-ax^(2)+2x+2a if a=7 and x=-5

Answer: 10.7 or 10.8

Step-by-step explanation:

so, first  [tex]a^{2} +b^{2} =c^{2}[/tex]

while [tex]a = 3.75[/tex] and [tex]b=10[/tex] and [tex]c=?[/tex]

so, it will be written as,

[tex]3.75^{2} +10^{2} =c^{2} \\[/tex]

[tex]14.0625+100=c^2[/tex]

[tex]114.0625=c^2[/tex] then square root both sides to have an answer of:

[tex]10.7=c[/tex]

That's if you are going to use the [tex]a=3.75[/tex]. as written in the question...

while if you're going to use [tex]a=4[/tex] (as shown in the figure) then only change the 3.75 with 4.

which will equal to...

[tex]4^2+10^2=c^2[/tex]

[tex]16+100=c^2[/tex]

[tex]116=c^2[/tex] then square root both sides to have an answer of:

[tex]10.77=c[/tex]

[tex]10.8[/tex] ≈ [tex]c[/tex]

hope you've understanded.!

Answer:a

Step-by-step explanation:

The inequality is written as 15x + 70y ≤ 920. Then the region below the line is the solution to inequality.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Serenity is assembling beaded jewelry with no more than 920 beads she presently has in inventory. Bracelets use 15 beads and necklaces use 70 beads.

Let 'x' be the number of bracelets and 'y' be the number of necklaces. Then the inequality is given as,

15x + 70y ≤ 920

The region below the line is the solution to inequality.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

Answer:

h(x) = 0.5x + 8

Step-by-step explanation:

We are being asked to write an equation where h(x) represents the soil depth in inches and x describes the number of bags. To do this, we need to find b (our y-intercept, ie the value of h(x) or y when x=0) and m (our slope).

"The depth of the soil is currently 8 inches": this means before any bags are added (ie when x=0), the soil depth starts at 8. This makes 8 our y-intercept (b in h(x)=mx+b) as we have to add it on to however much the bagged soil adds in order to get the total depth.

"For each bag of soil he adds, the depth will increase by 1/2 of an inch": this means that the soil depth from added bags is equal to the amount of bags times 0.5, which makes 0.5 our slope (m in h(x)=mx+b).

Therefore our answer is:

h(x) = 0.5x + 8

The equation of line is y = 1.5x + 5.5.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

We have the reference point as (-2, 2.5) and (-1, 4)

so, slope

= (4- 2.5)/ (-1 + 2)

= 1.5

and, the equation of line is

y- 2.5 = 1.5 (x+ 2)

y- 2.5 = 1.5x + 3

y = 1.5x + 5.5

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ1

Answer:

Step-by-step explanation:

(X=the number)

2x+13=-21

(-21)-13=34

34x2=68

Recall that the complex norm (or modulus) of a complex number z = a + bi is defined as the nonnegative square root of the product of the complex number and its conjugate, i.e., |z| = √(z × z*), where z* is the complex conjugate of z.

Using this definition, we can calculate the complex norm of each of the given complex numbers as follows:

A complex number is a number that can be expressed in the form [tex]a + bi[/tex], where a and b are real numbers, and i is the imaginary unit defined by [tex]i^{2} = -1[/tex]. The real part of the complex number is a, and the imaginary part is bi.

Complex numbers can be added, subtracted, multiplied, and divided in a manner similar to real numbers. They can also be graphed on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part.

To know more about real numbers visit:

https://brainly.com/question/10592345

#SPJ1

Answer:

Step-by-step explanation:

We can use algebra to solve for the unknown number. Let's call the number "x".

The equation can be written as:

9 + x * (-7) = -19

Expanding the product on the left side:

9 + -7x = -19

Subtracting 9 from both sides:

-7x = -28

Dividing both sides by -7:

x = 4

So the number x is 4.

Answer:

The complement of a set A, denoted A', is the set of all elements that are not in A. The complement of B, denoted B', is the set of all elements that are not in B.

Step-by-step explanation:

(a) A' = {b, d}

(b) B' = {a, c, d}

(c) A' U B = {a, b, c, d, e} (the union of A' and B contains all elements in both sets)

(d) A U B' = {a, b, c, e} (the union of A and B' contains all elements in both sets)

(e) A' n B = {} (the intersection of A' and B is an empty set)

(f) A n B' = {c} (the intersection of A and B' contains all elements that are in A but not in B)

(g) A' U A = {a, b, c, d, e} (the union of A' and A is the universal set, containing all elements)

(h) B' n B = {} (the intersection of B' and B is an empty set)

(i) A U B = {a, b, c, e} (the union of A and B contains all elements in both sets)

(j) A' U B' = {a, b, c, d, e} (the union of A' and B' is the universal set, containing all elements)

(k) [A n B]' = {b, d} (the complement of the intersection of A and B is the union of the complements of A and B)

(l) A' n B' = {} (the intersection of A' and B' is an empty set).

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The total area of the figure is 258cm². Thus, option 3 is corect.

Given:

shorter side: 18 centimeters

perpendicular height : 4 centimeters

portion from a point to a vertical line created by two vertices : 3centimeters

height : 12 centimeters

from figure we know that,  it is the vertex's height as well as the length of the sides to multiply together and we also have to divide since there is 5 sides

So , after multiplying the vertex height and sides and dividing it by the 5 , we get 258 cm²

Hence , the total area of the figure is 258cm².

Learn more about Composites figures at:

brainly.com/question/21135654

#SPJ1

The time it takes the bicycle to travel along the road is 20 seconds.

The rate of change of position of an object in any direction is called as Speed.

The formula for speed is Distance divided by Time.

So Time = distance / speed

we need to know the distance the bicycle travels to use this formula.

If we have this distance, we can divide it by the speed of 5 m/s to find the time.

Let the distance is 100 meters, then the time taken is:

time = distance / speed = 100 / 5 = 20 seconds

Hence, the time it takes the bicycle to travel along the road is 20 seconds.

To learn more on Speed click:

https://brainly.com/question/28224010

#SPJ9

The complete question is given below:

A bicycle travels along with the road at an average speed of 5 m/s work out the time it takes the bicycle to travel along the road of distance 100 meters.

Give your answer in seconds

Answer:

  b = 30

Step-by-step explanation:

You want the value of b given line y = 20x +b passes through the points (6, 150) and (11, 250).

The equation y = 20x +b can be solved for b:

  b = y -20x . . . . . . . . subtract 20x

Using the given point (x, y) = (6, 150), you have ...

  b = 150 -20(6) = 150 -120

  b = 30

The number of ways 3 man and 3 woman line up at the counter in a store is 720 ways.

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.

Given that, three men and three women line up at a checkout counter in a store.

a) Number of ways = 6!

= 6×5×4×3×2×1

= 720 ways

b) The first person in line is a woman, and then the line alternates by gender that is a woman, a man, a woman, a man, a woman, a man, and so on

There are 3 number of ways for woman standing in the odd position and for men standing in the even position.

So, number of ways = 3!×3!

= 3×2×1×3×2×1

= 36 ways

c) There are 3 men and 3 women.

Probability first is a woman is 3/6

Probability second is a man is 3/5

Probability third is a woman is 2/4

Probability fourth is a man is 2/3

Probability fifth is a woman is 1/2

Probability sixth is a man is 1/1

Multiply all these probabilities together and you get:

3/6 × 3/5 × 2/4 × 2/3 × 1/2 × 1/1 = 0.05

Therefore, the number of ways 3 man and 3 woman line up if the first person in line is a woman, and then the line alternates by gender that is a woman is 36 ways.

Learn more about factorials here:

brainly.com/question/25997932

#SPJ1

The points M(0, -1), and T(4, 6), on the diagonal [tex]\overline{MT}[/tex] of the rhombus MATH, indicates that the equation of the line containing the diagonal [tex]\overline{AH}[/tex], in slope and intercept form is; [tex]y = 3\frac{9}{14} - 4\cdot \frac{x}{7}[/tex]

A rhombus is a quadrilateral that has four congruent sides.

The specified shape of the quadrilateral MATH = A rhombus

The coordinates of the endpoints of the diagonal [tex]\overline{MT}[/tex] of the rhombus are;

The equation of the line that contains the diagonal [tex]\overline{AH}[/tex] of the rhombus can be found as follows;

The diagonals of a rhombus are perpendicular, therefore, the slope of the diagonal, [tex]\overline{AH}[/tex]is -1 divided by the slope of the diagonal [tex]\overline{MT}[/tex]

The slope of [tex]\overline{MT}[/tex] = (6 - (-1))/(4 - 0) = 7/4

The slope of [tex]\overline{AH}[/tex] = -1/(7/4) = -4/7

The diagonals of a rhombus bisect each other, therefore, the diagonals [tex]\overline{MT}[/tex] and [tex]\overline{AH}[/tex] intersect at the midpoint of point [tex]\overline{MT}[/tex]

Therefore, the midpoint of [tex]\overline{MT}[/tex] is a point on the diagonal line that contains the diagonal [tex]\overline{AH}[/tex]

The midpoint of [tex]\overline{MT}[/tex] = ((0 + 4)/2, (-1 + 6)/2) = (2, 2.5)

The equation of the line containing the diagonal [tex]\overline{AH}[/tex] is therefore;

y - 2.5 = (-4/7)·(x - 2)

y = -4·x/7 + 8/7 + 2.5 = -4·x/7 + 51/14

y = -4·x/7 + 51/14 = -4·x/7 + 3 9/14

y = [tex]3\frac{9}{14}[/tex] - 4·x/7

Learn more on perpendicular lines here: https://brainly.com/question/29526529

#SPJ1

The longest border of the Mann's park is 228.6 meter.

The Triangle Inequality It is a basic principle of geometry that the lengths of any two sides of a triangle must add up to more than the length of the third side. In other words, the longest side of any triangle must be shorter than the total length of the other two sides.

In this case, the shortest side of Mann Park measures 5 inches, and the two longer sides measure 7 inches and 9 inches.

So, the sum of the lengths of the two longer sides is:

' 7 inches + 9 inches = 16 inches.

Since 5 inches is less than 16 inches, we know that the 5-inch side is the shortest side, and the 9-inch side is the longest side.

One inch is approximately equal to 0.0254 meters, so we have:

= 9 inches x 0.0254 meters/inch

= 0.2286 meters

Since the shortest side is 1000 meters long, the longest side is:

= 1000 meters x 0.2286 meters/inch

= 228.6 meters long.

Therefore, the longest border of Mann Park is approximately 228.6 meters long.

To know more about Triangle check:

https://brainly.com/question/2773823

#SPJ1

Answer: The correct system of linear inequalities that represents Leslie's situation is:

4x + 10y ≥ 120 (to represent the requirement to raise at least $120)

x + y ≥ 18 (to represent the requirement to sell at least 18 items in total)

x ≥ 0, y ≥ 0 (to represent that Leslie must sell a non-negative number of keychains and t-shirts)

Where x represents the number of keychains sold and y represents the number of t-shirts sold. The first inequality represents the minimum amount of money Leslie needs to raise, and the second inequality represents the minimum number of items she needs to sell. The last two inequalities represent that Leslie can only sell a non-negative number of items.

Step-by-step explanation:

Answer:

1 this is the answer because 1 is more than other number

Answer:

A = 0.50x+20

B= 0.75x+22

4 games

$19

Step-by-step explanation:

For abbey, the 20 dollars she starts with is the initial value. the 50 cents per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be A = 0.50x + 20. For Bianca, the 22 dollars she starts with is her initial value. the 75 centers per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be B = 0.75x + 22.

We can find out when they will have the same amount of money left by making two small tables -> one for abbey and one for Bianca.

Abbey: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

Bianca: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

For both girls after four games, they have the same amount of money- $19.

Answer: 2: 56 degrees

4: 56 degrees

(Number 6 is not in the image)

Step-by-step explanation:

So for #2 we know the whole angle is 90 degrees, so all we have to do is 90-34 = 56

And for #4, we know the angle is 180 so all we have to do is 180-124=56

Step-by-step explanation:

7.

the probability of picking a defective missile with the first pull is

5/22

the probability of picking a working missile with the first pull is

17/22 = ((22-5)/22)

I have to assume that the picked missiles are not put back into the main pile after the check.

and I have to assume that the sequence of the pulled missiles don't matter.

a.

all are defective.

since there are only 5 defective missiles, there is only one possibility out of all the possibilities to pull 5 out of 22 to get 5 defective missiles.

the possible combinations to pull 5 out of 22 :

C(22, 5) = 22! / ((22 - 5)! × 5!) =

= 22×21×20×19×18×17/(5×4×3×2) =

= 22×21×19×3×17 = 447,678

and we have one desired situation (all 5 are defective).

so, the probability is

1/447678 = 0.000002233748364... = 2.233748364e-006

b.

all 5 are functional.

the total possible cases to pull 5 out of 22 are still

447,678.

the desired cases are all cases to pull 5 out of the 17 (22 - 5) functional missiles.

that is

C(17, 5) = 17! / ((17 - 5)! × 5!) =

= 17×16×15×14×13 / (5×4×3×2) =

= 17×2×14×13 = 6,188

so, the probability to get one of these cases is

6188 / 447678 = 0.013822435...

The probability of picking a defective missile with the first pull is 5/22

The probability of picking a working missile with the first pull is 17/22

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

If we assume that the picked missiles are without replacements and the sequence of the pulled missiles don't matter,

Therefore, the probability that:

a. all are defective is 2.233748364e-006

Since there are only 5 defective missiles, there is only one way to get 5 defective missiles out of 22 possible outcomes.

The possible combinations to pull 5 out of 22 :

C(22, 5) = 22! / ((22 - 5)! × 5!) =

= 22×21×20×19×18×17/(5×4×3×2) =

= 22×21×19×3×17 = 447,678

and we have one desired situation (all 5 are defective).

so, the probability is 1/447678 = 0.000002233748364... = 2.233748364e-006

b. all 5 are functional is 0.013822435

the total possible cases to pull 5 out of 22 are still 447,678.

The ideal scenario is for all incidents to result in the removal of 5 of the 17 (22 - 5) operational missiles.

that is

C(17, 5) = 17! / ((17 - 5)! × 5!) =

= 17×16×15×14×13 / (5×4×3×2) =

= 17×2×14×13 = 6,188

so, the probability to get one of these cases is

6188 / 447678 = 0.013822435

Read more about probability here:

https://brainly.com/question/24756209

#SPJ1

The requried teacher needs $59.5 more to buy cups and napkins, as of the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
To find out how much more money the teachers will need to buy cups and napkins, we can first calculate the cost of each item and then add those costs together.

Each package of cups costs $3.50

The teachers need to buy 12 cups

So the total cost of cups is = 12 cups × ($3.50 per package) = $42

Now let's do the same thing for the napkins:

Each package of napkins costs $4.25

The teachers need to buy 10 napkins

So the total cost of napkins is = 10 napkins × ($4.25 per package) = $42.50

To find out how much more money the teachers will need to buy cups and napkins,

= $42 + $42.50 - $25
= $59.50 - $25 = $59.5

Therefore, the teachers will need $59.5 more to buy cups and napkins.

Learn more about models here:
https://brainly.com/question/24861939
#SPJ9

The x-intercepts of the graph of the given polynomial function as described is; 2, 3 and -5.

The x-intercepts of a polynomial function are otherwise termed, roots, solutions or zeroes of the polynomial function.

On this note, the x-intercepts of the polynomial function which is as described in this scenario are;

x - 2 = 0; x = 2.

x - 3 = 0; x = 3.

x + 5 = 0; x = -5.

Ultimately, the x-intercepts of the polynomial function in discuss are; 2, 3 and -5.

Read more on x-intercepts of polynomial functions;

https://brainly.com/question/29136444

#SPJ1

now, we're making the assumption we're simply doing an identity proof, so

[tex]sec(\theta )-tan(\theta )sin(\theta )=\cfrac{1}{sec(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE 1st step} }{\cfrac{1}{cos(\theta )}-\cfrac{sin(\theta )}{cos(\theta )}\cdot sin(\theta )}\implies \cfrac{1}{cos(\theta )}-\cfrac{sin^2(\theta )}{cos(\theta )}\implies \cfrac{1-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )} \\\\\\ cos(\theta )\implies \cfrac{1}{sec(\theta )}[/tex]

7200+80x = 3200+120x

Reason:

Canton starts off with 7200 people. Add on 80x to represent the fact the town grows 80 people per year. That's how we end up with the expression of 7200+80x

Similarly, the expression 3200+120x represents the idea Holly Springs started off with 3200 people and grows at 120 people per year.

The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The interest is given as,

I = PRT / 100

Let 'x' be the amount invested in the first bank. Then the amount of investment in the second bank is (100,000 - x). Then the equation is given as,

x · 0.06 · 1 + (100,000 - x) · 0.08 · 1 = 7,200

0.06x + 8,000 - 0.08x = 7,200

-0.02x = -800

x = 40,000

The amount in the second bank is given as,

⇒ 100,000 - 40,000

⇒ 60,000

The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

More about the solution of the equation link is given below.

https://brainly.com/question/22613204

#SPJ1

The number of gallons of paint that the painter should buy is; 4 gallons

The parameters given are;

Side length of cube = 20 ft

Area that a gallon of paint can cover = 400 square feet

Since the room is shaped like a cube, then it will have 4 equal wall areas.

Area of one wall = 20 * 20 = 400 square feet

Area of 4 walls = 4 * 400 = 1600 square feet

Since 400 sq.ft  is covered by 1 gallon, then;

1600 sq.ft = (1600 * 1)/400

= 4 gallons

Read more about Algebra Word Problems at; https://brainly.com/question/21405634

#SPJ1

Check the picture below.

so the triangles are similar by AA.

[tex]\cfrac{GI}{10}~~ = ~~\cfrac{15}{12}\implies \cfrac{GI}{10}~~ = ~~\cfrac{5}{4}\implies 4GI=50\implies GI=\cfrac{50}{4}\implies GI=12.5[/tex]

Answer: a

Step-by-step explanation: it's increasing and it's a line

Step-by-step explanation:

a. £5,37

b.£2,07

c.£15,70