The perfect square trinomial and binomial of the expression [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] are [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] + [tex]\frac{25}{144}[/tex] and [tex](q + \frac{5}{12}) ^{2}[/tex]
What is a perfect square expression?Perfect squares are numbers or expressions that are the product of a number or expression multiplied to itself. 7 times 7 is 49, so 49 is a perfect square. x squared times x squared equals x to the fourth, so x to the fourth is a perfect square.
[tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] expression can be made into a perfect square by adding the square of half the coefficient of q
coefficient of q = [tex]\frac{5}{6}[/tex]
Half of [tex]\frac{5}{6}[/tex] = [tex]\frac{5}{12}[/tex]
square [tex]\frac{5}{12}[/tex] we have [tex](\frac{5}{12}) ^{2}[/tex] which becomes [tex]\frac{25}{144}[/tex]
so the perfect square trinomial = [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] + [tex]\frac{25}{144}[/tex]
the binomial is [tex](q + \frac{5}{12}) ^{2}[/tex]
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People were surveyed about pizza toppings. The results are shown in the Venn diagram. How many people like sausage or mushrooms?
a. 11
b. 30
c. 23
d. 12
The number of people that like sausage or mushrooms as shown in the Vann diagram is 30.
What is a Venn diagram?Venn diagrams are diagrams used to visually depict sets, relationships between sets, and operations on sets
To determine the number of people that like sausage or mushrooms from the Vann diagram, we use the Formula below.
Formula:
n (S ∪ M) = n (S) + n (M) − n (S ∩ M) ................. Equation 1
Where:
S = SausageM = Mushrooms∩ = Union∩ = Intersectionn (S ∪ M) = Number of people that like sausage and mushroomsn (S) = Number of Elements in the set Sn (M) = Number of element in set Sn (S ∩ M) = Number of element for S intersection MFrom the diagram,
Given:
n (S) = Add up all the numbers inside the circle for Sausage = 4+6+8+3 = 21 n (M) = Add up all the numbers inside the circle for Mushrooms = 5+4+4+8 = 21n (S ∩ M) = Add up all the numbers in side the region where the circle for Sausage and the circle for Mushrooms intersect. = 4+8 = 12Substitute these values into equation 1
n (S ∪ M) = 21+21-12n (S ∪ M) = 42-12n (S ∪ M) = 30Hence, the people who like sausage or mushrooms is 30
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For every 10 children 4 wore glasses. There were 30 children. How many did not wear glasses?
Answer:
18
Step-by-step explanation:
If 4 out of 10 wore glasses, then 6 out of 10 did not wear classes. This would be 60% or .6
.6x30 = 18
Winners buys a jacket from a manufacturer. Manufacturer offers 45% trade discount. Winners want to price the jacket for $150. What price should Winners pay for the jacket?
Question 1 options:
$82.50
55.60
53.50
$62.50
The price that Winners wants to pay for the jackets is $82.50
How to find the price that Winners wants to payThe question is a percentage problem, percentage deals with a fraction hundred and used as follows
45%
= 45 percent
= 45 / 100
= 0.45
The factor 0.71 is a discount factor so we subtract from 1
1 - 0.45 = 0.55
The price Winner wants to pay
= 0.55 * 150
= $82.50
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Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.
μ=77 and σ=14; n=64
The standard deviation of the sampling distribution of sample means using the given information is 1.8
What does the mathematical term "rounding" mean?
Rounding is a method for estimating a specific number in a situation. To determine how to round a number, look at the next digit in the appropriate position; if it is less than 5, round down, and if it is greater than 5, round up. The precise rounding of decimal figures is referred to as "rounding decimals."
What are the guidelines for rounding off decimal numbers?
To locate the rounding digit, look at its right side.
If the right-side numbers are less than 5, consider them to be equal to zero.
The digit on the right is increased by one and the other digits are treated as zero if the right-side digits are greater than or equal to 5.
The population standard deviation divided by the square root of the sample size, or n, gives the standard deviation of the sampling distribution of sample means, or x, for any given population. Therefore:
For the provided data, the sampling distribution's standard deviation of sample means is [tex]\frac{14}{\sqrt{64} }[/tex], or 1.8.
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Astorepays£98foramicroscope.Thestoremarksupthepriceby50%.Whatistheamountofthemark-up
Using percentage formula, the mark up price on the microscope is £49
Percentage
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Markup shows how much more a company's selling price is than the amount the item costs the company. In general, the higher the markup, the more revenue a company makes. Markup is the retail price for a product minus its cost, but the margin percentage is calculated differently.
Actual price = £98Markup percent = 50%Let's find 50% of £98
50 / 100 = x / 98
0.5 = x / 98
x = 0.5 * 98
x = 49
The mark up price is £49
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A theatre contains 414 seats and the ticket prices for a recent play were $47 for adults and $22 for children. If the total proceeds were $12,983 for a sold-out matinee, how many of each type of ticket were sold?
The system of linear equations shows that the adult tickets was 155 and children ticket was 259
System of Linear EquationIn algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."
To solve this problem, we can set up two equations for this
Let;
adult ticket = xchildren ticket = yx + y = 414 ...eq(i)
47x + 22y = 12983 ...eq(ii)
Solving both equations; the values of x and y are 155 and 259 respectively
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1/8 of the pupils at jake's school walked to school. 3/8 came by bus. waht fraction either walked or came by bus
By adding the two given fractions we will see that 1/2 of the students either walked or came by bus
What fraction either walked or came by bus?Let's say that there are N students in total. We know that a fraction of 1/8 of these N students walk to school.
And a fraction of 3/8 of the students go by bus to the school.
Then the fraction that either walks or came by bus to school is given by the addition between the two fractions above, then we just need to solve.
f = 3/8 + 1/8
We can see that we have the same denominator in both fractions, so we can directly add the numerators:
f = (3 + 1)/8 = 4/8
Now we can simplify the fraction to get:
f = 1/2
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The half-life of Radium-226 is 1590 years. If a sample contains 200 mg}, how many mg will remain after 1000 years?
_________mg
Give your answer accurate to at least 2 decimal places.
Answer:
137.11 mg
Step-by-step explanation:
divide 200 mg by 2 = 100 mg
divide 100 by 1590 = 0.0628930818
multiply this by 1000 = 62.8930818
subtract 62.8930818 from 200 = 137.1069182
137.1069182 rounded to 2 decimal places is 137.11 mg
therefore, the answer is 137.11 mg
answer the 4 questions attached below ⬇️
The area and perimeter of the composite figures are as follows;
Figure 1;
Perimeter = 70 km
Area = 200 km²
Figure 2
Perimeter = 28 cm
Area = 24 cm²
Figure 3
Perimeter = 40 m
Area = 88 m²
Figure 4
Perimeter = 64 m
Area = 96 m²
What is the area of a composite figure?The area of a composite figure is the sum of the areas of the parts or simple figures that make up the figure.
Figure 1
The perimeter = 10 + 10 + 5 + 20 + 5 + 10 + 10 = 70
The perimeter of the figure is 70 kilometersThe area = 10 × (10 + 5) + 10 × 5 = 200
The area of the figure is 200 km²Figure 2
The perimeter of the figure is; 6 cm + 5 cm + 2 cm + 3 cm + 2 cm + 3 cm + 2 cm + 5 cm = 28 cmArea of the figure is 5 cm × 2 cm + 2 cm × 2 cm + 5 cm × 2 cm = 24 cm²Figure 3
The perimeter of the figure is 12 m + 6 m + 4 m + 2 m + 8 m + 8 m = 40 mThe area of the figure is 6 m × 12 m + 8 m × 2 m = 88 m²Figure 4
Perimeter of the figure is 12 m + 12 m + 2 m + 8 m + 4 m + 8 m + 4 m + 8 m + 2 m + 4 m = 64 mArea of the figure is 12 m × 2 m + 4 m × 4 m + 4 m × 12 m + 4 m × 2 m = 96 m²Learn more about finding the area and perimeter of composite figures here:
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Which inequality is equivalent to x-6/x+5 ≥ x+7 /x+3? -13/x²+8x+15 ≥0 2x²+9x+17/x²+8x+15 ≥0 -15x-53/x²+8x+15 ≥0 9x+17/x²+8x+15 ≥ 0
The inequality (x - 6) / (x + 5) ≥ (x + 7) / (x + 3) is equivalent to (-15x - 53) / x² + 8x + 15 ≥ 0
Equivalent InequalityTwo or more inequalities are equivalent inequalities if they have the same solution set. Similar to equivalent equations, applying properties of Inequality to an inequality produces an equivalent inequality.
In the given inequality
(x - 6) / (x + 5) ≥ (x + 7) / (x + 3)
This can be reduced to
x < -5 or -53/15 ≤ x < -3
In the options given;
(-15x - 53) / x² + 8x + 15 ≥ 0 has the same reduction of x < -5 or -53/15 ≤ x < -3.
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(iv) A Nokia phone and Glo-Sim where sold for # 3,040 making a profit of 25% on the phone &
10% on the Sim card. By selling them for #3,070, the profit realised would have been 10% on
the phone and 25% on the sim. Find the cost price of each.
Answer:
phone's price = 1200
sim's price = 1400
Step-by-step explanation:
The cost of
maintaing libraries is 90.00
and this met from the expenditure on
Schools which is 6000.00. what percentage
Correct to
3 significant figures of the
expenditure on schools is spent on maintaining
Libraries ?
Find the volume of the solid generated by revolving the region bounded by y = x
and y = x²-3x about the x axis
The volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis will be x³/3-3x²/2+c.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
y = x²-3x
The volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis is obtained as,
[tex]=\int\:x^2-3x \ dx \\\\ = \int \:x^2dx-\int \:3xdx \\\\ =\frac{x^3}{3}-\frac{3x^2}{2} \\\\ =\frac{x^3}{3}-\frac{3x^2}{2}+C[/tex]
Thus, the volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis will be x³/3-3x²/2+c.
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Robbin's thumbnail is 1 5/8 centimeters long her pinky nail is 4/5 centimeters long. How much longer is robins thumbnail that pinky nail
A way to measure things is the metric system. Calculations and research use it all around the world.
What is Metric Units?In the metric system, the following units are used to measure length, weight, and capacity:
Length: There are five units of measurement for length, width, and height: the millimeter (mm), decimeter (dm), centimeter (cm), meter (m), and kilometer (km).Debit card thickness and length measurements, fabric length measurements, and distances between cities are a few examples.
Weight: Using instruments, we can determine an object's weight in grams (g) and kilograms (kg).The weight of fruits or our own body weight are two examples.
It is possible to measure how much liquid an object can hold using milliliters (ml) and liters (l).Calculating the volume of water in a water tank or the amount of juice in a juice can are two examples.
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The exponential model A=371.4e^0.0241 describes the population, A, of a county in millions, t years after 2003. Use the model to determine when the population of the country will be 677 million
After 598 years the population of the country will be 677 million
The exponential model of the population is
A = 371.4 e^ (0.0241×t)
Where A is the total population in t years
t is the number of years
The population of the country = 677 million
677 million = 677e^8
Therefore the exponential equation will be
6.77 × [tex]10^8[/tex] = 371.4e^(0.0241t)
e^(0.0241t) = 6.77 × [tex]10^8[/tex] / 371.4
Divide the terms
e^(0.0241t) = 1822832.526
0.0241t = ln(1822832.526)
t = ln(1822832.526) / 0.0241
Divide the terms
t = 598.17
t ≈ 598 years
Hence, after 598 years the population of the country will be 677 million
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Factor 5x^2+22x+8
Worth a large grade point, please help
You can subtract the right side and factor the result, or you can factor the left side then see what happens.
... 5x² +22x +8 = 5x +2
... 5x² + 2x +20x +8 = 5x +2 . . . . split the x term so we can factor by grouping
... x(5x +2) +4(5x +2) = (5x +2)
Now we can subtract the right side and finish the factoring.
... x(5x +2) +(4 - 1)(5x +2) = 0
... (x +3)(5x +2) = 0 . . . . . the factorization of your equation
_____
If we start by subtracting the right side, we are looking to factor ...
... 5x² +17x +6 = 0
... 5x² +2x +15x +6 = 0 . . . . . split the x-term to help factoring by grouping
... x(5x +2) +3(5x +2) = 0 . . . factor pairs of terms
... (x +3)(5x +2) = 0 . . . . . . . . combine the results
______ _____
Factoring quadratics with the leading coefficient not equal to 1 is similar to factoring when it is equal to 1. Here, (after subtracting the right side), we are looking for factors of 5·6 = 30 that add to 17, the coefficient of the x-term.
... 30 = 1·30 = 2·15 = 3·10 = 5·6
The sums of these factor pairs are 31, 17, 13, 11. We see that the factor pair (2, 15) is the one we want, as its sum is 17. You will note these are the numbers used to divide the x-term for factoring by grouping. We rewrote 17x as 2x +15x. (There are other ways to use these numbers, but this is perhaps the easiest to see and remember.)
Answer:
(5x + 2)(x + 4)
Step-by-step explanation:
So, we have the equation [tex]5x^2+22x+8[/tex] right?
To get the [tex]x^2[/tex] we are going to need 'something' x in the first x slots of our factor form, like this:
(?x ± ?)(?x ± ?)
5 is a prime number, so one of the x's will be a 5x, and the other one a 1x:
(5x ± z)(x ± q)
z * q must be 8, and 5 * q + z must be 22
2 * 4 is 8
Let's plug these values in:
(5x + 2)(x + 4)
Let's multiply this out:
[tex]5x^2+22x+8[/tex]
This matches with our original equation!
So, our answer is:
(5x + 2)(x + 4)
3. What is the proper ordering
(from greatest to least) of the
following numbers?
I.58/67
II.0.58%
III.58%
IV.5.8%
O I, III, II,
O III, IV, II, I
O I, III, IV, II
O IV, I, III, II
Answer:
C) I, III, IV, II
Step-by-step explanation:
Convert each number into a decimal:
[tex]\textsf{I.} \quad \dfrac{58}{67}=0.86567...[/tex]
[tex]\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058[/tex]
[tex]\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58[/tex]
[tex]\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058[/tex]
Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.
The next biggest tenth is 5, so 58% is the next largest number.
The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number. Therefore, 0.58% is the smallest number.
Therefore, the given set of numbers in order from greatest to least is:
I, III, IV, IIAnswer:
c) I, III, IV, II
Step-by-step explanation:
Values of l, ll, lll & lV respectively,
→ 58/67, 0.58%, 58%, 5.8%
→ 0.87, 0.0058, 0.58, 0.058
Arranging them in descending order,
→ 0.87 > 0.58 > 0.058 > 0.0058
→ 0.87, 0.58, 0.058, 0.0058
→ l, lll, lV, ll
Hence, the option (c) is correct.
(03.02 MC)
a
R
Which set of transformations would prove AQRS-AUTS?
Reflect AUTS over y = 2, and dilate AUT'S' by a scale factor of 2 from point S.
Reflect AUTS over y = 2, and translate AU'T'S' by the rule (x - 2, y + 0).
Translate AUTS by the rule (x + 0, y + 6), and reflect AUT'S' over y = 6.
Translate AUTS by the rule (x-2, y + 0), and reflect AU'T'S' over y = 2.
PLEASEEEEEEE HELP DUE NOWWWWWWWWW
Pls answer this is in khan academ pls answer fast rapidly
Answer:
26.009
Step-by-step explanation:
Let's break it down
(2*10) + (6*1) + (9*1/1000)
20+6+0.009
26.009
Hundreds- 0
Tens- 2
Ones- 6
Tenths- 0
Hundredths- 0
Thousandths- 9
Answer:
26.009
Step-by-step explanation:
since 2 is being multiplied by ten there are 2 tens
And since 6 is being multiplied by 1 there are 6 ones
and since 9 is being multiplied by 1/1000 there are 9 thousandths
And the rest of the place values are zero and should be written like
26.009
Hopes this helps please mark brainliest
The line 2y=3x intersects the ellipse x^2/8+y^2/18 = 1 at the points Q and R. What is the length of segment QR?
The distance between the points Q and R is 7.211 units.
What is an ellipse?In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base. It has two focal points.
Given an equation of ellipse x²/8+y²/18 =1, a line 2y = 3x intersect the ellipse at points Q and R,
x²/8+y²/18 =1........ (i)
2y = 3x....... (ii)
Use eq 2 in 1, we get
x²/8+(3x/2)²/18 = 1
On solving, we get,
x²/4 = 1
x = ±2
And,
(2y/3)²/8+y²/18 = 1
On solving, we get,
y = ±3
Therefore, we got, y1 = 3, y2 = -3, x1 = 2 and x2 = -2
Using the distance formula, D = √(x1-x2)²+(y2-y1)²
QR = √(-2-2)²+(-3-3)² = 7.211
|QR| = 7.211
Hence, The distance between the points Q and R is 7.211 units.
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Please help will mark Brainly
Your answer is -5.
Hope this helps.
21. Plot the numbers on the number line below. A.-5 1/2 B -6.3 C. -5.8 D. -6 7/10 E. -4.9 F. -6 9/10
The number line that contains each of these points marked is given by the image presented at the end of the answer.
How to plot numbers on a number line?It depends if the number to be plotted is an integer or if it is a decimal.
If the number is an integer number, then the symbol is just marked over the point representing the number.If the number is a decimal, we have to find between which two integers the decimal is located, and then verify the proportion to plot the number.The numbers that will be plotted in this problem are defined as follows:
A = -5.5, hence halfway between -6 and -5.B = -6.3, hence between -7 and -6, and closest to -6.C = -5.8, between -6 and -5, to the left of A, hence closest to -6.D = -6 and 7/10 = -6.7, also between -7 and -6, closest to -7, hence to the left of B.E = -4.9, hence slightly to the right of -5.F = -6 and 9/10, also between -7 and -6, and to the left of D.A similar problem, also featuring the number line, is presented at brainly.com/question/24644930
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solve ((-3) x (10 + (-7))) to the power of 2 /n3 - (-9) to the power of 2)
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
[-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove
that two triangles are congruent.
For each pair of triangles shown, select the correct statement.
a)
A: Congruent (SSS)
B: Congruent (SAS)
C: Congruent (ASA)
D: Congruent (RHS)
b)
58
68
54
68
9.2 cm
54
Not drawn
to scale
Not drawn
to scale
9.2 cm
58
68*
58
68*
54
A: Congruent (SSS)
B: Congruent (SAS)
C: Congruent (ASA)
D: Congruent (RHS)
E: Not congruent
F: Could be congruent
E: Not congruent
F: Could be congruent
b)
A
Resuelva:
1) |3 x-1|-|2 x+5-(5-x)|=0
2) |2(x+1)-4|=|2-2(2-x)|
3) |x-2/4|-1/3=x
4) 1/2|x-3|-1=|x-3|+2
The solutions to the absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0, |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 are 1/6, 1, 2/15 and no solutions respectively
Absolute FunctionAn absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.
In the questions given;
Question 1
|3x - 1| - |2x + 5 - (5 - x)| = 0
x = 1/6
Question 2
|2(x + 1) - 4| - 4| = |2 - 2(2 - x)|
x = 1
Question 3
|(x - 2) / 4| - 1/3 = x
x = 2 / 15
Question 4
1/2|x - 3| - 1 = |x - 3| + 2
This equation does not have a solution
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Identity the property of equality that was used for each step
Addition property
Subtraction property
Multiplication property
Division property
Transitive property
Symmetric property
Substitution property
Reflexive property
Distributive property
The property of equality that are used in each step is:
What is meant by Division property?According to the division property of equality, if both sides of an equation are divided by a common real integer that is not equal to zero, the quotients remain equal. The formula for this is as follows: If a, b, and c are real numbers, with a = b and c 0 respectively, then a c = b c.
Have you ever wondered what rules you have to follow when dealing with inequalities? The division property of inequality is one of those laws, and it basically states that if you divide one side of an inequality by a number, you can divide the other side of the inequality by the same amount.
2((2X/5)+8)= 4(14-(X/5))
2((2X/5)+8)/2= 4(14-(X/5))/2 ---------Division property
(2x/5+8)=2(14-x/5)
((2x/5)+8)=(28-(2x/5) ---------Distributive property
(2x/5)+8+(2x/5)=28-(2x/5)+(2x/5) --------Addition property
(4x/5)+8=28
(4x/5)+8-8=28-8 ---------subtraction property
4x/5=20
(4x/5)×(5)=20×(5) ---------Multiplicative property
4x=100
4x/4=100/4 --------- Division property
x=25 ----------Symmetric property
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Three of the exterior angles of an n-sided
polygon are 50° each,
two of its interior
angles are 127° and 135°,
and the remaining
interior angles are 173° each. Find the value of n.
Answer:
[tex]n=126[/tex]
Step-by-step explanation:
Using the formula for the sum of the angles of an [tex]n[/tex]-sided polygon, the sum of the angles is [tex]180(n-2)[/tex] degrees.
An exterior angle is supplementary to the corresponding interior angle. Using the given angle measures, the sum of the angles is [tex]2(180-50)+127+135+173n=522+173n[/tex] degrees.
Equating these two results,
[tex]180(n-2)=522+173n \\ \\ 180n-360=522+173n \\ \\ 7n-360=362 \\ \\ 7n=882 \\ \\ n=126[/tex]
Answer:
n=126
Step-by-step explanation:
180(n−2)=522+173n
180n−360=522+173n
7n−360=362
7n=882
n=126
Let U={b, c, d, e, f, g, h} and A={b, f, g, h}. Use the roster method to write the set A'
A'= {____ }
(Use a comma to separate answers as needed.)
The roster method to write the set A' will be {c, d, e}.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
Let U = {b, c, d, e, f, g, h} and A = {b, f, g, h}.
The roster method to write the set A' will be given as,
A' = U - A
A' = {b, c, d, e, f, g, h} - {b, f, g, h}
A' = {c, d, e}
The roster method to write the set A' will be {c, d, e}.
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4 1/5-(3 3/5-2 3/3) of 3/11
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