(From Unit 4 Lesson 1)
5. A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
a. Find a mixture that will make the same shade of green but a smaller amount.
b. Find a mixture that will make the same shade of green but a larger amount.
Findami

Answer:

A.) -9

Step-by-step explanation:

it is observed that triangles ABL and KML are similar triangles

hence the following ratios are valid:

LA / LK = LB/LM = AB/KM

we can see that LA/LK = LB/LM = 1/2

hence the above ratio becomes

1/2 = AB/KM  (rearranging)

KM = 2AB

We are given that KM = (x + 21) and AB = (x + 15)

hence

KM = 2AB

(x + 21) = 2 (x + 15)

x + 21 = 2x + 30

x - 2x = 30 - 21

-x = 9

x = -9

Answer:

-7/6x+y=5

Step-by-step explanation:

y=7/6x+5

y-7/6x=5

-7/6x+y=5

Answer:

Length of new radius 4 cm.

Step-by-step explanation:

Given radius of circle = 16 cm

Circle is dilated with scale factor 1/4

We need to find the new radius

To calculate New radius we need  to multiply radius of the circle with the dilated factor.

Hence new radius = [tex]16 \times \frac{1}{4}= 4\cm[/tex]

Hence Length of new radius is 4 cm.  

Answer:

1. Collinear

2. Parallel

3. Oblique

Step-by-step explanation:

1. The system of linear two variable equations are  

3x - 2y = 2 ........... (1) and  

6x - 4y = 4, ⇒ 3x - 2y = 2 ........... (2) {Dividing both sides with 2}

So, equations (1) and (2) are identical.  

Therefore, the lines are collinear. (Answer)

2. The system of linear two variable equations are  

4x - 3y = 12  

⇒ 3y = 4 x - 12

⇒ [tex]y = \frac{4}{3} x - 4[/tex] {In slope-intercept form} ......... (3)

And, - 12x + 9y = 10

⇒ 9y = 12x + 10

⇒ [tex]y = \frac{4}{3} x + \frac{10}{9}[/tex] {In slope-intercept form} .......... (4)

Since, equation (3) and (4) has the same slope, so, they are parallel. (Answer)

3. The system of linear two variable equations are  

3x + 2y = 19

⇒ [tex]y = - \frac{3}{2} x + \frac{19}{2}[/tex] ........... (5)

And, 4x - 5y = 10

⇒ [tex]y = \frac{4}{5}x - 2[/tex] ........ (6)

So, from the equations (5) and (6) we can say that the straight lines are oblique (intersecting). (Answer)

Answer:

first 10 of 5

5 10 15 20 25 30 35 40 45 50

First 10 of 6

6 12 18 24 30 36 42 48 54 60

Step-by-step explanation:

Just add 5 to 5 and that is your next multiple then keep going 10 time and same thing for 6.

Answer:

-29/6

Step-by-step explanation:

1 1/6=7/6

-3 2/3=-11/3

-11/3-7/6

-22/6-7/6=-29/6

Answer:

$290.25

Step-by-step explanation:

32.25 x 9 = 290.25

Answer:

$290.25

Step-by-step explanation:

You just need to multiply the money and the days together to get your answer

$32.26 times 9 days

Answer:

[tex]slope =\frac{5}{4}[/tex]

Step-by-step explanation:

A(0,-1)  B(5,3) is missing in the question

The points for A  and B are missing. A(0,-1)  B(5,3)

To find the slope of line AB using the formula

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

A(0,-1) is (x1,y1)

B(5,3) is (x2,y2). plug in the values in the formula

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

[tex]slope =\frac{5-0}{3+1}[/tex]

[tex]slope =\frac{5}{4}[/tex]

To calculate the slope of line CD, you need two points on the line. The slope is the 'rise over run' between these points, calculated with the formula (y2 - y1) / (x2 - x1), but coordinates for line CD were not provided.

To determine the slope of line CD, you need two points on line CD. The slope is found by calculating the rise over run between two points on the line. According to the information provided, we can use the general process for calculating slope which entails subtracting the y-coordinate of the starting point from the y-coordinate of the ending point (change in y), and dividing that by the subtraction of the x-coordinate of the starting point from the x-coordinate of the ending point (change in x). If we had the actual coordinates for line CD, the formula would look like this:

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

However, specific coordinates for line CD are not provided in the question. To accurately calculate the slope, you would need to refer to the graph or data given for line CD and choose two distinct points to use in the slope formula.

Answer:

It is not a right triangle.

Step-by-step explanation:

We can prove this by Pythagorean theorem because it represents to a right triangle.

Pythagorean theorem:

a² + b² = c²

Now substitute the values.

Note: the longest side will represent c

So,

a = 10 m

b = 16 m

c = 20 m

10² + 16² = 20²

The objective here is to make them equal.

100 + 256 = 400

356 ≠ 400

They are not equal so it is not considered a right triangle.

By applying the Pythagorean theorem to the triangle with side lengths of 10 metres,16 metres, and 20 metres, we can verify that it is a right-angled triangle due to the equality 10² + 16² = 20².

In Mathematics, specifically in Geometry, we can determine if a triangle is a right triangle using the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This formula is expressed as a² + b² = c² where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Applying the Pythagorean theorem to the triangle with side lengths of 10 metres,16 metres, and 20 metres, we set 20 metres (the largest measurement) as c (the hypotenuse) and the other two measurements as a and b. Thus, the equation becomes 10² + 16² = 20². After calculating, we find that 100 + 256 does indeed equal 400. Because these values are equal, the triangle is a right angled triangle.

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Answer:

y=-5x-36

Step-by-step explanation:

-66-(-61)= -5

6-5= 1

-5/1= -5

Y=-5x + B

-66= -5(6) + B

-66= -30 + B

-66 + 30 = (-30 +30) + B

-36 = B

Y= -5x-36

Answer:

The second option

Step-by-step explanation:

The second option because it is the one in which if you multiply f4 to the values of x, you would get y.

And that is why it is the second option.

Answer:

81 and -31

Step-by-step explanation:

x + (x - 112) = 50

2x - 112 = 50

2x = 162

x = 81

the other number is x-112 = 81 - 112 = -31

Final answer:

To find the two numbers, set up a system of equations based on the given information. Solve the system of equations to find the values of the two numbers, which are -31 and 81.

Explanation:

To find the two numbers, we can set up a system of equations based on the given information.

Let's assume one number is x, and the other number is y.

According to the problem, the sum of the two numbers is 50, so we can write the equation:

x + y = 50

We are also told that one number is 112 less than the other, so we can write another equation:

x = y - 112

Now we can solve this system of equations to find the values of x and y.

Substituting the value of x from the second equation into the first equation, we have:

(y - 112) + y = 50

Combining like terms, we get: 2y - 112 = 50

Adding 112 to both sides of the equation, we have: 2y = 162

Dividing both sides by 2, we get: y = 81

Substituting this value of y into the second equation, we have: x = 81 - 112

Simplifying, we get: x = -31

Therefore, the two numbers are -31 and 81.

Answer:

5,470,000

do the multiplication first and then add

When adding numbers in scientific notation, align the exponents and then add the coefficients. The sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.

To add these two numbers in scientific notation, we need to first align the exponents. In this case, we can rewrite the first number as 0.12 x 10^6 and the second number as 5.35 x 10^6. Now, we can add the numbers together:

0.12 x 10^6 + 5.35 x 10^6 = 5.47 x 10^6. Thus, the sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.

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Essentially, the slope that is parallel to the pair is the the slope of the pair of points.

Using the formula [tex]\frac{y_1-y_2}{x_1-x_2}[/tex], the answer is [tex]\frac{-2}{-12}=\frac{1}{6}[/tex]

Answer:

37 : 46

Step-by-step explanation:

I nickel is equivalent to 0.05 dollars.

So, 37 nickels are equivalent to (0.05 × 37) = 1.85 dollars.

Again, we can write 1 dime is equal to 0.1 dollars.

So, 23 dimes are equivalent to (23 × 0.1) = 2.3 dollars.

Therefore, to compare 37 nickels to 23 dimes as a ratio reduced to lowest term will be 1.85 : 2.3 = 185 : 230 = 37 : 46 (Answer)

Final answer:

To write the comparison of 37 nickels to 23 dimes as a ratio in lowest terms, you convert the value of nickels and dimes to cents and simplify the ratio value-wise, resulting in a simplified ratio of 37:46.

Explanation:

The student is asking to express the comparison of 37 nickels to 23 dimes as a ratio reduced to lowest terms. Since both nickels and dimes are types of coins, it helps to understand that their value does not directly translate to a quantity ratio but rather a value ratio. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, the value ratio of nickels to dimes is 5 cents per nickel to 10 cents per dime.

To find the simplified ratio, we can represent the comparison of the value of 37 nickels to 23 dimes as:

This ratio can be reduced by dividing both terms by the greatest common divisor of 185 and 230, which is 5:

So, the simplified ratio is 37:46.

1. Positive but not perfect: Figure 4

2. Correlation coefficient equal to 1:

3. Strongest linear relationship: Figure 2

Step-by-step explanation:

"Correlation is the link between two quantities"

The relationship is said to be positive if both are increasing and said to be negative if both are opposite i.e. one is increasing and one is decreasing.

In the Given figures

1. Positive but not perfect linear relationship:

The perfect positive relationship is when both the quantities are increasing and the scatter points are in a line that grows linearly. Here, The data set in figure 4  has positive correlation but as the points are scattered around a line so the correlation is positive but not perfect.

2. Correlation equal to 1

The correlation in figure 1 is the perfect correlation as the data points follow a straight line and both the quantities are increasing.

3. Strongest linear relationship:

The relationship in figure 2 has the strongest in figure 2 as the data points are more close to the best fit line

Keywords: Correlation, Scatter Plot

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Answer:x=1

Step-by-step explanation:

fist add like- terms in either side of the equation:

4x=2x+2.

next, you want to get both the X's on the same side of the equation. this means you need to subtract 2x from the left side of the equation and bring it to the right side of the equation. this means you have to subtract 2x from 4x. because what you do on one side of the equation you have to do on the other.

2x=2

next divide each side of the equation to get x alone.

x=1.

Answer:

The graph will show what the line is.

Step-by-step explanation:

y-3 = -5/6(x+3)

Distribute first:

y-3= -5/6x - 15/6

-15/6 is negative because when disributing, -5/6, the negative sign will follow it.

Single out the y:

this means to make the y alone! by doing this, just add 3 to the other side

y-3= -5/6x - 15/6

+3             +3

______________

y= -5/6x + 3/6

Simplify:

y= -5/6 +1/2

-> 3/6 can be simplified to 1/2

Find the Y-intercept on the graph

1/2 on the graph is between 0 and 1

Graph the slope:

from the Y-intercept, go down 5 units, and to the right 6 units.

Then you have your graph!

Answer:

C = 6500 + 225n

Step-by-step explanation:

It will cost $6500 to rent a truck plus $225 for each ton of sugar transported.

So, in the equation which relates the total cost for transporting sugar in a truck, $6500 will be the initial value and $225 will be the rate of transporting sugar per ton.

Hence, for transporting n tons of sugar, the total cost C in dollars is given by the following equation  

C = 6500 + 225n (Answer)

Answer:

It's C and D

Step-by-step explanation:

The points on the graph in which this was occurring is between points C and D.

This refers to the representation of data on an x-y plane showing the various cardinal points.

Hence, based on the fact that Carol's car is punctured by a nail and she had to drive slowly and then let off all the air in the tire, these actions most likely occurred between points C and D based on the fact that there is a change in speed.

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Answer:

The final answer is 4∛7 cm.

Step-by-step explanation:

Given:

Volume of cube is 448 cm³.

Now, to find the length side(a) of cube.

Putting the formula of volume(v) of cube to get the side:

[tex]V = a^{3}[/tex]

[tex]448= a^{3}[/tex]

[tex]\sqrt[3]{448} = a[/tex]

[tex]4\times 4\times 4\times 7 = a[/tex]

[tex]4\sqrt[3]{7} = a[/tex]

The length side of a cube = 4∛7 cm.

Therefore, the final answer is 4∛7 cm.

Answer:The greater value is 600 x 10⁻⁸. And the lesser value is 2 x 10⁻⁸. The number 600 x 10⁻⁸ is 300 times greater number 2 x 10⁻⁸.

Step-by-step explanation:⇒ 6 x 10⁻⁶ and 2 x 10⁻⁸⇒ 600 x 10⁻⁸ and 2 x 10⁻⁸The number  600 x 10⁻⁸ times greater than the number 2 x 10⁻⁸ will be ⇒ 600 x 10⁻⁸ / 2 x 10⁻⁸⇒ 300

Final answer:

The circumference of Saturn is not greater than that of Earth; Earth's circumference is greater. Saturn's circumference at 40,100 km is approximately 0.11 times that of Earth. Also, 0.037854921 rounded to the nearest hundredth is 0.04, and 6 x 10⁻⁶ is larger than 2 x 10⁻⁸.

Explanation:

To answer how many times greater the circumference of Saturn is than the circumference of Earth, we need to compare the two given circumferences. The circumference of Earth is 365,882 km, and the circumference of Saturn is given as 4.01 x 10⁴ km.

First, we convert Saturn's circumference to a standard numerical form: 4.01 x 10⁴ is 40,100 km. Now, we can divide the circumference of Saturn by the circumference of Earth: 40,100 km / 365,882 km which roughly equals 0.11. This means that Saturn's circumference is about 0.11 times the circumference of Earth, which indicates that Earth's circumference is actually greater, not Saturn's.

For the second part, estimating 0.037854921 to the nearest hundredth would result in 0.04 because the third digit after the decimal is 7, which rounds the second digit up to 4.

Comparing the numbers 6 x 10⁻⁶ and 2 x 10⁻⁸, 6 x 10⁻⁶ is larger because it is only 10⁻⁶ compared to 2 x 10⁻⁸ which is much smaller being 10⁻⁸.

Answer:

Part 1: Less.

Part 2: Greater.

Part 3: Greater.

Part 4: Less.

Part 5: Equal.

Step-by-step explanation:

Part 1: Assume that the value is x initially.

So, 55% decrease of value of x will give [tex]x(1 - \frac{55}{100}) = 0.45x[/tex].

Again, 25% increase of the value obtained will give [tex]0.45x(1 + \frac{25}{100}) = 0.45 \times 1.25 \times x = 0.5625x[/tex]

So, it is less than x. (Answer)

Part 2: Assume that the value is x initially.

So, 75% increase followed by [tex]33\dfrac{1}{3}  = 33.33[/tex]% decrease will give [tex]x \times (1 + 0.75) \times (1 - 0.333) = x \times 1.75 \times 0.667 = 1.167x[/tex]

So, it is greater than x.

Part 3: Assume that the value is x initially.

So, 20% decrease followed by 40% increase will give [tex]x \times (1 - 0.2) \times (1 + 0.4) = x \times 0.8 \times 1.4 = 1.12x[/tex]

So, it is greater than x.

Part 4: Assume that the value is x initially.

So, 30% increase followed by 30% decrease will give [tex]x \times (1 + 0.3) \times (1 - 0.3) = x \times 1.3 \times 0.7 = 0.91x[/tex]

Hence, it is less than x.

Part 5: Assume that the value is x initially.

So, 100% increase followed by 50% decrease will give [tex]x\times (1 + 1) \times (1 - 0.5) =x \times 2 \times 0.5 = x[/tex]

Hence, the final value is same as x. (Answer)

Answer:

the pictures uppppppppp

Answer:

1)121.5 sq.yards

2)157.92 m²

3)5.434 ft²

4)147.4513 cm²

5)147 cm²

6)56 in²

Step-by-step explanation:

1) Area of shaded region= Area of rectangle-Area of triangle

Area of rectangle= Length*Breadth=18*9 sq.yards=162 sq.yards(length=18 yards and breadth=9 yards)

Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]=[tex]\frac{1}{2}*9*9[/tex]=40.5 sq.yards(base=9 yards and height= 9 yards)

Therefore,Area of shaded region=162-40.5=121.5 sq.yards

2) In the following figure,

Length of rectangle, l= 21 m

breadth of rectangle, b= 15 m

Radius of circles, r= 5 m

Area of rectangle=l*b=21*15=315 m²

Area of circle= π[tex]r^{2}[/tex]=π*[tex]5^{2}[/tex]=78.54 m²

Therefore,Area of shaded region= Area of rectangle-2*Area of circle

                                                       =315-2*78.54=157.92 m²

3) In the following figure,

Radius of circle, r= 2 ft

Base of triangle, b= 6 ft

Height of triangle, h=6 ft

Area of circle= π[tex]r^{2}[/tex]=π*[tex]2^{2}[/tex]=12.566 ft²

Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]

                         =[tex]\frac{1}{2}*6*6[/tex]=18 ft²

Therefore,Area of shaded region= Area of triangle- Area of circle

                                                       = 18-12.566=5.434 ft²

4) In the following figure,

Radius of circle, r= 6 cm

Length of rectangle, l= 17 cm

breadth of rectangle, b= 2*r= 12 cm

Area of semi-circle= π[tex]\frac{r^{2}}{2}[/tex]=π*[tex]\frac{6^{2}}{2}[/tex]

                               =56.5487 cm²

Area of rectangle=l*b=17*12=204 cm²

Therefore,Area of shaded region= Area of rectangle- Area of semi-circle

                                                       = 204-56.5487=147.4513 cm²

5) In the following figure,

Side of bigger square, a=14 cm

Side of smaller square, b=7 cm

Area of bigger square= [tex]a^{2}[/tex]=[tex]14^{2}[/tex]=196 cm²

Area of smaller square= [tex]b^{2}[/tex]=[tex]7^{2}[/tex]=49 cm²

Therefore,Area of shaded region= Area of bigger square- Area of smaller                                                                                              square

                                                       =196-49=147 cm²

6) In the following figure,

Length of rectangle, l= 10 in

breadth of rectangle, b= 8 in

Base of triangle, b= 8 in

Height of triangle, h=6 in

Area of rectangle=l*b=10*8=80 in²

Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]

                         =[tex]\frac{1}{2}*8*6[/tex]=24 in²

Therefore,Area of shaded region= Area of triangle- Area of circle

                                                       = 80-24=56 in²

Answer:

60

Step-by-step explanation:

90=30%x

x=30

200%x=2x=60

Answer:

600

Step-by-step explanation:

30%=0.3

0.3x=90

x=90/0.3=300

200%=2

2(300)=600

Answer:

16 servings

Step-by-step explanation:

To calculate the servings of chicken, we need two pieces of information. We need to know how much money the food bank has and how many ounces of chicken is available. This information is given. Therefore, we can work out the servings of chicken by dividing the ounces of by the amount of money.

[tex]=1774.4/110.9=16[/tex]

So 16 servings of chicken can be provided for 110.9 pounds.

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ [tex]y=\frac{75}{x}-\frac{1}{4}x[/tex]

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ [tex]V=x^{2}(\frac{75}{x}-\frac{1}{4}x)[/tex]

∴ [tex]V=75x-\frac{1}{4}x^{3}[/tex]

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ [tex]\frac{dV}{dx}=75-\frac{3}{4}x^{2}[/tex]

∵ [tex]\frac{dV}{dx}=0[/tex] ⇒ greatest volume

∴ [tex]75-\frac{3}{4}x^{2}=0[/tex]

- Subtract 75 from both sides

∴ [tex]-\frac{3}{4}x^{2}=-75[/tex]

- Divide both sides by [tex]-\frac{3}{4}[/tex]

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ [tex]y=\frac{75}{10}-\frac{1}{4}(10)[/tex]

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ [tex]V=75x-\frac{1}{4}x^{3}[/tex]

∵ x = 10

∴ [tex]V=75(10)-\frac{1}{4}(10)^{3}[/tex]

∴ [tex]V=750-\frac{1}{4}(1000)[/tex]

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

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Answer:

21[tex]w^{10}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Given

3[tex]w^{5}[/tex] × 7[tex]w^{5}[/tex]

= 3 × 7 × [tex]w^{(5+5)}[/tex]

= 21[tex]w^{10}[/tex]

To solve this, subtract 2 from both sides, and you end up with x = 8. :)