which shows the correct substitution of the values a, b, and c Dr the equation 0=-3x^2-2x+6 into the quadratic formula? Quadratic formula: x= -b±√b^2-4ac/2a
​

Answer: 38°

Using cosine rule,

a² = b² + c² -2bc cos(A)

Insert values from diagram

14² = 18² + 22.8² - 2(18)(22.8) cos(A)

196 = 324 + 519.84 - 820.8 cos(A)

-820.8 cos(A) = 196 - 324 - 519.84

-820.8 cos(A) = -647.84

cos(A) = -647.84/-820.8

A = cos^{-1} (-647.84/-820.8)

A = 37.88°

A ≈ 38°

Answer:

[tex]\boxed {38^{o}}[/tex]

Step-by-step explanation:

Applying Law of Cosines :

⇒ a² = b² + c² - 2bc(cos A)

⇒ 14² = 22.8² + 18² - 2(22.8)(18)(cos A)

⇒ 820.8(cos A) = 519.84 + 324 - 196

⇒ 820.8(cos A) = 647.84

⇒ cos A = 647.84/820.8

⇒ cos A = 0.789278752

⇒ m ∠A = cos⁻¹ (0.789278752)

⇒ m ∠A = 37.88 ≈ 38°

The simplified form of the expression is [tex]4^{-1/3}[/tex]

Given the indices expression as shown;
[tex]\frac{(4^{1/3}\times 4^{2/6} )^{3/4}}{4^{5/6}}[/tex]

Applying the product and quotient law of indices

[tex]\frac{(4^{1/3+1/3})^{3/4}}{4^{5/6}}\\\frac{(4^{2/3})^{3/4}}{4^{5/6}}\\\frac{4^{1/2}}{4^{5/6}}\\[/tex]

Take the difference in the power to have:

4^(1/2 - 5/6)

4^(-2/6)

[tex]4^{-1/3}[/tex]

Hence the simplified form of the expression is [tex]4^{-1/3}[/tex]

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Step-by-step explanation:

0 = sqrt(x - 4) + 3 Set equation equal to 0

-3 = sqrt(x - 4). Subtract 3 from both sides

the principle square root will only output positive values, since if it every outputted a negative value it would not be a function since a function cannot have 2 outputs for the same input.

no x-intercept

Hey there!

[tex] \sf{ \purple{ \boxed{\bold{m = - \dfrac{7}{3} }}}} [/tex]

[tex] \\ [/tex]

We are given the points [tex] \sf{P_1(\overbrace{ \blue{8}}^{\blue{x_1}} ,\underbrace{\orange{-8}}_{ \orange{y_1}}) \: and \: P_2(\overbrace{ \green{5}}^{\green{x_2}} ,\underbrace{\red{-1}}_{\red{y_2} })} [/tex] . To find the slope [tex] \sf{\purple{m}} [/tex] of such a line, we use the slope formula which is the following:

[tex] \sf{ \purple{m} }= \dfrac{\Delta y}{\Delta x} = \dfrac{ \red{y_2} - \orange{y_1}}{ \green{x_2 }- \blue{x_1}} [/tex]

[tex] \\ [/tex]

⇢Now, by plugging in our values, we get :

[tex] \sf{ \purple{m}} = \dfrac{ \red{ - 1} - \orange{( - 8)}}{ \green{5} \: - \: \blue{8}} = \dfrac{ \: \: 7 \: }{ - 3 \: } \\ \\ \implies \sf{ \purple{ \boxed{m = - \dfrac{7}{3} }}}[/tex]

Therefore, the slope of the line is [tex] \sf{ \purple{ \boxed{m = - \dfrac{7}{3} }}} [/tex]

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of a linear function that goes through (8,-8) and (5,-1)?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Formula utilised, here [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

We utilise that formula because we have two points as our given information.

So, we

put in the values

[tex]\bf{\dfrac{-1-(-8)}{5-8}}[/tex] | subtract on top and bottom

[tex]\bf{\dfrac{-1+8}{-3}}[/tex] | simplify

[tex]\bf{\dfrac{7}{-3}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                [tex]\bf{=Slope=-\dfrac{7}{3}}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]

The value of (f + g)(x) is 2x + 8

Let f(x) = 4x + 3 and g(x) = -2x + 5.

Find (f + g)(x).

The functions are given as:

f(x) = 4x + 3

g(x) = -2x + 5

The composite function (f + g)(x) is calculated using

(f + g)(x) = f(x) + g(x)

Substitute known values

(f + g)(x)= 4x + 3 - 2x + 5

Evaluate the like terms

(f + g)(x)= 2x + 8

Hence, the value of (f + g)(x) is 2x + 8

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Answer:

4/9 of the students chose summer.

Step-by-step explanation:

Think about it this way. There are 9 students being asked what their favorite season is. 1 chose spring, 3 chose summer. Add those together, and you have 4 people that chose either spring or summer. That number goes on top of the fraction. The total amount of people that were asked goes on the bottom, which is 9.

The population after t hours is 160 x (1.3797)^t.

The first step is to determine the growth rate of the bacteria:

growth rate = (future population / initial population) ^(1/number of years) - 1

(800 / 160)^(1/5) - 1= 37.97

The exponential function : 160 x (1.3797)^t

Here is the complete question:

A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours

there will be 800 bacteria. Express the population after t hours as a function of t. population:

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Answer:

18

Step-by-step explanation:

30/5=6

6*3=18

Answer:

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

Step-by-step explanation:

x = 3g + 2 ( subtract 2 from both sides )

x - 2 = 3g ( divide both sides by 3 )

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

Answer:

Step-by-step explanation:

x =3g + 2

3g + 2 = x

3g = x - 2

g = 1/3 x - 2/3

Answer: g = 1/3x - 2/3

Answer:

Step-by-step explanation:

Ok so you are given the values of the slope-intercept form with m being the slope and b being the y-intercept. So since b is equal to -1 you want to plot a point at (0, -1) since that is the y-intercept (when x = 0). The next thing you want to do is look at the slope, which is essentially saying each time x increases by 5 the y-value decreases by 4 or in other words rise/run which is negative which is why you're going down. So from the point (0, -1) go forward 5 units and go down 4 units which should lead you to (5, -5) and the third point you can plot is by going backwards instead of forwards. So instead of every time x increases by 5 y decreases by 4 you're going to do the inverse. Every time x decreases by 5, y is going to increase by 4. So by doing this from the y-intercept (0, -1) you should go backwards 5 units and up 4 units which should lead you to (-5, 3). And then now just draw a line that goes through all those three points. Hope that helps :)

Answer:

13x = 39

x=3

y=10

The general equation

B is period and A is amplitude

RearrAnge

Period:-

So final equation

Option C

Answer:

d) 5.88×10^9

Step-by-step explanation:

Answer:

d) 5.88 × 10⁻⁹

Explanation:

[tex]\rightarrow \sf \left(1.2\cdot 10^7\right)\left(4.9\cdot 10^2\right)[/tex]

[tex]\sf apply \ exponent \ rule : a^b + a^c = a^{b + c}[/tex]

[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7}\cdot \:10^{2}[/tex]

[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7+2}[/tex]

[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^9[/tex]

[tex]\rightarrow \sf 5.88 \cdot \:10^9[/tex]

Answer: Quadrant III

Step-by-step explanation:

The slope is negative and the y-intercept is positive.

This means that it is impossible for both x and y to be negative, and thus it does not pass through Quadrant III

Answer:

200:1, Bryn is correct.

Step-by-step explanation:

Each 10 m is represented by a 5cm length on the diagram.  We first note that 100 cm = 1 meter.   5 cm is (0.5 cm)*(1 meter/100 cm) =0.05 meters.

The 0.05 meters on the diagram represents 10 meters on the actual building.  The ratio is (10 meters/0.05 meters) or 200:1.  This is what Bryn believes is the ratio.  

Answer:

160

Step-Step Explaining:

So I Know This ⏩ ⏩

Answer:

+ 9 and - 4

Step-by-step explanation:

9 × - 4 = - 36

9 + (- 4) = 9 - 4 = 5

Answer:

The two numbers are :

9 and -4

9 x -4 = -36

9 + (-4) = 5

Step-by-step explanation:

Hope It Helps!!!

Answer:

+ 10.53 % change

Step-by-step explanation:

Percent change is   4 more people added to 38

   4 / 38  * 100% = 10.53 %

Answer:

D

Step-by-step explanation:

d) A number plus eight is five times the number

Keywords within mathematical phrases can be "translated" into an algebraic equation.

Keywords

First, let's define some of these keywords that can help us answer the question.

Writing Out the Expression

In the figure, we see that the blocks "x" and "8" is equal to the block "5x". So, we can say that x plus 8 is equal to 5x. Then, using the keywords above we can replace the variables and numbers.

1 hamper box, curated by Jithu can be contained 5 cupcakes.

The total amount of cupcakes =665 nos.

Jithu wants to create a gift box, each of which contains 6 cupcakes.

We have to see first, whether 665 could be equally distributed or not.

Hence, 665/6= 110.84 unit

It is seen that the number is in a fraction.so, It can be said that 665 cakes cannot be equally distributed to each gift pack carrying 6 cakes.

Hence, 110*6=660 cupcakes.

∴665-660= 5 cupcakes in one box

So, it is concluded that Jithu could be prepared 110 gift boxes containing 6 cakes each & 1 box containing 5 cupcakes.

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The number of the specimens would be in the culture after 5 minutes will be 7,962.62.

Consider the function:

y = a (1 + r) ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

A bacteria culture grows at a rate of 20% per minute.

If the culture initially has 3,200 bacteria specimens.

Then the equation will be

y = 3200 (1 + 0.2) ˣ

y = 3200 (1.20) ˣ

Then the number of the specimens would be in the culture after 5 minutes will be

y = 3200 (1.20)⁵

y = 7962.62

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Answer:

Step-by-step explanation:

Answer:

the area of rectangle is 270 cm and its length is 18 cm

the breath of the perimeter of given rectangle respectively

used concept

area of rectangle l into b where is is v is breadth of the rectangle perimeter of rectangle 2 into l + b where I and b stands for same as the

solution

let's the length of rectangle is equal to l is equal to 18 cm

breath of rectangle is is equal to b is equal to

area of rectangle is equal to 270 CM

now according to the question and l into b is equal to a

18 into b is equal to 1070

b is equal to 270 upon 18

b is equal to 15 CM

p no no perimeter of the rectangle is equal to 2 into l + b

2 multiply 18 + 15

2 X 33

is equal to 66 cm

therefore the breath and the perimeter of rectangle are 15 cm and 66 respectively

The object moves 2 units to the left and then 3 units up.

Translation is a transformation technique used to change the position of an object on the xy-plane.

Given the translation vector (-2, 3), this translation shows a movement of an object to the left by 2units and 3 units in the upward direction

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Answer:

the answer is 6

Step-by-step explanation:

1. 3x+4=22

2. subtract 4 from both sides

3x+4=22

     -4=22

           -4

3. rewrite the equation   3x=18

4. divide 3 from both sides

3x/3=18/3

hint: 3x/3 cancels out so you just have x

5. divide 18 by 3

6.x=6

Utilizando trigonometría, veremos que la altura del arbol es 6m.

Podemos visualizar la situación como un triangulo rectangulo.

La altura del arbol será el cateto opuesto al angulo de 36.87°.

La distancia a la base del tronco, que es 8 metros, será el cateto adjacente a dicho angulo.

Entonces, podemos usar la relacion:

tan(θ) = (cateto opuesto)/(cateto adjacente).

Reemplazando lo que conocemos, y definiendo:

altura = cateto opuesto = H.

tendremos:

tan(36.87°) = H/8m

Resolviendo para H:

H = tan(36.87°)*8m = 6m

Así, concluimos que la altura del arbol es 6m.

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The value of the expression Z² + Q² is 4321

The radius of the chocolate spheres is given as:

r = 2

The maximum number of chocolates that can fit in a spherical capsule is calculated as:

Max = R³/r³

Where:

R represents the radius of the sphere.

For the spherical capsule whose radius is 8 inches, we have:

Z = 8³/2³

Evaluate

Z = 64

For the spherical capsule whose radius is 5 inches, we have:

Q = 5³/2³

Evaluate

Q = 15.625

Remove decimal

Q = 15

So, we have:

Z² + Q² = 64² + 15²

Evaluate the exponent

Z² + Q² = 4096 + 225

Evaluate the sum

Z² + Q² = 4321

Hence, the value of Z² + Q² is 4321

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Step-by-step explanation:

Hi There! Let me help you :)

[tex] = 8.8.8.8.8.8.8[/tex]

[tex] = ( \text{there \: are \: 7 \:numbers \: eight })[/tex]

[tex] \: [/tex]

So we can rewrite the above equation to be like this.

[tex] = 8.8.8.8.8.8.8[/tex]

[tex] = 8.(1 + 1 + 1 + 1 + 1 + 1 +1)[/tex]

[tex] = 8.7[/tex]

The value of n is 12. and m is 6root5

We have given the diagram,

The measurement of m,

n = 12

According to the altitude theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse.

24/n = n/6

The Cross multiply

24 * 6 = n²

144 = n²

n² = 144

n = √144

n = 12

[tex]m^2=6^2+n^2[/tex]

[tex]m^2=6^2+12^2\\m^2=36+144\\m^2=180[/tex]

[tex]m=\sqrt{180} \\m=2\cdot \:3\sqrt{5}\\m=6\sqrt{5}[/tex]

Hence the value of n is 12.

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Answer:

12

Step-by-step explanation: