Mathematics Middle School

What is the positive solution of x^2-36 = 5x

Answers

Answer 1

x^2-5x-36 =0

=》(×+4)(x-9) =0

=》 x = 9 or -4

positive solution for x is 9

Answer 2

For this case we must find the positive solution of the following quadratic equation:

[tex]x ^ 2-5x-36 = 0[/tex]

To find the solutions we factor, that is, we look for two numbers that when multiplied give as result -36 and when summed give as result -5.

These are:

-9 and +4

[tex]-9 * 4 = -36\\-9 + 4 = -5[/tex]

So, we have:

[tex](x-9) (x + 4) = 0[/tex]

The roots are:

[tex]x_ {1} = 9\\x_ {2} = - 4[/tex]

The positive solution is 9.

Answer:

Related Questions

Evaluate 3/2y - 3 + 5/3z when y=6 and z=3

Answers

Answer: 11

Step-by-step explanation:

3/2(6) - 3 + 5/3(3)= 11

what is the sum of an 8-term geometric series if the first term is -11, the last term is 180, 224, and the common ratio is -4

Answers

Answer:

The sum is [tex]144,177[/tex]

Step-by-step explanation:

we know that

The formula of the sum in a geometric sequence is equal to

[tex]S=a1[\frac{1-r^{n}}{1-r}][/tex]

where

a1 is the first term

r is the common ratio

n is the number of terms

we have

a1=-11

r=-4

n=8

substitute the values

[tex]S=(-11)[\frac{1-(-4)^{8}}{1-(-4)}][/tex]

[tex]S=(-11)[\frac{1-(65.536)}{5}][/tex]

[tex]S=144,177[/tex]

A triangular prism was sliced parallel to its base. What is the shape of the cross section shown in the figure?

a triangle that has the same dimensions as either base of the prism
a triangle that does not necessarily have the same dimensions as either base of the prism
a parallelogram that is not a rectangle
a rectangle

Answers

Answer:

The answer is a rectangle.

Step-by-step explanation:

A triangular prism was sliced parallel to its base. What is the shape of the cross section shown in the figure?

The answer is rectangle. If the base is a rectangle and we slice it parallel to the base in the same direction as the base, we will get smaller and smaller rectangles with each slice.

This can be clear with the picture attached. If we slice parallel to rectangular base, the cross section will be a rectangle.

Solve the equation 5|b+8|=30

Answers

Answer:

b = -2 or b = -14

Step-by-step explanation:

[tex]5|b+8|=30\qquad\text{divide both sides by 5}\\\\|b+8|=6\iff b+8=6\ or\ b+8=-6\qquad\text{subtract 8 from both sides}\\\\b=-2\ or\ b=-14[/tex]

Final answer:

To solve the equation 5|b+8|=30, we first isolate the absolute value by dividing by 5, then set up two separate equations for b + 8 = 6 and b + 8 = -6. Solving each gives us the solutions b = -2 and b = -14.

Explanation:

To solve the equation 5|b+8|=30, we will first divide both sides of the equation by 5 to isolate the absolute value expression.

So moving from the equation 5|b+8|=30, we get |b+8| = 6. This means that the expression inside the absolute value can be either positive 6 or negative 6.

We then write two separate equations to solve for the variable b:

b + 8 = 6b + 8 = -6

Solving the first equation, we subtract 8 from both sides to find that b = -2. Solving the second equation, we subtract 8 from both sides to find that b = -14.

Thus, the solution for the equation 5|b+8|=30 is b = -2 or b = -14.

does the equation y = 4.2 x represent a proportional relationship

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\stackrel{\stackrel{k}{\downarrow }}{4.2}x~~\checkmark~\hfill[/tex]

Answer: its proportional,

bud

Step-by-step explanation:

Help please what is the answer?

Answers

Answer:

C) 5.6

Step-by-step explanation:

AC = sqrt(11^2 + 2^2) = sqrt(125)

(1/2)AC = (1/2)sqrt(125)

(1/2)AC = 5.6

Answer: C) 5.6

Answer:

C, 5.6

Step-by-step explanation:

A midsegment is half of the side it is parallel to. This means that it is half of BC. They give us the coordinates for B and C so we can just use the distance formula (the square root of the change in x squared plus the change in y squared)

If you simplify it, you get root 125 which is about 11.2. 11.2 divided by 2 is 5.6, so your answer would be C.

What graph represents a reflection of abc over the line x=0

Answers

Answer: D

Step-by-step explanation: APEX

Answer:

The correct option is D)

Step-by-step explanation:

line x = 0 is y-axis (vertical line)

When graph is reflected along y-axis so, it will be in second quadrant.

so, the graph which satisfying these condition is only option D)

in which c ordinate are A has (-1,1) ,B has (-4,1) and C has (-3,3)

Hence, the correct option is D)

What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?

Answers

Answer: [tex](y-4)=3(x-1)[/tex]

Step-by-step explanation:

We know that the point slope form of a line that has a slope m and passing through point (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Given: Slope of a line: m = 3

Point through which line is passing : (1, 4)

The point slope form of a line that has a slope 3 and passing through point (1, 4) is given by :-

[tex](y-4)=3(x-1)[/tex]

– 4 = 3[(x – (–1)]

Step-by-step explanation:

Solve the inequality n/-3+ 8 > 6.
A.) n > -6
B.)n > 42
C.)n < 6
D.)n > -42

Answers

Answer:

C.) n < 6

Step-by-step explanation:

Subtract 8:

n/-3 > -2

Multiply by -3. The negative multiplier requires the comparison be reversed:

n < 6

Final answer:

To solve the inequality n/-3 + 8 > 6, we first subtract 8 from both sides of the inequality and then multiply by -3. This reveals that n < 6, which corresponds to option C.

Explanation:

To solve the inequality n/-3 + 8 > 6, we first isolate the term containing n by subtracting 8 from both sides of the inequality:

n/-3 + 8 - 8 > 6 - 8

n/-3 > -2

Now, we can multiply both sides of the inequality by -3 to find the value of n. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:

n/-3 × -3 < -2 × -3

n < 6

Thus, the correct answer to the inequality n/-3 + 8 > 6 is n < 6, which corresponds to option C.

Find the slope of the line through (2, -3) and (-4, 3).

-1
0
1

Answers

ANSWER

-1

EXPLANATION

The slope formula is given by

[tex]m = \frac{y_1-y_2}{x_1-x_2} [/tex]

The slope of the line through (2, -3) and (-4, 3) is found by substituting the points into the above formula;

[tex]m = \frac{ - 3 - 3}{2 - - 4} [/tex]

This simplifies to

[tex]m = \frac{ - 6}{ 6} = - 1[/tex]

The slope is -1

Answer:

-1

Step-by-step explanation:

The slope of a line is the ratio of its change in rise to its change in run. In the -xy-plane, this is the same as the ratio of the change in y coordinate to the change in x coordinate. In notation, we write this as

[tex]\frac{\Delta y}{\Delta x}[/tex]

and calculate it by finding the difference between y coordinates and dividing it by the difference between x coordinates. Here, our y coordinates are 3 and -3, and our x coordinates are -4 and 2, so our slope would be

[tex]\frac{3-(-3)}{-4-2}=\frac{3+3}{-6}=\frac{6}{-6}=-1[/tex]

tell whether the angles are complementary or supplementary. then find the value of x

Answers

Hello,

In Q5. Being a straight line the angles are supplementary to each other.

And x = 70°

In Q6.

The angles sum up to 90° , so 25x + 30° = 90

25x = 60°

x= 60°/25 = 2.4°

Hope this helps.

Answer:

see explanation

Step-by-step explanation:

x and 110 form a straight angle and are supplementary, thus

x + 110 = 180 ( subtract 110 from both sides )

x = 70

25x and 30 form a right angle and are complementary, thus

25x + 30 = 90 ( subtract 30 from both sides )

25x = 60 ( divide both sides by 25 )

x = [tex]\frac{60}{25}[/tex] = [tex]\frac{12}{5}[/tex]

if you spin the spinner twice what is the probability that it will land on an even number both times

Answers

The answer would be [tex]\frac{1}{4}[/tex] because half the chance of landing on an even number divided by 2 (2 times landing on the even number).

The probability that the spinner will land on an even number both times when spun twice is 1/4 or 25%.

To find the probability of two independent events occurring together, we multiply their individual probabilities. First, let's determine the probability of landing on an even number in a single spin. There are two even numbers (2 and 4) out of the four possible outcomes, so the probability of landing on an even number in one spin is 2/4 or 1/2.

Since we're spinning the spinner twice, the events are independent. This means that the outcome of the first spin does not affect the outcome of the second spin. Therefore, the probability of landing on an even number in both spins is the product of the individual probabilities. So, the probability of landing on an even number both times is:

Probability of landing on an even number in one spin = 1/2

Probability of landing on an even number twice = (1/2) * (1/2) = 1/4

To know more about probability here

https://brainly.com/question/11234923

#SPJ2

Martin can run 1 mile in 7 minutes. What proportions can be written from this information?

Answers

Answer:

[tex]\frac{1}{7}=\frac{3}{21}[/tex]

[tex]\frac{7}{1}=\frac{21}{3}[/tex]

Step-by-step explanation:

Verify each case

case 1) [tex]\frac{1}{7}=\frac{3}{21}[/tex]