Where would you put 2 1/8th on a number line?

Answer:

i) let x be the amount of money worth of drinks that Kevin sold.

ii) Kevin sells at most $60 worth of drinks.

iii) therefore the inequality can be written as

   x ≤ $60

Step-by-step explanation:

i) let x be the amount of money worth of drinks that Kevin sold.

ii) Kevin sells at most $60 worth of drinks.

iii) therefore the inequality can be written as

   x ≤ $60

The temperature increased by 15°C.

Temperature is a physical quantity that expresses the perceptions of hotness and coldness

Given that at midnight the temperature is -6°C. At midday the temperature is 9°C. Therefore, the difference in the temperature can be written as,

The difference in temperature

= Temperature in Midday - Temperature at midnight

= 9°C - (-6° C)

= 15° C

Therefore, The difference in the temperature is 15°C.

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Answer:

8

Step-by-step explanation:

[tex]\frac{is}{of} = \frac{percent}{100}[/tex]

[tex]\frac{x}{80} = \frac{10}{100}[/tex]

80x10 = 800

800 = 100x

800 divide 100 = 8

answer = 8

Hope this helped!! :)

Answer:

1 - 3/10 = 7/10 of the distance left

(3/7)(7/10) = 3/10 of the total distance

Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.

To find the fraction of the total distance traveled to Zachary's aunt's house, we need to combine the distances traveled and express it as a fraction of the total distance.

Given:

1. Zachary's family traveled [tex]\( \frac{3}{10} \)[/tex] of the total distance to his aunt's house.

2. Then, they traveled [tex]\( \frac{3}{7} \)[/tex] of the remaining distance.

Step 1: Calculate the total distance traveled by combining the two distances.

[tex]\[ \text{Total distance traveled} = \frac{3}{10} + \frac{3}{7} \][/tex]

Step 2: Find a common denominator for [tex]\( \frac{3}{10} \) and \( \frac{3}{7} \).[/tex] The least common multiple (LCM) of 10 and 7 is 70.

Step 3: Rewrite the fractions with the common denominator of 70.

[tex]\[ \frac{3}{10} = \frac{3 \times 7}{10 \times 7} = \frac{21}{70} \][/tex]

[tex]\[ \frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70} \][/tex]

Step 4: Add the fractions:

[tex]\[ \frac{21}{70} + \frac{30}{70} = \frac{21 + 30}{70} = \frac{51}{70} \][/tex]

Therefore, Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.

The solution is x = 8 and y = -5

Solution:

Given system of equations are:

x + y = 3 ------ eqn 1

3x + 2y = 14 ------ eqn 2

We have to find the solution to the equations

We can use substitution method to solve

From eqn 1,

x + y = 3

Isolate for "x"

x = 3 - y ------ eqn 3

Substitute eqn 3 in eqn 2

3(3 - y) + 2y = 14

9 - 3y + 2y = 14

-y = 14 - 9

-y = 5

Substitute y = -5 in eqn 3

x = 3 - (-5)

x = 3 + 5 = 8

Thus the solution is x = 8 and y = -5

Answer:

The greatest area possible is 729[tex]inch^{2}[/tex]

Step-by-step explanation:

i) If a = [tex]-w^{2} + 54w[/tex] where w is the width of the picture frame

  differentiating on both sides we get

  [tex]\frac{da}{dw} = -2w + 54[/tex]

Differentiating the above again on both sides we get   [tex]\frac{d^2a}{dw^2}[/tex]  = -2

 Since the second order derivative is negative then we can get the solution for the maximum area by equating the fist order derivative equation to 0.

 Therefore -2w + 54 = 0     therefore w  = 27.

ii) If we substitute w = 27 into the equation in ii) we get

   a  = [tex]-(27)^2 +(54\times 27)[/tex] = (54 - 27) [tex]\times[/tex](27)  = [tex]27^{2}[/tex] = 729

The cost of old computer is $ 357

Solution:

Let "x" be the cost of old computer

From given,

Cost of new computer = $ 709

Blairs new computer cost 5$ less than twice the cost of her old computer

Therefore,

Cost of new computer = twice the cost of old computer - 5

Cost of new computer = 2x - 5

709 = 2x - 5

2x = 709 + 5

2x = 714

Divide both sides by 2

x = 357

Thus the cost of old computer is $ 357

Answer:

$357

Step-by-step explanation:

709=2x-5      

+5           +5

cross the right column out

709+5 = 714

714=2x

divide 714 by 2 and get 357

HOPE THIS HELPS!!!

Answer:

They show as intersections with the x-axis

Step-by-step explanation:

For example, the quadratic y = x² - 1 has roots x = -1 and x = 1.

They show on the graph as intersections of the parabola with the x axis at x = -1 and x = 1.

x = 11 (or) x = –13

Solution:

Theorem:

If three or more parallel lines are cut by a transversal then they divide the transversals proportionally.

Given lines l, m, n are parallel lines cut by a two transversal lines.

Therefore, they are in proportion by the above theorem.

[tex]$\Rightarrow\frac{x+5}{10}=\frac{12.8}{x-3}[/tex]

Do cross multiplication.

[tex]$\Rightarrow(x+5)\times(x-3)=12.8\times10[/tex]

[tex]$\Rightarrow x^2+5x-3x-15=128[/tex]

[tex]$\Rightarrow x^2+2x-15=128[/tex]

Arrange all terms in one side.

[tex]$\Rightarrow x^2+2x-15-128=0[/tex]

[tex]$\Rightarrow x^2+2x-143=0[/tex]

[tex]$\Rightarrow x^2-11x+13x-143=0[/tex]

Take common terms outside

[tex]$\Rightarrow x(x-11)+13(x-11)=0[/tex]

[tex]$\Rightarrow (x-11)(x+13)=0[/tex]

[tex]$\Rightarrow (x-11)=0\ \text{(or)}\ (x+13)=0[/tex]

⇒ x = 11 (or) x = –13

Hence x = 11 (or) x = –13.

Answer:

43 questions in total

Step-by-step explanation:

the original equation with the unknown (total number of questions on the test) will look like this

[tex] \frac{total \: number \: of \: questions \: on \: exam}{24 \: answered \: questions} = 80\%[/tex]

we know this because to work out a percentage in the 1st place you need the total ÷ number (in this case it's ÷ how many questions out of the total she did answer)

now you rearrange.

you need to move the 24 to get the total on it's own here's how you do it

[tex] \frac{tot \: num \: of \: qs}{24} \times 24 = 80\% \times 24[/tex]

what you do to one side of equation you have to do to the other. the 24 and 24 on the left will cancel because 24÷24=1 and we don't write

got mum of Q's x 1= 80 x 24

now you convert % to decimal

[tex]80\% \times 100 = 0.80[/tex]

replace

[tex]tot \: num \: qs \: = 24 \times 0.80 = 19[/tex]

now you take the original and + the 19

[tex]24 + 19 = 43[/tex]

therefore there are a total of 43 questions on the exam

To find the total number of questions on the test, we set up a ratio where 24 questions represents 80%. By comparing it to a ratio where X represents 100%, and solving for X, we get the total number of questions.

The question pertains to the concept of percentages. In Sarah's case, she answered 24 questions correctly and got an 80%, meaning that these 24 questions represent 80% of the total questions on the test. Hence, to find the total number of questions on the test, we set up a ratio such as this: 24 is to 80 as X (total questions) is to 100. We solve for X by multiplying the cross products and dividing by 80. The result will give us the total number of questions on the test.

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Answer:

6 (StartFraction 5 over 6 EndFraction x + two-thirds) = negative 9(6)

5 x + 4 = negative 54

5 x = negative 58

Step-by-step explanation:

we have

[tex]\frac{5}{6}x+\frac{2}{3}=-9[/tex]

solve for x

Multiply by 6 both sides

[tex]6(\frac{5}{6}x+\frac{2}{3})=6(-9)[/tex]

[tex]5x+4=-54[/tex]

subtract 4 both sides

[tex]5x=-54-4\\5x=-58[/tex]

divide by 5 both sides

[tex]x=-\frac{58}{5}[/tex]

Answer:

6 (StartFraction 5 over 6 EndFraction x + two-thirds) = negative 9(6)

5 x + 4 = negative 54

5 x = negative 58

Step-by-step explanation:

Answer:

it's A.

Step-by-step explanation:

eqilateral means allsides equal while isosceles means two sides are equal.

Answer:

A

Step-by-step explanation:

Answer:

 n < -1

Step-by-step explanation:

3 < -5n+2n ⇔ 3 < -3n ⇔ -1 > n

Answer:

$12,000

Step-by-step explanation:

Let's say the husband's income was $H, and the Wife's was W.

h + w = 75,000

H = 5w + 15, 000

Substitute that for H.

5w + 15,000 + w = 75,000

6w + 15,000 = 75,000

6w=60,000

w=12,000, So the wife earned $12,000.

Answer:

1548

Step-by-step explanation:

Their are 36 inches in a yard multiply by 43 it’s 1548

Answer:

[tex] - 5 \frac{3}{4} \times \frac{8}{23} = - \frac{23}{4} \times \frac{8}{23} = - 2[/tex]

Answer:

Step-by-step explanation:

hello :

(7-2i)/(4 +3i)

=(7-2i)×(4-3i)/(4 +3i)×(4-3i)

but : (7-2i)×(4-3i) =28-21i-8i+6i²

(7-2i)×(4-3i) = 22-29i   ....i² = -1

(4 +3i)×(4-3i) = 4²-(3i)²...(identity)

                   = 16+9 =25

so :

(7-2i)×(4-3i)/(4 +3i)×(4-3i)

=(22-29i)/25

(7-2i)/(4 +3i) = 22/25 -29/25i

(form : a+ib)

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator.

To divide complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 4 + 3i is 4 - 3i. So, we have ((7 - 2i) * (4 - 3i)) / ((4 + 3i) * (4 - 3i)).

Multiplying the numerators and the denominators, we get (28 - 21i - 8i + 6i^2) / (16 - 12i + 12i - 9i^2).

This simplifies to (28 - 29i - 6) / (16 + 9).

Finally, dividing the real parts and the imaginary parts separately, the quotient is:

Quotient = (22 - 29i) / 25

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Answer:

15

Step-by-step explanation:

Because if you draw a line straight just like the one below the x, it will connect to the 15.

Answer:

18

Step-by-step explanation:

Because you add 9 more angles to the smaller triangle

Answer: you will be able to buy 13.20224719101124 bananas.

Answer:

Carlos is 8

Step-by-step explanation:

I solved this by subtracting 9 from her age, which gets rid of that. 57-9=48

Carlos is 48/6 years old, or 8

Answer:

The answer is 8

Step-by-step explanation:

Answer:

70,000

Step-by-step explanation:

In the population number 1,274,589 for Birmingham, the 7 is in the ten thousands place. Therefore, its value is 70,000.

This problem revolves around understanding of place values in Mathematics. Specifically, we are asked

what is the value of 7

in the population number 1,274,589 for Birmingham. A critical observation is that each position of a digit in a number has a different value. Counting from right (or the ones position) to left, we find that the number 7 is in the ten thousands place. Therefore, the value of 7 in this number is actually 70,000.

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The answer is gonna be 15

Answer:

Domain: -1 ≤ x ≤ 4

Range: -20 ≤ 5f(2x) ≤ 30

Step-by-step explanation:

Inputs of f are between -2 and 8

Input is now 2x, so

-2 ≤ 2x ≤ 8

-1 ≤ x ≤ 4

(Horizontal stretch, factor 1/2)

Range of f is -4 ≤ y ≤ 6

So,

-20 ≤ 5y ≤ 30

(Vertical stretch, factor 5)

The domain of g(x) is [-1, 4].

The  range of g(x) is [-20, 30].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Domain of f(x) = [-2, 8]

Range of f(x) = [-4, 6]

g(x) = 5 f(2x)

Since -2 ≤ x ≤ 8 and -2 ≤ 2x ≤ 8 = -1 ≤ x ≤ 4.

The domain of g(x) = [-1, 4]

Now,

The range of g(x) = [-20, 30]

Since -4 ≤ y ≤ 6,

5 x (-4) ≤ 5y ≤ 5 x 6

-20 ≤ 5y ≤ 30

Thus,

The domain and range of g(x) are

[-1, 4] and  [-20, 30].

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Answer:

[tex]t \geqslant 49[/tex]

Step-by-step explanation:

If Thomas earned $49 OR more, therefore he could have earned either $49 or greater. Please mark brainliest! : )

The inequality that describes the situation is t >= 49. This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.

The inequality that describes the situation is t >= 49.

This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.

For example, if Thomas earned $49, the inequality is true. If Thomas earned more than $49, the inequality is also true.

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Answer:

Geometric with common ration of 4/3

Step-by-step explanation:

12/9=4/3

16/12=4/3

To find the variance of the weights from the given standard deviation of 11.6118 kg, you square the value of the standard deviation, resulting in a variance of 134.9143 kg^2.

The question pertains to finding the variance of the weights from a given standard deviation. The standard deviation provided is 11.6118 kg. Variance is calculated as the square of the standard deviation, which helps in understanding the dispersion of a dataset relative to its mean. To calculate the variance, you square the value of the standard deviation.

Variance = Standard Deviation2

Thus, Variance = (11.6118 kg)2 = 134.9143 kg2. Therefore, the variance of their weights is 134.9143 square kilograms, rounded to four decimal places as required.

Answer:

Step-by-step explanation:

y intercept is 3

y - 4 = 3 ( x - 4)

y - 4 = 3x - 12

y < 3x - 8

not equal to because the line is dashed.

not greater than because the shading is below the line

Answer:

Step-by-step explanation:

Since the rectangle sits within the larger circle, let's look at it this way:

Area of Shaded Region = Area of Circle - Area of Rectangle

OR

(X) =( pi * r^2 ) - (rectangle length * rectangle width)

Now we fill in the numbers where we know the numbers:

(X) = (pi * (12 cm)^2) - (3cm * 10cm)

(X) = (pi * 144cm^2) - (30 cm^2)

(X) = 144pi - 30

(X) = 452.39 - 30

(X) = 422.39 cm^2

Take the area of the circle and subtract that with the area of the rectangle.

Area of circle= pi*r^2

Area of circle= pi*12^2

Area of circle=144pi

Area of circle= 452.16 cm^2

Area of rectangle: b*h

Area of rectangle: 10*3

Area of rectangle: 30 cm^3

452.16-30=422.16

So the area of the shaded region is 422.16 cm^2

Hope this helped!