On solving the provided question, we can say that triangle BIG and triangle FUN are similar to each other and are congruent, so angle N is congruent to angle G.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
we have been provided with that
triangle BIG and triangle FUN are similar to each other and are congruent.
Angle N is congruent to angle G.
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101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1
Distribute the summation over the sum.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]
Now plug in the known sums and simplify.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]
choose the correct option that explains what steps were followed to obtain the system of equations below x+6y = 5
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution of system B will be the same as the solution of system A.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
System A:
x + 6y = 5 and; 3x - 7y = -35
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3.
System B:
x + 6y = 5 and; - 25y = -50
The solution of system B will be the same as the solution of system A.
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I run 3 miles in 20 minutes. What was my average speed in miles per hour?
9 and 1/9 subtracted by 1 and 4/5
Answer:
7 14/45
Step-by-step explanation:
9 1/9 - 1 4/5
82/9 - 9/5
410/45 - 81/45
329/45
7 14/45
Answer:
●7.31
please mark as brainliest
Could you help me solve?
Answer:
1.14200738982×10^26
Step-by-step explanation:
Substitution can make this integral much easier to evaluate.
SubstitutionLet u = 7x² -x. Then du = (14x -1)dx. The limits on x become different limits for u:
for x = 1: u = 7(1²) -1 = 6
for x = 3: u = 7(3²) -3 = 60
Integral[tex]\displaystyle\int_1^3{(14x-1)e^{(7x^2-x)}}\,dx=\int_6^{60}{e^u}\,du=\left.e^u\right|^{60}_6\\\\=e^{60}-e^6\approx e^{60}\approx\boxed{1.14200738982\times10^{26}}[/tex]
Josue has a coin collection. He keeps 11 of the coins in his box, which is 5% of the collection. How many total coins are in his collection?
Answer:
220
Step-by-step explanation :
11 = 5%
100 ÷ 5 = 20
11 × 20 = 220
0.05 × 220 = 11 ✓
0.05 = decimal multiplier of 5%
Solve for x: 4(x + 2) = 3(x - 2) (1 point)
0-2
O-4
O-10
O -14
Answer:
its -14
Step-by-step explanation:
questions 1, 2 and 3 please!
will give brainliest to whoever answers
80 points
Answer:
a) [tex]f(x) = x + 3[/tex]
b) [tex]f(x) = -x - 5[/tex]
c) [tex]f(x) = 2x + 6[/tex]
Step-by-step explanation:
To determine the equation of a straight line, we need two things:
1. two known points (coordinates) on the line, used to calculate the gradient
2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)
Then we can use the equation:
[tex]\boxed {f(x) = ax + q}[/tex]
where a is the gradient and q is the y-intercept, to determine the equation of the line.
a) known points: (0, 3), (-4, -1)
y-intercept: 3
gradient = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]
⇒ [tex]\bf 1[/tex]
∴ a = 1 , q = 3
∴ equation:
[tex]{f(x) = ax + q}[/tex]
[tex]f(x) = 1x + 3[/tex]
⇒ [tex]\bf f(x) = x + 3[/tex]
b) known points: (-7, 2) , (0, -5)
y-intercept = -5
gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]
⇒ [tex]\bf -1[/tex]
∴ equation:
[tex]f(x) = -1x + (-5)[/tex]
⇒ [tex]\bf f(x) = -x - 5[/tex]
c) known points: (-3, 0), (0, 6)
y-intercept = 6
gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]
⇒ [tex]\bf 2[/tex]
∴ equation:
[tex]\bf f(x) = 2x + 6[/tex]
use technology to determine an approximate solution to each of the following systems of linear equations
a y=22x-9.5 and y=2.5x+4.1
b 8x+y-18=0 and 5x+9y+4=0
c 6x + y= 12 and 5x +8y =-100
From the given system of linear equations, we have;
a. x ≈ 0.697, y ≈ 5.84b. x ≈ 2.48, y ≈ -1.82c. x ≈ 4.56, y ≈ -15.35How can technology be used to solve the given equations?a. The system of linear equations can be expressed as follows;
y = 22•x - 9.5
y = 2.5•x + 4.1
Rewriting the equations to have the constants on the right, we have;
y - 22•x = - 9.5
y - 2.5•x = 4.1
Solving the above equations using matrices method on a calculator gives;
y = 5.84x = 0.697By direct solving, we have;
22•x - 9.5 = 2.5•x + 4.1
22•x - 2.5•x = 4.1 + 9.5
19.5•x = 13.6
x = 13.6 ÷ 19.5 ≈ 0.697
x ≈ 0.697y = 22•x - 9.5
y = 22×(13.6/19.5) - 9.5 ≈ 5.84
y ≈ 5.84b. 8•x + y - 18 = 0
5•x + 9•y + 4 = 0
Rewriting gives;
8•x + y = 18
5•x + 9•y = -4
Solving with technology gives,;
x ≈ 2.48y ≈ -1.82Solving directly gives;
y = 18 - 8•xy = -(5•x + 4)/9Which gives;
18 - 8•x = -(5•x + 4)/9
9×(18 - 8•x) = -(5•x + 4)
162 - 72•x = -(5•x + 4)
5•x - 72•x = -162 - 4 = -166
67•x = 166
x = 166 ÷ 67 ≈ 2.478
x ≈ 2.478y = 18 - 8•x
Therefore;
y = 18 - 8 × (166 ÷ 67) ≈ -1.82
y ≈ -1.82c. 6•x + y = 12
5•x + 8•y = -100
Solving the above linear system using technology, we have;
x ≈ 4.56y ≈ -15.35Solving directly, we have;
y = 12 - 6•x
5•x + 8•y = -100
y = (-100 - 5•x)/8
12 - 6•x = (-100 - 5•x)/8
8 × (12 - 6•x) = (-100 - 5•x)
96 - 48•x = (-100 - 5•x)
48•x - 5•x = 96 + 100
43•x = 196
x = 196/43 ≈ 4.56
x ≈ 4.56y = 12 - 6•x
Therefore;
y = 12 - 6×(196/43) ≈ -15.35
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If R={(1,2),(2,3),(3,9),(4,5)} find R-1
Answer:
[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}
Step-by-step explanation:
Solution Given:
To find the inverse we need to exchange Domain to Range and vice-versa.
so
[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}
write the explicit formula for this geometric sequence.
81,27,9,3, …
Find the common ratio, r.
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.
The geometric sequence 81, 27, 9, 3, … has common ratio:
r = 27/81 = 1/3
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
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The sum of two numbers is 43 . The smaller number is 9 less than the larger number. What are the numbers?
Answer:
17 & 26
Step-by-step explanation:
The equation
[tex]x+(x+9)=43\\2x+9=43[/tex]
[tex]2x=43-9\\2x=34[/tex]
[tex]x=34/2=17[/tex]
One number is 17
The other number is:
[tex]x+9=17+9=26[/tex]
Hope this helps
Which statement is true about the slope of the graphed line?
A graph is a line that extends from second quadrant to first quadrant with y-intercept at 4.
A.
The slope is negative.
B.
The slope is positive.
C.
The slope is zero.
D.
The slope is undefined.
Answer:
c
Step-by-step explanation:
because I had a test on these
To find the quotient of two fractions, you first need to rewrite the division problem as an equivalent multiplication problem. Find this quotient using multiplication.
Remove all perfect squares from inside the square roo
√28
Answer:
√2² cannot be answer yesah
Solve the following equation. Write your answer in reduced fraction form, if necessary. (7x−2)(x+6)=0
Answer:
x = 2/7
x = -6
Step-by-step explanation:
You can solve the equation by setting each set of parentheses equal to 0 and simplifying.
7x - 2 = 0 <----- First set of parentheses
7x = 2 <----- Add 2 to both sides
x = 2/7 <----- Divide both sides by 7
x + 6 = 0 <----- Second set of parentheses
x = -6 <----- Subtract 6 from both sides
I’m confused in the exponential
These are the laws of indices. You just have to memorise it, sorry : (
Hope it helps : )
There are 10 M&Ms of which 6 are green, in a bowl. You select 2 of them and eat each after it is selected. Is this a binomial experiment? Why or why not?
The experiment is not a binomial experiment.
What is a binomial experiment?
A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.
The conditions for a binomial experiment include:
1. Each trial should be classified either as a success or a failure.
2. There are a fixed number of observations
3. The trials are independent.
4. The number of trials are fixed.
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What fraction with a denominator of 32 is equal to 1/2?
Answer:
[tex]\frac{16}{32}[/tex]
Step-by-step explanation:
given
[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )
= [tex]\frac{16}{32}[/tex]
here is a polygon. draw a scaled copy of the polycon with scale factor 3
The scaled copy of the polygon is added as an attachment
How to draw the scaled copy?The complete question is added as an attachment
The coordinates of the polygon are
A = (-7, 6)
B = (-10, 8)
C = (-10, 10)
D = (-6, 10)
The scale factor is 3.
So, the rule of dilation is
(x, y) = (3x, 3y)
Using the above rule, we have:
A' = (-21, 18)
B' = (-30, 24)
C' = (-30, 30)
D' = (-18, 30)
See attachment for the scaled copy of the polygon
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Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.
Using simple interest, it is found that the APR is of 4.472%.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.The parameters are given as follows:
A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.
Hence the APR is found as follows:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]3067.08 = 3000(1 + 0.5r)[/tex]
[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]
1 + 0.5r = 1.02236
r = (1.02236 - 1)/0.5
r = 0.04472.
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there were 936,795 bankruptcy filings in 2018. If there were 310,061 chapter 13 filings, what percent were not chapter 13
66.90% of the total bankruptcy fillings are not chapter 13 fillings.
What is bankruptcy?
This is a situation where the management of a company declares that it could no longer pay its debt obligations as it does have the cash resources to do so.
In this case, the total number of bankruptcy fillings is 936,795, out of which 310,061 are chapter 13 filings
fillings that were not chapter 13=936,795-310,061
fillings that were not chapter 13=626,734
fillings that were not chapter 13 as % of total fillings=626,734/936,795
fillings that were not chapter 13 as % of total fillings=66.90%
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centered at the origin given its...
Give the equation of the circle centered at the origin and passing through the point (0, -5).
Step-by-step explanation:
the equation of a circle centered at the origin is
x² + y² = r²
r being the radius (the distance of the center to every point on the circle's arc).
so, we get a point on the arc : (0, -5).
what is its distance to the origin ?
the origin is (0, 0).
we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.
that means there is no distance between them in x direction.
the only distance is in y direction : 0 to -5.
a distance is always positive (no matter in what direction).
so, the distance from 0 to -5 is : 5 units.
that means r = 5.
and our equation is
x² + y² = 5² = 25
suppose that g is a continuous function, 3_integral^5
g(x)dx=18, and 3_integral^10 g(x)dx =36. Find
5_ integral^10 g(x)dx
those are intergral symbols with numbers on
top and bottom. please show work. thanks
The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
The question has to do with definite integrals
What are definite integrals?Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.
Given that
[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex] and also [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex] and we require [tex]\int\limits^{10}_5 {g(x)} \, dx[/tex]For any integral [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]
So, [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]
So, [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]
Since
[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex]and [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex]Substituting the values of the variables into the equation, we have
[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]
[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
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What does the acronym EDI stand for ? a ) Electronic data interchange b ) Electronic duty interruption c ) Estimated duration indication Extreme data interchange d )
electronic data interchange
How many words can be formed by using all the letters of the word AWILLO, if the two L's are to be separated?
In the figure below, the radius of the larger circle is 6,8 and the radius of the smaller circle is 4.5. Which of the following best approximates the area of the shaded region? Note: The figure is not drawn to scale. O 14.45 O 16.62 O 25.99 O 81.65 O 145.27
A circle is a figure bounded by a curved side which is referred to as circumference. Thus the area of the shaded region is option D. 81.65.
A circle is a figure bounded by a curved side which is referred to as circumference. Some of its parts are radius, diameter, sector, arc, etc.
The area of a circle can be determined by the given expression:
Area = π[tex]r^{2}[/tex]
where r is the radius of the circle and π = [tex]\frac{22}{7}[/tex]
So, the area of the shaded region can be determined as:
Area of the shaded region = area of the larger circle - area of the smaller circle
Area of the shaded region = π[tex](6.8)^{2}[/tex] - π[tex](4.5)^{2}[/tex]
= π (46.24 - 20.25)
= [tex]\frac{22}{7}[/tex] x 25.99
= [tex]\frac{571.78}{7}[/tex]
Area of the shaded region = 81.683
Thus the appropriate answer to the question is option D. 81.65.
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please help with this question
The value of angle TUS based on the information given about the circle will be 49°.
What is a circle?It should be noted that a circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Equivalently, a circle is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
The radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Here, the value of TUS will be:
= 1/2 × TRS
= 1/2 × 98°
= 49°
In conclusion, the correct option is 49°.
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Complete question:
Circle R has a radius of 6 inches. Points S, T, and U lie on circle R, clockwise in alphabetical order. If m∠TRS = 98°, what is m∠TUS?
You deposit $2000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $188,921.57.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount invested and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the deposit in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate n = number of years$2000 x [{(1.07^30) - 1} / 0.07] = $188,921.57
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Adam eats 20 % of a pizza, Bethany eats another 1/3 of the pizza, and Charlie eats the remaining 14 slices. How many slices total did the pizza originally have?
The pizza originally have 30 slices.
What is linear equation?
An equation in which the highest power of the variable is one is known as linear equation.
We will find number of pizza slices as shown below:
Let pizza originally have x slices.
Adam eats 20% of a pizza
= 0.2x
Bethany eats 1/3 of pizza
=1/3(x)
Charlie eats the remaining 14 slices
0.2x+1/3(x)+14=x
14 = x - 0.2x - 1/3(x)
14 = x - x/5 - x/3
14 = (15x - 3x - 5x)/15
14*15 = 7x
By dividing both sides by 7, we get
30 = x
x = 30
Hence, the pizza originally have 30 slices.
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