In the figure below, A shows the position of a house on the shore and B shows the position of a house on an island. To find the distance between the two houses,a surveyor measures from the house on shore to point C. An instrument is used to find

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:  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:

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:

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:

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:

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

Answers:

f(-3) = -1

f(-1) = 2

f(3) = 5

======================================

Explanations:

Draw a vertical line through -3 on the x axis. Make sure this vertical line crosses the orange graph. Mark this point of intersection and then draw a horizontal line from this point to the y axis. You should find that it touches -1 on the y axis. Check out the attached image to see this process in action.

Those steps basically say that x = -3 leads to y = -1. Since y = f(x), this means f(-3) = -1

Through similar steps, you should find that f(-1) = 2 and f(3) = 5

Note that the open hole/circle does not count. So if you land on an open hole, just keep going until you hit a closed circle on the other piece of the graph.

A) f (–3) = -1

B) f (–1) = 2

C) f (3) = 5

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

General formula

or

y = mx + c

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant

The formula for a gradient (m) between 2 points in a line

m = Δy / Δx

or we can use:

[tex]\rm \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}[/tex]

Piecewise Functions: functions that have different equations based on the input (x) value

We look for 3 pieces of function from the graph

1. graph 1 is a straight line that passes through 2 points : (-4.0) and (-1, -3) so that the straight line equation:

[tex]\rm \dfrac{y-0}{-3-0}=\dfrac{x+4}{-1+4}\\\\\dfrac{y}{-3}=\dfrac{x+4}{3}\\\\3y=-3(x+4)\\\\3y=-3x-12\\\\y=-x-4\Rightarrow \:for\:x<-1[/tex]

2. graph 2 is a straight line with the equation: \

[tex]\rm y=2\Rightarrow \:for\:-1\leq x<3[/tex]

3. graph 1 is a straight line that passes through 2 points,  (3.5) and (5.1) so that the straight line equation  :

[tex]\rm \dfrac{y-5}{1-5}=\dfrac{x-3}{5-3}\\\\\dfrac{y-5}{-4}=\dfrac{x-3}{2}\\\\2(y-5)=-4(x-3)\\\\2y-10=-4x+12\\\\2y=-4x+22\\\\y=-2x+11\:\Rightarrow for\:x\geq 3[/tex]

A function made up of 3 pieces:

a solid dot means "including",

an open dot means "not including"

[tex]\rm y=-x-4\:for\:x<-1[/tex]

[tex]\rm y=2\:for\:-1\leq x<3[/tex]

[tex]\rm y=-2x+11\:for\:x\geq 3[/tex]

A) f (–3) =

Because -3 <-1, the function used is y = -x-4, so

f (-3) = - (- 3) -4

f (-3) = 3-4

f (-3) = -1

B) f (–1) =

Because x = -1, the function used y = 2, so

f (-1) = 2

C) f (3) =

Because x = 3, the function used is = -2x + 11, so

f (3) = -2 (3) +11

f (3) = -6 + 11

f (3) = 5

Piecewise Functions

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the inverse of the function

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domain of the function

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The sum represented by the notation [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex] is 32

How to determine the sum represented by the notation

From the question, we have the following parameters that can be used in our computation:

[tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]

This means that we determine the value of the expression from i = 3 to i = 9 and then add them up

So, we have

2(3) - 9 = -3

2(4) - 9 = -1

2(5) - 9 = 1

2(6) - 9 = 3

2(7) - 9 = 5

2(8) - 9 = 7

2(9) - 9 = 9

2(10) - 9 = 11

Evaluate the sum

Sum = -3 - 1 + 1 + 3 + 5 + 7 + 9 + 11

Sum = 32

Hence, the sum represented by the notation is 32

Question

Find the sum of [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]

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:

The y intercept is -1

Step-by-step explanation:

y-14=6(x-2.5)

We need to get the equation in the form y = mx+b where b is the y intercept

Distribut the 6

y-14 = 6x -15

Add 14 to each side

y-14+14 = 6x-15+14

y = 6x-1

The y - intercept is -1

Answer:

(0, -1)

Step-by-step explanation:

y-14=6(x-2.5)

Distributive property:

y-14 = 6 * x - 6*2.5

y-14= 6x-15

Add 14 on each side:

y-14+14=6x-15+14

Simplify:

y=6x-1

In the form y=mx+b (slope-intercept form, as shown above), the y-intercept is (0, b). b is -1.

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

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:

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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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:

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:

5000.

Step-by-step explanation:

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

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:

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:

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:

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: 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:

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:

The volume of the cone is [tex]27cm^3[/tex]

Step-by-step explanation:

We know that formulas

Volume of cylinder is

[tex]V_1=\pi r^2 h[/tex]

Volume of cone is

[tex]V_2=\frac{1}{3}\pi r^2 h[/tex]

we are given

A cone and cylinder have the same height and the same base radius

So, both will have same radius and height

now, we can find ratios

[tex]\frac{V_2}{V_1}=\frac{\frac{1}{3}\pi r^2h }{\pi r^2h}[/tex]

now, we can simplify it

[tex]\frac{V_2}{V_1}=\frac{1}{3}[/tex]

we are given

the volume of the cylinder is 81 cm^3

so, [tex]V_1=81[/tex]

now, we can plug it and solve for V2

[tex]\frac{V_2}{81}=\frac{1}{3}[/tex]

[tex]81\times \frac{V_2}{81}=81\times\frac{1}{3}[/tex]

[tex]V_2=27[/tex]

So, the volume of the cone is [tex]27cm^3[/tex]

The volume of the cone, which has the same height and base radius as the cylinder with a volume of 81 cm³, is one-third that of the cylinder, equating to 27 cm³.

For a cone with the same height and base radius as the cylinder, the volume formula is V = ⅓πr²h, which is one-third of the volume of the cylinder. Given that the volume of the cylinder is 81 cm³, the volume of the cone can be found by dividing this value by 3, resulting in a volume of 27 cm³ for the cone. Therefore, the correct answer is B) 27 cm³.