7 out of 10 students can ride in a van on the field trip. In how many ways can the 7 students be selected

Answer:

[tex]-x^2+24x-70[/tex]

Step-by-step explanation:

[tex](x-1)^2+(2-x)^2-3(x-5)*(x-5)\\=> (x - 1)^2 + (2 - x)^2 - 3(x - 5)^2\\=> x^2 - 2x + 1 + 4 - 4x + x^2 - 3(x - 5)^2\\=> x^2 - 2x + 5 - 4x + x^2 - 3(x - 5)^2\\=> x^2 - 6x + 5 + x^2 - 3(x - 5)^2\\=> 2x^2 - 6x+5 - 3(x - 5)^2\\=> 2x^2 - 6x+5 - 3(x^2 - 10x + 25)\\=> 2x^2 - 6x+5 - 3x^2+30x-75\\=> -x^2 - 6x + 5 + 30x - 75\\=> -x^2 + 24x + 5-75\\=> -x^2+24x-70[/tex]

Formula used =

[tex](a-b)^2 = a^2+ 2ab + b^2[/tex]

Answer:

Step-by-step explanation:

option a

Answer:

Step-by-step explanation:

Given,

Area of a triangle = 40

Therefore,

Side of the square

[tex] = \sqrt{40} [/tex]

= 6.3245553203

= 6.3 (estimated) (Ans)

Answer:

∠1 = 56

Step-by-step explanation:

To find ∠1 we need to

∠1 + ∠2 = ∠ABD

∠1 + 17 = 75

∠1 = 75 -17

∠1 = 56

Answer:

2000 J

Step-by-step explanation:

We know that

KE = ½ mv²

KE = ½ × 10 × (20)²

KE = 5 × 400

KE = 2000 J

Now we have to,

find the required kinetic energy.

The formula we use,

→ KE = 1/2 mv²

The given information is,

→ Mass (m) = 10 kg

→ Velocity (v) = 20 m/s

Let's find the kinetic energy,

→ 1/2 mv²

→ 1/2 × 10 × (20)²

→ 5 x 400

→ [2000 J]

Thus, kinetic energy is 2000 J.

The simplified form of the expression is 2(31x-20).

Given the expression is -2(x-4)-8(6-8x).

Expressions in mathematics are mathematical statements containing at least two terms containing numbers or variables or both connected by an intermediate operator.

The given expression is solved by using the distributive property a(b+c)=ab+bc, we get

-2(x-4)-8(6-8x)=-2x-4(-2)-8(6)-8(-8x)

-2(x-4)-8(6-8x)=-2x+8-48+64x

Now, we will simplify the above expression by adding or subtracting like terms, we get

-2(x-4)-8(6-8x)=62x-40

-2(x-4)-8(6-8x)=2(31x-20)

Hence, the simplified form of the given expression -2(x-4)-8(6-8x) is 2(31x-20).

Learn more about distributive property from here brainly.com/question/8329981

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Answer:

1, 4, 9

Step-by-step explanation:

1 x 3 = 3

9 x 5 = 45

total = 48

median = 4

twice median = 4×2

= 8

sum = 8 + 40 = 48

48=48

Answer:

$624,000

Step-by-step explanation:

100-4 = 96

96/100 = 0.96

650,000 x 0.96 = 624,000

= $624,000

Answer:

Step-by-step explanation:

I think it’s translation because your just sliding the figure

Answer:

Distribute 2 to (x + 6) and 3 to (x – 4).

Step-by-step explanation:

While solving for:

2(x+6) = 3(x-4) + 5

Firstly, we need to open the parenthesis. For this, we've to distribute 2 to (x+6) and 3 to (x-4).

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

[tex]\frac{5+\sqrt{17}}{4}[/tex],      [tex]\frac{5-\sqrt{17}}{4}[/tex]

Step-by-step explanation:

One is asked to find the root of the following equation:

[tex]2x^2+1=5x[/tex]

Manipulate the equation such that it conforms to the standard form of a quadratic equation. The standard quadratic equation in the general format is as follows:

[tex]ax^2+bx+c=0[/tex]

Change the given equation using inverse operations,

[tex]2x^2+1=5x[/tex]

[tex]2x^2-5x+1=0[/tex]

The quadratic formula is a method that can be used to find the roots of a quadratic equation. Graphically speaking, the roots of a quadratic equation are where the graph of the quadratic equation intersects the x-axis. The quadratic formula uses the coefficients of the terms in the quadratic equation to find the values at which the graph of the equation intersects the x-axis. The quadratic formula, in the general format, is as follows:

[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]

Please note that the terms used in the general equation of the quadratic formula correspond to the coefficients of the terms in the general format of the quadratic equation. Substitute the coefficients of the terms in the given problem into the quadratic formula,

[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]

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

Simplify,

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

[tex]\frac{5(+-)\sqrt{25-8}}{4}[/tex]

[tex]\frac{5(+-)\sqrt{17}}{4}[/tex]

Rewrite,

[tex]\frac{5(+-)\sqrt{17}}{4}[/tex]

[tex]\frac{5+\sqrt{17}}{4}[/tex],      [tex]\frac{5-\sqrt{17}}{4}[/tex]

4 no. one i guess 10

not sure

Answer:

6. was Narbada alienated ...?

7. did Pratima make ...?

8. did Zayasha wander ...?

9. Did Sachin behave as if...?

10. did susan look ...?

12. do sarina and sazina jump ...? (plural noun)

13. Were ... and ... aghast to...?

Step-by-step explanation:

yes/ no question:

Past simple: Did + S + V-bare...?

Passive voice (Past simple): Was/ Were + S + V3/ed (past participle)

The decimal value 0.1 converts to the fraction 1/10

This is because the 1 in 0.1 represents "one tenth", as its in the tenths place.

So this means 2/0.1 is the same as 2/(1/10) or [tex]2 \div \frac{1}{10}[/tex]

Then we can follow these steps:

[tex]2 \div \frac{1}{10} = \frac{2}{1} \div \frac{1}{10}\\\\\\2 \div \frac{1}{10} = \frac{2}{1} \times \frac{10}{1}\\\\\\2 \div \frac{1}{10} = \frac{2*10}{1*1}\\\\\\2 \div \frac{1}{10} = \frac{20}{1}\\\\\\2 \div \frac{1}{10} = 20\\\\\\[/tex]

Note in the second step, we flip the second fraction to go from a division problem to a multiplication problem. The general rule is [tex]\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}[/tex]. The first fraction does not flip.

Answer:

The 1st term is -67

Step-by-step explanation:

I. When Sn = [tex]\frac{n}{2}[/tex]([tex]a_{1} + a_{n}[/tex])

   If  Sn = 124, n = 8 and [tex]a_{n}[/tex] = 98

                124 = 8/2(a + 98)

                124 = 4(a + 98)

                124 = 4a + 392

                124 - 392 = 4a

                -268/4 = a

                -67 = [tex]a_{1}[/tex]

Hope that help :D

Answer:

is it $21.75

Step-by-step explanation:

add it together

Answer:

$21.75

Step-by-step explanation:

$12.75+$9=$21.75.

Answer:

48.2

Step-by-step explanation:

We have a right angle so we can do our three trig ratios,

Sine Cosine Tangent

Remeber SOHCAHTOA.

We are given some angle theta, and we are given a side adjacent to the angle and the hypotenuse. We are going to use the cosine rule.

[tex] \cos(theta) = \frac{36}{54} [/tex]

[tex] \cos(theta) = \frac{2}{3} [/tex]

Take the inverse of both sides

[tex] \cos {}^{ - 1} ( \frac{2}{3} ) = x[/tex]

Theta is equal to

[tex]48.2[/tex]

Answer:

2.5

Step-by-step explanation:

Answer:

[tex]thank \: you[/tex]

Answer:

675 ÷ 3 - ( 225 - 144)

675 ÷ 3 - (81)

225 - 81

144

I hope it's helps you

Answer:

[tex]675 \div 3 - (15 - 12) {}^{2} \\ \\ 675 \div 3 - (225 - 144) \\ \\ 675 \div 3 - 81 \\ \\ 225 - 81 \\ \\ = 144[/tex]

Answer:

4+7(11)

Step-by-step explanation:

the square root of 121 is 11 so it would be 4+7(11)

Answer:

4 + 7 × 11

Step-by-step explanation:

[tex]4 + 7 \sqrt{ {5}^{3} - 4} [/tex]

[tex] = 4 + 7 \sqrt{125 - 4} [/tex]

[tex] = 4 + 7 \sqrt{121} [/tex]

simplify the square root of 121

[tex] \boxed{\green{\boxed{\bold{= 4 + 7 \times 11}}}}[/tex]

[tex] = 4 + 77[/tex]

[tex] = 81[/tex]

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Answer:

b= x

Step-by-step explanation:

[tex]\boxed{ {x}^{m} \times {x}^{n} = {x}^{m + n} }[/tex]

Applying the law of indices above:

[tex]b = {x}^{ \frac{1}{4} } \times {x}^{ \frac{3}{4} } [/tex]

[tex]b = {x}^{ \frac{1}{4} + \frac{3}{4} } [/tex]

[tex]b = {x}^{ \frac{4}{4} } [/tex]

[tex]b = {x}^{1} [/tex]

∴b= x

Answer:

It is b = x

Step-by-step explanation:

From law of indices:

[tex] {a}^{b} \times {a}^{c} = {a}^{(b + c)} [/tex]

for, multiplication: same coefficients, we sum up the powers.

[tex]b = {x}^{ \frac{1}{4} } \times {x}^{ \frac{3}{4} } \\ b = {x}^{( \frac{1}{4} + \frac{3}{4} ) } \\ b = {x}^{ \frac{4}{4} } \\ b = {x}^{1} \\ b = x[/tex]

Answer:

k=13

Step-by-step explanation:

3k+6+4k-7+90=180

7k+89=180

k=180-89/7

k=13

Answer:

13 inches

Step-by-step explanation:

in an equilateral triangle all sides had we the same length.

so, the perimeter is simply 3×one triangle side.

and the perimeter of the square is 4×one square side.

x = triangle side length

y = square side length

3x = 4y + 15

x = y + 7

we use the second equation as substitution in the first equation.

3(y + 7) = 4y + 15

3y +21 = 4y + 15

6 = y

x = y + 7 = 6 + 7 = 13 inches

same as we did for the other question,

5y=-x-20

then divide the 5

y= (-1/5)x-4

Step-by-step explanation:

f(x) = |x-7| + 3

when x is equal to 4, then

f(4) = |4-7| + 3

=-3+3

=0

Answer:

[tex]\boxed {\boxed {\sf f(4)= 6}}[/tex]

Step-by-step explanation:

We are asked to find f(4) for a function. We are finding the output or y-value when the input or x-value is 4.

[tex]f(x)= |x-7| +3[/tex]

Substitute 4 for x in the function.

[tex]f(4) = |4-7| +3[/tex]

Solve inside the absolute value signs.

[tex]f(4)= |-3|+3[/tex]

The absolute value of a number is its distance from 0 on a number line.  It is always the positive version of a number, so the absolute value of -3 is 3.

[tex]f(4)= 3+3[/tex]

Add.

[tex]f(4)= 6[/tex]

For the function f(x)= |x-7| +3, f(4) is equal to 6.

Identify which number??

Answer:

FOIL stands for multiply the first, outside, inside, and last terms together. When you FOIL a binomial times itself, the product is called a perfect square. For example, (a + b)2 gives you the perfect-square trinomial a2 + 2ab + b2.

Step-by-step explanation:

Answer:

12/99

Step-by-step explanation:

x=0.121212

100x=12.121212

100x-x=12.1212-0.1212

99x=12

x= 12/99

Answer:

6/50 is simplified to 3/25

Step-by-step explanation:

step 1 Address input parameters & values.

Input parameters & values: The decimal number = 0.12

parameters & values: The decimal number = 0.12step 2 Write it as a fraction

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100It can be written as 12% = 12/100 or 12/100

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100It can be written as 12% = 12/100 or 12/100step 4 To simplify 12/100 to its lowest terms, find LCM (Least Common Multiple) for 12 & 100.

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100It can be written as 12% = 12/100 or 12/100step 4 To simplify 12/100 to its lowest terms, find LCM (Least Common Multiple) for 12 & 100.4 is the LCM for 12 & 100

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100It can be written as 12% = 12/100 or 12/100step 4 To simplify 12/100 to its lowest terms, find LCM (Least Common Multiple) for 12 & 100.4 is the LCM for 12 & 100step 5 divide numerator & denominator by 4

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100It can be written as 12% = 12/100 or 12/100step 4 To simplify 12/100 to its lowest terms, find LCM (Least Common Multiple) for 12 & 100.4 is the LCM for 12 & 100step 5 divide numerator & denominator by 412/100 = (12 / 4) / (100 / 4)

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100It can be written as 12% = 12/100 or 12/100step 4 To simplify 12/100 to its lowest terms, find LCM (Least Common Multiple) for 12 & 100.4 is the LCM for 12 & 100step 5 divide numerator & denominator by 412/100 = (12 / 4) / (100 / 4)= 3/25

parameters & values: The decimal number = 0.12step 2 Write it as a fraction0.12/1step 3 Multiply 100 to both numerator & denominator(0.12 x 100)/(1 x 100) = 12/100It can be written as 12% = 12/100 or 12/100step 4 To simplify 12/100 to its lowest terms, find LCM (Least Common Multiple) for 12 & 100.4 is the LCM for 12 & 100step 5 divide numerator & denominator by 412/100 = (12 / 4) / (100 / 4)= 3/253/25 is a simplest fraction for the decimal point number 0.12