16. Jessica was given the area and the length of the base of a triangle. A = 17.5 units, b = 5 units. She solved the formula for area for h to find the height of the triangle. Determine if Jessica solved the equation correctly and found the correct answer. If not, describe what mistake she made and solve the formula for h correctly and justify your steps.

A = 1/2bh
1/2A • b = h
1/2 (17.5)(5) = h
43.75 = h

The height of the triangle is 43.75 units.

Answer:

C

Step-by-step explanation:

To get the approximate number of pages in the chapters, what we need to do is to substitute for the value of x in the line of best fit equation.

Thus, we have;

y = 15.261(8) + 8.83 = 122.088 + 8.83 = 130.918

This is approximately equal to 131

Answer:

( 1/25 x^-12 y^-14 )

Step-by-step explanation:

( 5 x^6 y^7 ) ^-2

We know that ( ab) ^c = a^ c * b^c

( 5^-2 x^6^-2 y^7^-2 )

We know that a^b^c = a^(b*c)

( 5^-2 x^-12 y^-14 )

We know that a^ -b = 1/ a^b

( 1/25 x^-12 y^-14 )

Answer:

33/2

Step-by-step explanation:

6 * 11/4 = 66/4 = 33/2

Answer:

Option (4)

Step-by-step explanation:

In the given picture,

Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.

Segment TU joins the midpoints of the sides PS and RQ.

Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."

Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]

7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]

7x - 26 = 6x + 10

7x - 6x = 26 + 10

x = 36

m(TU) = 7x - 26

          = 7(36) - 26

          = 252 - 26

          = 226

Therefore, Option (4) will be the answer.

Answer:

what expressions?

Step-by-step explanation:

Step-by-step explanation:

this is substitution method

Answer:

2x + y = 21

+

x - y = 6

_________

3x = 27

x = 27 ÷ 3

x= 9

x - y = 6

9 - y = 6

9 - 6 = y

3 = y

Therefore, x= 9 and y = 3

Answer:

The hikers each receive 2 1/3 cups of trail mix.

1. Multiply 8 by 3 1/4 to get how much cups of trail mix they have in total which  will come out as 28.

2. Then divide the 28 cups by the 12 hikers, and you will get 2 1/3 as your answer.

Answer:

a

Step-by-step explanation:

Answer:

The function is:

y = 150*x

where y is the number of calories consumed, and x is the number of pieces of candy consumed.

Now, the domain of a function is the possible values of x that you can input in the function.

For this particular case you can have:

x = 0 (no pieces candy)

x = 1 (one piece of candy)

x = 2 (two pieces of candy)

Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.

So we only use x = whole numbers.

Then the domain of the function is equal to all the natural numbers plus the zero, or:

D = {x ∈ N ∪ {0}}

"x belongs to the union between the set of the natural numbers and the zero"

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The domain of a function is the input values of the function for which it exists.

Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:

y = 150x

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.

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Answer:

[tex]4 \frac{1}{4} [/tex] hours

Step-by-step explanation:

Given,

Time spent in studies : [tex]1 \frac{3}{4} [/tex] hours

Time spent in playing cricket : [tex]2 \frac{1}{2} [/tex] hours

Now, let's find the time that he spent in all:

[tex]1 \frac{3}{4} + 2 \frac{1}{2} [/tex]

Add the whole number and fractional parts of the mixed numbers separately

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

Add the numbers

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

Add the fractions

[tex]3 + ( \frac{3 + 1 \times 2}{4} )[/tex]

[tex]3 + ( \frac{3 + 2}{4} )[/tex]

[tex]3 + \frac{5}{4} [/tex]

Convert the improper fraction into mixed number

[tex] 3 + 1\frac{1}{4} [/tex]

Write the mixed number as a sum of the whole number and the fractional part

[tex]3 + 1 + \frac{1}{4} [/tex]

Add the numbers

[tex]4 + \frac{1}{4} [/tex]

Write the sum of whole number and the fraction as a mixed number

[tex]4 \frac{1}{4} [/tex] hours

Hope this helps..

Best regards!!

Answer:

4 1/4 hours.

Step-by-step explanation:

1 3/4 + 2 1/2

= 1 + 2 + 3/4 + 1/2

= 3 + 3/4 + 1/2   The LCM of 2 and 4 is 4 so 1/2 = 2/4. and so we have:

3 + 3/4 + 2/4

= 3 + 5/4

= 3 + 1 1/4

= 4 1/4 hours.

Answer:

Step-by-step explanation:

inequality is a equation with |x|

a inequality equation is like this..

|x|>7

Answer:

The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)

Step-by-step explanation:

The coordinates of quadrilateral EFGH are;

Point E has coordinates (-1, 1)

Point F has coordinates (0, 4)

Point G has coordinates (3, 1)

Point H has coordinates (3, 0)

The coordinates of the translation are;

Point E' has coordinates (0, -3)

Point F' has coordinates (1, 0)

Point G' has coordinates (4, -3)

Point H' has coordinates (4, -4)

The change in the y-coordinate values (y values) are;

From point E to point E', we have;

(-3 - 1) = -4 which is four units down

The change in the x-coordinate values (x values) are;

From point E to point E', we have;

(0 - (-1)) = 2 which is two units to the right

The total change in translation is [tex]T_{(2, -4)}[/tex].

Answer:

Mark as BRAINLIEST plz

|x-323|<50: answer

Step-by-step explanation :

For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.

So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.

The equation that can be used to determine the maximum temperature at which water is a liquid can be given by :  x < 323 + 50

The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50

So the resultant equation can be written as :

|x-323|<50

The solution of inequality equation is  | x - 323 | < 50

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the temperature of the water be = x Kelvin

Now , the equation will be

For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K

So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323

Substituting the values in the inequality equation , we get

For maximum temperature ,

x should be 50 more than 323 and

For minimum temperature ,

x should be 50 less than 323

So ,

The inequality relation is

x > 50 + 323   be equation (1)

x < 323 - 50   be equation (2)

So , the modulus function is expressed as

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

Therefore , the value is | x - 323 | < 50

Hence , The solution of inequality equation is  | x - 323 | < 50

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Answer:

Option A is the correct option

Step-by-step explanation:

[tex]5x = 35[/tex]

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{35}{5} [/tex]

Calculate

[tex]x = 7[/tex]

Hope this helps...

Best regards!!

Answer:

Option A

Step-by-step explanation:

5x = 35

5x/5 = 35/5

x = 7

Answer:

WX = 8 mm

Step-by-step explanation:

To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].

We use the law of sines in the blue triangle to do such:

[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]

Now we can use this value in the larger right angle triangle where WX is the opposite side to angle  [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:

[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]

which rounded to the nearest integer gives

WX = 8 mm

Answer:

A, B, A

Step-by-step explanation:

(3)

Given

- 2x² + 10x + 12 ← factor out - 2 from each term

= - 2(x² - 5x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) and

- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A

(4)

[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

[tex]x^{4}[/tex] - 81

= (x² )² - 9²

=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares

= (x - 3)(x + 3)(x² + 9) ← in factored form

x² - 3 is not a factor → B

(5)

Given

5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term

= 5([tex]x^{4}[/tex] - 64) ← difference of squares

= 5(x² - 8)(x² + 8) → A

Answer: negative 2 minus radical 3

Step-by-step explanation:

We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:

tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]

Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.

Substituting these values, we get:

tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]

= ±√[(2+sqrt(3))/(2-sqrt(3))]

Multiplying the numerator and denominator by (2+sqrt(3)), we get:

= ±√[(2+sqrt(3))^2/(4-3)]

= ±√[(2+sqrt(3))^2]

= ±(2+sqrt(3))

Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)

Answer:

work is shown and pictured

The solution to the system of linear equation is (x, y) = (6, 2)

3x - 2y = 14 (1)

3x - 2y = 14 (1)5x + y = 32 (2)

From (2)

y = 32 - 5x

Substitute y = 32 - 5x into (1)

3x - 2y = 14 (1)

3x - 2(32 - 5x) = 14

3x - 64 + 10x = 14

13x = 14 + 64

13x = 78

x = 78/13

x = 6

Substitute x = 6 into (2)

5x + y = 32 (2)

5(6) + y = 32

30 + y = 32

y = 32 - 30

y = 2

(x, y) = (6, 2)

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Answer:

b=9.96≅10

Step-by-step explanation:

b^2=a^2+c^2−(2ac)cos(64)

b=√6²+11²-2(6*11)cos64

b=9.96≅10

Answer:

x + y = 500

215x + 615y = 187,500

Step-by-step explanation:

The first equation can show the amount of land.  The farmer has 500 acres to plant corn, x, and cotton, y.

x + y = 500

The second equation can show the cost.  The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.

215x + 615y = 187,500

The system of equations is

x + y = 500

215x + 615y = 187,500

The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

And, Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season.

Now,

Let us take  'x' is plant acres of corn and 'y' is acres of cotton.

Since, A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

So, we can formulate;

⇒ x + y = 500

And, He has $187,500 to invest this season for corn costs $215 per acre to produce, and cotton costs $615 per acre to produce.

So, We can formulate;

⇒ 215x + 615y = 187,500

Thus, The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

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How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.

-----------

Extra info:

Answer:

5.83 ft

Step-by-step explanation:

Given that

Scale factor, n = 10

Wall in blueprint = 7 in

To find:

Length of actual wall = ?

Solution:

Whenever a blueprint is created for any house or building, it is made smaller by a scale factor.

Here this factor is 10 times.

That means, the blueprint size is 10 times smaller than that of its actual size.

Or we can say that actual wall of building is 10 times the wall of blueprint.

So, wall of building = 10 [tex]\times[/tex] 7 = 70 inches

Now, we know that 12 inches = 1 ft

1 inch = [tex]\frac{1}{12}\ ft[/tex]

70 inches = [tex]\frac{1}{12}\times 70\ ft = 5.83\ ft[/tex]

so, the answer is Wall of building is 5.83 ft.

Answer:

7√2 cm

Step-by-step explanation:

Aquí, estamos interesados ​​en encontrar la longitud del lado de un cuadrado que tiene una longitud diagonal de 14 cm.

Una diagonal es una línea que se extiende desde un borde del cuadrado hasta el otro borde del cuadrado internamente.

Ahora, una diagonal de un cuadrado junto con dos lados de un cuadrado forman un triángulo rectángulo isósceles, siendo la diagonal la hipotenusa de este triángulo rectángulo.

Sabemos que los lados de un cuadrado tienen la misma longitud y, por lo tanto, llamemos a este lado desconocido x cm.

Matemáticamente, según el teorema de Pitágoras, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los otros dos lados.

Por lo tanto, tenemos;

14 ^ 2 = x ^ 2 + x ^ 2

196 = 2x ^ 2

dividir ambos lados por 2

98 = x ^ 2 x = √98

x = √ (49 * 2)

x = 7√2 cm

Por lo tanto, la longitud del lado del cuadrado es de 7√2 cm

Answer:

1/10

Step-by-step explanation:

there are 10 cards, numbered 1 through 10, there is one "5" card. so that's 1 card out of 10 cards, therefore a 1/10the chance or a 10% chance you'll get a 5 (or any specific number)

Answer:

$200 at 2%.

$2200 at 3.5%.

Step-by-step explanation:

Let the two amounts be x and y.

x earns 2% interest, and y earns 3.5% interest.

Since the total is $2400, then

x + y = 2400

Now we can solve for y and express the second amount in terms of x.

y = 2400 - y

The two amounts are x and 2400 - x.

In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.

2% = 0.02; 3.5% = 0.035

The x amount earns 0.02x interest.

The y amount earns 0.035y interest.

The total interest earned is the sum of the interest amounts of the two accounts.

0.02x + 0.035y

We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.

0.02x + 0.035(2400 - x) = 81

The equation above is the linear equation.

Now we solve it. Distribute on the left side.

0.02x + 84 - 0.035x = 81

Combine like terms on the left side.

-0.015x + 84 = 81

Subtract 84 from both sides.

-0.015x = -3

Divide both side by -0.015.

x = 200

$200 was deposited in the account earning 2%.

y = 2400 - x

y = 2400 - 200

y = 2200

$2200 was deposited in the account earning 3.5%.

Answer:

No

Step-by-step explanation:

He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.

Answer:

a^3 – 25a^2b^5 – 35b^4

He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.

Answer:

[tex] \boxed{\sf Length \ of \ leg \ y = 13} [/tex]

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore \\ \sf \implies {84}^{2} + {y}^{2} = {85}^{2} \\ \\ \sf {84}^{2} = 7056 : \\ \sf \implies 7056 + {y}^{2} = {85}^{2} \\ \\ \sf {85}^{2} = 7225 : \\ \sf \implies 7056 + {y}^{2} = 7225 \\ \\ \sf Substract \: 7056 \: from \: both \: sides : \\ \sf \implies (7056 - 7056) + {y}^{2} = 7225 - 7056 \\ \\ \sf 7056 - 7056 = 0 : \\ \sf \implies {y}^{2} = 7225 - 7056 \\ \\ \sf 7225 - 7056 = 169 : \\ \sf \implies {y}^{2} = 169 \\ \\ \sf 169 = {13}^{2} : \\ \sf \implies {y}^{2} = {13}^{2} \\ \\ \sf \implies y = \sqrt{ {13}^{2} } \\ \\ \sf \implies y = {13}^{ \cancel{2} \times \frac{1}{ \cancel{2}} } \\ \\ \sf \implies y = 13 [/tex]

So,

Length of leg y of the right triangle = 13

Answer:

45.29 miles per hour

Step-by-step explanation:

Speed is the distance over time.  To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.

Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)

Avg. Speed = 45.29 miles per hour

Hence the average rate of speed for the trip was 45.29 miles per hour.

Cheers.

--------------------------------------------------------

Edit:  Thanks to Chegsnut36 for calculation correction

Answer:

≅45.29

Step-by-step explanation:

Hey there!

To find the average rate speed we need to add all the same number.

188 + 197 = 385

4 + 4.5 = 8.5

Now to find the average rate we do,

385 ÷ 8.5 ≅ 45.29

Hope this helps :)

Answer: I hope it helps :)

Step-by-step explanation:

1.

[tex]Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}[/tex]

2.

[tex]Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23[/tex]

3.

[tex]Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6[/tex]

4.

[tex]Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}[/tex]

5.

[tex]Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y[/tex]

Answer:

The value of x is 30.

We have to find the value of x in the given equation.  

Using distributive property  

We have,

[tex]1/2(x+6)=18\\a.(b+c)=a.b+a.c\\1/2(x+3)=18\\1/2x=15\\x=3[/tex]

other are also solve by this methode;)

The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.

To solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 and value of x to be determined.

The equation is the well-organized link of the variables of two expressions that contain equal between them.

distributive properties are used to evaluate the math problem easily by distributing numbers to the numbers present in parenthesis. eg, if we apply the distributive property of multiplication to solve the expression
a( b + c ) = a.b + a.c

[tex]1/2(x+6) = 18[/tex]
Using distributive property a( b + c ) = a.b + a.c

[tex]1/2.x+1/2*6 = 18\\1/2x+3=18\\1/2x=18-3\\1/2x=15\\x=2*15\\x=30\\[/tex]

Thus, The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.

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