The value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10. Option C
How to determine the valueIt is important to note that for line TV to be parallel to line QS, the sides of the triangle must be divided equally.
Thus, we have
RT/TQ = RV/VS
RT = x + 10
TQ = x - 3
RV = x + 10
VS = x
Substitute the value
[tex]\frac{x + 4}{x-3} = \frac{x + 10}{x}[/tex]
Cross multiply
(x+ 4) × x = (x + 10) × (x-3)
x² + 4x = x² -3x + 10x -30
Divide through by x²
4x = -3x + 10x - 30
Collect like terms
4x + 3x - 10x = - 30
-3x = -30
x = -30/ -3
x = 10
Thus, the value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10 Option C
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By what percent will the fraction increase if its numerator decreased by 30% and the denominator decreased by 50%
Answer:
140%
Step-by-step explanation:
So a fraction can be expressed as: [tex]\frac{a}{b}[/tex] and if a number decreases by x%, the new number is (100-x)% the original value. So since the numerator decreases by 30%, it's not 70% the original value, and it's very similar with the denominator, with it only retaining 50% of it's original value. This gives you the formula: [tex]\frac{0.70a}{0.50b}[/tex]. You can rewrite the fraction as: [tex]\frac{1.4 * 0.5 * a}{0.5 * b}[/tex] in doing so it's easy to see that you can cancel out the 0.5 and get: [tex]1.4\frac{a}{b}[/tex]. This means the value is increasing by 1.4 or 140%
Answer:
140%
Step-by-step explanation:
since the numerator decreases by 30%, it isnt 70% the original value, This gives a formula: . You can rewrite the fraction as so, in doing so it's easy to see that you can cancel out the 0.5 and get: . This means the value is increasing by 1.4 or 140%.
There are 4 circles and 6 triangles. What is the simplest ratio of circles to triangles?
Answer:
2/3
Step-by-step explanation:
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be 4/6
4/6 when divided by two = 2/3 which is the simplest form of the fraction 4/6
The simplest ratio of circles to triangles would be; 2/3
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that there are 4 circles and 6 triangles.
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be as given;
4/6
when divided by two we get;
2/3
This is the simplest form of the fraction 4/6
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Given that A varies directly as B and inversely as C and that; A=12 when B=3 and C=2. Find B when A=10 and C=1.5
Answer:
B = 1.875
Step-by-step explanation:
given that A varies directly as B and inversely as C then the equation relating them is
A = [tex]\frac{kB}{C}[/tex] ← k is the constant of variation
to find k use the condition A = 12 when B = 3 and C = 2 , then
12 = [tex]\frac{3k}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
24 = 3k ( divide both sides by 3 )
8 = k
A = [tex]\frac{8B}{C}[/tex] ← equation of variation
when A = 10 and C = 1.5 , then
10 = [tex]\frac{8B}{1.5}[/tex] ( multiply both sides by 1.5 )
15 = 8B ( divide both sides by 8 )
1.875 = B
Simplify, state all restrictions.
The simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1[/tex]
Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Rewrite the expression as products
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1[/tex]
Express 4x^2 - y^2 as (2x - y)(2x + y)
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{x + y} -1[/tex]
Take the LCM
[tex]\frac{1 - x - y}{x + y}[/tex]
Hence, the simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
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A customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full. How many different combinations of boxes can be used for the customer's 15 chocolate pieces
There are 20 combinations of boxes that can be used for the customer's 15 chocolate pieces.
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression. When the coefficients are themselves variables, they may also be called parameters.
It is given that a customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full.
The coefficient of [tex]x^{15}[/tex] from the steps shown in the image is 20.
Hence, there are 20 possibilities.
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The ratio of the area of the shaded part to the unshaded part is______.
Answer: 1 : 3
Shaded area:
[tex]\Longrightarrow \sf Length \ \times \ Breadth = \dfrac{x}{4} \ \times \ x \ = \ \dfrac{1}{4}x^2[/tex]
Unshaded area:
[tex]\Longrightarrow \sf Length \ \times \ Breadth = (x - \dfrac{x}{4}) \ \times \ x \ = \ \dfrac{3}{4}x^2[/tex]
Ratio of shaded to unshaded:
[tex]\Longrightarrow \sf \dfrac{1}{4} x^2 \ : \ \dfrac{3}{4} x^2 = 1 : 3 \quad (simplified)[/tex]
Verbal
2. How can you tell whether an absolute value function
has two x-intercepts without graphing the function?
Without graphing an absolute value function, you can tell whether it has two x-intercepts by isolating the absolute value term to have an equation of the form |A| = B and then form two different equations.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols
Mathematically, the standard form of the equation for an absolute value function is given by:
y = a|x - h| +k.
Where:
h and k are the vertex of the graph.
Without graphing an absolute value function, you can tell whether it has two x-intercepts by isolating the absolute value term to have an equation of the form |A| = B and then form two different equations.
Lastly, solve each equation for the two x-intercepts.
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Pleaseeee helppppppp
Answer:
The second choice (-6, -5 2/5, -4 1/5)
Step-by-step explanation:
1) Find the nth term by using the rule given. Foil them out.
A(n) = -6 + 1/5n - 1/5
A(n) = 1/5n - 31/5
2) Find the first term by substituting 1 into n.
a1 = 1/5(1) - 31/5
a1 = -6
3) Find the fourth term by substituting 4 into n.
a4 = 1/5(4) - 31/5
a4 = -27/5 or -5 2/5
4) Find the tenth term by substituting 10 into n.
a10 = 1/5(10) - 31/5
a10 = -21/5 or -4 1/5
Therefore, the second choice (-6, -5 2/5, -4 1/5) is correct.
Question 2
Consider a right angled triangle where one of the non-hypotenuse sides has
length 3 and the angle it makes with the hypotenuse is 65. What is the area of
this triangle?
A: 3cos65/2 B: 9tan65/2 C: 9sin65/2 D: 9cos65/2 E: 3sin65/2
Using relations in a right triangle, the area of the triangle is given by:
B. 9tan(65º)/2.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem, we have one leg(length 3) and the angle with the hypotenuse(65º), hence the other leg can be found as follows:
[tex]\tan{65^\circ} = \frac{x}{3}[/tex]
x = 3tan(65º).
What is the area of a right triangle?The area of a right triangle is half the multiplication of it's legs, hence in this problem:
A = 1/2 x 3 x 3tan(65º) = 9tan(65º)/2.
Which means that option B is correct.
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Students were asked to write an expression equivalent to the expression below:
30a+12b-6a+ 2(9b+c+15)
Their answers are as follows:
36a-30b+2c +30
Ben wrote: 36a - 30b + 2c + 30
Martin:
24a+30b+2c +30
Sara wrote: 24a + 30b + 2c + 15
Martin wrote: 24a + 30b+2c +30
Which, if any, of those students wrote expressions that are equivalent to the original expression?
In the space provided below, either prove why each student's response is equivalent, or explain and correct the student's error.
Sara
| Ben:
Allie wrote: 2(12a + 15b+c+15)
24a+30b+ac+15
Allie:
2(13a +156+c+15)
The equivalent is 24a + 30b +2c + 30
How to determine the equivalent expressionGiven the original expression as;
30a+12b-6a+ 2(9b+c+15)
First, expand the bracket, we have
30a + 12b -6a + 18b + 2c + 30
Then, collect like terms
30a -6a + 12b + 18b + 2c + 30
24a + 30b +2c + 30
The equivalent is 24a + 30b +2c + 30
From the result, we have that Martin is correct.
Sara wrote the equivalent as 24a + 30b +2c + 15
She made a mistake in expand the bracket = 2( 9b +c +15) = 18b + 2c + 30
Ben wrote 36a - 30b + 2c + 30. He made a mistake in issuing the sign for 30b = 12b + 18b = +30b
Thus, the equivalent is 24a + 30b +2c + 30
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How many positive three-digit numbers are evenly
divisible by 33?
Answer:
27
Step-by-step explanation:
smallest multiple of 33 that is 3 digits is 132 (33*4), and largest is 990 (33*30)
then all the numbers between 4 and 30 would also be 3 digits
including 4 and 30, that makes 27 number in total
\sqrt{27} - \sqrt{ 12} + \sqrt{48 }
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
I'm assuming you're asking for most simplified form?
Original Equation:
[tex]\sqrt{27} - \sqrt{12} + \sqrt{48}[/tex]
Rewrite sqrt(27) using the exponent property: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]
[tex]\sqrt{9} * \sqrt{3} -\sqrt{12} + \sqrt{48}[/tex]
Simplify sqrt(9)
[tex]3\sqrt{3} -\sqrt{12} + \sqrt{48}[/tex]
Rewrite the radical sqrt(12)
[tex]3\sqrt{3} -\sqrt{4}\sqrt{3} + \sqrt{48}[/tex]
Simplify sqrt(2)
[tex]3 \sqrt{3} -2\sqrt{3} + \sqrt{48}[/tex]
Rewrite the radical sqrt(48)
[tex]3\sqrt{3} -2\sqrt{3} + \sqrt{16}\sqrt{3}[/tex]
Simplify the sqrt(16)
[tex]3\sqrt{3} -2\sqrt{3} + 4\sqrt{3}[/tex]
You can think of sqrt(3) as x, in which case you have 3x - 2x + 4x, so you just add the coefficients and leave the sqrt(3) alone.
Subtract 2 from 3
[tex]1\sqrt{3} + 4\sqrt{3}[/tex]
Add 1 and 4
[tex]5\sqrt{3}[/tex]
If g(x) = 4x² - 16 were shifted 9 units to the right and 1 down,
what would the new equation be?
[tex]9 \: units \: to \: the \: right \: = x - 9[/tex]
[tex]1 \: unit \: down \: = - 1[/tex]
[tex]g(x) = 4x {}^{2} - 16 \\ h(x) = 4(x - 9) {}^{2} - 17[/tex]
Letter AThe graphs below have the same shape. What is the equation of the blue
graph?
G(x) =
―
F(x)=x3
-6
O A. G(x) = (x+1)³
OB. G(x) = x³-1
OC. G(x) = (x-1)³
OD. G(x)= x³ +1
GX) = ?
Using translation concepts, it is found that the equation of the blue graph is given by:
C. G(x) = (x - 1)³.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function G(x) is a shift of one unit right of F(x) = x³, hence it's equation is:
G(x) = F(x - 1) = (x - 1)³.
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in which quadrant will you find the point (-2,-2)
⊱________________________________________________________⊰
Answer:
Quadrant 3Step-by-step explanation:
Points with both negative co-ordinates are found in the third quadrant.
[tex]\boxed{\begin{tabular}{c | 1} \sf{~~Quadrant 2 (-x,y)~~& Quadrant 1~ (x,y)~~} \\ \\\\\\\\\\\\ \cline{1-2} \sf{Quadrant \ 3 (-x,-y) \ & Quadrant \ 4 (x,-y)} \\\\\\\ \\\\\\\\\\\end{tabular}}[/tex]
done !!
⊱_____________________________________________________⊰
Is the function y = –9x^8+3 linear or nonlinear?
Answer:
It is nonlinear
Step-by-step explanation:
A given gas powered water pump delivers 42.50 gallons of water per minute. This value can also be expressed as _____________ L/s (Liters per second).
The rate at which the gas powered pump deliver water is 160.9 litres per seconds
How to convert rate?The gas powered water pump delivers 42.50 gallons of water per minute.
Therefore,
1 gallon = 3.78541 litres
42.50 gallons = ?
cross multiply
volume = 42.50 × 3.78541 = 160.879925 litres
Hence,
60 seconds = 1 minutes
1 second = ?
time = 1 / 60 = 0.01666666666 seconds
Hence,
rate = 160.9 litres per second
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Random assignment to treatments helps control for lurking variables ? true ? false.
It is true that Random assignment to treatments helps control for lurking variables
The main purpose for using randomization in an experiment is to create sure that the results are accurate. you wish to avoid biasis and lurking variables. Having a randomized experiment will facilitate your to create sure that your information is correct
The main purpose for using randomization in an experiment is to manage the lurking variable and establish a cause and effect relationship. Also, by randomizing an experiment the evidence is more supported
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Flo has two equations that she found to be valuable models for her research. She thinks that if she can find the solution of the two graphs, she will be able to identify a key point to her studies. What can Flo expect to be her outcome for the solutions of these two graphs?
The point of intersection is (-2,1) and this is the solution of the two graphs and the correct option is A.
What is a System of Equations?The system of equations is the set of equations that have a common solution.
The solution to the graph given is the answer to the Flo's model
The intersection point of the line of the two-equation is the solution to the two equations.
The point of intersection is (-2,1) and so the correct option is A.
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Which best explains if quadrilateral WXYZ can be a parallelogram?
A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is A.
What is a parallelogram?A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, the pair of opposite sides are equal and parallel. Therefore,
1.) For the first pair.
(x+8) = 15
x = 7
2.) For the second pair
(x+2)=(2x-5)
x + 2 = 2x - 5
2 + 5 = 2x - x
x = 7
(x+2) = (7+2) = 9
Since the measure of the pair of opposite sides is 15 units, the pair of the other two sides measure 9 units.
Hence, the correct option is A.
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Solve 4(5)^x= 500.
help please
Answer:
x=3
Step-by-step explanation:
Isolate x.
[tex]4(5)^x=500[/tex] Divide both sides by four
[tex]5^x=125[/tex] Take [tex]log_{5}[/tex] of both sides. In other words, what power must you raise 5 to in order to get 125? ([tex]5^3=125[/tex])
x=3
Which ordered pair below is a solution to the following system of equations?
-x + 2y = 5
x + y = 1
Answer:
The correct option is OPTION (A) .
Does this graph represent a function? Why or why not?
C A. Yes, because it passes the vertical line
test.
B. No, because it is not a
straight line.
No, because it fails the vertical line test.
O D. Yes, because it passes the horizontal line test.
Answer:
A. Because it passed the y axis
Discuss the implications of an infinite-dimensional space in generalization ability of the hard-margin SVM. What are the strategies we can use to improve generalization
The SVM classifier's generalization performance is improved by decreasing the VC dimension.
What is SVM ?SVM stands for Support Vector Machine .
A potent machine learning technique for classification and regression is called a Support vector machine. The selection of a margin type is crucial if we want to use it to solve an issue.
A soft margin or a hard margin can be chosen on the basis of the data , If the data is linearly separable , hard margin is used , If the data is not separable linearly and misclassifications can be allowed then soft margin is used.
The hard margin SVM's capacity for generalization is significantly influenced by VC.
the SVM classifier's generalization performance is improved by decreasing the VC dimension.
We contend that by using dimensionality reduction and bootstrapping techniques, the VC dimension of an SVM classifier can be decreased.
The SVM classifier's performance was now enhanced by bootstrapping both the original data and the projected data that is dimensionally reduced .
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to solve the system of equations below, Becca isolated x^2 in the firs equation and then substituted it into the second equation
The resulting equation if Becca isolated x² in the first equation and then substituted it into the second equation is (9-y²) / 25 - y²/36 = 1
Equationx² + y² = 9
x²/25 - y²/36 = 1
From (1)
x² = 9 - y²
substitute x² = 9 - y² into (2)
x²/25 - y²/36 = 1
(9-y²) / 25 - y²/36 = 1
Therefore, the resulting equation is option C; (9-y²) / 25 - y²/36 = 1
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Answer:
(9-y²) / 25 - y²/36 = 1
Step-by-step explanation:
What fraction of £1 is 31p?
The fraction of 1 pound to 31 penny is 31/100.
Given that, £1 and 31 p.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 pound = 100 penny
Now, the fraction of £1 is 31 p is
31/100
Therefore, the fraction of 1 pound to 31 penny is 31/100.
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Which expression is equivalent to (4 + 6)²?
Answer:
A) -20+48i
Step-by-step explanation:
[tex](4+6i)^2\\(4+6i)(4+6i)\\16+24i+24i+36i^2\\**i^2=-1*\\16+48i+36i^2(-1)\\16+48i-36\\-20+48i[/tex]
Please Help Asap Please And Thank You.
Answer:
m (slope) = -1/10; the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter; the y intercept is how tall the candle is at the beginning
Step-by-step explanation:
to find the slope of this line we can simply use the (y2 - y1) / (x2 - x1) formula
that gives us
(0 - 25) / (250 - 0)
or
-25/250
or
-1/10
the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter
the y intercept is how tall the candle is at the beginning
I don’t know what to do pls help me
Answer:
35
Step-by-step explanation:
Basically, since the angle HGF consists of HGE and EGF, then that means that HGF = HGE + EGF, and since EGF and HGF is given we plug this into the equation to get: 145 = HGE + 110, so HGE = 35.
Answer: 35°
Step-by-step explanation:
Hi!
The total angle is 145°
part of the angle is 110°
to find the missing angle, do 145 - 110 = 35°
Hope this helped :)
Two similar triangles have areas 16 and 4. if a side of the smaller triangle measures 2, find the length of the corresponding side in the larger triangle.
Answer: 4
Step-by-step explanation:
The ratio of the areas of similar figures is the square of the side length.
Since the ratio of the areas is 16:4 = 4:1, the ratio of the side lengths is 2:1.
So, the length of the corresponding side is 2(2) = 4.