for what value of x do the expressions 2x+3 and 3x-6 have the same value?

Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

Answer:

it is A trust me :)

Step-by-step explanation:

Answer:

AC is 2sqrt(13)

BD is 9

Step-by-step explanation:

AC is 2sqrt(13) from the pythagorean theorem

BD is equal to 9 after doing so trig

Answer:

center

Step-by-step explanation:

Answer:

I think it the first one is

Answer:

f(x)= -3x + 400

Step-by-step explanation:

\(\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }\)

\(\frac{x-3}{13-3} =\frac{y-391}{361-391}\)

-3 ( x-3 ) = (y - 391 )

-3x + 400

Answer:

he is correct

Step-by-step explanation:

Answer:

33 i think

Step-by-step explanation:

Answer:

1 3/7

Step-by-step explanation:

Step 1:

10/7 = 1 3/7

Answer:

1 3/7

Hope This Helps :)

Answer:

10/7 as a mixed number is 1 3/7

Answer:,

the answer is (4,2)

Step-by-step explanation:

is you look at the 2 equations and plug in the points where the lines intercets you would get the answer soo examples

4+2=6

the first one checks out

the second one

4+(2*2)=8

so the parinthises go first 2 times 2 = 4 plus 4 = 8

The surface area of hexagonal prism A is 9√3x² cm². We are given that hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2.

Therefore, all corresponding sides of prism A and prism B are in the ratio of 1:2. Let the side length of the base of hexagonal prism A be 'x'. Then, the side length of the base of hexagonal prism B is '2x'.

We know that the surface area of hexagonal prism B is 172 cm². Using the formula for the surface area of a hexagonal prism, we can write:

172 = 2(3√3)(2x)^2 + 6(2x)h

where h is the height of hexagonal prism B.

Simplifying this equation, we get:

172 = 24√3x² + 12xh

Dividing both sides by 12, we get:

14.33 = 2√3x² + h

Now, since hexagonal prism B is a dilation of hexagonal prism A by a scale factor of 2, the height of hexagonal prism A is half the height of hexagonal prism B. So, the height of hexagonal prism A is h/2.

Using the formula for the surface area of a hexagonal prism, we can write:

SA(A) = 2(3√3)x² + 6x(h/2)

Substituting h/2 for the height of hexagonal prism A, we get:

SA(A) = 2(3√3)x² + 3xh

Substituting 2√3x² + h/2 for h, we get:

SA(A) = 2(3√3)x² + 3x(2√3x² + h/2)

SA(A) = 6√3x² + 3√3x² + (3/2)xh

Substituting 2√3x² for h in the above equation, we get:

SA(A) = 6√3x² + 3√3x² + (3/2)x(2√3x²)

SA(A) = 9√3x²

Therefore, the surface area of hexagonal prism A is 9√3x² cm².

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Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  \(\boxed{y=\dfrac{-5}{2}x+1}\)

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This question is about to determine the conditional statement,  proposition and either that is true or false.

The explanation of each part in this question is given below:

a) The given proposition can be written as the conjunction of two conditional statements as follows:

If a = 2 (mod 8), then \((a^2 + 4a) = 4 (mod 8)\).

If \((a^2 + 4a) = 4 (mod 8)\), then a = 2 (mod 8).

b) To prove the first conditional statement, assume a = 2 (mod 8). Then, there exists an integer k such that a = 8k + 2. Substituting this value of a into \((a^2 + 4a)\), we get:

\(a^2 + 4a = (8k + 2)^2 + 4(8k + 2) = 64k^2 + 36k + 8\)

Reducing this expression modulo 8, we get:

a^2 + 4a ≡ 64k^2 + 36k + 8 ≡ 0 + 4k + 0 ≡ 4 (mod 8)

Therefore, we have shown that if a = 2 (mod 8), then (a^2 + 4a) = 4 (mod 8).

To prove the second conditional statement, assume (a^2 + 4a) = 4 (mod 8). Then, there exists an integer k such that (a^2 + 4a) = 8k + 4. Substituting this value of (a^2 + 4a) into the equation a^2 + 4a - 8k = 0, we can use the quadratic formula to solve for a:

a = (-4 ± √(16 + 32k))/2 = -2 ± √(4 + 8k)

Since a is an integer, it follows that √(4 + 8k) must be an integer as well. This implies that 4 + 8k is a perfect square. The only perfect squares that are congruent to 4 (mod 8) are those of the form 8m + 4 for some integer m. Therefore, we have:

4 + 8k = 8m + 4

k = m

Substituting k = m back into the expression for a, we get:

a = -2 + √(4 + 8k) = -2 + √(8m + 4) = -2 + 2√(2m + 1)

Since a is an integer, it follows that √(2m + 1) must be an integer as well. This implies that 2m + 1 is a perfect square. The only perfect squares that are congruent to 1 (mod 8) are those of the form 8n + 1 for some integer n. Therefore, we have:

2m + 1 = 8n + 1

m = 4n

Substituting m = 4n back into the expression for a, we get:

a = -2 + 2√(2m + 1) = -2 + 2√(8n + 1) = 2(√(2n + 1) - 1)

Therefore, we have shown that if (a^2 + 4a) = 4 (mod 8), then a = 2 (mod 8).

Since both conditional statements have been proven, the given proposition is true.

(c) The given proposition is true, as shown in the proofs of the two conditional statements in part (b).

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Answer:

x > 10

Step-by-step explanation:

the dot isn't filled, meaning x can't equal 10. it goes up, meaning x is greater than 10 :) hope this helps

Answer:

Farm Shop is cheaper and better value

Step-by-step explanation:

10kg Farm Carrots= £11

1kg of Farm carrot= 11/10= £1.1
1.5kg= 1kg+500g

500g of carrot= 1.1/2=0.55

1.5kg= £1.1+£0.55=£1.65

1.5kg of Supermarket carrot= £1.80

1.5kg of farm carrot= £1.65

Therefore, the carrots at the farm shop are of better value

Answer:

--------------------

Use area formula for circle:

Substitute 22/7 for π and 70 for r:

The area is 15400 m².

Answer:

15400 m²

Step-by-step explanation:

The formula to find the area of the circle is:

\(\sf A=\pi r^2\)

Given that,

r = 70 m

Let us find the area of the circle

\(\sf A=\pi r^2\\\\\sf A=\dfrac{22}{7}*70*70\\\\\sf A =15400 \:m^2\)

The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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The value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have given a hyperbola equation:

\(\rm \dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1\)

We know the standard form of a hyperbola is given:

\(\rm \dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\)

After comparing:

a² = 16 ⇒ a = 4

b² = 9 ⇒ b = 3

\(\rm c^2 = a^2+b^2\\\\\rm c^2 = 16+9 \Rightarrow 25\)

c = 5

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

(h, k) = (2, -1)

Vertices will be (a, 0) and (-a, 0):

(4, 0) and (-4,0)

Foci will be at (c, 0) and (-c, 0):

(5, 0) and (-5, 0)

Thus, the value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.

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The value of a=4 , b=3 , k=-1 and h=2 for the hyperbola having the equation

\(\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1\)

A hyperbola is the symmetrical open curve formed by the combination of a circular cone with a plane at a minimum angle with its axis than the side of the cone.

Here the general form of the equation of hyperbola will be:

\(\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1\)

And we have a equation given as:

\(\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1\)

By comparing the equation we the solutions

\(a=4 , b=3 , k=-1 \ and\ h=2\)

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The answer is C

A is a circle so no.

B has a curve so no.

D isn't connected so obviously no.

Given:

The price of 3 citrons and 4 fragrant wood apples is 36 units.

The price of 4 citrons and 3 fragrant wood apples is 41 units.

To find: The price of citron and the price of fragrant wood apple?

Explanation:

Let,

The price of citrons = x

The price of fragrant wood apple = y

We can write an equation as

The price of 3 citrons and 4 fragrant wood apples is 36 units.

and

The price of 4 citrons and 3 fragrant wood apples is 41 units.

Now, Here we use the elimination method,

So, multiply by 4 in Eq.1 and multiply by 3 in Eq. 2

We get,

Now, subract Eq.4 from Eq.3

Put y = 3 in Eq.1

We get,

Hence, x = 8 and y = 3

Therefore,

The price of citrons = x = 8 units

The price of fragrant wood apple = y = 3 units

Answer: The price of citrons is 8 units and the price of fragrant wood apple is 3 units.

Answer:

A: 3/4 - 3/10=9/20

B: 3 1/2 - 1 1/3=2 1/6

Decimal form

A: 0.45

B: 2.166667

Step-by-step explanation:

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

$16

Step-by-step explanation:

take 20 multiply it by 0.2 and you get 4 multiplied by 4 is 16 so it is 16 dollars

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

split the other three in half

Step-by-step explanation:

Answer:

8:30

Step-by-step explanation:

Because 6 ÷ 4 is 1.5. also know as 1.5hrs before bedtime.

Answer: I think the answer is 8:30

Step-by-step explanation:

6÷4= 1.5

8:30 + 1:30 = 10:00

Answer:

This is so confusing

Step-by-step explanation:

where is the image?

Answer:

Step-by-step explanation:

in this kinda question, you need to know that if a line is

parallel to another line, it will have the same slope if it's

perpendicular, it will be negative reciprocal of the slope

thus, if the line is parallel to the one in the question, it will have a slope of 3/4.

and now just substitute the point that is given. (it's a solution of the equation btw)

so -6 = 3/4 (0) + b (the reason we dont include the (-4) is because it will have a different y-interecept, so we need to solve for b)

b=-6.

so y=3/4x - 6

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The slope-intercept equation of the line with a slope of 8 and a y-intercept of (0, 9) is y = 8x + 9.

To find the slope-intercept equation of a line, we use the form y = mx + b, where m represents the slope and b represents the y-intercept.

Given:

Slope (m) = 8

Y-intercept (0, 9)

We can substitute these values into the slope-intercept form:

y = mx + b

y = 8x + 9

Consequently, y = 8x + 9 represents the slope-intercept equation for the line with a slope of 8 and a y-intercept of (0, 9).

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Answer:

\(P(-2<Z<2)=95\%\)

Step-by-step explanation:

From question we are told that

Sample mean \(\=x= 47\)

Standard deviation \(\sigma =7\)

Generally the  X -Normal is given as

      \(Z=\frac{x-\=x}{\sigma}\)

      \(Z=\frac{x-47}{9}\)

Analyzing the range

    \(P(47<x<65) = P(0< z<2.00)\)

    \(P(47<x<65) = 95/2\)

   \(P(47<x<65) = 47.5\%\)

Mathematically

\(Z_1 =\frac{47-47}{9} =0\)

\(Z_2 =\frac{65-47}{9} =2\)

Empirical rule shows that

\(P(-2<Z<2)=95\%\)

A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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