The equation models the cost of making different numbers of shirts, where y is the cost in dollars and x is the number of shirts produced is y = 7.5x - 750
To create an equation that models the cost of making different numbers of shirts, we need to determine the relationship between the number of shirts produced and the cost. One way to do this is to use the two-point form of the equation of a line, which is:
y - y₁ = (y₂ - y₁)/(x₂ - x₁) * (x - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.
Using the points (100, 600) and (250, 1387.50), we can find the slope of the line:
slope = (y₂ - y₁)/(x₂ - x₁) = (1387.50 - 600)/(250 - 100) = 7.5
Then, we can use the point-slope form of the equation of a line to write the equation:
y - y₁ = m(x - x₁)
where m is the slope and (x1, y1) is a point on the line. Using the point (100, 600), we get:
y - 600 = 7.5(x - 100)
Simplifying, we get:
y = 7.5x - 750
This equation models the cost of making different numbers of shirts, where y is the cost in dollars and x is the number of shirts produced.
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Solve for e: - 12e =6q -4
Answer:
e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
- 12e = 6q - 4 ( divide through by - 12 )
e = [tex]\frac{6}{-12}[/tex] q - [tex]\frac{4}{-12}[/tex] , that is
e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]
Write this trinomial in factored form.
9b^2 + 13b + 4
The factored form of the trinomial 9b² + 13b + 4 is ( 9b + 4 )( b + 1 ).
What is the factored form of the trinomial?Given the trinomial in the question:
9b² + 13b + 4
To factor the trinomial 9b² + 13b + 4, we need to find two binomials whose product equals 9b² + 13b + 4.
We can start by looking for two numbers that multiply to 9 × 4 = 36 and add up to 13. Those numbers are 9 and 4.
Now we need to use these numbers to factor the trinomial.
9b² + 4b + 9b + 4
Factor out the greatest common factor from each group
9b² + 9b + 4b + 4
9b( b + 1 ) + 4( b + 1 )
( 9b + 4 )( b + 1 )
Therefore, the factored form is ( 9b + 4 )( b + 1 ).
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5- When the equation x²- 6x + 9 = 49 is transformed into the equation
(x - p)² = q, what are the values for p and q?
A. -3 and 40
B. -3 and 49
C. 3 and 40
D. 3 and 49
The values for p and q in the equation (x² - 6x + 9 = 49) transformed into (x - p)² = q are p = 3 and q = 40, so the answer is option A: -3 and 40.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find unknown values of variables.
In the given question,
To transform the equation x² - 6x + 9 = 49 into the equation (x - p)² = q, we can first subtract 49 from both sides to get:
x² - 6x - 40 = 0
Next, we complete the square by adding (6/2)² = 9 to both sides:
x² - 6x + 9 - 40 + 9 = 0 + 9
(x - 3)² - 22 = 0
Now we can see that p = 3 and q = 22.
Therefore, the answer is D) 3 and 49.
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. Joe has 784 one-centimetre cubes.
He arranges all of the cubes into a cuboid.
The perimeter of the top of the cuboid is 30 cm.
Each side of the cuboid has a length greater than 2 cm.
Find the height of the cuboid.
The height of the cuboid is 14cm.
What is the perimeter?
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Here, we have
Given: Joe has 784 one-centimeter cubes.
He arranges all of the cubes into a cuboid.
The perimeter of the top of the cuboid is 30 cm.
Each side of the cuboid has a length greater than 2 cm.
We have to find the height of the cuboid.
1. a = 7, b = 8
V = 784
We know that
height = V/s
h = 784/56
h = 14cm
Hence, the height of the cuboid is 14cm.
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a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 441 gram setting. is there sufficient evidence at the 0.02 level that the bags are overfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.
Null hypothesis: Bags are filled correctly at 441 grams. Alternative hypothesis: Bags are overfilled (mean weight > 441 grams).
The null hypothesis (H0) is that the bags are filled correctly at the 441 gram setting, meaning the mean weight of the bags is 441 grams. The alternative hypothesis (Ha) is that the bags are overfilled, meaning the mean weight of the bags is greater than 441 grams. Thus, the hypotheses can be written as:
H0: μ = 441
Ha: μ > 441
To test these hypotheses, we can use a one-sample t-test with a significance level of 0.02. We will compare the sample mean weight of a random sample of bags to the population mean of 441 grams, using the t-test statistic and the corresponding p-value. If the p-value is less than 0.02, we can reject the null hypothesis and conclude that the bags are overfilled
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10% of a number is X. What is 100%? Assume X > 0
100% of the number is 100 times X.
What is percentage?A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
If 10% of a number is X,
0.1 * number = X
number = X / 0.1
number = 10 * X
As a result, if X represents 10% of a number, the whole number is 10 times X. To get 100% of the answer, simply multiply X by 10 again:
100% of the number = 10 * X * 10 = 100 * X
So, 100% of the number is 100 times X.
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The creator of two apps records the number of downloads over time a. From Week 6 to Week 8, which app has a greater average rate of change b. WHich app will eventually have a greater number of downloads? Explain.
he diameter of a semicircle is 23 centimeters. What is the semicircle's area?
Answer: in2
Step-by-step explanation:
answerd
The graph of EFG is shown. Graph the image of EFG after translation of 3 units left 1 unit down write the coordinates of the image
The coordinates for the image after the translation of EFG would be E'(-2, 3), F'(-4, 0), and G'(-1, -2).
How to translate an image ?To translate a point, you simply add or subtract the specified units from its x and y coordinates. In this case, you are asked to translate the points 3 units left and 1 unit down.
To translate 3 units left, subtract 3 from the x-coordinate, and to translate 1 unit down, subtract 1 from the y-coordinate.
For point E (1, 4):
E' = (1 - 3, 4 - 1) = (-2, 3)
For point F (-1, 1):
F' = (-1 - 3, 1 - 1) = (-4, 0)
For point G (2, -1):
G' = (2 - 3, -1 - 1) = (-1, -2)
The translated points are E'(-2, 3), F'(-4, 0), and G'(-1, -2).
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The slope at [1,pi/2] from -8x^3/siny
As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.
what is slope ?The slope of a line in mathematics serves as a gauge for how steep it is. Between any two locations on the line, it is the proportion of the shift in the vertical motion (y) to the shift in the horizontal position (x). If we take into account two points on a line, (x1, y1) and (x2, y2), we can use the following formula to get the slope of the line: slope equals (y2 - y1)/. (x2 - x1) . Depending on the line's direction, the inclination can be zero, positive, or negative. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.
given
Finding the derivative of the given function with respect to x can be our first step. By applying the quotient rule, we get:
F(x) = 8x 3 sin (y)
[tex][(sin(y))(-24x2)] = f'(x) - (-8x^3) (cos(y))(y')] / (sin(y))^2[/tex]
where the derivative of y with respect to x is denoted by y'.
We can change x=1 and y=pi/2 in the equation above since we are interested in the slope at the position [1, pi/2].
Due to the fact that cos(pi/2) = 0 and sin(pi/2) = 1, we can write:
[tex]f'(1) = [(1)(-24) (-24) - (-8)(1)(0)(y')] / (1)^2[/tex]
f'(1) = -24 + 0
f'(1) = -24
As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.
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Kira deposit $2000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first two years
Kira will be paid $120 in interest in the first two years.
How much interest will Kira be paid in the first two years?Simple interest is expressed as;
I = P × r × t
Where I is the interest, P is the principal amount, r is the interest rate per year, and t is the time in years.
Given that:
Principal P = $2000Elapsed time t = 2 yearsInterest rate r = 30% = = 3/100 = 0.003Interest I = ?Substituting the given values, we get:
I = P × r × t
I = 2000 × 0.03 × 2
I = $120
Therefore, the interest in the first two years is $120.
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11. You have a bank account in which
your balance increases annually at a rate of 7.25%. If your initial
investment was $250, write an
equation that represents your
balance after x years.
Initial Value (a):
Rate (r):
Time (x):
Equation:
The equation that represents your balance after x years is: [tex]250 * (1.0725)^x[/tex]
what is interest ?
To calculate simple interest, multiply the principal by the rate of interest rates, the duration, and several other variables. The marketing formula is simple returns = capital + interests + hours.
Initial Value (a): $250
Rate (r): 7.25% per year (or 0.0725 as a decimal)
Time (x): x years
The formula for calculating the balance after x years is:
[tex]Balance = a * (1 + r)^x[/tex]
Plugging in the values, we get:
[tex]Balance = 250 * (1 + 0.0725)^x[/tex]
So the equation that represents your balance after x years is:
[tex]Balance = 250 * (1.0725)^x[/tex]
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Identify the equation of the line graphed below. Prove by converting! A. 3x + 5y = 5 B. 3x - 5y = 5 C. 5x + 3y = 3 D. 5x - 3y = 3
The equation of the line which is as graphed in the task content is; Choice D; 5x - 3y = 3.
Which equation represents the graphed line?By observation, two points on the given line are; (0, -1) and (3, 4).
On this note, the slope of the line can be determined as the rate of change in y to change in x as follows;
slope, m = (4 - (-1)) / (3-0)
Slope, m = 5 / 3.
Using the point-slope form equation; using the slope, m = 5/3 and point (3, 4).
y - 4 = 5/3 (x - 3)
3y - 12 = 5x - 15
Therefore, 5x - 3y = 3.
Ultimately, the equation of the line is; Choice D; 5x - 3y = 3.
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Factor.
2d² + 11d + 9
Answer:
(d + 1) (2d + 9)
Step-by-step explanation:
2d² + 11d + 9
First, we rewrite 11d as 2d + 9d, we have the equation:
2d² + 2d + 9d + 9
We group them, so the equation will be
(2d² + 2d) + (9d + 9)
Factor out the GCF of each group
2d (d + 1) + 9 (d + 1)
Factor the polynomial by factoring out the greatest common factor, d+1
(d + 1) (2d + 9)
So, the answer is (d + 1) (2d + 9)
Alyssa received a leadership patch, as shown below, when she was elected Student Body President.
The patch is in the shape of a right triangle where the top section and the whole patch form similar triangles.
If x = 55 mm, z = 80 mm, and the tangent of the bottom angle, where the star is located, is equal to , what is the length of w?
A. 32 mm
B. 48 mm
C. 55 mm
D. 40 mm
The length of the side w is 55mm. Option C
How to determine the valueNote that the different trigonometric identities are;
sinetangentcosinesecantcosecantcotangentFrom the triangle shown, we have;
x = 45mm
z = 80mm
We also have tangent where the star is located is 1
Then,
tan θ = 1
find the tangent inverse of the values
θ = 45 degrees
As given in the diagram, the diagrams are similar
So both angles are 45 degrees
However, we can deduce that since the angles are equal, then, the sides are equal
x = w = 55mm
w = 55mmm
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pls hlp thx sososos much
The measure of the angle MSP, m∠MSP, obtained using the relationship between linear pair angles is 80°
What are linear pair angles?Linear pair angles are angles that have a sum of 180°. Linear pair angles come together to form a straight line.
The specified measure of the angle NSM is m∠NSM = 100°
The angles ∠NSM and ∠MSP are linear pair angles therefore;
m∠NSM + m∠MSP = 180°
Plugging in the known value of the angle NSM, we get;
100° + m∠MSP = 180°
Therefore; m∠MSP = 180° - 100° = 80°
The measure of the angle MSP, m∠MSP is 80°
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Write linear equation in slope intercept form:1/4x+y=-2/7
The given linear equation in slope intercept form is y = -1/4(x) - 2/7.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.By making "y" the subject of formula, we have the following:
1/4x + y = -2/7
y = -1/4(x) - 2/7
By comparison, we have the following:
Slope, m = -1/4.
y-intercept, c = -2/7.
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The signal from a certain satellite takes 0.0054 approximately seconds to reach Earth. Write this number in scientific notation.
The solution is, 5.4 × 10⁻³ is the number in scientific notation.
Given:
The signal from a certain satellite takes approximately 0.0054 seconds to reach earth.
we will write the number in a scientific notation
The scientific notation is the number that is between 1 and 9 multiplied by 10 raised to an exponent
So, the given number will be:
0.0054
=54/10000
=54/10 * 1/1000
=5.4 × 10⁻³
Hence, The solution is, 5.4 × 10⁻³ is the number in scientific notation.
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HELP PLEASE IF U DO I QILL GIVE 40 POINTS !!!!
Answer: c
Step-by-step explanation:
Question 19
By age 65 the number of Americans who experience hearing loss sufficient to affect communication is:
a. 1 in 2
b. 1 in 3
c. 1 in 4
d. 1 in 5
The number of Americans experience hearing loss sufficient to affect communication is: 1 in 4.
According to the National Institute on Deafness and Other Communication Disorders (NIDCD).
Approximately 1 in 4 adults in the United States aged 65 and older have hearing loss that is sufficient to affect communication.
This is based on data from a survey conducted by the NIDCD and the National Health Interview Survey.
NIDCD (National Institute on Deafness and Other Communication Disorders).
In the United States, 1 in 4 persons 65 and older suffer hearing loss severe enough to impair conversation.
This is based on information from surveys done by the National Health Interview Survey and the NIDCD.
The number of Americans who experience hearing loss sufficient to affect communication is: 1 in 4.
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How many milliliters is 0.005 L?A) 0.5 mL B) 5 mL C) 0.50 mL D) 0.000005 mL E) 200 mLAns: B Category: Medium Section: 1.9
After conversion, B) 5 mL is 0.005 L milliliters
The quantity given = 0.005 L
Using a unit conversion, the same property is stated in a different unit of measurement. Minutes can be used to measure time instead of hours, and feet, kilometres, or any other measurement method can be used to measure distance in place of miles.
To convert from litres to millilitres, it is required to multiply the quantity by 1000. This is because there are 1000 millilitres in one litre.
Therefore, converting the given value-
= 0.005 L x 1000 mL/L
= 5
Thus, the resultant value after conversion is 5mL
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(ASAP!) In the diagram the smaller triangle is an image of the larger triangle. a) Name the angle in the image that corresponds to in the preimage. b) List all pairs of corresponding sides.
1. ∠B is the primage of ∠B'. They are similar triangles.
2. AC ≈AC'
CB ≈ CB'
AB ≈ AB'
what is meant by the preimage when discussing angles?When discussing angles, the preimage refers to the original angle before any transformation has occurred.
In geometry, a transformation refers to the process of moving or changing the position, shape, or size of an object. For example, if an angle is rotated or reflected, the resulting image of the angle would be the transformed angle.
The preimage is the angle before the transformation occurred. It is used to determine the relationship between the original angle and the transformed angle, such as whether they are congruent, similar, or related by another geometric property.
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1. Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the close
for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if
the annual dividend amount paid was $40.96.
The quarterly dividend payment per share based on the question above will be: $0.02.
The close price for the week will be: $5.45.
What is the dividend?For one to find the closing price for the week, we have to divide the total cost of the shares by using the number of shares that was bought so it will be:
Close price = Total cost / Number of shares
= $2,790.40 / 512
= $5.45
To know the quarterly dividend payment per share, we have to calculate the annual dividend payment per share before we can get it so it will be:
Annual dividend per share = Total annual dividend / Number of shares
= $40.96 / 512
= $0.08
From the question, the dividend was paid quarterly, we then divide the annual dividend per share by 4 so as to get the quarterly dividend per share:
Quarterly dividend per share = Annual dividend per share / 4
= $0.08 / 4
= $0.02
Hence the quarterly dividend payment per share will be: $0.02.
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See text below
Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the clos for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if the annual dividend amount paid was $40.96. (7pts)
EARNINGS
52-WEEK
TICK
VOL.
WEEK'S
LATEST
THIS NEXT DIV
High Low
Name
Sym.
100s
Yld.
P/E Last Chg.
Year
Year
Year
Amt
8.50
3.20
Targa Resources
TRGP
412574 1.8
PO
dd
+0.41
0.25
0.18
0.12
Choose ALL answers that describe the quadrilateral below.
Answer:
parallelogram and rectangle
Step-by-step explanation:
the shape can’t be a rhombus or a square, because all sides of it are not the same length. it’s a parallelogram, because all 4 sides are parallel to each other, and it’s a rectangle, because it’s a parallelogram and all of its sides aren’t equal.
Paula comió un tercio de una pizza, Sofia un cuarto y Isabella el sexto. ¿Cuánto queda de pizza para Nicole?
what is the congruent segment of pr
Answer:
In geometry, congruent segments are segments that have the same length. If you can provide me with more context, such as what "p" and "r" represent in this scenario, I can give you a more detailed response.
Step-by-step explanation:
The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides. 5,2. 2360679775,5. 47722557505
An equation that expresses the relationship between the lengths of the three sides is a^2 + b^2 = c^2.
In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.
The relationship between the lengths of the three sides in a right triangle is described by the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
Mathematically, this can be represented as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
For the given right triangle with lengths 5, 2.2360679775, and 5.47722557505, we can plug in the values of a, b, and c to get:
5^2 + 2.2360679775^2 = 5.47722557505^2
which simplifies to:
25 + 5 = 30
This equation is true, indicating that the given lengths do indeed form a right triangle according to the Pythagorean Theorem.
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The given equation shows a proportional relationship betweenthe variables r and s. Which expression is equivalent to 6r. R=10/3s
The equivalent expression for 6r in terms of s is 20s, which we obtain by substituting the value of r from the given equation and simplifying.
The given equation, r = (10/3)s, shows that there is a proportional relationship between the variables r and s. This means that when one variable changes, the other variable changes in direct proportion to it. In other words, if we increase r by a certain factor, s will increase by the same factor, and vice versa.
To find an expression that is equivalent to 6r, we can substitute the value of r from the given equation and simplify.
r = (10/3)s (given equation)
6r = 6(10/3)s (substitute 6r for r in the equation)
6r = 20s (simplify by multiplying 6 and 10/3)
Therefore, the expression that is equivalent to 6r in terms of s is 20s. This means that if we know the value of s, we can use this expression to find the value of 6r in a proportional relationship. For example, if s = 2, then 6r = 20s = 20(2) = 40.
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Determina la altura del papalote con respecto al piso considerando los datos presentados.
The length of the string required to fly the kite at a height of 75 meters from the ground is 86.6 meters.
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the height of the kite (75 m), and the hypotenuse is the length of the string that we need to find. We can set up an equation using the sine function:
sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = 75/hypotenuse
We can simplify the equation using the value of the sine of 60 degrees, which is √3/2.
√3/2 = 75/hypotenuse
To solve for the length of the string, we can cross-multiply and simplify:
hypotenuse = 75/(√3/2)
hypotenuse = (75*2)/√3
hypotenuse = 150/√3
hypotenuse = (150/√3) * (√3/√3) (to rationalize the denominator)
hypotenuse = (150√3)/3
hypotenuse = 50√3 meters = 86.6 meters.
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Complete Question:
A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60 ∘ to the horizontal. Find the length of the string, assuming that there is no slack in it. [Take √ 3 =1.732].
i need help
please lol
Answer: Look below:
Step-by-step explanation:
when n = 1:
a1 = 4 x 3^(1-1) = 4 x 3^0 = 4 x 1 = 4
so a1 = 4
similarly working:
a2 = 4 x 3^1 = 12
a3 = 36
a4 = 108
a5 = 324
a6 = 972