The given sequence is not a geometric sequence, the quotients between consecutive numbers are different.
Which function describes this sequence?Remember that the recursive formula for a geometric sequence is:
f(n) = r*f(n - 1)
Where r is the common ratio.
Here we have the terms:
5, 11, 29, 83
To get the value of r, take the quotient between consecutive terms:
r = 11/5 = 2.2
r = 29/11 = 2.63
r = 83/29 = 2.86
We should get the same value of r for every ofthese quotients, then we can conclude that the given sequence of numbers is not a geometric sequence, is other type of sequence.
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How much carpet does Mrs. Baker need? Responses 192 ft2 192 ft2 228 ft2 228 ft2 336 ft2 336 ft2 576 ft2
Answer:
Step-by-step explanation:
its is 192 ft2
2. [3 pts] Use the laws of logarithms to write the expression as a single logarithm (combine). 2 log, x-log, y+log, z
The expression can be written as a single logarithm using the laws of logarithms as: 2logx(y)+logx(z/y).
The exponent or power to which a base must be increased in accordance with the laws of logarithms to arrive at a certain number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n
Using the laws of logarithms, we can combine the given expression as follows:
2 log(x) - log(y) + log(z)
Now, using the law of logarithmic addition, we can combine the second and third terms as follows:
2 log(x) + log(z/y)
Therefore, the given expression as a single logarithm is:
2 log(x) + log(z/y)
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Quadratic Equations, Ques Find the zero (s) of the following function. f(t)=t^(2)+7t+12
The zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.
To find the zeros of a quadratic function, we can either factor the equation or use the quadratic formula. In this case, we can easily factor the equation to find the zeros.
First, we need to find two numbers that multiply to give us 12 and add to give us 7. These numbers are 3 and 4.
Next, we can rewrite the equation using these numbers:
[tex]f(t) = t^(2) + 7t + 12 = (t + 3)(t + 4)[/tex]
Now, we can set each factor equal to zero and solve for t:
[tex]t + 3 = 0 -> t = -3[/tex]
[tex]t + 4 = 0 -> t = -4[/tex]
So, the zeros of the function are -3 and -4.
In conclusion, the zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.
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7.1 is what percent of 32? Round to the nearest hundredth.
if we take 32(origin amount) to be the 100%, what's 7.1 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 32 & 100\\ 7.1& x \end{array} \implies \cfrac{32}{7.1}~~=~~\cfrac{100}{x} \\\\\\ 32x=710\implies x=\cfrac{710}{32}\implies x\approx 22.19[/tex]
A family buys 6 airline tickets online. The family buys travel insurance that costs $18 per ticket. The total cost is $1,128. Let x represent the price of one ticket. Then find the price of one ticket.
Answer: $170
Step-by-step explanation:
6x + 18(6) = 1128.
6x + 108 = 1128
6x = 1020
x = 170
The price of one ticket is 170
If RSTU is a rhombus, find m∠UTS.
The measure m∠UTS is approximately 90 degrees.
What is rhombus and some of its properties?Rhombus is a parallelogram whose all sides are of equal lengths.
Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).
Its vertex angles are bisected by its diagonals.
The triangles on either side of the diagonals are isosceles and congruent.
We are given that;
Angle VUR=(10x-23)degree
Angle TUV=(3x+19)degree
Now,
Since RSTU is a rhombus, its diagonals are perpendicular bisectors of each other, which means that angle VUT is a right angle. Therefore, we have:
m∠VUR + m∠TUV + m∠VUT = 180°
Substituting the given values, we get:
(10x - 23) + (3x + 19) + 90 = 180
13x + 86 = 180
13x = 94
x = 7.23 (rounded to two decimal places)
Now, we can find m∠UTS as follows:
m∠UTS = m∠VUR + m∠TUV
Substituting the value of x, we get:
m∠UTS = (10x - 23) + (3x + 19)
m∠UTS = (10 × 7.23 - 23) + (3 × 7.23 + 19)
m∠UTS = 72.3 - 23 + 21.69 + 19
m∠UTS = 89.99
Therefore, the answer of the given rhombus will be 90 degrees.
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Help!!!!
Mr. Hamstra’s car holds 14 2/5 gallons of gas and averages 20 miles per gallon. About how far can Mr. Hamstra travel when his tank is 1/4 full?
By answering the above question, we may infer that Hence, when equation Mr. Haustra's tank is just 1/4 full, he can go around 70 miles.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
There are the following if Mr. Hamstra's automobile contains 14 2/5 gallons of fuel and his tank is only 1/4 full:
There are 3 1/2 gallons of gas in the tank (1/4) x 14 2/5.
If the automobile gets 20 miles per gallon on average, it may go as far as:
3 1/2 gallons x 20 miles per gallon is 70 miles.
Hence, when Mr. Hamstra's tank is just 1/4 full, he can go around 70 miles.
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If a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers. Then [[x,a+y,x+a],[y,b+y,y+b],[z,c+y,z+c]]
The value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.
According to the given equation, a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers, we can rearrange the equation to find the value of one of the variables in terms of the others. For example, we can rearrange the equation to find the value of x in terms of the other variables:
x = b+y-a = c+z+1-a
Similarly, we can rearrange the equation to find the value of y and z in terms of the other variables:
y = a+x-b = c+z+1-b
z = a+x-c-1 = b+y-c-1
Now, we can substitute these values into the given matrix to find the value of each element:
[[x,a+y,x+a],[y,b+y,y+b],[z,c+y,z+c]] = [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z+1-c-1]]
Simplifying the matrix, we get:
[[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]]
Therefore, the value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.
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Solve the equation. Don't forget to first simplify each side of the equation, if possible. 2(2z-3)=3(z+3)
The solution to the equation is z = 15.
To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.
On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:
2(2z) - 2(3) = 4z - 6
On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:
3(z) + 3(3) = 3z + 9
Now we can rewrite the equation as:
4z - 6 = 3z + 9
Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:
4z - 3z = 9 + 6
Simplifying gives us:
z = 15
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Use pythagorean theorem to answer.
The unknown side 'x' is found using pythagorean theorem as: x = 12.69.
Explain about the Pythagorean theorem?The Pythagorean Theorem has a name for Pythagoras of Samos, a religious figure and mathematician who held the view that everything in the cosmos is made up of numbers.
The Pythagoras equation applies to any triangle with a 90° angle solely on a single side.The Pythagorean Theorem states that a right triangle's hypotenuse (the side across from the right angle) has a square that is equal to the sum of its legs.Pythagorean Theorem is also known as:
a²+ b² = c²
Given sides are:
13, 3 and x.
Then,
3²+ x² = 13²
x² = 13² - 3²
x² = 169 - 9
x² = 160
x = √160
x = 12.69
Thus, the unknown side 'x' is found using pythagorean theorem as: x = 12.69.
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5/6 divided by 1 1/2
Answer:
5/33
Step-by-step explanation:
5/6 divided by 11/2
Invert the divider
5/6 x 2/ 11
10/66
Reduce to smallest fraction
5/33
Answer:
5/33
Step-by-step explanation:
Apply the fraction rule: a/b ÷ c/d = (a × d) ÷ (b × c) for 5/6 ÷ 11/2
a = 5
b = 6
c = 11
d = 2
(5 × 2) ÷ (6 × 11)
For "(6 × 11)", break 6 down into "2 × 3", so that you can cancel out the common factor, because there is also a 2 in "5 × 2".
= (5 × 2) ÷ (2 × 3 × 11) -- cancel out the 2's
= 5 ÷ (3 × 11) *****3 × 11 = 33*****
= 5/33
Wse the Law of Cosines to determine the indicated angle e0. (Assume \( a=69.01, b=39.28 \), and \( c=42.65 \), Round your answer to two decimal places.) \[ d= \] Neod Help?
The final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.
To determine the indicated angle, we can use the Law of Cosines, which states that: \[ c^2 = a^2 + b^2 - 2ab\cos(C) \]We can rearrange this equation to solve for the cosine of the indicated angle: \[ \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \]Plugging in the given values for a, b, and c, we get: \[ \cos(C) = \frac{69.01^2 + 39.28^2 - 42.65^2}{2(69.01)(39.28)} \]Simplifying the expression, we get: \[ \cos(C) = 0.7664 \]Now, we can use the inverse cosine function to find the indicated angle: \[ C = \cos^{-1}(0.7664) \]This gives us an angle of 40.32 degrees. However, the question asks us to round our answer to two decimal places, so the final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.
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Find the area of the circle which has a diameter 22 cm
Answer:
Exact form: 121π
Decimal form: 380.1327111...
Step-by-step explanation:
The area of the circle is given by the formula A = πr², where A is the area of the circle and r is the radius.
Given the diameter of 22cm, we know that the radius is 11cm, as the radius is half the diameter.
We can then put this into the formula to find the area of the circle:
A = πr²
A = π * 11²
A = 121π
Note that the answer here is given in terms of π so it can be expressed in its exact form, as 121π is an irrational number roughly equivalent to 380.1327111... The answer you need to provide will depend on whether the question asks for the exact form, or to a certain number of decimal places / significant figures. If it the latter, you can round off the decimal answer as appropriate.
Compare the graph of g(x) = 3x2 + 6 with the graph of f(x) = x2.
The graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The graphs of g(x) = 3x² + 6 and f(x) = x² are both quadratic functions, which means that their graphs are parabolas.
However, they have different coefficients and constant terms, which means that they will have different shapes and positions.
Here, the graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².
Both graphs have a vertex at the origin, but g(x) has a larger coefficient of x², which makes it steeper, and an added constant term, which shifts it upward.
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The formula occurs in the indicated application. Solve for the specified variable.A=P+Prt for r (principal plus interest) r=
To solve for r, we can divide both sides of the equation by Pt: r = (A-P)/Pt
The formula A=P+Prt is used to calculate the total amount of money (A) after a certain period of time when a principal amount (P) is invested at a certain interest rate (r) for a certain amount of time (t). To solve for the specified variable r, we need to rearrange the formula and isolate r on one side of the equation. Here are the steps to do so:
Step 1: Subtract P from both sides of the equation to get:
A - P = P + Prt - P
Step 2: Simplify the right side of the equation to get:
A - P = Prt
Step 3: Divide both sides of the equation by Pt to get:
(A - P) / Pt = r
Step 4: Simplify the left side of the equation to get:
r = (A - P) / Pt
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The area of a square living room is 256 ft2
. Which is the length of the room?
Answer:
squareroot(256)
16
Step-by-step explanation:
im genius
Can anyone help me with this I can't figure it out
60Answer: it would be 60
Step-by-step explanation:
it’s going up and down by 10
Rewrite 10^32 • 10^36 using a single exponent
[tex]10^{32} \times 10^{36}[/tex] can be written as [tex]10^{68}[/tex] using a single exponent.
What is an exponents?
In mathematics, exponents are a way to indicate the repeated multiplication of a number or phrase.
Exponents are numbers that are superscripted above other numbers. In other words, it denotes that a certain level of power has been conferred upon the base. Index and power are other names for the exponent. If m is a positive number and n is its exponent, the expression Mn means that m has been multiplied by itself n times.
Exponents are required for a more comprehensible representation of numerical quantities. Repeated multiplication is simple to write down when using exponents. If both n and x are positive integers, the expression xn means that x has been multiplied by itself n times.
When multiplying two numbers with the same base, we can add their exponents. Therefore:
[tex]10^{32} \times 10^{36 }= 10^{(32+36) }= 10^{68}[/tex]
Hence, [tex]10^{32} \times 10^{36}[/tex]can be written as [tex]10^{68}[/tex] using a single exponent.
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Use long division to fine the quotient
(4x^3-6x^2-4x+8) divided by (2x-1)
Using long division . The quotient of (4x^3-6x^2-4x+8) divided by (2x-1) is: 2x^2 - 2x - 2 with a remainder of 7.
How to find the quotient?Let use long division to determine the quotient of (4x^3-6x^2-4x+8) divided by (2x-1).
Long division:
2x^2 - 2x - 2
--------------------
2x - 1 | 4x^3 - 6x^2 - 4x + 8
- (4x^3 - 2x^2)
--------------
-4x^2 - 4x
+ (4x^2 - 2x)
--------------
-2x + 8
-(-2x + 1)
--------
7
Therefore, the quotient of (4x^3 - 6x^2 - 4x + 8) divided by (2x - 1) is:
2x^2 - 2x - 2 with a remainder of 7.
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Of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls. What is the probability that a student surveyed was either a boy or had a bicycle?
A. 620/1000 ≈ 0.62
B. 450/1000 ≈ 0.45
C. 680/1000 ≈ 0.68
D. 810/1000 ≈ 0.81
The probability that a student surveyed was either a boy or had a bicycle is 0.62.
What is probability?
The mathematical concept of probability is used to estimate an event's likelihood. It merely allows us to calculate the probability that an event will occur. On a scale of 0 to 1, where 0 corresponds to impossibility and 1 to a particular occurrence.
We are given that of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls.
So, Total number of boys = 490
Total number of girls with bicycle = 130
Total number of students that was either a boy or had a bicycle is
490 + 130 = 620
The probability is
620 / 1000 = 0.62
Hence, the probability that a student surveyed was either a boy or had a bicycle is 0.62.
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60 percent off 44. What is the answer to this Question?
Answer: 24
Step-by-step explanation:
Answer:
60% of 44 is 26.4
Step-by-step explanation:
a class consist of 12 boys of whom 5 are perfects. how many committee of 8 can be formed if its to have; a) 3 prefects b) at least 3 prefects
Step-by-step explanation:
a) To form a committee of 8 with 3 prefects, we need to choose 3 prefects from the 5 available prefects, and 5 non-prefects from the remaining 7 boys. We can do this by using the combination formula:
Number of ways = (Number of ways to choose 3 prefects) × (Number of ways to choose 5 non-prefects)
Number of ways to choose 3 prefects from 5 = C(5, 3) = 10
Number of ways to choose 5 non-prefects from 7 = C(7, 5) = 21
Therefore, the total number of committees of 8 with 3 prefects that can be formed is:
Number of ways = 10 × 21 = 210
b) To form a committee of 8 with at least 3 prefects, we need to consider two cases: one where we choose exactly 3 prefects, and one where we choose all 5 prefects. We can calculate the number of ways for each case using the combination formula:
Number of ways to choose exactly 3 prefects and 5 non-prefects = C(5, 3) × C(7, 5) = 210
Number of ways to choose all 5 prefects and 3 non-prefects = C(5, 5) × C(7, 3) = 35
Therefore, the total number of committees of 8 with at least 3 prefects that can be formed is:
Number of ways = (Number of ways to choose exactly 3 prefects and 5 non-prefects) + (Number of ways to choose all 5 prefects and 3 non-prefects)
Number of ways = 210 + 35 = 245
Ms. Rekha spends 165.31 , inclusive of a sales tax of 15 percent ,on oranges . Calculate the original price of oranges
The original value of the oranges is 143.75.
What is Percentage?A percentage is a number or a ratio that is expressed as a fraction of 100 i.e. out of 100.
In formula, x% of amount y = y*(x/100)
Given :
Tax paid by Rekha : 15%
Final Price paid by Rekha : 165.31
Let the original price of the oranges = x
The additional tax amount on oranges
= 15% of original price of x
= 15 * x / 100
= 0.15 x
Total price paid by Rekha = Original price of orange + Tax amount
165.31 = x + 0.15x
165.31 = (1 + 0.15)x
165.31 = 1.15x
x = 165.31/1.15
x = 143.75
Thus, the original value of the oranges is 143.75.
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at a local department store shirts were sold for 15 each.
This price was 80% of their regular price. What was the original price?
Therefore, the original price of the shirts was $18.75 each.
A mathematical equation: what does it mean?An equality on both sides of the equal to sign signifies a mathematical equation, which is a relationship between two expressions. Here is an example of an equation: 3y = 16.
If the selling price of the shirts was 80% of their regular price, then we can use the following equation to find the original price:
Original price * 0.8 = Selling price
Let's substitute the given values into the equation:
Original price * 0.8 = 15
To solve for the original price, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.8:
Original price = 15 ÷ 0.8
Original price = 18.75
Therefore, the original price of the shirts was $18.75 each.
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If the transformation from f to g is such that f(x)=e^(x) is verticall shrunk by a factor of ( 1)/(3) to make g(x), what is g(x) ?
After the transformation from f to g, g(x) = eˣ/3.
Vertical shrink refers to a transformation of a function that causes it to be compressed vertically. To perform a vertical shrink, you must multiply the output (y) values of the function by a constant value between 0 and 1.
The transformation of f(x) to g(x) involves a vertical shrink by a factor of 1/3. This means that the value of g(x) will be one third of the value of f(x). We can write this transformation as: g(x) = 1/3 · f(x).
Since f(x) = eˣ, we can substitute this into the equation for g(x) to find the final expression for g(x):
g(x) = (1/3)eˣ
Therefore, the function g(x) after the vertical shrink by a factor of 1/3 is g(x) = (1/3)eˣ or g(x) = eˣ/3.
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21. Suppose that a given population can be divided into two parts: those who have given disease and can infect Others, and those who do not have it but are susceptible. Let x be the proportion of susceptible individuals and y the proportion of infectious individuals; then x + y = 1. Assume that the disease spreads by contact between sick and well members of the population and that the rate of spread dy/dt is proportional to the number of such contacts. Further; assume that members of both groups move about freely among each other; so the number of contacts is proportional to the product ofx and y. Since =1 -Y, we obtain the initial value problem dy = ay( 1 ~y), y(0) = Jo; (22) dt where is positive proportionality factor, and Yo is the initial proportion of infectious individuals. A. Find the equilibrium points for the differential equation (22) and determine whether each is asymptotically stable, semistable. Or unstable. B. Solve the initial value problem 22 and verify that the conelusions You reached in part a are correet: Show that y(t) as 5 C, which means that ultimately the disease spreads through the entire population
The Initial value problem is defined
as [tex] \frac{dy}{dt} =\alpha y(1 -y), y(0) = y_0[/tex]
a) Equilibrium points or critical values are y = 0 and y = 1. Also, y = 0, is unstable and y = 1, is asymptomatic stable.
b) The solution of above initial value problem is y = 1 , which means at the end the disease will spread through the entire population.
We have a population data which can be divided into two parts. Let consider x be the proportion of susceptible individuals and y the proportion of infectious individuals; then x + y = 1. Now, Initial value problem ( that a differential equation) is, [tex] \frac{dy}{dt} = \alpha y(1 -y), y(0) = y_0[/tex]
a) we have to determine equilibrium points and nature of asymptote for above equation. To determine the equilibrium solution of equation we must put, dy/dt = 0, for all t values. At equilibrium, dy/dt = 0
=> αy(1 - y ) = 0
=> y( 1 - y) = 0
=> either y = 0 or 1 - y = 0
=> y = 0 or y = 1
so, y = 0 is unstable and y = 1 , asymptomatic stable.
b) Now, we have to solve initial value problem, [tex]\frac{dy}{y(1 - y)} = \alpha dt [/tex]
Using partial fraction decomposition,
[tex] \frac{1}{y(1 - y) }= \frac{1}{y} - \frac{1}{1 - y}[/tex]
integrating both sides,
[tex]\int {( \frac{1}{y} - \frac{1}{(1 - y)})dy } = \int{ \alpha dt }[/tex]
[tex]ln (y) - ln (1 - y) = \alpha t + c[/tex]
[tex] ln( \frac{ y}{1- y}) \: = \alpha t + c [/tex]
[tex] \frac{y}{1 - y}= e^{\alpha t} c_1 [/tex]
using initial condition, [tex]y(0) = y_0 [/tex]
[tex] \frac{y_0}{1 - y_0}= 1 ×c_1 [/tex]
[tex]c_1 = \frac{ y_0}{1 - y_0}[/tex]
[tex]so, \frac{y}{1 - y} = \frac{ y_0}{1 - y_0}e^{\alpha t} [/tex]
cross multiplication
[tex]y(1 - y_0) = ((1 - y) y_0 )e^{\alpha t} [/tex]
[tex]y - yy_0 = y_0e^{\alpha t} - yy_0 e^{\alpha t} [/tex]
[tex]y = \frac{ y_0}{y_0 + ( 1 - y_0) e^{-\alpha t} }[/tex]
as [tex]t→ ∞ , e^{- \alpha t } → 0[/tex]
[tex]y = \frac{ y_0}{y_0 }= 1 [/tex]
So, y = 1, means that ultimately the disease spreads through the entire population.
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In Southern California, there is a six-mile section of Interstate 5 that decreases 2,500 feet in elevation as it descends Grapevine Hill in the Tejon Pass. What is the angle of descent?
angle = tan⁻¹(2,500 / 31,680)
angle ≈ 4.51 degrees
Therefore, the angle of descent is approximately 4.51 degrees.
What does a math angle mean?When two rays collide at a given point, an angle is created. Indicated by the symbol is the "angle," also known as the "opening" between these two beams. Many angles, such as 60°, 90°, etc., are usually stated as numbers in degrees.
To find the angle of descent, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:
tan(angle) = opposite / adjacent
In this case, the opposite side is the change in elevation, which is 2,500 feet, and the adjacent side is the distance traveled, which is 6 miles or 31,680 feet (since 1 mile = 5,280 feet).
So we have:
tan(angle) = 2,500 / 31,680
To solve for the angle, we can take the inverse tangent (or arctangent) of both sides:
angle = tan⁻¹(2,500 / 31,680)
Using a calculator, we get:
angle ≈ 4.51 degrees
Therefore, the angle of descent is approximately 4.51 degrees.
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 can someone help me with these two questions I don’t need any explanation just answer and I would really appreciate you.
(a) m∠BAC = 73°
(b) The value of y is 2.
What is an isosceles triangle?A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.
(a) Given:
m∠BEA = 62°.
Assuming ABCD is a square.
The diagonal of the square divides the square into two isosceles right-angled triangles.
So, m∠BAD = 90° and m∠ABD = m∠ADB = m∠ABE = 45°.
So, the angle measure of ∠BAC,
m∠BAC = 180° - (45 + 62)
m∠BAC = 180° - 107°
m∠BAC = 73°
(b) Given:
BE = 6y + 2 and CE = 4y + 6.
Assuming ABCD is a square.
The diagonals of squares divide the diagonals into two equal parts.
So, BE = CE
6y + 2 = 4y + 6.
2y = 4
y = 2
Therefore, the value of y is 2.
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Gina has a collection of nickels and dimes worth $4.65. If she has 70 nickels and dimes, how many nickels does she have?
Answer:
Gina has 47 nickels
Step-by-step explanation:
Let's call the number of nickels that Gina has "n" and the number of dimes she has "d". We know that she has a total of 70 nickels and dimes, so:
n + d = 70 (equation 1)
We also know that the value of her nickels and dimes is $4.65, which is equal to 465 cents. Each nickel is worth 5 cents and each dime is worth 10 cents, so the value of n nickels is 5n cents and the value of d dimes is 10d cents. Therefore, we can write another equation based on the value of the coins:
5n + 10d = 465 (equation 2)
We can simplify equation 2 by dividing both sides by 5:
n + 2d = 93 (equation 3)
Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable. For example, we can solve equation 1 for d:
d = 70 - n
Substituting this expression for d into equation 3, we get:
n + 2(70 - n) = 93
Simplifying this equation, we get:
n + 140 - 2n = 93
-n + 140 = 93
-n = -47
n = 47
Therefore, Gina has 47 nickels and 23 dimes (since n + d = 70), and the total value of her coins is $4.65.
Answer:
47 nickels
Step-by-step explanation:
47 nickels
Can someone help me write a proof for this problem
The solution is, the triangle ABC and DBC are congruent, by the Side-Angle-Side Triangle Congruence Theorem.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
As we can seen from the given figure that two triangles are given.
The triangles ABC and BDC are :
AB = CD
AC = BD
BC = BC
Hence using the SSS theorem of the triangle, the triangle ABC and DBC are congruent, Thus the angle A is equal to angle D.
Hence the option D and E are correct. i.e. congruent by the Side-Angle-Side Triangle Congruence Theorem.
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