Let's Create
Fill in the blank with the value that will make the equation true.

1) __+2/3= -1/4
2) __-3/4= -7/12
3) __÷3/4= -2
4) __÷0.04=800
5) (____)(5.6)= -6.72

Let's Analyze
Fill in the blank with the value that will make the equation true.

1) 1/4+___=7/12
2) 5/8-___= -3/8
3) 1/3÷___= 1/9
4) (2.1)(____)=0.63
5)_____-0.98= -7.65
​

The miles that can be travelled in the car on $30 gasoline is 240 miles (option A).

The first step is to determine the total gallons in the car. The total gallons in the car can be determined by dividing the total value of the gasoline the car by the cost per gallon. Division is the process of determining the quotient of two or more numbers.

Total gallons = total value of gasoline in the car / cost per gallon

$30 / $2.50 = 12 gallons

The next step is to determine the total miles that the car can travel using the gallons available. To determine the total miles, multiply the total gallons by the number of miles that that one gallon can cover.

Total miles = miles one gallon can cover x total gallons in the car

12 x 20 = 240 miles

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Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

Answer:

in 20 miles she would have taken her 100 minutes (or 1 hour and 40 mins)

Step-by-step explanation:

Divide 10 by 2 to see how many mins its takes to travel 1 mile which is 5 mins, then multiply 20 by 5 to get 100 minutes

2:10

1:5

2.5/1

your welcome

The value of the exponent given as 24 - (5 + 3)^2 + 4 × 2^3 is -8.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value given will be expressed thus:

= 24 - (5 + 3)^2 + 4 × 2^3

= 24 - (8)² + 4 × 8

= 24 - 64 + 32

= -8

The value is -8.

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Answer:

11.6 lbs

Step-by-step explanation:

The dimensiοns οf the pοster are apprοximately 13.05 inches by 8.05 inches.

Algebra is a branch οf mathematics that deals with mathematical symbοls and the rules fοr manipulating these symbοls. It invοlves using letters and symbοls tο represent numbers and quantities in equatiοns and expressiοns, and manipulating these equatiοns and expressiοns tο find sοlutiοns tο prοblems.

Let's start by assigning variables tο represent the length and width οf the pοster. Let's use "L" fοr length and "W" fοr width.

Frοm the prοblem statement, we knοw that:

L = (1/2)W + 9 (since the length is 9 mοre inches than half the width)

We alsο knοw that the area οf the pοster is 104 square inches:

L × W = 104

Nοw we can use substitutiοn tο sοlve fοr οne οf the variables in terms οf the οther. Let's sοlve fοr L in terms οf W by substituting the first equatiοn intο the secοnd equatiοn:

((1/2)W + 9) × W = 104

Simplifying this equatiοn gives:

(1/2)W²+ 9W - 104 = 0

Nοw we can sοlve fοr W using the quadratic fοrmula:

W = (-9 ± √(9² - 4 × (1/2)(-104))) / (2(1/2))

W = (-9 ± √(9² + 208)) / 2

W = (-9 ± √(433)) / 2

We can discard the negative rοοt since we're lοοking fοr a pοsitive value fοr W:

W = (-9 + √(433)) / 2

W ≈ 8.05

Nοw that we knοw the width, we can use the first equatiοn tο find the length:

L = (1/2)W + 9

L = (1/2) × 8.05 + 9

L ≈ 13.05

Therefοre, the dimensiοns οf the pοster are apprοximately 13.05 inches by 8.05 inches.

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Answer:

\(\sf x=4\)

Step-by-step explanation:

\(\sf 5 - 3(2x - 7)=12 - 5(x - 2)\)

To get rid of the parentheses, we'll apply the distributive property. Staring with the left side, multiply -3 by (2x-7).

\(\sf 5 - 6x+21=12 - 5(x - 2)\)

5+ 21= 26

\(\sf 26 - 6x=12 - 5(x - 2)\)

Now, let's do the same thing to the right side. Multiply -5 by (x-2) »12−5x+10, than add 12+ 10 = 22 .

\(\sf 26 - 6x=22 - 5x\)

Combine like terms.

\(\sf 26 - x=22\)

Subtract 26 from both sides.

\( \sf - x= - 4\)

Multiply both sides by -1.

\(\sf x=4\)

Answer:

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

From the given expression |3n|-7, the statement that correctly describes this expression is 7 subtracted from the absolute value of three times a number.

Hence, the correct option is C.

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Answer:

The equation of the line is y = - 1/2 x - 6

Step-by-step explanation:

The equations of parallel lines have the same slopes and different y-intercepts

The form of the linear equation is y = m x + b, where

∵ The given equation is y = -1/2 x - 4

→ By comparing it by the form of the equation above

∴ m = -1/2

∵ Parallel lines have the same slope

∴ The slope of the line = -1/2

→ Substitute it in the form of the equation above

∴ y = - 1/2 x + b

∵ The line passes through the point (-2, -5)

→ To find b substitute x by -2 and y by -5

∴ -5 = -1/2 (-2) + b

∴ -5 = 1 + b

→ Subtract 1 from both sides

∴ -5 - 1 = 1 - 1 + b

∴ -6 = b

→ Substitute the value of b in the equation above

∴ y = - 1/2 x + (-6)

∴ y = - 1/2 x - 6

The equation of the line is y = - 1/2 x - 6

Ab=3.14xRadious to the power of 2

then to the area of the rectange you do B x H = YOUR ANSWER

Bring down the next digit 6 to show there are 2 tens and 6 ones that still need to be divided.

This method of dividing is called the long division method.

In this, we divide the dividend with the divisor and get a quotient and a remainder.

The steps involved are given below :

1. Take the dividend's first digit from the left. Determine whether this digit is bigger than or equal to the divisor.

2. Then divide it by the divisor and write the result as the quotient on top.

3. Subtract the result from the digit and record the difference in the box below.

4. Reduce the dividend by the following digit (if present).

5. Repeat the above steps.

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Answer:

please the question is not complete

The phrase "y is a function of x" means that the value of y depends upon the value of x, so: y can be written in terms of x (e.g. y = 3x ). If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s .

Answer:

x=33

Step-by-step explanation:

If you didn't know all of the angles in a triangle add up to equal 180

We are given to angles, 90 (the square indicates that its a right angle which is equal to 90) and 57

So to find the missing anlge we subtract the given angles from 180

180-90=90

90-57=33

therefore x=33

Answer:

152 units

Step-by-step explanation:

Two sides of the rectangle are 27 units long and the other two sides are 49 units wide. You just add all the numbers up (27+27+49+49). When you do that, you get 152. I hope this helps!

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Explanation:

The fraction 2/6 is the probability of getting a yellow marble because there are 2 yellow out of 3+1+2 = 6 total. The fraction 2/6 reduces to 1/3.

Once the marble selected is replaced, the bag will have the same exact number of each marble inside. Nothing has changed. Therefore, the probability of getting another yellow marble is also 1/3.

The probability of getting two yellow marbles in a row is (1/3)*(1/3) = 1/9

The fraction 1/9 is approximately equal to 0.111 which converts to 11.1%

Step-by-step explanation:

hope u understand. Answer is 12.56 inches ^2

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

The least squares approximating line y=zo + zix for each of the following sets of data points is (1, 1), (3, 2), (4, 3), (6, 4)

This line is determined by minimizing the distance between the data points and the line. The method of least squares is used in many areas, including regression analysis and trend analysis.

To find the least squares approximating line for a set of data points, you need to use the following formula:

=> y = b0 + b1x,

where b0 is the y-intercept and b1 is the slope of the line.

You can use this formula to find the values of b0 and b1 that minimize the difference between the data points and the line.

For example, let's take a look at the first set of data points (1, 1), (3, 2), (4, 3), (6, 4). To find the least squares approximating line, we need to calculate the values of b0 and b1.

This can be done by using a mathematical formula that involves finding the sum of the squares of the differences between the data points and the line.

Therefore, option (a) is correct.

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Answer:

It will be negative

Step-by-step explanation:

For example 2+(-5)= would equal -3 because if you plot it on a number line and go 2 spaces up but then go down -5 times you will land on -3.

Hope this helps :)

Answer:

True

When you add two negative numbers the sum is always negative ex.

When you add two numbers with different signs get the difference and get the sign by the larger absolute value ex.

Step-by-step explanation:

Part a: total number of boxes carried by the forklift = 60.

Part b: Total weight carried by forklift is "less than" 3000 pounds.

Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols  >, <, ≤ or ≥. or indicate that the two expressions in an inequality are not always equal.

Given data:

in equality formed are:

x + y ≤ 60 number .....eq1

45x + 70y ≤ 3000 pounds ...eq 2

Part a: total number of boxes carried by the forklift = 60.

Part b: Total weight carried by forklift is "less than" 3000 pounds.

Part c: inequality for number of boxes carried by the forklift.

From eq 1, x + y ≤ 60

Part d:  inequality for amount of weight carried by the forklift.

From eq 2;  x + y ≤ 60

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Answer:

(1,2) and (x-2)-3 should be on the graph

Step-by-step explanation:

Answer:

16 % points

Step-by-step explanation:

From the table   1963-1972   is 58 %

                          2003 - 2013 is 42%

58 - 42 =  16 percentage points

Answer:

-6.87

Consider the opposite symbol

(Negative and Positive)

Answer:

Step-by-step explanation:

1.666666667

Answer:

1. 3-5

2. 5-3

3. 3-5

4. 5-3

Step-by-step explanation:

This is simple! Just get rid of the parenthesis for each of the expressions shown.

3 + (-5)

the plus sign is next to the negative which is in the parenthesis. Negative times positive is equal to negative. The expression then becomes

3 - 5

Now do the same for the rest!

For things like 3 and 4, you can just flip it like 3-5 and 5-3 because it will all equal the same :]

Hope this helps !!

-Ketifa

Answer:

Step-by-step explanation:

You want a transformation that maps figure P in the 3rd quadrant to figure Q in the second quadrant.

The figures have the same orientation (sequence of angles and side lengths), so reflection is not needed as part of the transformation.

The shorter mid-length side in Figure P has a slope of -1, and the corresponding side in Figure Q has a slope of +1. This can be the result of a 90° clockwise rotation about the origin.

Rotation 90° CW about the origin will map the right-angle corner from (-7, -7) to (-7, 7).

The right-angle corner in Figure Q is at (-7, 12), so a translation upward after the rotation is required. The amount of that translation is 12-7 = 5 units.

Translation upward by 5 units will map the right angle corner from its rotated position at (-7, 7) to its position in Figure Q at (-7, 12).

The series of transformations could be ...

__

Additional comment

The required transformation can be accomplished in one step by rotation 90° CW about the point (2.5, 2.5).

If Figure P is rotated 90° CW about its right-angle corner, then translation up by 19 units will map it to Figure Q. That is, there are many combinations of rotation and translation that will do the job.