Tell whether the sequence is arithmetic. If It is what is the common difference?

x^2 = 4 -7x

Need to rewrite the equation in quadratic form.

Add 7x to each side:

x^2 +7x = 4

Subtract 4 from each side:

x^2 + 7x - 4 = 0

Now using the quadratic formula -b +/-√(b^2-4(ac)) / 2a

We can solve for x.

a = 1, b = 7 and c = -4

Replace the letters with their values:

-7 +/- √(7^2 -4(1-4)) / 2*1

Simplify:

-7 +/- √65 /2

The exact answers are:

X = -7 + √65 / 2 and X = -7 - √65 / 2

Answer:

X = -7 + √65 / 2 and X = -7 - √65 / 2

Step-by-step explanation:

Answer: 48 fl oz ( fluid ounces )

Explanation:

1 c = 8 fl oz

1 1/2 c = 12 fl oz

12 fl oz of milk × 4 Days =

48 fl oz in four days

Use the intersecting chords theorem: the labeled angle (WVZ) between the given chords has measure that is the average of the two arcs the chords intercept (WZ and XY):

[tex]81^\circ=\dfrac{m\widehat{XY}+52^\circ}2\implies m\widehat{XY}=110^\circ[/tex]

The requried measure of the arc XY is 110°. Option D is correct.

An arc is a portion of the circumference of a circle. It is defined by two endpoints on the circle and all the points on the circle between these endpoints. The length of an arc is proportional to the measure of the central angle that subtends it.

Here,
To use the intersecting chords theorem,
we can state that the measure of the labeled angle (WVZ) between the given chords is equal to the average of the measures of the two arcs intercepted by the chords, namely WZ and XY.

81 = mWZ+ mXY/2
81 = 52 + mXY / 2
mXY = 110°

Thus, the requried measure of the arc XY is 110°. Option D is correct.

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Answer:

[tex]d < \$20[/tex]

Step-by-step explanation:

Let

d----> the amount of money that Lena spent at the grocery store

we know that

The inequality that represent this situation is

[tex]d < \$20[/tex]

Answer:

d < $20

Step-by-step explanation:

Since they said less than $20 not less than or equal to $20.

12x18.2/2=109.2 is the area of the big triangle and also the same area could be found 20 x h=109.2 so

h= 109.2/20=5.46 m

Answer:

  (1, 1) is NOT a solution

Step-by-step explanation:

The only point of intersection of the graphs is (0, 2). The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection, so is NOT the solution to the system of equations.

The point (1,1) is not a solution to the system of equations because, when we substitute the coordinates into the equations, it matches the second equation but not the first.

To determine whether point (1,1) is a solution to the system of equations, we need to substitute the x and y values of the point into each equation and see if they produce true statements.

The first equation in the system is '3 times x plus 2', which we can write as 3x + 2. Substituting x = 1 in this equation gives us 3*1 + 2 = 5, which is not equal to the y-coordinate (1) of our input point.

The second equation is the |x - 1| + 1, which refers to the absolute value of (x minus 1) plus one. If we input x = 1, we get |1 - 1| + 1 = 1, which equals the y-coordinate (1) of our point. However, because the point didn't satisfy both equations, (1,1) is not a solution to the system.

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Answer:

e.

Step-by-step explanation:

Each side is multiplied by 5.

It is the multiplication property of equality.

Answer:

its option D

Step-by-step explanation:

The angle measures of triangle VUW is D) m∠V = 60°, m∠U = 90°, m∠W = 30°

All three angles in any triangle always upload as many as 180 degrees. So in case you best have of the angles with you, just upload them together, after which subtract the sum from 180. EX: A Triangle has three angles A, B, and C.

The method for finding the sum of the measure of the indoor angles is (n - 2) * 180. To discover the degree of 1 indoors perspective, we take that method and divide via the range of aspects n: (n - 2) * a hundred and eighty / n.

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The answer is:

The correct option is the third option;

[tex]-23\leq t\leq 50[/tex]

To find which of the options expresses the intersection of the three days as an inequality in terms of temperature "t" we need to find an inequality which starts at the lowest temperature (greater or equal) and finish at the highest temperature (less or equal).

So, we have that the lowest temperature is -23°F and the highest temperature is 50°F, there are two options for that range, but we need to consider that the temperature will range from -23° to 50°, so, the correct option is the third option;

[tex]-23\leq t\leq 50[/tex]

We can see that the inequality express that the temperature will range from -23°F being greater or equal than that, to 50°F being less or equal than that.

Have a nice day!

Answer:

[tex]\frac{15}{17}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

sin²x = 1 - cos²x

sinx = [tex]\sqrt{1-cos^2x}[/tex]

Hence

sinΘ = [tex]\sqrt{1-(8/17)^2}[/tex]

        = [tex]\sqrt{1-\frac{64}{289} }[/tex]

        = [tex]\sqrt{\frac{225}{289} }[/tex] = [tex]\frac{15}{17}[/tex]

Answer:

Step-by-step explanation:

2 sets of books

Answer:

[tex]y=5,067(0.989)^{x}[/tex]

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

y ----> the population of manatees in Florida since 2011

x ----> the time in years

a is the initial value

b is the base

we have

[tex]a=5,067\ manatees[/tex]

[tex]b=(100\%-1.1\%)=98.9\%=0.989[/tex]

substitute

[tex]y=5,067(0.989)^{x}[/tex] ----> exponential function that represent this scenario

Answer:

16/21 km

Step-by-step explanation:

The LCD here is 42.  Thus, 8  3/7 km = 8  18/42 and 7  4/6 km = 7  28/42 km.

The difference in the two distances is

 8  18/42  km

- 7   28/42 km

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

or:

 7  60/42 km         Here I have borrowed 42/42 from that 8.

- 7  28/42 km

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

     32/42 km,   or 16/21 km

Answer:

The equation that describe the situation is

[tex]b^{3}-9b^{2}-18,900=0[/tex]

Step-by-step explanation:

we know that

The volume of a square pyramid is equal to

[tex]V=\frac{1}{3}b^{2} h[/tex]

where

b is the length side of the square

h is the height of the pyramid

we have

[tex]V=6,300\ in^{3}[/tex]

[tex]h=(b-9)\ in[/tex]

substitute the values and solve for b

[tex]6,300=\frac{1}{3}b^{2} (b-9)\\ \\18,900=[b^{3}-9b^{2}]\\ \\b^{3}-9b^{2}-18,900=0[/tex]

Using a graphing calculator

[tex]b=30\ in[/tex]

[tex]h=(30-9)=21\ in[/tex]

Answer:

A is correct on edge 2022

Step-by-step explanation:

Answer:

  42 ft/s

Step-by-step explanation:

The change in velocity is given by the area under the curve from t=0 to t=6. The average acceleration over that period is (10+4)/2 = 7 ft/s^2, so the change in velocity is ...

  (7 ft/s^2)(6 s) = 42 ft/s

The velocity of the car at t=6 is 42 ft/s.

The velocity of the car at t=6 is 42 ft/s.

The change in velocity is given by the area under the curve from t=0 to t=6. The average acceleration over that period is [tex](10+4)/2 = 7 ft/s^2[/tex], so the change in velocity is ...

[tex](7 ft/s^2)(6 s) = 42 ft/s[/tex]

The velocity of the car at t=6 is 42 ft/s.

Answer:

48 minutes.

Step-by-step explanation:

Reggie can line [tex]\frac{1}{120}[/tex] of a football field in one minute.

Rosalinda can line [tex]\frac{1}{80}[/tex] of a football field in one minute.

[tex]\frac{1}{120}[/tex] + [tex]\frac{1}{80}[/tex] =  [tex]\frac{1}{48}[/tex], so together, they can line [tex]\frac{1}{48}[/tex] of a football field in one minute.

[tex]\frac{1}{48}[/tex] * 48 = 1

They can line 1 football field together in 48 minutes.

Answer:

88?

Step-by-step explanation:

Since XPY is a lot smaller and 23 degrees, 88 degrees makes the most sense.

Answer:

Out of the 6 observations when the temperature is between 90 and 99, 2 are on Thursday.

2/6 = 33%

Out of the 4 observations when the temperature is less than 90, 1 was on Monday.

1/4 = 25%

Out of the 26 observations when the temperature is greater than 89, 4 were on Friday.

4/26 = 15%

Out of the 6 observations when the temperature is between 90 and 99, 2 are on Thursday.

2/6 = 33%  

Out of the 1 observation when the temperature is between 110 and 120, none were on Sunday.

0%

To calculate probabilities of certain observations concerning different variables, we need relevant data pertaining to those variables. Without this data, it's challenging to calculate precise probabilities. In such cases, we use the closest available data or make educated assumptions.

To find the probability of different observations, we need specific data that relates to those situations. For example, to find the probability that an observation is on a Thursday when the temperature is between 90 and 99, we would need historic data that captures temperature observations on Thursdays. Similarly, other probabilities also need specific data. For instance, to know the probability of an observation being on a Monday with temperature less than 90, or a Friday where the temperature is greater than 89, we would need historic temperature measurements for these specific days. However, since the provided information doesn't include specific data needed to calculate the probabilities asked in the question, we can't provide precise probabilities. Probability in statistics is generally calculated based on relevant data that is representative of the situation of interest. In situations where it is necessary to estimate the probability without access to specific data, we might use available data that is as closely matching as possible, or might make educated assumptions.

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Answer:

The answer is 1 over 4

Step-by-step explanation:

Answer:

1/4.

Step-by-step explanation:

The spinner has 4 sections, and 1 out of those 4 is the black one, that of which we are seeing the probability of landing on it.

1 chance out of 4 for landing on black.

therefore, your answer is 1/4.

sorry if i'm late but I needed the points :)

Answer:

36 ft³

Step-by-step explanation:

The volume of a rectangular prism is computed by multiplying the length, width, and height:

V = LWH = (9 ft)(1 ft)(4 ft) = 36 ft³

Step-by-step Answer:

One of the properties of a least-squares regression line (line of best fit) is that the line always passes through the point (xbar, ybar).

Assuming the given "line of best fit" is a least-squares line, then we are given

a slope m=1.885 passing through (x0,y0)=(3.448,12.318).

Applying the standard point-slope formula:

(y-y0) = m (x-x0)

we get

y-12.318 = 1.885(x-3.448)

Expand and simplify,

y=1.885x -1.885*3.448 + 12.318, or

y=1.885(x) + 5.81852

(numbers to be rounded as precision dictates).

To find the y-intercept of the line of best fit, substitute the mean x and y values and the slope into the equation y = mx + b and solve for b. In this case, the y-intercept is 5.820.

To calculate the y-intercept of the line of best fit when you know the slope and the mean values of the x-coordinates and y-coordinates, you can use the formula for the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

Given:

We can substitute the means into the line equation:

12.318 = 1.885(3.448) + b

Now solve for b:

12.318 = 6.49836 + b

b = 12.318 - 6.49836

b = 5.81964

Therefore, the y-intercept b to three decimal places is 5.820.

Answer:

11.7

Step-by-step explanation:

a^2+b^2=c^2

10^2+6^2=c^2

100+36=c^2

add 100+36=136

square root of 136 = 11.6619037897

= 11.7

Value of x is 140

Tangent are present that means those angles are of 90° and 90° + 90° = 180°

One angle is already given 40°

By angle sum property of Quadrilateral

We can get its value

Love from India❤

Answer:

1/5

Step-by-step explanation:

If you only eat 3/5 of 1/3, you ate 3/5 × 1/3.  Multiply fractions straight across the top and straight across the bottom to get 3/15.  That reduces down to 1/5.  So you ate 1/5 of the large pizza.

Follow below steps:

The question asks how much of a pizza you ate if you initially claimed you could eat 1/3 of a large pizza but ended up eating only 3/5 of that amount. To solve this, you need to multiply the fractions. Multiplying 1/3 by 3/5 gives us:

When you multiply these two fractions, you get:

(1/3) * (3/5) = 3/15 = 1/5

Therefore, you ate 1/5 of the large pizza.

Answer:

B

Step-by-step explanation:

In slope intercept form, y = mx + b, the m is the slope, the b is the y intercept, and x and y can be subbed in from the point you are given of (1, 3).  We are told the slope, so everything we have fills in like this:

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

Now we just need to solve for b:

[tex]3-\frac{1}{4}=b[/tex] and

[tex]\frac{12}{4}-\frac{1}{4}=b[/tex] so

[tex]b=\frac{11}{4}[/tex]

Answer:

Step-by-step explanation:

[tex]12.\ a^v=1\to a^v=a^0\to v=0\\\\\text{because}\ a^0=1\ \text{for any}\ a\neq0.\\\\13.\ \ b^{-w}=\dfrac{1}{b^9}\to \dfrac{1}{b^w}=\dfrac{1}{b}\to b=9\\\\\text{because}\ a^{-n}=\dfrac{1}{a^n}\ \text{for any}\ a\neq0\\\\14.\ \dfrac{3^3}{3^y}=\dfrac{1}{9}\to\dfrac{3^3}{3^y}=\dfrac{3^0}{3^2}\to 3-y=-2\to y=5\\\\\text{used}\ \dfrac{a^m}{a^n}=a^{n-m}\\\\15.\ 5^8\cdot5^z=1\to5^{8+z}=5^0\to8+z=0\to z=-8\\\\\text{used}\ a^n\cdot a^m=a^{n+m}[/tex]

[tex]16.\ 7^n\cdot 7^m=1\to7^{n+m}=7^0\to n+m=0\to n=-m\\\\17.\ \dfrac{3^x\cdot2^2}{3^4}=\dfrac{4}{3}\to3^{x-4}\cdot2^2=3^{-1}\cdot2^2\to x-4=-1\to x=3[/tex]

Answer:

(0, 6)

Step-by-step explanation:

The given point A has coordinates (4,-2).

The mapping for a reflection over the line y=k, is given by:

[tex](x,y)\to (x,2k-y)[/tex]

Therefore the line y=2 is

[tex](4,-2)\to (4,2(2)--2)[/tex]

[tex](4,-2)\to (4,4+2)[/tex]

[tex](4,-2)\to (4,6)[/tex]

When this point is again reflected over the line x=2, we use the mapping

[tex](x,y)\to (2k-xx,y)[/tex]

[tex](4,6)\to (2(2)-4,6)[/tex]

[tex](4,6)\to (4-4,6)[/tex]

[tex](4,6)\to (0,6)[/tex]

Answer:

0,6

Step-by-step explanation:

Answer:

16.6 in

Step-by-step explanation:

The volume (V) of a pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × h

where h is the perpendicular height and area of base = 14² = 196

here V = 980, so

[tex]\frac{1}{3}[/tex] × 196h = 980 ( multiply both sides by 3 )

196h = 2940 ( divide both sides by 196 )

h = 15

Consider the right triangle formed by the height h from the vertex to the midpoint of the base and the slant height (s) ← the hypotenuse

Using Pythagoras' identity in the right triangle

s² = 15² + 7² = 225 + 49 = 274 ( take the square root of both sides )

s = [tex]\sqrt{274}[/tex] ≈ 16.6

Answer:

  D.  y = -1/5x +32/5

Step-by-step explanation:

The equation of the line passing through point (h, k) with slope m can be written ...

  y = m(x -h) +k

Filling in your given values, the equation is ...

  y = -1/5(x -(-3)) +7

  y = -1/5x -3/5 +7 . . . . eliminate parentheses

  y = -1/5x +32/5 . . . . . combine constants

Answer:

Every 70th visitor

Step-by-step explanation:

Find the least common multiple of 2, 10, and 7.

Write the prime factorization:

2 = 2

7 = 7

10 = 2×5

So the LCM is:

LCM = 2×5×7

LCM = 70

Every 70th visitor will get a bag containing all 3 items.