What is the solution to the system of equations? y = 1.5x – 4 y = –x

g(x) = (x - 5)^2 + 2x^3

At the root this function is equal to 0

(x - 5)^2 + 2x^3= 0

Rearrange:

(x - 5)^2 = -2x^3

Now if you plot these two functions you need to check how many times they intersect. For this you do not need to be precise just scetch approximately.

If you do that, you will see that they meet once. I cannot really use this site to plot, but you can use other tools for that if you do not know how to do it.

Answer:

Option A.

Step-by-step explanation:

The given matrix is

[tex]\left[\left.\begin{matrix}4 & 5\\ 7 & -4\end{matrix}\right|\begin{matrix}-16\\ 23\end{matrix}\right][/tex]

We need to find the system of equations which is represented by the matrix.

In the given matrix first row represents the first equation and second row represents the second equation of the system of equations.

Let two variables are x and y.

First column represents the coefficients of x and second column represents the coefficients of y.

Numbers on the right side of the matrix represents the numbers which are right side of the equations.

Now, the required equations are

[tex]4x+5y=-16[/tex]

[tex]7x-4y=23[/tex]

Therefore, the correct option is A.

Answer:

70.15 ft²

Step-by-step explanation:

The figure consists of two adjacent equilateral triangles (all angles are 60 degrees and all outer edges are 9 ft).

If we focus on one of these equilateral triangles, we can get the final area by multiplying the area of that one triangle by 2.

The formula for the area of a triangle is (1/2)(base)(height).  Remembering to multiply this by 2, we get

area of figure = (base)(height)

                                             √3

                       = (9 ft)(9 ft)(--------) = (81 ft²)(1.732) = 70.15 ft²

                                               2

Answer: 4 scoops

Step-by-step explanation:

2/3 % 1/6 = 4 scoops

Answer:

1/9 pounds

Step-by-step explanation:

2/3 divide by 6

flip the 6 when dividing and then change division sign to multiplication

2/3 (1/6)

[tex] \frac{2}{3} \times \frac{1}{6} [/tex]

then multiply and simplify 2/18

Answer:

The density of the material must be at least 1.5 g/cm³.

Step-by-step explanation:

Answer:19.1

Step-by-step explanation:

Answer:

B. 46.1 in

Step-by-step explanation:

First, we must find the hypotenuse of the triangle.

Since this is a right triangle, we can use Pythagorean Theorem.

a^2+b^2=c^2

where a and b are the legs and c is the hypotenuse.

13 and 14 are the legs, because they form the right angle. x is the hypotenuse because it is opposite the right angle.

13^2+14^2=x^2

Evaluate each exponent.

13^2=13*13=169

14^2=14*14=196

169+196=x^2

Add 169 and 96

365=x^2

Take the square root of both sides.

√365=√x^2

√365=x

19.1049732=x

Round to the nearest tenth.

19.1=x

The hypotenuse is 19.1 inches

Now, find the perimeter. Add up all the sides of the triangle: the legs (13 in and 14 in) and the hypotenuse (19.1 in)

13 in +14 in +19.1 in

46.1 in

The perimeter is 46.1 inches and B is correct.

Answer:

A. Positive

Step-by-step explanation:

Since 48 is way larger than 39, we know that if we subtract 39 from 48, we will still get a positive number.

Answer:

A. Positive

Step-by-step explanation:

Im not very good at explaining. I hope I helped :)

Answer:

Answer:

b. 100

Step-by-step explanation:

Answer:

correct answer is 2800.

Step-by-step explanation:

You take the area of the square which is 20x20 = 400.

There is 5 squares 400x5 = 2000

There is 4 triangles--which is 1/2 the area of 1 square (In this case).

One triangle = 200

200x4 = 800

2000 + 800 = 2800

Answer:

Step-by-step explanation:

550

Answer:

7x + 23

Step-by-step explanation:

Remember BPEMDAS.

Product of 7 and a number means 7 times a variable: 7x

23 more than part means 23 + whatever we just did, so:

7x + 23

Answer:

23+7x

Step-by-step explanation:

23 + (7 * x)

23+7x

Answer:

a^2+a-6

Step-by-step explanation:

(a+3)(a-2)

a^2-2a+3a-6

a^2+a-6

Hope this helps ;) ❤❤❤

Answer:

Step-by-step explanation:

[tex](a + 3)(a - 2)[/tex]

Multiply the second parentheses by each term from the first parentheses

[tex] = a(a - 2) + 3(a - 2)[/tex]

Distribute ' a ' through the parentheses

[tex] = {a}^{2} - 2a + 3(a - 2)[/tex]

Distribute 3 through the parentheses

[tex] = {a}^{2} - 2a + 3a - 6[/tex]

Collect like terms

[tex] = {a}^{2} + a - 6[/tex]

Hope this helps..

Best regards!!

Answer: 25% decrease

Step-by-step explanation:

We know that 28 dollars a share was at its 100 percent. So we can make the fraction 28/100. Equal this to 21/x.

so we have: 28/100 = 21/x

Now just cross-multiply and simplify.

And you get what x is.

You get x = 75. So to see how much it went down, we subtract 75 from 100.

Answer:

n = 7*m

Step-by-step explanation:

divide n by m and you will get the same value

so : n= 7*m

Answer:

D

Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

Answer:

The answer is given below

Step-by-step explanation:

From the diagram below,Let the line AB and CD be parallel line. Let transversal line EF cut AB at Y and transversal line EF cut CD at Z.

The bisector of ∠BYZ and ∠DZY meet at O. Therefore ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2

∠BYZ and ∠DZY are interior angles.

∠BYZ + ∠DZY = 180 (sum of consecutive interior angles)

∠BYZ/2 + ∠DZY/2 = 180/2

∠BYZ/2 + ∠DZY/2 = 90°

In ΔOYZ:

∠YZO + ∠ZYO + ∠YOZ = 180 (sum of angles on a straight line).

But  ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2

∠DZY/2 + ∠BYZ/2 + ∠YOZ = 180

90 + ∠YOZ = 180

∠YOZ = 180 - 90

∠YOZ = 90°

Therefore Angle bisectors of the same side interior angles are perpendicular.

FULL QUESTION:

Figure ABCD is a parallelogram.

Parallelogram A B C D is shown. The length of A D is 5 x + 3 and the length of B C is 38.

What is the value of x?

6

7

8

9

ANSWER:

B.) 7

Answer:

$252

Step-by-step explanation:

This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.

Jan's " give away " = Ami + 36, Jan - 108, Toy + 72

Toy's " give away " = Ami + 72, Jan + 36, Toy - 108

Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.

144 + 72 + 36 = 252 dollars ( in total )

Answer:

The answer is 252

Step-by-step explanation:

Answer: 16x+8

Step-by-step explanation:

(fоg)(x) is f of g(x). This means you plug in g(x) into f(x). Since we are given f(x) and g(x), we can directly plug in g(x) into x.

(fоg)(x)=8(2x+1)                [distribute 8]

(fоg)(x)=16x+8

Answer:

16x + 8 = (fºg)(x).

Step-by-step explanation:

If f(x) = 8x and g(x) = 2x+1, find (fºg)(x).

This is a composite function.  To form it properly, substitute g(x) = 2x + 1 for x in f(x) = 8x.  We get:

8(2x + 1)(x), or 16x + 8 = (fºg)(x).

Answer:

A. One point greater than the last test grade.

Step-by-step explanation:

One point greater than the last test grade can be written as an expression:

n + 1

The difference of Gina’s score and one can be written as an expression:

n - 1

The total cost less one dollar can be written as an expression:

n - 1

One minute less than Mickey’s previous time can be written as an expression:

n - 1

Answer:

A

Step-by-step explanation:

did the quiz

Answer:

y^5

Step-by-step explanation:

y^-2/y^-7

When we divide exponents with the same base, we subtract the exponents

y^ ( -2 - -7)

y^ ( -2+7)

y^ 5

Answer:

y^2

Step-by-step explanation:

One way of doing this problem is to multiply both numerator and denominator by y^7.  Doing this we get:

  y^(-2+7)

--------------- = y^2

 y^(-7+7)

Answer:

q=35

Step-by-step explanation:

x2 - 12x + q = 0

Let the two roots be r and r+2.

Factor the quadratic expression:

(x - r)[x - (r + 2)] = 0

Expand, simplify, group like terms, and get

x2 - 2(r + 1)x + r(r + 2) = 0

Compare to

x2 - 12x + q = 0

and set equal the coefficients of like terms:

Coefficient of x:

-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5

(Then the other root is r + 2 = 5 + 2 = 7)

Constant term:

r(r + 2) = q ⇒ 5(5 + 2) = q

q = 35

Test the solution:

(x - 5)(x - 7) = x2 - 12x + 35

With two roots differing by 2, you get an equation of the form

x2 - 12x + q = 0

with q = 35.

Answer:

d = 7

Step-by-step explanation:

Distance Formula: [tex]d = \sqrt{(x2 - x1)^2+(y2-y1)^2}[/tex]

Plug in our 2 coordinates:

[tex]d = \sqrt{(2-2)^2+(1+6)^2}[/tex]

And you should get 7 as your final answer.

Answer:

7 units

Step-by-step explanation:

Since the x coordinates are the same, we only have to look at the difference between the y coordinates to determine the distance

1 - -6 = distance

1+6 = 7

The distance is 7 units

Answer:a x=3 y=-4

Step-by-step explanation:

Answer:

260 meters.

Step-by-step explanation:

It is given that construction crews A,B,C and D build a 1200 meter long road.

[tex]A+B+C+D=1200[/tex]     ...(1)

Team A builds 1/2 of the total length built by the other 3 teams. So,

[tex]A:(B+C+D)=1:2[/tex]

It means total distance divided in 1:2.

[tex]A=1200\times \dfrac{1}{1+2}=1200\times \dfrac{1}{3}=400[/tex]

Similarly,

Team B builds 1/3 of the total length built by the other 3 teams.

[tex]B:(A+C+D)=1:3[/tex]

It means total distance divided in 1:3.

[tex]B=1200\times \dfrac{1}{4}=300[/tex]

C builds a section that is 1/4 of the length built by the other teams.

[tex]C:(A+B+D)=1:4[/tex]

It means total distance divided in 1:4.

[tex]C=1200\times \dfrac{1}{5}=240[/tex]

Now, put A=400, B=300 and C=240 in (1).

[tex]400+300+240+D=1200[/tex]

[tex]D=1200-940[/tex]

[tex]D=260[/tex]

Therefore, 260 meters build by D.

Answer:

the answer is D

Step-by-step explanation:

when expanded (a+b)^5 is a^5+5a^4 b+10a^3 b^2+10a^2 b^3+5ab^4+b^5

and as you can see the answer is 1 5 10 10 these are the first four coefficients

Answer:

Step-by-step explanation:

A

Answer:

Options (1), (2), (3) and (4)

Step-by-step explanation:

Two circles (yellow and blue) with their centers as (1, -1) and (-1, 1) have been given in picture.

Now we will check each option for the transformations of these points.

Option (1)

The yellow circle was translated left by 2 units and up by 2 units.

Then rule for translation will be,

(x, y) → [(x - 2), (y + 2)]

Following this rule (1, -1) will become,

(1, -1) → [(1 - 2), (-1 + 2)]

        → (-1, 1)

But the center of blue circle after translation is (-1, 1),

Therefore, this option will be the answer.

Option (2)

The yellow circle was reflected over both axis.

If (1, -1) is reflected over x-axis,

Rule to be followed,

(x, y) → (x, -y)

Followed by reflection over the y-axis,

rule for the reflection,

(a, b) → (-a, b)

By this rule, (x, -y) will become,

(x, -y) → (-x, -y)

By these transformations (1, -1) will become

(1, -1) → ( -1, 1)

By these transformations image of yellow circle is the blue circle.

Option (2) is the answer.

Option (3)

The yellow circle was reflected over the y-axis and translated up by 2 units.

Rule for reflection over y-axis,

(x, y) → (-x, y)

followed by the translation 2 units up,

(-x, y) → (-x, y+2)

By these transformations,

(1, -1) → (-1, 1)

Therefore, option (3) is the correct option.

Option (4)

The yellow circle was reflected over the x-axis and translated left 2 units

Rule for reflection over x-axis,

(x, y) → (x, -y)

Followed up by the translation of 2 units left.

(x, -y) → (x - 2, -y)

By this rule point (1, -1) will become,

(1, -1) → [(1 - 2), -(-1)]

        → (-1, 1)

Which is the center of blue of circle.

Therefore, Option (4) will be the answer.

All given options are correct.

Answer:

All of the above

Step-by-step explanation:

I know my math straight and I have this answer

I hope this helps you

Answer:

3  -√5

Step-by-step explanation:

(√5 + 1) / (2 + √5)

Multiply top and bottom of the fraction by the conjugate of 2 + √5 which is  2 - √5.

By doing this we rationalise the denominator:

= (√5 + 1 ) *  ( 2 - √5) /  (2 + √5)(2 - √5)

= (√5 + 1 ) *  ( 2 - √5)/ (4 - 2√5 + 2√5 - 5)

= (2√5 - 5 + 2 - √5) / (4 - 5)

= (√5 - 3) / -1

= 3  -√5

Answer:

4 seconds.

Step-by-step explanation:

The given equation is

[tex]h=-16t^2+64t[/tex]

where, h is height in feet of a golf ball above the ground after being hit into the air and t is the number of seconds elapsed since the ball was hit.

We need to find the time for the ball to hit the ground.

At ground level the height of ball is 0, i.e., h=0.

[tex]-16t^2+64t=0[/tex]

[tex]-16t(t-4)=0[/tex]

Using zero product property, we get

[tex]-16t=0\Rightarrow t=0[/tex]

[tex]t-4=0\Rightarrow t=4[/tex]

Therefore, it will take 4 seconds for the ball to hit the ground.

Answer:

4 seconds

That's your answer!!

Answer:

(6,5)

Step-by-step explanation:

The ordered pair is ( x,y)

The ordered pairs in the table are

(3,4)  (4,4)  (5,2) and (6,5)