use the elimination method to solve 4x+8y=16 4x-8y=0

An obtuse triangle and right angle triangle can always be used as counter examples to the given statement.

What is acute angle?

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle

What is obtuse angle?

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

What is right angle?

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles..

Hence, an obtuse triangle and right angle triangle can always be used as counterexamples to the given statement " All angles in a triangle are acute".

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Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

b) m+g < and = 20
re arrange
m < and = 20- g
put values of g to find value of m that will always be less or equal

similarly,
15m +20g > and = 300
re arrange  m >=  \(\frac{300-20g}{15}\)

put different values of g to find different values of m which will always be greater or equal.

c) intersecting points of the graph

Answer:

The cost of the carpet at Magic Carpet is: 90 + 9*(area of carpet)

The cost of carpet at Carpeteria is: 50 + 13*(area of carpet)

The algebraic expression for which the cost is the same is: 90 + 9*(area of carpet) = 50 + 13*(area of carpet)

The area of carpet for which the cost is the same is: 10 square yard

Step-by-step explanation:

6a) The cost for magic carpet:

This company charges a fixed fee and a price for each square yard of carpeting, therfore the expression for the cost is:

cost = 90 + 9*a

Where a is the area of carpet to be installed.

6)b) The cost for Capeteria:

This company also charges a fixed fee and a price for each square yard of carpeting, so the expression is:

cost = 50 + 13*a.

6) c) The algebraic expression for the cost to be the same in both stores:

90 + 9*a = 50 + 13*a

6) d) We need to solve the expression above for a:

50 + 13*a = 90 + 9*a

13*a - 9*a = 90 - 50

4*a = 40

a = 40/4 = 10

To determine the number of miles Andrew can run in one hour, we need to know the rate at which he runs. From the given information, we know that Andrew can run ½ of a mile in 1 hour.

To calculate the number of miles Andrew can run in one hour, we divide the distance by the time:

Distance ÷ Time = Speed

In this case, the distance is ½ mile and the time is 1 hour. So, we have:

½ mile ÷ 1 hour = ½ mile/hour

Therefore, Andrew can run ½ mile in one hour.

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Answer:

the ratio of distance descended over time

Step-by-step explanation:

The road crew will take approximately 0.304 hours, or 18.26 minutes, to repave the 35-mile road. This can be answered by the concept of Time and Distance.

To find the time it takes for the road crew to repave the road, we divide the length of the road (35 miles) by the rate at which they can repave (115 miles per hour). This gives us the following calculation:

Time = Distance / Rate

Time = 35 miles / 115 miles per hour

Simplifying, we get:

Time = 0.304 hours

Converting hours to minutes, we get:

Time = 0.304 hours × 60 minutes per hour

Time = 18.26 minutes

Therefore, the road crew will take approximately 0.304 hours, or 18.26 minutes, to repave the 35-mile road.

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Answer:

Between $59.50 and $61.50

Step-by-step explanation:

Since this is about, we have to round the numbers.

85.58 is rounded to 86

24.98 is rounded to 25

2.49 is rounded to 2.50

Therefore:

86 - 25 - 2.50 = 59.50

So the correct answer is #3

Answer:

10 goals

Step-by-step explanation:

total goals=9+9+7=25

2/5*25

2*5

10

Answer:

$45 - 13($2) = $45 - $26 = $19

Jack had $19 left.

There is a change of 1/2 for Adam to get strictly more heads than Ben.

The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)

If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.

Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.

Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.

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Answer: They’re a type of soft coral I’m pretty sure

Step-by-step explanation:

The function f(t) giving the position of the maglev at time t is: f(t) = 0.3t^2 + 8t. This function represents the position of the maglev in feet from its starting point along a straight stretch of track, given the time t in seconds.

To find the function f(t) giving the position of the maglev at time t, we need to integrate the velocity function v(t) with respect to time.

We know that the velocity function v(t) = 0.6t + 8, so we can integrate it to find the position function f(t) by taking the antiderivative of v(t) with respect to t:

f(t) = ∫(0.6t + 8) dt = 0.3t^2 + 8t + C

where C is a constant of integration. To find the value of C, we can use the initial condition that the maglev is at the station when t = 0. Since the position of the maglev is 0 when it is at the station, we have:

f(0) = 0 = 0.3(0)^2 + 8(0) + C

Solving for C, we get C = 0.

Therefore, the function f(t) giving the position of the maglev at time t is:

f(t) = 0.3t^2 + 8t

This function represents the position of the maglev in feet from its starting point along a straight stretch of track, given the time t in seconds.

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1.17

because

1

0.82

0.35  +

---------

1.17

1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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The completed two-column table that proves ΔQTU is congruent to ΔRSU can be presented as follows;

Statement          \({}\)                           Reasons

1. \(\overline{RS}\) ⊥ \(\overline{RT}\)                          \({}\)          Given

2. \(\overline{QT}\) ⊥ \(\overline{QS}\)                         \({}\)          Given

3. \(\overline{QU}\) ≅ \(\overline{RU}\)                              \({}\)    Given

4. ∠Q ≅ ∠R \({}\)                                  All 90° angle are congruent

5. ∠QUT ≅ ∠RUS \({}\)                        Vertical Angle Theorem

6. ΔQTU ≅ ΔRSU \({}\)                        ASA

Congruent triangles are triangles that have the same size and shape.

The details of the reasons that are used to prove that the triangles ΔQTU and ΔRSU are congruent, can be presented as follows;

All 90° angle are congruent

The segments \(\overline{RS}\) and \(\overline{RT}\) are perpendicular, which indicates that the angle ∠R is a 90° angle. Similarly, segments \(\overline{QT}\) and \(\overline{QS}\) are perpendicular, therefore, ∠Q is a 90° angle, which indicates that we get;

m∠Q = m∠R = 90°

The definition of congruent angles, indicates; ∠Q ≅ ∠R

Vertical Angle Theorem

The vertical angle theorem states that the vertical angles formed by two intersecting lines are congruent.

ASA

The Angle-Side-Angle, (which can be abbreviated as ASA) congruence postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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Answer:

(x+2)^2 or (x+2)(x+2)

Step-by-step explanation:

x^2+4x+4 simplified is (x+2)^2 or (x+2)(x+2)

Answer:

(x+2)^2 or (x+2)(x+2)

Step-by-step explanation:

Brainly pls :D I tried for a while just to do this

25 degrees is the measure of angle x from the rectangle.

The given figure is a triangle and each of the triangle is isosceles is nature that is the base angles are equal.

In order to determine the value of x, we will use the expression below:

x + x + (180 - 50) = 180

x + x + 130 = 180

Simplify to have:

2x + 130 = 180

Subtract 140 from both sides

2x = 180 - 130

2x = 50

x = 50/2

x = 25 degrees

Hence the measure of the angle x from the diagram is 25 degrees.

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The solution of the equation is,

⇒ x = - 2/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

a) Now, We can solve the expression by using change of base formula:

⇒ \(log_{b} y = \frac{log y}{log b}\)

Hence, We get;

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

Take log both side we get;

⇒ log 5³ˣ⁻² = log 5⁶ˣ

⇒ (3x - 2) log 5 = 6x log 5

⇒ (3x - 2) = 6x

⇒ - 2 = 6x - 3x

⇒ - 2 = 3x

⇒ x = - 2/3

b) Solve for another method as;

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

By comparing,

⇒ 3x - 2 = 6x

⇒ 3x - 6x = 2

⇒ - 3x = 2

⇒ x = - 2/3

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Answer:

12 and 93.

Step-by-step explanation:

Let the grandsons age be x then Mr. Roger's age = 8x - 3.

Five years ago the grandson's age was x-5 and Mr Rogers was 8x - 8 years old , so:

8x - 8 - (x - 5) = 81

8x - 8 - x + 5 = 81

7x = 81 + 8 - 5 = 84

x = 12.

So the grandson is 12 and Mt Rogers is  8*12 - 3 = 93.

Since the triangles are the same, just flipped that means that all angles and segments are the same as well

I'm not sure if that's the "correct" way to prove it but that's why they're equal

Answer:

Step-by-step explanation:

In ΔEGF & ΔEGH,

EF ≅ EH           {given}

FG ≅ HG          { midpoint  theorem}

EG ≅ EG            {Reflexive property}

ΔEGF ≅ ΔEGH            { S S S congruent }

∠1 ≅ ∠2                    {Corresponding parts of congruent triangles are equal}

Answer:

Y= 65

Step-by-step explanation:

Y= 5(9)+20

Y=45+20

Y=65

The correct answer is "b. t-test for a single sample". This hypothesis-testing procedure is used to determine whether a sample mean is significantly different from a known population mean when the population variance is unknown.

The correct answer is "b. t-test for a single sample". This hypothesis-testing procedure is used to determine whether a sample mean is significantly different from a known population mean when the population variance is unknown. The t-test for a single sample is a statistical test that compares the sample mean to a hypothetical population mean, using the t-distribution. It helps researchers determine whether the sample mean is a reliable estimate of the population mean, or whether the difference between the two means is due to chance.

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The number in the log as a power of the base y = -6.

What is  logarithmic identity ?

Logarithmic identities are mathematical formulas or rules that are used to manipulate logarithmic expressions. These identities are derived from the properties of logarithms and can be used to simplify or solve logarithmic equations.

The following are some commonly used logarithmic identities:

Product rule: log_a (x * y) = log_a (x) + log_a (y)

This identity states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers.

Quotient rule: log_a (x / y) = log_a (x) - log_a (y)

This identity states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers.

According to the question:
To write the number in the log as a power of the base, we can use the following logarithmic identity:

log_a (x) = y is equivalent to\(a^y = x\)

Using this identity, we can rewrite the logarithmic expressions as follows:

y = log3 243 can be written as \(3^y = 243\)

y = log2 1/64 can be written as \(2^y = 1/64\)

Now, we can solve for y by taking the appropriate power of both sides of each equation:

For the first equation, we can write:

\(3^y = 243\)

\(3^y = 3^5 (since 243 = 3^5)\)

Therefore, y = 5.

For the second equation, we can write:

\(a^y = 1\)

Since any non-zero number raised to the power of 0 is equal to 1, we have:

\(a^y = a^0\)

Therefore, y = 0.

For the third equation, we can write:

\(2^y = 1/64\)

\(2^y = 2^-6 (since 1/64 = 2^-6)\)

Therefore, y = -6.

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Answer: 8 shirts 5 jeans

Step-by-step explanation:

Answer:

\(1 \frac{2}{6} \)

Step-by-step explanation:

\(8 \times \frac{1}{6 } = \frac{8}{6} = 1 \frac{2}{6} \)

Answer:

Step-by-step explanation:

Find the graph attached. The formula for finding the equation of a line is expressed as:

y = mx+c

m is the slope

c is the intercept (point where the line cuts the y axis)

m = y2-y1/x2-x1

Using the coordinate (1,22) and (4, 40) to calculate the slope of the line, we will have:

m = 40-22/4-1

m = 18/3

m = 6

For the intercept:

From the grapg, it can be seen that the line cuts the y axis at y = 18. Hence the intercept c = 18

The equation of the line will be:

y = 6x+18

Substitute y = 134 into the formula to get x as shown:

134 = 6x+18

134-18 = 6x

116 = 6x

x = 116/6

x = 19.33

True. If matrix A is an n × n matrix with linearly independent eigenvectors v1, v2, ..., vn, then the n × n matrix P = [v1 v2 ... vn] forms a matrix of eigenvectors. In other words, the columns of matrix P are the eigenvectors of matrix A.

1. When a matrix A has linearly independent eigenvectors v1, v2, ..., vn, it means that each eigenvector corresponds to a distinct eigenvalue. The eigenvectors span the entire vector space of dimension n.

2. The matrix P = [v1 v2 ... vn] is constructed by arranging the eigenvectors v1, v2, ..., vn as columns. Since the eigenvectors are linearly independent, the matrix P formed by these columns is invertible.

3. When we multiply matrix P by its inverse P^(-1), we obtain the identity matrix I. This implies that P^(-1) exists and is the inverse of P.

4. Now, let's consider the equation A * P = P * D, where D is a diagonal matrix that contains the eigenvalues corresponding to the eigenvectors v1, v2, ..., vn along its diagonal.

5. Multiplying both sides of the equation by P^(-1) from the left, we get P^(-1) * A * P = P^(-1) * P * D, which simplifies to P^(-1) * A * P = D.

6. Since P^(-1) exists, we can rewrite the equation as A = P * D * P^(-1). This equation shows that matrix A can be diagonalized using the matrix P formed by the eigenvectors and its inverse P^(-1).

7. Therefore, matrix P = [v1 v2 ... vn] is indeed an n × n matrix consisting of linearly independent eigenvectors of matrix A.

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Answer:

See below for proof.

Step-by-step explanation:

Given:

\(\log_ab \times \log_ba=1\)

To prove the given equation, begin by changing the base of the two logs so that they have the same base.

\(\boxed{\textsf{Change of base}: \quad \log_pr=\dfrac{\log_xr}{\log_xp}}\)

Change the base of both logs to x by using the change of base formula:

\(\implies \log_ab=\dfrac{\log_xb}{\log_xa}\)

\(\implies \log_ba=\dfrac{\log_xa}{\log_xb}\)

Substitute into the equation:

\(\implies \log_ab \times \log_ba=\dfrac{\log_xb}{\log_xa} \times \dfrac{\log_xa}{\log_xb}\)

\(\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times \dfrac{b}{d}=\dfrac{a \times b}{c \times d}:\)

\(\implies \dfrac{\log_xb \times \log_xa}{\log_xa \times \log_xb}\)

Apply the commutative property of multiplication to the numerator:

\(\implies \dfrac{\log_xa \times \log_xb}{\log_xa \times \log_xb}\)

Cancel the common factor logₓb:

\(\implies \dfrac{\log_xa}{\log_xa}\)

\(\textsf{Apply the fraction rule} \quad \dfrac{n}{n}=1:\)

\(\implies \dfrac{\log_xa}{\log_xa}=1\)

Hence proving that:

In one calculation:

\(\begin{aligned}\implies \log_ab \times \log_ba & =\dfrac{\log_xb}{\log_xa} \times \dfrac{\log_xa}{\log_xb}\\\\&=\dfrac{\log_xb \times \log_xa}{\log_xa \times \log_xb}\\\\&=\dfrac{\log_xa \times \log_xb}{\log_xa \times \log_xb}\\\\&=\dfrac{\log_xa}{\log_xa}\\\\&=1\end{aligned}\)