The area of rectangle abcd is 28 cm a) what is the length of side ab in terms of x? length of ab = 4 cm x cm 6 cm x cm b) if the area of rectangle abcd is 28 cm?, we can show that x2 + ax = b where a and b are integer values. work out the values of a and b. a : (1) b= (1) total marks: 3
Answers
The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.
The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).
The area of rectangle is calculated by the formula-
Area = length × breadth
Keep the values in formula -
28 = (4 + x) (6 + x)
Performing multiplication of both brackets with each other
28 = 24 + 4x + 6x + x²
Solving and rewriting the equation
x² + 10x = 4
Equation in question - x² + ax = b
Comparing both the equations, we get a = 10 and b = 4.
Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.
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Related Questions
Find all possible values of x for which these two triangles are simliar.
Please help quickly!!!
Answers
The possible value of x which the two triangles are similar is x=60°.
What do you mean by triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Method:
Given that two angles of the triangle are specified, the triangles can be
similar for only one value of x.
According to the given data in the question,
The two triangles are similar when we have;
x + 10° = 2x - 50°
Which gives;
2x - x = 50° + 10° = 60°
x = 60°
Checking gives;
x + 10° = 2·x - 50° = 70°
Two angles of the first triangle are 70° and 60°
Then, the third angle of the first triangle is (180° - (70° + 60°)) = 50°
The three angles of the first triangle are therefore; 70°, 60° and 50°.
Two angles of the second triangle are 70° and 70°.
The third angle of the second triangle is (180° - (70° + 70°)) = 40°
The three angles of the second triangle are therefore; 70°, 70° and 40°
Therefore, the two triangles are similar by AAA similarity.
The two triangles are similar when, x = 60°
When x = 50°, we have;
x + 10° gives;
50° + 10° = 60°
∴ ∠(x + 10°) = 60°
The two angles of the first triangle are; 60° and 50°
The third angle on the second triangle is 180° - (60° + 50°) = 70°
On the second triangle, we have;
2·x - 50° gives;
2 × 50° - 50° = 50°
∴∠(2·x - 50°) = 50°
Therefore, the two angles of the second triangle are 70° and 50°
The third angle on the second triangle is 180° - (70° + 50°) = 60°
Therefore, the two triangles are not similar when x = 50°
Similarly, the two triangles are not similar when x + 10° = 50°
Hence, the possible value of x which the two triangles are similar is x = 60°.
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a triangular flower garden in the front of the house to increase curb appeal she has 12 square feet of space to work with . What are 2 possible dimensions for her flower garden ? Sketch a picture and justify your answer mathematically .
Answers
The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6).
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The area of a triangle is given as (1/2) × base × height.
The given area of the triangle = 12 feet².
Thus,
12 = (1/2) × base × height
Base × height = 12 × 2
Base × height = 24
The combination of two quantities gives 24 by multiplying will be (12,2),(8,3), and (4,6).
For example, the triangle with dimensions (4,6) is attached below.
Hence "The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6)".
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1. Find the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10).
Hint: Use quadratic regression to find the standard form.
Answers
The standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile travelling under the pull of gravity will travel along a curve similar to this one.For parabolas that open either up or down, the standard form equation is y = ax² + bx + cThe equation of parabola in standard form is y = ax² + bx + c
We have given the points,
(1, 0), (2, -3), and (3,-10)
Let's put each point in parabola equation and form three equation as,
Equation for point (1, 0)
0 = a * (1)² + b * 1 + c
a + b + c = 0 --------------------eq(i)
Now, equation for point(2, -3)
-3 = a * (2)² + b * 2 + c
4a + 2b + c = -3 --------------------eq(ii)
And, equation for point (3, -10)
-10 = a * (3)² + b * 3 + c
9a + 3b + c = -10 ---------------------eq(iii)
Now, we have three equation let's put them together
a + b + c = 0 --------------------eq(i)
4a + 2b + c = -3 --------------------eq(ii)
9a + 3b + c = -10 ---------------------eq(iii)
Now, form equation which is of two variable.
For that, we take first two equation and subtract eq(ii) from eq(i)
4a+2b+c = -3
a + b + c = 0
- - - -
------------------------
3a + b = -3 ---------------eq(a)
Now, subtract eq(iii) from eq(ii)
9a + 3b + c = -10
4a + 2b + c = -3
- - - -
------------------------
5a + b = -7 ------------------eq(b)
Now, we get eq(a) and eq(b) consist of two variable.
3a + b = -3 ---------------eq(a)
5a + b = -7 ----------------eq(b)
Now, solve this equation simultaneously and find the value of a and b.
3a + b = -3
5a + b = -7
- - -
----------------
-2a = 4
a = -2
put a = -2 in eq(a) to find b
3a + b = -3
⇒3 * -2 + b = -3
⇒-6 + b = -3
⇒b = 3
We get the values of a and b. And, left with value of c for that just put the a and b value in eq(i) and find c
a + b + c = 0
-2 + 3 + c = 0
c = -1
Now, we get all the necessary values for equation.
Next, just put a, b and c values in parabola equation.
y = ax² + bx + c
y = -2x² + 3x - 1
Hence, the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
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an experimenter would like to construct a 99% confidence interval with a width at most 0.5 for the average resistance of a segment of copper cable of a certain length. if the experimenter knows that the standard deviation of such resistances is 1.55. how big a sample should the experimenter take from the population? what happens if the standard deviation and the width of the confidence interval are both doubled?
Answers
64 is the standard deviation and the width of the confidence interval are both doubled .
What is standard deviation in math?
Your dataset's average level of variability is represented by the standard deviation. It reveals, on average, how far away from the mean each value is. A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.Margin of error(E)=0.5
Standard deviation(σ)=1.55
Significance level(α)=100%-99%=1% or 0.01
From Z distribution Critical value table
the Critical value(Zc)=2.58 at significance level=0.01
we know formula for the Margin of error
E = Zc * σ/√n
0.5 = 2.58 * 1.55/√n
√n = 2.58 * 1.55/0.5
√n = 3.999/0.5
√n = 7.998
n = ( 7.998)²
n = 63.968004
Aproximately
n = 64
the realtionship between the sample size and margin of error is inversly proportional.
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For a snack, Miss Johnson gives her class graham crackers. She has a package of 30
graham crackers to share equally among twelve students.
How many graham crackers should each student receive?
Dividing
?
graham crackers among
Each student gets
crackers.
students can be found by solving
Answers
Answer:
each student get 2.5 of graham crackers
Step-by-step explanation:
[tex]total \: students \: = 12 \\ graham \: crackers \: = 30 \\ 30 \div 12 \\ = 2.5[/tex]
One share of kimcos common stock pays an annual dividend of 1. 43. Today kimco closed at 19. 09 with a net cahnge of +0. 72. The stock yield yesterdays closing price is about 8
Answers
With a net change of +0.72 yesterday's closing price was 19.81 and stock dividend yield for yesterday's closing price is 7.2%.
How to calculate the Dividend Yield?
To calculate dividend yield, all you have to do is divide the annual dividends paid per share by the price per share.
Dividend Yield = Annual Dividends Paid Per Share / Price Per Share
According to the given question:
Net change = today's price - yesterday's price
0.72 = 19.09 - yesterday's price
∴ Yesterday's price = 19.81
Stock dividend yield
= (1.43/19.81) x 100
= 7.2%
Therefore the stock yield of yesterday's closing price is 7.2%
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help is needed please and thank you
Answers
The required value of g(-4) = 1 in the given function is represented in the shown graph.
What is a graph?A graph can be defined as a visual representation or a diagram that represents data or values.
The function is given in the represented graph of g(x)
We have to determine the value of g(-4) of the given function in the graph
According to the given graph, we can see that the value of the domain of the given function g(x) when the value of variable x is -4 when the value of the variable y is 1. this means the value of g(-4) = 1.
Therefore, the required value of g(-4) = 1 in the given function is represented in the shown graph.
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you have a deck and you take one card at random and guess what the card is. what is the probability you guess right?
Answers
There are 52 cards in the deck and so the probability of guessing the card right is 1/52.
What is probability?Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.
Here,
We can find this probability by seeing that
=1/4×1/13
=1/52
Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.
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Evaluate y² ÷ 8 if y = 4
I wasn't here when they learned this old show work
Answers
Answer:
2
Step-by-step explanation:
y² = 4²= 16 (in substitution way)
16÷8= 2
mark me on brainliest please follow me to
Answer:
2
Step-by-step explanation:
y^2/8
4^2/8
16/8
2
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Charities can claim an extra 25% of the value of a donation back from the government. This is called gift aid. Work out how much gift aid a charity can claim on a donation of £273.50. Give your answer to the nearest penny
Answers
Answer:
Gift aid 68.38 £
Step-by-step explanation:
Proportion:
273.50 £ - 100%
X £ - 25%
Gift aid:
X = 273.50·25% / 100% = 273.50 / 4 ≈ 68.38 £
The area of a rectangle is given as 90 cm² and the length is 3 cm longer than its width. Find the length and the width of the rectangle.
Answers
Answer:
Step-by-step explanation:
Area of a rectangle is given by the formula :
A = L × W
Substituting 90 with A , x with W and (x+3) with L, we get :
90 = (x+3)×x
Simplifying the right side by expanding the bracket :
x(x+3) =
x²+3x
90=x²+3x
Now we can make a quadratic by subtracting both sides by 90 :
x²+3x-90 =0
I'm not sure about the rest
Terry sees this offer.
Refurbished phone
35% OFF
Now only £78
How much was the phone before the discounted price?
Answers
Answer: The phone was £120 before the discount.
Which point is collinear with points A and B?
Answers
As stated in the preceding statement the point R is collinear with points A and B.
What is a collinear?An axis is a term used to describe a line upon whatever points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points become trivially collinear.
How are collinear points discovered?Two lines may coincide if they have a same point and have the same slope. To put it another way, if A, B, as well as C are three points there in XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.
then
m A B = m BC ( = m AC ).
The point is collinear with points A and B.
Therefore, the correct answer is option (d) R.
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Please help me with my math
Answers
The product of a number minus 17 and 5 are equivalent to: 5 (n - 17) .
How do you find the equivalent expressions?X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two phrases are equal if and only if each of their terms is the same.
the sum of a number less than 17 and five
If x is an ambiguous number,
The sign for minus is -
A number less than 17 is denoted by x-17.
The multiplication is the product.
Add x-17 and (x-17)5 to get the answer.
In this case, the expression is 5 (n - 17).
When two numbers are multiplied together, the outcome is known as the product.
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Write inequalities to represent the situations below.
Ann exercises no less than 40 minutes per day.
Use t to represent Ann's amount of exercise (in minutes per day).
Answers
The inequalities to represent the Ann situation is t > 40.
How to model a situation with inequalities?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
In Mathematics, the relationship between two values that are not equal is defined by inequalities.
Therefore, an expression with an inequalities have the signs <, >, ≤ and ≥.
Let's represent the situation with an inequalities.
Therefore, Ann exercises no less than 40 minutes per day.
let
t = Ann's amount of exercise (in minutes per day).
The inequalities to represent the situation is as follows:
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PLEASE HELP I NEED IT TODAY
QUESTION IS ON THE IMAGE DOWN BELOW
PLEASE ANSWER QUESTION AS A double number line
Answers
Answer:
I agree with her the reason? because she is right
67.50/6= 11.25 meaning it's $11.25 per ticket
47/4= 11.75 meaning it's $11.75 per ticket
Step-by-step explanation: Jamar spent 11.25 per ticket
Aaron spent 11.75 per ticket meaning she spent more than Jamar
22. A train travels 3 hours at 20km per
hour. How long will it take another
train to travel the same distance at
10km per hour?
(a) 6²/³ hours
(b) 6¹/2hours
(c) 6 hours
(d) 3 hours
(e) 2 hours
What I
Answers
The train takes 6 hours to travel the same distance.
From the question, we have
A train with 20km per hour takes 3 hours to travel the distance .
Another train with 10km per hour takes = (3*20)/10 hours
=6 hours
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Hong made $153 for 9 hours of work.
At the same rate, how many hours would he have to work to make $187?
hours
X
Answers
187/17=11
The answer is 11
Answer:
11 hours
Step-by-step explanation:
153 divided by 9 (which is 17) 17$ per hour so add 17 and 17 together which would be 34 and add it to 153 which would be 187$ he worked 2 more hours so in total he worked 11 hours.
and i know that was a bad explanation but its whatever hope this helped.
Please solve the equation
[tex]5 {}^{2x + 1} - 26(5 {}^{x} ) \: + 5 = 0[/tex]
Answers
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
The formula for log [tex]x^n[/tex] = n log x
The value of x is 0.043
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
[tex]5^{2x + 1} - 26(5^x) + 5 = 0[/tex]
[tex]5^{2x + 1} + 5 = 26(5^x)[/tex]
The formula for log [tex]x^n[/tex] = n log x
Taking logs on both sides.
log [tex](5^{2x + 1} + 5)[/tex] = log [tex]26(5^x)[/tex]
log [tex]5^{2x + 1}[/tex] + log 5 = log 26 + log [tex]5^{x}[/tex]
(2x + 1) log 5 + log 5 = 1.41 + x log 5
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
(2x + 1) x 0.69 + 0.69 = 1.41 + 0.69x
1.39x + 0.69 + 0.69 = 1.41 + 0.69x
0.70x = 1.41 - 1.38
x = 0.03 / 0.70
x = 0.043
Thus,
The value of x is 0.043
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select all equations that are equivalent to (5x+6)/2=3-(4x+12)
Answers
The equivalent equation of the equation, [tex]\frac{5x+6}{2}=3-(4x+12)[/tex] is 5x + 6 = -18 - 8x
How to find equivalent equation?Two equations are said to be equivalent when they have the same solution set.
Equivalent equations are algebraic equations that have identical solutions or roots.
Therefore, let's find the equivalent equation of the equation.
[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]
Let's open the bracket on the right side
[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]
[tex]\frac{5x+6}{2}=3 - 4x - 12[/tex]
[tex]\frac{5x+6}{2}=(-9-4x)[/tex]
cross multiply
5x + 6 = 2(-9 - 4x)
5x + 6 = -18 - 8x
5x + 8x = -18 - 6
13x = - 24
divide both sides by 13
x = - 24 / 13
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Three children split a land inheritance in the ratio of 2:4:5. The land is made up of 2,750 acres. The one with the largest parcel of land from the inheritance decides to sell that parcel for $600 an acre. How much money does this person make on the sale of his share of the inheritance?
Answers
Using the properties of ratio we calculate that the largest land inheritance was sold at $825000 .
The ratio in which the land is divided is 2:3:5
Let the common ratio be x .
Hence the land is divided which has a combined area of 2750 acres.
Now, 2x+3x+5x = 2750
or, 10x = 2750
or, x = 275
Now the person with the highest inheritance will be having land:
= 5× 275
= 1375 acres
Cost of the land at $600 per acre
= 600 × 1375
= $825000
therefore the cost of the land is $825000
A ratio can therefore be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value represented by this fraction.
Ratios of counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of two numbers is a dimensionless number when they are measured using the same unit, which happens frequently.
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Jordan saved $225 and continues to save $45 each week. RayAnn saved $150 and continues to save $60 each week. Write and solve a system of equations using any method for the given situation.
Equation for Jordan:
Equation for RayAnn:
Solution:
??please help???
Answers
The equations using any method for the given situation illustrated that:
The equation for Jordan: 225 + 45w
The equation for RayAnn: 150 + 60w
How to calculate the equation?Let the number of weeks be represented by w. Jordan saved $225 and continues to save $45 each week. The equation for this will be:
= 225 + (45 × w)
= 225 + 45w
RayAnn saved $150 and continues to save $60 each week. The equation will be:
= 150 + (60 × w)
= 150 + 60w
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Which comic section is formed in the image
Answers
Answer:hyper bola
Step-by-step explanation:
All you have to do is look up all the answers on images and then pick the one that looks the most similar
Can someone at least explain this to me I’m very confused.
Answers
For given line segments RS = TR
In this question, we have been given two line segments QS and TU intersected at point R.
Also, we have been given QS = TU, QR = RU
We need to prove, RS = TR
We can observe that,
QS = QR + RS
and UT = UR + RT
QS = TU ................(Given)
QR + RS = UR + RT
QR + RS = QR + RT .............(Given QR = RU )
QR + RS - QR = QR + RT - QR .............(subtraction property of equality)
RS = TR
Hence proved.
Therefore, for given line segments RS = TR
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reimond needs to order crushed rock for a courtyard what is the cost of 4.5 t at $12.50 per tonne?
Answers
The cost of 4.5 tonnes of rock is $56.25
Given,
cost of 1 tonne of rock=$12.50
then
to find cost of 4.5 tonnes of rock, multiply 12.50 with 4.5,
cost of 4.5 tonnes of rock = 4.5* 12.50 = $56.25
Thus ,the cost of 4.5 tonnes of rock is $56.25.
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Hello I’m doing my math homework I just need the answers for 23 and that’s just it . ABCDEF all right thank you please get me ASAP,
Answers
Answer:
A. -9, -6, 8, 13
B. -4/5, -1/2, -.2, .25
C. -8/3, -2 1/2, 9/2, 4.75
D. -8, -3, -1, 4
E. -1/2, -1/4, .5, 3/4
F. -3/2, -5/4, -4/5, 1.5
Step-by-step explanation:
The easiest thing to do is to put them all in the same format. Fractions are just division problems, so just divide. 4/5 is 4 divided by 5, which is .8.
Remember, the farther a negative number is from 0 on the number line, the smaller it is. So, -8 is smaller than -5. -5 is smaller than -2, etc.
Which of the following is the correct factorization of the polynomial below?
x³-18
A. (x+3)(x-6)
B. (x-3)(x+6)
C. (x+3)(x² - 4x+6)
D. The polynomial is irreducible.
SUBMIT
Answers
Answer: D. The polynomial is irreducible.
From the explanation below we do not get polynomial .
Step-by-step explanation:
A.(x+3)(x-6)
= x^2-6x+3x-18
=x^2-3x-18
B.(x-3)(x+6)
=(x^2+6x-3x-18)
=x^2+3x-18
C.(x+3)(x^2-4x+6)
=x^3-4x^2+6x+3x^2-12x+18
=x^2-x^2-6x+18
D.The polynomial is irreducible
HELP!! SOLVER GETS ALL MY POINTS
Answers
The accounting profit is $10,800 and economic profit is - $14,200.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
The saving of Sarah = $50,000
The interest on $25,000 Sarah withdrew at the rate of 4% = $1000
The interest on $30,000 Sarah borrowed at the rate of 4% = %1200
The amount paid for ingredients = $27,000
Total investment = 27,000+30,000+ 1000+1200 = $59,200
Revenue of Sarah = $70,000
Accounting profit of Sarah = $70,000 - $59,200 = $10,800
Economic profit of Sarah = $70,000 - ($59,200+$25,000)
= - $14,200
The accounting profit is $10,800 and economic profit is - $14,200.
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A new gaming chair costs $239.87. You have already saved $118.37 and earn $40.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
40.5w + 118.37 = 239.87; w = 3
40.5w − 118.37 = 239.87; w = 9
40.5w − 239.87 = 118.37; w = 9
40.5 + 118.37w = 239.87; w = 3
Answers
Answer:
40.5w + 118.37= 239.87; w=3
Step-by-step explanation:
You already saved 118.37.
239.87
118.37
111.50
40x3=120. So you'll need 3 more weeks to buy a gaming chair. And you also get 8.50 dollars extra in profit.
Answer:
40.5w + 118.37= 239.87; w=3
Step-by-step explanation:
A polynomial can be factored by grouping if:
