A box had twice as many grapes as a basket. Once 2 kg of grapes were added to the basket, it contained 0.5 kg more than the box. How many kilograms of grapes are in the basket now? (it's not 3kg or 1.5kg)

Answer:

x = 6 cm

Step-by-step explanation:

• in the parallelogram, if we consider the side of length 12

  as the base then the corresponding height is 5.

In this case the area of our parallelogram = 5 × 12 = 60 cm²

………………………………………………

• in the parallelogram, if we consider the side of length 10

  as the base then the corresponding height is x.

In this case the area of our parallelogram = 10 × x = 10x cm²

………………………………………………

In order to determine x ,we equate the two different results

that we got for the same area .

In other words ,we have to solve the equation 10x = 60.

10x = 60

⇔ x = 60/10 = 6

Answer:

Step-by-step explanation:

the 2 triangles are similar, we can solve with an equation

12 : 10 = x : 5

x = 12 * 5 : 10

x = 60 : 10

x = 6 cm

See below for the calculations of the slopes of the graphs

The slope of a line is calculated using:

m= (y2 - y1)/(x2 - x1)

Using the above formula, we have:

Line 1: (-2, 0) and (3, 2)

Slope, m= (2 - 0)/(3 + 2)

m= 2/5

Hence, the slope is 2/5

Line 2: (2, -3) and (-2, 4)

Slope, m= (4 + 3)/(-2 - 2)

m= -7/4

Hence, the slope is -7/4

Line 3: (-4, -2) and (1, 3)

Slope, m= (3 + 2)/(1 + 4)

m= 1

Hence, the slope is 1

Line 4: (0, 0) and (-3, -4)

Slope, m= (-4 - 0)/(-3 - 0)

m= 4/3

Hence, the slope is 4/3

Line 5: (0, 0) and (-1, -4)

Slope, m= (-4 - 0)/(-1 - 0)

m= 4

Hence, the slope is 4

Line 6: (-2, 1) and (3, 2)

Slope, m= (2 - 1)/(3 + 2)

m= 1/5

Hence, the slope is 1/5

Line 7: (-2, -1) and (2, -4)

Slope, m= (-4 + 1)/(2 + 2)

m= -3/4

Hence, the slope is -3/4

Line 8: (-2, -3) and (-1, -4)

Slope, m= (-4 + 3)/(-1 + 2)

m= -1

Hence, the slope is -1

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The minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.

The standard deviation is given as (σ) = 1.69.

The mean number of dresses given (μ) = 7.6.

Margin of error given (M.E.) = 0.14.

Confidence level given = 98%.

Z-Score corresponding to 98% confidence interval (Z) = 2.33.

We are asked to find the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval.

We assume the size of the sample to be n.

By the formula of Margin of Error:

M.E. = Z*(σ/√n).

Substituting the values, we get:

0.14 = 2.33*(1.69/√n),

or, √n = 2.33*1.69/0.14 = 28.126429,

or, n = 791.096 ≈ 791 (As sample size needs to be a whole number).

Thus, the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.

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Answer: 8.2 mm

Step-by-step explanation:

[tex]\sin 60^{\circ}=\frac{v}{9.5}\\\\v=9.5 \sin 60^{\circ} \approx \boxed{8.2 \text{ mm}}[/tex]

There are 1,16,280 different recital programs possible.

Given: A pianist plans to play 4 pieces at a recital from her repertoire of 20 pieces and is carefully considering which song to play first, second, etc.

It means the repetition of pieces is not allowed.

When repetition is not allowed, then the number of ways to arrange n things where r things taken together is given by:-

[tex]^{n} P_{r} =\frac{n!}{(n-r)!}[/tex]

Now, the number of different recital programs are:-

[tex]^{20} P_{4} =\frac{20!}{(20-4)!}=\frac{20*19*18*17*16!}{16!}=116280[/tex]

Hence, there are 1,16,280 different recital programs possible.

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Answer:

HI: 17.9

GH: 22.1

Step-by-step explanation:

1) There are three trigonometric ratios for right-angled triangles.

Sin = opposite/hypotenuse

Cos = adjacent/hypotenuse

Tan = opposite/adjacent.

2) Opposite to the 90° lies the hypotenuse. Opposite to the given angle lies the opposite.

Beside the given angle lies the adjacent.

3) The value of G given to us is 54°. The length of GI is 13. We are asked to find the lengths of HI and GH. We cannot find GH (we can, but I prefer the current method) without the length of HI. Let's find HI.

Tan(54) = x/13

Tan(54) × 13 = x

x = 17.89

4) We can use the Pythagorean theorem to find the length of GH. His theorem is c² = a² + b².

c² = a² + b²

c² = 13² + 17.89²

c² = 489.0521

c = √489.0521

c = 22.11

5) Round off the answers to the nearest tenth.

HI = 17.9

GH = 22.1

The equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

An equation that has an infinite number of solutions would be in the form

a = a

This means that both sides of the equation would be the same

Start by simplifying the options

3(x – 1) = x + 2(x + 1) + 1

3x - 3 = x + 3x + 2 + 1

3x - 3 = 4x + 3

Evaluate

x = 6 ----- one solution

x – 4(x + 1) = –3(x + 1) + 1

x - 4x - 4 = -3x - 3 + 1

-3x - 4 = -3x - 2

-4 = -2 ---- no solution

[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

2x + 3 = 2x + 1 + 2

2x + 3 = 2x + 3

Subtract 2x

3 = 3 ---- infinite solution

Hence, the equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

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Complete question

Which equation has infinite solutions?

3(x – 1) = x + 2(x + 1) + 1

x – 4(x + 1) = –3(x + 1) + 1

[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]

[tex]\frac 13(6x - 3) = 3(x + 1) - x - 2[/tex]

Answer:

Hence, 0.026 can be expressed as [tex]$2.6 \times 10^{-2}$[/tex].

Step-by-step explanation:

- Given 0.026

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 0.026

[tex]$$\Rightarrow 2.6$$[/tex]

Decimal has moved 2 places to right.

The power will be negative as original no. is less than 1 .

[tex]$$\begin{aligned}&2.6 \times 10^{-2} \\&0.026=2.6 \times 10^{-2} .\end{aligned}$$[/tex]

The image of G when A IMG is rotated 180 around the origin is (-2,-4).

To rotate a figure 180 degrees around the origin, we reverse the signs of both the x-coordinate and the y-coordinate. In the image, the point G has coordinates (2,4). Reversing the signs of these coordinates gives us (-2,-4).

Rotate the figure 180 degrees around the origin. This means that we imagine the figure being flipped over the origin.

Reverse the signs of both the x-coordinate and the y-coordinate of the point G. This is because when we rotate a figure 180 degrees around the origin, the signs of both the x-coordinate and the y-coordinate are reversed.

The new coordinates of G are the coordinates of the point that is the result of rotating the figure 180 degrees around the origin and reversing the signs of the coordinates of point G. In this case, the new coordinates of G are (-2,-4).

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The magnitude and direction of line UV is 19.7° South of West for 8.1 miles

The magnitude of the vector line UV is given by the length of the line UV,

d = √[(x₂ - x₁)² + (y₂ - y₁)²] where

Substituting the values of the variables intot he equation, we have

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(-2 - 2)² + (-4 - 3)²]

d = √[(-4)² + (-7)²]

d = √[4² + 7²]

d = √[16 + 49]

d = √65

d = 8.06 miles

d ≅ 8.1 miles

So, the magnitude of vector line UV is 8.1 miles

The direction of the vector line UV is given by Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)] where

Substituting the values of the variables into the equation, we have

Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)]

Ф = tan⁻¹[(-4 - 3)/(-2 - 2)]

Ф = tan⁻¹[(-7)/(-4)]

Ф = tan⁻¹[7/4]

Ф = tan⁻¹[1.75]

Ф = 60.26°

Ф ≅ 60.3°

Its bearing from the north-south line is α = 90° - Ф

= 90° - 60.3°

= 19.7°

So, its direction is 19.7° South of West

So, the magnitude and direction of line UV is 19.7° South of West for 8.1 miles

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answers

6. y = -1/2x + 8

7. y = 15

8. y = -3/4x + 1

9. y = 6x + 3

10. y = 1/3x - 4

steps

equation of the line that is perpendicular means the number next to the x should be a negative reciprocal

number next to the x is the slope

6. y=2x+5

y = mx + b

m = 2

b = -5

negative reciprocal would be

-1/2x

m = -1/2

(2, 7) means x = 2 y = 7

substitute

7 = -1/2(2) + b

7 = -1 + b

b = 8

answer is y = -1/2x + 8

7.

y = 5; (11, 15)

b = 5

m would be 0 because there is no slope

15 = 0*11 + b

b = 15

y = 15

8.

line goes through

(0,-2) and (3,2)

get slope

y2-y1/x2-x1

2-(-2) / 3 - 0

4/3

y = 4/3x

point slope form

y - y1 = m (x-x1)

y - -2 =  4/3 (x - 0)

y+2 =  4/3x

y = 4/3x - 2

negative reciprocal slope would be for perpendicular

-3/4x

(12, 10)

y = mx + b

10 = 3/4(12) + b

10 = 9 + b

1 =  b

b = 1

y = -3/4x + 1

9.

y = -1/6x + 1; (− 2, — 9)

negative reciprocal slope would be for perpendicular

+6x

(− 2, — 9)

y = mx + b

get b

-9 = 6(-2) + b

-9 = -12 + b

b = 3

y = 6x + 3

10.

6x+2y=14; (12, 0)

2y= -6x+14

y= -3x+7

negative reciprocal slope would be for perpendicular

1/3x

y = mx + b

get b

0 = 1/3(12) + b

0 = 4 + b

b = -4

y = 1/3x - 4

What would be the effect of this change is: a). both area rate and flow rate would increase.

Assuming a driver shift into third gear in which there was reduction in the engine speed while on the other hand the tractor speed increase.

The effect of the change will result in the increase in area rate as well as the  flow rate.

Therefore the correct option  is A.

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Answer:

[tex]y=\dfrac {60} {x}[/tex]   or   [tex]xy=60[/tex]   (depending on your teacher's format preference)

Step-by-step explanation:

Proportionality is sometimes called "variation".   (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

From these examples, we see that two things:

In our question, y is inversely proportional to x, so the equation we're looking at is the following [tex]y=\dfrac {k} {x}[/tex].

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it:  "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

General Inverse variation equation...

[tex]y=\dfrac {k} {x}[/tex]

Substituting known values...

[tex](12)=\dfrac {k} {(5)}[/tex]

Multiplying both sides by 5...

[tex](12)*5= \left ( \dfrac {k} {5} \right ) *5[/tex]

Simplifying/arithmetic...

[tex]60=k[/tex]

So, for our situation, k=60.  So the inverse proportionality relationship equation for this situation is [tex]y=\dfrac {60} {x}[/tex].

The way your question is phrased, they may prefer the form: [tex]xy=60[/tex]

Answer:

261.81818181

Step-by-step explanation:

400÷275=x

x×180

Answer:

If 275 gallon of oil tank costs $400 to fill.

Then 180 gallon of oil tank costs $261.8 to fill.

Step-by-step explanation:

Step 1 of 2

If 275  gallon of oil tank costs $400  to fill.

Then the cost to fill 180  gallon of oil tank can be found by forming a proportion.

Let the required cost be x.

[tex]$$\begin{aligned}\frac{\text { cost }}{\text { Gallons of Gas }} &=\frac{\text { cost }}{\text { Gallons of Gas }} \\\frac{\$ 400}{275} &=\frac{x}{180}\end{aligned}[/tex]

Multiplying both sides by 180 we get,

[tex]$$\begin{aligned}\frac{\$ 400}{275} \times 180 &=\frac{x}{180} \times 180 \\x &=\frac{\$ 400}{55} \times 36 \\x &=\$ 261.8\end{aligned}$$[/tex]

Step 2 of 2

To check if the answer is reasonable, we substitute it back in the formed proportion

[tex]$\frac{\$ 400}{275}=\frac{x}{180}$$[/tex]

We found x=$261.8 hence,

[tex]$\frac{\$ 400}{275}=\frac{\$ 261.8}{180}$$$\$ 1.45=\$ 1.45$$Here, $L H S=R H S$[/tex]

Hence, our answer is correct.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. The volume of rectangular prism A = 64 m³

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So, area of first figure = k² × area of second figure

Similarly, Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

Given that the Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 1/2.

Scale factor =  (Length of rectangular prism B)/(Length of rectangular prism A)

1/2 = (Length of rectangular prism B)/(Length of rectangular prism A)

Now, the volume of the rectangular prism can be written as,

(Scale factor)³ = (Volume of rectangular prism B)/(Volume of rectangular prism A)

(1/2)³ = 8 m³ /(Volume of rectangular prism A)

The volume of rectangular prism A = 64 m³

Hence, The volume of rectangular prism A = 64 m³

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If the function is vertically compressed, the resulting function will be g(x) = 3/4x^2

Quadratic functions are functions that has a leading degree of 2. Given the parent function f(x) = ax^2

where

2 is the exponent/degree

If the function is vertically compressed, the value of a must be less than 1, hence the possible expression when vertically compressed is g(x) = 3/4x^2

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The equation of the line in the graph given is: y = -3x - 1.

Find the slope of the line, which is: m = rise/run.

Rise of the line = 3 units

Run = 1

Slope (m) = -3/1 = -3

Y-intercept (b) = -1 (at this point, x equals zero)

Substitute m = -3 and b = -1 into y = mx + b

y = -3x + (-1)

y = -3x - 1

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(You could do this shorter, but by the time i realized that it was too late.)

First, we need one of the variables (x or y) to have the same coefficient.
Lets use the variable y, since it uses smaller numbers.

Multiply the first equation by the denominator of y, which is 3. Then multiply the second equation by the denominator of y in the second equation, which is 4.

You get:
1st equation: [tex]\frac{3}{2} x+ y = 27[/tex]
2nd equation: [tex]\frac{12}{5}x - 3y=-12[/tex]
Now we need to multiply the first equation by 3, so we can have "3y" in both of the equations.
1st equation: 9/2x + 3y = 81
2nd equation: [tex]\frac{12}{5}x - 3y=-12[/tex]
Now we can subtract both of the equations.
12/5x + 9/2x = 69 We need to make the common denominator for x.
24/10x + 45/10x = 69
69/10x=69
x=10
Now we substitute x into the first equation (or the second, doesn't matter).
1/2 * 10 + 1/3y=9
5 + 1/3y = 9
1/3 y = 4
y = 12

Answer:

(10, 12 )

Step-by-step explanation:

let's begin by clearing the fractions from both equations

[tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{3}[/tex] y = 9 ( multiply through by 6 ( the LCM of 2 and 3 to clear ) )

3x + 2y = 54 → (1)

[tex]\frac{3}{5}[/tex] x - [tex]\frac{3}{4}[/tex] y = - 3 ( multiply through by 20 ( the LCM of 5 and 4 to clear ) )

12x - 15y = - 60 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x )

- 12x - 8y = - 216 → (3)

add (2) and (3) term by term to eliminate x

0 - 23y = - 276

- 23y = - 276 ( divide both sides by - 23 )

y = 12

substitute y - 12 into either of the 2 equations and solve for x

substituting into (1)

3x + 2(12) = 54

3x + 24 = 54 ( subtract 24 from both sides )

3x = 30 ( divide both sides by 3 )

x = 10

solution is (10, 12 )

Answer:

h ≤ 70 I'm pretty sure I could be wrong

The correct inequality for the maximum height, h, of a fighter pilot is h ≤ 77.

Given that the height of the fighter pilot (h) must be less than or equal to 77 inches.

The symbol "≤" represents "less than or equal to," and 77 inches is the maximum allowable height for a fighter pilot.

The inequality h ≥ 77 would be incorrect since it states that the height of the fighter pilot should be greater than or equal to 77 inches, which would not be a maximum height requirement.

Similarly, the inequality h ≤ 70 would also be incorrect as it would imply a height limit of 70 inches, which is lower than the actual maximum height allowed.

Lastly, h ≥ 70 would not be suitable as it would permit heights greater than or equal to 70 inches, potentially exceeding the specified maximum height of 77 inches.

In conclusion, the correct inequality to represent the maximum height of a fighter pilot is h ≤ 77, ensuring that their height does not exceed 77 inches.

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The solution set of -4(x + 3) ≤ -21 is x ≥ 2.25

The inequality is given as:

-4(x + 3) ≤ -21

Divide both sides by -4

x + 3 ≥ 5.25

Subtract 3 from both sides

x ≥ 2.25

This means that the solution set of -4(x + 3) ≤ -21 is x ≥ 2.25

See attachment for the number line

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Answer:5

Step-by-step explanation:

Answer:

z = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the altitude- on- hypotenuse theorem

(leg of large Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 8 × (8 + 1) = 8 × 9 = 72 ( take square root of both sides )

z = [tex]\sqrt{72}[/tex] = [tex]\sqrt{36(2)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex]

Answer:

[tex]z = 6 \sqrt{2} [/tex]

Step-by-step explanation:

The solution is in the image

Answer:

its an odd number

Step-by-step explanation:

Answer:0

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

x² - 36 = 0 ← is a difference of squares and factors as

(x - 6)(x + 6) = 0

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 6 = 0 ⇒ x = 6

(b)

x² - 5x + 4 = 0

consider the product of the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)

the factors are - 1 and - 4 , since

- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then

(x - 1)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

(c)

x² - 2x = 3 ( subtract 3 from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the product of the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are + 1 and - 3 , since

1 × - 3 = - 3 and 1 - 3 = - 2 , then

(x + 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

(d)

6x² - 11x - 10 = 0

consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 10 = - 60 and sum = - 11

the factors are + 4 and - 15

use these factors to split the x- term

6x² + 4x - 15x - 10 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 2) - 5(3x + 2) = 0 ← factor out (3x + 2) from each term

(3x + 2)(2x - 5) = 0

equate each factor to zero and solve for x

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]

Answer: x=9.

Step-by-step explanation:

Triangle ABC is similar to triangle FED     ⇒

[tex]\frac{77}{21} =\frac{11x+11}{30} \\\\\frac{7*11}{7*3}=\frac{11*(x+1)}{30} \\\\\frac{11}{3}*30 =11*(x+1)\\\\\frac{11*3*10}{3} =11*(x+1)\\\\11*10=11*(x+1)\\10=x+1\\9=x.[/tex]

Good luck an' have a nice day!

Answer:

none of these are correct

Step-by-step explanation:

The solution of the equations will be the point of intersection of the two lines

A line is the shortest distance between two points. The equation of a line in standard form is given as Ax + By = C

According to the question, we are to pot the following lines.

4y +3x = 0

4y - x = 16

The solution of the equations will be the point of intersection of the two lines as attached.

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Answer:

1?

Step-by-step explanation:

Answer:

If the population of the United States on July 4,2010 was almost 310000000 then, the number in scientific notation is [tex]$3.1 \times 10^{8}$[/tex].

Step-by-step explanation:

- Given

Population of the United States on July 4,2010 was almost 310000000 .

- To write the number in scientific notation.

- Firstly, move the decimal point so that the first factor is greater than or equal to 1 but less than 10 .

- Then, count the number of decimal places, n, that the decimal point was moved.

- Then, write the number as a product with a power of 10.

- Finally, check the scientific notation.

Step 1 of 2

Moving the decimal point-

Move the decimal after 3 . so that 3.10000000 is between 1 and 10 .

Now, we know the decimal point was moved 8 places to the left.

Step 2 of 2

Writing the number as a product with a power of 10 -

Since, 310000000 is greater than 1 so the power of 10 will have the exponent 8 .

Therefore, the number becomes-

[tex]$$31000000=3.1 \times 10^{8}$$[/tex]

Now, checking the scientific notation-

[tex]$$\begin{gathered}3.1 \times 10^{8}=3.1 \times 100000000 \\=310000000\end{gathered}$$[/tex]