Identify which of the labeled angles in the figure are acute.
Question 3 options:

A)

∠2 and ∠3

B)

∠3 and ∠4

C)

∠1 and ∠3

D)

∠1 and ∠2

Let the amount of pizza be 1:

Amount ate by devon = 0.25 = 1/4

Amount ate by his friends = 3/8 + 1/8 = 4/8

The total fraction consumed = 1/4 + 4/8

The total fraction consumed = (2+4)/8

The total fraction consumed = 6/8

The fraction of the pizza left unconsumed = Total amount of pizza - amount consumed

The fraction of the pizza left unconsumed = 1 - 6/8

The fraction of the pizza left unconsumed = (8-6)/8

The fraction of the pizza left unconsumed = 2/8

The fraction of the pizza left unconsumed = 1/4

Hence the amount of pizza left is 1/4

To test whether each of the regression parameters (represented by the coefficients in the regression equation) are equal to zero at a 0.05 level of significance, we can perform a hypothesis test.

The null hypothesis for each coefficient would be that it is equal to zero, and the alternative hypothesis would be that it is not equal to zero. We would then calculate a t-statistic for each coefficient and compare it to a t-distribution with n-2 degrees of freedom (where n is the sample size).

If the p-value for a coefficient is less than 0.05, we would reject the null hypothesis and conclude that the coefficient is significantly different from zero at the 0.05 level of significance. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the coefficient is different from zero at the 0.05 level of significance.

The interpretations of the estimated regression parameters depend on the context of the study and the variables involved. In general, however, the coefficients represent the change in the dependent variable (the outcome we are interested in) for a one unit increase in the corresponding independent variable (the predictor variable). A positive coefficient indicates a positive relationship between the two variables, while a negative coefficient indicates a negative relationship. The magnitude of the coefficient also tells us the strength of the relationship - a larger coefficient indicates a stronger relationship between the two variables.

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The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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The orthogonal projection of v onto the subspace of R^3 spanned by u1 and u2 is given by:

proj_v = ((v * u1)/(u1 * u1)) * u1 + ((v * u2)/(u2 * u2)) * u2

where "*" denotes the dot product.

Using the given values, we have:

v = [5, -1, 79]

u1 = [-6, -6, -1]

u2 = [-4, -12, 0]

proj_v = (([5, -1, 79] * [-6, -6, -1])/([-6, -6, -1] * [-6, -6, -1])) * [-6, -6, -1] + (([5, -1, 79] * [-4, -12, 0])/([-4, -12, 0] * [-4, -12, 0])) * [-4, -12, 0]

After calculating the dot products and simplifying the equation, we get:

proj_v = [-5, -5, 0]

Therefore, the orthogonal projection of v onto the subspace spanned by u1 and u2 is [-5, -5, 0].

To find the orthogonal projection of a vector onto a subspace, we need to first find a basis for the subspace. In this case, the subspace is spanned by u1 and u2. Then, we can use the formula for projecting a vector onto a subspace, which involves taking the dot product of the vector and each basis vector, dividing by the dot product of the basis vector with itself, and multiplying by the basis vector.

The resulting vector is the projection of the original vector onto the subspace. In this case, we plug in the given values for v, u1, and u2 into the formula and simplify to obtain the orthogonal projection of v onto the subspace spanned by u1 and u2, which is [-5, -5, 0].

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Answer:

x = 20

x = -18

x = 7/15

x = 5

3990 is the lowest common multiple (LCM) of 105 and 190.

To work out the lowest common multiple (LCM) of 105 and 190, we need to first draw the prime factor tree for 190. According to the prime factor tree for 190 is:

Next, we can find the prime factors of 105 using a similar method. According to, the prime factorization of 105 is 3 x 5 x 7.

To find the LCM of two numbers, we need to multiply together the highest powers of all the prime factors that appear in either number. In this case, the prime factors that appear in either number are 2, 3, 5, 7, and 19.

\(2^1 \times 3^1 \times5^1 \times 7^1 \times 19^1 = 3990\)

So, the lowest common multiple (LCM) of 105 and 190 is 3990.

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Answer:

It is 8 ft ......... ok? I hope it helps

The solution is, the value of x is, x = 12.

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,

from the given figure, we get,

the triangles are similar,

so, we know that, the sides are proportional to each other.

i.e. 8:4 = x: 6

or, x = 8 * 6 / 4

or, x  = 2 * 6

or, x = 12

Hence, The solution is, the value of x is, x = 12.

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Answer:

  a.  0

Step-by-step explanation:

You want the limit of (k(x) -h(x))/k(x) as x approaches 0 when k(x) = sin(x)/x {x≠0} and h(x)=x+1 {x<1}.

Since we're concerned about the limit as x → 0, we don't have to be concerned with the fact that the expression is undefined at x = 0.

The function h(x) is defined as h(0) = 1, so we can just be concerned with the value of ...

  lim[x→0] (k(x) -1)/k(x)

The limit of k(x) as x → 0 is 1, so this becomes ...

  lim[x→0] (k(x) -1)/k(x) = (1 -1)/1 = 0

At x=0, sin(x)/x is the indeterminate form 0/0, so its limit there can be found using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim[x→0] sin(x)/x = lim[x→0] cos(x)/1 = cos(0) = 1

The fact that k(0) = 0 is irrelevant with respect to this limit.

__

Additional comment

We like to use a graphing calculator to validate limit values. The attachment shows the various functions involved. It also shows that as x gets arbitrarily close to 0 from either direction, the value of g(x) does likewise. This is all that is required for (0, 0) to be declared the limit. The lack of definition of g(x) at x=0 simply means the relation has a (removable) discontinuity there.

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Answer:

3.125%

Step-by-step explanation:

1/8=0.125

3+0.125=3.125

Answer:

the answer is

1/32

Step-by-step explanation:

let me know of its right

The volume of the given solid over the indicated region of integration, f(x,y) = 2x + 2y - 5 and R = {(x,y): -4 ≤ x ≤ 1, 3 ≤ y ≤ 6}, is 63 units³.

To find the volume, we will integrate the function f(x,y) over the region R. Follow these steps:

1. Set up the double integral: ∬R (2x + 2y - 5) dA

2. Set up the limits of integration: ∫(from -4 to 1) ∫(from 3 to 6) (2x + 2y - 5) dy dx
3. Integrate with respect to y: ∫(from -4 to 1) [(2xy + 2y²/2 - 5y)] (evaluated from 3 to 6) dx
4. Simplify and evaluate: ∫(from -4 to 1) [6x + 18 - 5(6-3)] dx
5. Integrate with respect to x: [3x² + 18x - 15x] (evaluated from -4 to 1)
6. Simplify and evaluate: (3 + 18 - 15) - (-12 + 72 + 60)
7. Calculate the final result: 6 - (-30) = 36

The volume of the region is 63 units³.

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Tessa over the weekend did 15 problems

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

The total number of problems assigned = x

On Saturday she did = 3/5x

The remaining problems are = 1 - 3/5x

The remaining problems are = 2/5x

On Sunday she did = 1/3 * (2/5x)

On Sunday she did = 2/15x

The remaining problems= (1 - 1/3)*(2/5x)

The remaining problems= (2/3) * (2/5x)

The remaining problems= 4/15x

As that the final number of problems remaining are 4, we get:

4/15x = 4

x = 4 (15/4)

x = 15

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The equations are x - 5 = 7, x - 7 = 5 and x - 4 = 8

The solution to the equation is given as

x = 12

The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true.

Using the above as a guide, we have the following:

Each of these equations is equivalent to x = 12, since we have simply subtracted the same value from both sides of the equation.

Hence, the solution to each of these equations is x = 12.

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Answer:Explanation: The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

Step-by-step explanation:

The circle equation has a center located at (2, 5) and passes through the point (10, 3) is (x - 2)² + (y - 5)² = 68

An equation is an expression that shows the relationship between two or more variables and numbers.

The circle has a center located at (2, 5) and passes through the point (10, 3), hence:

\(Radius=\sqrt{(3-5)^2+(10-2)^2}=8.25\)

The equation of the circle is:

(x-2)² + (y-5)² = 8.25²

(x - 2)² + (y - 5)² = 68

The circle equation has a center located at (2, 5) and passes through the point (10, 3) is (x - 2)² + (y - 5)² = 68

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Answer:

A: 6 boxes right, 9 boxes down, 9 boxes left, connect back to start.

B: 3 boxes right, 9 boxes up, (diagonal 6 right, 12 down), 9 boxes up, 6 boxes right.

C: 1 box right, 2 boxes down, 1.5 boxes right, 1 box up, .5 box right, 2.5 boxes down, 3 boxes left, 3.5 boxes up to connect.

D: (diagonal 1 up, 1 right), 1 box right, (diagonal 1 down, 1 right), 1 box down, (diagonal 3 down, 3 left), 3 boxes left

Step-by-step explanation:

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer:

I can't see properly try a better view of it

Answer:

\(x=12, y=0\)

Step-by-step explanation:

\(22+\frac{1}{5}yi=2x-2 \\ \\ (24-2x)+\frac{1}{5}yi\)=0\)

Setting the real and imaginary parts of the left hand side equal to 0,

\(24-2x=0 \implies x=12 \\ \\ \frac{1}{5}y=0 \implies y=0\)

Yes, all real numbers have a decimal expansion. A decimal expansion is the representation of a real number in the base-10 numeral system.

It involves writing the integer part of the number, followed by a decimal point, and then the decimal part. The decimal part consists of an infinite sequence of digits, which may repeat or terminate. For example, the real number 1/9 has a decimal expansion of 0.111111..., where the digits 1 repeat infinitely. On the other hand, the real number 2/5 has a decimal expansion of 0.4, which terminates after one digit. Even irrational numbers like 13−−√ have decimal expansions, albeit non-repeating and non-terminating. For example, the decimal expansion of 13−−√ is approximately 3.605551275464... It is important to note that every real number has a unique decimal expansion, although some numbers may have more than one way of being expressed in decimal form.

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If $550 is deposited in an acount paying 8.6% annual interest, compounded semiannually the account will take approximately 5.2 years to increase to $850.

To calculate the time it takes for the account to increase to $850, we can use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)\)

Where:

A is the final amount ($850),

P is the initial deposit ($550),

r is the annual interest rate (8.6% or 0.086),

n is the number of times the interest is compounded per year (semiannually, so n = 2),

and t is the time in years.

Rearranging the formula to solve for t, we have:

t = (1/n) * log(A/P) / log(1 + r/n)

Plugging in the values, we get:

t = (1/2) * log(850/550) / log(1 + 0.086/2)

Calculating this expression gives us approximately 5.2 years, rounded to the nearest tenth. Therefore, it will take around 5.2 years for the account to increase to $850.

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Answer:

B

Step-by-step explanation:

a)

2x + x + 5x -9 = -6 + 9x - x + 3

8x - 9 = 8x -3

8x - 8x = -3+9

0

Has no solution.

b)

10x -6x -4-1 = 7-12+2x+2x

    4x - 5 = 4x - 5

      0 = 0

therefore has infinite solutions.

c)

7x + 5 + 4 - 9x = x + 2 - 4 +8x

-2x + 9 = 9x -2

-11x = -11

x = 1

Soluble and has a solution.

d)

5x - 2x - 3 -9 = x -12 + 3x + 3x

3x -12 = 7x -12

-4x = 0

x = 0

Has a solution.

Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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Step-by-step explanation:

\(\frac{120+30}{\frac{66}{1126}-8*3+17-4*4 }\)

\(\frac{-42225}{6458}\)

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

Exponential decay

Step-by-step explanation:

Because the values are exponentially decreasing.

Answer:

the answer for n is 5

Step-by-step explanation:

2 + n = 7

n = 7-2

n = 5

Step-by-step explanation:

Step 1:  Determine the axis of symmetry

The axis of symmetry is middle of the parabola.  In this equation we see that at x = -1 we have the vertex and also the middle of the parabola.  So our axis of symmetry is x = -1.

Step 2:  Determine the vertex

The vertex is the minimum or maximum of a parabola and is bent in a crest form.  In this example the vertex is at (-1, -3) because we are using the tip of the graph.

Step 3:  Determine the y-intercept

The y-intercept is where the graph intersects with the y-axis.  In this example we intersect the y-axis at -4 so that means that our point would be (0, -4) meaning that we intersect x = 0 at -4.

Step 4:  Determine if the vertex is a min or max

Looking at the graph we can see that the rest of the red line is beneath the vertex point which means that the vertex is a max.

Step 5:  Determine the domain

The domain is the x-values that we are going to be using and we know that we are reaching toward positive and negative inifity which means that we are using all real numbers.

Step 6:  Determine the range

The range is the y axis and what y values we are able to reach using the graph.  In this example we can see that all y-values above -3 are not being used therefore the range is \(y \leq -3\)