Which number line shows the solution to the inequality 5x-15>-65

Answer:

The answer is going to be A. [tex]8x^{3} + 16x^{2} - 4x + 15[/tex]

Step-by-step explanation:

The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

The function for this given problem is defined as follows:

y = 1.5x² + 4x - 2.

a 1.5, b 4, c -2.

By Solving the equation we get these values,

x = -3.09, hence function passes through the point (-3.09, 0).

x = 0.43, hence function passes through the point (0.43, 0).

The y-intercept of this function is given by coefficient c = -2, hence the function also passes through the point (0, -2).

The x-coordinate vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

Missing Information

The problem asks for the graph of the following function is given below:

y = 1.5x² + 4x - 2.

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The angle of depression of the escalator is approximately 10.1 degrees.

To find the angle of depression, we need to draw a right triangle where the vertical distance is the opposite side, the horizontal distance is the adjacent side, and the angle of depression is the angle opposite the hypotenuse.

Let's call the angle of depression θ. Then we have

tan(θ) = opposite/adjacent

We know the vertical distance (opposite) is 194.7 feet and the horizontal distance (adjacent) is the length of the escalator, which is 1085.5 feet. So we can plug in these values and solve for θ:

tan(θ) = 194.7/1085.5

θ = tan^-1(194.7/1085.5)

θ ≈ 10.1 degrees

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In the three-month period, the water level was 6.5 inches, 6.3 inches, and 6.7 inches, respectively. This is lower than the yearly average of 7.2 inches

Water level is a term used to describe the height of a body of water, usually in reference to an ocean, lake, river, or other body of water. It can also refer to the height of the water above sea level or other reference points.

The table indicates that the water level of the reservoir for the three-month period is lower than the yearly average. This can be seen by comparing the data in the table.

This could be due to a number of factors, including decreased precipitation and increased evaporation during the three-month period.

Ultimately, the data shows that the water level of the reservoir for the three-month period is lower than the yearly average. This could be a cause for concern in the long-term, as the water level of the reservoir could become too low to sustain local populations and ecosystems in the area.

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It will take the second skater 20 seconds to catch up to the first skater and pass him/her.

In physics, speed and motion are related concepts that describe the movement of objects in space.

Speed is a scalar quantity that measures how fast an object is moving. It is the rate at which an object covers distance, typically measured in meters per second (m/s), kilometers per hour (km/h), or some other unit of distance per unit of time.

Motion, on the other hand, is the change in position of an object over time, with respect to a reference point. In physics, motion can be described in terms of displacement, velocity, and acceleration. Displacement refers to the change in position of an object relative to a reference point, while velocity describes how fast an object is moving in a specific direction.

Acceleration refers to the rate at which an object's velocity changes over time, either by increasing or decreasing in speed or changing direction.

In summary, speed is a measure of how fast an object is moving, while motion is the change in position of an object over time.

We can start by setting up an equation to represent the distance each skater travels, with t representing the time it takes for the second skater to catch up to the first skater:

Distance traveled by the first skater = Distance traveled by the second skater + 40 meters

Using the formula distance = rate × time, we can plug in the given rates and the unknown time to get:

12t + 40 = 14t

Simplifying this equation, we get:

40 = 2t

t = 20 seconds

Therefore, it will take the second skater 20 seconds to catch up to the first skater and pass him/her.

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There will be 663 pupils if there are 17 instructors.

The discipline and study of character, structure, area, and change is mathematics. Mathematicians use rigorous deduction from carefully selected axioms and definitions to look for patterns, make new hypotheses, and establish the veracity of their findings.

Teachers Students

5                   130

10                   390

15                   585

20                   780

To find the unit rate, we need to divide the number of students by the number of teachers. For example, for the first row, the unit rate would be:

Unit rate = students/teachers = 130/5 = 26 students per teacher

We can repeat this calculation for each row:

For the second row, the unit rate is 390/10 = 39 students per teacher.

For the third row, the unit rate is 585/15 = 39 students per teacher (same as the previous row).

For the fourth row, the unit rate is 780/20 = 39 students per teacher (again, the same as the previous rows).

So, the unit rate is 39 students per teacher.

If there are 17 teachers, we can use the unit rate to find the number of students:

Number of students = unit rate x number of teachers

Number of students = 39 x 17 = 663

Therefore, if there are 17 teachers, there are 663 students.

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1.....30 | 18.97
     50 | 24.49
     60 | 26.83
     90 | 32.87

2..... 54.77 mph

a. To complete the table of values, we need to plug in the given values of d into the equation v(d) = √12d and solve for v.

For d = 30:
v(30) = √12(30) = √360 = 18.97 mph

For d = 50:
v(50) = √12(50) = √600 = 24.49 mph

For d = 60:
v(60) = √12(60) = √720 = 26.83 mph

For d = 90:
v(90) = √12(90) = √1080 = 32.87 mph

So the completed table of values is:

d | v
---|---
30 | 18.97
50 | 24.49
60 | 26.83
90 | 32.87

b. To evaluate v(250), we simply plug in the value of d into the equation and solve for v:

v(250) = √12(250) = √3000 = 54.77 mph

So the velocity of the car when the length of its skid marks is 250 feet is 54.77 mph.

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The evaluated expressions are 2, -7, -2, -12, -8, and 7.

To evaluate the expressions without using a calculator, we need to substitute the given values of the variables into the expressions and simplify.

a. Substitutex=4into the expressionx−2

=4-2

=2

b. SubstituteB=−5into the expressionB−2

=-5-2

=-7

c. Substitutew=−2into the expression−w−4

=-(-2)-4

=2-4

=-2

d. Substitutey=−3into the expression(y)4

=(-3)4

=-12

e. Substitutet=4into the expression−t2

=-(4)2

=-8

f. SubstituteR=−10into the expression−R−3

=-(-10)-3

=10-3

=7

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The total surface area of the two hemispherical domes is 6.16m^2

To find the TSA (total surface area) of two hemispherical domes, we need to first find the surface area of one hemispherical dome, and then multiply it by 2.

The surface area of one hemispherical dome can be found using the formula:

SA = 2πr^2

where r is the radius of the base of the hemisphere.

Given that the base radius of each hemisphere is 0.7m, the total diameter of each hemisphere is 1.4m (since the diameter is twice the radius), and therefore the radius is 0.7m.

So the surface area of one hemisphere is:

SA = 2π(0.7m)^2

= 3.08m^2

Therefore, the TSA of two hemispherical domes is:

TSA = 2 × SA

= 2 × 3.08m^2

= 6.16m^2

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A: The vertex of the equation f(x)=x^2+2x−8 can be found by using the formula (-b/2a, f(-b/2a)) where a=1, b=2, and c=-8. Plugging in the values gives us the vertex (-1, -9).

B: The line of symmetry can be found by using the formula x=-b/2a. Plugging in the values gives us the equation x=-1.

C: The x-intercepts can be found by setting f(x)=0 and solving for x. This gives us the equation x^2+2x-8=0. Using the quadratic formula, we get x=(-2±√(2^2-4(1)(-8)))/(2(1)). Simplifying gives us x=(-2±√36)/2, which gives us the x-intercepts (-5.24, 1.24). The y-intercept can be found by setting x=0 and solving for y. This gives us the equation y=-8.

D: The domain of the function is all real numbers, or (-∞,∞).

E: The range of the function is all real numbers greater than or equal to -9, or [-9,∞).

F: The increasing interval of the function is (-1,∞).

G: The decreasing interval of the function is (-∞,-1).

H: The end behavior of the function is as x→+∞,y→∞ and as x→-∞,y→∞.

I: To graph the function, first plot the vertex (-1, -9) and the x-intercepts (-5.24, 0) and (1.24, 0). Then, plot two additional points on either side of the vertex, such as (-2, -6) and (0, -8). Connect the points with a smooth curve to complete the graph.

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Calculate acceleration using this equation: acceleration = delta v / time. expressions  To solve for acceleration, enter the values you calculated for delta v and the amount of time it took the object to change directions.

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

An object's acceleration adjusts together with its direction. You may use the next several stages to get the object's acceleration at this point:

Calculate the object's initial and ultimate velocities before and after a direction change.

Subtract the end velocity from the beginning velocity to determine the change in velocity (delta v). This will reveal how much the velocity has changed.

Establish the time difference. This is the amount of time it takes for the velocity to switch from one direction to the other.

Calculate acceleration using this equation: acceleration = delta v / time. To solve for acceleration, enter the values you calculated for delta v and the amount of time it took the object to change directions.

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Minimum - 2

First Quartile - 4

Median - 8

Third Quartile - 13

Maximum - 15

Simplifying the exponents gives us n^(30)p^(-120) and this is our final simplified answer, expressed using exponents.

To simplify the expression (n^(-3)p^(12))^(-10), we can use the power rule of exponents. The power rule states that when you have an exponent raised to another exponent, you multiply the exponents together.

So, in this case, we would multiply the exponents -3 and -10 together for the n term, and the exponents 12 and -10 together for the p term. This would give us:

n^((-3)*(-10))p^((12)*(-10))

Simplifying the exponents gives us:

n^(30)p^(-120)

And this is our final simplified answer, expressed using exponents.

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The length of the top surface in standard form is [tex]H(x) = (60x^2 + 16x + 1)/(6x + 1)[/tex]

Algebraic expressions are mathematical phrases that involve numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division. They can also involve exponents, roots, and other mathematical symbols.

In algebra, variables are often represented by letters, such as x, y, or z, and they can take on different values. The values of the variables can be manipulated using the arithmetic operations to obtain new expressions that represent relationships between the variables.

For example, the expression 3x + 2 is an algebraic expression that involves the variable x. It represents a relationship between x and a number that is 2 more than 3 times x.

Algebraic expressions are used to represent mathematical relationships and solve problems in many different areas, including science, engineering, economics, and finance. They are an essential tool for understanding and manipulating mathematical concepts and formulas.

The area of a rectangle can be found by multiplying its length and width. In this case, the area of the top surface is given by the function [tex]F(x) = 66x^2 + 17x + 1[/tex], and the width of the top surface is given by the function [tex]G(x) = 6x + 1[/tex]. Therefore, the length of the top surface can be expressed as:

Length x Width = Area

[tex]Length x (6x + 1) = 66x^2 + 17x + 1[/tex]

Expanding the left side of the equation, we get:

[tex]6x^2 + x Length = 66x^2 + 17x + 1[/tex]

Bringing all the terms to one side, we get:

[tex]60x^2 + 16x + 1 - Length x = 0[/tex]

Rearranging the terms, we get:

[tex]Length x = 60x^2 + 16x + 1[/tex]

Finally, dividing both sides by the width function G(x), we get the expression for the length of the top surface in standard form:

[tex]H(x) = (60x^2 + 16x + 1)/(6x + 1)[/tex]

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The quotient of -2 1/2 and -3 1/3 is = 9/16

In the end, the quotient is what we obtain when we divide a number. Putting things into equal groups is a division operation in mathematics. It is symbolised by the glyph (). For instance, there are three groups of 15 balls each that must be distributed equally.

When we divide the balls into three equal groups, the division formula is 15/3 = 5. The quotient is 5 in this case. This indicates that each set of balls will include five balls.

In this case let us first convert the improper fractions into proper fractions:

-2 1/2 = -4+1/2 = -3/2

-3 1/3 = -9+1/3 = -8/3

Now to find the quotient we have to multiply the fraction's reciprocals:

-3/2 × 3/-8

= -9/-16

=9/16

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Answer:

2. (x^2 + 3y)(x^2 - 3y)

Step-by-step explanation:

According to algebraic formula:

x^2 - y^2 = (x + y)(x - y)

We have x^4 - 9y^2 => (x^2)^2 - (3y)^2

=> (x^2 + 3y)(x^2 - 3y) or  (x^2 - 3y)(x^2 + 3y)

Answer:

(2) (x²-3y)(x²+3y)

Step-by-step explanation:

x⁴-9y²

Factor/GCF:

x⁴ = (x²)(x²)

-9y² = (-3y)(3y)

Combine:

(x²-3y)(x²+3y)

Answer:

(a) The probability that a selected component of this type will last more than 4 years is 0.69.

(b) The probability that a two-year-old component of this type will last an additional 4 years is 0.57.

(c) The 25th percentile of the lifetimes of such components is 3.38 years.
Explanation:

(a) The Gamma distribution has the following probability density function:
f(x) = (λ^α/Γ(α))x^(α-1)e^(-λx)
Where α is the shape parameter, λ is the rate parameter, and Γ(α) is the Gamma function. The mean and variance of the Gamma distribution are:
Mean = α/λ
Variance = α/λ^2
Given that the mean is 5 years and the variance is 25 years^2, we can solve for α and λ:
5 = α/λ
25 = α/λ^2
Solving for α and λ gives us α = 5 and λ = 1. So the probability density function is:
f(x) = (1^5/Γ(5))x^(5-1)e^(-1x)
The probability that a selected component will last more than 4 years is the integral of the probability density function from 4 to infinity:
P(X > 4) = ∫_4^∞ f(x) dx = 0.69

(b) The probability that a two-year-old component will last an additional 4 years is the conditional probability:
P(X > 6 | X > 2) = P(X > 6 and X > 2)/P(X > 2) = P(X > 6)/P(X > 2) = 0.57

(c) The 25th percentile of the lifetimes of such components is the value of x such that the cumulative distribution function is 0.25:
F(x) = 0.25
∫_0^x f(x) dx = 0.25
Solving for x gives us x = 3.38 years.

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Answer:

Step-by-step explanation

So first do 12-6=6 then multiply 14x6 which is 84 so 84 bags in 14 weeks is 3 and a half months.

The number of total books there to start with were 70

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Let's start by using "x" to represent the total number of books on the bookshelf before Kian removed any books.

According to the problem, 40% of the books on the shelf were non-fiction, which means that 60% of the books were fiction. We can express this as an equation:

0.4x = number of non-fiction books

0.6x = number of fiction books

If Kian removed 6 non-fiction books, there are now 22 non-fiction books remaining, so we can write:

0.4x - 6 = 22

Solving for x, we can add 6 to both sides and then divide by 0.4:

0.4x = 28

x = 70

Therefore, there were 70 books in total on the bookshelf before Kian removed any books.

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step 1: convert to improper fraction

57/7 - 26/7

step 2: subtract numerators

31/7

step 3: change to a mixed number

4 3/7

The correct answer is B. 3.

To solve this problem, we can plug in the value of Q and see how the value of p changes.
If Q = 1, then:
p = 11 - 3(1) = 11 - 3 = 8
If Q = 2, then:
p = 11 - 3(2) = 11 - 6 = 5
As we can see, when Q increases by 1 unit, the value of p decreases by 3.

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The original price of the given pair of shoes is; £59.4

It is known the original price is:

OP=(100+DP)/100X.... (i), where,

OP = Original Price

CP = Cost Price = £54,

DP = Discount percentage = 10%.

Substituting the values in equation (i), we get:

OP = (100+10)/100X54 ,

Or, OP = 110/100x54 = 59.4.

Therefore the Original Price of the Pair of Shoes is £59.4.

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The value of ratio of lime juice to mint is 3/2.

And the amount of lime juice is 3/2 of the amount of mint leaves.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

The ratio of lime juice to mint is 3/4: 1/2. therefore the value of this ratio = 3/4 ÷ 1/2 = 3/2

therefore the amount of lime juice = 1/2 × 3/2 = 3/4

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Answer: See attached.

Step-by-step explanation:

     The first one is incorrect because this equation shows 5 / 2, not 2/5.

     The second one is correct. 7/4 = 7/4.

     The third one is also correct. 12/4 = 12/4.

     It can help to rewrite both sides of the equation in the same format to make it easier to compare.

Therefore, the value of angle A is approximately 76.16°, and the value of angle C is approximately 8.24°.

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is the simplest polygon that can be formed in Euclidean geometry, and it is widely studied in mathematics and geometry. Triangles can be classified based on their sides and angles. By side length, a triangle can be classified as equilateral (all sides are equal), isosceles (two sides are equal), or scalene (no sides are equal). By angle measure, a triangle can be classified as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is exactly 90 degrees). Triangles have many interesting properties and are used in a variety of applications, including in architecture, engineering, and physics.

Here,

Sure, I can help you with that! We can use the Law of Cosines to find the values of angles A and C in triangle ABC. The Law of Cosines states that:

c² = a² + b² - 2ab cos(C)

where c is the side opposite angle C.

First, let's find the value of side c:

c² = a² + b² - 2ab cos(C)

c² = (782)² + (1435)² - 2(782)(1435) cos(115.6°)

c² = 613524 + 2055225 - 2238015.52

c²  = 594733.48

c = √(594733.48)

c ≈ 771.1 cm

Now, we can use the Law of Cosines again to find angle A:

cos(A) = (b² + c² - a²) / 2bc

cos(A) = (1435² + 771.1² - 782²) / (2 * 1435 * 771.1)

cos(A) = 0.2354

A = cos⁻¹*²³⁵⁴⁾

A ≈ 76.16°

Finally, we can find angle C by using the fact that the angles in a triangle add up to 180°:

C = 180° - A - B

C = 180° - 76.16° - 115.6°

C ≈ 8.24°

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Answer: C. 1/2

Step-by-step explanation:

The coefficient is the number being multiplied by q. The sum is the additive total. To add fractions, they need a common denominator.

2/3 = 4/6

Adding a negative is the same as subtracting.

4/6 + (-1/6) = 4/6 - 1/6 = 3/6 = 1/2

Hope this helps!

The velocity of the car is 80m/s

v= u + at²

The parameters given are:

velocity= ?

initial velocity(u)= 0

acceleration(a)= 5

time(t)= 4

The velocity can be calculated as follows

v= 0 + 5(4²)

v= 0 + 5(16)

v= 0 + 80

v = 80

Hence the velocity of the car is 80m/s

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The length of QS to 3 significant figures is 26.9 cm. QS is the side of the triangle that is adjacent to the angle of 27°.

An adjacent angle is an angle that shares a common side and a common vertex with another angle. Adjacent angles are commonly seen when two lines intersect, forming four angles.

QS is the side of the triangle that is adjacent to the angle of 27°. To calculate the length of this side, we can use the Law of Sines. The Law of Sines states that for any triangle with sides a, b and c and angles A, B and C respectively, the following equation holds true:

a/sin A = b/sin B = c/sin C

Therefore, for our triangle, we can use the equation as follows:

11/sin 27° = QS/sin 90°

Rearranging this equation, we can solve for QS:

QS = (11/sin 27°) x sin 90°

QS = 26.9 cm

Therefore, the length of QS to 3 significant figures is 26.9 cm.

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The response to the given question would be that As a result, when equation comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

When two statements are connected by a mathematical equation, the equals sign (=) implies equality. An equation in algebra is a mathematical statement that proves the equivalence of two mathematical expressions. For instance, the equal sign separates the numbers in the equation 3x + 5 = 14. It is possible to determine the relationship between the two sentences on either side of a letter using a mathematical formula. The logo for the particular piece of software is frequently the same. as 2x - 4 = 2, for instance.  

From Quesnel Lake to Lake Baikal, the distance is 506 metres.

Lake Baikal is 5369 ft (or 1637.74 m) deep (one foot is equal to 0.3048 m).

Ratio of depths is 506 / 1637.74 0.31 (Depth of Quesnel Lake/Deep of Lake Baikal).

Around 31% of Lake Baikal's depth is in Quesnel Lake.

Great Slave Lake to Quesnel Lake: Quesnel Lake is 506 metres deep.

Great Slave Lake's depth is 2015 feet, or 614.18 metres (1 foot = 0.3048 m).

Ratio of depths is 506 / 614.18 0.82 (Depth of Quesnel Lake / Depth of Great Slave Lake).

Hence, Quesnel Lake's depth is equivalent to 82% of Great Slave Lake's depth.

As a result, when comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

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a) The three measures of central tendency are the 18 (mean), 14.5 (median, and 10 and 21 (mode).

(b) The range, interquartile range, variance and standard deviation for these data is 19, 12, 39.636, and 6.296, respectively.

(a) The three measures of central tendency are the mean, median, and mode.

Mean: (15 + 10 + 7 + 24 + 22 + 12 + 17 + 10 + 21 + 23 + 26 + 21)/12 = 18

Median: (12 + 17)/2 = 14.5

Mode: 10 and 21 (both appear twice in the data set)

b) Range: 26 - 7 = 19

Interquartile Range: Q3 - Q1 = 22 - 10 = 12

Variance: SS/11 = (15-18)² + (10-18)² + (7-18)² + (24-18)² + (22-18)² + (12-18)² + (17-18)² + (10-18)² + (21-18)² + (23-18)² + (26-18)² + (21-18)² / 11 = 39.636

Standard Deviation: √39.636 = 6.296

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