A student committee is to consist of 2 freshmen, 5 sophomores, 4 juniors, and 3 seniors. If 6 freshmen, 13 sophomores, 8 juniors, and 14 seniors are eligible to be on the committee, in how many ways can the committee be chosen

Answer:

The vertex is the point of coordinates (-2 , 5)

Step-by-step explanation:

we notice that the equation of the parabola is given in vertex form :

y = -4(x + 2)² + 5

then

y = -4(x − (-2))² + 5

Therefore

The vertex of the graph is the point (-2 , 5)

Answer:

-12 ≤ p ≤ 12

Step-by-step explanation:

If the absolute value inequality is

|p| ≤ 12,

then the answer is

-12 ≤ p ≤ 12

Answer: 28,278.10

Step-by-step explanation:

[tex]a_{7} =16500(1.08)^7[/tex]

[tex]a_{7} =28278.1[/tex]

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]

Answer:

21/4

Step-by-step explanation:

Answer:

[tex]\frac{42}{8}[/tex]

Step-by-step explanation:

• First multiply the numerators:

6 x 7 = 42

• Then multiply the denominators:

(6 doesn't have a denominator, which is the same as having a denominator of 1)

1 x 8 = 8

∴ The answer is [tex]\frac{42}{8}[/tex] .

Answer:

13x = 39

x=3

y=10

Answer:

Step-by-step explanation:

The equation is 1.56 + 20x = 33.96 and the value of x is 1.62.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Here, Based on the given conditions, formulate: 1.56 + 20 × x = 33.96

Rearrange unknown terms to the left side of the equation:  20x = 33.96-1.56

Calculate the sum or difference: 20x = 32.4

Divide both sides of the equation by the coefficient of variable: x = 32.4/20

Calculate the product or quotient: x = 1.62

get the result: x = 1.62

Thus, the equation is 1.56 + 20x = 33.96 and the value of x is 1.62.

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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:

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 :)

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:

lklklkj

Step-by-step explanation:

67890-

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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Answer:

 its a geometric sequence where each term is 3 times the previous term.

Step-by-step explanation:

{2,6,18,54,162,486,1458...}

Step-by-step explanation:

yes right angle measure 90 degrees

mark me brainliest

Answer:

a

2

−

b

2

Since both terms are perfect squares, factor using the difference of squares formula,

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

where

a

=

a

and

b

=

b

.

The general equation

B is period and A is amplitude

RearrAnge

Period:-

So final equation

Option C

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:

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

Answer:

swap x and y

Step-by-step explanation:

You can find an inverse function by replacing "x" and "y"

for example:

y = mx + b

becomes

x = my + b

if your equation is:

f(x) = 3(x²) - 3

{remember, f(x) means the same thing as y}

y = 3(x²) - 3

inverse:

x = 3(y²) - 3

this is it, hope this is helpful!!

Answer:

make every (x) a (y)

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°

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

Answer:

-1

Step-by-step explanation:

the answer snis negative One

The equation of this circle in standard form is (x-2)² + (y+3)² = 18

The center of the circle is at the point  (2,-3), and its radius is 4.2426 units

Circle is the 2D geometry which is round in shape with radius R.

Given is the general form of the equation of a circle is

7x² + 7y² − 28x + 42y − 35 = 0.

Dividing by 7, we get

x² -4x + y² + 6x = 5

Completing the squares, we have

x² -4x + 4 + y² +6x + 9 = 5 +4 + 9

(x-2)² + (y+3)² = 18 = (3 √2)²

Circle's center is (2,-3) and  radius = 3 √2 = 4.2426 units

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Answer:

(x-2)^2 + (y+3)^2 = 18,

2,-3

3(2^(1/2)) units

Step-by-step explanation:

Below

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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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.

Answer:

75 km

Step-by-step explanation:

(50km/h)(1.5h) = 75km

[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]

Answer:

Step-by-step explanation:

Just took the test:

6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=

2sqrt15/5 cis (5pie/6)

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:

D

Step-by-step explanation:

The product of the slopes of two perpendicular lines is -1.

If the slopes of the diagonals are 1 and -1, then their product is -1, and they are perpendicular.

Answer: D

A sentence that describes what Talia should do to show that the diagonals of the square are perpendicular is: D. show that the slope of SQ is 1 and the slope of PR is -1.

In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other.

Therefore, we would have to calculate the slope of each side by using this mathematical equation:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m₁) of SQ = (a - 0)/(a - 0)

Slope (m₁) of SQ = a/a = 1.

Slope (m₂) of PR = (a - 0)/(0 - a)

Slope (m₂) of PR = -a/a = -1.

Based on the condition for two (2) perpendicular lines, we have:

m₁ × m₂ = -1

1 × -1 = -1

-1 = -1

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