A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is
the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation
x+y=24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions
The test contains 10 three-point questions and 14 five-point questions
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.

Answer:

4 1/2

Step-by-step explanation:

Answer:

4 1/2

Step-by-step explanation:

He made the recipe 3 times. 1 1/2*3=4 1/2

Answer:

-4x^9-12x^4+2x^3-7x+8

Answer:

=−4x9−12x4+2x3−7x+8

Step-by-step explanation:

Distribute the Negative Sign:

=2−4x9+3x3+−1(7x+x3−6+12x4)

=2+−4x9+3x3+−1(7x)+−1x3+(−1)(−6)+−1(12x4)

=2+−4x9+3x3+−7x+−x3+6+−12x4

Combine Like Terms:

=2+−4x9+3x3+−7x+−x3+6+−12x4

=(−4x9)+(−12x4)+(3x3+−x3)+(−7x)+(2+6)

=−4x9+−12x4+2x3+−7x+8

The question is missing the figure. So, the figure is attached below.

Answer:

The area of the base of the pyramid is 36 square inches.

Step-by-step explanation:

Given:

Volume of the pyramid is, [tex]V=108\ in^3[/tex]

The height of the pyramid is, [tex]h=9\ in[/tex]

Let the area of the base be 'A'.

So, the volume of the pyramid is given as:

[tex]V=\frac{1}{3}Ah[/tex]

Rewrite the given formula in terms of 'A'. This gives,

[tex]A=\frac{3V}{h}[/tex]

Now, plug in 108 for 'V', 9 for 'h' and solve for 'A'. This gives,

[tex]A=\frac{3\times 108}{9}\\\\A=3\times 12\\\\A=36\ in^2[/tex]

Therefore, the area of the base of the pyramid is 36 square inches.

Answer:

[tex]\angle CST,\angle TSC[/tex]

Step-by-step explanation:

we know that

You can name a specific angle by using the vertex point, and a point on each of the angle's rays. The name of the angle is simply the three letters representing those points, with the vertex point listed in the middle

In this problem

The vertex point is S and the points on each of the angle's rays are C and T

so

[tex]\angle z=\angle CST=\angle TSC[/tex]

therefore

[tex]\angle CST,\angle TSC[/tex]

Answer:

y = 1x + 2

please mark me as brainliest, thank you and have a good day!

Answer:

y = 5/8x + 9/4

but it can be

y=5/8x+6

or

y=5/8x+1

Explaination:

but there can be other solutions

First let's find the slope (5/8(

(-2,1) and (6,6)

let plug those numbers in

[tex]\frac{6-1}{6-(-2)}[/tex]

which becomes

[tex]\frac{5}{8}[/tex]

that's your slope, plug that into the slop-intercept equation

y = mx + b tp y = 5/8x + b

b can be either y-values (1 or 6) but 9/4 is also an answer

the variable qould b and aStep-by-step explanation:

Answer: B, D, E

Step-by-step explanation:

Using function concepts, it is found that the correct options are:

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

A similar problem is given at https://brainly.com/question/13421430

Answer:

A. h(x)= -5.86x^2 + 23.37x + 34

Step-by-step explanation:

If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.

Then, the combined yield [tex]h(x)[/tex] of the two farms is just the yield of the first farm plus the yield of the second farm:

[tex]h(x)=f(x)+g(x)[/tex].

Now, since

[tex]f(x)= -2.43x^2+10.37x+9[/tex]

and

[tex]g(x)= -3.43x^2+13x+25[/tex],

then

[tex]h(x)= (-2.43x^2+10.37x+9)+(-3.43x^2+13x+25)[/tex]

we add the coefficients of the  corresponding terms to get:

[tex]h(x)= (-2.43x^2-3.43x^2)+(10.37x+13x)+(9+25)[/tex]

[tex]\boxed {h(x)=-5.86 x^2 + 23.37 x + 34.}[/tex]

Which is choice A.

Answer:

Step-by-step explanation:

7 + 3 + 5 + 15 = 30

Answer:

Step-by-step explaination:

I would try to help u but im not big brain and i really need the points

Answer:

Lisa = 7 hours and 15 minutes

Naila = 10 hours and 45 minutes

Step-by-step explanation:

Naila = N

Lisa = L

Naila worked:

N = 3.5 + L

In total, they worked:

N + L = 18

Lisa worked:

L = h

Substitute values into the total equation

3.5 + L  + L = 18

Solve

2L = 14.5

L = 7.25 = 7 hours and 15 minutes

N = 7.25 + 3.5 = 10.75 = 10 hours and 45 minutes

Hope this helps :)

Hey Kim! :)

Glad to see you on Brainly.

Look below and watch how we solve this problem.

Ask any questions if you need it! I'll respond when you need it!

[tex]Remove \\parentheses. \\7+30-2=7 * 3\\\\7 + 30 - 2 = 161\\37 - 2 = 161\\\\35 = 161\\ \\ No solution.[/tex]

Answer:

B.  Exponential.

Step-by-step explanation:

Each year you can find the estimated population for the following year by multiplying by  1 + 1.7%  = 1.017.

The population estimate in  x years time =  78,918 (1.017)^x.

Answer: The answer is B

Step-by-step explanation:

Good evening ,

Answer :

A.

x = ±20

Step-by-step explanation:

x² − 1 = 399 ⇔ x²= 400 ⇌ x² = 20² ⇌ x² − 20² = 0 ⇌ (x-20)(x+20) = 0

⇌ x = 20 or x = -20.

:)

X=20 and x=-20 are the solutions to the equation [tex]x^{2} -1 = 399[/tex]

A quadratic equation exists as an algebraic equation of the second degree in x. The quadratic equation in its standard form exists [tex]ax^{2} + bx + c = 0[/tex], where a and b exist as the coefficients, x is the variable, and c stands as the constant term.

Given,

[tex]x^{2} -1 = 399[/tex]

To find,

The solutions to the equation.

Step 1

[tex]x^{2} -1 = 399[/tex]

Move terms to the left side

[tex]&x^{2}-1=399 \\[/tex]

[tex]&x^{2}-1-399=0[/tex]

Subtract the numbers

[tex]&x^{2}-1-399=0 \\[/tex]

[tex]&x^{2}-400=0[/tex]

Use the quadratic formula

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

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic equation.

[tex]&x^{2}-400=0 \\[/tex]

a=1

b=0

c=-400

[tex]&x=\frac{-0 \pm \sqrt{0^{2}-4 \cdot 1(-400)}}{2 \cdot 1}[/tex]

[tex]&x=\frac{-0 \pm \sqrt{(0^{}-1600)}}{2 }[/tex]

[tex]$x=\frac{\pm 40}{2}$[/tex]

[tex]$x=\frac{40}{2}$[/tex]

[tex]$x=\frac{-40}{2}$[/tex]

Hence,

[tex]$x=20$[/tex]

[tex]$x=-20$[/tex]

Thus, Option A. X=20 and x=-20 are the solutions to the equation [tex]x^{2} -1 = 399[/tex]

To learn more about Quadratic equations refer to:

https://brainly.com/question/1214333

#SPJ2

Answer:

6.855

Step-by-step explanation:

I don't know how to explain that, you can use a calculator.

18 km

Step-by-step explanation:

The vector appears as shown in the attached illustration. This is tantamount to finding the ? side of the right-angled triangle. The formulae is;

a² + b² = c²

24² + x² = 30²

x² = 30² – 24²

= 900 - 576

x² = 324

x = 18

Learn More:

For more on vectors check out;

https://brainly.com/question/10435343

https://brainly.com/question/12006588

#LearnWithBrainly

Final answer:

By using the Pythagorean theorem on the right triangle formed by the paths of the two airplanes, it is determined that the eastbound airplane has traveled 18 kilometers.

Explanation:

The question involves a geometrical problem that can be solved using the Pythagorean theorem. We are given that two airplanes leave the same airport, one heading north and the other heading east. After a certain time, the northbound airplane has traveled 24 kilometers. We are asked to find out how far the eastbound airplane has traveled, given that the two airplanes are now 30 kilometers apart.

To solve this, we can consider the path of the two airplanes as two sides of a right triangle, with the distance between the two airplanes being the hypotenuse. Using the Pythagorean theorem which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), or a2 + b2 = c2, we have:

Let x be the distance traveled by the eastbound airplane.

242 + x2 = 302

x2 = 302 - 242

x2 = 900 - 576

x2 = 324

x = √324

x = 18 kilometers

The eastbound airplane has traveled 18 kilometers.

Answer:

p=40

w=l-8

40=w+l

40=2(l-8)+2l

40=2l-16+2l

40=4l-16

56=4l

14=l

length=14

w=14-8=6

l=14

w=6

Main equation:

2L + 2w = 40

We know that

w = L - 8

Substitute in known value

2L + 2(L - 8) = 40

Solve

2L + 2L - 16 = 40

4L = 24

L = 6

Length = 6 inches

Width =  14 inches

Hope this helps :)

Answer:

use photomath

Step-by-step explanation:

Answer:

The value of the expression is [tex]\frac{9}{20}[/tex]

Step-by-step explanation:

In order to sum or subtract these fractions we need to find their LCM.

The overall LCM is 20.

Thus:

The we get:

= -16/20+25/20

Which gives:

=9/20

Answer:

Step-by-step explanation:

Since the sale price is always less than the original, we take the original and subtract from it the percent off to give us the sale price.  Putting that into equation form:

s = r - .10r

which says, in words, that the sale price is equal to the regular price minus 10% of the regular price.

Answer: First option.

Step-by-step explanation:

You can idenfity in the figure that [tex]\angle FCE[/tex] is formed by two secants that intersect outside of the given circle.

It is important to remember that, by definition:

 [tex]Angle\ formed\ by\ two\ Secants=\frac{1}{2}( Difference\ of\ intercepted\ Arcs)[/tex]

Knowing this, you can set up the following equation:

[tex]m\angle FCE=\frac{1}{2}(BD-FE)[/tex]

Therefore, you must substitute values into the equation and then evaluate, in order to find the measure of the angle [tex]\angle FCE[/tex].

This is:

[tex]m\angle FCE=\frac{1}{2}(112\°-38\°)\\\\m\angle FCE=37\°[/tex]

Answer:

4.

a)  [tex]4x^4-4x^3-16x^2+16x[/tex]

b)  [tex]4x^4-4x^3-16x^2+16x[/tex]

5. Yes

Step-by-step explanation:

The distributive property is:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

It can be extended to a lot of terms as well.

We will use this to multiply both of the probelms shown.

4 a)

[tex](4x^2-4x)(x^2-4)=(4x^2)(x^2)-(4)(4x^2)-(4x)(x^2)+(4x)(4)=4x^4-16x^2-4x^3+16x=4x^4-4x^3-16x^2+16x[/tex]

The answer is [tex]4x^4-4x^3-16x^2+16x[/tex]

4 b)

[tex](x^2+x-2)(4x^2-8x)=(x^2)(4x^2)-(8x)(x^2)+(x)(4x^2)-(8x)(x)-(2)(4x^2)+(2)(8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x=4x^4-4x^3-16x^2+16x[/tex]

The answer is  [tex]4x^4-4x^3-16x^2+16x[/tex]

5. Yes

Answer:

A)  The equation has no solution

B ) The equation has one solution

C ) The solution of equation is 1

D ) The solution of equation is 20

E ) The solution of inequality is  x [tex]<[/tex] 8

Step-by-step explanation:

Given as :

A ) The equation is written as

5 ( x - 9 ) = 5 x

So, solving the equation

i. e  5 x - 5 × 9 = 5 x

or, , (5 x - 5 x) - 45 = 0

or, (0) - 45 = 0

∵ The equation do not have any variable terms

So, the equation has no solution

B) The equation is written as

- 2 ( x - 1 ) = 2 x - 2

So, solving the equation

i.e - 2 x + 2 = 2 x - 2

or, ( - 2 x - 2 x ) = - 2 - 2

or, - 4 x = - 4

∴ x = [tex]\dfrac{-4}{-4}[/tex]

I.e x = 1

So, The equation has one solution

C) The equation is written as

3 x + 6 = 9

So, solving the equation

I.e 3 x = 9 - 6

or, 3 x = 3

∴ x = [tex]\dfrac{3}{3}[/tex]

I.e x = 1

So, The solution of equation is 1

D) The equation is written as

[tex]\dfrac{x}{4}[/tex] - 1 = 4

Or, [tex]\dfrac{x}{4}[/tex] = 1 + 4

or, [tex]\dfrac{x}{4}[/tex] = 5

∴ x = 5 × 4

I.e x = 20

So, The solution of equation is 20

E) The equation of inequality is written as

9 x [tex]<[/tex] 72

Or, x [tex]<[/tex] [tex]\dfrac{72}{9}[/tex]

∴  x [tex]<[/tex] 8

So, The solution of inequality is  x [tex]<[/tex] 8

Hence , A)  The equation has no solution

B ) The equation has one solution

C ) The solution of equation is 1

D ) The solution of equation is 20

E ) The solution of inequality is  x [tex]<[/tex] 8

Answer

Answer:

The number of adults tickets sold is 165

The number of students tickets sold is 35

Step-by-step explanation:

Given as :

The total people that concert venue hold = 200 people

The price of adults tickets = $50

The price of students tickets = 50% less than adults tickets

I.e The price of students tickets = $50 - 50% of $50

Or, The price of students tickets = $25

The total revenue earn = $9125

Let The number of adults tickets sold = A

The number of students tickets sold = S

Now, According to question

The total people that concert venue hold = 200

Or, A + S = 200        ...........1

The total revenue earn = The number of adults tickets sold × The price of adults tickets +  The number of students tickets sold × The price of students tickets

Or, A × $50 + S × $25 = $9125

Or, 50 A + 25 S = 9125           ..........2

Solving both equations

(50 A + 25 S) - 25 × (A +S) = 9125 - 25 × 200

Or, (50 A - 25 A) + (25 S - 25 S) = 9125 - 5000

Or, 25 A + 0 = 4125

∴ A = [tex]\dfrac{4125}{25}[/tex]

I.e A = 165

So, The number of adults tickets sold = A = 165

Put the vale of A in eq 1

I.e A + S = 200

So, S = 200 - A

∴ S = 200 - 165

I.e S = 35

So. The number of students tickets sold = S = 35

Hence The number of adults tickets sold is 165 and

The number of students tickets sold is 35   Answer

Final answer:

To solve the multiplication problem 3/4 × 8/9, multiply the numerators and denominators, then simplify the fraction.

Explanation:

To solve the multiplication problem 3/4 × 8/9, we multiply the numerators (3 × 8) to get 24, and multiply the denominators (4 × 9) to get 36. So the result of the multiplication is 24/36. To simplify the fraction, we find the greatest common divisor of 24 and 36, which is 12. Dividing both the numerator and denominator by 12, we get 2/3. Therefore, the answer to the problem is 2/3.

Answer:

1) The slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]

2) The slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]

3) The slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]

4) The slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]

5) The slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]

6) The slope for the given points (-16,-20) and (12,5)  is [tex]m=\frac{25}{28}[/tex]

7) The slope for the given points (13,20) and (14,-14)  is [tex]m=-34[/tex]

8) The slope for the given points (18,15) and (3,0) is [tex]m=1[/tex]

Step-by-step explanation:

To find the slope of the line through each pair of points:

1) Given points are (6,7) and (-10,4)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (6,7) and (-10,4) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{4-7}{-10-6}[/tex]

[tex]m=\frac{-3}{-16}[/tex]

[tex]m=\frac{3}{16}[/tex]

Therefore the slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]

2) Given points are (17,4) and (13,20)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (17,4) and (13,20) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{20-4}{13-17}[/tex]

[tex]m=\frac{16}{-4}[/tex]

[tex]m=-4[/tex]

Therefore the slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]

3) Given points are (12,19) and (14,18)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (12,19) and (14,18) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{18-19}{14-12}[/tex]

[tex]m=\frac{-1}{2}[/tex]

Therefore the slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]

4) Given points are (-11,0) and (18,13)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-11,0) and (18,13) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{13-0}{18-(-11)}[/tex]

[tex]m=\frac{13}{29}[/tex]

Therefore the slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]

5) Given points are (3,6) and (-8,20)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (3,6) and (-8,20) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{20-6}{-8-3}[/tex]

[tex]m=\frac{14}{-11}[/tex]

[tex]m=-\frac{14}{11}[/tex]

Therefore the slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]

6) Given points are (-16,-20) and (12,5)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-16,-20) and (12,5) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{5-(-20)}{12-(-16)}[/tex]

[tex]m=\frac{5+20}{12+16}[/tex]

[tex]m=\frac{25}{28}[/tex]

Therefore the slope for the given points (-16,-20) and (12,5)  is [tex]m=frac{25}{28}[/tex]

7) Given points are (13,20) and (14,-14)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (13,20) and (14,-14) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-14-20)}{14-13}[/tex]

[tex]m=\frac{-34}{1}[/tex]

[tex]m=-34[/tex]

Therefore the slope for the given points (13,20) and (14,-14)  is [tex]m=-34[/tex]

8) Given points are (18,15) and (3,0)

The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points  (18,15) and (3,0) respectively

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{0-15}{3-18}[/tex]

[tex]m=\frac{-15}{-15}[/tex]

[tex]m=1[/tex]

Therefore the slope for the given points  (18,15) and (3,0) is [tex]m=1[/tex]

Answer:

39.95 × 3 = $119.85

Estimated at $40 each

3 pairs total $120

Answer: OPTION A.

Step-by-step explanation:

Let be "e" the number of tickets that the radio station gave away to employees and "l" the number of tickets that the radio station gave away to listeners.

Based on the data given in the exercise, you can set up the following System of equations:

[tex]\left \{ {{e+l=192 } \atop {l=5e}} \right.[/tex]

Finally you must apply the Substitution Method to solve the System of equations.

To apply it, you must substitute the second equation into the first one and then you must for the variable "e".

Through this precedure you get the following value of "e":

[tex]e+l=192\\\\e+(5e)=192\\\\6e=192\\\\e=\frac{192}{6}\\\\e=32[/tex]

Answer:

Step-by-step explanation:

Incomplete question.

Answer:

The maximum value of P is 34 and the minimum value of P is 0

Step-by-step explanation:

we have the following constraints

[tex]x+y \leq 6[/tex] ----> constraint A

[tex]2x+3y \leq 16[/tex] ----> constraint B

[tex]x\geq 0[/tex] ----> constraint C

[tex]y\geq 0[/tex] ----> constraint D

Solve the feasible region by graphing

Using a graphing tool

The vertices of the feasible region are

(0,0),(0,5.33),(2,4),(6,0)

see the  attached figure

To find out the maximum and minimum value of the objective function P, substitute the value of x and the value of y for each of the vertices in the objective function P, and then compare the results

we have

[tex]P=5x+6y[/tex]

For (0,0) ----> [tex]P=5(0)+6(0)=0[/tex]

For (0,5.33) ----> [tex]P=5(0)+6(5.33)=31.98[/tex]

For (2,4) ----> [tex]P=5(2)+6(4)=34[/tex]

For (6,0) ----> [tex]P=5(6)+6(0)=30[/tex]

therefore

The maximum value of P is 34 and the minimum value of P is 0

Option B

7569 number of people are going to vote for the other candidate

Solution:

Given that candidate took a phone poll of 110 people

Of the 110 people polled, 87 said they would vote for the other person

There are 9570 people in the district

You can set up this problem like a proportion

Let "x" be the number of people who would vote for the other candidate

[tex]\frac{87}{110} = \frac{x}{9570}[/tex]

To solve proportions, you cross-multiply. This means you multiply the numerator by the other denominator, and the denominator by the other numerator

[tex]87 \times 9570 = 110 \times x[/tex]

832590 = 110x

x = 7569

Thus 7569 number of people are going to vote for the other candidate

Answer:

Your answer is B. 7569 people hopefully this helps!