Which expression can be used to model the phrase “the sum of three and a number”?

Answer:

A =147 cm^2

Step-by-step explanation:

A = pi r^2

The radius is 7 and let pi = 3

A = 3*7^2

A = 3*49

A =147

Answer:

This would be a .04 or 4% decay.....

for every "time unit" (x in this case) you will be multiplying

the amount by .96 ... in other words if you started with one dollar

the results would be 96 cents... after two "time" steps you would have

only 92 cents (.96 *.96)

Step-by-step explanation:

Answer:

[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]

Answer:

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]

Simplify:

[tex]-66 = k(17 + x_k)[/tex]

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

[tex]x_ n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]

Then the last term is given by:

[tex]x_k = 17 - 4(k-1)[/tex]

Substitute:

[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Answer:

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]

[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]

Answer:

Step-by-step explanation:

The diagonal of this rectangular box serves as the hypotenuse of the 2 right triangles that exist within this rectangle. The length is one leg, the hypotenuse is...well, the hypotenuse, so we need to use Pythagorean's Theorem to find the missing leg.

[tex]10^2=8^2+x^2[/tex] and

[tex]100-64=x^2[/tex] and

[tex]x^2=36[/tex] so

x = 6. The width is 6.

- X + 3Y = 2  (*)

⇔X = 2 - 3Y  (1)

- Y = 2X + 3   (2)

(1),(2)⇒ Y = 2(2 - 3Y) +3

       ⇔ Y = 4 - 6Y + 3

       ⇔ Y = 1  (**)

(*),(**)⇒ X + 3×1 =2

       ⇔ X = -1

Answer:

vertical

Step-by-step explanation:

The line x = -5 includes all points where the value of x is -5, regardless of the value of y. This can be graphed as a vertical line going through (-5, 0), as the line represents the only place where x is the value -5.

Answer: The range is  [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

Explanation:

The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.

The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.

Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

This translates to "y is a real number such that y is -6 or smaller".

So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.

See below for a visual example of what's going on.

Use distributive law

[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]

Now

[tex]\\ \sf\longmapsto 2x(x-y)+3y(x-y)[/tex]

[tex]\\ \sf\longmapsto 2x^2-2xy+3xy-3y^2[/tex]

[tex]\\ \sf\longmapsto 2x^2-3y^2-2xy+3x^2[/tex]

[tex]\\ \sf\longmapsto 2x^2-3y^2+xy[/tex]

Taking common

Answer: 2x (x-y) + 3y (x-y)

             = ( x-y ) ( 2x-3y )

Step-by-step explanation:

[tex]s = \pi \times {r}^{2} = \pi \times {6}^{2} = 36\pi[/tex]

[tex]h = 18 \times \sin(60) = 9 \sqrt{3} [/tex]

[tex]v = s \times h = 36\pi \times 9 \sqrt{3} = 324 \sqrt{3} \pi[/tex]

Answer:

x=-2

Step-by-step explanation:

Answer:

Since a = 2, the equation for the directrix line will be y = −2.

Step-by-step explanation:

Answer:

2 × 2 × 3 × 5

Step-by-step explanation:

Given that,

The number = 60

To find,

Factors of 60 greater than 1 = ?

Procedure:

As we know,

Any of various numbers multiplied together to form a whole.

To find the factors of a number, we will have to do its prime factorization.

So,

The prime factorization of 60:

1 * 2 * 2 * 3 * 5 = 60

Since the factors greater than 1 are asked, the factors would be;

2 * 2 * 3 * 5

Thus, 2 * 2 * 3 * 5 is the correct answer.

The triangle is missing and so i have attached it.

Answer:

x = 93°

Step-by-step explanation:

From the triangle attached, we can say that;

<SQP + <SQR = 180°

This is because sum of angles on a straight line equals 180°.

Secondly, we know that sum of angles in a triangle also equals 180°.

Thus;

<SQR + <QSR + <SRQ = 180

From the attached triangle, we see that;

<QSR = 35°

<SRQ = 58°

Thus;

<SQR + 35° + 58° = 180°

<SQR + 93° = 180°

<SQR = 180° - 93°

<SQR = 87°

From earlier on, we saw that;

<SQP + <SQR = 180°

Plugging in <SQR = 87°, we have;

<SQP + 87° = 180°

<SQP = 180° - 87°

<SQP = 93°

We are told in the question that <SQP is denoted by x.

Thus;

x = 93°

Answer:

The value of x is answer D: 93

Answer:

56000 ft

Step-by-step explanation:

4000 steps a day.

7 days in a week.

2 ft per step

so, we calculate how many steps in a week

4000 × 7 = 28000

and then we calculate the distance by saying each of these steps is 2 ft

so,

28000 × 2 = 56000 ft

as a little extra thought :

there are 5280 ft in a mile.

so, the person walks

56000 / 5280 miles = 10.61 miles

in a week.

9514 1404 393

Answer:

  -4/3

Step-by-step explanation:

Quadratic ax² +bx +c can be written in factored form as ...

  a(x -p)(x -q)

for zeros p and q. The expanded form of this is ...

  ax² -a(p+q)x +apq

Then the ratio of the constant term to the leading coefficient is ...

  c/a = (apq)/a = pq . . . . the product of the zeros

For your quadratic, the ratio c/a is -4/3, the product of the zeros.

_____

Additional comment

You will notice that the sum of zeros is ...

  -b/a = -(-a(p+q))/a = p+q

Answer:

[tex] \green{ \boxed{ \bf \: product \: of \: the \: zeros \: = - \frac{4}{3} }}[/tex]

Step-by-step explanation:

We know that,

[tex] \sf \: if \: \alpha \: and \: \beta \: \: are \: the \: zeroes \: of \: the \: \\ \sf \: polynomial \: \: \: \pink{a {x}^{2} + bx + c }\: \: \: \: then \\ \\ \small{ \sf \: product \: of \: zeroes \: \: \: \alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} } } \\ \\ \sf \implies \: \pink{ \boxed{\alpha \beta = \frac{c}{a} }}[/tex]

Given that, the polynomial is :

[tex] \bf \: 3 {x}^{2} - 2x - 4[/tex]

so,

[tex] \sf \: so \: product \: of \: zeroes \: \: = \frac{ - 4}{3} = - \frac{4}{3} [/tex]

Answer:

Hamid initially invested $1,125.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After 10 years, Hamid's account earned $900 in interest.

This means that [tex]t = 10, E = 900[/tex]

Interest rate of 0.08:

This means that [tex]I = 0.08[/tex]

How much did Hamid initially invest?

We have to find P. So

[tex]E = P*I*t[/tex]

[tex]900 = P*0.08*10[/tex]

[tex]P = \frac{900}{0.8}[/tex]

[tex]P = 1125[/tex]

Hamid initially invested $1,125.

Answer:

12

Step-by-step explanation:

We can say that two polygons are similar to each other if both of the polygons have the same shape and their corresponding sides are in the same proportion, hence the ratio of their corresponding sides are equal to each other.

As we can see from the problem since both of the polygons are similar, hence the ratio of their corresponding sides are in the same proportion, therefore let x represent the missing length, hence:

[tex]\frac{x}{15} =\frac{32}{40} =\frac{32}{40} \\\\\frac{x}{15} =\frac{32}{40} \\\\x=\frac{32*15}{40} \\\\x=12[/tex]

Answer:

Area of the slice of pie = 22.09 ft²

Step-by-step explanation:

Area of the slice of pie = Area of the sector of the circle with the central angle 45°

Area of the sector = [tex]\frac{\theta}{360^{\circ}}(\pi r^{2} )[/tex] [Here, r = radius of the circle]

                              = [tex]\frac{45^{\circ}}{360^{\circ}}(\pi )(\frac{15}{2})^2[/tex]

                              = 22.09 ft²

Area of the slice of pie = 22.09 ft²

Answer:

22.08ft^2

Step-by-step explanation:

A = πr^2(x/360) d = 15

Since r is half of diameter this means that r = 15/2 =7.5

so Lets use the Area of Sector formua

A =3.14(7.5)^2 (45/360)

A =3.14(56.25) (45/360)

A = 176.625 (45/360)

A = 176.625 (0.125)

A = 22.078125

rounded to the nearest 10th would make it 22.08

Answer:

emily fills 3 racks

3 basketballs are Left!

Step-by-step explanation:

15/4 = 3.3

Answer:

2 is the answer . the explanation is in the attachment .

Answer: A x> -2

Step-by-step explanation:

Step-by-step explanation:

between -5 and -62

-7,-10,-60...so..on

between -1/7 and 1/8

Multiply any number by number with both the numbers but it should be multiplied by both the numbers:

for example:

-1/7×3/3= -3/21 ; 1/8×3/3= 3/24

So,

-2/21,2/24,1/24

hope it helps

Answer:

13.25×5+13, cost per day with a helmet.

Step-by-step explanation:

Numerical Expressions • Practice

Answer:

13.25×5+13, Per day without a helmet

Step-by-step explanation:

Answer:

(2,1)

Step-by-step explanation:

2x - 2y = 2

5x + 2y = 12

again just add them in this case

7x = 14

x = 2

4 - 2y = 2

-2y = -2

y = 1

Answer:

I think it's 43 and 43 degrees. I just subtracted 180-94, got 86, and divided it so yea.

Answer:

Its AA similaroty theorem