The answer for the equation:
7x+31 = 8x -1/3(27x+3) is x=-4
is 1.030030003 a whole number a natural number an integer a real number a rational number or irrational number
Real numbers are numbers that are continous on the number line. They include positive and negative numbers. They can be integers, natural numbers, rational or irrational numbers.
In this exercise the number 1.030030003 is a real number because it can be found on the real number line
It is also a rational number because it is a repeating decimal
Can someone please help answer the attached?
The variables we need to use in the question are defined. We will call the price of a knife as [tex]k[/tex] and the price of a spoon as [tex]s[/tex].
The total price of [tex]12[/tex] spoons and [tex]16[/tex] knives is then given. Let's write knives instead of [tex]4[/tex] spoons.
[tex]12s+16k=105.64[/tex][tex]3k+16k=105.64[/tex][tex]k=5.56[/tex] per knife.===================================================
Explanation:
k = cost of one knife
s = cost of one spoon
costs are in pounds
12s = cost of 12 spoons
16k = cost of 16 knives
12s+16k = 105.64 pounds is the total cost
We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.
So,
12s+16k = 105.64
12s+16(4s) = 105.64
12s+64s = 105.64
76s = 105.64
s = 105.64/76
s = 1.39 pounds is the cost of one spoon
k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife
----------------------
Check:
1 spoon = 1.39 pounds
12 spoons = 12*1.39 = 16.68 pounds
1 knife = 5.56 pounds
16 knives = 16*5.56 = 88.96 pounds
12 spoons + 16 knives = 16.68+88.96 = 105.64 pounds total
This fully verifies the answer.
Solve the following LP formulation and determine the number of Surplus units in constraint B.
SOLUTION
From the what is given
[tex]\begin{gathered} x+y\le5 \\ x\ge3 \\ 2y\le8 \\ x\ge0 \\ y\ge0 \end{gathered}[/tex]We have the graph as shown below
We are told that the MAX is
[tex]5x+2y[/tex]Substituting these required points into the equation, our maximum becomes
[tex]\begin{gathered} 5x+2y \\ \text{For (3, 2)} \\ 5(3)+2(2)=15+4=19 \\ \text{For }(3,\text{ 0)} \\ 5(3)+2(0)=15+0=15 \\ \text{For (5, 0)} \\ 5(5)+2(0)=25+0=25 \end{gathered}[/tex]We can see that the maximum is 25 at for units of 5, that is x = 5
But we are told in (B) that
[tex]x\ge3[/tex]Hence the surplus unit is
[tex]5-3=2[/tex]Hence the answer is 2
Someone please answer this I'm offering all my points.
complete the number bond and write the number sentence to match the tape diagram
In the first graph, we have that the whole figure is 1
it is divided in 4 parts:
Then, we want to divide 1 into 4 parts. That is
[tex]1\div4=\frac{1}{4}[/tex]Then, we have that:
It is the same for the second figure:
Each 1/4 corresponds to each part. Then if we add them:
[tex]1=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}[/tex]The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). If (x,y)--> (x+4, y+6), give the vertices of △A′B′C′.
PLEASE HELPPPP
Answer:
A' = (6, 3)
B' = (1, 1)
C' = (8, 7)
Step-by-step explanation:
Vertices of triangle ABC:
A = (2, -3)B = (-3, -5)C = (4, 1)Given mapping rule:
(x, y) → (x + 4, y + 6)
This notation tells you that the x-coordinate is translated 4 units to the right, and the y-coordinate is translated 6 units up.
Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':
⇒ A' = (2 + 4, -3 + 6) = (6, 3)
⇒ B' = (-3 + 4, -5 + 6) = (1, 1)
⇒ C' = (4 + 4, 1 + 6) = (8, 7)
Please help thank you
The value of the unknown angle in the triangle is as follows;
m∠S = 40 degreesHow to find the angle of a triangle?The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words, an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
The external angle is ∠JRS.
Therefore, m∠S can be found as follows:
∠JRS = m∠S + m∠T
Hence,
m∠S = 3x + 4
m∠T = 8x + 4
∠JRS = 140°
Hence,
140 = 3x + 4 + 8x + 4
140 = 3x + 8x + 4 + 4
140 = 11x + 8
140 - 8 = 11x
132 = 11x
x = 132 / 11
x = 12
Therefore,
m∠S = 3(12) + 4 = 40 degrees.
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Even though I already got the question right,I need someone to show the work on how to get the answer for this question.
Given
Answer
[tex]\begin{gathered} \sin x=\frac{P}{H} \\ \sin x=\frac{5}{8.3} \\ x=\sin ^{-1}(\frac{5}{8.3}) \end{gathered}[/tex]Which is triangle 2
You deposit $200 each month into an account earning 4% interest compounded monthly.
a) How much will you have in the account in 25 years?
$
b) How much total money will you put into the account?
$
c) How much total interest will you earn?
$
1. There will be $102, 826 in the account in 25 years.
2. The total amount of money you will put into the account is $60, 000
3. The total interest that you would have earned is $42,826.
How do you calculate total interest?For us to calculate the future value of the account in 25 years, we shoud use the formula; FV = P x (((1 + r)^nt - 1) / r)
When we insert the values, it will be
FV = 200 x (((1 + 0.04/12)^(12 x 25) - 1) / (0.04/12))
= 102, 825. 9. If we round this up, we should get
$102, 826
For us to calculate the total amount of money you put into the account, we should us the formula;
Total Deposits = Monthly Deposit x Number of Months
If we insert the values it wil be
200 x (25 x 12)
60,000
Lasty, if we are to find the total interest earned:
Total Interest = Future Value - Total Deposits
$102, 826 - 60,000
= $42,826
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Ali is planning a party. He wants to buy some cakes and some sausage rolls. The cakes are sold in boxes. There are 12 cakes in each box. Each box of cakes costs £2.50. The sausage rolls are sold in packs. There are 8 sausage rolls in each pack. Each pack of sausage rolls costs £1.20. Ali wants to buy more than 60 cakes and more than 60 sausage rolls. He wants to buy exactly the same number of cakes as sausage rolls. What is the least amount of money Ali will have to pay?
The amount Ali will pay is £25.80
Define Multiples
A number that can be divided by another number without a remainder.
Multiples of 8 and 12
8 : 8 , 16, 24, 32, 40, 48, 56, 64, 72
12 : 12, 24, 36, 48, 60, 72
common element is 72
72 cakes cost for 12 cakes in each box = 72/12
= 6 packs
cost of 6 packs = 6 * £2.50 = £15
72 sausage rolls for 8 sausage in each box = 72 / 8
= 9 packs
cost of 9 packs = 9 * £1.20 = £10.80
Total cost will be = £15 + £10.80 = £25.80
Hence, the amount Ali will pay is £25.80
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A data set includes the following numbers: eighteen over 5, two and four fifths, 97%, and 1.74. Part A: What is the order of the numbers from least to greatest? Write your answer using the numbers in their original form. (2 points) Part B: Did you use estimation or rewrite the numbers in equivalent forms? Please explain your answer. (2 points)
Answer:the answer is a
Step-by-step explanation:
I need help understanding, how do I solve this?
3 – [–(–1)]
Answer:
3-[1]
3-1
2
Step-by-step explanation:
=//7777/))_+++++++4
a bag contains 275 marbles. some are red and the rest are black. there are 24 red marbles for every black marble. how many red marbles are in the bag?
There are 264 red marbles in a bag.
What is Marbles?
A marble is a tiny, sphere-shaped object that is frequently fashioned of agate, glass, clay, steel, or plastic. They come in a variety of sizes, but the most have a diameter of about 13 mm (12 in). These toys can be made into works of art or utilized in a variety of marble-based activities. They can also be used in races or runs. They are frequently collected for their pleasing colors and nostalgic appeal.
Let x = Number of red marbles
y = Number of black marbles.
A bag contains 275 marbles.
So, x + y = 275 ..(1)
There are 24 red marbles for every black marble.
x = 24y ..(2)
Plug value of x in equation (1).
24y + y = 275
25y = 275
y = 11
Put y = 11 in equation (2),
x = 24(11)
x = 264
Hence, there are 264 red marbles in the bag.
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The shape below is enlarged using a scale factor of 3 and centre (3,7) to give the dashed shape.
What are the coordinates of B'?
The point B has a coordinates of (-3, 7) after the dilation
How to determine the coordinates of the point B?From the question, the coordinates of the point B are given as
B = (1, 7)
The scale factor of dilation is given as
k = 3
The center of dilation is given as
Center = (3, 7)
The rule of the dilation is calculated using
B' = (k(x - a) + a, k(y - b) + b)
Where
(a, b) = (3, 7)
k = 3
(x, y) = (1, 7)
So, we have
B' = (3 * (1 - 3) + 3, 3 * (7 - 7) + 7)
Evaluate
B' = (-3, 7)
Hence, the coordinates of the point B is (-3, 7)
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FIND THE MEASURE OF EACH ANGLE<1 and <2 form a linear pair and m<2= 52 degrees.
Linear pair angles are the ones that form a straight line, in other words they will form a 180º angle. Therefore if the angle 2 measures 44 degrees we can find the angle 1 by doing as follows:
[tex]\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \measuredangle1+52=180 \\ \measuredangle1=180-52 \\ \measuredangle1=128 \end{gathered}[/tex]The angle one is equal to 128 degrees.
The Pythagorean Theorem
What is the distance between the points (1.7,-1) and (3.2,-1.8)?
Answer:
i hope it was good for you
arlett is playing a video game. She spends 900 minerals to create 18 workers. Each worker costs the same number of minerals.
Write an equation to describe the relationship between m, the amount of minerals, and w, the number of workers.
The required equation is m/w = 900/18
What is meant by an equation?
An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Differential equations are equations in which one or more functions and their derivatives are involved. They are solved by locating a function expression that does not use derivatives. Differential equations are used to represent processes with variable rates of change in fields such as physics, chemistry, biology, and economics.
The required equation is m/w = 900/18
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Cost of 100 grams. Cereal=49p
Pasta=14p
Leah buys 400 grams of cereal and 250 grams of pasta.
Work out the total cost in £
what is the answer
5+3=3+5
Answer:
They are equal
Step-by-step explanation:
5+3=8 and 3+5=8
If you are seeking the answer in terms of evaluation, then the answer would be 8 = 8. Both sides of the equation are equal, so in addition to this, the given equation is true.
5 + 3 = 8
3 + 5 = 8
So, if you were to attempt breaking down the equation, you could easily write it as 8 = 8.
Hope this helps!
HELP ME PLSS OMLLL IMA CRY
Answer:
1. 15 pieces of candy
2. 48 cows
3. 81 ham subs
4. 24 boys
Step-by-step explanation:
Assuming you just want answers, but lmk
Question 3 (5 points)
Find the equation of a parabola with a focus at (-2,-3) and a directrix at y = -5
The equation of a parabola with a focus at (-2,-3) and a directrix at y = -5 is y = 1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)
What is Parabola?
A parabola is the location of a moving point whose distance from a given focus point and directrix line, respectively, is always constant.
let's keep it simple: (x, y). Focus is on (7,5)
When the separation from focus is
[tex]\sqrt{(x - (-2)^{2}) + (y - (-3)^{2} ) }[/tex] . Its distance from directrix y = -5 i.e.
y + 5 = |y + 5|^2
Hence, equation of parabola:
(x - (-2))^2 + (y - (-3))^2 = |y + 5|^2
or, (x + 2)^2 + (y + 3)^2 = |y + 5|^2
x^2 + 4x + 4 + y^2 + 3y + 9 = y^2 + 10y + 25
or, x^2 + 4x + 13 + y^2 + 3y = y^2 + 10y + 25
x^2 + 4x - 12 = 7y
y = (x^2 + 4x - 12)/7
y = 1/7(x^2 + 4x +4 - 4) - 12/7
y = 1/7(x + 2)^2 - 12-4/7
y = 1/7(x + 2)^2 - 8/7
Hence, parabola's equation is y = 1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)
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What is the slope of this line?
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer: 1
Step-by-step explanation: Rise over run, Rise/run. The rise is how much the line goes up or down vertically. The run is how far the line goes until it intersects through a square. The slope is 1 because if you look at the line specifically at the first dot, you just have to go down one and right one as it intersects the square to find the slope.
Select all ratios equivalent to 13.14
52:56. 39:42. 3:4
what is the answer for n? 5i + 7i =n
Answer: [tex]n=12i[/tex]
Step-by-step explanation:
Combine like terms.
Corey is designing a rectangular garden. the garden's diagonal must be 15.6 feet, and the ratio between the garden's base and height must be 12 : 5. find the length of the garden's base and height.
The base of the garden is 14.4 feet.
The height of the garden is 6 feet.
Given,
Corey is designing a rectangular garden;
The diagonal of the garden = 15.6 feet
Ratio between garden's base and height = 12:5
We have to find the length of base and height of the garden.
Here,
Diagonal of a rectangle, d = [tex]\sqrt{base^{2}+ height^{2} }[/tex]
Base = 12x
Height = 5x
Then,
Diagonal, 15.6 = [tex]\sqrt{(12x)^{2} + (5x)^{2} }[/tex]
15.6 = [tex]\sqrt{144x^{2} +25x^{2} }[/tex]
15.6 = √169x²
15.6 = 13 √x²
15.6 = 13x
x = 15.6/13
x = 1.2
Then,
Base of the garden = 12 x 1.2 = 14.4 feet
Height of the garden = 5 x 1.2 = 6 feet
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528 = 14y + 10
y =
Stuck again
Prove that (X+2)^2+(X-2)^2=2(x^2+4) for all values of x
Answer:
see explanation
Step-by-step explanation:
consider the left side
(x + 2)² + (x - 2)² ← expand factors using FOIL
= x² + 4x + 4 + x² - 4x + 4 ← collect like terms
= 2x² + 8 ← factor out 2 from each term
= 2(x² + 4)
= right side , thus proven
Please help ( geometry)
Fill in the missing proof
The missing proof in the given congruence of triangle is;
∠FAB = ∠FBA.
What is defined as the isosceles triangle?An isosceles triangle would be one with 2 sides of equal length. Below is a collection of some isosceles triangle properties:If two sides of an isosceles triangle are equal, therefore the angles opposite the two sides correspond with each other and are always equal.The two angles B and C, opposite the equal sides AB as well as AC in the isosceles triangle shown above, are equal.The isosceles triangle does have three acute angles, which means they are less than 90°.The sum of an isosceles triangle's three angles is always 180°.For the given question;
The given data in the triangle FAB is;
FD ≅ FCDA ≅ CBIn the step two,
FA = FB (Property of isosceles triangle)
Then, step 4 will be ∠FAB = ∠FBA.
Thus, the missing proof will be ∠FAB = ∠FBA.
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I need help can’t work out the right answer. What is the equation of the sinusoid shown in graph?
1) The general form of a cosine function is:
[tex]y=acos\left(b\left(x-h\right)\right)+k[/tex]2) Let's pick from the graph, the amplitude, the period, the horizontal and the vertical shift.
We can tell that half of the distance between the maximum point and the minimum point is 2
Let's find the period
[tex]P=\frac{2\pi}{\frac{2\pi}{3}}=2\pi *\frac{3}{2\pi}=3[/tex]3) Let's resort to the picture. The only cosine function that has an amplitude of 2 and a period of 3 is C and y=2cos(3x) has a vertical shift =0
On the scale drawing of a small town, 1 inch equals 15 feet. On this scale drawing, a parking lot measures 4 2/5 in. by 8 3/5 in.
What is the area of the actual parking lot?
_________ square feet.
Answer:
Step-by-step explanation:
4 and 2/5 inches by 8 and 3/5 inches.
60 and 6 feet by 120 and 9 feet.
66 by 129 feet
8514 feet squared