solve the inequality for v: 7v/4 + 6 > -2

The equation is:

R - 8 = 4

So to get R all by itself, you can add+8 to BOTH sides of the equation. This will 'cancel' the -8 that is next to R.

R - 8 + 8 = 4 + 8

-8 + 8 = 0 so let's simplify:

R + 0 = 4 + 8

Simplify a little more:

R = 12

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Step-by-step explanation:

(x-2)^2 + (y-9)^2   = r^2

this is of the form fora circle with center  h,k and radius r

(x-h)^2 + (y-k)^2 = r^2

for the equation given   center =   2, 9    and radius = r

Answer:

a) The amount financed is the purchase price minus the down payment, which is:

$15,000 - $3,000 = $12,000

Therefore, the amount financed is $12,000.

b) The total amount of monthly payments is the monthly payment multiplied by the number of payments, which is:

$300 x 48 = $14,400

Therefore, the total amount of monthly payments is $14,400.

c) The finance charge is the total amount of payments minus the amount financed, which is:

$14,400 - $12,000 = $2,400

Therefore, the amount of the finance charge is $2,400.

Check the picture below.

since the pyramid is a hexagonal one, so the base of it is a regular hexagon in this case, that means that we can split up the base into six equilateral triangles, keeping an eye on the equiateral triangle in the picture, let's find it's altitude of "y", which is the perpendicular distance from the center to a side.

[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=6 \end{cases}\implies h=\cfrac{6\sqrt{3}}{2}\implies h=3\sqrt{3}\implies h=\sqrt{27}=y[/tex]

now, since we know what "y" is, let's use that green triangle on the right, to find the altitude of each triangular face in the pyramid, namely "z".

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{z}\\ a=\stackrel{adjacent}{\sqrt{27}}\\ o=\stackrel{opposite}{8} \end{cases} \\\\\\ (z)^2= (\sqrt{27})^2 + (8)^2\implies z^2=27+64\implies z^2=91\implies z=\sqrt{91} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \textit{area of six triangles} }{6\left[\cfrac{1}{2}(\underset{b}{6})(\underset{h}{\sqrt{91}}) \right]}\implies 18\sqrt{91} ~~\approx ~~ \text{\LARGE 171.71}\impliedby \textit{lateral area}[/tex]

The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

Here, we have,

we know that,

The sum of the angles in a triangle add to 180

x+2x+6x = 180

Combine like terms

9x= 180

Divide by 9

9x/9 = 180/9

x = 20.

Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

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complete question:

The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.

Answer: 5 + 3 = 8

This statement represents the addition of 5 and 3, which equals 8.

Step-by-step explanation:

Step-by-step explanation:

12  4/5 ft    *   1/4 in / ft = 3.2 inches  

The approximate value of the ratio of the large spiral to the smaller spiral is 16:1.

To find the ratio of the large spiral to the smaller spiral, we can divide the length of the large spiral by the length of the smaller spiral.

Ratio = Length of large spiral / Length of small spiral

Given:

Length of large spiral = 144 units

Length of small spiral = 9 units

Ratio = 144 units / 9 units

To simplify the ratio, we can divide both the numerator and denominator by the greatest common divisor (GCD) of 144 and 9, which is 9.

Ratio = (144 units / 9 units) / (9 units / 9 units)

= 16 / 1

= 16

Therefore, the approximate value of the ratio of the large spiral to the smaller spiral is 16:1.

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The scale factor used to create the image is 4. Option D, 4, is the correct answer. This indicates that the dilated polygon A'B'C'D' is four times larger than the original polygon ABCD in terms of both the horizontal and vertical dimensions.

To determine the scale factor used to create the image, we can compare the corresponding sides of the original polygon ABCD and the dilated polygon A'B'C'D'.

Let's consider the horizontal distance between points A and B in the original polygon. It is 3 - 1 = 2 units. Now, let's consider the horizontal distance between points A' and B' in the dilated polygon. It is 12 - 4 = 8 units.

The scale factor can be calculated by dividing the corresponding side lengths of the dilated polygon by the corresponding side lengths of the original polygon. In this case, we have:

Scale factor = (Horizontal distance between A' and B') / (Horizontal distance between A and B)

Scale factor = 8 / 2

Scale factor = 4

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The perimeter of the figure is 58 m.

To find the perimeter of the given figure we can divide the figure in three rectangles.

Rectangle 1:

Perimeter= 2 (l + w)

= 2(5 + 2)

= 2 x 7

= 14 m

Rectangle 2:

Perimeter= 2 (l + w)

= 2(5 + 1)

= 2 x 6

= 12 m

Rectangle 3:

Perimeter= 2 (l + w)

= 2(14 + 2)

= 2 x 16

= 32 m

So, the perimeter of the figure is

= 14 + 12 + 32

= 58 m

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Damian wants to buy a gift for his friend Luna. Giving gifts to our loved ones, friends and family is a tradition that has been around for centuries. It is a way of expressing love, appreciation, gratitude and affection. It also strengthens relationships and brings people closer together.

Damian should consider what Luna likes and dislikes. This is important because giving a gift that someone doesn't like or appreciate is not thoughtful. He can also consider her interests and hobbies. For example, if Luna likes reading, he can buy her a book by her favourite author or a new release that she has been looking forward to.

If Luna is someone who loves to travel, then a travel-themed gift such as a travel journal, a passport holder or a world map can be a good idea. He can also give her a gift that relates to her profession or career. For instance, if she is a musician, then a new musical instrument, a music stand or sheet music can be a perfect present.

In summary, Damian should consider Luna's likes and interests when buying her a gift. This shows that he values her and cares about her. It is the thought that counts, so he doesn't have to spend a lot of money on the gift, but rather, put in effort and time to select something special that will make her happy.

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Let's assume x represents the number of glasses of skim milk and y represents the number of quarter-pound servings of lean meat.

We have the following information:

1 glass of skim milk supplies 0.1 mg of iron and 8.6 g of protein.

1 quarter pound of lean meat provides 3.5 mg of iron and 24 g of protein.

The person on a special diet needs 7.5 mg of iron and 91.0 g of protein.

We can set up the following system of equations based on the given information:

0.1x + 3.5y = 7.5 (for iron)

8.6x + 24y = 91.0 (for protein)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From the first equation, we can solve for x in terms of y:

0.1x = 7.5 - 3.5y

x = (7.5 - 3.5y) / 0.1

Substituting this value of x into the second equation, we get:

8.6[(7.5 - 3.5y) / 0.1] + 24y = 91.0

Simplifying:

86(7.5 - 3.5y) + 240y = 910

Expanding and rearranging:

645 - 301y + 240y = 910

-61y = 265

y = -265 / 61

y ≈ -4.34

Since the number of servings cannot be negative, we can conclude that y ≈ 4.34.

Substituting this value of y back into the equation for x:

x = (7.5 - 3.5(4.34)) / 0.1

x = (7.5 - 15.19) / 0.1

x ≈ -76.9 / 0.1

x ≈ -769

Again, the number of glasses cannot be negative, so x ≈ 769.

Since we cannot have fractional servings, we can round the values to the nearest whole number:

Approximately, 769 glasses of skim milk and 4 servings of quarter-pound lean meat will provide 7.5 mg of iron and 91.0 g of protein for the person on the special diet.

Answer:

x=8

Step-by-step explanation:

Step-by-step explanation:

Since both lines are tangent to the circle, and just by looking at how WX and XY are positioned; we can form 2 right triangles. This is a technique used and taught to me by my math teacher. Making us to say that WX=XY. Also, VX is congruent to itself by the reflective property of congruence. With WX=XY, we can write the equation 2x+5=3x-3 to solve for x. Lets add 3 by both sides, we get 2x+8=3x, and 2x can be subtracted by both sides. That would equal 8=x. Good luck with your IXL! I know that it is torture when you get a question wrong, you go down a bunch of points. I believe in you

To find the distance that the plane has flown, we can use the concept of trigonometry. In the given scenario, we have a right triangle ABC, where AB represents the horizontal distance flown by the plane, BC represents the vertical distance gained (750 ft), and AC represents the total distance flown.

We are given that angle BAC is 20°, and BC is 750 ft. We need to find AC, the distance flown.

Using trigonometry, we can use the sine function to relate the angle and the sides of the triangle:

sin(angle) = opposite/hypotenuse

In this case, sin(20°) = BC/AC

Rearranging the equation, we have:

AC = BC / sin(angle)

Substituting the given values, we get:

AC = 750 ft / sin(20°)

Using a calculator, we can evaluate sin(20°) ≈ 0.3420

AC = 750 ft / 0.3420 ≈ 2192 ft

Therefore, the distance that the plane has flown is approximately 2192 feet.

The length of arc PR in the circle is 8π units.

The arc length PR in the circle can be found as follows:

Arc length is the distance between two points along a section of a curve. In other words, an arc length is measured by taking a part of the whole circle

arc length = ∅ / 360 × 2πr

where

Therefore,

∅ = 120 degrees

r = 8 units

Hence,

arc length = 120 / 360 × 2 × π × 8

arc length = 1 / 2 × 16π

arc length = 8π

Therefore,

arc length = 8π units

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The cost price of the shorts is K22.50.

To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.

Let's assume the cost price of the shorts is represented by C.

The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.

117% of the cost price C can be calculated as (117/100) * C.

GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.

Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.

Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:

Selling price before GST = Selling price - (Selling price × R)

In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:

K29.25 = Selling price - (Selling price × 0.17)

Simplifying the equation

K29.25 = Selling price × (1 - 0.17)

K29.25 = Selling price × 0.83

Selling price = K29.25 / 0.83

Now we can substitute the selling price in terms of the cost price:

K29.25 / 0.83 = (117/100) × C

Simplifying the equation:

C = (K29.25 / 0.83) × (100/117)

Calculating the cost price C:

C = K22.50

Therefore, the cost price of the shorts is K22.50.

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The direction of rotation used to create the image is 90°  counterclockwise rotation. To determine the direction and degree of rotation used to create the image, we can compare the positions of the vertices of the original triangle ABC with the corresponding vertices of the image triangle A' B' C'.

Let's analyze the changes in the coordinates of the vertices.

Original Triangle ABC:

A(-4, -4)

B(3, -3)

C(0, -10)

Image Triangle A' B' C':

A'(4, -4)

B'(3, 3)

C'(10, 0)

By comparing the coordinates, we can observe that the image triangle has undergone a 90° counterclockwise rotation.

To determine this, we can focus on a single vertex, such as A. The original point A(-4, -4) has been rotated counterclockwise by 90° to its new position A'(4, -4). This rotation is evident in the change of sign for the y-coordinate (-4 to -4) and the swapping of the x-coordinate (-4 to 4). This pattern is consistent across all three vertices.

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Answer:

Counterclockwise rotation of 90° about the origin

Answer:

Step-by-step explanation:

Direction: Opens Up

Vertex:

(

0.784

¯¯¯¯

09

,

551.69488

¯¯¯¯

63

)

Focus:

(

0.784

¯¯¯¯

09

,

551.75170

¯¯¯¯

45

)

Axis of Symmetry:

x

=

0.784

¯¯¯¯

09

Directrix:

y

=

551.63806

¯¯¯¯

81

Select a few

x values, and plug them into the equation to find the corresponding

y values. The

x values should be selected around the vertex.

Replace the variable

x

with

0

in the expression.

f

(

0

)

=

4.4

(

0

)

2

−

6.9

⋅

0

+

554.4

Simplify the result.

Tap for more steps...

554.4

The

y

value at

x

=

0

is

554.4

.

y

=

554.4

Replace the variable

x

with

−

1

in the expression.

f

(

−

1

)

=

4.4

(

−

1

)

2

−

6.9

⋅

−

1

+

554.4

Simplify the result.

Answer:

Question 1: The appropriate measures of center for this data set would be (1) Mean and (2) Median. There is no mode in this data set as there are no repeating values.

Question 2: To find the standard deviation, we first need to find the mean:

Mean = (513 + 490 + 496 + 380 + 490 + 513 + 503 + 513 + 500 + 492) / 10 = 494.0

Next, we find the difference between each data point and the mean:

(513 - 494.0), (490 - 494.0), (496 - 494.0), (380 - 494.0), (490 - 494.0), (513 - 494.0), (503 - 494.0), (513 - 494.0), (500 - 494.0), (492 - 494.0)

19, -4, 2, -114, -4, 19, 9, 19, 6, -2

Then we square each difference:

361, 16, 4, 12996, 16, 361, 81, 361, 36, 4

The sum of these squared differences is:

361 + 16 + 4 + 12996 + 16 + 361 + 81 + 361 + 36 + 4 = 14136

To find the variance, we divide the sum of squared differences by the number of data points minus one:

Variance = 14136 / 9 = 1570.7

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √1570.7 ≈ 39.6 (rounded to the tenths place)

Step-by-step explanation:

Correct answer is option c and this ia how to solve it

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Answer:

Each leg is 13√2 cm long

Step-by-step explanation:

The hyotenuse of a right  triangle is calculated by the formula

c² = a² + b²

where c is the hypotenuse and a, b the other sides

and then finding the square root of the above

For a right isosceles triangle the two sides a = b

So c² = a² + a² = 2a²

In the given problem the equal sides are given as x

So c² = 2x²

c = √2x

We are given c = 26

26 = √2x

x = 26/√2

Rationalizing the denominator we get

x = 26 · √2 /2

= 13√2

Answer:

The number of different committees that can be formed from a list of 10 people is given by the combination formula:

n C r = n! / (r! * (n-r)!)

where n is the total number of people, and r is the number of people to be selected for the committee.

In this case, we have n = 10 and r = 5, so the number of different committees that can be formed is:

10 C 5 = 10! / (5! * (10-5)!) = 252

Therefore, there are 252 different committees that can be formed from a list of 10 people.

Step-by-step explanation:

The calculated values of x in the figures are x = 70, x = 48 and x = 55

Figure (a)

In this figure, we have

Angles = 55 and 70 degrees

Also, we have

Two isosceles triangles

So, we have

PRQ = (180 - 70)/2

PRQ = 55

The sum of angles on a line is 180

So, we have

x + 55 + 55 = 180

Evaluate

x = 70

Figure (b)

In this figure, we have

Angle = 98 degrees

Also, we have

One isosceles triangle and One parallelogram

So, we have

MNR = 180 - 2x

The sum of angles on a line is 180

So, we have

180 - 2x + 98 = 180

Evaluate

x = 48

Figure (c)

The value of x is calculated as

2x = 180 - 70

So, we have

2x = 110

Evaluate

x = 55

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Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

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Answer:

Step-by-step explanation

Answer:

84

34

27

Step-by-step explanation:

The correct equation representing the Line of fit is ŷ = 3.8x - 109.2.

The line of fit for the given data, we can use regression analysis with technology. The equation that represents the line of fit is in the form ŷ = mx + b, where ŷ is the predicted value, x is the average daily temperature, m is the slope of the line, and b is the y-intercept.

Using the given data and regression analysis, we obtain the equation:

ŷ = 3.8x - 109.2

Therefore, the correct equation representing the line of fit for the data is ŷ = 3.8x - 109.2.

This equation indicates that for every increase of 1 degree Fahrenheit in the average daily temperature, the total ice cream sales are predicted to increase by 3.8 units. The negative y-intercept of -109.2 suggests that when the average daily temperature is 0 degrees Fahrenheit, the predicted ice cream sales would be $109.2.

the negative sign in front of the x coefficient (-3.8x) or (-6.5x) would not be appropriate in this case since we observe a positive correlation between the temperature and ice cream sales. Therefore, the equations ŷ = −3.8x − 109.2 and ŷ = −6.5x − 279.1 are incorrect.

In conclusion, the correct equation representing the line of fit is ŷ = 3.8x - 109.2.

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Quotient: x³

Remainder: 5

(a) To perform synthetic division, we set up the table as follows:

markdown

  5 |  1  0  -24  -6  5

     |___

We start by bringing down the coefficient of the highest power term, which is 1, into the bottom row:

markdown

  5 |  1  0  -24  -6  5

     |___

     1

Next, we multiply the divisor, 5, by the value in the bottom row (1) and write the result under the next coefficient:

markdown

  5 |  1  0  -24  -6  5

     |___

     1

    -5

Then, we add the values in the second row:

  5 |  1  0  -24  -6  5

     |___

     1

    -5

    ---

     0

We repeat the process with the new result, 0:

  5 |  1  0  -24  -6  5

     |___

     1

    -5

    ---

     0  0

Continuing, we multiply the divisor by the value in the second row (0) and write the result under the next coefficient:

  5 |  1  0  -24  -6  5

     |___

     1

    -5

    ---

     0  0

      0

Again, we add the values in the third row:

  5 |  1  0  -24  -6  5

     |___

     1

    -5

    ---

     0  0

      0

    ---

     0

We continue until we reach the constant term, 5:

  5 |  1  0  -24  -6  5

     |___

     1

    -5

    ---

     0  0

      0

    ---

     0  0

      0

    ---

     5

(b) The quotient is given by the coefficients in the second row, which are 1, 0, 0, and 0. Therefore, the quotient is x³ + 0x² + 0x + 0, which simplifies to just x³.

The remainder is the value in the last row, which is 5.

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