The second term of an arithmetic sequence is 7. The sum of the first 4 terms of the arithmetic sequence is 12. Find the first term, and the common difference, d, of the sequence.

*Please help*

[tex]\bf -\cfrac{5}{1-cos(-x)}\implies -\cfrac{5}{\underset{\textit{symmetry identity}}{1-cos(x)}}\impliedby \begin{array}{llll} \textit{let's multiply top/bottom}\\ \textit{by the conjugate 1+cos(x)} \end{array} \\\\\\ \cfrac{-5}{1-cos(x)}\cdot \cfrac{1+cos(x)}{1+cos(x)}\implies \cfrac{-5(1+cos(x))}{\underset{\textit{difference of squares}}{[1-cos(x)][1+cos(x)]}} \\\\\\[/tex]

[tex]\bf \cfrac{-5[1+cos(x)]}{1^2-cos^2(x)}\implies \cfrac{-5-5cos(x)}{\underset{\textit{pythagorean identity}}{1-cos^2(x)}}\implies \cfrac{-5-5cos(x)}{sin^2(x)} \\\\\\ \cfrac{-5}{sin^2(x)}-\cfrac{5cos(x)}{sin^2(x)}\implies -5\cdot \cfrac{1}{sin^2(x)}-5\cdot \cfrac{1}{sin(x)}\cdot \cfrac{cos(x)}{sin(x)} \\\\\\ -5\cdot csc^2(x)-5\cdot csc(x)\cdot cot(x)\implies \boxed{-5csc^2(x)-5csc(x)cot(x)}[/tex]

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]

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:

ABCD is an isosceles trapezoid.

Step-by-step explanation:

The line AB will be horizontal (parallel to the x axis), because the y values are both 3. It is 9--2 = 11 units long.

CD is also parallel to the  x axis because the y values of C and D are both 6. Itis 5 - 2 = 3 units long.

The x values of the four points are all different so ABCD is a trapezoid.

Let's check the lengths of the line segments AC and BD:

AC = √((5--2)^2 + (6-3)^2 = √58.

BD =  √((9-2)^2 + (3-6)^2 = √58.

They are equal in length so:

ABCD is an isosceles trapezoid.

hope it helps you!!!!!!!!!!!!!!

Answer:

12.62

Step-by-step explanation:

you divide 3 by 8, then add the quotient of that to 3, then subtract that from 16

Answer:

Givens

First, we need to the number of pages dedicated to advertisements.

Let's transform the mixed number into a fraction

[tex]3\frac{3}{8}=\frac{27}{8}[/tex]

Now, let's multiply this fraction with the number of pages

[tex]\frac{27}{8} \times 16= 54[/tex]

That is, there are 54 pages dedicated to advertisements.

Pages without advertisements are 5/8, which is

[tex]\frac{5}{8} \times 16=5(2)=10[/tex]

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.

I believe it is 60 but I’m not sure

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:

d is the answer i believe

Step-by-step explanation:

The formula of the surface area of a cube is 6 x s²

→ s = 9

→ s² = 9²

→ s² = 81

→ 6 x 81 = 486

So, the surface area of the cube is 486 units².

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!

Answer:

The minimum number of boxes needed is [tex]4[/tex] and the cost is [tex]\$10.40[/tex]

Step-by-step explanation:

step 1

Find the cost of one box

by proportion

[tex]\frac{5}{13}=\frac{1}{x}\\ \\x=13/5\\ \\x=\$2.60[/tex]

step 2

Find the number of boxes for 48 ounces of pasta

by proportion

[tex]\frac{1}{12}=\frac{x}{48}\\ \\x=48/12\\ \\x=4\ boxes[/tex]

step 3

Find the cost of 4 boxes

we know that

The cost of one box is [tex]\$2.60[/tex]

so

The cost of 4 boxes is

[tex]\$2.60(4)=\$10.40[/tex]

Final answer:

To determine the cost for 48 ounces of pasta, one must calculate the cost per box and multiply by the number of boxes required to reach 48 ounces. The cost for the needed 4 boxes is $10.40.

Explanation:

The cost of one box of pasta is calculated by dividing the total cost of the pasta by the number of boxes. Since the total cost of 5 boxes of pasta is $13, to find the cost per box, we divide $13 by 5, which is $2.60 per box. To find the cost of the minimum number of boxes needed to total 48 ounces of pasta, we then determine how many boxes are needed. Since each box contains 12 ounces of pasta, we need 48 ounces / 12 ounces per box = 4 boxes of pasta. Finally, we multiply the number of boxes by the cost per box, which is 4 boxes × $2.60 per box = $10.40.

Answer:

its D

Step-by-step explanation:

Answer:

2 2/3 cups of sugar

Step-by-step explanation:

If your ratio is 3 flour to 4 sugar, and you use 2 cups of flour, set up your proportion as follows:

[tex]\frac{3}{4}=\frac{2}{x}[/tex]

Cross multiply to get 3x = 8 and x = 8/3 which is 2 and 2/3 cups of sugar.

The cups of sugar used is 3/2 corresponding to 2 cups of flour.

If we are using the ratio of 3 flour to 4 sugar.

We have 2 cups of flour.

Let us consider the amount of sugar be 'y'.

By writing the proportion /as follows:

[tex]\frac{3}{4} = \;\frac{2}{y}[/tex]

4y =6

y =3/2

Thus, the amount of sugar used is 3/2.

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

The last answer is the correct one.

Answer:

A. at (8,7) the maximum value is 98

Step-by-step explanation:

First draw the region, that is bounded by all inequalities. This is the triangle with vertices (6,1), (2,5) and (8,7).

Now you can see where the line f(x,y)=7x+6y intersect this region. The maximum value will be at endpoints of this region:

Thus, the maximum value of the function is 98 at the point (8,7).

Answer: Is it 169? i think that wright maybe.

Answer: 530.92916

Step-by-step explanation:

A=πr2=π·132≈530.92916

Answer:

[tex]7\sqrt[11]{x^{5}}[/tex]

Step-by-step explanation:

we know that

[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]

In this problem we have

[tex]7x^{\frac{5}{11}}[/tex]

therefore

[tex]7x^{\frac{5}{11}}=7\sqrt[11]{x^{5}}[/tex]

Answer:

The negative solution is between -3 and -2

The positive solution is between 11 and 13

Step-by-step explanation:

we have

[tex]0=x^{2} -10x-27[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2} -10x-27=0[/tex]  

so

[tex]a=1\\b=-10\\c=-27[/tex]

substitute in the formula

[tex]x=\frac{10(+/-)\sqrt{-10^{2}-4(1)(-27)}} {2(1)}[/tex]

[tex]x=\frac{10(+/-)\sqrt{208}} {2}[/tex]

[tex]x=\frac{10(+)\sqrt{208}} {2}=12.21[/tex]

[tex]x=\frac{10(-)\sqrt{208}} {2}=-2.21[/tex]

therefore

The negative solution is between -3 and -2

The positive solution is between 11 and 13

Answer:

Negative solution is between -3 and -2

Positive solution is between 12 and 13

Step-by-step explanation:

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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The answer is the last one . =

π

2

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:

  -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.

For this case we must find the area of the figure composed of a triangle and a rectangle.

Triangle area:

[tex]A_ {t} = \frac {b * h} {2}[/tex]

Where b is the base and h is the height.

Area of the rectangle:

[tex]A_ {r} = a * b[/tex]

Where a and b are the sides.

The base of the triangle measures:

[tex]13-5 = 8[/tex]

We find the height by trigonometry:

[tex]tg (45) = \frac {h} {b}\\1 = \frac {h} {b}\\b = h[/tex]

So:

[tex]A_ {t} = \frac {8 * 8} {2}\\A_ {t} = 32 \ ft ^ 2[/tex]

On the other hand:

[tex]A_ {r} = 5 * 8\\A_ {r} = 40 \ ft ^ 2[/tex]

Thus, the total are the sum:

[tex](32 + 40) ft ^ 2 = 72 \ ft ^ 2[/tex]

Answer:

Option A

Option is A~ the answer is A

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:

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

With

[tex]\vec r(t)=4t\,\vec\imath+6t\,\vec\jmath-t^2\,\vec k[/tex]

we have

[tex]\mathrm d\vec r=(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt[/tex]

The vector field evaluated over this parameterization is

[tex]\vec f(x,y,z)=\vec f(x(t),y(t),z(t))=4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k[/tex]

so the line integral is

[tex]\displaystyle\int_{-1}^1(4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k)\cdot(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_{-1}^1(16t+6t^2-12t^2)\,\mathrm dt=-4[/tex]

To evaluate the line integral c f · dr, substitute the values of r(t) into f(x, y, z) to get a new vector function f(t). Find the derivative of r(t) using the chain rule. Take the dot product of f(t) and r'(t) and integrate the result with respect to t over the given bounds.

To evaluate the line integral c f · dr, we need to find the dot product of the vector function f and the derivative of r(t). Since c is given by r(t) and the bounds are -1 ≤ t ≤ 1, we can substitute the values of r(t) into f(x, y, z) and compute the dot product.

Compute the integral to find the final answer.

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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: 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