In the given triangle QST where TRQ represents as a right angled triangle the value of QR is equal to 1.36 .
As given in the question,
In the triangle QST,
Line passing through vertex Q intersect QS at R such that TRQ is a right angled triangle.
RS = 1.3
QT = ST ( both are 4.7 )
⇒ ∠Q ≅∠S
⇒∠Q and ∠S are not right angle.
⇒ In ΔTRQ , TR ⊥ QS
In ΔTRS,
Using Pythagoras theorem,
ST² = RS² + RT²
⇒ 4.7² = ( 1.3 )² + RT²
⇒RT = 4.5
In ΔTRQ,
QR² = QT² - RT²
⇒QR = √ 4.7² - 4.5²
⇒QR = 1.36
Therefore, the value of QR in the given triangle with given conditions is equal to 1.36.
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Which type of polynomial is x² 9x 20?
The answer to the polynomial x^2 + 9x + 20 is x^2 + 9x + 20.
This is a second-degree polynomial, which is a polynomial with the highest power of the variable being 2. It is written in the standard form as ax^2 + bx + c, where a, b, and c are coefficients, and x is a variable. In this case, a = 1, b = 9, and c = 20.
To calculate this polynomial , we first substitute each value into the formula:
1x^2 + 9x + 20
Next, we multiply each coefficient with its corresponding variable:
1(x^2) + 9(x) + 20
Finally, we expand the terms and add them together to find the sum:
x^2 + 9x + 20
The answer to the polynomial x^2 + 9x + 20 is x^2 + 9x + 20.
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Points A through H are translated to the right to create points A' through H'. All of the following are
rectangles: GHBA, FCED, KH'C'J, and LJE'A'. Which is greater, the area of blue rectangle DFCE or
the total area of yellow rectangles KH'C'J and LJE'A'?
The area of yellow rectangles KH'C'J and LJE'A' is greater than the area of blue rectangle DFCE. .
What is rectangle?Rectangle is a flat, four-sided shape with four right angles and a pair of parallel lines. It is one of the most basic and commonly used shapes in geometry. It is also the most common shape used in architecture and construction. Rectangles have area, perimeter, and diagonal measurements, which makes them a useful tool for measuring and calculating. They are also used in a variety of other applications, such as designing window frames, creating art, and laying out floor plans.
To determine the area of DFCE, multiply the length of the base (DF) by the height (CE). The area of the two yellow rectangles, KH'C'J and LJE'A', can be determined by adding the area of each rectangle. The area of rectangle KH'C'J is equal to the product of the length of its base (KH') and the height (C'J). The area of rectangle LJE'A' is equal to the product of the length of its base (LJ) and the height (E'A'). Adding the areas of both yellow rectangles gives us the total area of both, which is greater than the area of blue rectangle DFCE.
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Rectangles have the following properties:
(pick all that apply)
Multiple select question.
A)
Diagonals are congruent
B)
Opposite angles are congruent
C)
Adjacent sides are parallel
D)
All 4 angles are 90 degrees
E)
Opposite sides are congruent
F)
Consecutive angles add to 360 degrees
G)
Cannot be a parallelogram
Rectangles have the following properties:
The diagonals are congruent Opposite sides are congruentAll 4 angles are 90 degreesWhat are the properties of Rectangles?A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
A rectangle's opposite sides are the same length (congruent). A rectangle's angles are all congruent (the same size and measure.) The term "right angle" refers to an angle that is 90 degrees or more. A rectangle therefore has four right angles. A rectangle's opposing angles are congruent.
Therefore, options A, B, D , are correct.
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The figure on the right is an isometry of the figure on the left. Are their orientations the same or opposite? Which type of isometry is shown?
a. Opposite; Reflection
b. Opposite; Translation
c. Same; Rotation
d. Same; Glide Reflection
The type of isometry is shown, there are orientations with the same; rotation. The correct answer would be an option (C).
What is isometry?Any isometry in the plane is a miracle combination of a rotation, a reflection, and a translation. In three dimensions, the issue becomes a little more difficult since each isometry is a combination of a translation, a reflection, and a rotation about a particular axis.
The figure on the right is an isometry of the figure on the left.
As per the question,
The type of isometry is shown, there are orientations with the same and rotation.
Hence, the correct answer would be option (C).
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Is the relation shown below a function? Explain.
Is the relation shown below is not a function.
Define function?A relationship between two sets known as the domain and the co domain, where there is one output for each input, is called a function. The amounts represent a relation if you have more than one output for a specific input, or if the elements of A and B do not map uniquely. The vertical line test, which states that at any point if a vertical line produces two intercepts of the curve, the curve cannot be a function, can be used to demonstrate that a relationship graph is a function.Given are two sets with {5,10,15,20} and {10,20,30,40,50} where there is a mapping.We find that while 5,10,15 have unique mappings while 20 have two mappings.Since there is an element in the I set have two images, this cannot be a function.To learn more about function refer to:
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Micah saved $6 on a $40 pair on pants. ________
what is the smallest integer greater than 38 that cannot be the length of the hypotenuse of a right triangle with integer side lengths?
The smallest integer greater than 38 which cannot be the length of the hypotenuse of a right triangle is 39.
Since 39 is divisible by 3, it cannot be the hypotenuse in any Pythagorean triples. Because for primitive Pythagorean triples, the hypotenuse is never divisible by 3.
What is a primitive Pythagorean triple?A primitive Pythagorean triple is one where a, b and c are coprime (which is, they have no common divisor larger than 1). For example, (3, 4, 5) is a primitive Pythagorean triple while (6, 8, 10) is not. For any primitive Pythagorean triple the integer c or the hypotenuse cannot be divisible by 3. Divisibility by 3 is only reserved for spots a and b.
There are an infinite number of Pythagorean triples. If 2n+1 is a square, it forms a Pythagorean triple. But 2n+1 comprises all the odd numbers; each of other square numbers is odd; there are an infinite number of odd squares; thus, there are an infinite number of Pythagorean triples.
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The owner of a sporting goods store randomly surveys 150 customers, of whom 95 are first-time customers. During the next week, the store has 900 customers. Based on the data from the survey, how many of the customers can the store owner expect to be first-time customers?
Answer: 570
Step-by-step explanation: In survey the total customers were 150 so our sample size is 150.
Total number of First time customer = 95
Probability of being a first time customer = 95/150 = 0.63
So on first day using same probability the first time customers will be 900 × 0.63 = 570
The pie chart represents the results when 120 people in a shopping centre were asked which country they were born in.
What fraction of people were born in France?
Give your answer in its simplest form.
The fraction of people were born in France is 7/24 .
What is a Pie Chart?
A pie chart is a graphical representation used to describe the composition of a data using degrees or percentages.
Given,
The pie chart represents the results when 120 people in a shopping centre were asked which country they were born in.
So, from the given pie chart
105° is given as the number of people that were born in the France
That's about: 105/360 × 120 = 35 people.
35 out of 120 people would give us a fraction of: 35/120 = 7/24 .
Hence, The fraction of people were born in France is 7/24 .
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Which is a correct ordered pair using Sabah's function? *
O ($1125, $500)
O ($1250, $505)
O ($1300, $505)
O ($1600, $532)
Using Sabah's function, ($1125, $500) is the right ordered pair. It is not a function if any of the x values are the same, but this is not true if the y values are different.
What is a ordered pair function in math?A set of ordered pairs is not a function if an x value has more than one y value associated with it. For instance, in the relation (4, 1), (4, 2), the x-value of 4 has y-values of 1 and 2, indicating that this relation is not a function. The connection is a function if each x-value has a single corresponding y-value.
An ordered group of pairs makes up a relation (x, y). A pair that has two values stated in a specific order between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate). For greater visual comprehension, it helps to locate a point on the Cartesian plane. An ordered pair of numbers can have either fractional or integer values.
Therefore the correct answer is ($1125, $500) .
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what is the prior probability of the bid being successful (that is, prior to the request for additional information)
a)The prior probability of the bid being successful is 50%.
b) The conditional probability is 71%.
c) The posterior probability is 64.55%.
a) Prior Probability = P(B)
[tex]= \frac{Number of favourable outcomes for n event}{Total number of outcomes}[/tex]
= [tex]\frac{1}{2}[/tex]
= 0.5 = 50%
b) Conditional probability of a request for additional information given that the bid will ultimately be successful.
Conditional Probability = P(A|B)
= [tex]\frac{71}{100}[/tex]
= 0.71 = 71%
c) Posterior probability that the bid will be successful given a request for additional information.
P(B)=0.5
P(A|B) = 0.71
P(A) = P(B)P(AB) + P(B')P(AB)
P(A) = (0.5 * 0.71) + (0.5 * 0.39)
P(A) = 0.335 + 0.195
P(A) = 0.550
Posterior Probability = P(B|A)
[tex]= \frac{P(B) * P(B|A)}{P(A)}[/tex]
[tex]= \frac{0.5 * 0.71}{0.550}[/tex] = 0.6455 = 64.55%
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a) Find out the prior probability.
The complete question is:
A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 71% of the successful bids and 39% of the unsuccessful bids, the agency requested additional information.
a) What is the prior probability of the bid being successful (that is, prior to the request for additional information) (in decimals)?
b) What is the conditional probability of a request for additional information given that the bid will ultimately be successful (in decimals)?
c) Compute the posterior probability that the bid will be successful given a request for additional information (in decimals).
What is the slope of the line (- 3 4 and 0 2?
The slope of the line (-3, 4) and (0, 2) is -2/3.
In the given question, we have to find the slope of the line (-3, 4) and (0, 2).
A line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
The given points are (-3, 4) and (0, 2).
We can find the slope from the given point using the formula
m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
From the given points;
x(1) = -3, y(1) = 4, x(2) = 0, y(2) = 2
Now putting the values in the formula;
m = (2 - 4)/(0 - (-3))
m = (-2)/(0 + 3)
m = -2/3
Hence, the slope of the line (-3, 4) and (0, 2) is -2/3.
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3x+6y = 18
2x+5y= 24
Pls use elimination!
Answer:
Step-by-step explanation:
3x+6y = 18
y=4
2x+5y= 24
y=9.5
a rectangle has a perimeter of 116 units if the length is 2 less than 5 times the width what’s the width
The width of rectangle is 10 units.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Perimeter of rectangle = 116 units
let the width be x.
then the length is 5x - 2.
so, Perimeter of rectangle = 116 units
2 (5x -2 + x)= 116
2(6x - 2) = 116
6x - 2 = 58
6x = 60
x= 10
So, the width is 10 units and length is 5(10)-2 = 48 units
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pls help me with this
-9x+5=-9x-1+6 is the equation which has no solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -7x+2x+5-4x=_x+6
Add the variable on left hand side
Minus seven times of x plus two times of x plus five minus four times of x equal to x plus six.
-9x+5=-9x-1+6
Hence, -9x+5=-9x-1+6 is the equation which has no solution.
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-2x-4-(-10 + 3x)
pls help
Answer: -5x+6
Step-by-step explanation:
simplify by distributing the numbers on the outside, to the ones in the binomial
Answer:
-5x + 6
Step-by-step explanation:
First, rearrange the terms, you will have -2x-4(3x-10) Next, Distribute, you will have -2x-4-3x+10. Now, add the numbers without variables, you'll get -2x+6-3x. Finally, combing the like terms and you arrive with -5x+6.
I need help asap help me with all questions and please put. The number for the question so I know thank you
Answer:
1. 6
2. 8
3. 80
4. 11
5. 60
6. 3
7. 30
8. 0.8
9. 5
10. 600
11. 150
12. 110
13. 15
14. 1.1
15. 36
Hope it helps
if. david has 19 bills in his wallet worth 125 all fives and tens how many of each bill does he have
Answer:
T=6 NUMBER OF TEN DOLLAR BILLS.
F=13 NUMBER OF FIVE DOLLAR BILLS.
Step-by-step explanation:
F+T=19 F=19-T
5F+10T=125 NOW SUBSTITUTE (19-T) FOR F IN THIS EQUATION & SOLVE FOR T
5(19-T)+10T=125
95-5T+10T=125
5T=125-95
5T=30
T=30/5
PROOF
5*13+10*6=125
65+60=125
125=125
What do we mean when we say numeric.
Answer: Numeric is anything of, relating to, or containing numbers. The numbering system consists of ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If a value is an alphanumeric, it contains letters and numbers.
Step-by-step explanation:
In the picture triangle A' B' C' is an image of triangle ABC after a rotation
Since triangle A'B'C' is an image of triangle ABC after a rotation and the center of rotation is D, the length of side B'C' is equal to 4 units.
What is a rotation?In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Generally speaking, rotation simply refers to a type of transformation that preserves both the shape and side lengths of a geometric figure.
In this context, we can reasonably infer and logically deduce that the magnitude of side length BC before a rotation of the triangle would be equal to side length BC B'C' after rotation:
Side BC = side B'C'
4 = 4
In conclusion, the length of side B'C' is equal to 4 units.
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Complete Question:
In the picture triangle A'B'C' is an image of triangle ABC after a rotation. The center of rotation is D.
What is the length of side B'C'?
correct answer gets brainliest ( please help me asap)
What is teh value for the expression 6 + 9w - 5s when w = 7 and s = 2?
The value for the expression 6 + 9w - 5s is 59.
How do you locate the algebraic expression?You must substitute a number for each variable and carry out the arithmetic procedures to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the case above equals 6. If we are aware of the values of our variables, we can replace the variables with those values before evaluating the expression.
When the variables and constants of an expression are given values, the outcome of the computation it describes yields the expression's value. The quantity that the function assumes for these argument values is the value of the function, given the value(s) assigned to its argument(s).
The expression 6 + 9w - 5s when w = 7 and s = 2.
6 +(9*7 - 5*2) = 6+63 - 10 = 59.
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select the two values of x that roots of this equation x^2+3x-5=0
The solution to the equation x² + 3x - 5 = 0 are ( -3 - √( 29 ))/2 and ( -3 +√( 29 ))/2.
What are the solutions to the given equation?The quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the equation in the question;
x² + 3x - 5 = 0
Hence;
a = 1
b = 3
c = -5
We substitute this values into the quadratic formula above.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -3 ± √( 3² - ( 4 × 1 × -5) )) / ( 2 × 1)
x = ( -3 ± √( 9 - ( -20 ) )) / ( 2 )
x = ( -3 ± √( 9 + 20 )) / 2
x = ( -3 ± √( 29 )) / 2
x = ( -3 - √( 29 ))/2, x = ( -3 +√( 29 ))/2
Therefore, the two values of x are ( -3 - √( 29 ))/2 and ( -3 +√( 29 ))/2.
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please please helpp!!
The value of 'n' in this right-angled triangle is n = 8.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sum of all the interior angles in a triangle is 180°.
Therefore, From the given information 3.4n + 9.2n - 10.8 = 90.
12.6n = 100.8
n = 100.8/12.6.
n = 8.
So, The value of n is 8.
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Is a quadratic parent function a parabola?
Yes, the quadratic parent function is the parabola.
The term parent function in math is defined as the simplest function of a family of functions that preserves the definition or shape of the entire family.
Here we have to identify that whether the quadratic parent function is a parabola or not.
According to the definition of parent function, the quadratic parent function is written as,
=> f(x) = x²
And here we also know that the quadratic function is one of the form
=> f(x) = ax² + bx + c
here a, b, and c are refers the numbers with a not equal to zero.
Here we all know that the graph of a quadratic function is a curve called a parabola.
which tells, the the quadratic parent function also have the graph as parabola.
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I need help your supposed to write it into an equation and solve it
Answer: 542+(87+41) = 670
Step-by-step explanation:
How do you find the area of an l angle?
A compound shape is a shape that is made up of other simple shapes. In this article, we will be working out the area of an L shape (made up of two rectangles). To find the area of a compound shape, follow these simple steps:
Step 1: Work out the missing lengths around the edge of the compound shape.
Step 2: Divide your L shape into two rectangles. This can be done in 2 different ways (both methods will give the same answer).
Step 3: Work out the area of each rectangle. Do this by multiplying the base of the rectangle by the height of the rectangle.
Step 4: Add the areas of the rectangles together to give the total area of the L shape.
Complete question: How do you find the area of an L angle?
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What is the derivative of 7e to the 7x?
The derivative of 7e to the 7x is 7e to the 7x * 7ln(e) * 7. The derivative of 7e to the 7x can be found by first taking the natural logarithm of the base, in this case e7x.
1. Take the natural logarithm of the base: ln(e7x)
2. Take the derivative of the natural logarithm: 7x*ln(e)
3. Apply the chain rule: 7e7x * 7ln(e) * 7
The derivative of 7e to the 7x can be found by first taking the natural logarithm of the base, in this case e7x. The natural logarithm of e7x is ln(e7x). Taking the derivative of the natural logarithm yields 7x*ln(e). We then apply the chain rule to get the final result of 7e7x * 7ln(e) * 7. In other words, the derivative of 7e to the 7x is equal to 7 multiplied by e raised to the 7x power, multiplied by 7ln(e), and then multiplied by 7 once more. This can be simplified to 7e7x * 7ln(e)7.
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does someone mind helping me with this problem? Thank you!
Answer:
The first step in solving this system of equations by elimination method is to eliminate one of the variables by adding or subtracting the two equations.
-9x - 4y = 1
3x + 3y = 3
If we multiply the first equation by 3 and the second equation by -9, we get:
-27x - 12y = 3
-27x - 27y = -27
Now we can add these two equations:
-12y = -24
y = 2
Now we can substitute this value of y back into one of the original equations to find the value of x.
-9x - 4(2) = 1
-9x - 8 = 1
-9x = 9
x = -1
So the solution of this system of equations is (x,y) = (-1,2)
Answer:
You just have to plug in one equation into the other, though you might already know this but the answer would be,
(-1,2)
Thank you please help
Answer:
[tex]\frac{2}{3}[/tex]
Hope this helps!
Step-by-step explanation:
Slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
b = ( -2, 0 )
a = ( -5, -2 )
[tex]slope = \frac{0 - (-2) }{-2 - ( -5)}[/tex]
slope = [tex]\frac{2}{3}[/tex]