The angles of a triangle are 2x, 3x and 7x respectively. If the sum of the angles of a triangle is 180°What is the measure of each angle of the triangle?​

Answer:

v=9

Step-by-step explanation:

-18 = 7v + 9 - 10v

combine like terms

-18 = -3v + 9

-9             -9

-27 = -3v

divide both sides by -3

9 = v

or

v = 9

Hope this helps!!!

The solution of x in terms of w and k from 3(x - k)/w = 4 is;

Option A; ⁴/₃w + k

We are given;

3(x - k)/w = 4

We want to find x in terms of w and k.

Step 1; Using multiplication property of equality, let us multiply both sides by w to get;

(3(x - k)/w) × w = 4 × w

⇒ 3(x - k) = 4w

Step 2; Using division property of equality, divide both sides by 3 to get;

3(x - k)/3 = 4w/3

x - k = 4w/3

Step 3; Using addition property of equality, add k to both sides to get;

x = ⁴/₃w + k

In conclusion the solution to the question is; x = ⁴/₃w + k

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The length of the YZ for the two similar triangles will be 9 inches.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that triangle, ABC is similar to triangle XYZ. The value of the side YZ will be calculated by the similarity property,

YZ / BC = XZ / AC

x / 3 = 15 / 5

x = ( 15 x 3 ) / 5

x = 3 x 3

x = 9 inch

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Answer:

D

Step-by-step explanation:

D is correct because the sqrt of 91 is 9.5 and 9<9.5<10 makes absolute sense

C is not correct because the sqrt of 33 is 5.7 and 6<5.7<7 does not make sense

B is not correct because the sqrt of 13 is 3.6 and 4<3.6<5 does not make sense

A is not correct because the sqrt of 65 is 8.06 and 7<8.06<8 does not make sense

Answer:

yes

Step-by-step explanation:

they both equal to 2 pedestirans: 1 day

Answer: Yes.

Step-by-step explanation: By simplifying both ratios you get 2 pedestrians : 1 day.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given parametric equations

STEP 2: Rewrite equation 1

STEP 3: Make t the subject of the equation

STEP 4: Substitute the value of t above into equation 2 and solve in terms of x

Hence, the answer in the simplest form solved for y is given as:

Proof that the given theorem is false: Consider the function

f(x) = -x.

Then,

e^f(x) = e^(-x),

so that

e^f(x)/(1+e^f(x)) = 1/(e^x+1).

This function has limit 1/2 as x→0, but f(x) itself has no limit at x=0.(b) The value of L where the theorem is true:Let L = lim e^f / 1+e^f(x), then as per L’Hospital’s Rule,lim f(x) = lim d/dx ln(e^f(x))= lim (e^f(x) * f′(x))/e^f(x)/(1+e^f(x))= L * lim f′(x)/(1+e^f(x))= L * lim f′(x)/e^(f(x)).

Since we are given that f(x) has a limit L’ ≠ 0, then by the continuity of

e^x and ln(x), f(x)→0 as x→a.

Thus, the theorem is true if and only if the limit of

f'(x)/e^f(x)

exists as x→a.To prove that the limit of

f'(x)/e^f(x)

exists, we first show that f(x)→0 as x→a:Since we are given that f(x) has a limit L ≠ 0, then by the continuity of e^x and ln(x), f(x)→0 as x→a.Now, consider g(x) = e^f(x). Then, lim g(x) = lim e^f(x) = L and we are given that lim g(x)/(1+g(x)) exists. By L’Hospital’s Rule, lim

g'(x)/(1+g(x)) = L/(1+L), so that lim f′(x)g(x)/(1+g(x)) = L/(1+L).

Therefore, we have the following inequality:

(e^f(x)/(1+e^f(x))) |f′(x)| ≤ L/(1+L).

This implies that f′(x)/e^f(x) is bounded as x→a, and therefore the limit of f'(x)/e^f(x) exists. Hence the theorem is true for the given conditions on L where the limit of f'(x)/e^f(x) exists as x→a. We are required to establish the truth of a given theorem and also show that it is false under certain conditions. According to the theorem, if the limit of e^f(x)/(1+e^f(x)) exists, then the limit of f(x) also exists. We will begin by showing that the theorem is false in general. In order to do that, we can come up with a counterexample that proves that the theorem does not hold.

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Answer:

74.90d + 0.13m = Total cost of the car rental

Step-by-step explanation:

Hmmm you didn't give enough information but....

let d represent the number of days

let m represent the number of miles driven

74.90d + 0.13m = Total cost of the car rental

For example Tyee rents the car for 2 days and drives 100 miles

149.8 + 13 = Total cost of the car rental.

$162.8 is the Total cost of the car rental.

Answer:

(5/2,5)

Step-by-step explanation:

Answer: The one on the bottom right.

Step-by-step explanation:

Symmetry is basically like a mirror. The line of symmetry is the exact point where it starts to reflect.

A symmetrical shape can also be folded onto itself equally.

Looking at the photo, the picture on the bottom right is the left part of the figure.

The value of the integral ∫(π/2 to π/4) csc(t) cot(t) dt is -√2 + 1.

To evaluate the integral ∫(π/2 to π/4) csc(t) cot(t) dt, we can use trigonometric identities and integration techniques.

First, let's rewrite the integrand using trigonometric identities:

Substituting these identities, the integral becomes:

∫(π/2 to π/4) (1/sin(t)) * (cos(t)/sin(t)) dt

Now, we can simplify the expression:

∫(π/2 to π/4) (cos(t)/sin²(t)) dt

To evaluate this integral, we can use the substitution method. Let u = sin(t), then du = cos(t) dt. We need to find the new limits of integration when t = π/2 and t = π/4.

When t = π/2, u = sin(π/2) = 1.

When t = π/4, u = sin(π/4) = 1/√2.

The integral becomes:

∫(1 to 1/√2) (1/u²) du

Simplifying further, we have:

∫(1 to 1/√2) u^(-2) du

Now, we can integrate:

∫(1 to 1/√2) u^(-2) du = [-u^(-1)] evaluated from 1 to 1/√2

Evaluating the definite integral, we have:

[-u^(-1)] from 1 to 1/√2 = [-(1/√2)^(-1) - (-1)^(-1)] = [-√2 - (-1)] = -√2 + 1

Therefore, the value of the integral ∫(π/2 to π/4) csc(t) cot(t) dt is -√2 + 1.

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Answer:

1800

Step-by-step explanation:

cube have 6 faces

6*300=1800

Given the graph of the hyperbola:

The general equation of the given hyperbola is:

Where (h, k) is the center of the hyperbola

So, by comparing the equations:

Center = (h, k) = (-5, -2)

The hyperbola opens up and down

Since a =

The coordinates of the vertices are: (h, k + a ) and (h, k - a)

h = -5, k = -2, a = 6

So, the coordinates are:

The slopes of the asymptotes are:

The equation of the asymptotes are:

The rocket hits the ground after 9 seconds (t = 9).

To determine when the rocket hits the ground, we need to find the time when the height (h(t)) equals zero.

Given the equation for the height of the rocket as h(t) = -16t^2 + 144t, we can set it equal to zero:

-16t^2 + 144t = 0

We can factor out a common term of -16t:

-16t(t - 9) = 0

Setting each factor equal to zero gives us two possible solutions:

-16t = 0, which implies t = 0.

t - 9 = 0, which implies t = 9.

Since time (t) cannot be negative in this context, we discard the t = 0 solution.

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The logarithmic properties of a linear system are used to solve the equation.

The x-value of the intersection is x =46.

It is a system of an equation in which the highest power of the variable is always 1.

A one-dimension figure that has no width.

It is a combination of infinite points side by side.

Given

The pond can hold 400 water liters.

\(\rm y = 3.915(1.106)x\) is an expression.

Let x be the day and y be the hold of water.

When pond can hold 400 liters of water the x will be;

400 = 3.915(1.106)ˣ

(1.106)ˣ = 400/3.915    

(1.106)ˣ = 102.17

Taking logarithm on both sides, we get

log (1.106)ˣ = log (102.17)

x log (1.106) = log (102.17)                       [log aˣ = x loga] x = [log (102.17)/log (1.106)]    

x = 45.92

x = 46

Thus, the x-value of the intersection is x =46.

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Answer:

Graphing y = 3.915(1.106)x and y = 400, then finding the x-value of the intersection

Step-by-step explanation:

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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This is indicated by presuming that the bonds were converted into common stock.

The conversion is assumed to have occurred at the start of the period, or, if later, at the time the convertible bonds were issued. The numerator is enhanced by the after-tax interest that would have been avoided if the bonds had not been outstanding.

The if-converted method is used by investors to determine the value of convertible securities if they are converted into fresh shares. This is accomplished by examining the convertible security's conversion ratio and then comparing the conversion price to the stock's current market price.

The if-converted technique also informs investors about a company's earnings per share (EPS) depending on the number of currency shares, as well as earnings if all convertible securities were converted to common stock. Diluted EPS is calculated when all convertible securities are converted to common stock.

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Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

Answer:

-19

Step-by-step explanation:

ok so since they give you all the variables you can substitute their values

for example instead of 3xy you can write 3*(-4)y

so that is the basic idea for this problem

after substituting, the new equation is 3*(-4)*2 +5

i plan on using order of operations, or PEMDAS

3*(-4)=(-12)

(-12)*2=(-24)

-24+5=-19

so the answer is -19

hope this helps!

In the provided problem, the sampling mean  for a random sample of 35 employees from a population of hourly workers in South Carolina with an average hourly wage of $17.52 and a standard deviation of $6.00 per hour is being sought after.

Even if the underlying population is not normally distributed, the central limit theorem predicts that with a high sample size, the sampling distribution of the means will be about normally distributed.

In this case, since the sample size is large enough (n=35), we can assume that the sampling distribution of the means will be approximately normally distributed with a mean of $17.52 and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.

In summary, a small survey of 35 employees from the Carolina group of hourly workers yielded a mean of $17.5 as determined by the  testing distribution of means.

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Answer:

1. $11

2. $10.75

3. new median: 12

new mean: $11.75

Answer:

(7x + 2) = 6x

x = -2

Step-by-step explanation:

(7x + 2) = 6x

-2 -2

———————

7x = 6x - 2

-6 -6

———————

1x = -2

=

x = -2

the interest rate for this compound interest account is 1.5%.

Compound interest is the amount of interest calculated on both the principal amount and the interest previously earned by the account. The formula for compound interest accounts can be written as:\(A = P(1 + r/n)^(nt)\) where A is the amount accumulated, P is the principle, r is the interest rate, n is the number of compounding periods per year, and t is the time in years.To find the interest rate, we can use the formula and plug in the given values. We have:A = $90,000, P = $60,000, t = 15 years, and the interest is compounded monthly, so n = 12. Substituting these values into the formula, we get:90,000 = 60,000\(A = P(1 + r/n)^(nt)\))We need to solve for r, the interest rate. First, we can divide both sides of the equation by \(60,000:1.5 = (1 + r/12)^(12*15)\)Next, we can take the natural logarithm of both sides of the equation:ln(1.5) = \(ln[(1 + r/12)^(12*15)]\)Using the property of logarithms that says ln(a^b) = b*ln(a), we can simplify the right side of the equation:ln(1.5) = 12*15*ln(1 + r/12)Now we can divide both sides of the equation by 180 (12*15) to isolate ln(1 + r/12):ln(1.5)/180 = ln(1 + r/12)Finally, we can take the exponent of both sides of the equation to isolate r:(1 + r/12) = \(e^(ln(1.5)/180)r/12 = e^(ln(1.5)/180) - 1r = 12[e^(ln(1.5)/180)\)- 1]Using a calculator, we can evaluate the right side of the equation and round to 3 decimal places to get:r ≈ 0.015 or 1.5%Therefore.

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Answer:

Two solutions

Step-by-step explanation:

Geometric means

32, ax1, ax2, ax3, 162

___________________________

S1 = 32 = a1 r^(n-1)

S5 = 162 = a1 r^ (n-1)

________________

32 = a1 r^0

32= a1

S5 = 162 = a1 r^ (5-1)

S5 = 162 = 32 r^ (4)

162/ 32 = r^ (4)

r= 3/2

____________

Sn = 32 (3/2)^ (n-1)

_____________

n=2

S2 = 32 (3/2)^ (2-1)

S2 = 32 (3/2)^ (1)

S2 = 48

n=3

S3 = 32 (3/2)^ (3-1)

S3 = 32 (3/2)^ (2)

S3 = 32 (9/4)

S3= 72

n=4

S4 = 32 (3/2)^ (4-1)

S4 = 32 (3/2)^ (3)

S4 = 32 (27/8)

S4= 108

__________________

Answer

32, 48, 72, 108, 162

Answer:

0.015252

Step-by-step explanation:

Multiply the two together using a calulator and you will get the same answer as me.

Have a great day!

Answer:

The unknown value is 3

Explanation:

Given that

52 = 12

Let

13 = x

Then

52x = 12 * 13

52x = 156

Divide both sides by 52

52x/52 = 156/52

x = 3

The match of vector field f for  f(x, y) = y, x is graph II .

We can say that some points for the given function are F(1,2)= (2,1) F(2,1) =(1,2) F(0,1) = (1,0) F(2,3) = (3,2) F(0,2)=(2,0) .

That means arrow heads should start with these points and this is shown accordingly in graph II only.

Therefore ,

option A matches with figure 2

option B matches with figure 1

option C matches with figure 3

option D matches with figure 4

A vector field is a way to visualize them as represented by a number of small arrows each having a magnitude or a direction.

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The slope of an object is the ratio of the rise to the run. It measures the degree of steepness of an object or a projection. Hence. The slope of the slide is 1.5

Slope = Rise / Run

From the question ;

Hence,

Slope = 9 / 6 = 3/2 = 1.5

Therefore, the slope of the water slope ls 1.5.

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