Consider the following equation

0=x^2-10x-27

Complete each statement about the solutions to the equation.
The negative solution is between ..(A)...and ..(B)...
(A ) -2,-13,-3,12
(B)-1,-11,-2,-12

The positive solution is between...(B)...and..(C)...
(B)11,2,12,1
(C)3,12,13,2

Answer:

  a6 = -26

Step-by-step explanation:

Fill in n=6 and do the arithmetic.

  a6 = -2·6 -14 = -12-14 = -26

Solution:

Given, Tn = -2n - 14

To Find : What is the 6th value in the sequence

Solution: Simply Substitute the value of n as 6 .

Tn = -2n-14

Tn = -2(6) -14

Tn = -12 - 14

Tn = -14 - 12

Tn = -26

Therefore -10 is the 6th value in the sequence.

Answer:

Part 1) Sphere The surface area is equal to [tex]SA=196\pi\ m^{2}[/tex] and the volume is equal to [tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]

Part 2) Cone The surface area is equal to [tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex] and the volume is equal to [tex]V=\frac{112}{3}\pi\ units^{3}[/tex]

Part 3) Triangular Prism The surface area is equal to [tex]SA=51.57\ mm^{2}[/tex] and the volume is equal to [tex]V=17.388\ mm^{3}[/tex]

Step-by-step explanation:

Part 1) The figure is a sphere

a) Find the surface area

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter

substitute

[tex]SA=4\pi (7)^{2}[/tex]

[tex]SA=196\pi\ m^{2}[/tex]

b) Find the volume

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (7)^{3}[/tex]

[tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]

Part 2) The figure is a cone

a) Find the surface area

The surface area of a cone is equal to

[tex]SA=\pi r^{2} +\pi rl[/tex]

we have

[tex]r=4\ units[/tex]

[tex]h=7\ units[/tex]

Applying Pythagoras Theorem find the value of l (slant height)

[tex]l^{2}=r^{2} +h^{2}[/tex]

substitute the values

[tex]l^{2}=4^{2} +7^{2}[/tex]

[tex]l^{2}=65[/tex]

[tex]l=\sqrt{65}\ units[/tex]

so

[tex]SA=\pi (4)^{2} +\pi (4)(\sqrt{65})[/tex]

[tex]SA=16\pi +4\sqrt{65}\pi[/tex]

[tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex]

b) Find the volume

The volume of a cone is equal to

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

we have

[tex]r=4\ units[/tex]

[tex]h=7\ units[/tex]

substitute

[tex]V=\frac{1}{3}\pi (4)^{2}(7)[/tex]

[tex]V=\frac{112}{3}\pi\ units^{3}[/tex]

Part 3) The figure is a triangular prism

a) The surface area of the triangular prism is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the prism

Find the area of the base B

[tex]B=\frac{1}{2} (2.7)(2.3)=3.105\ mm^{2}[/tex]

Find the perimeter of the base P

[tex]P=2.7*3=8.1\ mm[/tex]

we have

[tex]L=5.6\ mm[/tex]

substitute the values

[tex]SA=2(3.105)+(8.1)(5.6)=51.57\ mm^{2}[/tex]

b) Find the volume

The volume of the triangular prism is equal to

[tex]V=BL[/tex]

where

B is the area of the triangular base

L is the length of the prism

we have

[tex]B=3.105\ mm^{2}[/tex]

[tex]L=5.6\ mm[/tex]

substitute

[tex]V=(3.105)(5.6)=17.388\ mm^{3}[/tex]

Answer:

c. first year: 240,000  

second year: 150,000

Step-by-step explanation:

We let the number of cars made in the second year be X. Consequently, the number of cars made in the first year would be X+90000 since we are told that 90,000 more cars were made in the first year than in the second year. Furthermore, we are also told that the total number of cars constructed in these two years is 390,000, implying that;

X+X+90000=390000

2X+90000=390000

2X=390000-90000

2X=300000

X=150000; number of cars made in second year

The number made in the first year is thus;

150000+90000 = 240000

Answer:

Option c is correct

So, the cars made in 1st year = x = 240,000

and the cars made in 2nd year = 150,000

Step-by-step explanation:

in this question we have to find the number of cars made in each year by The Flat Rock auto assembly plant.

Given:

the plant constructed a total of 390,000 cars and 90,000 more cars were made in the first year than in the second year

Let cars made in 1st year = x

and cars made in 2nd year = y

then the plant constructed a total of 390,000 will be :

x+ y = 390,000       (i)

and

90,000 more cars were made in the first year than in the second year can be written as:

x=90,000 +y         (ii)

Solving equation (i) and (ii) we can find the values of x and y

Putting value of x from eq (ii) into eq(i)

(90,000 + y) + y = 390,000

90,000 +y +y =390,000

2y = 390,000 - 90,000

2y= 300,000

y= 150,000

Putting value of y in equation (ii) we can find the value of x

x= 90,000 + y

x= 90,000 + 150,000

x= 240,000

So, the cars made in 1st year = x = 240,000

and the cars made in 2nd year = 150,000.

Answer:

(x,y) --> (x, y-5)

Step-by-step explanation:

the y-intercept of f(x) = (0,2)

the y-intercept of g(x) = (0, -3)

-3 - 2 = -5

Answer:

8 ft

Step-by-step explanation:

The area (A) of a triangle = [tex]\frac{1}{2}[/tex] bh

where b is the base and h the perpendicular height

Using b = 20 and h = 12, then

A = 0.5 × 20 × 12 = 120 ft²

Using b = 30 and perpendicular height = h, then

0.5 × 30 × h = 120

15h = 120 ( divide both sides by 15

h = 8

According to lots of Pythagorean theorem,

h=7

I really don’t want to show my work because it took a while to solve this lol but if you want me to show my work just comment

Answer:

y = 30.

Step-by-step explanation:

As they are similar corresponding sides are in the same ratio.

So (y + 20) / 20 = 100/40

(y + 20) / 20 = 5/2

2(y + 20) = 5*20

y + 20 = 50

y = 30 (answer).

Final answer:

Jason thinks it's a bad idea to use the emergency fund for a car down payment as it should be reserved for unforeseen financial emergencies, not planned expenses like a vehicle purchase.

Explanation:

Jason may consider it a bad idea for Beth to use the emergency fund for a down payment on a car because the emergency fund is supposed to be a safety net for unforeseen and critical financial needs, such as sudden medical expenses, job loss, or urgent home repairs.

Depleting the emergency fund for a car purchase, despite the fact that car payments are affordable, puts them at risk should multiple unplanned expenses arise simultaneously.

Financial advisers often recommend keeping 3-6 months of expenses saved for emergencies to maintain financial security. Therefore, it might be better to save up for the down payment separately or consider a less expensive car.

Final answer:

Jason may be concerned about using the emergency fund for a car downpayment since emergency funds are meant for unforeseen and urgent financial needs. Adding new debt could make them vulnerable to financial strain.

Explanation:

The concern Jason may have with Beth taking $2,000 out of their emergency fund for a down payment on a new car is that the emergency fund should be reserved for unforeseen circumstances, such as medical expenses, unexpected home repairs, or job loss. Using it for a car down payment, even if it seems manageable within their budget, could leave them vulnerable if a real emergency arises. Additionally, even though the car payments fit within Dave Ramsey's guidelines of being less than a quarter of their take-home pay, it introduces new debt—which they have worked hard to eliminate, except for their mortgage—and could potentially add financial strain if their income situation changes.

Answer:

B. The graph rises on the left side.

Step-by-step explanation:

The limit provided on the image is interpreted as; The limit of the function f(x) as x approaches negative infinity is infinity.

X is approaching negative infinity, this means that along the x-axis we are moving towards the left where the values of x become increasingly negative.

On the other hand, f(x) is approaching positive infinity, meaning that along the y-axis we are moving upwards where the values of y become increasingly positive.

This typically implies that as we move towards the left the graph of f(x) is moving upwards or basically the graph rises on the left side.

Answer:

b. the graph rises on the left side

Answer:

C

Step-by-step explanation:

From the graph you can see that y changes from -2 to 2, so the range of the function is [tex][-2,2].[/tex]

Since the range of the functions [tex]y=\cos x[/tex] and [tex]y=\sin x[/tex] is [tex][-1,1][/tex] and the range of the functions [tex]y=k\cos x[/tex] and [tex]y=k\sin x[/tex] is [tex][-k,k],[/tex]  we can state that the correct option is  C: [tex]f(t)=-2\cos 3t.[/tex]

Check the value at t=0:

[tex]f(0)=-2\cos 3\cdot 0=-2\cos 0=-2.[/tex]

Two events are dependent if the outcome of the first event affects the outcome of the second.

The last answer is the correct one.

The answer is the last one . =

π

2

Answer:

  -8

Step-by-step explanation:

Let n represent the number. The stated relationship is ...

  5n -(-10) = -30

  5n = -40 . . . . . . . add -10

  n = -8

The number is -8.

Final answer:

To solve the equation given in the student's question, convert the operation of subtracting a negative number into addition, subtract 10 from both sides to isolate the term with x, and then divide by 5 to find that the number in question is -8.

Explanation:

The student's question is a linear algebra problem, which can be turned into a simple equation to find the unknown number.

According to the question, we multiply a number by five and then subtract a negative ten to get a difference of negative thirty.

Mathematically, this can be expressed as the equation 5x - (-10) = -30, and we can solve for x. First, we should simplify the equation by turning the subtraction of a negative number into an addition. This makes our equation 5x + 10 = -30.

To find the value of x, we then subtract 10 from both sides of the equation, which gives us 5x = -40.

Finally, we divide both sides by 5 to solve for x, leading us to an answer of x = -8.

Answer:

if you take into consideration the run from yesterday,

Joe needs to run at least three more days

y > = 3

if you don't take into consideration the 3 mile run from yesterday,

The answer is

He needs to run 4 or more days toachieve his goal

y > = 4

Step-by-step explanation:

12 miles as a minimum

that means

let x be the total amount of miles ran

x > = 12

Let y be the number of days in which Joe runs

3*y > = 12

y > = 4

Joe needs to run for at least 3 more days to meet his goal of running at least 12 miles this week, considering that each run is 3 miles.

We can set up an inequality. Joe has already run 3 miles, so we need to find out how many more miles he needs to run. If Joe runs 3 miles each day, the inequality representing the situation is 3d + 3 \\geq 12, where d is the number of additional days Joe must run.

We can solve the inequality as follows:

This means Joe needs to run for at least 3 more days to meet his goal of 12 miles.

The answer is:

C. 1.556.

[tex]csc(40\°)}=1.556[/tex]

To solve the problem using our calculator we need to set it to "Degree" mode in order to avoid miscalculations.

Also, we need to remember that the cosecant (csc) is the inverse function of the sine, so:

[tex]csc(40\°)=\frac{1}{sin(40\°)} =\frac{1}{0.6427}=1.556[/tex]

Hence, the answer is C. 1.556.

Have a nice day!

For this case we have the following fusions:

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

We must find [tex](a * b) (x):[/tex]

By definition:

[tex](a * b) (x) = a (x) * b (x)\\(a * b) (x) = (3x + 1) * (\frac {1} {x} -4)\\(a * b) (x) = \frac {3x} {x} -12x + \frac {1} {x} -4\\(a * b) (x) = 3-12x + \frac {1} {x} -4\\(a * b) (x) = - 12x + \frac {1} {x} -1[/tex]

The domain of the function will be given by all the values for which the function is defined, that is, all real numbers except zero.

Answer:

(-∞, 0) U (0,∞)

Answer:

28

Step-by-step explanation:

Add 42, 85, and 69 together and you get 196 but you need to divide that by 7 and you get 28

Answer:

28

Step-by-step explanation:

We are given that

June has sports books=42

June has mystery books=85

June has nature books=69

Total number of shelves=7

We have to find the number of books are on each shelf.

Total number of books=42+85+69=196

To find the number of books on each shelf we will divide the total number of books by 7.

Number of books on each shelf=[tex]\frac{196}{7}[/tex]

Number of books on each shelf=28

Hence, number of books on each shelf=28

Answer:

B. $26.05

Step-by-step explanation:

Since this was a multiple choice question, I used process of elimination. I got rid of A because $13.95 - the ice cream ($13) would be no where near $43. For B, i did ($26.05) + ($26.05 - $13) which equals $39.10 and then i did ($39.10 + ($26.06 x 0.15) and that gave me $43 in all.

[tex]\bf P(\stackrel{x}{1},\stackrel{y}{-3})\qquad \qquad cot(\theta )=\cfrac{\stackrel{\stackrel{adjacent}{x}}{1}}{\stackrel{\stackrel{opposite}{y}}{-3}}[/tex]

The value of Cotangent or cot is: [tex]cot \;\theta= \frac{1}{-3}[/tex]

Trigonometric ratios are the ratios of the length of sides of a triangle.

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent.

Given ordered pair P(1, -3).

As we know that Cotangent is ratio of base : perpendicular i.e.,

adjacent of x: opposite y

So, [tex]cot \;\theta= \frac{1}{-3}[/tex]

Now, Hypotenuse = [tex]\sqrt{base^{2}+perpendicular^{2} }[/tex]

                              = [tex]\sqrt{1^{2} + (-3)^{2}} =\sqrt{10}[/tex]

and,

[tex]sec\;\theta= \frac{\sqrt{10} }{1} \\cosec\;\theta =\frac{\sqrt{10} }{(-3)}[/tex]

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Answer:

2.72

Step-by-step explanation:

Here, we use a z-score table or calculator to look up the probability and find the corresponding z-score.

P(z < ?) = 0.9967 at z = 2.72.

Using the normal distribution principle, the Zscore which corresponds to the area under the normal curve at P(Z < z) = 0.9967 is 2.716

To obtain the Zscore in this scenario, which is the number of standard deviations from the mean value for a given score ; we make use of Zscore calculator or a normal distribution table ;

Using a normal distribution table;

Therefore, the Zscore value is 2.716

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Answer:

its D

Step-by-step explanation:

Answer:

Step-by-step explanation:By AA similarity postulate

△ADB∼△ABC∼△BDC

therefore the sides of the triangles are proportional, in particular

ADAB=ABAC ACBC=BCDC

By algebra we have the following equations

AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC

this is the same as

AD⋅AC=AB2AC⋅DC=BC2

"Equals added to equals are equal" allows us to add the equations

AD⋅AC+AC⋅DC=AB2+BC2

By distributive property

AC(AD+DC)=AB2+BC2

but by construction AD+DC=AC.

Substituting we have

AC⋅AC=AB2+BC2

this is equivalent to

AB2+BC2=AC2

which is what we wanted to prove

The Pythagorean theorem uses similar triangles, This is equivalent to AB^2+BC^2=AC^2.

We have given that,

the converse of the Pythagorean theorem using similar triangles.

The converse of the Pythagorean theorem states that when the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle.

[tex]hypotenuse ^2=side^2+side^2[/tex]

By AA similarity postulate

△ADB∼△ABC∼△BDC

Therefore the sides of the triangles are proportional, in particular

ADAB=ABAC  ACBC=BCDC

By algebra, we have the following equations

AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC

This is the same as

AD⋅AC=AB^2AC⋅DC=BC^2

Equals added to equals are equal allows us to add the equations

AD⋅AC+AC⋅DC=AB^2+BC^2

By distributive property

AC(AD+DC)=AB^2+BC^2

but by construction AD+DC=AC.

Substituting we have

AC⋅AC=AB^2+BC^2

This is equivalent to

AB^2+BC^2=AC^2

Hence the proof.

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Answer:

  30%

Step-by-step explanation:

24 of (40 +24 +16) = 3/10 of the turkey sandwiches were made with wheat bread. As a percentage, that is ...

  3/10 = 30/100 = 30%

Answer:

A. True

Step-by-step explanation:

The given function is;

[tex]f(x)=3x^3+x^2+2x[/tex]

The leading coefficient of this polynomial function is positive.

The degree of the polynomial is odd.

This implies that, the function will rise on the left and keep rising on the right.

Hence, the end behavior of the function tells  us that, the function rises as x-values grow very large.

The correct option is True

Answer:

-csc⁡(14°)

Step-by-step explanation:

The given trigonometric expression is csc(-166°)

-166° is in the third quadrant.

It makes an angle of 14° with the x-axis.

Hence the principal angle for -166° is 14°

In the third quadrant the cosecant function is negative.

This implies that;

csc(-166°) =-csc(14°)

The correct choice is the second option.

The sum is the answer to an addition problem. 2+4=6. so, 3÷6=0.5

The quotient of three divided by the sum of two and four will be 0.5.

The number system is a way to represent or express numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given,

Three divided by the sum of two and four

3/(2 + 4) = 3/6 = 0.5

Hence "The quotient of three divided by the sum of two and four will be 0.5".

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Answer: The answer is A: 8.6

Step-by-step explanation: In this case, the side you're trying to figure out is the opposite and the side measurement given is the hypotenuse.

This means that out of the sin, cos, and tan we will be using sin.

Sin(Ф)= opposite/hypotenuse

Plug in the numbers you know: Sin(35)=x/15

Take the 15 to the other side to get x by itself

Then plug into your calculator 15Sin(35)=x

This gives you 8.6

Answer:

25

Step-by-step explanation:

The radius of the circle, which is the perpendicular bisector of a 48-inch diameter kitchen breakfast bar template, is 30 inches. The correct option is C).

Let's break down the information given in the problem:

PQ is the perpendicular bisector of VW, and Q is the midpoint of VW. This means that PQ passes through the center of the circle.

The length of PQ (perpendicular bisector) is 18 inches.

VW is 48 inches in diameter, which means its radius is half of that, i.e., 48 inches / 2 = 24 inches.

Since PQ is the radius of the circle, and it is also the perpendicular bisector of VW, it divides VW into two equal parts, each measuring 24 inches (as VW has a diameter of 48 inches, and Q is the midpoint).

Now, we have a right-angled triangle, with PQ as the hypotenuse and two legs measuring 18 inches and 24 inches. We can use the Pythagorean theorem to find the length of PQ (the radius of the circle):

PQ² = 18² + 24²

PQ² = 324 + 576

PQ² = 900

PQ = √900

PQ = 30 inches

So, the radius of the circle is 30 inches.

The correct answer is option c) 30 inches.

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I believe it is 60 but I’m not sure

The spanish song Decima has ten lines

Final answer:

A decima is a Spanish form of poetry that consists of ten lines per stanza, with a fixed rhyme pattern of ABBAACCDDC, representing a distinct structure from other forms like sonnets or haikus.

Explanation:

The decima is a form of Spanish poetry. Unlike a sonnet, which typically comprises fourteen lines and may follow various rhyme schemes such as the Shakespearian or Petrarchan forms, the decima is characterized by its ten-line stanzas. These stanzas adhere to a specific rhyme pattern and are traditionally written in eight-syllable lines. Each line in a decima ends with a rhyme following the pattern ABBAACCDDC. The form is quite popular in Spanish literature and folk music, and it is distinct in its total line count from other forms like the sonnet, sestina, and haiku.

3h

The set cost is 25, because c=25 when h=0. So, this leaves 3h as the hourly rate.

The hourly rate of the carpet cleaning is specified correctly by: Option A: 3

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

c = rental cost of a carpet cleaner

h = number of hours the carpet cleaner is rented.

c = 25 + 3h can be written as:

c = 25 + (3+3+3+...+3) (h times)

That shows that 3 is added h times, which is the number of hours, so for each 1 of h hours, there is one 3 added in the final rental cost. (assuming nothing complex is going to happen)

That shows that the hourly rate is 3.

Thus, the hourly rate of the carpet cleaning is specified correctly by: Option A: 3

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