The number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.
Given that, Bette used 3 jumbo cans of frosting to frost 105 cupcakes and 5 jumbo cans of frosting to frost an additional 175 cupcakes.
What are proportions?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Let number of jumbo cans of frosting would she need to frost 280 cupcakes be x.
Now the proportion is
3/105 = 5/175 = x/280
⇒ 5/175 = x/280
⇒ 175x = 280 × 5
⇒ x = 1400/175
⇒ x = 8
Therefore, the number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.
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2. If f(x) = 3x³ - 4x + 6and g(x)= x³ + 3x² + x - 3, then find
A.(f+g)(x)
B.(f- g)(x)
C.(3f+2g)(x)
D. (3f-2g)(x)
Answer:
Below in bold.
Step-by-step explanation:
f(x) = 3x³ - 4x + 6 and g(x) = x³ + 3x² + x - 3
A. (f+g)x = 3x³ - 4x + 6 + x³ + 3x² + x - 3 = 4x³ + 3x² - 3x + 3.
B. (f-g)x = 3x³ - 4x + 6 - (x³ + 3x² + x - 3) = 2x³ - 3x² - 5x + 9.
C. (3f+2g)(x) = 9x³ - 12x + 18 + 2x³ + 6x² + 2x - 6 = 11x³ + 6x² - 10x - 12.
C. (3f-2g)(x) = 9x³ - 12x + 18 - (2x³ + 6x² + 2x - 6) = 7x³ - 6x² - 14x - 24.
g/8 + 64 = 68
solve for g.
Answer: G=32
Step-by-step explanation:
Please help meeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!
Use vocabulary words to describe how to completely factor the expression 4x^-5 + 16x^-3, and write the factors using only positive exponents.
Vocabulary-monomial expression
negative exponents law
scientific notation
significant digits
The factorized expression is (4/x³)(1/x² + 4).
The expression given to us is 4x^-5 + 16x^-3.We need to factorize the above expression.We need to use only the positive exponents.The number of times a number has been multiplied by itself is referred to as an exponent. There are four different sorts of exponents: positive, negative, zero, and rational/fractional. By interpreting the exponent as the total number of times the base number must be multiplied by the same base, one may determine the value of the number.We will use the laws of exponents.a^(-m) = 1/a^mWe can rewrite the expression as 4/x^5 + 16/x³.Now take out the common from the two terms.The expression becomes (4/x³)(1/x² + 4).Thus, we have successfully factorized the expression using only the positive exponents.To learn more about exponents, visit :
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represented by the equation 5x + 2y = 10.
How is the slope of the line related to values of
A, B, and C in standard form Ax + By = C?
-Can you please explain how to solve this problem? I wouldnt want only the answer. Thank you so much
The equation given 5x + 2y = 10 given, represents the slope considering the form Ax + By = C: by slope = - A/B = -5/2
How to find the slope of the lineAx + By = C
rewriting in standard form which is y = mx + c, where m is the slope, is done as follows
By = -Ax + C
y = ( - Ax + C ) / B
y = - Ax/B + C/B
comparing with standard form the slope, m is - A/B
using the other equation 5x + 2y = 10
rewriting gives
y = -5x/2 + 10/2
the slope here is -5/2
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you are driving on a road that has a 8% uphill grade. this means that the slope of the road is 8/100. approximate the amount of vertical change in your position when you drive 200 feet.
the amount of vertical change in your position when you drive 200 feet is 16 feet
you are driving on a road that has a 8% uphill grade.
this means that the slope of the road is 8/100.
approximate the amount of vertical change in your position when you drive 200 feet
Therefore our proportion is: (where x is the "vertical" rise)
Slope is defined as rise so
8/100 = x/200
(8*200)/100 = x
16 feet = x
Hence , the amount of vertical change in your position when you drive 200 feet is 16 feet
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Please give the answer.
The simplified fraction for the expression [tex]a^{-3} / b ^{-2[/tex] is 36/125.
What are exponents?The exponent of a number shows how many times the number is multiplied by itself.
For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, [tex]x^n[/tex] means that x is multiplied by itself for n times.
Given:
[tex]a^{-3} / b ^{-2[/tex]
Now, a= 5 and b=6
So, substituting the above values in the expression as
= [tex]5^{-3} / 6 ^{-2[/tex]
Using the law of exponents we have
[tex]a^{-m[/tex] = 1/[tex]a^m[/tex]
Thus,
= 6² / 5³
=6 x 6 / 5x 5 x 5
=36 / 125
Hence, the simplified fraction is 36/125.
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if angles k and j are supplementary and adjacent, which statement about the two angles is true ?
Let's evaluate the statements:
Supplementary angles: that means the sum of ∠K and ∠J is 180°.
Adjacent angles: that means that ∠K and ∠J common side and a common vertex.
So, let's observe the angles:
Given:
Linear pairs of angles are those two adjacent angles whose sum is 180°.
Answer: ∠K and ∠J are linear pairs.
11=u/28 what does U =
U=308
11=308/28
it right trust me
Answer:
What do you mean by what does U? if is what I think it is, then:
Step-by-step explanation:
Solve for you by simplifying both sides of the equation, then isolating the variable.
u=308
Amy has 4 pound of ground pork to make meatballs she uses 3/8 pound per meatball to make 9 meatballs.how many 1/8 pound meatballs can Amy make with the remaining turkey ?
Amy can make 29 meatballs from the remaining beef.
What are mathematics operations?
An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.A zero-arity operation, also known as a nullary operation, is a constant.The mixed product is an example of an arity 3 operation, also known as a ternary operation.Amy has 4 pounds of ground beef to make meatballs and he uses 3/8 pound per meatball to make 9 meatballs
We have to subtract 3/8 from 4
= 4 - 3/8
= 29/8
There are 29/8 pounds of ground beef left
Therefore the number of 1/8 pound meatball that can be produced from 29/8 pounds of ground beef can be calculated as follows;
= 29/8 ÷ 1/8
= 29
Hence Amy can make 29 meatballs
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round to 1 significant figure
Round to 1 significant figure
What is Rounding?
To estimate a certain number in a context, rounding is a process. Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up. The term "rounding decimals" describes the accurate rounding of decimal figures.
How to round a figure
It rounds to the most important figure in the number. To round to a significant figure: look at the first non-zero digit if rounding to one significant figure. look at the digit after the first non-zero digit if rounding to two significant figures.
To understand this term lets take and example:
24982 correct to 1 significant figure
If we round up, then the answer is
30,000
but if we were to round down, the answer would be
20,000;
If we want to determine which one is correct, we have to look at the second digit of the original number, which is
4
Since the second digit is less than 5
we can round down, so the answer would have to be
20,000
Hence, 24982 round to 1 significant figure is 20,000
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do you think you can help me with this problem this is what the question is about a glass bottle filled with oil that weighs 590 grams. After Sophia uses 200 milliliters of oil, the bottle of oil weighs 400grams. so do u think u can help me?
The function formula of the mass of the bottle to the function of the volume of the oil is M = 590 - 0.95V
How to write function formula?The glass bottle filled with oil weighs 590 grams.
After Sophia uses 200 millilitres of oil, the bottle of oil weighs 400grams.
Therefore, the weight M of the bottle of oil in grams is a function of V, the volume, in millimetres of oil Sophia has used.
Therefore, the formula of the function can be represented as follows
density = mass / volume
200 mm reduces the weight of the bottle by 590 - 400 = 190 grams.
V mm will reduce it to ?
cross multiply
190 × V / 200 = 19 / 20 V = 0.95V
where
V = volume of the oil reduced from the bottle
Therefore, the function formula will be as follows:
M = 590 - 0.95V
Where,
M = weight of the oil.
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Determine the range of the following graph:
After inspecting the picture of the given graph, the range of the function is represented by the following set:
Inequality notation: - 5 ≤ y ≤ 0
Interval notation: y ∈ [- 5, 0]
What is the range of a given function?
Functions are characterized by the following three features:
Domain - Set of the input variables, represented by the horizontal axis.Range - Set of the output variables, represented by the vertical axis.Relation - How the input and output variables are related to each other.In this question we find the case of a function with one input variable and one output variable. That is:
x → f(x)
After inspecting the picture shown in the image we notice that the range of the graph is formed by the following set:
Inequality notation: - 5 ≤ y ≤ 0
Interval notation: y ∈ [- 5, 0]
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There is a proportional relationship between the amount of dark chocolate (in ounces), x, and the amount of almonds (in ounces), y, in each package of Sweet and Salty trail mix.
x (ounces of dark chocolate) 2 y (ounces of almonds) 8
Answer:
y = 4x
Step-by-step explanation:
You want an equation that represents the proportional relationship between ounces of chocolate (x) and ounces of almonds (y) when we know (x, y) = (2, 8).
Proportional relationA proportional relation can be written using the equation ...
y = kx
where k is a constant.
The value of k can be found if a pair of values is known for x and y.
k = y/x . . . divide by x
k = 8/2 = 4 . . . . use (x, y) = (2, 8) from the table.
The equation for the relationship is ...
y = 4x
The proportional relationship that accounts between the amount of dark chocolate and the amount of almonds is y = 4x.
What is ratio and proportion?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. An equation known as proportion shows that the two ratios presented are equal to one another. A ratio is the comparative or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio can be defined as the number that can be used to represent one quantity as a percentage of another.
Given, for 2 ounces of dark chocolate(x), 8 ounces of almonds(y) are put in.
Taking the ratio as y to x, we have:
y/x = 8/2 ⇒ y/x = 4 ⇒ y = 4x
Thus, the proportional relationship that accounts between the amount of dark chocolate and the amount of almonds in each package of Sweet and Salty trail mix is y = 4x.
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What is the correct form of the partial fraction decomposition for the expression
13x-7
(x+2)(4x-3)
?
Answer:
fraction decomposition for the expression
13x - 7/(x+2)(4x-3)
Points X(6,4) and Y(-4,-6) are the endpoints of XY. What are the coordinates of point Z on XY such that XZ is 4/5 the length of XY
Answer:
(-2, -4)
Step-by-step explanation:
Z_x = (Y_x - X_x) * (4/5) = (-4 - 6) * (4/5) = -8
Z_y = (Y_y - X_y) * (4/5) = (-6 - 4) * (4/5) = -8
-8 + 6 = -2
-8 + 4 = -4
i came up to some degree, but not sure. i will post my notes after.
Note that sides AD and BE are perpendicular on the same side AC. So the angles CAD and CBE, both are equal to 90 degrees.
Beig the corresponding angles, ADC and BEC are also equal.
And the angle ACD is the common angle in both the triangles.
Therefore by the AAA criteria, the triangles CAD and CBE are similar.
So their corresponding sides must be proportional,
[tex]\begin{gathered} \frac{AD}{BE}=\frac{AC}{BC} \\ \frac{4\sqrt[]{138}}{\sqrt[]{138}}=\frac{6\sqrt[]{3}+BC}{BC} \\ 4=\frac{6\sqrt[]{3}+BC}{BC} \\ 4BC=6\sqrt[]{3}+BC \\ 3BC=6\sqrt[]{3} \\ BC=2\sqrt[]{3} \end{gathered}[/tex]simplify using suitable property -4/5+-1/3+1 2/5+7/3
PLEASE DONT SPAM
WILL MARK BRAINLIEST
Answer:
2
Step-by-step explanation:
[tex]=-\frac{12}{15} + -\frac{5}{15} + \frac{12}{15} + \frac{35}{15} \\=\frac{30}{15} \\= 2[/tex]
Answer:
39/15
Step-by-step explanation:
-4/5+-1/3+1 2/5+7/3
Convert all to fractions having the least common denominator. The mixed denominators of 3 and 5 could be converted to denominators of 15, thereby allowing them to be numerically combined.
-4/5+-1/3+1 2/5+7/3
(-4/5)(3/3) = -12/15
(-1/3)(5/5) = -5/15
(+1 2/5) = (5/5 + 2/5) = (7/5)(3/3) = 21/15
(7/3)(5/5) = 35/15
Since we have a common denominator (15) we can now sum the individual fractions by adding their numerators:
-12 -5 + 21 + 35 = 39
Now add back the denominator
The result is 39/15
A school has 14 rooms with 28 desks in each room. How many desks are in the school?
Answer:
392
Step-by-step explanation:
There are 14 desks with 28 rooms, or
14 x 28
392
I'm trying to rank up so if you could mark this brainliest, it would really help
A recent survey showed that 73% of elementary school students have a pet, what is the ratio of students who have a pet to the students who don't have a pet
Answer:idek
Step-by-step explanation:
plsssssssssssssss helpppppppppppppppppppppp
What is the value of f(-1) when f(x) = 2x + 2?
Enter your answer in the box.
f(−1) = □
(can someone explain it instead of just giving answer, the teachers suck at teaching anymore at least where i go)
The value of f(-1) when f(x) = 2x + 2 will be 0.
How to illustrate the expression?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this situation, we want to know the value of f(-1) when f(x) = 2x + 2. This will be Illustrated as:
f(-1) = 2x + 2
= 2(-1) + 2.
= -2 + 2
= 0
The value is 0.
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A trough at the end of a gutter spout is meant to direct water away from the house. The
homeowner makes the trough from a rectangular piece of of aluminum that is 20 in. long and 12
in. wide. He makes a fold along the long sides a distance of x inches from the edge. If he wants the
trough to hold 360 in³ of water, how far from the edge should he make the fold?
Answer:20 in * (12 in - 2X in) * (X in) = 360 in3
This can be simplified by dividing both sides by 20 in:
20 in * (12 in - 2X in) * (X in) = (360 in3/ 20 in)
After dividing both sides by 20 in:
(12 in - 2X in) * X in = 18 in2
Distribute X in. across (12 in -2X in):
12X in2 - 2X2 in2 = 18 in2
1.Subtract 18 in2 from both sides:
12X in2 - 2X2 in2 - 18 in2 = 0
2. Rearrange the equation:
-2X2 in2 + 12X in2 - 18 in2 = 0
This for matches the form for a quadratic equation (Ax2 + Bx +C = 0)
You can then plug these values into the quadratic formula to solve for X
so your answer is X=3
jacob said that -3 is a rational number. aaron said that -3 is an irrational number. who is correct?explain
Any number in the form of p/q where q not equal to zero is called as rational Number. -3 is rational number and Jacob is correct.
What are Rational numbers and Irrational Numbers?Any number in the form of p/q where q not equal to zero is called as rational Number.
An Irrational Number is a real number that cannot be written as a simple fraction: 1.5 is rational, but π is irrational. The root values will also be irrational.
The number -3 is a rational number. We can write -3 in the form of p/q, i.e -3/1 where p is -3 and q is 1.
All rational numbers are obtained by dividing one integer by another.
Since it is possible to obtain -3 by dividing the integer
i.e -3 by 1, as in -3/1,
So -3 is a rational number.
Hence -3 is not a irrational number because -3 we can written as a simple fraction.
So Jacob is correct.
Hence -3 is rational and Jacob is correct.
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Mr.Johnson orders gravel to cover his driveway. Below is a top view of the driveway. The gravel will be spread 3 inches deep.Write the depth of the gravel in ft
If Mr. Johnson orders gravel to cover his driveway, below is a top view of the driveway and the gravel will be spread 3 inches deep, then the depth of the gravel in feet is 0.25 feet
The gravel will be spread 3 inches deep
Here we have to convert the depth in inches to the depth in feet
To convert the inches to feet, we have to divide the inches by 12.
Then,
3 inches = 3/12 feet
= 0.25 feet
Hence, if Mr. Johnson orders gravel to cover his driveway, below is a top view of the driveway and the gravel will be spread 3 inches deep, then the depth of the gravel in feet is 0.25 feet
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250 word minimum essay on the steps of solving for both the x and y intercept.
Answer:
Step-by-step explanation:
In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y and an x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system. To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis. When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable. For example In algebra, 2-dimensional coordinate graphs have a horizontal axis, or x-axis, and a vertical axis, or y-axis. The places where lines representing a range of values cross these axes are called intercepts. The y-intercept is the place where the line crosses the y-axis and the x-intercept where the line crosses the x-axis. For simple problems, it is easy to find the x-intercept by looking at a graph. You can find the exact point of the intercept by solving algebraically using the equation of the line.
Hope this helped out!
Write a rule of reflection
???????
The rule for the reflection is (x, y) ---> (x+6, y).
what is Reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection.
Given:
The coordinates of L is ( -3, 6).
Now, after the reflection
The x- coordinates increases +6 units on right side.
and, y- coordinates remains the same.
Hence, the rule for the reflection is (x, y) ---> (x+6, y).
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If x = 15 units and h = 12 units, then what is the area of the rhombus pictured above?
A.
225 square units
B.
45 square units
C.
180 square units
D.
60 square units
The rhombus has an area value of 180 square units
How to calculate the area of the rhombus?From the question, the given parameters arr
Shape = Rhombus'
Base = x
Height = h
Also, from the question, we have
x = 15
h = 12
The above parameters mean that
Base = 15
Height = 12
The area of the rhombus is then calculated using the following area formula
Area = Base * Height
Substitute the known values in the above equation
This gives
Area = 15 x 12
Evaluate
So, we have the following equation
Area = 180
Hence, the area is 180 square units
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The area of the rhombus is 180 square units, which is the correct answer would be an option(C).
What is the area of the rhombus?The area of the rhombus is calculated as the product of its height and base.
The formula of the area of the rhombus is following
Area of the rhombus = Height × Base
The given rhombus has :
Height (h) = 12 units
Base (x) = 15 units
Area of the rhombus = Height × Base
Area of the rhombus = h × x
Substitute the values of x = 15 and h = 12 in the above equation
Area of the rhombus = 15 × 12
Area of the rhombus = 180 square units
Hence, the area of the rhombus is 180 square units
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Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
The required coordinates are
Q'(-8, -9)
R'(-8, -1)
S'(-1, -10)
What is coordinate?
In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such Euclidean space, uniquely using one or more numbers, or coordinates.
You want the coordinates of Q', R', and S' after rotating figure QRS 90° CCW. You are given Q(-9, 8), R(-1, 8) and S(-10, 1).
Rotation CCW 90°
The transformation that maps coordinates to their image after rotation 90° CCW is
(x, y) ⇒ (-y, x)
The image points are
Q(-9, 8) ⇒ Q'(-8, -9)
R(-1, 8) ⇒ R'(-8, -1)
S(-10, 1) ⇒ S'(-1, -10)
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A competency test has scores with a mean of 82 and a standard deviation of 2. A histogram of the data shows that the distribution is normal. Between what two values do about 99.7 of the values lie?
Answer:
Between 76 and 88
. A swim coach has at most $800 to buy equipment for the swim team. Each
pull buoy costs $5.50 and each kickboard costs $10. Let X represent the
number of pull buoys and y represent the number of kickboards.
a. Write an inequality for the scenario..
5.50x+10y_< 800 I already wrote the inequality now graph the inequality
The inequality for number of pull buoys and the number of kickboards is; 5.50x + 10y ≤ 800.
How do you define a inequality?A statement of an order relationship between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
For the given question.
Let 'x' represent the number of pull buoys.
Let 'y' represent the number of kickboards.
The cost of each pull buoy = $5.50.
The cost of each kickboard costs = $10.
The total swim budget = $800.
The inequality for the scenario is -
5.50x + 10y ≤ 800.
Plot the graph;
Put x = 0; y = 80 ; (0, 80)
Put y = 0, x = 145.5 (145.5, 0)
Plot the obtained points on the graph.
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