The question is.. "The expression 5(3r - 10) means the product of 5 and the difference of three times r minus 10. If r = 4, the value of the expression is [?] This is 6th grade math and im kinda stuck here

Answer:

[tex]x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10} [/tex]

Step-by-step explanation:

Ensure that the equation is in the form of ax² +bx +c= 0.

5x² -x +1= 3

5x² -x +1 -3= 0 (-3 on both sides)

5x² -x -2=0

Here, a= 5, b= -1, c= -2.

Use the quadratic formula below to solve for x.

[tex]\boxed{x = \frac{ - b± \sqrt{b^{2} - 4ac } }{2a} }[/tex]

[tex]x = \frac{ - ( - 1)± \sqrt{( -1 )^{2} - 4(5)( - 2)} }{2(5)} [/tex]

[tex]x = \frac{1± \sqrt{1 + 40} }{10} [/tex]

[tex]x = \frac{1± \sqrt{41} }{10} [/tex]

[tex]∴x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10} [/tex]

Step-by-step explanation:

First, lets understand the question. When it says to find all the "real" solutions, that means you should not give any solutions containing an imaginary number.  An imaginary number is basically where we accept that there exists an i  (imaginary number) that is equal to [tex]\sqrt{-1\\}[/tex]  (square root of negative 1). So we are not considering this concept in this question.

Let's start solving then. Can you think of an equation that may help you solve this problem? The biggest clue is that x is squared.  If you said the quadratic formula, then you are perfectly correct!

Remember in order to use the quadratic formula, you must get your equation into the form:

[tex]ax^{2} +bx +c=0[/tex]

Let's do it! Right now we have:

[tex]5x^{2} - x +1=3[/tex]

Get rid of the 3 by subtracting it from both sides:

[tex]5x^{2} -x+1 -3 = 3 - 3\\5x^{2} -x-2=0[/tex]

Okay! it looks like our quadratic form now! By comparing it we can figure out what a, b, and c are in this case:

[tex]a = 5,{ }\\ b = -1, { }\\c = -2[/tex]

Let's get out our quadratic formula now:

[tex]\frac{ -b\frac{+}{} \sqrt{b^{2} -4ac} }{2a}[/tex]

All that's left to do is insert values and solve! (Be really careful when dealing with the negatives):

[tex]\frac{ -1\frac{+}{} \sqrt{(-1)^{2} -4(5)(-2)} }{2(5)}[/tex]

[tex]=\frac{ -1\frac{+}{} \sqrt{41} }{10}[/tex]

Removing the plus/minus we get two answers:

[tex]=\frac{ -1+ \sqrt{41} }{10}\\\\or\\\\=\frac{ -1-\sqrt{41} }{10}[/tex]

These are the most simplified forms!  It turns out we didn't even have to worry about imaginary solutions because we didn't end up with a negative sign under the square root. Hope this helps, and good luck!

Technically, we don't have enough info so it could go either way.

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Explanation:

We can see that the sides are proportional to each other, but we don't know anything about the angles. We need to know if the angles are the same. If they are, then the hexagons are similar. If the angles are different, then the figures are not similar.

Right now we simply don't have enough info. So they could be similar, or they may not be. The best answer (in my opinion) is "not enough info". However, your teacher likely wants you to pick one side or the other. We can't pick "similar" so it's best to go with "not similar" until more info comes along the way.

Answer:

Adobe Family Tools

Step-by-step explanation:

Answer:

0.07

Step-by-step explanation:

To round a decimal to the nearest hundredth, look at the thousandths place.

If the number in the thousandths place is greater than or equal to 5, we will round up the hundredths place.

If it is smaller than 5, we will keep the number the same.

In the number 0.065, the thousandths place value is 0.005. So, we will round up the hundredths place.

The hundredths place value is 0.06, so we will round it up to 0.07.

So, 0.065 will round to 0.07.

Answer:

l=40

Step-by-step explanation:

The area is calculated as

A = wl

1200=30l

1200/30=l

40=l

Answer:

(10x5+15x3)-7

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

To find the slope given two points

m = ( y2-y1)/(x2-x1)

    = ( 8 - 2)/( -3 -3)

    = 6 / -6

    = -1

Answer:

f(4) = -4

Step-by-step explanation:

f(x) = 4x - 20

Let x= 4

f(4) = 4*4 - 20

Multiply first

     = 16 -20

Then subtract

    = -4

Answer:

-4

Step-by-step explanation:

Hope it helps

Answer:

79 inches

Step-by-step explanation:

2 m * 100cm/m * 1 in/2.54cm = 78.7401574803 in

rounded

79 inches

Answer:

4.47

Step-by-step explanation:

A squared + B squared = C squared

4*4=16 2*2=4  16+4=20  

the square root of 20 is 4.472135955, rounded to the nearest hundreth is 4.47

Step-by-step explanation:

We have a diameter and vertical angles so

231.

180+51=231

Answer:

231

Step-by-step explanation:

The measure of arc WX is 51

XZ is a straight angle so its arc measures 180 degrees

The measure of arc WYZ

WYZ= WX + XZ

        = 51 + 180

            231

Answer:

[tex]\frac{1}{3(x-2)}[/tex]

Step-by-step explanation:

Hi there!

We need to multiply the fractions:

[tex]\frac{x+3}{12x}[/tex]×[tex]\frac{4x}{x^{2}+x-6}[/tex]

Before we multiply, we can cancel out and factor the polynomials to make multiplying easier

First, we can factor x²+x-6

1 (in front of +x) is the sum of two numbers and -6 is the product of those numbers

Those numbers are -2 and 3

so when we factor, we get:

(x-2)(x+3)

here are the fractions so far:

[tex]\frac{x+3}{12x}[/tex]×[tex]\frac{4x}{(x+3)(x-2)}[/tex]

we can cancel out x+3 on both fractions

[tex]\frac{1}{12x}[/tex]×[tex]\frac{4x}{x-2}[/tex]

we can also cancel out 4x from both fractions

[tex]\frac{1}{3}[/tex]×[tex]\frac{1}{x-2}[/tex]

now multiply the fractions together

[tex]\frac{1}{3(x-2)}[/tex]

So the first option is your answer

Hope this helps! :)

Answer:

d = 67.5

e = 22.5

Step-by-step explanation:

d + e = 90

d = 3e

Therefore, we can simply divide 90 by 4, which gives us 22.5, and also tells us what e equals. Then, multiply that by 3 to get d.

Hope that this helps!

Answer:

a

Step-by-step explanation:

(-2)² + (+5)² = (-2)*(-2)  + 5 * 5

                   = 4 + 25

                   = +29

Given:

Different relations in the options.

To find:

The relation which is a function.

Solution:

A relation is a function if there exist unique output for each input value. In other words, there exist only one y-value for each x value.

In option A, [tex]y=0,1, 2, 3[/tex] for [tex]x=4[/tex]. So, this relation is not a function.

In option B, [tex]y=8, 10[/tex] for [tex]x=10[/tex]. So, this relation is not a function.

In option C, [tex]y=6, -2[/tex] for [tex]x=-2[/tex]. So, this relation is not a function.

In option D, all x-values are different. So, their exist unique output for each input value. It means this relation is a function.

Therefore, the correct option is D.

Answer:

It's [tex]3x^4+22x^3+31x^2-6[/tex]

Step-by-step explanation:

Area is L times width

LW=H

and the length is [tex]3x^2+4x-1[/tex] times the width [tex]x^2+6x+3[/tex]

basically you multiply yhem togetheer and combine like terms and voila

The answer is 3x^4 + 24x^2 - 6

explanation:

A = l × w

= (3x^2+4x-2)(x^2+6x+3)

=(3x × x) + (4x×6x) + (-2×3)

= 3x^2 + 24x^2 - 6

Answer:

x=10

Step-by-step explanation:

To solve for x, you need to draw an imaginary line connecting the right end of side x to the left side with length 15. This forms a triangle with side lengths 6 and 8, and hypotenuse x. Using the Pythagorean Theorem to solve for x, we get 6^2 + 8^2 = x^2, 36 + 64 = 100, [tex]\sqrt{100}[/tex] = 10.

Answer:

It's 10

Step-by-step explanation:

C^2=A^2+B^2blank

C=√(A^2+B^2)

If c is x and a and b are the side lengths the we can use Pythagoras's theorem to calculate the length of the line. A=6 B=8 and in the end when you calculate all that doohickey stuff you get x=10

Answer:

1-2i

Step-by-step explanation:

Divide: 5 + 2i by 3 + 4i.

Given data

5 + 2i by 3 + 4i.

We have the expression as

(5 + 2i)/(3 + 4i)

Rationalize the denominator

(5 + 2i)/(3 + 4i)* (3 -4i)/(3 -4i)

=(5*3-20i+6i-8i^2)/9-12i-12i+16i^2

=15-14i+8/9-16

=7-14i/-7

=1-2i

Answer:

2.4

6 divided by 2.5= 2.4

Step-by-step explanation:

Hope this is correct, if not feel free to let me know and I can fix it. I'm sorry in advance if it is incorrect.

Answer:

The answer is indeed 2.4:

Step-by-step explanation:

Answer:

[tex]f(x)\neq g(x)[/tex]

[tex]when ~x=3[/tex]

[tex]So, the ~third~ option~is ~your~ answer[/tex]

Answer:

A=4cm

ok to do this we do the formula

A=PiR^2

A=3.14*4^2

A=3.14*16

A=50.24

and the area of circle B is 4 times the area of a so

50.24*4=200.96

200.96=3.14*X^2

Since  r  is on the right side of the equation, switch the sides so it is on the left side of the equation. 3.14 ⋅ r 2 = 200.96  Divide each term by  3.14  and simplify.

r 2 = 64

r=8

CIRLCE A=50.24

CIRLCE B=8

Answer:

cone a is the correct answer

the third choice is the cirrect answer.

the cone with a 4.5 cm height and a 8cm diameter

hope this helps :)

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Explanation:

Use of a calculator will show that

2/3 = 0.6666...

where the 6's go on forever. Your teacher only wants 2 significant figures though. That means you'll round to the nearest hundredth to get 0.67

The 0 to the left of the decimal point is not a significant figure. The reason being is because we can rewrite 0.67 into 6.7*10^(-1); we can see the coefficient 6.7 having two sig figs.

Answer:

30 dólares es la ganancia neta.

Step-by-step explanation:

En la primera transacción, el hombre está perdiendo 50 dólares:

1. -50 dólares

En la segunda transacción, el hombre gana 70 dólares:

2. -50 + 70 = +20 dólares

En la tercera transacción pierde 80 dólares:

3. 20 - 80 dólares = -60 dólares

Y en la última transacción, la ganancia es de 90 dólares. Así, la ganancia neta es:

4. -60 dólares + 90 dólares =

Answer:

9/7 =a

Step-by-step explanation:

9 / -a + 15 = 8

Subtract 15 from each side

9 / -a + 15 -15 = 8-15

9 / -a = -7

Multiply each side by -a

9/-a * -a = -7 * -a

9 =7a

Divide each side by 7

9/7 = 7a/7

9/7 =a

Answer:

9 / 7 = a

Step-by-step explanation:

9 / - a + 15 = 8

Determined the defined range

9 / ( - a ) + 15 = 8 , a ≠ 0

subtract 15 from each side

9 / - a + 15 - 15 = 8 - 15

calculate the difference

9 / - a = - 7

multiply both side of equation by - a

9 / - a × - a = - 7 × - a

9 = 7 a

divide each side by of equation by 7

9 / 7 = 7 a / 7

9 / 7 = a

Both equations represent straight lines

The first line has slope of 2 and y-intercept at -3

The second line gas slope of 2 and y-interceot at +3

you may now try to plot these two lines on the paper

Answer: B: 1/8

Step-by-step explanation: the formula for volume of a cube is a^3, so I 1/2^3 = 1/8

your answer is B: 1/8