The temperature outside changed from 72°F to 42°F over a period of six days. If the temperature changed by the same amount each day, what was the daily temperature change?

Answer:

to solve a system of linear equations graphically we graph both equations in the same coordinate system, the solution to the system will be in the point where the 2 lines intersect.

Answer:

8(8+3)

Step-by-step explanation:

64+24

(8×8) + (8×3)

8×(8+3)

8(8+3)

The dimension of the triangle are base = 18 ft , height = 14 ft .

It is given that height of a triangle is 4 ft less than the base x which can be represented as height = x - 4   ....(2)  and base = x

Putting above values in equation (1) , we get

   \(126=\frac{1}{2} \times(x-4)\times x\\252=x(x-4)\\252=x^2-4x\\x^2-4x-252=0\)

On factorizing , we get

  \(x^2-(18x-14x)-252=0\\(x^2-18x)+(14x-252)=0\\x(x-18)+14(x-18)=0\\(x+14)(x-18)=0\)

On equating it with zero , we get

  \(x+14=0\\x=-14\)

as length cannot be in negative so , we will not consider this solution.

   \(x-18=0\\x=18\)

Using equation (2)

Height will be = 18 - 4 = 14 ft.

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Answer:

D

Step-by-step explanation:

Because 24000 + 900 = 24900 then 0, and 2 added is 24902

Answer:

Step-by-step explanation:

eq. of any circle with center (h,k) and r=1 is

(x-h)²+(y-k)²=1²

points (-18,15) and (-20,15) lie on it.

(-18-h)²+(15-k)²=1

(15-k)²=1-(-18-h)²

and (-20-h)²+(15-k)²=1

(15-k)²=1-(-20-h)²

so 1-(-18-h)²=1-(-20-h)²

-(18+h)²=-(20+h)²

324+36h+h²=400+40h+h²

40h-36h=324-400

4h=-76

h=-19

(15-k)²=1-(-18-(-19))²=1-1=0

k=15

so center is (-19,15)

This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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Answer:

so if we take 450 an divide it by 6 you get 75. So take 75 times 18 and you get 1,350 so he would need 1,350 kilograms of rice for 18 people

Step-by-step explanation:

hope this helps :D

when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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The exponential function that models the population of tiger gar in the lake is given as follows:

\(y = 322.63(1.25)^x\)

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

Considering x as the number of years since 2016, the points are given as follows:

(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).

Inserting these points into an exponential regression calculator, the equation is given as follows:

\(y = 322.63(1.25)^x\)

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9514 1404 393

Answer:

  1/2 + 1/6

Step-by-step explanation:

  2/3 = 1/2 + 1/6

__

The sum of unit fractions is called an Egyptian Fraction. There are several different algorithms for finding such a sum. Here, we are starting with the form ...

  2/p

where p is a small prime. Then the sum can be written as ...

  1/((p+1)/2) +1/(p(p+1)/2) = 1/(4/2) +1/(3(4/2)) = 1/2 + 1/6

A different algorithm is used when p is a composite number.

__

Using the "greedy" algorithm, we can find the largest unit fraction less than 2/3 to be ...

  1/ceil(3/2) = 1/2

Then the largest unit fraction in the remainder is similarly found. The remainder is ...

  2/3 -1/2 = 1/6 . . . . already a unit fraction

So, the sum is ...

  2/3 = 1/2 + 1/6

In the "no-intercept" model Yi = Bixi + Ei, where Yi, Y2, ..., Yn is an iid sample of data from the RVs Yi with finite mean and variance, and X1, X2, ..., Xn are fixed data we wish to use to predict the Yi, the parameter B1 is the slope of the regression line.

The objective of this model is to find an estimate of B1 that best fits the data. One way to do this is to use the ordinary least squares (OLS) method, which minimizes the sum of the squared residuals.

The residual for a given data point (Yi, Xi) is the difference between the observed value of Yi and the predicted value of Yi based on the model:

Ei = Yi - B1Xi

The sum of squared residuals (SSR) is the sum of the squared residuals for all n data points:

SSR = Σ(Ei²)

The OLS estimate of B1 is the value of B1 that minimizes the SSR.

To find the OLS estimate of B1, we can set up the estimating equation as follows:

Σ(Ei²) = Σ(Yi - B1Xi)²

Differentiating concerning B1 and setting the derivative equal to zero, we get:

2Σ(Yi - B1Xi)(-Xi) = 0

Solving for B1, we get:

B1 = (Σ(YiXi)) / (Σ(Xi²))

This is the OLS estimate of B1. To find the estimate, we simply need to calculate the sum of the products of the Yi and Xi, and the sum of the squares of the Xi, and plug these values into the equation.

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In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer: 2 cakes.

Step-by-step explanation:

There will be a total number of 6 people at Eli's cake party.

You want that each one of these 6 people to eat at least 1/5 of a cake.

Then you need to make, at least, 6 times 1/5 of a cake.

This is equal to:

6*(1/5) of a cake = 6/5 of a cake.

And we can rewrite this as:

(6/5) of a cake = (5 + 1)/5 of a cake = (5/5 + 1/5) of a cake = 1 cake + 1/5 of a cake.

But you can not bake only 1/5 of a cake, we need whole numbers.

Then we need to round up to the next whole number, which is 2.

This means that you need to bake at least 2 cakes.

Answer:

rational numbers and irrational numbers

Step-by-step explanation:

Answer:

domain = {-5, -3, -2, 4, 8, 12}

Step-by-step explanation:

The domain is the set containing the x-coordinates of all ordered pairs.

domain = {-2, -3, 12, 8, 4, -5}

If you'd like, you can put the numbers in ascending order:

domain = {-5, -3, -2, 4, 8, 12}

Answer:

c becues its a bigger number

Step-by-step explanation:

Answer: A.  (-1, -3)

This point is on the boundary line, but the boundary line is a dashed line. So this point is not part of the solution. The dashed line is like an electric fence you can get closer to, but you cannot touch it. It's due to the fact there isn't any "or equal to" as part of the inequality sign. So that's why (-1,-3) is not in the solution set. If the boundary line was solid, then (-1,-3) would be a solution.

Points like (5,1), (20,-5) and (0,0) are solutions because they are in the pink shaded region, and they aren't on the boundary.

Answer:

x = 60

Step-by-step explanation:

The 60° angle and angle x both have 2 marks, so they are congruent.

x = 60

9514 1404 393

Answer:

  D.  8 (m +12)

Step-by-step explanation:

One cannot factor the coefficient from the first term and apply that to both terms. The result is NOT equivalent.

  8m +12 ≠ 8(m +12) = 8m +96

The value of angle ADC is 157.4°

The sum of angles in a trapezoid-like other quadrilateral is 360°. So in a trapezoid ABCD, ∠A+∠B+∠C+∠D = 360°. Two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°. The length of the mid-segment is equal to 1/2 the sum of the bases.

Therefore angle A + angle D = 180

using trigonometry,

cos A = 12/13

A = cos^-1(0.923)

A = 22.63°

therefore angle D = 180-22.63

= 157.4° ( 1 dp)

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ANSWER

480 pounds of silver and 320 pounds of silver alloy

EXPLANATION

The alloy contains 30% silver and 55% silver alloy.

Let the amount of silver be s.

Let the amount of silver alloy be a.

So, we have that the total amount of alloy is 800 pounds.

This must mean that if we add the amount of silver and silver alloy, we will get 800:

s + a = 800 ____(1)

Also, 30% of s and 55% of a make up 40% of 800 pounds of alloy.

This means that:

30% * s + 55% * a = 800 * 40%

=> 0.3s + 0.55a = 800 * 0.4 (convert percentages to decimals)

=> 0.3s + 0.55a = 320 ____(2)

We now have two simultaneous equations:

s + a = 800 ____(1)

0.3s + 0.55a = 320 ____(2)

From (1):

a = 800 - s

Put that in (2):

0.3s + 0.55(800 - s) = 320

0.3s + 440 - 0.55s = 320

Collect like terms:

0.3s - 0.55s = 320 - 440

-0.25s = -120

Divide through by -0.25:

s = -120 / -0.25

s = 480 pounds

Recall:

a = 800 -s

=> a = 800 - 480

a = 320 pounds

Therefore, 480 pounds of silver and 320 pounds of silver alloy must be used.

Answer:

\( c(1+2+4+5) =1\)

\( c =\frac{1}{12}\)

Now we can find the expected value with this formula:

\( E(Y) =\sum_{i=1}^n Y_i P(Y_i) =\sum_{i=1}^n cy_i *y_i = cy^2_i\)

And replacing we got:

\( E(Y) = \frac{1}{12} (1^2 + 2^2 + 4^2 +5^2) = \frac{46}{12}= \frac{23}{6}\)

Step-by-step explanation:

For this case we know the following probability mass function given:

\( P(y) = cy , y= 1,2,4,5\)

For this case we need to satisfy the following condition in order to have a probability distribution function:

\(\sum_{i=1}^n P(y_i) =1\)

And we have this:

\( c(1+2+4+5) =1\)

\( c =\frac{1}{12}\)

Now we can find the expected value with this formula:

\( E(Y) =\sum_{i=1}^n Y_i P(Y_i) =\sum_{i=1}^n cy_i *y_i = cy^2_i\)

And replacing we got:

\( E(Y) = \frac{1}{12} (1^2 + 2^2 + 4^2 +5^2) = \frac{46}{12}= \frac{23}{6}\)

Answer:

should be complementary angles

Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

Answer:

4/6=t/(t+1)

Step-by-step explanation:

4/6=t/(t+1)

Answer:

y = 2/3x + 1/2

Step-by-step explanation:

First, make the equation into a slope-intercept form:

2y + 3x = 1

2y = -3x + 1

y = -1.5x + 0.5

You can make it into a fraction:

y = -3/2x + 1/2

Now here's the equation:

y = 2/3x + 1/2

Hope this helps!

Let me know if I'm wrong :)

The result of adding -4 (row 1) to row 3 is determined as (0  - 9   2)|12.

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  2  1] | -5

To multiply row by -4, we will multiply each entity by 4 as shown below;

= -4(1 2  1) | -5

= (-4  -8  - 4) |20

To add the result to 3;

(-4  -8  - 4)|20 + (4  - 1   6) | -8

= (0  - 9   2)|12

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.

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