Hello, can you please review attached and help me with the answer ?

To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.

For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:

x^2 + x - 6 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:

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

Setting each factor equal to zero:

x + 3 = 0 or x - 2 = 0

Solving for x in each equation:

x = -3 or x = 2

Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.

To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.

Answer:

g ≤ 6

Step-by-step explanation:

The number of goldfish that can live in the tank is less than or equal to 6.

Answer:

62b+27nb-12n-12

Step-by-step explanation:

u gotta combine like terms

Answer:

-0.7 .................

Answer:

12

Step-by-step explanation:

The sum of the exterior and interior angles = 180°

let x be the measure of the exterior angle then interior angle is 5x and

5x + x = 180

6x = 180 ( divide both sides by 6 )

x = 30

The sum of the exterior angles of a polygon = 360°, thus

number of sides = \(\frac{360}{30}\) = 12

Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

4/9 or 0.4

Step-by-step explanation:

Answer:

\(\textsf{B)} \quad -8 \frac{4}{7} \quad -8.\.{2} \quad \dfrac{25}{3} \quad \sqrt{70}\)

Step-by-step explanation:

Given:

\(\sqrt{70} \quad -8.\.{2} \quad \dfrac{25}{3} \quad -8 \frac{4}{7}\)

Convert the given numbers into decimals:

\(\sqrt{70}=8.366...\)

\(-8.\.{2} =-8.222...\)

\(\dfrac{25}{3}=8.333...\)

\(-8 \frac{4}{7}=-8.571...\)

Order the decimals from least to greatest:

\(-8.571... < -8.222... < 8.333... < 8.366...\)

Therefore:

\(-8 \frac{4}{7} < -8.\.{2} < \dfrac{25}{3} < \sqrt{70}\)

Answer:

negative eight and four sevenths, negative 8.2 repeating, twenty five thirds, square root of 70

Answer:

y=x+6

Step-by-step explanation:

Put (-7,-1) into

y-y1=m(x-x1) form, and m=1 (the slope)

y+1=1(x+7)

y+1=x+7

y=x+6

Happy Holidays!

Given:

The given equation is

\(60=5(1.07)^x\)

To find:

The initial value and growth/decay factor.

Solution:

The general exponential growth/decay model is

\(y=a(1+r)^x\)     ...(i)

where, a is initial value, if r>0, then |r| is growth factor, if r<0, then |r| is decay factor and x is time.

We have,

\(60=5(1.07)^x\)

It can be written as

\(60=5(1+0.07)^x\)        ...(ii)

On comparing (i) and (ii), we get

\(a=5\text{ and }r=0.07\)

Here, initial value is 5 and growth factor is 0.07, i.e., 7%.

Therefore, the correct option for first question is d and correct option for second question is a.

Answer:

see image

Step-by-step explanation:

Plato/Edmentum

Answer:

length l = 32.25 m

width w = 8223.75 m

height h = 12.5 m

diagonal d = 8223.82273 m

total surface area Stot = 736831.875 m2

lateral surface area Slat = 206400 m2

top surface area Stop = 265215.938 m2

bottom surface area Sbot = 265215.938 m2

volume V = 3315199.22 m3

Step-by-step explanation:

Answer:

- 19

Step-by-step explanation:

The ratio of the height to the perimeter of this mural 57 : 152.

We are given that:

Length = 135 feet

height = 285 feet

Mural is of a rectangular shape

We will first find the perimeter.

Perimeter = 2(l + w)

Perimeter = 2(95 + 285)

Perimeter = 2(380)

Perimeter = 760 feet

We will now find the ratio of the height to the perimeter of this mural.

Height : perimeter = 285 : 760

Reduce to lowest terms

Height : perimeter = 57 : 152

Therefore, we get that, the ratio of the height to the perimeter of this mural 57 : 152.

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15 because 25% = 0.25 then you multiply 12×0.25=15

The corresponding z score for speed of 62 mph, 47 mph, and 56 mph is 1.5, -2.25 and 0 respectively.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma }\)

Where x is raw score, μ is mean, σ is standard deviation

Given that:

σ = 4, μ = 56, hence

for x = 62:

\(z=\frac{62-56}{4 } =1.5\)

for x = 47:

\(z=\frac{47-56}{4 } =-2.25\)

for x = 56:

\(z=\frac{56-56}{4 } =0\)

The corresponding z score for speed of 62 mph, 47 mph, and 56 mph is 1.5, -2.25 and 0 respectively.

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The measure of the angles formed between parallel lines and their transversals indicates;

9. m∠3 = 97°, m∠5 = 97°, m∠10 = 97°, m∠7 = 83°

Parallel lines are lines that  maintain the are equidistant from each other and have the same slope on the coordinate plane.

The angles formed between the parallel lines and their transversal are;

1. Alternate exterior angles; (c) ∠9 and ∠16
2. Supplementary angles (e);  ∠15 & ∠11

3. Alternate interior angles (a); ∠10 & ∠15

4. Vertical angles (d); ∠12 & ∠15

5. Corresponding angles (b); ∠9 & ∠11

6. None (f); ∠9 & ∠15

7. Supplementary angles (e); ∠13 & ∠14

8. Alternate interior angles; ∠14 & ∠11

9. The alternate interior angles theorem indicates that we get;

(a + 28) = 2·a

Therefore; 2·a - a = 28

2·a - a = a, therefore;

a = 28

∠MNP = (a + 28)° = (28 + 28)° = 56°

10. The alternate interior angles theorem indicates that we get;

5·y° = (2·y + 78)°

Therefore;

5·y - 2·y = 78

3·y = 78

y = 78/3 = 26

The measure of the angle WXZ, m∠WXZ = 5·y°

Therefore; m∠WXZ = 5 × 26 = 130

m∠WXZ = 130°

9. ∠2 ≅ ∠3 (Vertical angles theorem)

m∠2 = m∠3

Therefore; m∠3 = m∠2 = 97°

m∠5 + m∠6 = 180° (Linear pair angles theorem)

m∠5 + 83° = 180°

m∠5 = 180° - 83° = 97°

∠10 and ∠2 are corresponding angles, therefore;

m∠10 = m∠2 = 97°

∠7 and ∠6 are vertical angles, therefore;

m∠7 = m∠6 = 83°

∠9 and ∠3 are same side interior angles, therefore;

m∠9 + m∠3 = 180°

m∠9 = 180° - m∠3

m∠9 = 180° - 97° = 83°
∠8 and ∠6 are linear pair angles, therefore; m∠8 = 180° - 83° = 97°

∠16 and ∠6 are same side exterior angles, therefore;

m∠16 + m∠6 = 180°

m∠16 = 180° - 83° = 97°

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Step-by-step explanation:

The statements that describe the graph are,

The ball travels 24 cm in 1s.

It takes the ball 2s to complete a cycle

The midline is at f(x)=0

I hope it helped you

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"v" varies directly with "x"}}{v = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} x=32\\ v=20 \end{cases} \\\\\\ 20=k(32)\implies \cfrac{20}{32}=k\implies \cfrac{5}{8}=k\hspace{8em}\boxed{v=\cfrac{5}{8}x} \\\\\\ \textit{when x = 24, what's v?}\qquad v=\cfrac{5}{8}(24)\implies v=15\)

The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Answer:

D. f(x) = 2^x

Step-by-step explanation:

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

The base is always 2. The exponent changes and is x.

Answer: D. f(x) = 2^x

Answer: the transformation of ABC to MNO preserves both side lengths and angle measures of the triangle.

Step-by-step explanation:

Answer:

B - The transformation of triangle ABC to triangle MNO preserves both the side lengths and angle measures of the triangle.

Answer: 117/40 or 2.925

Answer:

Its A

Step-by-step explanation:

Answer:

Line AC goes from the base of the triangle all the way to its highest point so it is a Altitude

Answer:

Variable

x which stands for no. of toppings on pizza

equation

7 + 1.5x = 11.50

solution

the no. of toppings = 3

Step-by-step explanation:

Let the number of topping be x.

Cost of 1 topping = $1.50

Cost of x topping = x*Cost of 1 topping = $1.5*x = $1.5x

Cost of cheese pizza = $7.00

Total cost for cheese pizza for x topping = Cost of cheese pizza + Cost of x topping

Total cost for cheese pizza for x topping = 7 + 1.5x

Given that The total charge for Megan's pizza was $11.50

thus,

7 + 1.5x = 11.50

1.5x = 11.50 - 7

1.5x = 4.5

x = 4.5/1.5 = 3

Thus, there were three toppings

______________________________________

Variable

x which stands for no. of toppings on pizza

equation

7 + 1.5x = 11.50

solution

the no. of toppings = 3

Answer:

Step-by-step explanation:

Hyp = √(3² + 4²) = 5

cosx = adj/hyp = 3/5

tanx = opp/adj = 4/3

3/5 / 4/3 = 3/5•3/4 = (3•3)/(5•4) = 9/20

Answer:

-8*F, -7.9*F, -7.2*F, -3.5*F, -3*F, 0*F, 2*F, 18*F

Step-by-step explanation:

Answer:

x= $4.25

$4.25 per sundae

Step-by-step explanation:

The equation is 8.25 + 6x = 33.37

subtract 8.25 from both sides

6x=25.5

Divide each side by 6

x=4.25

Answer:

see below

Step-by-step explanation:  5 23  8 03

the lenght of the longer leg of a right triangle is 9 ft longer than the lenght of the shorter leg x. The hypotenuse is 9 ft shorter than twice the lenght of the shorter leg.

shorter leg    = x

longer leg     = x + 9

hypotenuse  =  2x - 9

Pythagorean theorem  =    a² + b²  = c²

             shorter-leg² + longer-leg² = hypotenuse²

                         x²  +  (x+9)²  = (2x - 9)²                  solve for x

                  x² +  (x+9) (x+9)  =  (2x - 9)(2x - 9)

                 x² +  (x²+18x+81)  =  (4x² - 36x + 81)

                       (2x²+18x+81)  =  (4x² - 36x + 81)

                                          0 =   2x² -54x

                                          0 =  x(2x - 54)  

                           0 = x      and         0 = 2x -54  

                                                       54 = 2x

                                                      27 =  x

shorter leg    = 27        

longer leg     = 36

hypotenuse  =  45

divided all the values by 9 and you get a 3, 4, 5  right triangle, so the answer checks correct  

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)