3. Consider the expression 4x + 15.
(a) Write a real-world problem that can be solved using the expression. What does the variable represent
in your problem?

The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

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Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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Answer:

60 slices

Step-by-step explanation:

1 pizza = 10 slices

6 pizzas = 10 slices * 6 = 60 slices

Answer:

86m^2

Step-by-step explanation:

Answer:

A) ∃y(¬P(y))

B) ∀y(P(y) ^ Q(y))

C) ∀y(P(y) ^ Q(y))

D) ¬∃y(P(y) ^ Q(y))

E) ∃y(¬P(y) ^ Q(y))

Step-by-step explanation:

We will use the following symbols to answer the question;

∀ means for all

∃ means there exists

¬ means "not"

^ means "and"

A) Something(y) is not in the correct place is represented by;

∃y(¬P(y))

B) For All tools are in the correct place and are in excellent condition, let all tools in the correct place be P(y) and let all tools in excellent condition be Q(y).

Thus, we have;

∀y(P(y) ^ Q(y))

C) Similar to B above;

∀y(P(y) ^ Q(y))

D) For Nothing is in the correct place and is in excellent condition:

It can be expressed as;

¬∃y(P(y) ^ Q(y))

E) For One of your tools is not in the correct place, but it is in excellent condition:

It can be expressed as;

∃y(¬P(y) ^ Q(y))

Answer:

x<1

Step-by-step explanation:

[1x + 1]< 2

Simplify both sides of the inequality.

x+1<2

Subtract 1 from both sides.

x+1−1<2−1

x<1

Answer:

x<1

On the graph line, the circle is open on number 1 and is going left

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

Answer:

$13 per movie

Step-by-step explanation:

Each movie costed $13 because if Jessica had $95 to spend on 6 movies, and she had $17 after buying all of them, the 6 movies costed a total of $78, and 78 divided by 6=$13 per movie. Hope it helps!

Answer:

13

Step-by-step explanation:

95-17 = 78.

then divide 78 by 6 which equals 13

Heres the answer welcome btw

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To solve this problem, we need to perform the indicated operations in order. The first step is to simplify the expressions inside the parentheses.

(3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

The next step is to combine like terms within each parentheses:

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

Finally, we can add the two expressions:

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

= 56x - 3x² - 8x + 2x³ + 3 + 7

= 56x - 3x² - 8x + 2x³ + 10

The final answer is 56x - 3x² - 8x + 2x³ + 10.

Equation of the vertical line passing through point (-3, -5) is given by x = -3.

As given in the question,

Line passes through the point (-3, -5)

It represents the x- coordinate is equal to -3

And y- coordinate is equal to -5.

Condition for the line is given as vertical line.

Vertical line represent the value of x- coordinate remain constant.

It represent x-intercept

x = -3

x-intercept represents the equation of the vertical line.

Therefore, equation of the vertical line passing through point (-3, -5) is given by x = -3.

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9514 1404 393

Answer:

  x ≥ -8

Step-by-step explanation:

The absolute value does nothing when its argument is non-negative.

  x +8 ≥ 0

  x ≥ -8 . . . . . . . subtract 8 from both sides

Answer:

Well, if Alice buys 12 shirts which each cost $18.99 the equation would be 18.99 * 12 which = 227.88

Alice spent $227.88 on 12 shirts

Step-by-step explanation:

Answer:

Well, if Alice buys 12 shirts which each cost $18.99 the equation would be 18.99 * 12 which = 227.88

Step-by-step explanation:

Given:

The diagram of a cone.

To find:

The lateral area, surface area and volume of the cone.

Solution:

From the given diagram, we get

Radius of the cone = 6

Slant height of the cone = 10

Suppose \(h\) be the height of the cone.

According to Pythagoras theorem:

\(hypotenuse^2=Perpendicular^2+Base^2\)

Using the Pythagoras theorem, we get

\(10^2=(6)^2+h^2\)

\(100=36+h^2\)

\(100-36=h^2\)

\(64=h^2\)

Taking square root on both sides, we get

\(\sqrt{64}=h\)

\(8=h\)

The lateral area of a cone is:

\(A_L=\pi rl\)

\(A_L=\pi (6)(8)\)

\(A_L=48\pi\)

The surface area of a cone is:

\(A_S=\pi rl+\pi r^2\)

\(A_S=\pi (6)(8)+\pi (6)^2\)

\(A_S=48\pi +36\pi\)

\(A_S=84\pi\)

Volume of cone is:

\(V=\dfrac{1}{3}\pi r^2h\)

\(V=\dfrac{1}{3}\pi (6)^2(8)\)

\(V=\dfrac{288}{3}\pi \)

\(V=96\pi \)

Hence, the lateral area of a cone is \(48\pi\) sq. units, the surface area of a cone is \(84\pi\) sq. units and the volume of the cone is \(96\pi\) cubic units.

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

D. 32x² - 50

Step-by-step explanation:

P = perimeter (units²)

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

P = 8x² + 20x - 20x - 50 + 12x² + 30x + 12x² - 30x

P = 32x² - 50

Answer:

4x + 7x - 2 + 5x - 10 = 180

16x - 12 = 180

16x = 192

x = 12

m<A= 4x = 4(12) = 48

m<B = 7x - 2 = 7(12) - 2 = 84 - 2 = 82

m<C = 5x - 10 = 5(12) - 10 = 60 - 10 = 50

Step-by-step explanation:

.

Answer:

Step-by-step explanation: To find (f+g)(x), we simply add the two functions:

(f+g)(x) = f(x) + g(x)

= (3x - 5) + (7x - 3)

= 10x - 8

Therefore, (f+g)(x) = 10x - 8.

To find (f-g)(x), we subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

= (3x - 5) - (7x - 3)

= -4x - 8

Therefore, (f-g)(x) = -4x - 8.

From the pie graph,

14% chose mathematics

24% chose ELA

22% chose science

27% chose social studies

The total number of students is 140

To know the number of students that chose math

Since 14% of the class chose maths

To calculate the number of students that chose maths

Then, Total number of students that chose maths= Percentage of the class that chose maths x total number of students

Total number of students = 140

Percentage of the class that chose maths = 14%

Total number of students that chose maths = 14/100 x 140

= 0.14 x 140

= 19.6

Approximately 20

The number of students that chose maths is 20

To know the number of people that chose Elective

Firstly, we will need to sum up the percentage

14 + 24 + 22 + 27 + E = 100

87 + E = 100

Make E the subject of the formula

E = 100 - 87

E = 13%

Therefore 13% of the class chose ELECTIVE as their favorite class

To calculate the number of students that chose Elective as their favorite class

Then, The number of students that chose ELECTIVE = Percentage of the class x total number of students

The number of students = 13% x 140

The number of students = 13/100 x 140

The number of students = 0.13 x 140

The number of students = 18.2 students

Approximately 18 students

The number of students that chose elective is 18

Question 3

since 24% of the class chose ELA

Then the number of students that chose ELA = 24% x 140

= 0.24 x 140

= 33.6

Approximately 34

Since 34 students chose ELA

Then, the total number of students that did not chose ELA is

= Total number of students - Number of students that chose ELA

= 140 - 34

= 106 students

106 students did not chose ELAof studeE = 1

Answer:

See below for answers

Step-by-step explanation:

Problem 1

\(\frac{1}{sin\theta}=2cos\theta\: ; \: 0\leq\theta < 2\pi\\\\1=2sin\theta cos\theta\\\\1=sin2\theta\\\\\frac{\pi}{2}+2\pi n=2\theta\\ \\\frac{\pi}{4}+\pi n=\theta\\ \\\theta=\bigr\{\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\bigr\}\)

Therefore, the second option is correct.

Problem 2

\(cos(2x)+1=sin(x)+2\:;\: 0\leq x < 2\pi\\\\1-2sin^2x+1=sin(x)+2\\\\-2sin^2x=sin(x)\\\\0=2sin^2x+sinx\\\\0=sinx(2sinx+1)\)

\(0=sinx\\\\x=\pi n\\\\x=0,\pi\)

\(0=2sinx+1\\\\-1=2sinx\\\\-\frac{1}{2}=sinx\\ \\x=\frac{7\pi}{6}+2\pi n,\frac{11\pi}{6}+2\pi n\\\\x=\frac{7\pi}{6},\frac{11\pi}{6}\)

Therefore, the solution set is \(x=\bigr\{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\bigr\}\), making the second option correct.

Problem 3

\(2cos^2x=-cosx\: ;\: 0^\circ\leq x < 360^\circ\\\\2cos^2x+cosx=0\\\\cosx(2cosx+1)=0\)

\(cosx=0\\\\x=\frac{\pi}{2}+\pi n\\ \\x=90^\circ+180n^\circ\\\\x=90^\circ,270^\circ\)

\(2cosx+1=0\\\\2cosx=-1\\\\cosx=-\frac{1}{2}\\\\x=\frac{2\pi}{3}+2\pi n,\frac{4\pi}{3}+2\pi n\\ \\x=120^\circ+360n^\circ,240^\circ+360n^\circ\\\\x=120^\circ,240^\circ\)

Therefore, the solution set is \(x=\bigr\{90^\circ,120^\circ,240^\circ,270^\circ\bigr\}\), making the fourth option correct

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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Answer:

Neither is correct

Step-by-step explanation:

Look at each side of the smaller figure and compare it to the larger figure. That will give you the scale: (Larger figure length)/(Smaller figure length)

Let's take the base
Smaller figure is 6 units
Larger figure is 9 units

Scale = 9/6 = 1.5

Take the vertical height
Smaller figure = 4

Larger figure = 8
So here the scale is 2

Scaling is inconsistent for different sides of the figure

So neither of them is right. For a figure to be scaled, all its sides must be scaled by the same number

Step-by-step explanation:

To know wgich scale factore the Original sketch was increased with Compare the measurements of the original sketch and the student's sketch.

HOW?

do the proportion with relations to each and every side to see by how much each side increased.

For the bases it will be>>>>>>> The base of the student's sketch/ The base of the Original sketch(distance)

=10/7

10/7Adjacent side of the Student's Sketch/Adjacent side of the Original sketch

10/7Adjacent side of the Student's Sketch/Adjacent side of the Original sketch=9/5

upper side os student's sketch / upper side of original sketch

upper side os student's sketch / upper side of original sketch =4/3

Before I go any further you can see that for any side there is no certain(constant) scale factor whuch was used to increase the original Sketch to the Student's Sketch. Fir each and every side the Scale factor keeps on Changing This brings us to a conclusion that NEITHER OF SASHA AND RANDY IS CORRECT.

HOPE THIS HELPS

The graph of the functions (A) y=x+5 (B) y=-(x+5)  and  (C) y=|x+5| are added as an attachment

From the question, we have the following parameters that can be used in our computation:

To mark all points on the same coordinate plane, we simply plot the graphs of the three functions on the same graph

Using the above as a guide, we have the following:

The graph of the functions (A) y=x+5 (B) y=-(x+5)  and  (C) y=|x+5| are added as an attachment

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The expression, the company can use to predict the value of the car is v =32000 (0.8)^t

The company which provides term life or accidental or death insurance in terms of money when one subjects to any of the conditions.

Given is an insurance company estimates that the value of a car depreciates by 20% each year (That also means it retains 80% of its value each year). The company used an exponential function to predict the value of a car, v, as a function of time, t, in years.

The rate of interest r in percentage = 100 - 20 = 80%

If the value of a brand new car is  P =$32,000.00.

The value of car will be

value =  P x r^t

v = $32,000 x(0.8)^t

Thus, this is the expression insurance company uses to find the value of car.

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Answer:

Let's solve for m.

3m + 4n = 625

Step 1: Add -4n to both sides.

3m + 4n + −4n = 625 + −4n

3m = −4n + 625

Step 2: Divide both sides by 3.

3m/3 = 4n + 625/3

m = -4/3 n + 625/3

C) The variable m in the equation represents the number of hours Amy traveled on the

first train.

D) The variable n in the equation represents the number of hours Amy traveled on the

second train.

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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