Answer:
x=40,y=20
Step-by-step explanation:
a{2x+5y=180
b{3x+3y=180
b-a
x-2y=0
x=2y
substitute:
2×2y+5y=180
9y=180
y=20
substitute:
x=2y
x=2×20
=40
The bill for two book came to $28. 48. One book cot $7. 44. What wa the cot of the other one
Answer:
Step-by-step explanation:
Ok:
If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price
2. 28.45-7.44=$21.01
3. Answer: The cost of the other one is $21.01
A hall can accommodate 600 chairs arranged in rows Each row has the same number of chairs The chairs are rearranged such that the number of row is increased by 5 but the number of chairs per row is decreased by 6 a) Find the original number of rows of chairs in the hall b) After the re-arrangement 450 people were seated in the hall leaving the same number of empty chairs in each row. Calculate the number of empty chairs per row.
The 600 chairs capacity of the hall and the arrangement such that an increase in the number of rows by 5 decreases the number of chairs per row by 6 is a word problem that indicates;
(a) There are originally 20 rows of chairs in the hall
(b) The number of empty chairs per row is 6 empty chairs
What is a mathematics word problem?A word problem is a question in which the information required to find the solution and the description of the situation is provided using sentences, or regular verbal statements rather that symbols, expressions or operators.
(a) The number of chairs the hall can accommodate = 600
Let x represent the number of rows of chairs, therefore;
The number of chairs per row = 600/x
When the number of rows is increased by and the number of shares per row is decreased by 6, we get;
New number of rows = x + 5
New number of chairs per row = (600/x) -6
The equation for the number of chairs in the hall becomes;
(x + 5) × ((600/x) - 6) = 600
600·x + 6·x² - 570·x - 3000 = 0
6·x² + 30·x - 3000 = 0
x² + 5·x - 500 = 0
(x + 25)·(x - 20) = 0
x = -25 and x = 20
The number of rows is a positive number, therefore;
The original number of rows, x = 20(b) After re-arrangement, the number of rows, x = 20
The new number of chairs per rows = (600/20) - 6 = 24
The new number of rows = 20 + 5 = 25
Let E represent the number of empty chairs, the number of people in each row becomes 24 - E, which indicates;
25 × (24 - E) = 450
450 ÷ 25 = 18 = 24 - E
E = 24 - 18 = 6
The number of empty chairs per row, E = 6
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Tracy is saving to buy a new guitar that costs $253. 77 (including tax). Tracy has saved $136. 27, and she can save $23. 50 each week. How many more weeks will it take her to save enough money?.
Tracy need 5 weeks to save enough money to buy a new guitar.
Given that,
Tracy is saving to buy a new guitar. Which having costs $253.77(including tax).
Tracy has already saved $136. 27.
Now she needs = 253. 77- 136. 27
= $117.50
she can save each week = $23. 50
Tracy will take weeks to save enough money
= [tex]\frac{117.50}{23.50}[/tex]
= 5 weeks.
Therefore, Tracy need 5 weeks to save enough money to buy a new guitar.
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What is 3x+6 I don’t know what this is
Answer:
it is a function.
Step-by-step explanation:
The answer is just 3x+6
Answer:
3x+6 can be be the result of 3(x+2) and then you distribute to get 3x+6
If you are asking how to solve you need an equal sign in the equation for example: 3x+6=27 you would have to solve to figure out wht x is. x is any unknown number we use x or any letter in the alphabet to fill in. You have to olve for the variable now.
A General Rule for Solving Equations
Simplify each side of the equation by removing parentheses and combining like terms.
Use addition or subtraction to isolate the variable term on one side of the equation.
Use multiplication or division to solve for the variable.
Step-by-step explanation:
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and ∠Y ≅ ∠E
XZ ≅ FG and ZY ≅ GE
XY ≅ EF and ZY ≅ FG
∠Z ≅ ∠G and XY ≅ FE
intuitive distortion
The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and XY ≅ FE .
What is ASA and AAS?The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.
The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.
From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.
Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:
∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .
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helpppppp maeeeeeeee
Answer:
x= -7
Step-by-step explanation:
The sum of the angles in a triangle is 180°. This can be abbreviated to ∠ sum of ∆.
Adding the angles in the triangle,
84° +(x +59)° +(x +51)°= 180° (∠ sum of ∆)
2x= 180 -84 -59 -51
2x= -14
Divide both sides by 2:
x= -14 ÷2
x= -7
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PLEASE ILL DO ANYTHING I ALREADY OFFERED AS MUCH POINTS AS POSSIBLE
Answer:
A, B, D, E
Step-by-step explanation:
Given expression:
(0.06) · (0.154)When multiplying decimals, multiply as if there are no decimal points:
[tex]\implies 6 \times 154 = 924[/tex]
Count the number of digits after the decimal in each factor:
0.06 → 2 digits0.154 → 3 digitsTherefore, there is a total of 5 digits.
Put the same number of total digits after the decimal point in the product:
[tex]\implies (0.06) \cdot (0.154)=0.00924[/tex]
-----------------------------------------------------------------------------------------------
Answer option A
[tex]\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}[/tex]
When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.
Therefore:
6 ÷ 100 = 0.06154 ÷ 1000 = 0.154[tex]\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)[/tex]
Therefore, this is a valid answer option.
Answer option B
[tex]\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}[/tex]
Multiply the numbers 6 and 154:
[tex]\implies 6 \times 154 = 924[/tex]
Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).
[tex]\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924[/tex]
Therefore, this is a valid answer option.
Answer option C
[tex]\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}[/tex]
Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:
[tex]\implies 6 \cdot 154 = 924[/tex]
Count the number of digits after the decimal in each factor:
0.1 → 1 digit0.01 → 2 digitsTherefore, there is a total of 3 digits.
Put the same number of digits after the decimal point in the product:
[tex]\implies 0.924[/tex]
Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.
Answer option D
[tex]\boxed{6 \cdot 154 \cdot (0.00001)}[/tex]
Again, employing the technique of multiplying decimals.
As there are a total of 5 digits after the decimals:
[tex]\implies 6 \cdot 154 \cdot (0.00001)=0.00924[/tex]
Therefore, this is a valid answer option.
Answer option E
[tex]\boxed{0.00924}[/tex]
As we have already calculated, (0.06) · (0.154) = 0.00924.
Therefore, this is a valid answer option.
What is 5% of 60 use a double number line diagram to show your work
Using the proportion , the 5% of 60 would be 3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that the number of 5% of 60.
5% of 60
= 0.05 x 60
= 3
Therefore, the 5% of 60 would be 3.
Using the proportion , the 5% of 60 would be 3.
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what does it mean for two shapes to be proportional.
Answer:
It means that the quantities have the same relative size. In other words they have the same ratio.
Step-by-step explanation:
For example look at the attached files
Evaluate the expression when b=9
4b+10-b
Group of answer choices
37
47
27
17
Answer:
37
Step-by-step explanation:
4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37
Dan buys a car for £700.
It depreciates at a rate of 5.5% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
The value of car after 6 years is £498.53
Define Modeling Exponential Decay
A model for decay of a quantity for which the rate of decay is directly proportional to the amount present.A(1 - r)^tA = Present value , r = rate, t = timeGiven that,
Dan buys a car = £700
Depreciates at a rate of = 5.5% per year
The value after 6 years = 700 (1 - 5.5 / 100) ^6
= 498.527 or 498.53
Therefore, the value of car after 6 years is £498.53
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How to solve Solve 3! what the exclamation point means but it part of the problem
Answer:
3! = 3*2*1 = 6
Step-by-step explanation:
! is factorial meaning that you multiply that number by all of the number below it
9! = 9*8*7*6*5*4*3*2*1
1011 = 1011*1010*1009*1008...3*2*1
jadaa maake 55 ccups of blueberry jam and divided the jam equally amoung 4 containers how much jam went in each container a 2t third of a cup b 1 cup c 3over 2 of a cup and d 24 cups
When the denominator is bigger than the numerator, a fraction is expressed as one with a numerator and a denominator. 55 cups of jam divided equally into 4 containers yields 13.75 cups per container. 13.75 cups of jam are contained in each container.
What is a fraction?When the denominator of a fraction is greater than the numerator, the fraction is expressed as a pair of numbers. A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator. Example: 1/2, 1/3 is a fraction.We have,
55 cups of blueberry jam were produced by Jada, who then evenly distributed the jam across 4 containers.
jam content of each container.
= 55 cups / 4 container
= 13.75 cups / 1 container
This indicates that there are 13.75 cups of jam in each container.
55 cups of jam are divided into 4 equal containers in this manner.
13.75 cups / 1 container
The amount of jam in each container is 13.75 cups of jams.
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12. A rectangle is drawn so that the base lies on thex-axis, and the top corners are on the curvey=48−x 2. Draw a diagram. Find the maximum area of such a rectangle.
the maximum area of such a rectangle will be 144 unit²
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
The area of rectangle is A = a*b
A = 2x*(48-x²) = 96x - 2x³
We are asked to maximize the Area as changes so hopefully, we can identify a critical point of
It an associated with a maximum, So we need to find [tex]\frac{dA}{dx}[/tex] = 0
96 - 6x² = 0
x² =96/6 = 16
x = ±6
So the width = 12
Height = 48 - 36 = 12
So the area = 144 unit²
Hence the maximum area of such a rectangle will be 144 unit²
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Which properties are present in a table that represents a logarithmic function in the form y = logo when b>
1. The y-values are always increasing or always decreasing.
II. The point (0, 1) exists in the table.
III. The y-values will decrease rapidly as the x-values approach zero.
IV. There will only be one x-value in the table with a y-value of zero.
O
O
O
O
I only
I and II only
1, 111, and IV
II and III only
Mark this and return
Save and Ex
Submit
Answer:
Step-by-step explanation:
i think its 1
the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that span{v1, . . . , vk}
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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Randall need 24 erving of ice cream for
a cla party. If each erving i 1
/8 quart,
how many quart of ice cream will he need? (PLEASE HELP FAST!)
A: 3 quart
B: 5 quart
C: 6 quart
D: 8 quart
Randall needs 3 quarts of ice cream.
What is the quarts?
An English measurement of volume equal to one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system. One litre is roughly equivalent to each. It is divided into either four cups or two pints.
If Randall needs 24 servings, that means that there would be 24 kids in his class.
If each kid in his class would have 1/8 quart,
you would do 24 x 1/8 which is 3 quarts.
3 quarters
Hence, Randall needs 3 quarts of ice cream.
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Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
three to the one third power all over three to the one sixth power
A. the square root of three to the one sixth power
B. the ninth root of three squared
C. the square root of three to the sixth power
D. the sixth root of three
Answer:
D. The sixth root of three
Step-by-step explanation:
Translate from words to math symbols:
three to the one third power all over three to the one sixth power
[tex]\frac{3^{\frac{1}{3} } }{3^{\frac{1}{6} } } \\[/tex]
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} }[/tex]
Simplify:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} } = \frac{\sqrt[3]{3} }{\sqrt[6]{3} } * \frac{\sqrt[6]{3^{5} } }{\sqrt[6]{3^{5} } } = \frac{\sqrt[3]{3} *\sqrt[6]{3^{5} } }{\sqrt[6]{3^{6} } } = \frac{3^{\frac{1}{3} }*3^{\frac{5}{6} } }{3^{\frac{6}{6} } } = \frac{3^{(\frac{1}{3} +\frac{5}{6} )} }{3} = \frac{3^{(\frac{2}{6} +\frac{5}{6} )} }{3} = \frac{3^{\frac{7}{6} } }{3} = \frac{3^{\frac{1}{6} } *3}{3} = \\\\3^{\frac{1}{6} } = \sqrt[6]{3}[/tex]
Answer:
[tex]\sqrt[6]{3}[/tex]
D. the sixth root of three
A mountain climber found that the relationship between his altitude and the surrounding air temperature is linear. The function
represents this relationship, where is the altitude in meters and is the temperature in degrees Fahrenheit. According to this function, by how much is the temperature decreasing for every meter that the mountain climber’s altitude increases?
The temperature decrease for every meter that the mountain climber's altitude increases is given by:
-100 ºF.
What is the temperature decrease?The function that models this situation is a linear function, which has the format defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope of the function, representing by how much y changes when x is increased by one.b is the y-intercept of the function, representing the numeric value of y when x = 0.In the context of this problem, the function is defined as follows:
f(a) = -100a + 75.
Hence the slope of the function is of:
-100.
Representing the temperature decrease for each meter of altitude increase of the climber.
Missing InformationThe function is defined as:
f(a) = -100a + 75.
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Can walk 4 miles in one hour and can run 8 miles in one hour what percent of average running speed is her average walking speed 
Answer: 50% of her average running speed is her average walking speed
Step-by-step explanation:
60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.
Activity class has 20 women and 13 men. A committee of five is chosen at random. Find (a) p(the committee consists of all women). (b) p(the committee consists of all men) (c) p(the committee consists of all of the same sex) Activity Suppose that a die is loaded (biased) such that 3 appears twice as often as each other number but that the other 5 numbers are equally likely. What is the probability that an odd number appears when we roll this die?
the probability of the committee consisting of all women is 6.53%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
number of women = 20
number of men = 13
Total number of persons = 20+ 13 = 33
A committee of 5 people is chosen at random. Total number of ways in which the committee of 5 can be chosen N
N = C(33 5) = 33! / 5!*28!
N = 237336
p(the committee consists of all women) = C (20 3)*C(13 0)/N
p = 15504 / 237336
p = 0.0653
Hence, the probability of the committee consisting of all women is 6.53%
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I need help please im so confused
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
What is the force should be applied to a piston with radius of of 1 to create a pressure of 8? (you'll have to rearrange the equation)
Force applied on the piston is 8π.
Given , Radius = 1 , Pressure = 8
Since , the units of pressure and radius are not given, let us assume radius is in cm and pressure is in [tex]\frac{Newton}{cm^{2} }[/tex].
Now , it becomes
Radius(r) = 1 cm
Pressure(p) = 8 [tex]\frac{Newton}{cm^{2} }[/tex]
Now , We know that
Force = Pressure × Area
∴ F = p × a
or F = 8 × π×[tex]1^{2}[/tex] [∵ Area of Piston = π[tex]r^{2}[/tex]]
∴ F = 8π
Hence ,Force applied on the piston is 8π.
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please help im suffering right now
Answer:
C
Step-by-step explanation:
If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.
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Which expression is equivalent to log2-log6
Answer: log2-log6=-log3
Step-by-step explanation:
[tex]\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3[/tex]
Which expression is equivalent to quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity?.
The expression "(-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.
(-3 1/4d + 3/5) - (2 7/8d + 7/10)
⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10
⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10
⇒ (-13/4 - 23/8)d + 6/10 - 7/10
⇒ (-26/8 - 23/8)d - 1/10
⇒ -49/8 d - 1/10
Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.
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drag the description from the torres-porras experiment on to the position it represents in the scientific method.
These are the general steps that every experiment takes, however no two research programs are the same. The aforementioned steps can be changed.
What is hypothesis in math?
A hypothesis is a proposition that makes sense in light of the available information but has neither been confirmed nor refuted.
A statement on which hypothesis testing will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).
Of the 10 targets, you mislabeled two. Both the forecast and the hypothesis were messed up by you. Remember that a hypothesis usually offers less detail than a prediction.
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Write the equation of the line that passes through the points (4, -8) and (7,-8) fully reduced PLEASE HELP
The equation of the line that passes through the points (4, -8) and (7,-8) is 5.33x + y = 13.22.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given two points,
(x1 = 4 ,y1 = -8) and (x2 = 7, y2 = -8)
The equation's general form will be written first:
y = mx + c
We may compute the slope of the equation (m) as follows:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{-8-8}{7-4}[/tex]
m = -16/3
m = -5.33
equation is y = -5.33x + c.
By entering the values of the x and y coordinates, we can now determine the value of the y-intercept (c):
For the point (4,-8),
-8 = -5.33(4) + c
-8 = -21.32 + c
c = 13.32
So the equation become ;
y = -5.33x + 13.32
or, 5.33x + y = 13.22
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Given that z=x + i y, find the values of real numbers x and y such that z - 4iz' + 3 = 0, when z' is the conjugate of z.
THANKS IN ADVANCE!!!
The value of z = 0 + 0i
What is complex numbers ?
A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1.
( x + iy ) - 4i ( x - iy ) = 0
x + iy - 4ix + 4i²y = 0
x + i (-4x + y ) + 4y = 0
x + 4y + ( - 4x + y )i = 0
Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation
x + 4y = 0 ⇒(1)
-4x + y = 0 ⇒ (2)
Multiplying equation (1) with 4
4x + 16y = 0
Solving the equations
4x + 16 y = 0
-4x + y = 0
17 y = 0
y = 0
Putting the value of y in (1)
x + 4(0) = 0
x = 0
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It cost $255 for 30 students to see the musical. How much will it cost 85 students to see the
play? Write and solve a proportion to answer the question.
Answer:
$722.5
Step-by-step explanation:
Since $225 is 30 students we can do 85/30 and multiply 225 by that.
For the proportion, it would be: 255/30=x/85
85/30=2.8 1/3
2.8 1/3*255=722.5
So it would be $722.5 for 85 students
Answer:
$722.5
Step-by-step explanation:
$255/ 30= 8.5
8.5* 85= $722.5
