Step-by-step explanation:
a11 = 4 × a2
a + 10d = 4 × (a + d)
a + 10d - 4d = 4a
a + 6d = 4a
6d = 4a - a
6d = 3a
(6/3)d = a
2d = a ----- eq. 1
now, sum of 7 terms = s7 = 175
7/2 {2a+6d} = 175
7/2 { (2 × 2d ) + 6d} = 175
7 ( 4d + 6d ) = 175 × 2
7 ( 10d ) = 350
70d = 350
d = 350/70
d = 5
Now from eq. 1,
2d = a
2(5) = a
a = 10, d = 5
THANK YOU........
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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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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two numbers that multiply to equal 20 and that also equal -12
Answer:
-10 and -2
Step-by-step explanation:
ONLY IF ITS two number that mutiply to equal 20 and their sum is -12
how do you find the angle of 2/5ths of a circle
Answer:
You divide 360 by 5 which is 72 & Then muiltiply that by 2.
Your answer would be 144 tho.
For which function is f(5) = 2?
By evaluating the linear function f(x) = x - 3 at x = 5 and discarding the another function in the table given, we conclude that f(5) = 2 belongs to that linear equation.
What function contains a given relationship?
In this problem we must check if the given relationship between the independent variable (x) and the dependent variable (y) exists in any of the two functions: (i) a table, (ii) an expression.
After a quick analysis, we conclude that f(5) = 2 is a point of the linear function f(x) = x - 3. Here is the proof:
f(5) = 5 - 3
f(5) = 2
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Answer:A which is x-3
Step-by-step explanation:
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
The following data set is the age of customers at the ice cream shop:
18, 52, 42, 36, 5, 31, 29, 22
Find the mean.
Answer: About 29
Step-by-step explanation: First you need to add all the numbers together. Then you divide the sum, 235, by however many numbers you have (8). And BOOM: you got your answer :)
PS: If you have a decimal number, just round it up or down ( 5 and above give it a shove; 4 and below let it lie low)!
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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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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Is the function y = –9x^8+3 linear or nonlinear?
Answer:
It is nonlinear
Step-by-step explanation:
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:
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.
The complete question is mentioned in the below image.
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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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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 !!
⊱_____________________________________________________⊰
Calculate XY, if UV=25 and WZ=39
Answer:
Step-by-step explanation:
UV = [tex]\frac{XY+WZ}{2}[/tex]
[tex]\frac{XY+39}{2}[/tex] = 25
XY + 39 = 50
XY = 11
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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Use the Pythagorean identity
to find cos X.
15
19
?]√
sin x =
COS X =
Answer:
Step-by-step explanation:
So sin is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. and cosine is defined as [tex]\frac{adjacent}{hypoteunse}[/tex]. So we need the adjacent side. Since we already have the opposite, and hypotenuse, you can use the Pythagorean identity to solve for the missing side: [tex]a^2+b^2 = c^2[/tex]
[tex]15^2 + b^2 = 19^2[/tex]
[tex]225 + b^2 = 361[/tex]
[tex]b^2 = 136[/tex]
[tex]b = \sqrt{136}[/tex]
[tex]b = \sqrt{4} * \sqrt{34}[/tex]
[tex]b = 2\sqrt{34}[/tex]
This is the adjacent side, so now plug this into the cosine equation and you get: [tex]\frac{2\sqrt{34}}{19}[/tex]
If you anwser the question i give you brainly
A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.
What is the inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'
The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.
Hence, the correct option is A.
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Describe how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x3 + 1. Include the average rate of change in your answer.
The average rate of change of the function given is 56
Rate of change of a functionThe formula for calculating the rate of change of a function is expressed as;
f'(x) = f(b)-f(a)/b-a
where
b = 4
a = 2
f(4) = 2(4)^3 +1
f(4) = 129
f(2) = 2(2)^3 + 1
f(2) = 17
Substitute
f'(x) = 129-17/4-2
f'(x) = 112/2
f'(x) = 56
Hence the average rate of change of the function given is 56
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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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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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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]
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]
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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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]
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.
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 AI 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 :)