Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
O x + y = 29, 5x + 2y = 100
Ox+y = 100, 5x + 2y = 29
O 5x + y = 29, 2y + x = 100
O 2x + y = 100, 5y + x = 29

Answer:

3

Step-by-step explanation:

2x-xy

2(x)-(x)(y)

2(-1/2)-(-1/2)(8)

-1 - (-4)

-1 + 4

3

Answer:

3

Step-by-step explanation:

2x-xy

Let x = -1/2 and y = 8

2(-1/2) - (-1/2)(8)

Multiply

-1 - (-4)

Subtracting a negative is like adding

-1+4

Add

3

It's the third option.

Completing the square yields

x ² + 9x + 7 = 0

(x ² + 9x + 81/4) + 7 = 81/4

(x + 9/2)² + 7 = 81/4

Now solving for x gives

(x + 9/2)² = 53/4

x + 9/2 = ± √(53/4) = ± √53/2

x = (-9 ± √53)/2

Answer:

24n^7/m^16

Step-by-step explanation:

Just simplify and rewrite what ever you get simplify again 2 times and now make the calculation as you see every big number is a whole number and is a pair.

The process of copying an angle through construction involve ensuring

that the distance between the two rays forming the angle is the same or

equal in the original and copy of the angle at a given equal distance from

the vertex of both angles

The step where the error occur is step 4. She measured the incorrect length

The reason for the above selection is as follows:

The steps to copy an angle are as follows;

A critical step in the copying process involves the finding the distance

between the initial line and the terminal line EF at a given distance DG =

AE from the angle vertex

The step where the error occur is in step 4. by opening the compass

between points A and E which are points on the same line and placing the

compass at point G on line l to draw an arc intersecting the arc created

from point D at H, thereby making the radial distance between the two lines

forming the angle, in the copied angle at a distance E from the vertex,

equal to AE rather than EF

Therefore, the error occurred in step 4. She measured the incorrect length

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Answer:

26ft

Step-by-step explanation:

10^2 +24^2 =AB^2

AB=26

Answer: 26 ft

Step-by-step explanation:

a^2+b^2=c^2

10^2+24^2 = c^2

100+576=c^2

Sqrt 676 = c

C = 26

Step-by-step explanation:

A = 12.25cm2

P perimeter 14cm

Answer:

A=12.25cm²

P=14

Answer:

the the 3rd one Is the one

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

One piece will be length x and the other piece will be 20 cm longer, so it will be x + 20 cm long.  

Added together the length of these two boards will equal 86 cm. So you can write an equation:  

x + (x + 20) = 86  

Remove the parentheses and add the two x's together to get:  

2x + 20 = 86

Subtract 20 from both sides:  

2x = 66  

Divide both sides by 2 and you have:  

x = 33  

The short piece is 33 cm and the other piece is 20 cm longer or 33 + 20 = 53 cm.

Answer:

4

Step-by-step explanation:

7+sqrt(7) is an irrational number

Answer:

p = 8 when b = 16 and p = -8 when

b = -16

Step-by-step explanation:

x² + bx + 64 = x² + 2px + p²

Cancel x² on both sides,

bx + 64 = 2px + p²

Now, by comparing both sides, you'll get the following equations,

1. b = 2p

2. p² = 64

From equation (2),

p = ±√64

= 8 or -8

Substitute p = 8 and p = -8 into equation (1),

b = 2(8) and b = 2(-8)

b = 2(8) and b = 2(-8) = 16 = -16

Therefore, p = 8 when b = 16 and p = -8 when

b = -16

Answer:

i think 1/58 is correct

i hope its help you

Answer:

$480

Step-by-step explanation:

Let original price be x

{Original price - discount amount = sale price}

So, x - (x * 35/100) = 312

x - 35x/100 = 312

100x - 35x / 100 = 312

65x/100 = 312

65x = 31200

x = 31200/65

x = $480

So I think the original price of desk was $480

The original price of the desk is $480.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a desk is being sold for $312.

Let the original price of the desk be x.

Here, x-35% of x =312

x- 35/100 ×x=312

x-0.35x=312

0.65x=312

x=312/0.65

x=480

Therefore, the original price of the desk is $480.

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9514 1404 393

Answer:

Step-by-step explanation:

Let b represent the length of the base. Then (b+4) is the height and the area of the triangle is ...

  A = 1/2bh

  70 = 1/2(b)(b+4)

  b² +4b -140 = 0 . . . . . multiply by 2, put in standard form

  (b +14)(b -10) = 0 . . . . factor

  b = 10 . . . . the positive solution

The base of the triangle is 10 yards; the height is 14 yards.

Answer:

Following are the solution to the given question:

Step-by-step explanation:

The population std. dev of the dog weight=8

[tex]\sigma=8\\\\P(\text{guess with in 16 lbs}) = P(|X-\mu|\leq 16)\\\\=P(-2 \leq Z \leq 2) = 0.9544\\\\[/tex]

Calculating the payout w s.t:

[tex]E[netpay]=0=(-5) \times 0.9544+w\times (1-0.9544)\\\\ w =(5 \times \frac{0.9544}{1-0.9544}) =\$ 104.65[/tex]

therefore, we assume that the weight of the dog is a normal distribution with std. deviation that is 8.

Answer:

inductive - . Inductive reasoning makes broad generalizations from specific observations.

casual correlation

quality ( i think)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i just did it

Answer: 10 km

Step-by-step explanation:

1cm is equal to 10km on ground.

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary across a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of scale significant in two different ways.

Given

A scale of 1:1,000,000 means that anything on the map that is 1 ‘unit’ in length represents something that is one million ‘units’ in length.

So two points 1 cm apart on the map will be one million centimetres apart in real life. Divide a million by 100 if you prefer the distance in metres. And divide that figure by 1,000 if you want it in kilometres.

1,000,000/100*1000 = 10km

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Bar graphs are used to represent data, where the vertical axis represents the frequency and the horizontal axis.

The percentage that is over 50 is 15.6%:

The data on the bar graph can be represented as:

Under 17 [tex]\to[/tex] 25

18 - 24 [tex]\to[/tex] 35

25 - 34 [tex]\to[/tex] 40

35 - 50 [tex]\to[/tex] 35

Over 50 [tex]\to[/tex] 25

So, the total customer surveyed are:

[tex]Total = 25 + 35 + 40 + 35 + 25[/tex]

[tex]Total = 160[/tex]

The percentage over 50 are:

[tex]\%Over\ 50 = \frac{Over\ 50}{Total } * 100\%[/tex]

[tex]\%Over\ 50 = \frac{25}{160} * 100\%[/tex]

[tex]\%Over\ 50 = 0.15625* 100\%[/tex]

[tex]\%Over\ 50 = 15.625\%[/tex]

Approximate

[tex]\%Over\ 50 = 15.6\%[/tex]

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Answer: -21/2

Concept:

Usually, when doing mathematics operation, it goes by the PEMDAS order:

However, since the question asks to solve the order of operation from left to right, then we would be doing [addition] --> [Divison]

Solve:

Given

(-5/2) + 3/4 ÷ 1/6

Operate with addition

=(-10/4) + 3/4 ÷ 1/6

=(-7/4) ÷ 1/6

Operate with division

=(-7/4) × 6/1

=-42 / 4

=-21 / 2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

45 days

Step-by-step explanation:

Based on the giving information, 30*15/10.

Reduce the fraction by canceling the greatest common factor: 3*15 = 45

Answer:

ask in English then I can help u

You need to re copy and paste it, I can’t see the full possible answers/question.

Answer:

Carmen:27

Abdul:17

David=34

Step-by-step explanation:

Carmen+Abdul+David = 78

Carmen-Abdul=10

David=2Abdul

Carmen=Abdul+10

Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78

4Abdul=68

Abdul = 68/4=17

Carmen = 17+10=27

David = 2 * 17 = 34

27+17+34=78

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

Answer:

there would be 21 girls and 14 boys

Step-by-step explanation:

I split the kids down in half and then added seven to the girls and when added up 21+14=35 and that’s is 7 more girls then boys

9514 1404 393

Answer:

  1/63

Step-by-step explanation:

There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:

  4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63

The larger fraction is 1/63 unit larger than the smaller fraction.

Answer:

-7

Step-by-step explanation:

x = y - 6

2x = 5y - 9

Use the internet for full steps

x = -7

y = -1

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

Answer:

A. 50º

Step-by-step explanation:

we are given the exterior angles 140º and 90º

exterior angles + corresponding interior angles = 180º

that means the two other angles of the triangle are:

180 - 140 = 40º

and

180 - 90 = 90º

the sum of interior angles in a triangle = 180

p = 180 - (40 + 90)

p = 180 - 130

p = 50º