Which statement is true about solutions to 11 -x<7

Answer:

The 18th term would be "-70"

Answer:

-70

Step-by-step explanation:

The solutions of the given quadratic equation is;  (1/4) + √7i/4 and  (1/4) - √7i/4

We are given the quadratic equation as;

2x² - x + 1 = 0

To solve this to find the root, we will use the quadratic formula which is given by;

x = [-b ± √(b² - 4ac)]/2a

Now, from the given quadratic equation, we can say that the values of a, b and c are;

a = 2; b = -1 and c = 1

Thus;

x = [-(-1) ± √((-1)² - 4(2 * 1))]/2(2)

x =  [1 ± √(1 - 8)]/4

x = [1 ± √(-7)]/4

x = (1/4) ± √7i/4

Thus;

x = (1/4) + √7i/4 and  (1/4) - √7i/4

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Answer: -0.6

Step-by-step explanation:

Probability of people needing corrective shoes or dental work is 0.36.

The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive".

Here, the two events getting corrective shoes and getting dental work are not mutually exclusive events.

P(corrective shoes or dental work) = P(corrective shoes) + P(dental work) - P(corrective shoes and dental work)

P(corrective shoes or dental work)  = 0.16 + 0.23 - 0.03

P(corrective shoes or dental work)  = 0.36

Hence, the probability of people needing corrective shoes or dental work is 0.36.

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Using the Heron's formula, the area of the triangle is: D. 95 square inches.

Area = √[s(s - a)(s - b)(s - c)] where s is half the perimeter, or (a + b + c)/2.

Given the following:

s = semi-perimeter = 1/2(50) = 25 in.

a = length of side a = 22 in.

b = length of side b = 13 in.

c = length of side c = 50 - 22 - 13 = 15 in.

Plug in the values

Area = √[25(25 - 22)(25 - 13)(25 - 15)]

Area = √[25(3)(12)(10)]

Area ≈ 95 square inches.

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Answer:

d

Step-by-step explanation:

The system of equations is -x + y = 4 and -2x + y = 0

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system

The above is represented in the (a) part of this solution

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

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The absolute value of the number upon the given evaluation is; 22.

It follows from the task content that the number given is; -27 on the number line and subsequently, there's a movement of 5 integers to the right.

On this note, the absolute value of the result upon the evaluation is; |-27+5| = |-22| = 22.

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Answer: D. 2x + 4x = 150

Step-by-step explanation:

We know that the section of 2x and 4x together equal 150 degrees because they are vertical angles.  The 150 degrees is vertical to the section with 2x and 4x.  So you would use equation D to solve for x.

In order to create the reverse of the 150 angle, when two angles meet, 2x and 4x are combined.

Thus, the angles formed by 2x, 4x, and 150 are vertical. We know that vertical angles are equivalent, .Therefore, the labeled angles are equivalent.

Answer :-

[tex]\bf D. \: 2 {x}^{o} + 4 {x}^{o} = 15 {0}^{o} [/tex]

Answer:

30%   discount

Step-by-step explanation:

(35 - 24.50) / 35  * 100% = 30%

Step-by-step explanation:

Volume of the right circular cone=31πr2h=31×π×6×6×10=120πcm3

Answer:

Volume =  405π unit^3

which is

1272.35 unit^3 to nearest hundredth.

Step-by-step explanation:

Volume of the given cone

= 1/3 πr^2 h

= 1/3π(6)^2*10

=  120π unit^3.

The cone similar to it with radius 9 will have a volume equal to

(9/6)^3 times the given cone

= 120π * 729/216

= 405π unit^3.

Answer:

[tex](1*10^{15} )(5*10^{14})[/tex] or 1.5×10^14

Step-by-step explanation:

The answer is [tex](1*10^{15} )(5*10^{14})[/tex] or 1.5×10^14.

Hope this helps!

Mr. Cahn’s total earnings in a year is $18,900.

The total earnings is a function of the annual salary, commission and Christmas bonus.

Total earnings = annual salary + commission + Christmas bonus

Commission = 6% x (160,000 - 20,000)

6% x $140,000

0.06 x 140,000 =  $8,400

Total earnings =  $8,400 + 10,000 + $500 = $18,900

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Based on the information provided, it can inferred that letter A is equivalent to 4.

The image shows B + B+ A = A. This is only possible if letter adding 2 letters B is equal to 10. Now 10/2 = 5. This means B = 5.

It is known 5 + A + A = A. This is only possible is A is 4. 5 + 4+ 4 + 1 (from the previous addition) = 4 (+2 that is added in the next column).

Note: This question is incomplete below I add the missing image.

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Answer:

x = y = 6.5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

the triangle is isosceles, both base angles are 45° then the 2 legs are congruent , that is x = y

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 13[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = y = 6.5[tex]\sqrt{2}[/tex]

Answer:

[tex]\huge\boxed{\sf 8:32\ AM}[/tex]

Step-by-step explanation:

Woke up = 7:30 AM

Time to:

Altogether:

= 14 + 9 + 39 min

(As we know that, 1 hour = 60 minutes)

So,

Time he reached the school:

7 hr 30 min + 1 hr 2 min

Combine like terms

7 hr + 1 hr + 30 min + 2 min

OR

[tex]\rule[225]{225}{2}[/tex]

Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to finish his breakfast and 39 minutes to commute to school. At what time did he reach the school?

In this question we are asked to calculate the time paul reach the school.

Altogether time paul took to get ready, to finish his breakfast and to commute to school.

(14 + 9 + 39) minutes

→ (23 + 39) minutes

→ 62 minutes

Now we will convert minutes into hour.

62 ÷ 60

→ 1 hr 2 min

Now we will calculate the time he reached his school.

7 hr + 30 + 1 hr 2 min

[tex]\begin{array}{cc}7 \sf{hrs} \: & \: 30 \sf{min} \\ \underline{1 \: \sf{hr}} & \underline{2 \sf{min} } \\ \pmb{8 \sf{hrs}}& \pmb{32 \sf{min}}\end{array}[/tex]

He will reach the school at 8:32 AM.

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.

Slope:

−

1

3

y-intercept:

(0 , 3)

Any line can be graphed using two points. Select two

x

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

y

values

Graph the line using the slope and the y-intercept, or the points.

Slope:

−

1

3

y-intercept:

(0 , 3)

The quadrants of the points are

The points are given as:

A(2, 4)    B(0, -3)   C(1, -1)

E(-4,1)     G(-3,-2)   I(0, 2)

D(3, 3)     F(2,0)    H(-2, 3)

J(-1,-4)

Next, we plot each coordinate on a graph (see attachment)

From the attached graph, we have the following categories

Quadrant 1: Points A and D

Quadrant 2: Points E and H

Quadrant 3: Points G and J

Quadrant 4: Points C

x-axis: Point F

y-axis: Point B and I

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The CORRECT answer is Option C.

.

.

Mark BRAINLIEST!

Answer:

A= 54

B=3

Step-by-step explanation:

I hope this helps!

The equation of the circle with a center (-5, -6) and a radius of 5 is (x + 5)² + (y + 6)² = 25.

The standard equation for writing the equation of a circle is: (x - h)² + (y - k)² = r².

Given the following:

Center (-5, -6) = (h, k)

Radius = 5 = r

Plug in the values into the formula

(x + 5)² + (y + 6)² = 5²

(x + 5)² + (y + 6)² = 25

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The best interpretation of 0.8^a in this exponential equation is that: C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = aeˣ

Based on the information provided, we can logically deduce that the atmospheric pressure (p) exerted on an airplane flying at an altitude of a miles above sea level is defined by the following exponential function:

p = 14.63 × 0.8^a

Next, we would evaluate as follows;

At a = 0, we have:

p = 14.63 × 0.8^(0)

p = 14.63 psi.

At a = 1, we have:

p = 14.63 × 0.8^(1)

p = 11.704 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(2)

p = 9.3632 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(3)

p = 7.4906 psi, and this is 20% less than a mile before.

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Complete Question:

Atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below. What is the best interpretation of 0.8^a in this equation?

p = 14.63 × 0.8^a

A. If the airplane reaches the outer extent of the Earth's atmosphere, the atmospheric pressure will be 0.8 psi.

B. If the airplane is at sea level, the atmospheric pressure will be 0.8 psi.

C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

D. For each mile that the altitude increases, the atmospheric pressure increases 20%.

The equation of the function is −3<x<1. See the explanation below.

Given the graph of function f is a parabola,

Thus, equation of parabola  is y=(x+3)(x+1)

⇒y=x² +4x+3

⇒y−3+2²

= x²+2× x ×2+2²

⇒y+1=(x+2)²

We can rewrite this as

 (x+2)² =4× (1/4) ×(y+1)

Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,

(h,k)≡(−2,−1)

Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1

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If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point  of view,

Toss a coin twice, and then then roll a 6-sided number cube.

How can he play a statistically fair game to get exactly 24 outcomes?

The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.

The first of the alternatives is the only one with a sample space of 24 elements.

Flip two coins, then roll a D6.

The results of each coin toss are 2:  (tails and heads).

There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)

The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:

C = 2 × 2 × 6

C = 24

Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.

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The algebraic expression for: the sum of a number and 5 decreased by twice the number is (n + 5) - 2n

let

sum of a number and 5

= n + 5

decreased by twice the number

= -2(n)

= - 2n

sum of a number and 5 decreased by twice the number

= (n + 5) - 2n

= n + 5 - 2n

= 5 - n

Therefore, the algebraic expression which can be used to represent; the sum of a number and 5 decreased by twice the number is (n + 5) - 2n

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Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;

a. The height of the tree is approximately 31.2 m.

b. i. The distance of Q from the base of the tree is 50•√5 m.

ii. The angle of elevation of the top of the tree from Q is approximately 15.6°

iii. The bearing of the tree from Q is 296.565°

a. tan(32°) = Height/50

Height = 50 × tan(32°) = 31.243 m.

b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;

d = √(100² + 50²) = 50•√5

ii. The angle of elevation is given by trigonometric ratios as follows;

[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]

Which gives;

[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]

iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;

Angle = arctan(50/100) ≈ 26.565°

The angle between the direction north of Q and a line from Q to the tree is therefore;

90° - 26.565° = 63.435°

The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;

Bearing = 360° - 63.435° = 296.565°

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Answer: $37.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

sin(28) = 2184 / x

x= 2184/ sin(28) = 2184 / 0.4694 = 4652.75

4652.75 / 12  =  387.7 ft

ANSWER: 387.7ft

In the given case, The length of the zipline needed is approximately 96.7 feet.

To find the length of the zipline needed, we can use trigonometry. Let's start by drawing a sketch to visualize the problem. | | zipline | | | | | | | | | | John | Building 28°

John's location, with the angle of elevation labeled as 28°. John is 182 feet away from the base of the building, and he is 71.5 inches tall.

To find the length of the zipline, we can use the tangent function.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is John's height, and the adjacent side is the distance between John and the building. Using the tangent function, we have: tan(28°) = opposite / adjacent

We want to find the length of the zipline, which is the hypotenuse of the right triangle formed by John, the building, and the zipline. Let's call this length "x".

Therefore, we can rewrite the equation as: tan(28°) = 71.5 inches / 182 feet To solve for x, we need to convert the units so that they match.

Let's convert inches to feet: 71.5 inches = 71.5 inches * (1 foot / 12 inches) ≈ 5.96 feet (rounded to the nearest hundredth)

Now, let's solve for x: tan(28°) = 5.96 feet / 182 feet

To isolate x, we can multiply both sides by 182 feet: x ≈ tan(28°) * 182 feet Using a calculator, we find that tan(28°) ≈ 0.5317.

Multiplying this by 182 feet, we get: x ≈ 0.5317 * 182 feet ≈ 96.7 feet (rounded to the nearest tenth) .

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The ship's horizontal distance from the lighthouse is 1930.59 feet. Using trigonometric ratio 'tanθ' the distance is calculated.

The trigonometric ratios are used for determining the lengths of the right-angled triangle. There are six basic trigonometric ratios. they are:

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

cosec θ = hypotenuse/opposite

cot θ = adjacent/opposite

It is given that,

The height of the bacon-light is 135 feet above the water

Consider the horizontal distance between the boat and the lighthouse = x feet

The angle of elevation is given as 4°

Constructing a model as below in the figure.

From the trigonometric ratios, we have

tan θ = 135/x

⇒ tan 4° = 135/x

⇒ x = 135/tan 4°

∴ x = 1930.589 feet ≅ 1930.59 feet (rounding to the nearest hundredth of a foot)

Therefore, the ship's horizontal distance from the lighthouse is 1930.59 feet.

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Please see the explanation of this question to see procedure for the dilation of the triangle ABC and the image attached below to know the result.

In this question we must apply a kind of rigid transformation known as dilation. A dilation of a point around a point of reference is defined by the following operation:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]     (1)

Where:

Let assume that the point P is the origin of a rectangular system of coordinates. Then, the coordinates of the three vertices of the triangle ABC respect to the origin are: A(x, y) = (- 1, 2), B(x, y) = (- 1, - 1), C(x, y) = (2, 0).

Then, the vertices of the resulting triangle A'B'C' are, respectively:

A'(x, y) = (0, 0) + 3 · [(- 1, 2) - (0, 0)]

A'(x, y) = (- 3, 6)

B'(x, y) = (0, 0) + 3 · [(- 1, - 1) - (0, 0)]

B'(x, y) = (- 3, - 3)

C'(x, y) = (0, 0) + 3 · [(2, 0) - (0, 0)]

C'(x, y) = (6, 0)

Finally, we draw the resulting triangle with the help of a graphing tool.

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