Find the value of the expression 4a + 7 when a = 1/2

.

The measure of angle B is 141 degrees

Given,

In the question:

There is a seven sided polygon ABCDEFG

The measure of angle BCD is 148 degrees,

The measure of angle DEF is 142 degrees,

The measure of angle EFG is 130 degrees,

The measure of angle FGA is 129 degrees,

and the measure of angle GAB is 120 degrees.

Angle CDE is a right angle.

To find the m∠B.

Now, According to the question:

The sum of angles in a polygon adds up to 180(n - 2), where n is the number of sides of the polygon

The angles are given as:

∠BCD = 148

∠DEF = 142

∠EFG = 130

∠FGA = 129

∠GAB = 120

∠CDE = 90

So, the measure of angle B is calculated using:

∠B + 148 + 142 + 130 + 129 + 120 + 90 = 180(n - 2)

∠B + 759 = 180(n - 2)

The value of n is 7

∠B + 759 = 180(7 - 2)

∠B + 759 = 180 x 5

∠B = 900 - 759

∠B = 141

Hence, the measure of angle B is 141 degrees

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21 miles per hour is the speed of boat still in water and 9 miles per hour is the speed of current.

Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream.

Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The term "upstream speed" in this context refers to the boat's net speed.

13) Given that, a boat traveled 280 miles downstream and back.

Time taken by boat in downstream is 7 hours and in upstream is 14 hours.

Let the speed of a boat be x miles per hour and the speed of a current be y miles per hour.

So, the total speed in downstream is x+y miles per hour and the total speed in upstream is x-y miles per hour.

We know that, Distance = Speed × Time

Now, 280=(x+y)×7

⇒ x+y=40 ------(I)

Here, 280=(x-y)×14

⇒ x-y=20 ------(II)

Add equation (I) and (II), we get

x+y+x-y=40+20

⇒ 2x=60

⇒ x=30 miles per hour

So, x+y=40

⇒ y=10 miles per hour

14) Given that, a boat traveled 252 miles downstream and back.

Time taken by boat in downstream is 12 hours and in upstream is 84 hours.

Let the speed of a boat be p miles per hour and the speed of a current be q miles per hour.

So, the total speed in downstream is p+q miles per hour and the total speed in upstream is p-q miles per hour.

We know that, Distance = Speed × Time

Now, 252=(p+q)×12

⇒ x+y=21 ------(I)

Here, 252=(p-q)×84

⇒ p-q=3 ------(II)

Add equation (I) and (II), we get

p+q+p-q=21+3

⇒ 2p=24

⇒ p=12 miles per hour

So, p+q=21

⇒ q=9 miles per hour

Therefore, the speed of boat still in water is 21 miles per hour and the speed of current is 9 miles per hour.

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Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.

What is Bar graph?

A bar chart or bar chart is a chart or graph that represents categorical data in rectangular bars whose height or length is proportional to the value they represent. Bars can be drawn vertically or horizontally. Column charts are sometimes called vertical bar charts.

Bar charts show comparisons between discrete categories. One axis of the chart shows the specific category to be compared and the other axis represents the measured values. Some bar charts represent bars grouped into multiple groups to show values ​​for multiple measurement variables.

Therefore, Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.

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To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).

We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

Plugging in the values for the given points and solving for m, we get:

m = (12 - (-2)) / (5 - (-2))

= 14 / 7

= 2

Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):

y = mx + b

-2 = 2(-2) + b

-2 = -4 + b

b = -2 + 4

b = 2

Therefore, the equation of the line in slope-intercept form is:

y = 2x + 2

This is the equation of the line that passes through the points (-2,-2) and (5,12).

if f(x)= 2x+7

f(x)= two points

-10 and +5

the solution is : A,,,,f(-10)=2(-10)+7

= -20+7

= -13

and

B,,,,, f(5)= 2(5)+7

= 10+7

= 17

The points on the line 2x - 6y = 12 is

x                y

0               -2

6                0

9                -1

12               2

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

a)The equation is 2x - 6y = 12

For x = 0,

[tex]2 \times 0- 6y = 12\\6y = -12\\y = -\frac{12}{6}\\y = -2[/tex]

For x = 6,

[tex]2 \times 6 - 6y = 12\\6y = 0\\y = 0[/tex]

For x = 9

[tex]2 \times 9 -6y = 12\\18 - 6y = 12\\6y = 12 - 18\\6y = -6\\y = -\frac{6}{6}\\y = -1[/tex]

For x = 12

[tex]2 \times 12 - 6y = 12\\-6y = 12 - 24\\-6y = -12\\y = \frac{12}{6}\\y = 2[/tex]

x                y

0               -2

6                0

9                -1

12               2

b) The graph has been attached

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Answer: 5

Step-by-step explanation:

Pythagorean theorem a^2 + b^2 = c^2

5^2 + x^2 = 5sqrt(2) ^ 2

25 + x^2 = 50

x^2 = 25

x = 5 square root both sides

Christina has 46 baseballs and Spencer has 74 baseballs in their collections.

Two or more expressions with an Equal sign is called as Equation.

Given,

Christina and Spencer have 120 baseballs together.

Let christina has x baseballs

Spencer has 28 more

than Christina

x+28 has Spencer

So x+x+28=120

2x+28=120

Subtract 28 from both sides

2x=120-28

2x=92

Divide both sides by 2

x=46

Hence, Christina has 46 baseballs and Spencer has 46+28=74 baseballs in their collections.

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Answer:

-10

Step-by-step explanation:

When a problem asks you to find f("a number"), it's just telling you to replace x with "a number." So, substitute x with 72 to get the equation [tex]f(72)=-12+\frac{72}{36}[/tex]. The fraction simplifies to 2, and -12 plus 2 is just -10.

Answer:

Locate the given point in the coordinate plane: for example; (−9,4)

Ans: Given that the x and y coordinate of the point are −9 and 4, respectively.

Here, the given point (−9,4) is located in the coordinate plane.  It will be located on the top left side of the coordinate plane if you drew it out.

Step-by-step explanation:

1. You have to draw two perpendicular lines, \ (x-\)axis and \ (y-\)axis.

2. From the point of origin, you have to move 5 units to the right side along the positive \ (x-\)axis.

3. Now, you have to move \ (6\) units up, parallel to the positive \ (y-\)axis

4.  Here, you mark the point of intersection and mark it as \ ((-9, 4).\)

Rectangles are plane figures with common length of opposite sides. Thus the required value of ED is 14 units.

A rectangle is a family of quadrilateral which has two equal opposite sides, with two adjacent sides at right angle to each other. Some properties of a rectangle are:

From rectangle ABCD, it can be deduced that:

AB = DC

AD = BC

AC = BD

So that;

9x + 1 = 13x - 11

11 + 1 = 13x - 9x

12 = 4x

x = [tex]\frac{12}{4}[/tex]

  = 3

Therefore, we have;

BD = 13x - 11

     = 13(3) - 11

BD = 39 - 11

     = 28

But ED = [tex]\frac{BD}{2}[/tex]

So that;

ED = [tex]\frac{28}{2}[/tex]

     = 14

ED = 14 units

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Answer:

Step-by-step explanation:

The equation that that model the number of 2-point shots, x, and the number of 3-point shots, y is x + y = 21, 2x + 3y = 38

Destiny scored 38 points during a recent basketball game. She only made 2-point shots and 3-point shots. In total, Farrah made 21 shots.

The unique equations that model the number of 2-point shots, x, and the number of 3-point shots, y, that Destiney made in the game is as follows:

where

Therefore, the equation that represent the situation is as follows:

x + y = 21

2x + 3y = 38

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The percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.

The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian term per cento, which means "for a hundred," gradually shrank to become the sign for "percent," which is now used globally. It eventually vanished entirely. The word "per" was frequently shortened to "p."

Given,

If the oil price increases at a higher than normal state,

Demand for the compact cars=1400

Demand for the sub-compact cars=2600

If the oil price increases at a normal rate,

Demand for the compact cars=3500

Demand for the sub-compact cars=2300

Assuming that the probability of price increases at higher than the normal rate is 50% and at a normal rate is 50%.

Then,

Demand for compact cars=50%(1400)+50%(3500)

=(50/100)×1400+(50/100)×3500

=700+1750

=2450

Demand for the sub-compact cars=50%(2600)+50%(2300)

=(50/100)×2600+(50/100)×2300

=1300+1150

=2450

Therefore, the percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.

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The inequality which represents the situation is 22x + 42y < 400.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

Cost of medium photos = 22x

Cost of large photo = 42y

Total cost < 400

22x + 42y < 400

Hence "The scenario is represented by the inequality 22x + 42y < 400.".

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Answer:

20w

Step-by-step explanation:

If you have 20 bottles, and each contains w ounces, we can use the following example to solve.

If there were 4oz per bottle,

20 * 4 = 80

80oz

We have w oz per bottle,

20 * w = ?

20w

Answer:

Step-by-step explanation:

The first step is combining like terms 3000 and 3000. The next step is to use the distributive property of equality. After that, combining like terms is the next step, and the last step will be the division property of equality to get the final answer.

hope this helps!! :3

Answer: No

Step-by-step explanation:

No, Mr.Hill can not divide 20 balls into 3 equal groups because 20/3 does not get you a whole number, and you can not have 0.66666667 of a ball.

Answer:

No.

Step-by-step explanation:

20/3 = 5 balls per team and five are left over. No he cannot, this is because Mr. Hill would need to have twenty one balls and he only has 20. So there is not enough. It’s because there are going to be leftovers.

The x-intercept of both the functions is 0. Therefore, option A is the correct answer.

The given functions are f(x)=2x/(x+4) and g(x)= -log3(x+3)+1.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.

For f(x)=2x/(x+4)

Vertical Asymptotes: x=-4

Horizontal Asymptotes: y=2

No Oblique Asymptotes

For g(x)= -log3(x+3)+1

An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (0,0)

y-intercept(s): (0,0)

The x-intercept of both the functions is 0. Therefore, option A is the correct answer.

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The solution is Option C.

4cm , 6cm , 10 cm does not form a right angle triangle

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be ABC which is a right angle triangle

Now , the sides of the triangle is given as

a)

6cm , 8cm , 10cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

10² = 8² + 6²

100 = 64 + 36

100 = 100

Therefore , it is a right angle triangle

b)

12 cm , 35 cm , 37 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

37² = 35² + 12²

1369 = 1225 + 144

1369 = 1369

Therefore , it is a right angle triangle

c)

4 cm , 6 cm , 10 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

10² = 6² + 4²

100 = 36 + 16

100 ≠ 52

Therefore , it is not a right angle triangle

d)

10 cm , 24 cm , 26 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

26² = 24² + 10²

676 = 576 + 100

676 = 676

Therefore , it is a right angle triangle

Hence , the triangle with sides 4cm , 6cm , 10 cm does not form a right angle triangle

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A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³,y = sinx.

As per the given graph,

The point where the slope is zero and the smallest among its neighborhood points then it will be relative minima.

In the given graph the point b is the smallest among its neighborhood thus b will be the relative minimum.

Hence "A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima".

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The standard deviation gives information about how values are distributed around the mean. The range between the lowest and highest number is more constrained when the standard deviation is low. Values will so tend to group together around the mean.

What is explained by the standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

                                     When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30.

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Answer:

y = 6.08871x + 63.9274

Step-by-step explanation:

You can use Desmos a free graphing calculator to do this.  

Answer: -5-2x

Step-by-step explanation:

The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.

The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, hence its perimeter is equal to the sum of those three lengths.The perimeter of a form can be calculated by adding the lengths of all its sides. A perimeter example is what? A field with a length of 24 yards and a width of 15 yards, for instance, will have a perimeter of 78 yards.

calculation

In order to construct a hog pen, I have 800 feet of fencing.

Assume that "l" represents the rectangle's length and "w" its width.

One of your properties borders a river that I own.

I can secure my property with fencing on its three sides.

because of this, the fencing's necessary perimeter p = l + 2w

The fencing's perimeter is now equal to

⇒ l + 2w = 800

= l = 800 - 2w

now the  rectangle's area  = A = lw

Therefore,  A = l * w = w ( 800 - 2w ) = 800w - [tex]2w^{2}[/tex]

By diffusing the area equation, we can figure out the rectangle's greatest area.

Therefore, A' = 800 - 4w

Again, A" = -4

The rectangle has the largest area since the second order differentiation is constant negative.

Put simply, we obtain: A' = 0 , A' = 800- 4w

⇒800- 4w = 0

⇒ 4 w = 800

⇒ w = 200

So the rectangle has a 200-foot width.

The rectangle's length is currently:

l = 800 - 2w = 800 - 2 ( 200 ) = l = 400 feet

The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.

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Answer:

Look at the attached image below

Step-by-step explanation:

[tex]\tt 3x-8\ge \:7[/tex]

Add 8 to both sides:-

[tex]\tt 3x\ge 7+8[/tex]

Add 7 and 8 to get 15:-

[tex]\tt 3x\ge 15[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3x}{3}\ge \cfrac{15}{3}[/tex]

[tex]\tt x\ge \:5[/tex]

Yes Data can be modeled by a cubic function

Using finite differences to determine the degree of the polynomial function that fits the data, you know when a set of data could be modeled by a cubic function if you obtain a third difference that is nonzero and constant.

The entities that contain the measures and dimensions make up the relational graph that is the Cube data model. The term "cubes" for entities in Cube was adopted from OLAP cubes. They are essentially data tables with a semantic meta layer that describes the measures, dimensions, and connections between the cubes.

The basic primitives of dimensions and measurements are the basis on which Cube operates. These primitives can be combined to create metrics by the user.

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Ordered pairs of graphs III and IV represents a function.

How do you find out if a set of ordered pairs is a function or not?

For a set of ordered pairs to be a function, there must not be any two points that have the same first elements.

This means that, the x-coordinates must not repeat for any two given points.

According to the given question:

Graph I - Clearly x coordinate repeats for the ordered pairs (-8, 12) and (-8, -8). Therefore ordered pairs of Graph I does not represents a function.

Graph II - Clearly x coordinate repeats for the ordered pairs (9, 2) and   (9, -10). Also for (18,4) and (18, -14) Therefore ordered pairs of Graph II does not represents a function.

Graph III - Every ordered pair of this graph is unique hence the ordered pairs of the graph III represents a function.

Graph IV - Every ordered pair of this graph is unique hence the ordered pairs of the graph IV represents a function.

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Step-by-step explanation:

[tex]6x^2+60x+144\\\\6(x^2+10x+24)[/tex]

You are looking for two numbers that add to 10 and multiply to 24:

6 + 4 = 10

6 * 4 = 24

so [tex]x^2 + 10x + 24 = (x+6)(6+4)[/tex]

factored: [tex]6(x+6)(x+4)[/tex]