What is the value y of 3x + y = 9 y = –4x + 10

Answer: 1

Step-by-step explanation:

Method #1: Using the log rules (+ → x and - → ÷)

  log₂4 + log₂16 - log₂32

= log₂[tex](\frac{4*16}{32})[/tex]

= log₂[tex](\frac{64}{32})[/tex]

= log₂2

= 1

Method #2: Using log rules to simplify each expression

log₂4 = x              log₂16 = x                  log₂32 = x

      4 = 2ˣ                    16 = 2ˣ                       32 = 2ˣ

      2² = 2ˣ                   2⁴ = 2ˣ                       2⁵ = 2ˣ

        2 = x                      4 = x                          5 = x

log₂4 = 2               log₂16 = 4                 log₂32 = 5

             2     +                      4       -                        5     =     1

Answer:

Sue // 6 More blocks

Step-by-step explanation:

Sue has more blocks because 34>28.

34-28 is 6 so sue has 6 more.

Answer:

X= (300 s + 200 b + 42 d )mg

Step-by-step explanation:

Amount of spinach=300 ml

Amount of berries =200 ml

amount of dressing = 42 ml

Vitamin C in one ml of spinach = s mg

Vitamin C in 300 ml of spinach = 300 s mg

Vitamin C in one ml of berries=b mg

Vitamin C in 200 ml of berries = 200 b mg

Vitamin C in one ml of dressing = d mg

Vitamin C in 42 ml of dressing = 42 d mg

Let total vitamin C be = x

Then

X= (300 s + 200 b + 42 d )mg

is the required expression

To divide fractions, multiply the first fraction (-7/10) by the reciprocal of the second one (5/2). This gives -35/20 which simplifies to -7/4 or -1 3/4.

When dividing fractions, the conventional method is to multiply the first fraction, which is the dividend, by the reciprocal of the second fraction, which is the divisor. In this case, let's take the content loaded -7/10 divided by 2/5.

The reciprocal of 2/5 is 5/2. So, to divide -7/10 by 2/5, we instead multiply -7/10 by the reciprocal of 2/5.

-7/10 * 5/2 = -35/20.

Finally, we simplify this to its simplest form, by reducing to the lowest terms. We find that, -35/20= -7/4 or -1 3/4 if expressed as a mixed number.

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Answer:

4

Step-by-step explanation:

Only one plane can be drawn perpendicular to plane B through point A in three-dimensional space. The correct answer is option 1) that is One.

The question at hand involves geometric concepts, specifically the relationship between planes and lines in three-dimensional space. If point A lies in plane B, then there can be one and only one plane drawn perpendicular to plane B through point A; this is because in three-dimensional space, a point defines a line and only one perpendicular plane can contain that line.

This principle is similar to how any three points not on a single straight line determine a plane and how two lines intersect at a single point or not at all. The perpendicular plane would form a 90-degree angle along every line in plane B that passes through point A.

The correct answer is option 1) that is One

Answer:

Do not qualify

Step-by-step explanation:

Yearly income = $58000

Monthly income = [tex]\frac{58000}{12}[/tex] = $4833.33

Median annual income = $47778

Monthly expenses = $4600

Income < Median Income ? 58000 < 47778 -> No

x = (Monthly income - expenses) * 60

  = (4833.33 - 4600) * 60

  = 233.33 * 60

  = 13999.8

x < 10000 ? 13999.8 < 10000 -> No

So, Do not qualify

Answer:

The family does not qualify for bankruptcy

Step-by-step explanation:

Expenses=$4,600

Yearly income=$58,000

Monthly income=Yearly income / 12

Monthly income=$58,000/12

Monthly income=$4,833.333333

Rounded to the nearest cent:

Monthly income=$4,833.33

Flowchart

                                                           No

                                                                  Mean test. Calculate

Income=$58,000<$47,778=Median  →   (Monthly income - expenses)*60

                                              Income       ($4,833.33-$4,600)*60

                                                                 ($233.33)*60

                                                                  $13,999.80

                                                                  Call this number X.           No

                                                                  X=$13.999.80 < $10,000   →  Do not

                                                                                                                   qualify

The family does not qualify for bankruptcy

Okay # 1

Y = 6x (I don't know why there's two answer choices)

# 2

Uhh it should be increasing linear but the (3,8) kinda threw it off

The rule for the first set of ordered pairs is y = 6x, representing a linear, increasing function.

The relationship between the number of college courses and time spent on homework is increasing and non-linear.

The ordered pairs (1, 6), (2, 12), (3, 18), (4, 24), and (5, 30) show that for each value of x, y is always six times as much.

Thus, the rule that represents this function is y = 6x.

When you plot these points on a graph, the line will be straight, showing it's a linear function, and because y increases as x increases, it is an increasing function.

Looking at the other set of ordered pairs for the number of college courses versus the time spent on homework, we can see that as the number of courses increases, the time spent also increases, showing that the relationship is increasing.

However, the increase in time is not consistent (3, 6, 8, 12), which suggests the relationship is non-linear.

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

(2, 0), (-3, 3), (9, 1), (-3, 5)  NOT

(9, 1), (-3, 4), (2, 1), (9, 2)     NOT

(2, 4), (-3, 2), (9, 1), (-7, 2)     YES

(2, 4), (-3, 6), (2, 3), (-7, 2)     NOT

Answer:

divide 100 ml and 1.2 liter

Step-by-step explanation:

You will get the answer in percent

Answer:

10

Step-by-step explanation:

Answer:

k(x) = 4x - 2

Please refer attachment for the graph.

Step-by-step explanation:

Given :

g(x) = 3x

h(x) = 2- x

k(x) = g(x)-h(x)

k(x) =3x -(2-x) = 3x -2 +x =4x -2

∴k(x) = 4x - 2

Answer:

m=1

Boys: Girls

2:1

Step-by-step explanation:

To find the slope from 2 point we use the formula

m = (y2-y1)/(x2-x1)

m = (-13--10)/(3-6)

  = (-13+10)/(3-6)

   = -3/-3

   = 1

Boys: Girls

16:8

We can divide each number by 8

16/8: 8/8

2:1

Boys: Girls

2:1

Answer:

Step-by-step explanation:

The length can be found by setting up a proportion.  If the width is reduced by some ratio, then the length will share the same ratio.

3 / 8 =  x / 10                    Multiply both sides by 10.

3 * 10 / 8 = x                     Multiply first

30/8 = x                            Divide next. You don't need to do it in this order.

3 6/8                                 Simplify

3 3/4                                 Give another choice

3.75                                

The length = 3.75 inches

If none of these are correct, please leave a note with your choices.

Answer:

The length = 3.75 inches

Step-by-step explanation:

Answer:

5000.

Step-by-step explanation:

1000 milliliter is one liter. So if you have 5 liters 5 x 1000 can fit inside.

Answer:

D

Step-by-step explanation:

A) True. Alternate interior angles are congruent so

[tex]\angle c\cong \angle e[/tex]

B) True. Considering the sum of these three angles is equal to a straight angle. Since ∠a+∠d  supplementary to ∠e

[tex]\angle a+\angle e+\angle d=180[/tex]

C) True. Since the line segments form a triangle having a (black) line as triangle base.

D) False. ∠b is congruent to its corresponding angle, and ∠e is not its corresponding angle. The corresponding angle of ∠b is the angle vertex opposed to ∠d (not identified).

Answer: x = 5

Step-by-step explanation:

1 = -4 + x

We have to isolate x, and remember, what we do to one side we do to the other.

1 + 4 = -4 + 4 + x

5 = x

Check:

-4 + 5 = 1

1=1

Answer:

y = 4.25x

Step-by-step explanation:

Answer:

y = 4.25x

Step-by-step explanation:

Cheddar cheese cost 4.25 per pound . This means the cost of cheddar cheese is 4.25 for every pound in weight. Assuming we put a currency to the value we can say 1 pound of cheddar cheese is equals to 4.25 dollars($4.25). Mathematically, it can be represented as

4.25 is the cost for 1 pound of Cheddar cheese

Let the cost of the equation be y as required from the question.

y = cost of the cheddar cheese

x is the weight value in pounds of the Cheddar cheese.

The equation can be best represented as

y = 4.25x

In the equation above if the amount in pounds is 3 pound . the value will be inputted for x and the cost will be gotten which is y.

Answer:

With a number line with two points opposite from each other on a number line, the middle of it is always going to be 0.  Therefore, both points are the same distance away from 0 just in opposite directions. That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.

This method only works when it is specifically stated that the two points are opposite from each other.

Hope this helps!

xx,

myara

The location of Point Q on the number line is the opposite of the location of Point P. If Point P is at +a, then Point Q is at -a, and vice versa.

In order to determine the location of Point Q, we first need to know the location of Point P on the number line. If we assume that point P is positive and located at +a, then Point Q, being the opposite of Point P, would be located at -a on the number line. Conversely, if Point P was negative and located at -a, the opposite, Point Q, would be on the +a location on the number line. The important thing to remember here is that opposite points on a number line are simply reflection of each other with respect to the origin (0).

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Answer:  The probability of selecting a chip with an even number given that the chip is black = 5/6

Step-by-step explanation:

Let B represents the event of getting black chip,

While E represents the event of getting even chip.

So, according to the question,

It is given, The probability of selecting a black chip with an even number is,

[tex]P(B\cap E)=\frac{1}{2}[/tex]

And,  The probability of selecting a black chip is,

[tex]P(B)=\frac{3}{5}[/tex]

Thus, the probability of selecting a chip with an even number given that the chip is black,

[tex]P(\frac{E}{B} )= \frac{P(B\cap E)}{P(B)} = \frac{1/2}{3/5}[/tex] ( By the conditional property )

⇒ [tex]P(\frac{E}{B} )= \frac{5}{6}[/tex]

Answer:

a < -11 (picture included)

Step-by-step explanation:

To solve an inequality, you work it like a regular equation, with a few exceptions, such as flipping the inequality sign when you multiple or divide a number by a negative. Let's solve.

-6a > 66

Divide both sides by -6 and flip the inequality sign because we divided by a negative number.

a < -11

On a number line, it should look like the picture. It has an open hole because the inequality sign does not have a line under it.

-6a > 66      change the signs

6a < -66     divide both sides by 6

a < -11

Answer:

None of the above

Step-by-step explanation:

x-1/3 = k

We know that k=3, so we can substitute that into the equation

x-1/3 = 3

Add 1/3 to each side

x-1/3 + 1/3 = 3+1/3

x = 3 1/3 or as an improper fraction 10/3

Answer:

23/44 < 33/64

Step-by-step explanation:

if you don't want to  get common denominators multiply the denominator of the second fraction by the numerator of the first (1,427) and the denominator of the first one to the numerator of the second (1,452) the bigger number is greater. 1,427 < 1,452

By converting both fractions into decimals (23/44 becomes 0.5227; 33/64 becomes 0.5156), it is clear that 23/44 is greater than 33/64.

To compare which fraction, 23/44 or 33/64, is greater, you need to find a common denominator and then compare the numerators. The calculation can be simplified by converting these fractions into decimals. To do so, divide the numerator by the denominator. Therefore, 23/44 becomes 0.5227 and 33/64 becomes 0.5156. Therefore, 23/44 is greater than 33/64.

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First off, the length of MN is 2√10, not 8. This is because using Pythagorean Theorem, you get that MN=√4+36=2√10, which is (3).

The midpoint of MN can be found by finding the average of the coordinates of M and N. Therefore, our first part to solving this question is to find the coordinates of M and N. M is (2,5) and N is (4,-1). Finding the average of the x-coordinates gives us 3. Finding the average of the y-coordinates gives us 2, Therefore, the midpoint of MN is (3,2), or answer choice (3).

Answer:

C

Step-by-step explanation:

The line has a positive slope which means it slopes upwards from left to right

A and B  slope downwards so can be excluded

C and D have the correct upward slope but C has the y-intercept of - 3

Thus C is the required line

Answer:

2*2*3*3*5

Step-by-step explanation:

Factor 180 into prime numbers that multiply together to give 180

180 = 20 *9

  =  4*5 * 3*3

  = 2*2* 5 * 3*3

Now rewrite them from smallest to largest

2*2*3*3*5

Answer:

560x^3

Step-by-step explanation:

The formula is

(r + 1)th term of (a + x)^n = nCr a^(n-r)x^r

So 5th term = (4 + 1)th term

= 7C4 x^(7-4) (-2)^4

=  35x^3*16

= 560x^3