How do I solve this complicated problem?

Answer:

A

Step-by-step explanation:

A trinomial can be factored into two binomials, when the discriminant of the trinomial is greater than or equal to 0.

The discriminant for trinomial [tex]ax^2+bx+c[/tex] is he expression [tex]D=b^2-4ac.[/tex]

Check all options:

A.

[tex]D=3^2-4\cdot 1\cdot 2=9-8=1,[/tex]

then

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}=\dfrac{-3\pm\sqrt{1}}{2}=-2,\ -1.[/tex]

Thus,

[tex]x^2+3x+2=(x-x_1)(x-x_2)=(x-(-2))(x-(-1))=(x+2)(x+1).[/tex]

B.

[tex]D=4^2-4\cdot 1\cdot 5=16-20=-4<0,[/tex]

so this trinomial cannot be factored.

C.

[tex]D=5^2-4\cdot 1\cdot 7=25-28=-3<0,[/tex]

so this trinomial cannot be factored.

D.

[tex]D=6^2-4\cdot 1\cdot 10=36-40=-4<0,[/tex]

so this trinomial cannot be factored.

Answer:

Step-by-step explanation: It is 1/2 of 14 = 7 hours to the moot

And plug in 7 hours to the equation  4*7+14*7=126 divide that by 2 and the distance is 63

y=x+1.75

substitute for y in equation 2.

4x-2(x+1.75)=4

4x-2x-3.5=4

2x=7.5

x=3.75

y=3.75+1.75

y=5.5

The solution of the system as an ordered pair is (3.75, 5.5).

The correct option is first box.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

System of equations,

y = x + 1.75  {equation 1}

4x - 2y = 4   {equation 2}.

Substituting the value of y top the equation 2,

4x - 2(x + 1.75) = 4

4x - 2x - 3.5 = 4

2x = 7.5

x = 3.75

And y = 5.5

Therefore, the solution is x = 3.75 and y = 5.5.

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Answer:

Length of third side = 37-(18+11)

= 37 - 29

= 8 m

Hope this helps!

Answer:

8 m

Step-by-step explanation:

Answer:

[tex]x=\frac{1}{9},-\frac{1}{9}[/tex]

Step-by-step explanation:

[tex]3 + |x*-9|=4\\|x*-9|=1\\|x|=\frac{1}{9}\\ \\x=\frac{1}{9},-\frac{1}{9}[/tex]

The value of x for the given condition will be either 1/9  or -1/9.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.

Given that 3 + x × (-9) = 4

In the first case  if the value of x is positive

3 - 9x = 4 ⇒ x = -1/9

In the second case if the value of x is negative

3 + 9x = 4 ⇒  x = 1/9

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Answer:

20

Step-by-step explanation:

to find the mean, it means to find the average.

steps:

first, you add up all the numbers.

then you divide that total number by the total number of numbers you have.

and that is ur answer!!

17+19+21+23=80          add up all numbers

80÷4=20                      divide total by the amount of numbers

The average/mean is 20.

plz give brainliesttttt

Answer:20 is the mean

Step-by-step explanation:

if you add them all you get 80 then divide it by 4 because its 4 numbers and ya get 20

are you missing something there's no data and there's no question

There isn't enough information.

Answer:

D)

Step-by-step explanation:

Answer:

Step-by-step explanation:

assuming that the X is a multiplication symbol and not a variable, because the multiplication symbol is * not x, 5*5/2*7=25/14=1 and 11/14

Answer:

11 years old

Step-by-step explanation:

If four brothers have the average age 6, then the sum of their ages is

[tex]4\cdot 6=24[/tex]

years.

Let x years be the age of sister. If four brothers and their sister have the average age 7, then

[tex]\dfrac{24+x}{5}=7.[/tex]

Multiply this equation by 5:

[tex]24+x=35\Rightarrow x=35-24=11.[/tex]

The sister is 11 years old.

Answer:

Sometimes, but not always.

Step-by-step explanation:

A parallelogram is a quadrilateral with two pairs of parallel sides, but there are no requirements for its interior angles. A rectangle, on the other hand, must have four interior 90 degree angles. So a rectangle is always a parallelogram, but a parallelogram is not always a rectangle.

A parallelogram is usually defined as a quadrilateral with 2 pairs of equal, opposite and parallel sides. It can also form right angles between adjacent sides. Therefore, not all rectangles are squares, not all parallelograms are rectangles.

Hope I could help! :)

The answers is:

The first mechanic's rate is $70 per hour.

The second mechanic's rate is $110 per hour.

Let's write the given information in order to make the equations that will help us to solve this problem.

Let be "x" the first mechanic's rate and "y" the second mechanic's rate, so:

If the first mechanic worked for 5 hours and the second mechanic worked for 15 hours, and the together charged a total of $2000.

[tex]5x+15y=2000[/tex]

Also, we know that the sum of the two rates was $170 per hour, so:

[tex]x+y=180[/tex]

Then, isolating "x" and replacing it into the first equation, we have:

[tex]x=180-y[/tex]

[tex]5(180-y)+15y=2000[/tex]

[tex]900-5y+15y=2000[/tex]

[tex]10y=2000-900[/tex]

[tex]10y=1100[/tex]

[tex]y=\frac{1100}{10}=110[/tex]

So, the second mechanic's rate is $110 per hour.

Now, to calculate the first mechanic's rate we need to replace "y" into the second equation:

[tex]x+y=180\\x+110=180\\x=180-110=70[/tex]

So, the first mechanic's rate is $70 per hour.

Have a nice day!

30% chance of losing money.

40% chance of breaking even

Added together  = 70% of not making any money or losing money.

Only a 30% chance of making money.

The company should not invest, since they only have a 30% chance of making money.

Answer:   [tex]\bold{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt{2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\sqrt7-5}{\sqrt7+\sqrt8}\bigg(\dfrac{\sqrt7-\sqrt8}{\sqrt7-\sqrt8}\bigg)=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{7-8}=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{-1}\\\\\\=\boxed{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt2}[/tex]

[tex] \frac{6}{11} \div \frac{2}{5} = \frac{6}{11} \times \frac{5}{2} = \frac{3 \times 5}{11} = \frac{15}{11} [/tex]

Step-by-step explanation:

6/11 ÷ 2/5

Formula: a/b ÷ c/d = a/b x d/c = ad/bc

1. Change it to multiplication x by switching 2/5 to 5/2

6/11 x 5/2

= 30/22

2. Simplify

= 15/11 <------- Answer

Hope this Helped!!!

~Shane

Answer:

it is going to be a

Step-by-step explanation:

but u have to add the number and move your demical

Answer:

Option b 17.2

Step-by-step explanation:

Given is a probability distribution of a random variable say x in table form.We have to find the mean.

All probabilities lie between 0 and 1 and add to 1.

Hence this is a valid prob distribution.

To find mean we multiply the random variable x value with probability and add.

Mean = E(X) = [tex]\Sigma p_i x_i = 15(0.1)+16(0.3)+17(0.2)+18(0.2)+19(0.1)+20(0.1)\\=1.5+4.8+3.4+3.6+1.9+2\\= 17.2[/tex]

Hence option b is right answer.

6, 6 are the solutions of the given equation.

It is a mathematical statement which contains two algebraic expressions on both sides of an ' = ' sign.

Equation shows the equality between the expressions in left hand and right hand side.

The given equation is [tex]6x^{2} -2x+36=5x^{2} +10x[/tex]

Solving the equation, [tex]6x^{2} -5x^{2} -2x-10x+36=0[/tex]

⇒ [tex]x^{2} -12x+36=0[/tex]

⇒ [tex](x-6)^{2} =0[/tex]

∴ The equation have double root, the values of x are 6, 6

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Answer:

Range

Step-by-step explanation:

Answer:

The total area of the prism is 30 cubic feet

Step-by-step explanation:

To find the area multiply 3 by 2 by 5

Answer:

Final answer is [tex]3x^2-4x+15[/tex]

Step-by-step explanation:

we have been given an expression [tex](5x^2+3)-(2x^2+4x-12)[/tex].

Now we need to subtract them.

We can subtract like terms only that has same variable with same exponent.

[tex](5x^2+3)-(2x^2+4x-12)[/tex]

[tex]=5x^2+3-2x^2-4x+12[/tex]

[tex]=5x^2-2x^2-4x+3+12[/tex]

[tex]=(5-2)x^2-4x+(3+12)[/tex]

[tex]=(3)x^2-4x+(15)[/tex]

[tex]=3x^2-4x+15[/tex]

Hence final answer is [tex]3x^2-4x+15[/tex]

Answer:

(5x^2+3)-(2x^2+4x-12) = 3x²-4x+15.

Step-by-step explanation:

We have given the expression:

(5x²+3)-(2x²+4x-12)

We have to subtract.

(5x²+3)-(2x²+4x-12)

5x²+3-2x²-4x+12

5x²-2x²-4x+3+12

3x²-4x+15

3x²-4x+15 is the answer.

Answer:

x = − 15 − 8 y

y=-7/8x-19/8

Step-by-step explanation:

If you are trying to solve for x the answer for first problems is

x = − 15 − 8 y

second problem the slope intercept form is:

y=-7/8x-19/8

I'm not sure exactly what you are looking for but I hope that is it.

in degrees the answer is 30° since a full rotation is 360°, divide by 12 and 1/12 of a full rotation is 30°

1/12 of a full rotation in mathematics refers to an angle of 30 degrees. This is calculated by dividing the full rotation (360 degrees) by 12. For example, each hour on a clock represents 1/12 of a full rotation.

In Mathematics, a full rotation is defined as 360 degrees. Therefore, to find 1/12 of a full rotation, you would divide 360 by 12. This results in 30 degrees. Hence, 1/12 of a full rotation refers to an angle of 30 degrees in a circular motion. This concept is often applied in geometry and other mathematical applications. For instance, imagining a clock, where each hour signifies 1/12 of a full rotation. The difference in the angle from 12 to 1 on the clock is therefore 30 degrees.

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Answer:

[tex]y - 3 = \frac{1}{4}(x+2)[/tex] or choose any line with slope 1/4

Step-by-step explanation:

The slope of this line is -4. The slope of the line perpendicular to this line will be the negative reciprocal or 1/4.

Write the equation using the slope m=1/4 and the point slope form.

[tex]y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x+2)[/tex]

This is the equation of the line that is perpendicular and passes through the same point (-2,3) as the equation listed.

Answer:

[tex]y=\frac{1}{4} x+c[/tex]   where [tex]c[/tex] can be any number.

Step-by-step explanation:

First we need to clear for y:

[tex]y-3 =-4(x+2)\\y=-4(x+2)+3\\y=-4x-8+3\\y=-4x-5[/tex]

and now we have an equation of the form:

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept.

in this case [tex]m=-4[/tex] and [tex]b=-5[/tex]

to find and equation perpendicular to this line, the following must be true:[tex]m*m_{1}=-1[/tex]

where m is the slope of the original line that i just mentioned, and [tex]m_{1}[/tex] is the slope of the new line. Substituting [tex]m=-4[/tex]

[tex]-4*m_{1}=-1[/tex]

clearing for [tex]m_{1}[/tex]

[tex]m_{1}=\frac{-1}{-4} \\m_{1}=\frac{1}{4}[/tex]

thus, the new perpendicular line must have the form:

[tex]y=m_{1}x+c\\y=\frac{1}{4}x+c[/tex]

where the y-intecept [tex]c[/tex] can be any number, some examples are:

[tex]y=\frac{1}{4}x+3\\y=\frac{1}{4}x-8[/tex]

and so on, the important thing to be a perpendicular line is that the slopes are related to the equation [tex]m*m_{1}=-1[/tex].

Answer:

Step-by-step explanation:

2 1/4 divided by 1 2/5

8/4 + 1/4 divded by 5/5 +2/5

9/4 divided by 7/5

9/4 times 5/7

9 times 5 over 4 times 7

45 over 28

Answer:

[tex]\frac{2+\sqrt{3} }{4}[/tex]

Step-by-step explanation:

We can use the identity [tex]Cos^2(x)=\frac{1}{2}+\frac{1}{2}Cos(2x)[/tex] to write it as:

[tex]Cos^2(\frac{\pi}{12})=\frac{1}{2}+\frac{1}{2}Cos(2(\frac{\pi}{12}))\\=\frac{1}{2}+\frac{1}{2}Cos(\frac{\pi}{6})\\=\frac{1}{2}+\frac{1}{2}(\frac{\sqrt{3} }{2})\\=\frac{1}{2}+\frac{\sqrt{3} }{4}\\=\frac{2+\sqrt{3} }{4}[/tex]

Note: The value of [tex]Cos(\frac{\pi}{6})[/tex]  is  [tex]\frac{\sqrt{3} }{2}[/tex]

The answer is the 2nd one, [tex]\frac{2+\sqrt{3} }{4}[/tex]

If r = 20, then plug 20 into the equation.

so instead of r - 9, it's 20 - 9

20 - 9 = 11

The answer is:

The expression for the number of sweets that Sara and Tim have now, are:

[tex]Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}[/tex]

To write the expressions for the number of sweets that Sara and Tim have now, we need to follow the next steps:

Sara starts with 24 sweets and Tim starts with 24 sweets

[tex]Sara=24 Sweets\\Tim=24 Sweets[/tex]

Then, Sara gives Tim x Sweets

[tex]Sara=(24-x)Sweets\\Tim=(24+x)Sweets[/tex]

Then. Sara eats 7 of her Sweets

[tex]Sara=(24-x-7) Sweets\\Sara=(17-x )Sweets\\Tim=(24+x) Sweets[/tex]

Then, Tim eats half of his sweets

[tex]Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}[/tex]

So, the expression for the number of sweets that Sara and Tim have now, are:

[tex]Sara=(17-x) Sweets\\\\Tim=\frac{(24+x)Sweets}{2}[/tex]

Have a nice day!

The correct answer is d

The vertex of the graph is at minimum or maximum option (D) (1, -1); the minimum is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have shown a graph of a parabola in the picture.

As the graph opens up and has a vertex at (1, -1)

The minimum value of graph,

At x = 1

y = -1

Thus, the vertex of the graph is at minimum or maximum option (D) (1, -1); the minimum is correct.

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Answer:

1 Triangle

Step-by-step explanation:

By adding all these 3 angle measures (45°, 75°, 60°) we are getting 180° in sum. And as we know that normal triangle has 180° , so that it equal only to one triangle.

Final answer:

The sum of the angles of a triangle is always 180 degrees. With angles of 45°, 75°, and 60°, a single unique triangle can be formed.

Explanation:

The sum of the angles in a triangle is always 180 degrees. In this case, the measures of the three angles are 45°, 75°, and 60°. To determine how many triangles can be formed, we need to consider if these angles can form a valid triangle.

Add the given angles: 45° + 75° + 60° = 180°. Since the sum is 180°, a triangle can be formed.

Considering unique triangles: If two angles are the same, only one unique triangle can be formed. If all angles are different, multiple triangles can be formed.

Conclusion: With angles of 45°, 75°, and 60°, a single unique triangle can be formed.

Profit = 8%

If the briefcase was marked down 20% from 1500 you multiply 1500 x .2 = 300 in order to calculate the discount.

Calculate the discounted price:

1500 - 300 = 1200

Calculate 10% discount of 1200:

1200 x .1 = 120

Calculate the sales price:

1200 - 120 = 1080

The last step is to calculate the profit/loss is the cost is 1000.

The briefcase sold for 1080 and the company paid 1000 for it, so there was a profit of 80.

The percentage is calculate by dividing 80/1000 = 8% profit

Final answer:

The briefcase was originally priced at Rs 1500, discounted twice first by 20% and then by an additional 10%, leading to a final selling price of Rs 1080. With a cost of Rs 1000, the profit is Rs 80, resulting in a profit percentage of 8%.

Explanation:

The briefcase was initially selling for Rs 1500 and was marked down by 20%. Therefore, the sale price after the first discount can be calculated as: Rs 1500 - (20% of Rs 1500) = Rs 1500 - Rs 300 = Rs 1200. This briefcase was then marked down by an additional 10% of the promotion sales price, which becomes Rs 1200 - (10% of Rs 1200) = Rs 1200 - Rs 120 = Rs 1080. The cost of the briefcase is given as Rs 1000, so the profit is the final selling price minus the cost: Rs 1080 - Rs 1000 = Rs 80.

To find the profit percentage, we use the formula: (Profit/Cost) x 100. Substituting the values we get: (Rs 80/Rs 1000) x 100 = 8%. So, the profit percentage is 8% after both the discounts.