If the area of the rectangle is 40 square centimeters and length is 7 cm less than 3 times the breadth then the length will be 8 cm and breadth will be 5 cm.
Given area of the rectangle is 40 square centimeters and length is 7 centimeters less than 3 times the breadth.
let the breadth of rectangle be x.
According to question
Length=3x-7
Breadth=x
Area of rectangle=length* breadth
=[tex](3x-7)x[/tex]
=[tex]3x^{2} -7x[/tex]
Area is given as 40 square centimeters.
40=[tex]3x^{2} -7x[/tex]
[tex]3x^{2} -7x-40=0[/tex]
By factorization
[tex]3x^{2} -15x+8x-40=0[/tex]
3x(x-5)+8(x-5)=0
(3x+8)(x-5)=0
3x+8=0
x=-8/3
x-5=0
x=5
We should neglect x=-8/3 because side cannot be negative. So we have taken x=5.
Put x=5 in 3x-7 to get length
length=3(5)-7
=15-7
=8
Hence the length will be 8 cm and breadth will be 5 cm.
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A researcher gets a list of all 500 members of the National Association of Social Work in Yourtown that she wants to include in her study. She only has the funding and time to survey 50 members. She takes her list of members, randomly selects a starting point, and then selects every tenth name from the list to be included in her sample. In this example, the sampling interval is:
In this example, the sampling interval is 10.
A researcher gets a list of all 500 members of the National Association of Social Work in Yourtown that she wants to include in her study. She only has the funding and time to survey 50 members. She takes her list of members, randomly selects a starting point, and then selects every tenth name from the list to be included in her sample.
In this example, the sampling interval is 10.
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Victor borrowed money at 5.25 percent simple annual interest. At the end of the year, the interest on the loan is $255.94. What was the amount of the loan?
can someone help me ?
Answer:
∠ C = 26°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
∠ A + ∠ B + ∠ C = 180°
120° + 34° + ∠ C = 180°
154° + ∠ C = 180° ( subtract 154° from both sides )
∠ C = 26°
1-secA+tanA/1+secA+TanA = secA+tanA-1/secA+tanA+1
It has been proven that the trigonometric Identity (1 - secA + tanA)/(1 + secA + TanA) is equal to; (secA + tanA - 1)/(secA + tanA + 1)
How to prove trigonometric Identities?
We want to prove that;
(1 - secA + tanA)/(1 + secA + TanA) = (secA + tanA - 1)/(secA + tanA + 1)
We know from trigonometric identities that;
(secA)² – (tanA)² = 1 ----(1)
Also, from algebra we know that;
a² - b² = (a + b)(a - b)
The numerator of LHS of the original given Identity is:
1 - sec A - tan A
Using equation 1, we can say that;
(secA)² – (tanA)² - (sec A + tan A)
⇒ (sec A + tan A)(sec A - tan A) - (sec A - tan A)
This can be factorized to get;
(sec A - tan A)(sec A + tan A - 1)
Similarly, the denominator can be expressed as;
(sec A - tan A)(sec A + tan A + 1)
Thus, combining the numerator and denominator together gives us:
[(sec A - tan A)(sec A + tan A - 1)]/[(sec A - tan A)(sec A + tan A + 1)]
⇒ (secA + tanA - 1)/(secA + tanA + 1)
That expression is equal to the Right hand side and as such the Trigonometric Identity is proved.
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For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions
34. f(x) = 4 − x, g(x) = −4x
Answer:
The value of [tex]$(f \circ g)(x)$[/tex] is [tex]$4+4 x$[/tex] and [tex]$(g \circ f)(x)$[/tex] is [tex]$4 x-16$[/tex].
Step-by-step explanation:
It is given in the question functions f(x) as 4-x and g(x)=-4x.
It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].
To find [tex]$(f \circ g)(x)$[/tex], substitute g(x)=-4x for x in f(x) and simplify the expression.
To find [tex]$(g \circ f)(x)$[/tex], substitute f(x)=4-x for x in g(x) and simplify the expression.
Step 1 of 2
Substitute g(x)=-4x for x in f(x) and simplify the expression.
[tex]$$\begin{aligned}&(f \circ g)(x)=f(g(x)) \\&(f \circ g)(x)=4-g(x) \\&(f \circ g)(x)=4-(-4 x) \\&(f \circ g)(x)=4+4 x\end{aligned}$$[/tex]
Step 2 of 2
Substitute f(x)=4-x for x in g(x) and simplify the expression.
[tex]$$\begin{aligned}&(g \circ f)(x)=g(f(x)) \\&(g \circ f)(x)=-4 f(x) \\&(g \circ f)(x)=-4(4-x) \\&(g \circ f)(x)=4 x-16\end{aligned}$$[/tex]
Ria surveyed 20 classmates to ask what types of pets they had at home. calculate the relative frequency of each pet type.
write your response in exact decimals.)
pet type
count
relative frequency
dog
8
cat
7
bird
3
fish
2
total
20
The relative frequencies for all pets are given-
The relative frequency for dog is 0.4.
The relative frequency for cat is 0.35.
The relative frequency for bird is 0.15.
The relative frequency for fish is 0.1
What is relative frequency?The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency.
Relative Frequency = Subgroup frequency/ Total frequency.
Relative Frequency = f/ n.
where, f = total frequency
n = subgroup frequency
Calculation for the relative frequencies of the pet types:
(1) Relative frequency for dog:
Total frequency is 20.
The frequency for dog is 8.
Relative frequency for dog = frequency for dog/total frequency
= 8/20
= 0.4
Relative frequency for dog = 0.4.
(2) Relative frequency for cat:
Total frequency is 20.
The frequency for cat is 7.
Relative frequency for cat = frequency for cat/total frequency
= 7/20
= 0.35
Relative frequency for cat = 0.35.
(3) Relative frequency for bird:
Total frequency is 20.
The frequency for bird is 3.
Relative frequency for bird = frequency for bird/total frequency
= 3/20
Relative frequency for bird = 0.15.
(4) Relative frequency for fish:
Total frequency is 20.
The frequency for fish is 2.
Relative frequency for fish = frequency for fish/total frequency
= 2/20
Relative frequency for fish = 0.1.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Inequality expressionsInequality are expressions not separated by an equal sign. Given the inequality expression below;
–3(2x – 5) < 5(2 – x)
Expand
-6x + 15 < 10 - 5x
Collect the like terms
-6x + 5x < 10 - 15
-x < -5
x > 5
Hence the correct representations of the inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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Compare the graphs f(x)=(x-10)^2+8 with the graph of f(x)=x^2
Answer:
b. The graph of g(x) is a translation 10 units right and 8 units up from the graph of f(x).
Step-by-step explanation:
See attached image.
Use the image below to complete the questions!
Step One: We need to fill in the two points that are highlighted on the graph.
Point A: (−1, ? )
Point B: ( ? ,0)
Step Two: To get from Point B to Point A, we must rise 4 and run __? So using rise over run we have m= __?
(Giving 50 points and Brainly!)
Point A: ( -1, 4 )
Point B: ( 1 ,0 )
To get from Point B to Point A, we must rise 4 and run -2 So using rise over run we have m = -2
Explanation:
After observing:
Point A is (-1, 4)Point B is (1, 0)And
[tex]\sf slope \ (m) : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{rise}{run} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) = \dfrac{rise}{run} = \dfrac{4-0}{-1-1} = \dfrac{4}{-2} = -2[/tex]
In a function why berries directly with X in the constant of variation is two which table could represent the function
The correct option is (D)
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
the complete question is attached below
As, per the data given we can say that
the variation of quantity is 2.
So, the equation can be
y=2x
This equation defined by part (4) of the question.
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If the critical z-value for a hypothesis test equals 2.45, what value of the test statistic would provide the least chance of making a Type I error
2.46
A Type I error is rejecting the null when it is true.
If the critical value is 2.45, and you have a test statistic of 2.46, you have the least chance among the other choices of rejecting the null and it happens to be true.
We got another hypothesis here and our alternative that is less than five. So that's how we're gonna write it.
We're gonna be looking at a left tail test since it's less than the mean, Our means, always going to be in the middle here. And what we're trying to calculate is the probability that this is true.
The level of significance which is selected in
Step 1 (e.g., α =0.05) dictates the critical value.
For example, in an upper-tailed Z test, if α =0.05 then the critical value is Z=1.645.
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Perimeter of ABCD=
Help me please. Stuck on this question
Answer:
42
Step-by-step explanation:
Perimeter of quadrilateral with inscribed circle:Two tangents from a point outside the circle to some point to a circle are of equal lengths.
CB = 3+ 5 = 8
CD = 3+ 4 = 7
DA = 4 + 9 = 13
AB = 9+ 5 = 14
Perimeter = 8 + 7 + 13 + 14
= 42
what does the Symbol z- stands
Determine the vertex of the quadratic relation y=2(x+2)(x-6).
Answer:
V = (2,-32)
Step-by-step explanation:
Hello!
The vertex of a quadratic lies on the Axis of Symmetry (AOS). The axis of symmetry is exactly in the middle of the roots of the Quadratic. We can solve for the AOS by finding the average of the two roots.
Rootsy = 2(x + 2)(x - 6)0 = 2(x + 2)(x - 6)0 = (x + 2)(x - 6)0 = x + 2: x = -20 = x - 6: x = 6The two roots of the quadratic are 6 and -2.
Solve for the AOS[tex]AOS = \frac{r_1 + r_2}{2}[/tex][tex]AOS = \frac{6-2}{2}[/tex][tex]AOS = \frac42[/tex][tex]AOS = 2[/tex]The Axis of symmetry of the quadratic is 2.
VertexSince the vertex lies on the AOS, we know the x-value of the vertex. We can solve for the y-value by plugging in the value of the AOS in the equation.
Find the Vertex
y = 2(x + 2)(x - 6)y = 2(2 + 2)(2 - 6)y = 2(4)(-4)y = 2(-16)y = -32The Vertex of the quadratic is at (2,-32).
Consider the relation given by the graph below.
a) Is the relation a function? Why or why not?
b) Determine the domain and range of the graph.
(a) The relation is a function because each value of x maps onto only one value of y.
(b) Domain is [tex](-\infty, 3][/tex], range is [tex][-1, \infty)[/tex].
complete mapping of the vertices of DEF what is the rule that describes a reflection across the line y=x
The rule that describes a reflection across the line y = x is given as (x, y) ⇒ (y, x)
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right on the coordinate plane.
The rule that describes a reflection across the line y = x is given as (x, y) ⇒ (y, x)
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In the figure, CD is the bisector of ACB. If AD = AE then prove that: EAC = ABC.
Answer:
If AD=AE the the bisector CD. will be the coefficient of AE
Pat won the lottery!! She won 23 million dollars. Of course she had to pay the income tax of 33%. She decides to take the rest in monthly payments for twenty years. How much money will
Pat get each month?
Answer:
$64,208.33
Step-by-step explanation:
100% - 33% = 67%
Since she pays 33% in taxes, she will only get 67% of the $23 million.
1 year = 12 months
20 years = 20 × 12 months = 240 months
There are 240 months in 20 years.
monthly amount = 67% of $23 million / 240
monthly amount = 0.67 × $23,000,000 / 240
monthly amount = $64,208.33
1. Which statement about this figure is true?
a propartional relationship is shown below, please help me with the slope answer and how to write it in the graph!!!
The slope of the line that represents the relationship is 0.7692
slope of a lineThe formula for calculating the slope of a line is expressed as;
Slope = y2-y1/x2-x1
Using the coordinate points (1.3, 1) and (2.6, 2)
Substitute
Slope = 2-1/2.6-1.3
Slope = 1/1.3
Slope = 0.7692
Hence the slope of the line that represents the relationship is 0.7692
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True or False. Both distributions are bell-shaped and symmetric but where the peak falls on the number line is determined by the mean.
Both distributions are bell-shaped and symmetric but where the peak falls on the number line is determined by the mean.
The given statement is false.
A bell curve is a graph depicting the ordinary distribution, which has a shape harking back to a bell. The top of the curve suggests the mean, mode, and median of the records accrued.
The everyday distribution is a bell-fashioned and symmetrical distribution this is used to calculate the opportunity. in the everyday distribution, the mathematics means, mode, and median are usually the same, and the normal distribution is likewise called the Gaussian distribution.
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What’s the answer to the question
Find the principal which amounts to $918 in 1 year at a simple interest
of 2% per annum
Answer:
P = $900
Step-by-step explanation:
Simple Interest Formula: [tex]A = P(1+rt)[/tex]
Where A is the final amount,
P = Principal
r = Interest Rate in Percent or [tex]\frac{r}{100}[/tex] per annum
t = time in years
From the information given in the question,
A = $918
r = 2% per annum or [tex]\frac{2}{100}[/tex]
t = 1 year
Lets substitute these values to find P, the principal.
[tex]P(1+(\frac{2}{100} )(1))=918\\P(1+0.02)=918\\1.02P=918\\P = \frac{918}{1.02} \\=$900[/tex]
Therefore, P = $900
If a submarine dives 378 feet in 14 seconds, the average change in elevation is
feet per second.
Answer: The average change in elevation is 27 feet per second.
Step-by-step explanation:
A submarine dives = 378 feet
Time taken in the total diving = 14 seconds.
So, according to the question, the average change in the elevation can be calculated by
⇒ Feet per second = feet/ second
⇒ the average change = 378/14
⇒ elevation = 27 feet per second.
Change in elevation is basically the distance covered in one second.
Finding probability, please help!! show all work!!
Answer:
9/28 and 32.1%
Step-by-step explanation:
So the sample space consists of all products for (5 * 1, 5 * 2, 5 * 3.... and the same thing for 6, 7, and 8)
This gives you the sample space: {5, 10, 15, 20, 25, 30, 6, 12, 18, 24, 30, 36, 7, 14, 21, 28, 35, 42, 8, 16, 24, 32, 40, 48}.
The size of the sample space is 4 * 6, since for each number (5, 6, 7, 8), there are 6 products (the dice have six numbers). This means the sample space has 24 combinations, you can also verify this by manually counting the sample space.
Now filtering the sample space so you only get a product that is 28 or higher you get: {30, 30, 36, 28, 35, 42, 32, 40, 48} which has 9 possible combinations that have a product greater than or equal to 28. Divide this by the entire sample space and you get a probability of: 9/28, which in decimal form is approximately: [tex]0.3214[/tex]. Multiplying this by 100 gives you: [tex]32.1[/tex]%
Identity the construction that the figure represents
The construction is the construction of the Perpendicular bisector.
How to illustrate the information?The steps for the construction of perpendicular bisectors are as follows:
Open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.
Call the two points where these two arcs meet X and Y. Draw the line between X and Y.
So, the point where this line meets the line segment; M is called the mid point and the line XY is the perpendicular bisector of the line AB.
The figure is a construction of perpendicular bisector.
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pls help asap..............
The ratio of the side lengths of the triangle will be 3:10 or 3/10.
How to illustrate the ratio?From the information given, the first triangle has sides 6 and 9 while the large triangle has sides 20 and 30.
Based on this, the ratio will be:
= 6/20 = 9/20
= 3/10 = 3/10
Therefore, the ratio is 3:10.
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how many centigram are equal to 9.95 milligram
Answer:
0.995 centigram
Step-by-step explanation:
divide the mass value by 10
Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing two hours later
Rate is the distance between the cars increasing two hours later is 52 miles/hr
Let x(t) be distance of first car from starting point at time t
Let y(t) be distance of second car from starting point at time t
Let s(t) be distance between the two cars at time t. We need to evaluate ds/dt at time t = 2.
We know x2(t) + y2(t) = s2(t). Therefore 2x * dx/dt + 2y * dy/dt = 2s * ds/dt. The 2s cancel.
At t=2 hours, x = 96 miles. and y = 40 miles.
We will need the distance between the cars at t=2:
s(2) = √x(2)2 + y(2)2 = √96 2 + 40 2 = √10816 = 104.
Now fill in x * dx/dt + y * dy/dt = s * ds/dt at time t = 3 and solve for ds/dt:
96 * 48 + 40 * 20 = 104 * ds/dt
ds/dt = 5408/104 = 52 miles/hr
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What is the smallest positive integer that has a square root that is greater than 10?
The smallest positive integer that has a square root that is greater than 10 is 101
How to determine the integer?Let the integer be represented by n
The square root is greater than 10.
So, we have:
[tex]\sqrt n > 10[/tex]
Square both sides
n > 100
The above means that the integer is greater than 100.
The smallest integer greater than 100 is 101
Hence, the smallest positive integer that has a square root that is greater than 10 is 101
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