4-3 practice solving quadratic equations by factoring

The solution to the system of equations is (1, 8).

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

y-x=7 y=3x+5

To find the solution to the system of equations y - x = 7 and y = 3x + 5, we can substitute the second equation into the first equation to eliminate y:

y - x = 7

y = 3x + 5

Substituting y = 3x + 5 into the first equation:

3x + 5 - x = 7

2x = 2

x = 1

Now that we have found x = 1, we can substitute it back into either equation to find y:

y = 3x + 5

y = 3 * 1 + 5

y = 8

So the solution to the system is (x, y) = (1, 8).

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The probability of rolling a total score greater than or equal to 9 conditional upon rolling a 5 with the first dice is 0.5.

Probability is defined as the ratio between the number of favorable outcomes to the all possible outcomes. The probability of an event A can be computed as:

P(A) = n(A) / n(S)

Where:

n(A) = number of event A can happens

n(S) = total possible outcomes

If two dices are rolling, the number of all possible outcomes is 36. However, in this case, the result of the first die is known, which is 5. Hence, the probability that the total score is greater or equal to 9 is equal to the probability of rolling a 4, a 5, or a 6 with the second dice.

Hence,

P(9 | d1 = 5) = P₂(4, 5, 6)

                   = 3/6 = 1/2 =0.5

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Step-by-step explanation:

1. 605 feet = 7260 inches

  15:7260 = 1:484 = Circle number 2

2. 8/12 = 2/3

    10/15=2/3

   14/21 = 2/3

The correct similarity statement is Circle C, ABC is similar to DEF

3. 2.5/1.5 = 25/15=5/3

    8/4.8=80/48=10/6=5/3

   These 2 statements show that the quadrilaterals are similar.

Similarity statement = Circle 2 = JKML is similar to PQRS

4. ABC is similar to ACE, which is similar to CBE, therefore, the correct answer is Circle 3.

5. Using the similarity of triangle ADB and BDC, 5/y = 3/x = 4/3.

   5/y = 4/3, 15 = 4y, y = 15/4

   3/x = 4/3, 9 = 4x, x = 9/4

 The correct answer is Option 2

6.  Does your diagram mean that Angle PQS and SQR are equal?

7. You can use AA similarity to prove they are equal. (They both have a 72 degree angle, and the opposite angles of the intersection of the lines are equal.

Answer:

  about 7.8 miles

Step-by-step explanation:

You want the straight line distance between Newport and Lakewood, given that Newport is 5 miles north of home, and Lakewood is 6 miles east of home.

The Pythagorean theorem gives the relation between the sides of a right triangle. The geometry of this problem can be modeled by a right triangle with side lengths a=5 and b=6 (miles). Then the hypotenuse of the triangle (c) will be ...

  c² = a² +b²

  c² = 5² +6² = 25 +36 = 61

  c = √61 ≈ 7.81

The straight-line distance between Newport and Lakewood is about 7.8 miles.

We can do it by splitting the coins into 2 piles. A small pile consists of 10 coins, and the other pile consists of 90 coins. Then, flip over all the coins in the small pile.

By picking any 10 coins and make a small pile, we now have 90 coins in the large pile. We do not know where the heads are, yet we do know that there are 10 coins in total, and thus, no matter how many heads there are in the large pile, there is 10 minus this many in small pile.

So, now we know that:

Small pile contains:

- n heads

- 90 – n tails

Large pile contains:

- 10 – n heads

- the balance tails = n tails. Since out of 10 coins, 10 – n are heads, it means the number of tails is 10 – (10 – n) = n tails.

Thus, the large pile has n heads and the small pile has n tails. So, we know that there are always the same number of heads in the large pile as there are tails in small pile, even if we do not know what number that is to be exact. Hence, flip over all the coins in small pile, now we have the same number of heads in both piles.

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Answer:

Step-by-step explanation:

When the graphs are parallel, a system of linear equations cannot have a solution. If  (a₁/a₂) = (b₁/b₂)  (c₁/c₂) there won't be any solution.

When the graphs are on the same line, a system of linear equations has an infinite number of solutions.

Multiple equations in algebra are known as simultaneous equations or systems of equations, and they must be solved simultaneously (i.e., the answer must satisfy every equation in the system). For a system to have a singular solution, the number of equations and unknowns must be equal.

There won't be a solution if (a₁/a₂) = (b₁/b₂)  (c₁/c₂). This type of equation system is known as a pair of inconsistent linear equations. There won't be a solution to the system of equations because the graph's lines will be parallel.

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The number of lattice points that lie on the hyperbola x^2-y^2 are 2 times the number of integers between 0 and the maximum y value.

The coordinates of a point on a graph can be described as integers, also known as lattice points.

To find out how many lattice points are on the hyperbola x^2 - y^2,

we can calculate the number of points that satisfy the equation.

To do this, we can set the equation equal to 0 and solve for x and y. Doing this, we can find that the equation has two solutions:

(x,y) = (sqrt(y^2),y) and (x,y) = (-sqrt(y^2),y).

Since there are two solutions for every y value, this means that the number of lattice points on the hyperbola is equal to twice the number of y values.

Therefore, the number of lattice points on the hyperbola is 2 times the number of integers between 0 and the maximum y value.

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For slope equals to 1/3 the value of k in the line is 3 by slope intercept form.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The equation of the line :

3y - 5 = 1/9 kx

The slope of line is 1/3

3y - 5 = 1/9k x

by slope intercept form

1/9k = 1/3

k = 3

So, for slope equals to 1/3 the value of k in the line is 3 by slope intercept form.

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Answer:

20x - 1/5

Step-by-step explanation:

20x-3/15

20x - 1/5

We can't simplify any more, so the answer is

20x - 1/5

Getting the variable on one side of an equation with a variable on both sides is the first step in solving the equation. The process of adding or subtracting one of the terms from the variable is reversed to achieve this.

What does variable answer mean?

A variable is a quantity that can be altered depending on the mathematical issue. The general letters that are utilized in many algebraic expressions and equations are x, y, and z.

                       A variable, then, is a symbol denoting a number whose value is unknown. as in x + 5 Equals 10, for instance. "X" in this case is a variable.

What is a variable example?

A trait that is measurable and capable of taking on several values is known as a variable. There are many variables, including height, age, wealth, province of birth, academic standing, and kind of dwelling.

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The minimum value for the given linear equation will be 19.

What are linear equations?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

For the minimum value of C=2x+3y

we have to find the area in the graph where given inequalities intersect and that's where C will have minimum value i.e. (5,3)

Hence,

For (5,3)  C=2*5+3*3

C=19

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The area of the circle with one sector area of 412 inches² is

1808.78 inches²

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The whole sector of a circle is 360°.

Now,

One sector area of the circle = 412 inches²

This is,

82° = 412 inches²

Multiply 360/82 on both sides.

360° = 360/82 x 412

360° = 1808.78 inches²

Thus,

The area of the circle is 1808.78 inches²

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Answer:

No

Step-by-step explanation:

because 1600 ÷ 2 = 133.3333333333333

Answer:

(-infinity, 4] U [7,infinity)

Step-by-step explanation:

domain is everywhere where x exists and by inspection of the graph x exists from negative infinity noninclusive to 4 inclusive and 7 inclusive to infinity noninclusive

Answer: The scale of a map represents the relationship between the distance on the map and the actual distance in the real world. To find the scale of a map, you can use the formula:

Scale = actual distance / distance on the map

In this case, the actual distance between the two cities is 24 miles, and the distance on the map is 4 1/2 inches. So, the scale of the map is:

Scale = 24 miles / 4 1/2 inches

If the scale on a different map of the same area is 1 inch = 1 mile, so the distance between the two cities in inches will be the same as the actual distance in miles.

So, the distance between the two cities on the new map will be 24 inches.

Step-by-step explanation:

The following formula may be used to get the 95% confidence interval for the population mean difference between the model 10 and model 9 phones:

The formula to calculate the confidence interval is,

[tex]\rm CI= (X_1 - X_2) \pm t \times \sqrt{\dfrac{s_1^2} { n_1} + \dfrac{s_2^2} { n_2}}[/tex]

We can do this computation using a pooled standard deviation since the sample sizes are comparable and the prerequisites for inference have been satisfied.

The t-distribution table can be used to calculate or compute the critical value t, depending on the confidence level and degrees of freedom used. The critical value is around 1.990 for a 95% confidence level and (40+40-2) = 78 degrees of freedom.

Substituting these values into the formula,

[tex]\rm CI= (14.4 - 12.8) \pm 1.990 \times \sqrt{\dfrac{2.1^2} { 40} + \dfrac{2.3^2} { 40}}\\CI = 1.6 \pm 0.9798[/tex]

The 95% confidence interval for the difference in population means is presented last.

Confidence Interval ≈ (0.6202, 2.5798)

Thus, a 95% confidence level prediction places the difference in battery life between the model 10 and model 9 phones between 0.6202 hours and 2.5798 hours.

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If the layer sum of wxyz equals 2014, then the value of w + x + y + z = 13.

If wxyz is a four-digit positive integer with w ≠ 0, the layer sum of this integer equals wxyz+xyz+yz+z.

We are given the example -

The layer sum of 4089 is 4089+089+89+9 = 4276.

And that the layer sum of wxyz = 2014

Now we will find the values of w, x, y, and z using the given layer sum formula by guessing.

we have, 2014 = wxyz + xyz + yz + z

Here, we can clearly see that we have four z which should equal 4 from 2014. This is possible only when z = 1 or z = 6.

let us consider,

when z = 1, we will have

wxy1  + xy1 + y1 + 1 = 0004

Here, we will have no carryover from the sum of digits in units place, so the next step would be to find the value of y such that we could get 1 as the answer, which is possible only when y = 7 which gives the value of 3y = 21 from which 2 will be carried over.

wx71  + x71 + 71 + 1 = 0014

Now to find the value x such that 2x + 2(carried over) gives 0. This is possible when only when x = 4 which would give us

2x + 2 = 2(4) + 2 = 10 from which 1 will be carried over.

w471  + 471 + 71 + 1 = 0014

Finally, we are given that w ≠ 0 and we know that w cannot be 2 as it will not fit our tailored solution.

So the only possibility is w = 1, also it fits as we add the carried-over 1 to the w=1 to get 2014.

1471  + 471 + 71 + 1 = 2014

Since z = 1 satisfies our answer, the other case of z = 6 would not be possible.

Now, we have w = 1, x = 4, y = 7, z = 1.

Hence, the value of w + x + y + z = 1 + 4 + 7 + 1 = 13.

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The complete question is -

If wxyz is a four-digit positive integer with w ≠ 0, the layer sum of this integer equals wxyz+xyz+yz+z. For example, the layer sum of 4089 is 4089+089+89+9 = 4276. If the layer sum of wxyz equals 2014, what is the value of w + x + y + z?

The equation of line is y = 12x - 28 , where the slope is m = 12 and the y intercept is b = -28

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The time is represented as x = { 0 , 0.5 , 1 , 1.5 }

The depth in feet is represented as y = { -28 , -22 , -16 , -10 }

Now , the slope of the line between the points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -16 - ( -22 ) ) / ( 1 - 0.5 )

On simplifying the equation , we get

Slope m = 6 / 0.5

Slope m = 12

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -16 ) = 12 ( x - 1 )

On simplifying the equation , we get

y + 16 = 12x - 12

Subtracting 16 on both sides of the equation , we get

y = 12x - 28

Hence , the equation of line is y = 12x - 28

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Statistics is the field that issues the collection, company, evaluation, interpretation, and presentation of statistics. In applying records to a systematic, business, or social hassle, it is conventional to start with a statistical populace or a statistical version to be studied. Populations can be numerous agencies of people or objects such as "anybody living in a rustic" or "each atom composing a crystal". facts deals with each component of statistics, consisting of the making plans of information series in phrases of the layout of surveys and experiments.

Whilst census facts can't be amassed, statisticians acquire records with the aid of growing particular test designs and survey samples. representative sampling assures that inferences and conclusions can reasonably expand from the sample to the population as a whole.

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The correct answer exists

A- translation of 4 units up

B - verticals stretch with a scale factor of 2

C - vertical compression with a scale factor if 1/2.

A graph transformation is a method for altering an existing graph or graphed equation to create a different version of the graph that follows. The modification of algebraic equations is a typical form of algebraic issue.

A transformation is a method for changing the two-dimensional position of a polygon or other object on a plane or coordinate system. Two-dimensional figures can move across a plane or coordinate system via mathematical transformations. The shape in two dimensions before any alteration is known as a preimage or inverse image.

Translation, rotation, reflection, and dilation are the four basic forms of transformations. A rotation about any point, a reflection over any line, and a translation along any vector are all possible according to the description of the transformation. These are rigid transformations in which the image is identical to its starting point.

Therefore, the correct answer exists

A- translation of 4 units up

B - verticals stretch with a scale factor of 2

C - vertical compression with a scale factor if 1/2.

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The graph of a quadratic function is called a parabola.

A parabola is a type of graph that is in the shape of a symmetrical "U" or "V", and it can be defined as a set of all points that are equidistant to the focus point F and the directrix.

The graph of a quadratic function is a parabola. A parabola can open upward or downward, depending on the sign of the quadratic term.

A parabola can be either concave up or concave down. A parabola that opens upwards is called an "upward-opening parabola" and a parabola that opens downwards is called a "downward-opening parabola".

It is also commonly referred to as a parabolic curve or a parabolic reflector.

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The parent function for a horizontal line is the identity function, f(x) = x.

The identity function is a type of function that returns the same value that is input into it. This means that the output is always equal to the input. A horizontal line is a line with a constant y-value, no matter what the x-value is. This is the same concept as the identity function, as the output is always the same as the input. Therefore, the parent function for a horizontal line is the identity function, f(x) = x. This is because the output of the identity function will always be the same as the input, which is the same behavior as a horizontal line.

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Answer:

the balancing point is centroid

Step-by-step explanation: In other words, if you made the triangle out of cardboard, and put its centroid on your finger, it would balance.

The opposite sides of a parallelogram are congruent so a is 15.

3a+7a+2a=180 because the sum of the angles in the triangle BCD is 180 degrees.

3a+7a+2a=180

12a=180

a =180/12

a= 15

(I. e) 3a= 3(15)= 45

7a=7(15)=105

2a=2(15) =30

As a result, angle A=angle C (OPP. Angles of a Parallelogram are Equal) = A = B, D = A (OPP. angles of a parallelogram are equal)

In light of this, 7a=c = c = 105.

OPP sides in a parallelogram are parallel and equal, therefore AB is parallel to CD and BD is a transversal; as a result, angle d=2a (alternative internal angles are equal) translates to d=30.

as well as b=3a (alternative interior angles are equal) resulting in b=45

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We can utilise the laws of cosines to find the missing side of a scalane triangle c2 = a2 + b2 - 2ab cos(c),

A scalene triangle is a type of triangle in which all the three sides have different lengths.

A triangle with three uneven sides is known as a scalene triangle. Because there are differences between the three sides, it follows that there are likewise differences between the three angles. It is one of three different kinds of triangles that may be identified by the characteristics of their sides. So, a triangle is said to be scalene when none of its sides are equal.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. However, the sum of all the internal angles of the scalene triangle is unaffected by the various measurements. Scalene triangles satisfy the angle sum property of triangles because the sum of their three internal angles is always 180 degrees.

To determine a scalene triangle's missing side, we can utilise the laws of cosines. The equation is: c2 = a2 + b2 - 2ab cos(c), where c is the angle across from the third side.

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