A rope 24m long is dividend into three pieces in the ratio 2:1:5. the length of the shortest piece is

Answer:

90

Step-by-step explanation:

The angles are on either side of the line are in proportion.

Hence,

⇒ [tex]\frac{10}{8} = \frac{x}{72}[/tex]

⇒ [tex]\frac{5}{4} = \frac{x}{72}[/tex]

⇒ [tex]x = \frac{5 \times 72}{4}[/tex]

⇒ [tex]x = 5 \times 18[/tex]

⇒ x = 90

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{8}{10}=\dfrac{72}{x}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{4}{5}=\dfrac{72}{x}[/tex]

[tex]\\ \rm\Rrightarrow 4x=360[/tex]

[tex]\\ \rm\Rrightarrow x=90[/tex]

How you do it is add the 44% of 132 to 132 (132 + (132×44%))

First you have to find out how much 44% is. Change it into decimal form (0.44) and then multiply the two together. 132 × 0.44 is 58.08 miles. Then you add that to the rest of the trip, 132 miles. (132 + 58/08 is 190.08)

Answer:

y = 4 - 2x

Step-by-step explanation:

That is the formula, in y = a + mx but it you want it in y = mx+c, it is y = -2x + 4

Exact Form:

5

27

Decimal Form:

0.

¯¯¯¯¯¯

185

i hope this helps please have a nice day/night

Answer:

Exact Form:

5

27

Decimal Form:

0.

¯¯¯¯¯¯

185

i hope this helps please have a nice day/night

Step-by-step explanation:

area of square = s×s

9×9

81cm²

hope it helps...!!!

Answer:

81 cm^2

Step-by-step explanation:

A square is a 2d shape with side lengths all the same.

To find the area, all you need is one side length, which is 9cm in this case.

Then you just square the number (9 x 9) to get 81 cm^2 (centimetre squared).

The measure of the missing angle x is 23.22 degrees

The expression for representing cosine rule is expressed as:

c² = a² + b² - 2ab cos C

Given the following parameters

a = 26

b = 50

c = 29

Substitute

c² = a² + b² - 2ab cos C

29² = 26² + 50² - 2(26)(50) cos C

841 = 676 + 2500 - 2600cosC

2335 =2600cos C
cos C = 2335/2660

C = 23.22 degrees

Hence the measure of the missing angle x is 23.22 degrees

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Answer:

23.2 is the correct answer given you need to round to the nearest tenth.

Step-by-step explanation:

please mark me as brainlest

The equation is y = 27x. The amount she pays for an 8-day rental will be $ 216. Then the domain and range will be (0, ∞) and (0, ∞).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Connie Nardelli rents a car for $27 per day.

The total cost is a function of the number of days she rents the car.

Let x be the number of days ad y be the total rent cost.

Then the equation will be

y = 27x

The amount she pays for an 8-day rental will be

y = 27 × 8

y = 216

The domain and range will be (0, ∞) and (0, ∞).

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Answer:

[tex](x+5)^2+y^2=117[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given:

[tex]\implies (x-(-5))^2+(y-0)^2=r^2[/tex]

[tex]\implies (x+5)^2+y^2=r^2[/tex]

To find r², input the coordinates of the given point (4, -6) into the equation:

[tex]\implies (4+5)^2+(-6)^2=r^2[/tex]

[tex]\implies 81+36=r^2[/tex]

[tex]\implies r^2=117[/tex]

Therefore, the equation of the circle is:

[tex]\implies (x+5)^2+y^2=117[/tex]

Answer:

Standard form = (x + 5)² + y² = 117

General Form = x² + 10x + y² - 92 = 0

Explanation:

(x - h)² + (y - k)² = r²

Find radius using:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]\rightarrow \sf radius : \sqrt{(-5-4)^+(0-(-6))^2} \ = \ 3\sqrt{13} \ \ units[/tex]

Find equation inserting values:   Given center: (-5, 0)

⇒ (x - (-5))² + (y - 0)² = (3√13)²

⇒ (x + 5)² + y² = 117

⇒ x² + 10x + 25 + y² - 117 = 0

⇒ x² + 10x + y² - 92 = 0

Answer:

150

Step-by-step explanation:

Let :

⇒ The numbers can be denoted as x, 3x, and 5x

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

Solving :

⇒ It mentions their sum is 270

⇒ x + 3x + 5x = 270

⇒ 9x = 270

⇒ x = 30

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

Largest number :

⇒ 5x

⇒ 5(30)

⇒ 150

Answer :

Step by step explaination :

Here we have been given with the ratio of three numbers that is 1 : 3 : 5. So let us assume a common factor for them , we are assuming it as y.

Therefore,

Sum of them is 270 :

>> 1y + 3y + 5y = 270

>> 4y + 5y = 270

>> 9y = 270

>> y = 270 / 9

>> y = 90 / 3

>> y = 30

Henceforth, value of y is 30.

★ Finding out first number :-

>> First number = 1y

>> First number = 1 × 30

>> First number = 30

★ Finding out second number :-

>> Second number = 3y

>> Second number = 3 × 30

>> Second number = 90

★ Finding out third number :-

>> Third number = 5y

>> Third number = 5 × 30

>> Third number = 150

Step-by-step explanation:

volume of a sphere is given by 4/3 × pi × r³

hence, the answer is 523.33

comment if you have any doubts

Work Shown:

[tex]V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*5^3\\\\V \approx 523.33\\\\[/tex]

The true statement about the pumpkin include:

The median is a value or quantity lying at the midpoint of a frequency distribution of observed values or quantities.

Here, the median pumpkin weight is 35 lb and 75% of pumpkins in the sample have weights higher than the mean.

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Answer:

here we have to divide the number of words per hour to the number of minutes per hour.

Step-by-step explanation:

5400÷60

=90.

therefore in a minute she types 90 words.

The matched pair of rational numbers are as follows;

[tex]\frac{-2}{a^{2}b }+\frac{2}{ab^{2} } = \frac{2(a-b)}{a^{2}b^{2} }[/tex]

[tex]\frac{1}{2ab} +\frac{-1}{4a^{2} b^{2} } =\frac{2ab-1}{4a^{2}b^{2} }[/tex]

[tex]\frac{2}{a^{2} b^{3} } +\frac{-2}{ab} =\frac{2(1-ab^{2} )}{a^{2} b^{3} }[/tex]

[tex]\frac{1}{ab^{3} } +\frac{-1}{a^{2} b} =\frac{a-b^{2} }{a^{2}b^{3} }[/tex]

The matched pair of rational numbers are as follows:

[tex]\frac{-2}{a^{2}b }+\frac{2}{ab^{2} } = \frac{-2b+2a}{a^{2} b^{2} } = \frac{2(a-b)}{a^{2}b^{2} }[/tex]

[tex]\frac{1}{2ab} +\frac{-1}{4a^{2} b^{2} } =\frac{2ab-1}{4a^{2}b^{2} }[/tex]

[tex]\frac{2}{a^{2} b^{3} } +\frac{-2}{ab} =\frac{2 - 2ab^{2} }{a^{2}b^{3} } =\frac{2(1-ab^{2} )}{a^{2} b^{3} }[/tex]

[tex]\frac{1}{ab^{3} } +\frac{-1}{a^{2} b} =\frac{a-b^{2} }{a^{2}b^{3} }[/tex]

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Answer:

B

Step-by-step explanation:

When you have a double negative (ie. 5 -(-10)) they cancel eachother out and become a plus. If you have + and - together, its always a minus, if you have + and + or - and -, its always plus.

Since in 4-(-3), the two minuses cancel each other out and become a plus, you move 3 to the right, since right is the positive direction.

subtracting a negative number changes the equation to an addition.

4 -(-3) becomes 4 + 3 = 7

you would start at 4 and move 3 places to the right.

the answer is B.

The value of x is 8 from the diagram given.

The corresponding sides of a similar triangle are said to be in proportion if and only if the corresponding angle are also equal.

To calculate the side of line x (|x|), we have to determine the ratios of the corresponding sides as:

[tex]\mathbf{\dfrac{BC}{DC} = \dfrac{AC}{EC}}[/tex]

[tex]\mathbf{\dfrac{x}{10} = \dfrac{12}{15}}[/tex]

x = 120/15

x = 8

Therefore, we can conclude that the value of x is 8.

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The system of equations that models the given situation is given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

He had 25 customers, hence:

x + y = 25.

He charges $15 for a single lawn and $25 for a front and back lawn, and made a total of $475, hence:

15x + 25y = 475

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Answer:

ok soo

Step-by-step explanation:

45, 56, 61, 75

middle of 56 and 61 add them so 117 then half 117 which is 58.5-

Hey there!

4 3/5 - 2 5/6

= 23/5 - 17/6

= 53/30

≈ 1 23/30

Therefore, the answer should be:

53/30

OR

1 23/30

(Either should work because they are equivalent to each other)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Value of the given mixed fraction [tex]4\frac{3}{5} -2\frac{5}{6}[/tex] is equals to [tex]1\frac{23}{30}[/tex] .

" Mixed fraction is defined as the fraction representing whole fraction along   with the quotient and remainder."

Convert mixed fraction into improper fraction

[tex]m\frac{p}{q} = \frac{q*m+p}{q}[/tex]

According to the question,

Given mixed fraction,

   [tex]4\frac{3}{5} -2\frac{5}{6}[/tex]

Convert mixed fraction into improper fraction we get,

[tex]=\frac{23}{5} -\frac{17}{6} \\\\=\frac{138-85}{30} \\\\=\frac{53}{30}\\ \\= 1\frac{23}{30}[/tex]

Hence, value of the given mixed fraction [tex]4\frac{3}{5} -2\frac{5}{6}[/tex] is equals to [tex]1\frac{23}{30}[/tex] .

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Answer:

y = 3x - 12

Step-by-step explanation:

Forming the slope-intercept equation :

y = mx + b

Substitute m = 3 and b = -12 in the equation :

Answer:

y = 3x - 12

Step-by-step explanation:

The slope intercept form of a line is y = mx + b, where m is the slope and b is the y intercept. Here, m = 3 and b = -12. Therefore, the slope intercept form for this line is y = 3x - 12.

Answer:

x=1 y=1

Step-by-step explanation:

Let's use the elimination method.
3x+4y=7
2x-y = 1 (multiply both sides by 4)
8x-4y=4
3x+4y=7

(add both equations together)
11x=11
x=1
Plug x=1 into either of the equations
2(1) - y=1
2-y=1
2=1+y
y=1

Simplification form of the provided expression is -x⁴-2x³+2x+5 option (B) is correct.

It is defined as the combination of constants and variables with mathematical operators.

The options are:

A) -x⁴ - 2x - x + 2

B) -x⁴ - 2x³ + 2x + 5

C) -2x³ + 1

D) -x - 2x² + 2x + 5

We have an expression:

= (x + 3) - [(x + 2)(x³ - 1)]

[tex]\rm =x+3-\left(x+2\right)\left(x^3-1\right)[/tex]

[tex]\rm =x+3-x^4+x-2x^3+2[/tex]

[tex]\rm =-x^4-2x^3+2x+3+2[/tex]

[tex]\rm =-x^4-2x^3+2x+5[/tex]

Thus, simplification form of the provided expression is -x⁴-2x³+2x+5 option (B) is correct.

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Answer:

51.63 ft

Step-by-step explanation:

Tangent 25 = opposite / adjacent

tan 25 = height/100

Height = 100 tan 25 = 46.63 feet ABOVE the head of the victim

victim head height = 5 ft

46.63 + 5 = 51.63 ft

Answer:

[tex]\large\boxed{\sf x^3 - 7x^2 + 7x - 10}[/tex]

Explanation:

Given:

(a) f(x) = x³ - 3x² + 2x - 3

(b) g(x) = 4x²- 5x + 7

Solve for (f - g)(x) = f(x) - g(x) :

⇒ x³ - 3x² + 2x - 3 - (4x²- 5x + 7)

distribute inside parenthesis

⇒ x³ - 3x² + 2x - 3 - 4x² + 5x - 7

group the variables

⇒ x³ - 3x² - 4x² + 2x + 5x - 3 - 7

add or subtract variables

⇒ x³ - 7x² + 7x - 10

Answer:

x³ - 7x² + 7x - 10

Step-by-step explanation:

Subtracting functions: (f - g)(x) is equivalent to f(x) - g(x)

Given:

Simplify:

(x³ - 3x² + 2x - 3) - (4x² - 5x + 7)

(x³ - 3x² + 2x - 3) - (4x²) + - (- 5x) - (7)

x³ - 3x² + 2x - 3 - 4x² + 5x - 7

x³ - 3x² - 4x² +2x + 5x - 3 - 7

x³ - 7x² + 7x - 10

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The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.

If the given sphere is of radius r units, then its volume is given as:

[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]

A glass marble has a diameter of 18 millimeters.

The radius is 9

[tex]V= \dfrac{4}{3} (3.14) (9)^3 \: \rm unit^3\\\\V = 3,052.08 cubic millimeters[/tex]

The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.

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