Question 2 of 11
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?

Answers

Answer 1

If the number of multiple-choice questions is x and the number of short answer questions is y, then:

[tex]x+y=28\\\\3x+5y=100[/tex]


Related Questions

Help is needed with this math problem!

Answers

Answer:

expression for (g + h)([tex]x\\[/tex]) = [tex]2x[/tex] + [tex]3x^2\\[/tex] and for (g - h)([tex]x[/tex]) = [tex]2x[/tex] - [tex]3x^2[/tex]

value of (g .h)(2) = 24

Step-by-step explanation:

function operations: Functions with overlapping domains can be added, subtracted, multiplied and divided. If f(x) and g(x) are two functions, then for all x in the domain of both functions we can find the sum, difference, product and quotient

given :

g([tex]x[/tex]) = [tex]2x[/tex]

h([tex]x[/tex]) = [tex]3x^2[/tex]

we know that ;

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

              =  [tex]2x[/tex]  + [tex]3x^2[/tex]

similarly;

(g - h)([tex]x[/tex]) = g([tex]x[/tex]) - h([tex]x[/tex])

             =  [tex]2x[/tex] - [tex]3x^2[/tex]

now,  

(g . h)([tex]x[/tex]) = 2([tex]3x^2\\[/tex])

             = 6[tex]x^2\\[/tex]

for (g .h)(2) = 6([tex]2^2[/tex])

                  = 6 × 4

                  = 24

learn more about function operations at :

brainly.com/question/27915566

#SPJ10

Triangle P Q R is shown. Angle P Q R is a right angle. The length of hypotenuse P R is q, the length of P Q is r, and the length of Q R is p.,
Which cosine ratios are correct for ΔPQR? Check all that apply.

cos (P) = StartFraction r Over q EndFraction
cos (P) = StartFraction p Over q EndFraction
cos (Q) = StartFraction r Over p EndFraction
cos (R) = StartFraction r Over p EndFraction
cos (R) = StartFraction p Over q EndFraction

Answers

The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.

We have,

Δ PQR,

Length of hypotenuse PR = q

The length of PQ = r,

And the length of QR = p

NOw,

We know that Trigonometric ratios of CosineΘ;

CosineΘ = Base/Hypotenuse

So,

CosineP = r/q

And,

CosineR = p/q

So, from the above find out values we can say that these values are given in option (a) and option (d).

Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.

Learn more about Trigonometric ratios here:

https://brainly.com/question/13724581

#SPJ10                  



6 out of 11 players played well on the baseball team. What percent is it?

Answers

It would be 54.5% or 55%. If you divide 6/11 you get .545 so you move the decimal place 2 to the left and that’s how you get the percentage.

Answer: 54%

Step-by-step explanation:

You will need to divide these numbers.

[tex]6/11=0.54[/tex]

After you divide that, simplify that to a percentage by multiplying it by 100.

[tex]0.54 *100=54%[/tex]%

I hope this helps!!

What is 3/4 divided by 1/2

Answers

Answer:
Fraction: 3/2
Decimal: 1.5

Answer:

1 1/2

Step-by-step explanation:

Convert both fractions into decimals

⇒ 3/4 (0.75) and 1/2 (0.50)

Divide the decimals:

⇒0.75 ÷ 0.50

Find the quotient

⇒ 1.5

Convert the quotient to a fraction

⇒ 1 1/2

Terms:

Operations with fractions

Which expression is equivalent to √48x5, if x> 0?
A. 12x³√3x
B. 4x³√3
C. 4x²√3x
D. 12x²√

Answers

Answer:

C. 4x²√(3x)

Step-by-step explanation:

if x > 0

[tex]\sqrt{48x^{5}} =\sqrt{48} \times \sqrt{x^{5}}[/tex]

          [tex]=\sqrt{16\times 3} \times \sqrt{x^{4}\times x}[/tex]

          [tex]=\sqrt{16} \times \sqrt{3} \times \sqrt{x^{4}} \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times \sqrt{\left( x^{2}\right)^{2} } \times \sqrt{x}[/tex]

          [tex]=4\times \sqrt{3} \times x^{2}\times \sqrt{x}[/tex]

          [tex]=4\times x^{2} \times \sqrt{3} \times \sqrt{x}[/tex]

          [tex]=4\times x^{2}\times \sqrt{3x}[/tex]

Question is attached………

Answers

Answer:

d. 11:15

Step-by-step explanation:

1) officer1: distance 75 miles, velocity 60mil/h; officer2: distance 25 miles, velocity 55mil/h;

2) time, which is spent officer1 is: 75/60=1.25[h]=75 [min]. If the officer1 leaves his office at 10:00, the arrival time is 11:15;

3) time which is spent officer2 is: 25/55=5/11[h]≈27[min]. The arrival time is 10:27.

4) finally, the both officers are in the required location at 11:15.

The parabolas y = -x² and y= -x² - 4x + 6 are graphed below. What are the y-values of the solutions to this system of equations?

y= 1,9
y= 1,6
y= -0,6
y= -3,1

Answers

Answer:

y = 1, 9.

Step-by-step explanation:

They are the y values of the points of intersection of the 2 parabolas.

y = 1, 9.

3. What are the roots of the polynomial y = x³ - 8?

Answers

Step-by-step explanation:

x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.

[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]

Cube root of x^3 is x.

Cube root of 8 is 2

So

a=x

b= 2.

[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]

Set these equations equal to zero

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

[tex] {x}^{2} - 2x + 4 = 0[/tex]

If we do the discriminant, we get a negative answer so we would have two imaginary solutions,

Thus the only real root is 2.

If you want imaginary solutions, apply the quadratic formula.

[tex]1 + i \sqrt{ 3 } [/tex]

and

[tex]1 - i \sqrt{3} [/tex]

Simplify cube root of 5 over fourth root of 5 . (5 points) 5 to the power of 1 over 4 5 to the power of 1 over 12 5 to the power of 7 over 12 5 to the power of 4 over 3

Answers

Answer:

[tex] {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

Step-by-step explanation:

[tex] \frac{ \sqrt[3]{5} }{ \sqrt[4]{5} } = {5}^{ \frac{1}{3} } \div {5}^{ \frac{1}{4} } = {5}^{ \frac{4}{12} } \div {5}^{ \frac{3}{12} } = {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

THIS IS THE ANSWER: 5 to the power of one-twelfth (Take a look at the image if this does not make sense) :))

:))

:)))   HAPPY SLAPPY!!!!

:))))

"UPDATE" : This was correct on my test. Also I realized to see the image in this answer keep your cursor on the side of your screen, not on the image :D

The graphs below have the same shapes. What is the equation for the red graph?

Answers

The equation for the red graph is f(x) = -x².

How to depict the equation?

From the information given, g(x) = 4 - x².

The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:

(x, y) = (x, y -4).

The equation of the function will be:

f(x) = g(x) - 4

f(x) = (4 - x²) - 4

f(x) = -x²

Learn more about equations on:

brainly.com/question/9681517

#SPJ1

PWhat are the x- and y-intercepts of the line y = 4x + 12?
A. x-intercept = 3; y-intercept = -12
B. x-intercept = -3; y-intercept = 12
C. x-intercept = -12; y-intercept = 3
D. x-intercept = 12; y-intercept = -3
PLEASE HELP

Answers

Answer:

B

Step-by-step explanation:

when x is 0 y=4(0)+12 y=12

y is 0 y=4(-3) +12 = 12=12

Y-6.37x=-3 which of the following function notation corresponds to the equation below

Answers

Wheres the other part of the question

What is the equation of the parabola? (3 points)

A) y = -1/8x^2 +5

B) y = 1/8x^2 +5

C) y = 1/8x^2 - 5

D) y = -1/8x^2 -5

Answers

Answer:

A.

Step-by-step explanation:

The parabola opens down, so the "a" value (the number in front of x^2) must be negative. The y-intercept is (0, 5) so the constant must be positive 5.

A student wants to simulate 37 ​birthdays, but she does not have a calculator or software program​ available, so she makes up 37 numbers between 1 and 365. Is it okay to conduct the simulation this​ way? Why or why​ not?

Answers

It is not okay to conduct the simulation because people generally favor some numbers.

How to illustrate the information?

From the information given, the student wants to simulate 37 birthdays, but she does not have a calculator or software program available.

In this case, it's not okay to conduct the simulation because people generally favor some numbers.

Learn more about simulation on:

brainly.com/question/24912812

#SPJ1

A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?

Answers

She says “I apologise” because she feels bad that she made a bad smell and she says “excuse me” because she wants you to accept her apology

If xy=3 yz=6 zx=2 find x+y+z​

Answers

Answer: 1+3+2=6
Explanation: 1x3=3
3x2=6
2x1=2


[tex] \displaystyle \sum_{n = 1}^{ \infty } {4}^{ - n} [/tex]
evaluation of the sum above ​

Answers

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]

The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.

To find the first term in the series, substitute n = 1 into the expression:

[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]

The common ratio of the geometric series can be found by dividing one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]

As | r | <  1  the series is convergent.

When a series is convergent, we can find its sum to infinity (the limit of the series).

Sum to infinity formula:

[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]

where:

a is the first term in the seriesr is the common ratio

Substitute the found values of a and r into the formula:

[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]

Therefore:

[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]

Learn more about Geometric Series here:

https://brainly.com/question/27737241

https://brainly.com/question/27948054

What is 2(x+3) / 4(x+1)

Answers

Answer:

x² + 4x + 3

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

       2

---- => fraction line

Which expression is equivalent to this polynomial?
x2+12
OA. (X +2v3i)(c – 2v3i)
OB. (x+6i)(x - 6i)
OC. (x + 2√3)²
OD. (x + 2√3)(x − 2√3)

Answers

x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).

What are Polynomials?

Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.

The given expression is x² + 12.

We have the identity (a + b) (a - b) = a² - b²

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²

                                = x² - (2² × √3² × i²)

We know that i² = -1, where i is the imaginary number in complex numbers

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)

                                = x² + 12

Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.

To learn more about Polynomials, click:

https://brainly.com/question/11536910

#SPJ1

If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).
A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5

Answers

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

Answer:

[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]

Step-by-step explanation:

Given functions:f(x) = x + 8g(x) = -4x - 3Solution:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

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

Emily is shopping at the toy store. In that store all dolls are sold at the same price and all dresses are sold at the same price. If Emily buys one doll and one dress, it will cost her $21.00. If Emily buys two dolls and three dresses, it will cost her $51.00. What is the price of one doll at that store?​

Answers

Answer:

$12.

Step-by-step explanation:

1) if price of one doll is 'x', of one dress is 'y', then the condition 'buys one doll and one dress, it will cost her $21.00' can be written as x+y=21;

2) the condition 'buys two dolls and three dresses, it will cost her $51.00' can be written as 2x+3y=51;

3) it is possible to make up the system:

[tex]\left \{ {{x+y=21} \atop {2x+3y=51}} \right. \ = > \ \left \{ {{x=12} \atop {y=9}} \right.[/tex]

4) the price of one doll is 12$.

Can anyone please help me with this question?

Karl receives his first mark of the year in his law course. He scores 94th percentile. What is his mark!?

Answers

Answer:

Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.

So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.

PLEASE HELP ASAP I WILL GIVE BRAINLYEST!!!

Answers

Answer:

Step-by-step explanation:

the numerator goes in side of the radical

Find BC.
plssss helpp!!!

Answers

Answer:

BC is 22.5 mi

Step-by-step explanation:

Using the pythagorean theorem formula. c² = a² + b²

BC² = AB² + AC²

BC² = 19² + 12²

BC² = 361 + 144

BC² = 505

BC² = 505

BC = 22.5

Therefore BC is 22.5 mi

Please help me answer this question genius

Answers

(i) The Maclaurin's series is:

1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

(ii) Integral of limit o to 1∫ e^sinx is 0

Maclaurin's expansion is as follows:

y(x) = y₀ ₊ x y₁(0) ₊ x²/2! y₂(0) ₊ x³/3! y₃(0) ₊ ........

y = e^sinx

y(0) = e^sin0

y(0) = 1

Differentiate y with respect to x

y₁(x) = e^sinx . cos x

y₁(0) = 1 [i.e y₁ = cosx.y]

y₁(0) = 1

Differentiate y₁ with respect to x

y₂(x) = cosc . y₁ ₋ sinx . y

∴ y₂(0) = 1 ₋ 0 = 1

Differentiate y₂ with respect to x

y₃ = cosx . y₂ ₋ (2 sinx ₊ cosx)y₁

y₃(0) = 1 ₋(0 ₊ 1)1

y₃(0) = 0

Differentiate y₃ with respect to x

y₄ = cosx . y₃ sinx . y₃ ₋ (2sinx ₊ cosx)y₂ ₋ (2cos x ₋ sinx) y₁

y₄(0) = 0 ₋ (3 . 0 ₊ 1)1 ₋ (2 ₋ o) 1

y₄(0) = -3

∴ From maclaurin's equation we get:

e^sinx = 1 ₊ x . 1 ₊ x²/2! . 1 ₊ x³/3! (0) ₊ x⁴/4! (₋3) ₊ ....

           =1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

Hence we get the the series expansion as 1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

(ii) limit 0 to 1∫e^sinx

integration formula ∫e^x dx = e^x + c

                    limit 0 to 1 ∫e^sinx = [e^sinx + c ]limit 0 to 1

                                                 = e^sin0 ₋ e^sin1

                                                 = 1 ₋ 1

                                                 = 0

Hence we get the answer as 0

Learn more about "Integration" here-

https://brainly.com/question/22008756

#SPJ10

Select the correct answer. Which number best represents the slope of the graphed line? A linear function on a coordinate plane passes through (minus 6, minus 7), and (4, minus 2) also intercepts the x-axis at 8 units and the y-axis at minus 4 units. A. B. C. D.

Answers

The number best represents the slope of the graphed line is 1/2.

We have given the two points,

(-6,-7) and (4,-2) and slope-intercept is 8 units

What is the slope-intercept form of a line?

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

y = y coordinate of the second point

[tex]y_1[/tex] = y coordinate of point one

m = slope

x = x coordinate of the second point

[tex]x_{1}[/tex]= x coordinate of point one

Therefore the

[tex]slope=\frac{y_2-y_1}{x_2-x_!}[/tex]

[tex]=\frac{-2-(-7)}{4-(-6)} \\=\frac{5}{10}\\ =\frac{1}{2}[/tex]

Therefore the correct option is 1/2.

To learn more about the slope visit:

https://brainly.com/question/3493733

#SPJ1

please help with this problem
thanks so much

Answers

Answer:

5/17

Step-by-step explanation:

If we do the multiplication first, we get:

[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]

If we do the division next, we get:

[tex]\frac{4+1}{13+4} = 5/17[/tex]

f(x)=1/x at x=1 find slope of tangent

Answers

Answer:

f'(1)=-1

Step-by-step explanation:

You can just find the derivative using the power rule for d/dx (x^-1)=-1x^-2=-1/x^2 then find f'(1)=-1.

I used the limit definition of the derivative to find the slope in the picture attached

What should be added to -2 1/9 to get 11

Answers

Answer:

u should add 118/9

Step-by-step explanation:

please mark me as brainlest

The following lots of Commodity Z were available for sale during the year. Beginning inventory 9 units at $50 First purchase 16 units at $50 Second purchase 21 units at $59 Third purchase 16 units at $62 The firm uses the periodic system, and there are 23 units of the commodity on hand at the end of the year. What is the ending inventory balance at the end of the year according to the FIFO method?

Answers

According to the FIFO method, the ending inventory balance for Commodity Z is $1,405

How much inventory is left under FIFO?

FIFO means that earlier inventory is sold first and later inventory would be the last goods left.

Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:

= (16 x 62) + (7 x 59)

= 992 + 413

= $1,405

Find out more on the FIFO method at https://brainly.com/question/11493725.

#SPJ1

Other Questions
Kaye bought 7 mangoes for $49, 4 apples for $24, and 3 oranges for $15. Which fruit is very cheap in price? Need help with algebra homework Mateeka loves to play soccer and her team has finally made it to the championship game; however, her coach has been screaming at them for days and Mateeka has had a stomach ache and has not been able to sleep. She is extremely nervous going into the game and doesn't feel well. She performs poorly as do her teammates and they lose the game. How does the Yerkes-Dodson law explain this Simplify this problem!!! Please help answer needed asap NEED HELP ASAP! ITS IN THE IMAGE BELOW. ive done the graph which is part a and b but i need help in part c and d, help will be appreciated! Suppose A and B are complements, while B and C are supplements. If mA=3x+17, mB=55x, and mC=67(x/31), then mA=44, mB=46, and mC=134. TRUE OR FALSE? Please show your work. Describe an example of a sustainable yield model, other than a forest, that could help you make decisions about how to use your island resources. Read the poem "Not Waving but Drowning by Stevie Smith.Nobody heard him, the dead man,But still he lay moaning:I was much further out than you thoughtAnd not waving but drowning.Poor chap, he always loved larkingAnd now hes deadIt must have been too cold for him his heart gave way,They said.Oh, no no no, it was too cold always(Still the dead one lay moaning)I was much too far out all my lifeAnd not waving but drowning.How does the phrase "much too far out all my life in the last stanza add a layer of meaning to the poem?It compares the drowning mans inescapable fate to the speakers feeling of isolation.It refers to both the speakers position on the shore and the drowning mans death.It contrasts the drowning mans increasing hopelessness and the speakers determination.It refers to both the speakers inability to help and the drowning mans position in the water. bill's bookbag is half as heavy as julio's bag. if it takes one extra book to make bill's bag feel heavier, it will take two extra books to make julio's bag feel heavier. this best illustrates: if the third place value of a number is 64 , What base is the number in ? A) 2B) 4 C) 8 D) 16 Jill has c comic books. Tonya has 4 more than twice Jill's comic books. What variable expressions represents the total number of comic books Jill & Tony have all together? Find the area.help pls sodium and glucose are transported together from the intestinal lumen into an intestinal cell. the carrier is an ______ and the process is called _______ What happened to the blue bitmoji selfie with the dropping jaw on sc? Please answer!! 100 Points! Use graphing to determine the solution to the system of linear equations x=-1 y=3x+1 Which substance completes passive transport and facilitated diffusion can somebody please answer correctly i will give brainlist? What are two models of light? how does each model explain part of the behavior of light? your patient is a 7 year old boy with an unfused gap between the frontal bones in his cranium. this is known as a: