4. Nine fruit juice bottles contain 4 1/2 litres of fruit juice between them.
How much juice do five bottles hold?
[tex]4 \frac{1}{2} litres[/tex]
​

Answer:

Step-by-step explanation:

The best way to do this is to first remove the parenthesis by distributing the negative into them. Then we will group the like terms together, moving their respective signs with them, then we will simplify.  For the first one, after distributing the negative into the parenthesis (remember that a negative in front of a set of parenthesis containing a polynomial changes the signs in front of each term within the polynomial; negatives become positives and positives become negatives):

[tex]3x^2-6x+11-10x^2+4x-6[/tex] and then grouping like terms next to each other:

[tex]3x^2-10x^2-6x+4x+11-6[/tex] (this step is not completely necessary; I just encourage new learners to do it so as to not miss any of the like terms)

The above then simplifies to

[tex]-7x^2-2x+5[/tex]

The next one, after distributing the negative into the parenthesis:

[tex]-3x^2-5x-3+10x^2+7x-2[/tex] and then grouping like terms next to each other (remember to move their signs with them!):

[tex]-3x^2+10x^2-5x+7x-3-2[/tex] which simplifies to

[tex]7x^2+2x-5[/tex]

Now for the last one:

[tex]12x^2+6x-5-5x^2-8x+12[/tex] and

[tex]12x^2-5x^2+6x-8x-5+12[/tex] which simplifies to

[tex]7x^2-2x+7[/tex]

Answer:

y = 8.5x

Step-by-step explanation:

A proportional relation in one in which change of value of y with respect to change of value of x remains proportional. It can be represented by equation

y = kx, where k is constant of proportionality

________________________________________________

Let  the  relation be

y = kx

but we have a as 3 and b as 25.5

thus

substituting value of and a and b in y = kx , we have

25.5 = k*3

=> k = 25.5/3 = 8.5

Thus, equation which can represent this relation is y = 8.5x

Answer:

Angles that sum up to 90° are called complementary angles. For example if there are two angles with measures 40° and 50° they are know to be complementary cuz they sum up to 90.

All the very best for your math exam by the way :)

Answer:

$2000

Step-by-step explanation:

3,000,000/1500=$2000

Answer:

Step 2.

-11/12 > -1.5

1.6 > 5/4

1 < 5/4

Step-by-step explanation:

Eval should have swapped the numerator and denominator of 4/9 when she replaced division by multiplication.

Answer:

(x - 7)(x - 2)

----------------- = x - 2 for x ≠ 7    

     x - 7

Step-by-step explanation:

Please use parentheses to show clearly that you are dividing by (x - 7):

 x^2 - 9x - 14

-------------------       or    (x^2 - 9x - 14) ÷ (x - 7)

       x - 7

x^2 - 9x + 14 factors into (x - 7)(x + 2).  After rewriting x^2 - 9x + 14 in factored form, the task of division becomes simpler:

(x - 7)(x - 2)

----------------- = x - 2 for x ≠ 7    

     x - 7

Answer:

Approximately 7.2 kilometers

Step-by-step explanation:

4.5(miles walked)*1.6(kilometers in mile)=7.2(kilometers in 4.5 miles)

Answer:

7.2 kilometres

Step-by-step explanation:

4.5 * 1.6

Answer:

x = 2

y = 4

or (2 , 4)

Step-by-step explanation:

Since both equations are equal to y we can substitute one of the equations to fill in the spot of y so that both equations are equal to each other with no y variable.

[tex]3x-2 = x+2\\[/tex]

Now we can solve x.

[tex]3x= x+4\\[/tex]

[tex]2x = 4\\[/tex]

x = 2

Now that we have solved for one variable we can plug this back into either equation and solve for y.

[tex]y = 2 + 2\\[/tex]

y = 4

Answer:

shawty a lil baddie

Step-by-step explanation:

i like ur mom bro

The percentage of salad bars offered to customers in 1998 is; 70%.

The percentage refers to the value of a variable contained in a whole number.

The percentage is the ratio that a variable is contained in another.

Percentages, which are over 100, are depicted using the percentage sign (%).

Data and Calculations:

We are Given that Of the markets in a certain city, 7/10 offered customers a salad bar in 1998 .

7/10 salad bars were offered to customers,

The conversion to percentage = 70% (7/10 x 100)

Thus, the percentage of salad bars offered to customers in 1998 would be equal to 70%.

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Answer:

2

Step-by-step explanation:

50 and 112 are significantly different from the other data

Answer:

See Explanation

Step-by-step explanation:

The answers are in the attachment already; I guess you need an explanation.

For the first answer

- The bars of Paris, Oslo and Munich are not properly drawn.

This is so because distance between the bats of a bar chart is expected to be the same between all bars.

From the attachment above, it doesn't look so because the bats of these three cities are out of position.

In other words, the vertical lines of the bars must align with the vertical lines of the grid in the graph.

- The Temperature in the y axis doesn't start with 0

When plotting a graph, the origin must be 0 but in the attachment above, Joan used an origin of 2, which is totally incorrect.

- In Munich, the bar graph for x axis is taken more than 1 unit.

The bars of the bar graph should maintain a constant width but from the attachment above, the width of the bar is wider than the width of other bars

Step-by-step explanation:

This question gives us a point on a line and the slope of that line. So, the easiest way to answer this question is to use point-slope form, which is written as:

y-y₁ = m(x-x₁)

So, first of all, we are trying to find y (y, not y₁ which is the y-coordinate of the point we were given). We can go ahead and add y₁ to both sides to get:

y = m(x-x₁) + y₁

We can now simplify the equation to:

y = m·x - m·x₁ + y₁

Now we just input the given information.

m = 5 (slope)

x = 21

x₁ = 5

y₁ = 6

Now we have all the information we need and we can solve.

y = 5·21 - 5·5 + 6

y = 105 - 25 + 6

y = 86

So y, when x = 21, is equal to 86.

Answer:

256

Step-by-step explanation:

Assuming that the length of his garage is the longer dimension (16), the area of the square yard must be 16*16=256 square units. Hope this helps!

Steps to solve:

5x^3 * 2x^2

~Apply exponent rule

5x^3+2 * 2x

~Simplify

5x^5 * 2x

~Combine like terms

10x^5

Best of Luck!

Answer:

Option (3)

Step-by-step explanation:

PB is a tangent and PV, PU are the secants drawn to the circle.

[tex]m(\widehat {VB})[/tex] = 60° and [tex]m(\widehat{BS})[/tex] = 30°

By theorem of tangent and secants,

"When a tangent and secant are drawn from a point outside the circle, then the measure of the angle formed is one half the difference of intercepted arcs."

m∠BPV = [tex]\frac{1}{2}[m(\widehat{BV}-m(\widehat{BS})][/tex]

    m∠3 = [tex]\frac{1}{2}[60-30][/tex]

    m∠3 = 15°

Therefore, Option (3) will be the answer.

Answer:

Step-by-step explanation:

Translation: You move the shape by moving the points on the shape by the number, it changes the location of the shape.

Reflection: There is a line of reflection and the shape will be reflected by that, like a mirror, so it will be the same shape, same size.

Rotation: There is a point of rotation and the shape will just move around that point and will change the positioning if the shape. Always has coordinates

Answer:

C

Step-by-step explanation:

Both A and B are true identities.

See attachment.

Answer:

Hope this helps.

Step-by-step explanation:

So for ASA, the two triangles have to have two angles congruent, and in the middle of those angles, they have to have a line that's congruent.

For SAS, the two triangles have to have two lines congruent, and in the middle of those lines, they have to have an angle that's congruent.

For AAS, the two triangles have to have two angles congruent, but the line that's congruent has to be on the side, not in the middle.

The length of AC will be equal to 20 units for the given line.

Distance is defined as the length between the two points here we have a line AC divided into two parts having a length of AB = 4 and BC is 16.

The length of the line AC will be calculated as:-

AC  =  AB  +  BC

Ac   =  4  +  16

AC  =  20 units.

Therefore the length of AC will be equal to 20 units for the given line.

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Answer:

hdhufhduh

Step-by-step explanation:

Answer:

112

Step-by-step explanation:

find LCM

4,7,8,16=112

Answer:

y = 3x

where y is the plant height in cm and x is the time in months

at 12 months, height would be 36 cm

Step-by-step explanation:

Here, we want to model the data

let’s call the months x and the height y

What do you notice?

we can clearly see that the height is always 3 times the month

3 * 3 = 9

5 * 3 = 15

7 * 3 = 21

9 * 3 = 27

so we can say that;

Time in months * 3 = Plant height in cm

using the x and y notation;

x * 3 = y

or simply y = 3x

Now the height at 12 months can be calculated by substituting the value of x for 12

y = 3 * 12 = 36 cm

Answer:

1) Yes

Product of Means = Product of Extremes

4 × 21 = 7 × 12

84 = 84

2) No

Product of Means = Product of Extremes

2 × 2 = 3 × 3

4 ≠ 9

3) No

Cross multiplying

3 × 6 = 4 × 8

18 ≠ 32

4) Yes

Cross Multiplying

1 × 25 = 5 × 5

25 = 25

Answer:

Step-by-step explanation:

1) 4 : 7   ? 12 : 21

If product of mean is equal to product of extremes, then they are proportion

Product of extremes = 4*21  = 84

Product of mean = 7 * 12 = 84

Product of extremes = Product of mean

They are in proportion

4 : 7 :: 12 : 21

2) 2 : 3 ? 3: 2

Product of extremes = 2*2 = 4

Product of mean = 3*3 = 9

Product of extremes ≠ Product of mean

They are not in proportion

2 : 3 ≠ 3 : 2

3) 3/4 ?  8/6

3 : 4 ?  8:6

Product of extremes = 3 * 6   = 18

Product of mean = 4 * 8 = 24

Product of extremes ≠ Product of mean

They are not in proportion

3 : 4 ≠ 8 : 6

4) 1/5  ? 5/25

1:5  ? 5 : 25

Product of extremes = 1 * 25 = 25

Product of mean = 5 * 5 = 25

Product of extremes = Product of mean

They are in proportion

1 : 5  :: 5 : 25

Answer: [tex]f^{-1}(x)=\frac{x}{7}+\frac{1}{14}[/tex]

Step-by-step explanation:

If we have y=7x-1/2, the inverse is where we solve for x instead of y.

We can isolate x to get 7x=y+1/2, then divide by 7 to get x=y/7+1/14.

Therefore, [tex]f^{-1}(x)=\frac{x}{7}+\frac{1}{14}[/tex].

Hope that helped,

-sirswagger21

Answer:

X=1550-10y

Step-by-step explanation:

X+10y=1550

Subtract 10y from each side

X+10y- 10y=1550-10y

X=1550-10y

Answer:

[tex]x = 1550 - 10y[/tex]

Step-by-step explanation:

[tex]x + 10y = 1550 \\ x + 10y - 10y = 1550 - 10y \\ x = 1550 - 10y[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

i) 2x² + 4x + 7x + 14

= 2x² + 11x + 14

ii) 2x² - 5x - 12x + 30

= 2x² - 17x + 30

Answer:

1.13 cm

Step-by-step explanation:

V=1/3 * pi*r^2*h

h=12 cm (assuming, since that's what you gave)

V=16

r=1.13 cm

Answer:

(0,7)

Step-by-step explanation:

This is in the form

y = mx+b where m is the slope and b is the y intercept

y = -5x +7

The slope is -5 and the y intercept is 7

(0,7)

Answer:

(0,7)

Step-by-step explanation:

y=mx+b

y=-5x+7

so y intercept is (0,7)

Answer:

y = 1/2x - 1

Step-by-step explanation:

The easiest was you do this is to first rearrange the equation into slope-intercept form (y = mx + b).  After rearranging, you can find the slope (m).

2x + y = -5

y = -2x - 5

The slope is -2.  Since the line we are trying to find is perpendicular, find the inverse and multiply it by -1.

-2  =>  1/2

Now use the point-intercept form to find the new equation.  Use the slope (1/2) and the given point (-1, -2).

y - y₁ = m(x - x₁)

y - (-2) = 1/2(x - (-2))

y + 2 = 1/2(x + 2)

y + 2 = 1/2x + 1

y = 1/2x - 1

The equation of the line perpendicular to line WX is  y = 1/2x - 1.

The equation is y = (1/2)x -(3/2) ; y = one half x − three halves.

The correct option is D.

What is the equation of a Straight Line?

An equation of the straight line is given by y = mx+c,

Here m is the slope and c is the intercept on y-axis.

The equation of the line WX is 2x+y = -5

y = -2x -5

The product of the slopes of the line and the line perpendicular to this line will be -1

Therefore the slope of the line perpendicular to the line WX is -2 * m = -1,

m = 1/2

y = (1/2)x +c

The line passes through the points (-1, -2)

-2 = (1/2) (-1) +c

c = -2 +(1/2)

c = (-4 +1) /2

c = -3/2

Therefore, the equation is y = (1/2)x -(3/2) ; y = one half x − three halves.

The correct option is D.

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constant it will keep going up and it won't stop

In the graph, the line is increasing from left to right. Therefore, option A is the correct answer.

We need to check whether the given graph is increasing, decreasing, or constant.

Increasing: A function is increasing, if as x increases (reading from left to right), y also increases. In plain English, as you look at the graph, from left to right, the graph goes uphill. The graph has a positive slope.

From the given graph we can see that the line is increasing from left to right.

In the graph, the line is increasing from left to right. Therefore, option A is the correct answer.

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