6. 3/5 - 3/10
7. 4/6 - 1/12
8. 4/6 - 1/2
9. 3/4 - 1/3
10. 7/8 - 3/4

There is 1/6 gallon of milk left in Leo's jug.

The step by step fraction subtraction are as follows:

The first step would be to deduct the 3/4 gallon of milk with 1/3 he uses to make the soup.

3/4 - 1/3 = (3x3)/(4x3) - (1x4)/(3x4) = 9/12 - 4/12 = 5/12

Then out of 5/12 gallon of milk left in the jug, he pours 1/4 of the remaining milk into a glass.

5/12 - 1/4 = 5/12 - (1x3)/(4x3) = 5/12 - 3/12 = 2/12 = (2÷2)/(12÷2) = 1/6

So Leo has 1/6 gallon of milk left in the jug.

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When Z=6 and Y=64 the given proportionality value of x = 1/2.

What is proportionality?

  The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount. Two integers that each represent a component of a whole are compared to determine their proportion. In essence, a percentage declares that two fractions are the same even if the amounts are different. For instance, half of 10 marbles is equal to half of 50 marbles in terms of proportion.

Here Z varies jointly as the square root of the product of X and Y.

Then,

=> Z∝[tex]\sqrt{XY}[/tex]

=>Z=k[tex]\sqrt{XY}[/tex]

Where k is constant . Now put X=3 , Y = 12, Z=3.

=> 3=k*[tex]\sqrt{12*3}[/tex]

=> k = 6/3 = 2 .

Then the equation is ,

=> Z==3[tex]\sqrt{XY}[/tex]

Now put Z=6 and Y=64

=> 6 = 3[tex]\sqrt{x*64}[/tex]

=> 2/8 =[tex]\sqrt{x}[/tex]

=>[tex]\sqrt{x}[/tex] = 1/4

=> x = 1/2.

Hence the value of x is 1/2.

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Answer:

y=0.6x+3

Step-by-step explanation:

Slope intercept form: y=mx+b

m- slope

b- y intercept

to find slope with y2-y1/x2-x1

3-0/0-(-5)

3/5

0.6is the slope

y intercept is 3 since it intersects at 3 on the y axis

Hopes this helps please mark brainliest

Answer:

82

Step-by-step explanation:

1.) Recognize that this is the Pythagorean Triple 9, 40, 41, just multiplied by two (9*2 = 18, 40*2 = 80).

2.) Now, to find the third number, we just multiply 41 by 2 to get 82.

Answer:

The hypotenuse is equal to 82 centimeters.

Step-by-step explanation:

Using the Pythagorean theorem (a^2 + b^2 = c^2), which states that the legs of a right triangle (a and b) squared, equal the hypotenuse squared, we can plug in the values of the legs of the right triangle into spots a and b.  This gets us the equation 80^2 + 18^2 = c^2. We can then square the values to get 6400 + 324 = c^2. We then get 6724 = c^2, and then take the square root of both sides to get the value of c, the hypotenuse. This gets us c = 82, so the hypotenuse is equal to 82 centimeters.

The mean of the frequency distribution is 591.446.

Let the values be 'x' and frequency be 'f'

To find the mean of the frequency distribution use formula,

[tex]Mean=\frac{Sum of values}{Total number of values}[/tex]

where, sum of the values = ∑fx

Total number of values=∑f

From table,

First find fx,

[tex]f1x1=624*12=7488\\\\f2x2=541*8=4328\\\\f3x3=606*10=6060\\\\f4x4=577*15=8655\\\\f5x5=586*5=2930\\\\f6x6=610*6=3660[/tex]

Now,

∑fx=[tex]7488+4328+6060+8655+2930+3660=33121[/tex]

Now , the total number of values,

∑f=[tex]12+8+10+15+5+6=56[/tex]

Now,

[tex]Mean=\frac{33121}{56} =591.446[/tex]

Thus, the mean of the frequency distribution is 591.446.

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△MPQ: M(-4,3), P(-5,8), Q(-1,6). Translation: along (-4,-4) Reflection: in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).

Here we need to find translation along (-4,-4) and reflection in y=x.

First we will find translation,

⇒ (x,y)→ (x-4,y-4)

M(-4,3 )→ M'(-8,-1) ,  

P(-5,8) → P'(-9,4)

Q(-1,6) → Q'(-5,2)  

now we will do reflection,

⇒(x,y) → (y,x)

M'(-8,-1) →  M''(-1.-8)

P'(-9,4) →  P''(4,-9)

Q'(-5,2) → Q''(2.-5).

Therefore translation along (-4,-4) and reflection in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).

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The radius of the circle is 5.91mm

What is the area of the circle?

The area of the circle is the product of mathematical constant pi and square of the radius. radius is the distance of a point on the circle from the center of the circle.

The area of the circle is 110 mm^2

We have to find the radius to do that we first substitute the value of area in the area of circle formula and then compute the value of the radius

We know that,

The area of the circle

= π·r^2

110=22/7*r^2

35 = r^2

r= 5.91mm

Hence The radius of the circle is 5.91 mm

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The linear function y = -12x + 360, representing Amir's height at a time of x minutes, is graphed at the end of the answer.

The slope-intercept representation of a linear function is given by the rule shown as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the test, his rate is of -12 m/s, hence the slope of the function is given as follows:

m = -12.

When x = 30, y = 0, hence the intercept b of the linear function can be obtained as follows:

0 = -12(30) + b

b = 30 x 12

b = 360.

Thus the equation is:

y = -12x + 360.

The domain in which the function is graphed is:

x ≥ 0.

As time cannot assume negative values.

The problem asks for the graph of the linear function, considering that:

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Answer:

x=4

Step-by-step explanation:

The amount of time spent on bicycle by Jim =6.5 hours

The amount of time spent on walking by Jim =2.5 hours

To calculate speed, divide the distance travelled by the time it took to complete the voyage, so speed = distance divided by time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.

Distance divided by time equals speed. Distance = time * speed

To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.

Given,

Distance=270miles

Time=9 hours

Speed by walk=4 miles/hour

Speed by cycle=40 miles/ hour

t= time for riding a bicycle

9-t= time for walking

Distance= Speed ×Time

270=40t+4(9-t)

40t+36-4t=270

36t=234

t=6.5

Time spent on bicycle = 6.5 hours

Time spent on walking = 9-6.5

=2.5 hours

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His percentage of change in the amount of quarts is 82.22%.

Initial amount of lemonade = 45 quart

End amount of lemonade = 8 quart

Change in amount = 45 - 8

                               = 36

Percent = [tex]\frac{change in value}{initial value}*100[/tex]

             = [tex]\frac{37}{45}*100[/tex]

             = 0.8222 * 100

             = 82.22%

Hence, his percentage of change is 82.22%.

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The given two triangles ΔQRS and ΔTUV are similar.

What is similar figures?

The same shape between two figures is referred to as similarity. If two figures have congruent corresponding angles and equivalent length ratios on their corresponding sides, they are said to be similar mathematically. The scale factor is the name of this often used ratio.

Given: Two triangles ΔQRS and ΔTUV.

The angles of ΔQRS  are 28°, 76° and 76°.

The angles of ΔTUV are 28°, 76° and 76°.

So, the angles of given two triangles are congruent.

Now consider, the sides of the triangle.

The sides of ΔQRS are, 4, 4, 2 and

The sides of  ΔTUV are 12, 12, 6.

It seems that the sides of the triangle are in proportion.

Therefore, the given two triangles ΔQRS and ΔTUV are similar.

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Answer:

-10

-7

-4

Step-by-step explanation:

287 = [tex]a_{1[/tex] + (n-1)3

287 = [tex]a_{1}[/tex]+ (100-1)3

287 = [tex]a_{1}[/tex] + 99(3)

287 = [tex]a_{1}[/tex] + 297  Subtract 297 from both sides

-10 = [tex]a_{1}[/tex]

If the first term is -10  The second term is 3 greater -7 and the third terms is 3 greater than that. -4

Answer:10

Step-by-step explanation:Step-by-step explanation:

James's age = x

Jack's age = y

y = 7x

y + 5 = 5(x + 5)

y = 7x

y + 5 = 5x + 25

7x - y = 0

5x - y = -20

7x - y = 0

-5x + y = 20

2x = 20

x = 10

James's age: x = 10

By using the graph, the employee's hourly wages is calculated as $10.6

Graph:

Basically, a graph is a collection of points, called vertices, and lines between those points, called edges.

Given,

Here we have the graph with straight line.

And we need to determine the employee's hourly wage.

While we looking into the graph we have identified that the x axis refers the number of hours the employ is working and the y axis refers the money earned by them.

In order to find the wages for one hour, we need to select one point from the graph.

Here we have take the point  (5,53)

The first point refers the number of hours that is 5.

And the second one refers the wages for 5 hours that is 53.

So, the one hour wages is calculated as,

=> 53/5

=> 10.6

Therefore, the employee's hourly wage is $10.6.

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f(x) represents the distance, in miles, remaining on a trip z hours into the trip. The value of f(3) is 95 miles and it  represents the total distance remaining after 3 hours.

A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

Function:

f(x) = 260 -55x

When f(3)

f(3) = 250 - 55(3)

f(3) = 250 - 165

f(x) = 95

95 miles; f(3) represents the total distance remaining after 3 hours.

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If a woman has a total of $11,000 to invest. The she invested in each account is: 4000 at 8%, 7000 at 7 %.

Total amount of money invested = $11000

x+y=11000,

Total interest for the year= $760

0.07×x+0.08×y=810

x=11000-y

We substitute for x

0.07×(11000-y)+0.08×y=810

We multiply out

770-0.07y+0.08×y=810

We combine like terms.

0.01×y=40

Divide both side by 0.01y

y = 40 /0.01

y= 4000 at 8%

x=11000-y

Calculate x

x = 11,000 - 4,000

x=7000 at 7 %

Therefore she invested 4000 at 8%, 7000 at 7 %.

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From trigonometric ratio, we used the tangent of the angle to determine that the flagpole is leaning by an angle of 47.12°

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In the question, we can assume the point of view and the flagpole makes a right angle triangle.

Since we have the opposite and adjacent, we can find the acute angle by using the tangent of the angle

tanθ = opposite / adjacent

tan θ = 14 / 13

θ = tan⁻¹(14/13)

θ = 47.12°

The flagpole is leaning with an acute angle of 47.12 degrees

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The area of the triangle is x + 1 cm², while the area of the rectangle is x cm². Therefore, there is no value of x that makes the areas of both figure equal, because there is no solution to the equation.

A triangle's area = 1/2(base)(height)

A rectangle's area = length × width.

Area of the green triangle = 1/2(x + 1)(2)

Area of the green triangle = x + 1 cm²

Area of the rectangle = x × 1

Area of the rectangle = x cm²

Setting both areas equal, we have:

x + 1 = x

x - x = -1

0 = -1 [not true]

There's no solution or the values of x.

Therefore, we can conclude that there are no values of x for which the areas of both shapes are equal, because there is no solution to the equation.

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The value of ''a'' will be 1

What is Matrix?

A set of numbers arranged in rows and columns so as to form a rectangular array, is called Matrix.

Given that;

1,2 and 3 are the eigen values of matrix A.

Now,

We know that;

The product of eigen values of a matrix is equal to the determinant of that matrix.

So, We find the determinant of matrix as;

[tex]A = \left[\begin{array}{ccc}2&0&1\\0&2&0\\a&0&2\end{array}\right][/tex]

Hence, We get;

| A | = 2 (4 - 0) - 0 (0 - 0) + 1 (0 - 2a)

| A | = 8 - 2a

And, The product of eigen values = 1 x 2 x 3 = 6

Hence, We get;

| A | = 8 - 2a

6 = 8 - 2a

2a = 8 - 6

2a = 2

a = 1

Thus, The value of ''a'' will be 1

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Answer:

0.33=0.33

Step-by-step explanation:

it is answer 0.33=0.33

The slope of line h that is perpendicular to line g is: -4/3.

The slope values of any two lines that are perpendicular to each other are values that are negative reciprocals to each other.

The equation of of line g is given as y = 3/4x + 3/4, it is expressed in slope-intercept form as y = mx + b. This means that the value of the slope of line g is 3/4.

The negative reciprocal of 3/4 is -4/3. Therefore, the slope of line h that is perpendicular to line g would be -4/3.

The slope of line h is: -4/3.

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We can use the graph of the line y = 11/7(x) - 58/7 to find the distance between the points

The slope-point equation of a line is given as:

y-y1 = m(x−x1)

where m is the slope of the line, and slope (m) = y2−y1 / x2−x1

Given: the points (-3, -13) and (11, 9)

x1 = -3, y1 = -13 and x2 = 11, y2 = 9

slope(m) = 9-(-13) / 11-(-3) = 22/14 = 11/7

Using y-y1 = m(x−x1), put m = 11/7 and make y the subject:

y-y1 = m(x−x1)

y-(-13) = 11/7(x-(-3))

y + 13 = 11/7(x+3)

y + 13 = 11/7(x) + 33/7

y = 11/7(x) + 33/7 - 13

y = 11/7(x) - 58/7

Therefore, the graph of the line y = 11/7(x) - 58/7 could be used to find the distance between the points

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Answer: The answer is A

Step-by-step explanation:

The line is:

y = 400*x + 2000

And the statements are:

The original purchase price of the computer is given by the y-intercept, which is $2,000

The change in the price of the computer is the slope, which is 400.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

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

Using the graph we can identify two points like:

(1, 1600) and (5, 0)

Then the slope is:

a = (0 - 1,600)/(5 - 1) = 400

And the y-intercept is 2,000, as we can see on the graph.

Then the line is:

y = 400*x + 2,000

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Answer:

53 oranges.

Step-by-step explanation:

To find this, we must set up a proportionality formula.

6                   8

-        =          -

40                 x

Our goal is to find x.

First we cross multiply and get:

6x=320

Now we can divide each side by 6 to get x by itself.

x=53.33,

however, because you cannot have less than a whole orange in a box, each box contained 53.

The conditional statement has a true truth value if neither the hypothesis nor the conclusion is true.

A conditional statement is phrased as follows if we have the two propositions P and Q:

Q if P is true.

where P denotes the premise and Q denotes the result

The following are conditional statements' truth values:

The conditional statement is true if P and Q are true.

The conditional statement is false if P is false and Q is true.

The Conditional statement is false if P is true and Q is false.

The conditional statement is true if P and Q are both false.

Therefore, the conditional statement's truth value is true if both the hypothesis and the conclusion are false.

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Answer:

7)

so

100-16=84

then

84÷7=12

each book costs 12 dollars

The saline concentration of the mixture expressed as a percentage is 42%

A percentage is the expression of a quantity as a fraction that has a denominator of 100.

The volume of the solution that is 30% saline = 80 ml

The volume of the solution that is 90% saline = 20 ml

The concentration of the saline in the mixture; Required;

The table of values can be presented as follows;

Component [tex]{}[/tex] Unit Value [tex]{}[/tex] Amounts (ml) [tex]{}[/tex]  Value

30% saline [tex]{}[/tex]   0.3          [tex]{}[/tex]    80          [tex]{}[/tex]          0.3×80

Solution

70% saline  [tex]{}[/tex]   0.7          [tex]{}[/tex]    20           [tex]{}[/tex]        0.7×20         [tex]{}[/tex]        

solution

Mixture          [tex]{}[/tex]x          [tex]{}[/tex]       100           [tex]{}[/tex]       100 × x

0.3 × 80 + 0.9 × 20 = (80 + 20) × x

42 = 100·x

The concentration of the saline mixture is x = 42/100 = 0.42

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Answer: M = -11/3

Step-by-step explanation: