In the equation 6x-2 = -4x + 2, Spencer claims that the
first step is to add 4x to both sides. Jeremiah claims that
the first step is to subtract 6x from both sides. Who is
correct? Explain.

​

Answer:

[tex]\large\boxed{Q1.\ x>1}\\\boxed{Q2.\ x>1}\\\boxed{Q3.\ x\leq-3}[/tex]

Step-by-step explanation:

[tex]Q1.\\7x+3>10\qquad\text{subtract 3 from both sides}\\\\7x+3-3>10-3\\\\7x>7\qquad\text{divide both sides by 7}\\\\\dfrac{7x}{7}>\dfrac{7}{7}\\\\\boxed{x>1}\\\\Q2.\\-3+5x<7x-5\qquad\text{add 3 to both sides}\\\\-3+3+5x<7x-5+3\\\\5x<7x-2\qquad\text{subtract 7x from both sides}\\\\5x-7x<7x-7x-2\\\\-2x<-2\qquad\text{change the signs}\\\\2x>2\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}>\dfrac{2}{2}\\\\\boxed{x>1}[/tex]

[tex]Q3.\\-2x+5\geq3x+20\qquad\text{subtract 5 from both sides}\\\\-2x+5-5\geq3x+20-5\\\\-2x\geq3x+15\qquad\text{subtract 3x from both sides}\\\\-2x-3x\geq3x-3x+15\\\\-5x\geq15\qquad\text{change the signs}\\\\5x\leq-15\qquad\text{divide both sides by 5}\\\\\boxed{x\leq-3}[/tex]

x>1

x>1

X>-3

Step-by-step explanation:

Answer:

15 teams, 4 girls and 3 boys on each team.

Step-by-step explanation:

What's the greatest common multiple of 60 and 45?  It's 15.

This is the greatest number of teams that can be formed.

60/15 = 4; thus, there will be 4 girls on each team.

45/15 = 3; thus, 3 boys on each team

The greatest number of co-ed basketball teams that can be formed with an equal number of girls and boys is 3, with each team consisting of 4 girls and 3 boys.

To determine the greatest number of co-ed basketball teams that can enter the tournament with an equal number of girls and boys, you need to find the greatest common divisor (GCD) of the number of girls and boys. In this case, we have 60 girls and 45 boys. The GCD of 60 and 45 is 15, which means the largest number of teams that can be formed where each team has the same number of girls and boys is 15 (since 60 \/ 15 = 4 girls per team and 45 \/ 15 = 3 boys per team).

Answer 1: The greatest number of teams that can enter are 3 teams.

Answer 2: There would be 4 girls and 3 boys on each team.

Hey there!

Let's start by adding 5 to both sides. This eliminates the -5.  

1 = r/20

Now to solve for r we can multiply both sides by 20.

20 = r

Check

-4 = 20/20 - 5

-4 = 1 - 5

-4 = -4

Your answer is r = 20.

Hope this helps!

Answer:

Step-by-step explanation:

-4 = [tex]\frac{r}{20}[/tex] - 5

⇒ -4 + 5 = [tex]\frac{r}{20}[/tex]

⇒ 1 = [tex]\frac{r}{20}[/tex]

⇒ 1 × 20 = r

⇒ 20 = r

Answer:

(x-8)(x+3)

Step-by-step explanation:

Final answer:

To factor the quadratic expression x² - 5x - 24, we find the factors that multiply to -24 and add to -5, which are -8 and 3. Therefore, the factored form of the expression is (x - 8)(x + 3).

Explanation:

To factor the quadratic expression x² - 5x - 24 completely, we need to find two numbers that multiply to -24 (the constant term) and add to -5 (the coefficient of the x term). The numbers that fit this criteria are -8 and 3. So, our expression factors into:

(x - 8)(x + 3)

We can check our factoring by expanding these factors to see if we get the original expression:

(x - 8)(x + 3)
= x² + 3x - 8x - 24
= x² - 5x - 24

Thus, the original expression is correctly factored as (x - 8)(x + 3).

Answer:

Step-by-step explanation:

Plug x for y and y for x.

y = 2x^2 + 2

x = 2y^2 + 2

Then isolate the y variable.

x - 2 = 2y^2

sqrt(x - 2) = 2y

(sqrt(x - 2))/2 = y

• They're 180°

• Short, thin, or thick

• Could be curved, zig-zag, straight, bent etc.

• Perpendicular

A line is characterized by its length exceeding its width and the path it takes. Its qualities can express emotions and control the viewer's attention, with variations such as curved or angular, smooth or staccato, and different thicknesses. Lines play a crucial role in defining shapes and in expressive forms of writing such as calligraphy.

The characteristics of a line in design are defined by its length being greater than its width and by the paths it takes. A line is essentially a point in motion and is characterized by how it is used in art to determine motion, direction, and energy. When speaking of the qualities of a line, we refer to its character which can animate a surface. Lines can be curved or angular, and can progress smoothly or with a staccato rhythm, and they can be thick or thin, pale or bold.<\/p>

Lines have an emotional and expressive content that is understood both rationally and emotionally; they can control the viewer's attention and direction. Different types of lines like outline or contour line define shapes. Moreover, lines are integral to objects and writing symbols, where they denote meaning and can be expressive in themselves, illustrating their significance in calligraphy and other forms of art.<\/p>

Gestures are also related to lines, where a line produced by the artist's movement can be interpreted in various ways, like conveying calm with evenly drawn horizontal lines or rigidity with straight lines, which can be impactful depending on the context.<\/p>

Answer:

Vf = 118.365 m3

Step-by-step explanation:

Vcil = Pi*[(20)^2]*(100=

Vcil = 125.600 m3

Vesf = (4/3)*Pi*(12)^3

Vesf = 7235 m3

Then

Vf = Vci - Vesf

Vf = 125.600 - 7235

Vf = 118365 m3

Best regards

Answer:

what is her error?

Step-by-step explanation:

Answer:

Do you have a picture?

Answer:

8

Step-by-step explanation:

6 / .75(3/4)

The image would be (-1, 5)

Answer:

[tex]\large\boxed{y+3=\dfrac{3}{2}(x+4)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have

[tex]m=\dfrac{3}{2},\ (-4,\ -3)[/tex]

Substitute:

[tex]y-(-3)=\dfrac{3}{2}(x-(-4))\\\\y+3=\dfrac{3}{2}(x+4)[/tex]

Answer:

Step-by-step explanation:

include the striking deviation because it may explain an unusual occurrence is correct. Striking deviations or outliers can be useful in describing data set.

Explanation:

When looking at x on number lines, x is represented by the bold line. The x value can be anything on the bold line and therefore the line must respect the restrictions of x.

This question says -2 ≥ x which means "-2 is greater than or equal to x". Inversely, this also means that x is less than or equal to -2 because the original question can also be written as x ≤ -2. So, we are looking on the number line for the bold line that starts at -2 and continues to the left of -2, where the numbers that are less than -2 will be found.

The correct answer would be B.

Hope this helps!

Answer:

40 m

Step-by-step explanation:

A= b(h)

A= 8(5)

A= 40 m

Answer:

It is a parallelogram and the area is 40.

Step-by-step explanation:

The area of a parallelogram is a=bh.

The base is 8 and the height is 5. All you do is times 8 and 5 to get 40.

Answer:the answer is -7

Step-by-step explanation:

156=2b+5(-8-6b)

2b+5(-8-6b)

expand 2b+5(-8-6b) ---> -28b-40

-28b-40=156

add 40 to both sides

-28b-40+40=156+40

simplify

-28b=196

divide both sides by -28

(-28b/-28b) = (196/-28b)

simplify

b=-7

Answer:

4 possible outcomes

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]  

In this problem

The probability of choose a blue card is

[tex]x=7[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{7}{25}[/tex]

The probability of choose a green card is

[tex]x=4[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{4}{25}[/tex]

The probability of choose a red card is

[tex]x=6[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{6}{25}[/tex]

The probability of choose a yellow card is

[tex]x=8[/tex]

[tex]y=7+4+6+8=25[/tex]

substitute

[tex]P=\frac{8}{25}[/tex]

The sum of the probabilities of the 4 possible outcomes  is equal to

[tex]\frac{7}{25}+\frac{4}{25}+\frac{6}{25}+\frac{8}{25}=\frac{25}{25}[/tex] ----> represent the 100%

Answer:

Step-by-step explanation:

55-20 is less than or equal to (d)

i think...

Answer:

The solution would be d ≥ 75

Step-by-step explanation:

To find this we know that we have at least 55, which can be modeled as:

d ≥ 55

And then we need to add 20

d ≥ 55 + 20

d ≥ 75

Answer:

60 / 120 is terminating, the rest are repeating.

Answer:

56/72 is repeating, 21/22 is repeating, 11/121 is repeating, and 60/120 is terminating

Step-by-step explanation:

When repetition is allowed, there can be 64 different 3-letter words made from the letters 'FGHI'. When repetition is not allowed, there can be 24 different 3-letter words made from those letters.

In this question, we are asked to find the number of 3-letter words that can be made from the letters 'FGHI' with and without repetition. When repetition is allowed, each letter can be chosen independently for each position, so we have 4 choices for each position. Therefore, the total number of words is 4*4*4 = 64. When repetition is not allowed, each letter can only be used once, so we have 4 choices for the first position, then 3 choices for the second position, and finally 2 choices for the third position. Therefore, the total number of words is 4*3*2 = 24.

https://brainly.com/question/29594564

#SPJ12

Answer:

2. y = 25 km

Step-by-step explanation:

To find the dimensions, write a proportion. A proportion is an equation of ratios.

[tex]\frac{scale}{factor} = \frac{Actual}{Model}[/tex]

Then solve for the unknown value by cross multiplying.

2. [tex]\frac{2}{5} = \frac{10}{y}[/tex]

2y = 5*10

2y = 50

y = 25

Answer:

yes

Step-by-step explanation:

sum:

• `x+y=6`

• `y=6-x`

Difference:

• `y-x=6`

• `y=x+6`

Answer:

yes 12-6 has a difference of 6 and a sum of 6

Step-by-step explanation:

Answer:

[tex]\large\boxed{y=3(x-2)^2-8}[/tex]

Step-by-step explanation:

The vertex form of an equation of a parabola y = ax² + bx + c:

[tex]f(x)=a(x-h)^2+k[/tex]

(h, k) - vertex

[tex]h=\dfrac{-b}{2a},\ k=f(h)[/tex]

We have the equation:

[tex]y=3x^2-12x+4\\\\a=3,\ b=-12,\ c=4[/tex]

Substitute:

[tex]h=\dfrac{-(-12)}{2(3)}=\dfrac{12}{6}=2\\\\k=f(2)=3(2^2)-12(2)+4=3(4)-24+4=12-24+4=-8[/tex]

Finally:

[tex]y=3(x-2)^2+(-8)=3(x-2)^2-8[/tex]

Answer:7/8

Step-by-step explanation:

7 divided by 8 = 7/8

if you split that with 8 people, you multiply 7/8 and 8, and you'll get 7, which is the number of soup cans you started with.

Answer:

Pi is not a terminating decimal

Step-by-step explanation:

1234567890

Answer:

Yes!

Step-by-step explanation:

3.14 ends and it does not repeat. Otherwise it would be a repeating decimal.

Answer:

24 and 144

Step-by-step explanation:

a = 4

t4 = 864

864 = 4*r^(4 - 1) divide by 4

216 = r^3            Take the cube root of 216

6 = r

Note you can find the cube root of any number by using your calculator.

t2 = a * r^(2 - 1)

t2 = 4 * 6^1

t2 = 24

=================

t3 = a*r^(3 -1)

t3 = 4 * 6^2

t3 = 4 * 36

t3 = 144

Answer

24 and 144

Answer:   [tex]\bold{\dfrac{-2\pm \sqrt{22}}{3}}[/tex]

Step-by-step explanation:

[tex]3x^2+4x-6=0\quad \rightarrow \quad a=3,\ b=4,\ c=-6\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(4)\pm \sqrt{(4)^2-4(3)(-6)}}{2(3)}\\\\\\.\ =\dfrac{-4\pm \sqrt{16+72}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm \sqrt{88}}{2(3)}\\\\\\\\.\ =\dfrac{-4\pm 2\sqrt{22}}{2(3)}\\\\\\\\.\ =\dfrac{-2\pm \sqrt{22}}{3}[/tex]

a. Angles ABC and CBD are supplementary, so you know that [tex]m\angle ABC=180^\circ-24^\circ=156^\circ[/tex]

The interior angles of any triangle sum to 180 degrees in measure, so that [tex]m\angle ACB=180^\circ-156^\circ-16^\circ=8^\circ[/tex].

By the law of sines, we then have

[tex]\dfrac{\sin8^\circ}{7600\,\mathrm{ft}}=\dfrac{\sin16^\circ}{BC}\implies BC=\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}[/tex]

b. In triangle BCD, we have

[tex]\sin24^\circ=\dfrac{CD}{BC}[/tex]

and so

[tex]CD=\sin24^\circ\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin8^\circ}\approx6122\,\mathrm{ft}[/tex]

Answer:

116 cm²

Step-by-step explanation:

The area of a circle = πr² ← r is the radius

shaded area = external area - internal area

                      = π × 6.5² - π × 2.3²

                      = π( 42.25 - 5.29)

                      = π × 36.96 ≈ 116 cm²

Answer:

Step-by-step explanation:

Area of a circle = πr²

Shaded area = External area - Internal area

                      = π × 6.5² - π × 2.3²

                      = π × (42.25 - 5.29)

                      = π × 36.96 = 116.113 cm²

Answer:

Step-by-step explanation:

AThe shortest column of the line plot

BThe shortest bar of the bar graph

CThe column farthest to the left on the line plot

DThe average bar height of the bar graph

Answer:

The shortest column of the line plot