The hypotenuse of a 30°-60°-90°
triangle has a length of 12 cm.
Which could be the length of a leg
of the triangle?

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

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: Option D) 15 miles

Step-by-step explanation:

if Jordan drives 3 miles in one hour

Then, 3 miles = 1 hour

while Z miles = 5 hours

cross multiply

3 miles x 5 hours = Z miles x 1 hour

15 = Z

Thus, jordan drove through a distance of 15miles

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

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.

Answer:

3/25

Step-by-step explanation:

You know that percent is out of 100, so that's 12/100

Then simplify the fraction to 6/50 then 3/25

Final answer:

Gigi spent 12% of her birthday money on sunglasses, which is equivalent to 3/25 of her birthday money when converted and simplified from a percentage to a fraction.

Explanation:

Gigi spent 12% of her birthday money on a new pair of sunglasses. To find out what fraction of her birthday money this represents, we convert the percentage to a fraction. Percent means 'per hundred,' so 12% can be written as 12 per 100 or, more simply, 12/100. However, this fraction can be simplified further. Both the numerator (12) and the denominator (100) can be divided by their greatest common divisor, which is 4. Dividing both by 4, we get 3/25. Therefore, Gigi spent 3/25 of her birthday money on the new sunglasses.

Answer:

92

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

23 x 4 = 92

Answer:

6.157

Step-by-step explanation:

A=πr^2=π·14^2≈615.75216

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

⭐ Answered by Foxzy0⭐

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Answer:

11 minutes.

Step-by-step explanation:

To find the median queing time from the cumulative frequency curve, we find

[tex] \frac{1}{2} \sum \: f[/tex]

and trace it on the cumulative frequency curve.

From the graph, that total frequency is 100.

Half of this 50.

We trace the 50th item.

First locate 50 on the vertical axis and trace to the horizontal axis.

This corresponds to 11.

Note that each box is 0.5 units on the queing time axis.

Answer:

Step-by-step explanation:

Area of parallelogram=base*height

So 1.75*1.5=2.625cm²

Answer:

2.625

Step-by-step explanation:

Step-by-step explanation:

Let's select values for X, and find the corresponding Y values:

X = -3, Y = 8.5

X = -2, Y = 7

X = -1, Y = 5.5

X = 0, Y = 4

X = 1, Y = 2.5

X = 2, Y = 1

X = 3, Y = -0.5

So our coordinates are:

(-3, 8.5) ; (-2, 7) ; (-1, 5.5) ; (0, 4) ; (1, 2.5) ; (2, 1) and (3, 0.5)

Graph these on a chart to visualize:

(In picture)

We can see that this is a decreasing linear function, not quadratic. Quadratic functions create a symmetrical curve, which this is not.

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

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:

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:

2 • (y3 - 2y + 5)

Step-by-step explanation:

mark me brainliest please

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:

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:

-5/2

Step-by-step explanation:

Since they are both parallel they have the same rate of change. this means they have the same slope

Final answer:

Since line w is parallel to line v, which has a slope of -5/2, the slope of line w is also -5/2.

Explanation:

When two lines are parallel, they have the same slope. In this case, the slope of line w will be the same as the slope of line v.

Therefore, the slope of line w is -5/2.

The question asks about the slope of two parallel lines. By definition, parallel lines have the same slope. Given that line v has a slope of -5/2, and line w is parallel to line v, the slope of line w must also be -5/2. Therefore, line w, being parallel to line v, has a slope of -5/2.

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:

one $10 bill

Step-by-step explanation:

First you have to add them all together then subtract the sum by $69. That's how you get the answer.

Answer:

The answer is 290°

Step-by-step explanation:

Final answer:

To find the bearing of point X from point Z, we can use the given bearings of points X, Y, and Z. Start with the bearing of point Z from point X, add the bearing of point Z from point Y, and subtract the bearing of point Y from point X.

Explanation:

To find the bearing of point X from point Z, we can use the given bearings of points X, Y, and Z. Here's how:

The result is the bearing of point X from point Z. So, the bearing of point X from point Z is 165°.

Well, since the graph starts at (0,50), making our y-intercept 50, we can knock off D as an option.

The next step is to find the slope. To do this, find two points and subtract the y values over the x values. (Just make sure that whichever y value you start with - start with the same x value).

So we have >>> (50, 200) and (0,50) from earlier.

200 - 50 / 50 - 0 = 150/50 or 3/1, or 3.

This makes the correct answer A since the equation is represented as y = mx + b, where m is the slope and m has a value of 3.

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%

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:

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.

1. X1 Y1. X2, Y2

(-1,-6). ( -4,3)

Formula for slope which is m

Y2 -Y1 divide by X2-X1

3- -6/ -4 - -1= 9/-3= -3

So M = -3

Y=mx+b

-6= -3 (-1) +b

-6= 3+b

-3=-3

-9=b

Answer Y= -3x-9

2. X, Y

(-5,13)

Y=mx+b

13= 10+b

-10=-10

3=b

Answer C y= mx+b

y=-2x+3

3. (X1,Y1). (X2,Y2)

(3,-4). (5,-6)

Formula for m which is slope y2-y1 / x2-X1

-6- -4 / 5-3 = -2/2= -1 so m = -1

X, Y

(3,-4)

Y=mx+b

-4= -1(3)+b

-4= -3+b

+3=+3

-1. = b

Y= m x+b

-4= (-1) 3 +b

-4= -3. + b

+3= +3

-1. = b

Answer A y= -1x-1

Answer:

Answer Y= -3x-9 Answer C y= mx+b y=-2x+3 Answer A y= -1x-1

Step-by-step explanation:

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

Learn more about quadratic function here:

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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