A = {1,4,5,7}
B = {1,7,9,12}
Find A ∩ B.

A) {1,4,5,7,9,12}
B) {1,7}
C) {1}
D) {7}

Answer:

In 1 seconds after being thrown will the stone reach its maximum height.

Step-by-step explanation:

Given : Ming throws a stone off a bridge into a river below.  The stone's height (in meters above the water), 3 seconds after Ming threw it, is modeled by : [tex]h(x) = -5(x - 1)^2 + 45[/tex].

To find : How many seconds after being thrown will the stone reach its maximum height?

Solution :

The maximum height is attain by getting the vertex of the model.

The vertex form of the quadratic equation or parabola is

[tex]f (x) = a(x - h)^2+ k[/tex]

Where, (h,k) are the vertex.

On comparing with the given model, [tex]h(x) = -5(x - 1)^2 + 45[/tex]

a=-5, h=1 and k=45

The vertex of the equation is (h,k)=(1,45).

Now the maximum height is 45 m and number of second is 1 sec.

Therefore, In 1 seconds after being thrown will the stone reach its maximum height.

Answer:

Is this a book ????

Step-by-step explanation:

but roman

The winner of a match between Roman Reigns and Goldberg at WrestleMania is predetermined by WWE's creative team based on storytelling needs and is not an actual competitive event.

The outcome of a wrestling match between Roman Reigns and Goldberg at WrestleMania would depend on the storytelling and booking decisions made by the WWE's creative team.

Wrestling matches are choreographed and the winners are predetermined for entertainment purposes. Thus, it's not possible to predict who would win in a real competition since the outcomes are planned.

However, looking at both wrestlers' track records and their standing with the WWE at the time of your question could give us an idea of who the company might favor to write as the victor.

Answer:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Exact Form:

x= −20/3

Decimal Form:

x= −6.66...

Mixed Number Form:

x= −6  2/3

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

23 x 4 = 92

Final answer:

The probability of selecting a girl to represent the class on the student council, from a class of 12 boys and 14 girls, is 7/13 or approximately 53.85%.

Explanation:

This question demands basic understanding of probability

The question relates to determining the probability that a student selected at random to represent a class at student council is a girl. Given there are 12 boys and 14 girls in the class, the total number of students is 12 + 14 = 26. The probability of selecting a girl is therefore the number of girls divided by the total number of students, which is 14/26. Simplified, this probability is 7/13, which can be approximated to 0.5385 or 53.85%.

Therefore, as per the above explaination, the correct answer is 53.85%

Answer:

C - 2/5

Step-by-step explanation:

Using the formula for slope

m = (y_2 - y_1) / (x_2 - x_1)

Given two points

( 4 , 5) (-1 , 3)

x_1 = 4

y_1 = 5

x_2 = -1

y_2 = 3

Insert the values into the equation

m = (y_2 - y_1) / (x_2 - x_1)

m = ( 3 - 5) / ( -1 - 4)

= -2 / -5

- $ - cancels out

m = 2/5

Slope = m = 2/5

Annie uses 6 meters of yarn for each scarf and 2 meters for each beanie, based on creating a system of equations from the given data and solving it.

The student is asking to solve a system of equations to find out how much yarn is required for each scarf and beanie that Annie is knitting. To determine the amount of yarn needed for each project, we will use the information given for two separate days. On the first day, 3 scarves and 2 beanies used a total of 22 meters of yarn. On the second day, 1 scarf and 2 beanies used a total of 10 meters of yarn. Let's denote the amount of yarn needed for a scarf by 'S' and for a beanie by 'B'.

We can set up the following system of equations:

Subtract the second equation from the first to eliminate 'B' and solve for 'S':

Now, we can substitute 'S' back into the second equation to solve for 'B':

Therefore, each scarf requires 6 meters of yarn and each beanie requires 2 meters of yarn.

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Answer:

6.157

Step-by-step explanation:

A=πr^2=π·14^2≈615.75216

Answer:

7x=3x+24

4x=24

x=6

Answer:

[tex]x=6\\[/tex]

Step-by-step explanation:

[tex]7x=3x+24[/tex]

[tex]7x-3x=3x-3x+24[/tex]

[tex]4x=24[/tex]

[tex]\frac{4x}{4} =\frac{24}{4}[/tex]

[tex]x=6[/tex]

Answer:

-63

You say PEMDAS I say BIDMAS. So first you gotta do brackets. So -25 + 4². To do this you need to find out 4² = 16. -25 + 16 = -9. Now -9 x 7 = -63

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We see here that $1 will buy 5 ounces of ground turkey.

To find out how much $1 will buy, we can set up a proportion using the given information.

We know that $8 buys 40 ounces of ground turkey. Let's set up the proportion:

$8/40 ounces = $1/x ounces

To solve the proportion, we can cross-multiply:

$8 × x ounces = 40 ounces * $1

Simplifying further:

$8x = $40

To isolate x (the number of ounces that $1 will buy), we can divide both sides of the equation by $8:

x = $40 / $8

x = 5 ounces

Therefore, $1 will buy 5 ounces of ground turkey.

Alternatively, we can set up a ratio using the given information:

$8 for 40 ounces

To find out how much $1 will buy, we can find the unit price:

Unit price = Total cost / Total quantity

Unit price = $8 / 40 ounce

Unit price = $0.20 per ounce

Since $1 is equal to 100 cents, we can divide $1 by the unit price:

$1 / $0.20 per ounce = 5 ounces

Therefore, $1 will buy 5 ounces of ground turkey.

Complete question:

$8 buys 40 ounces of ground turkey, how much will $1 buy?

Answer:

6

Step-by-step explanation:

you first divide 81 by 18 and get 4.5, that is the number of children per adult.

next you'll divide 27 by 4.5 and 6.

that's the answer.

Final answer:

With an initially provided ratio of 18 adults for 81 children, the simplified ratio is 1 adult for every 4.5 children. Hence, for a group of 27 kids, 6 adults are needed to maintain the same supervision ratio.

Explanation:

To determine the number of adults needed for a group of 27 kids on a field trip when there are 18 chaperones supervising 81 children, we can calculate the adult-to-child ratio. We start with the given total ratio of 18 adults for 81 children. This simplifies to 1 adult for every 4.5 children, as 81 divided by 18 equals 4.5. Therefore, for a group of 27 children, we divide 27 by 4.5 to find the number of adults needed.

27 kids
/ 4.5 kids/adult = 6 adults

Thus, 6 adults are needed for a group of 27 kids to maintain the same supervision ratio.

Answer:

13.8

Step-by-step explanation:

First, lets convert to fraction

20.7 = 207/ 10

1.5 = 15/10

therefore,

20.7 / 1.5 becomes;

(207/10) / (15/10)

this becomes;

(207/10) * (10/15)

10 cancels out

= 207/15

Divide both numerator and denominator by 3

=69/5

=13.8

Answer:

3.04

Step-by-step explanation:

The factorization of 30x^2 + 40xy + 51y^2 over the integers appears not to be possible due to the coefficients and a discriminant that is unlikely to be a perfect square. Advanced methods may be needed to factorize it if at all possible.

The factorization of the expression 30x^2 + 40xy + 51y^2 is a task in algebra, which involves breaking down the given quadratic expression into products of its factors. However, this specific expression does not factorize neatly over the integers. When factoring, one would typically look for two binomials that multiply to the quadratic expression, but in this case, due to the coefficients and the lack of a clear common factor or a pattern that matches a known factoring formula, it is likely that the quadratic expression cannot be factored over the rational numbers without resorting to more advanced techniques or numerical methods. To completely verify this, you would use the quadratic formula to find the roots of the corresponding quadratic equation and see if they are rational numbers. If they are not, then exact factoring over the rationals is impossible.

Remember, for a quadratic expression ax^2+bx+c to be factorizable over the rationals, the discriminant, which is b^2-4ac, must be a perfect square. In the case of 30x^2 + 40xy + 51y^2, calculating the discriminant may help determine the factorizability of the expression. If the discriminant is not a perfect square, the expression cannot be factored into rational factors.

Value of h(1.5) is 33

Step-by-step explanation:

⇒ h(1.5) = 22 × 1.5 = 33

Final answer:

To find h(2) when x = 1.5, you first determine the constant of variation (k) using the given information h(x) = 44 when x = 2. This leads to k = 22. Plugging x = 1.5 into the direct variation equation h(x) = k*x, we get h(1.5) = (option D) 33.

Explanation:

If h(x) varies directly with x, then we can express this relationship as h(x) = k*x, where k is the constant of variation. We're given that h(2) = 44, so we can solve for k by plugging in the values:

44 = k*2 => k = 22.

Now that we have the value of k, we can find h(1.5) by multiplying k by 1.5:

h(1.5) = 22 * 1.5 = 33.

Therefore, the value of h(2) when x = 1.5 is (option D) 33.

Answer:

Step-by-step explanation:

Area of parallelogram=base*height

So 1.75*1.5=2.625cm²

Answer:

2.625

Step-by-step explanation:

The value of k is –6.

Solution:

Given equation:

[tex]$\frac{5 \cdot 5^{k}}{5^{-8}}=5^{3}[/tex]

To find the value of k:

[tex]$\frac{5 \cdot 5^{k}}{5^{-8}}=5^{3}[/tex]

Using exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]

[tex]$\frac{5^{1+k}}{5^{-8}}=5^{3}[/tex]

Using exponent rule: [tex]\frac{1}{a^{-m}} = a^{m}[/tex]

[tex]$ 5^{1+k} \cdot 5^{8}=5^{3}[/tex]

Using exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]

[tex]$ 5^{1+k+8}=5^{3}[/tex]

[tex]$ 5^{k+9}=5^{3}[/tex]

If the bases are same then, we can equate the powers of the bases.

i. e. If [tex]a^m = a^n[/tex] then m = n.

k + 9 = 3

Subtract 9 from both sides of the equation, we get

k = –6

Hence the value of k is –6.

Answer: A roll of plain wrapping paper costs $17, while a roll of holiday wrapping paper costs $20.

Step-by-step explanation: First let us represent a roll of plain wrapping paper with letter p and a roll of holiday wrapping paper would be represented by d. If Eduardo sold 5 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for $185, then we can express this as

5p+ 5d= 185

Also if Sarawong sold 14 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for $338, then this too can be expressed as

14p + 5d = 338

Now we have a pair of simultaneous equations which are,

5p + 5d = 185 ———(1)

14p + 5d = 338 ———(2)

Since all the variables have coefficients greater than 1, we shall use the elimination method. Note that the coefficients of the d variable are both 5, so straight away we subtract equation (1) from equation (2) and we now have;

(14p - 5p) + (5d - 5d) = 338 - 185

9p = 153

Divide both sides of the equation by 9

p = 17

Having calculated p, we can now substitute for the value of p into equation (1)

5p + 5d = 185

5(17) + 5d = 185

85 + 5d = 185

Subtract 85 from both sides of the equation

5d = 100

Divide both sides of the equation by 5

d = 20

Hence, the cost per roll of plain wrapping paper is $17, while the cost per roll of holiday wrapping paper is $20.

Solution:

Given that,

[tex]f(x) = 2x^2 + 5\sqrt{x + 2}[/tex]

We have to find f(2)

To find f(2), plug in x = 2 in given f(x) and solve to get the answer

Plug in x = 2 in f(x)

[tex]f(2) = 2(2)^2 + 5 \sqrt{2+2}\\\\f(2) = 2 \times 4 + 5\sqrt{4}\\\\Simplify\\\\f(2) = 8 + 5 \times 2\\\\f(2) = 8 + 10\\\\f(2) = 18[/tex]

Thus the value of f(2) is 18

Answer:

remainder is 9

Step-by-step explanation:

multiples of 25 are:

25 , 50 , 75

84-75 = 9

Answer:

The remainder is 9

Step-by-step explanation:

Step 1:  Find the remainder

84/25

25 goes into 84 3 times.

84 - 3(25)

84 - 75

9

Answer:  The remainder is 9

Answer:

It has no solution

Step-by-step explanation:

3x - 2y = 3

6x  - 4y = 1

To fond the number of solutions, we will first of all solve this system of equation.

We can solve this system of equation by either substitution method or elimination method  or both method

We will be using both method to solve this system of equation.

3x - 2y = 3 ------------------------------------(1)

6x  - 4y = 1 ------------------------------------(2)

we will first eliminate y, to do that, lets multiply equation (1) by 4 and then multiply equation(2) by 2

12x - 8y  = 12 ----------------------------------(3)

12x -  8y = 2 ------------------------------------(4)

Subtract equation (4) from equation (3)

0 = 10

But 0≠  10

This system of equation has no solution

Answer:

No solution.

Step-by-step explanation:

3x-2y=3

6x-4y=1, or 2(3x-2y)=1, 2×3=1, 6=1

Since 6 cannot be equal to 1, this system of equations has no solution

Answer:

Step-by-step explanation:

Given equation is StartFraction 2 Over 9 EndFraction x + two-thirds x = 7.

It can be written as [tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]

That is to find the Least common Multiple of the denominators.

[tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]

[tex]\frac{2x+2x(3)}{9}=7[/tex] ( here LCM of 9 and 3 is 9 so we take 9 as  LCM )

Answer: the answer is 9

Step-by-step explanation: I took the test and its right

Answer:

7/24 feet.

Step-by-step explanation:

That would be 7/16 of 2/3

= 2/3 * 7/16

= 14/48

= 7/24 feet.

The new length of the board after being cut to 7/16 of its original length is 7/24 foot.

Yes, the thing you need to understand here is that you've to multiply the length of the board by the fraction given to find the new length. So, in this problem, the original length of the board was 2/3 foot and it was cut to 7/16 of its original length. Hence, to find the new length, you multiply 2/3 foot by 7/16.

This results in 14/48 foot, which when simplified/reduced gives 7/24 foot. Therefore, the new length of the board after it is cut is 7/24 foot.

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Answer:

x = 28

Step-by-step explanation:

Step 1:  Make an equation to represent the words

In an equation what number do you subtract from 59 to get 31?

59 - x = 31

Step 2:  Solve for x

59 - x - 59 = 31 - 59

-x / -1 = -28 / -1

x = 28

Answer:  x = 28

Answer:

see the explanation

Step-by-step explanation:

we have

Felicia

[tex]-5(3x+2)+10x[/tex]

Apply distributive property

[tex]-5(3x)-5(2)+10x[/tex]

[tex]-15x-10+10x[/tex]

Combine like terms

[tex]-5x-10[/tex]

Let

a ----> the missing term with coefficient x in Gregory's expression

b ----> the missing constant  term in Gregory's expression

so

[tex]-12-4x+ax+b[/tex]

equate Gregory's expression to Felicia's expression

[tex]-12-4x+ax+b=-5x-10[/tex]

so

[tex]-12+b=-10[/tex] ----->[tex]b=2[/tex]

[tex]-4x+ax=-5x[/tex] ------> [tex]a=-1[/tex]

so

Gregory's expression is

[tex]-12-4x+2-x[/tex]

therefore

The missing terms are 2 and -x

Observe that [tex]16r^4[/tex] is the square of [tex]4r^2[/tex], and 625 is the square of 25.

So, your expression is a difference of squares, and as such we can rewrite it as

[tex]16r^4-625=(4r^2+25)(4r^2-25)[/tex]

Now again, [tex]4r^2[/tex] is the square of [tex]2r[/tex], and 25 is the square of 5. So, we have a sum and a difference of squares.

But if we think of 25 as [tex]-(5i)^2[/tex], we have again the difference of two squares, so we have

[tex]4r^2+25=(2r+5i)(2r-5i)[/tex]

[tex]4r^2-25=(2r+5)(2r-5)[/tex]

Option A is the correct expression equivalent to 16r⁴-625.

The options in the question must have r in place of x.

The imaginary number 'i' is the solution of the algebraic equation x²+1.

Thus, x²+1=(x+i)(x-i).

We can observe that (a+bi)(a-bi)=(a²+b²)+i(-ab+ba)=a²+b².

Hence the factorization of a²+b² is (a+bi)(a-bi)

16r⁴-625

=(4r²-25)(4r²+25)

=(2r-5)(2r+5)(2r+5i)(2r-5i)

So, option A is the correct expression equivalent to 16r⁴-625.

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Answer:

7 > 5

Step-by-step explanation:

On a number line, 7 is to the right of 5.

On the number line, a number is greater than a number to its left.

7 is greater than 5

7 > 5

Answer:

x=-0.37 or 5.37

Step-by-step explanation:

The quadratic formula is;

[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

The expression to be solved is

[tex] {x}^{2} - 5x - 2 = 0[/tex]

Comparing this to the general form of the quadratic equation,

[tex] a{x}^{2} + bx + c = 0 [/tex]

a=1, b=-5 and c =-2.

We substitute these values into the quadratic formula

[tex] \implies x = \frac{ - ( - 5)\pm \sqrt{ { (- 5)}^{2} - 4(1)( - 2)} }{2(1)} [/tex]

Simplifying we obtain,

[tex] x = \frac{ 5\pm \sqrt{25 + 8}}{2} [/tex]

[tex] \implies x = \frac{ 5\pm \sqrt{28}}{2} [/tex]

[tex] \implies x = \frac{5 + 2\sqrt{7} }{2}or \frac{5 - 2 \sqrt{7} }{2} [/tex]

[tex]\implies x = \frac{5}{2} + \sqrt{7} or \frac{5 }{2} - \sqrt{7} [/tex]

x=5.37 or -0.37

The solutions to the quadratic equation x² - 5x - 2 = 0 are:

x = (5 + √33) / 2

x = (5 - √33) / 2

To solve the quadratic equation x² - 5x - 2 = 0 using the quadratic formula, we can use the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a, b, and c represent the coefficients of the quadratic equation.

For the equation x² - 5x - 2 = 0, we can identify the values of a, b, and c:

a = 1

b = -5

c = -2

Substituting these values into the quadratic formula, we have:

x = (-(-5) ± √((-5)² - 4 × 1 × (-2))) / (2 × 1)

Simplifying:

x = (5 ± √(25 + 8)) / 2

x = (5 ± √33) / 2

Therefore, the solutions to the quadratic equation x² - 5x - 2 = 0 are:

x = (5 + √33) / 2

x = (5 - √33) / 2

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