex]
The solution of the inequality is the shaded area above the dashed line
[tex]y=-\frac{1}{2}x+2[/tex]
The slope of the dashed line is negative
The y-intercept of the dashed line is (0,2)
The x-intercept of the dashed line is (4,0)
therefore
The graph in the attached figure
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