What is the correct algebraic expression for the phrase
15 miles less than Devra biked

(x^2  - 5x -  14 = 0) has the solution set as F: "x = 7 , -2" .

Solve the equation by factorization method.

x^2 - 5x - 14 = 0

x^2 -  7.x + 2.x - 14 = 0

taking x common from the frist two terms and +2 common from the last two terms.

[ x(x - 7 ) PLUS (+) 2 (x -7) ] = 0

[( x - 7) . (x + 2)] = 0

x - 7 = 0 , &   x + 2  =0

x = 7  , & x = -2

Thus the solution is x = 7 and x = -2.

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Answer:

-9

Step-by-step explanation:

-7x = 63

Divide both sides by -7.

-7x/-7 = 63/-7

Simplify.

x = -9

Follow directions and input only the -9

[tex]-7x=63[/tex]

1. Divide both sides by -7.

[tex]\frac{-7x}{-7} = \frac{63}{-7}[/tex]

[tex]x=-9[/tex]

-9 would be your answer.

If n=2k  (means even value) is always possible to dissect a rectangle into n right triangles.

Dissect means to separate a dead person's or animal's body into its component for closer examination.

Dissect is to consider or talk about the specifics of something in order to fully comprehend it.

To dissect is to separate into components.

For n=2, it is easy to show that it is possible (just insert the diagonal).

For n=3, it is not possible ( I tried on some examples but not able to do it).

For n=4, it is possible first make two rectangle from the original rectangle then use the case of n=2

So if n=2k  (means even) then it is always possible.

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The smaller of the numbers, given the ratio and the larger number, can be found to be 393.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

The ratio is given such that it is 5 : 3 . What this means is that for every 3 of the smaller number, there is 5 of the larger number.

Given that the larger number is 655 therefore, the smaller number would be:

= ( Ratio of smaller number x Larger number ) / Ratio of larger number

Ratio of smaller number = 3

Ratio of larger number = 5

Larger number = 655

The smaller number is:

= ( 3 x 655 ) / 5

= 1, 965 / 5

= 393

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So, on solving the provided question we can say  their balloon payment will be $380,040.19.

A balloon loan is a type of loan arrangement where only a portion of the original balance is repaid during the course of the loan's relatively short repayment term. When only a fraction of the initial debt is repaid during the duration of the loan's relatively short repayment term, the loan is referred to as a "balloon loan."

the monthly fixed payment. there is a formula

Pmt = (A * i * (1 + i)ⁿ) / ((1 + i)ⁿ - 1)

Pmt - monthly payment;

A is  Loan amount;

i is periodic interest rate; and

n is  number of periods.

Mortgage amount: $425,500

[tex]Term in years: 8 years[/tex]

Interest rate: 6.55%

Amortization period is - 30 years.

pmt=(425500*6.55*(1+6.55)^12)/((1+6.55)^12-1)

Balloon payment=[tex]$380,301.82.[/tex]

Total interest paid[tex]$211,630.52.[/tex]

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Always use alpha=0.05 since it's the most commonly used one. Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H0.

When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha. Generally speaking, you should reject the null hypothesis less frequently when there is a greater risk of doing so, which happens as you lower the significance level.

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According to the concept of probability, the sample space for the experiment is explained below.

The term probability in math is called as the occurrence of a random event and the sample space is defined as a collection or a set of possible outcomes of a random experiment.

Here we have know that the same space of this experiment is the possible outcomes of selecting two out of the three breakfast.  

Here let us consider that the sample space is B

And the the sample space is written as.

=> {(cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal)}

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There is a 0.2209 = 22.09% probability that three students will arrive during a randomly chosen office hour.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

According to our question-

The number of successes is x.

The Euler number is e = 2.71828.

is the average over the specified range.

When a professor of statistics sets an office hour for student assistance, she discovers that on average, 3.3 students show up.

It follows that

Determine the likelihood that three students will arrive during a randomly chosen office hour.

So, P(X = 3).

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Step-by-step explanation:

you know how equations are transformed ?

by applying the same operation on both sides of the equation (so that the equality remains).

x + 38 = 79

to get "x = ...", we need to eliminate the "+ 38" in the x side.

clearly we need to subtract 38.

again, whatever e do, we have to do on both sides, otherwise the equality relation is destroyed.

so,

x + 38 - 38 = 79 - 38

x = 41

that is the height of the avocado tree : 41 in.

it is 38 in shorter than 79 in (the fig tree).

that's all that is to this. it is a really simple method.

the same applies to any operation you want to do (+, -, ×, ÷, ...).

The missing piece of information in the proof is that m ∠ DOA and m ∠ BOC are vertical opposite angles.

According to the equality's subtraction property, equality is unaffected by removing the same amount from both sides of an equation. When the same quantity or value is removed from both sides of an equation, the resultant difference is also identical on both sides.

Both the equality's addition and subtraction properties are related. The same integer added to or subtracted from both sides of an equation maintains equality on both sides.

To prove that m ∠ BOC = 90°.

Given that m ∠ AOB exists a right angle triangle.

Therefore; m ∠ BOC must also be equivalent to 90°.

Since m ∠ BOC and m ∠ AOB are right angles, it follows that m ∠ DOA and m ∠ BOC are also vertical opposing angles and, as such, are equal.

So, the fact that m ∠ DOA and m ∠ BOC are vertical opposing angles is the crucial piece of information missing from the proof.

The complete question is:

Given: AOB is a right angle

Prove: m BOC = 90°

Since AOB is a right angle, it is 90°. AOB is supplementary to BOC,

so m AOB + m BOC = 180°. By the substitution property of equality,

90 + m BOC = 180°. Applying the subtraction property of equality,

m BOC = 90%. What statement is missing from the proof?

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Answer:

sorry, No answer I have no idea for this

Answer:

Step-by-step explanation:

As you see in the X coloum they have already given you the number for x. So what you do is plug in -2 for x. so it would be 6(-2)+3y=18. it will be -12+3y=18. Put like terms on the same side. Meaning you would add 12 to both sides. it will end up being 3y=30. Divide both sides by 3 so the variable can stay alone and that would mean y=10. So when x=-2, y=10. You can always plus it back in the equation to double check if the answer is right. 6(-2)+3(10)=18. Do the same thing for the remaining ones and youre all set!!! Hope th

Step-by-step explanation:

5^(2x-1) = 1/125

5^2x = 5/125 => (1/25) = 5^2x

5^-2=5^2x

equating both sides

-2=2x

X=-1

hope this helps you.

The point that is equidistant of the points (7, 3) and (13, -1) is (3.33, -9)

Remember the distance between two points (x₁, y₁) and (x₂, y₂) can be written as:

distance = √( (x₂ - x₁)² + ( y₂ -  y₁)²)

We want to find a point (x, y), that lies on the line y = -9 that is equidistant to  (7, 3) and (13, -1)

We can rewrite our point as (x, -9)

And the distances to the given points are:

distance = √( (x - 7)² + ( -9 - 3)²)

distance = √( (x - 13)² + ( -9 + 1)²)

These distances must be equal, (that is what equidistant means) so we can write:

√( (x - 7)² + ( -9 - 3)²) = √( (x - 13)² + ( -9 + 1)²)

Now we can remove the square root and simplify the equation:

(x - 7)² + ( -9 - 3)² =  (x - 13)² + ( -9 + 1)²

(x - 7)² + 144 = (x - 13)² + 64

x^2 - 14x + 49 + 144 = x^2 - 26x + 169 + 64

-14x + 26x = 169 + 64 - 49 - 144

12x = 40

x = 40/12

x = 3.33

The point is (3.33, -9)

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The FG slope is 1/5 and the HJ slope is -2. Because slopes are not connected to one another, they are neither parallel nor perpendicular.

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). A slope is the steepness of a hill. The same is true for a line's steepness. The slope is defined as the ratio of the vertical change between two places, known as the rise, to the horizontal change between those same two points, known as the run.

Here,

F(3, 1), G( 8, 2), H(2, 4), and J(1, 6)

a. FG=2-1/8-3

=1/5

HJ=6-4/1-2

=-2

b. Since slopes are not related to each other it is neither parallel nor perpendicular.

The slope of FG is 1/5 and slope of HJ is -2. Since slopes are not related to each other it is neither parallel nor perpendicular.

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On solving the provided question, we can say that a function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution. The solution provides the list's range.

A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).

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The correct expression for the given error interval is; 12.5 cm ≤ l ≤ 13.4

Error intervals are defined as the limits of accuracy when a number has been rounded or truncated. These error intervals are the range of possible values that a number could have been before it was rounded or truncated.

Now, we can also say that Error interval is the range of values (between the upper and lower bounds) in which the precise value could possibly be.

Now, since the precise value is given as 13 cm after approximation to the nearest centimeter, then the lower bound will be 12.5 because it is the lowest number that can be approximated to 13. Meanwhile the upper bound will be 13.4 cm as it is the largest values that can be approximated to 13 cm. Thus, the inequality is;

12.5 cm ≤ l ≤ 13.4

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The third side of the right angle triangle is 5 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, using Pythagoras's theorem,

6² - (√11)² = b²

36 - 11 = b²

b² = 25

square root both sides of the equation

b = √25

b = 5 units

Therefore.

third side = 5 units.

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Answer:

Option 2

Step-by-step explanation:

The data is not periodic, so the model is not is not a trigonometric equation.

Setting [tex]x=0[/tex] eliminates Option 1.

Therefore, Option 2 is the only remaining option

Answer:

16x feet

Step-by-step explanation:

A scale of 1/4" = 4' means that every 1/4 inch on the drawing or map represents 4 feet in the actual measurement. To find the actual length of a line on the drawing or map, you need to multiply the length of the line in inches on the drawing by the denominator of the scale, and then divide by the numerator of the scale.

The formula is:

Actual length = (length on the drawing or map x scale denominator) / scale numerator.

In this case, the length on the drawing or map is x inches, and the scale is 1/4" = 4'.

So the actual length is: (x inches x 4') / 1/4" = 16x feet

Therefore, the actual length of the line on the drawing or map is 16x feet.

The location on negative integers will be on left side of zero.

A number system is defined as a system of writing to express numbers.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

On a number line the integers were represented.

Integers are collect of positive numbers, negative numbers and zero.

On the right side of zero the number are positive 1,2,3..

To the left side of zero there are negative integers -1,-2,-3...

Fom left to right the value of numbers be increases.

Hence, the location on negative integers will be on left side of zero.

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Answer:

9.68

Step-by-step explanation:

x*(x-4)=55; x approximately equals 9.68

Answer:

[tex]x=16y^2-5[/tex]

Step-by-step explanation:

Lets solve for x.

[tex]\frac{\sqrt{x+5} }{4} =y[/tex]

Multiply both sides of the equation by 4.

[tex]\sqrt{x+5}=4y[/tex]

Eliminate the square root on the left side raising both sides of the equation to the power of 2.

[tex]\sqrt{x+5}^2=(4y)^2[/tex]

The square root and the exponent on the left side cancel out leaving us with

[tex]x+5=(4y)^2[/tex]

Distribute the exponent on the right side.

[tex]x+5=4^2y^2[/tex]

Simplify.

[tex]x+5=16y^2[/tex]

Subtract 5 from both sides.

[tex]x=16y^2-5[/tex]

The equation of the line is y = -5/2x + 5.

1. We know that the equation of a straight line is given by y = mx + c, where m is the slope of the line and c is the y-intercept.

2. We need to find the slope of line l. To find the slope, we can use the formula: m = (y2-y1)/(x2-x1). In this case, we have y2 = 1, y1 = 5, x2 = 2, and x1 = 0. Therefore, m = (1-5)/(2-0) = -4/2 = -2.

3. We now have the slope of line l, so we can find the equation of the line which is parallel to l and which passes through the point (3,0). To do this, we can use the formula y = mx + c, where m is the slope of the line and c is the y-intercept.

4. In this case, m = -2 and c is the y-intercept, which is the point at which the line intersects the y-axis.

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By finding the Greatest Common Factor we can conclude that the possible dimensions of the sports field are a width of 70 yards and a length 9-6d yards.

There are two theories needed to solve the problem:

Dimensions of an object are defined as a measure of length, width, or height extended in a certain direction.

The Greatest Common Factor (GCF) of two or more numbers is the largest number that can be evenly divisible by these numbers.

We can assume that the sports field is a rectangle since we know that:

- the width is at least 50 yards

- the area is (630-420d) yard square

To find the dimension of the sports field, we have to find the GCF of 490 and 210, by enumerating their prime factors and multiplying those factors both numbers have in common.

490 = 2 × 5 × 7 × 7

210 = 2 × 5 × 3 × 7

So the GCF is 2 × 5 × 7 = 70

This GCF depicts one of the dimensions of the sports field, which we denote as d₁.

By substituting the value of one dimension, the value of another dimension (d₂) can be obtained:

Area = d₁ x d₂

d₂ = Area / d₁

    = (630-420d) / 70

    = 9-6d

Thus we can conclude that the possible dimensions of the sports field are width 70 yards and length 9-6d yards.

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Answer:

d. y = 5x/2 + 1, y = 5x/2 + 7

Step-by-step explanation:

Both lines have the same slope (5/2) , so they are parallel.

The height of the tree is 381.05 ft.

The given distance between the man and the tree's base is 220 feet.

Let the tree's height be x feet.

A group of figures known as the trig ratios is characteristic of each angle.

They can be defined when the angle is in a right triangle.

as in this:

Angle's tangent (tan): (opposite leg) divided by (adjacent leg)

Angle's cotangent (cot): (adjacent leg) divided by (opposite leg)

To see the summit of the tree, we must now gaze up at a 60-degree angle.

in the form of a trigonometric ratio,

Tan60= perpendicular/base

√3=x/220 (Tan60 = √3)

x= 220×√3

x= 381.05 ft

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The offered statement states that 42 cups of grain are required to produce three loaves of bread.

As a completely volunteer hot meal service in 1983, Breads & Fishes quickly evolved into a pre-packaged shopping bag contribution program for locals. This nonprofit's first year's budget was $6,500, at which time the pantry supplied food to about 50 homes.

We know we need four times 10 1/2 cups of flour since 12 was 4 times higher than three (3 * 4 = 12).

We only have to calculate 10.5 * 4 = x but then just solve for x.

42 cups - grain (10.5 * 4)

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The complete question is-

10 1/2 cups of flour are needed to make 3 loaves of bread. How many cups are needed for 12?

Answer: 126 marbles

Step-by-step explanation:

Let the marbles with Sam be x

so, marbles with Ravi will be 4x

we know total marbles are 630 which means

    x + 4x = 630

      x     =  126

so marbles with Sam & Ravi will be 126 & 504.

To make marbles equal each should have 315 marbles.

So, Ravi has to give 315 - 126 = 189 marbles to Sam.

To calculate the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10, we can use a normal approximation to the binomial distribution.

First, we need to calculate the mean and standard deviation of the proportion of mixed couples in a sample of 200.

The mean is calculated as:

mean = n * p

where n is the sample size (200) and p is the proportion of mixed couples in the population (assumed to be .10).

So: mean = 200 * .10 = 20

The standard deviation is calculated as:

standard deviation = sqrt(n * p * (1-p))

where n is the sample size (200), p is the proportion of mixed couples in the population (assumed to be .10), and sqrt is the square root function.

So: standard deviation = sqrt (200 * .10 * .90) = sqrt (18) = 4.24

We can use the standard normal distribution to calculate this probability. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. We can convert our random variable X to a standard normal variable using the following formula:

Z = (X - mean) / standard deviation

So: Z = (X - 20) / 4.24

To find the probability that X is greater than .10, we can use a standard normal table or calculator to find the probability that Z is greater than (X - 20) / 4.24

This probability is 0.48, so the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10 is 48%.

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The subtraction of the expression 27 g^7 k^3 z^4 - 9 g^2 K^5 z is 18(g⁷k³z⁴ - g²k⁵z)

Algebraic expressions are described as expressions that are known to consist of terms, coefficients, constants, variables and factors.

They are also described as expressions composed of arithmetic operations, such as;

It is also important to note that index forms are mathematical representation of variables or values too large or small in more convenient forms.

From the information given, we have the expression;

27 g^7 k^3 z^4 - 9 g^2 K^5 z

Subtract the coefficient

18(g⁷k³z⁴ - g²k⁵z)

Hence, the value is 18(g⁷k³z⁴ - g²k⁵z)

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