Mathematics High School

## Answers

**Answer 1**

The solution of the equation is 4, 7, 10 and 13

What is a equation?

Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given: y =3x+4

Put x=0

y=4

Put x=1

y= 7

Put x=2

y= 3*2+4

y= 10

Put x=3

y= 13

Hence, the solution are 4, 7, 10 and 13

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## Related Questions

Write an inequality for the situation. all real numbers y that are less than –3 or greater than 18.

### Answers

According to the statement

18

y < -3

y > 18

Combining both:

-3 > y > 18

Write 6 1/4% as a decimal.

### Answers

The decimal is 0.0625

6 1/4 % as decimal

6 1/4 = 6 + 0.25 = 6.25

6 1/4 % =6.25%

6.25/100

= 0.0625

Simplify the expression 6√2

____

√3

A. 2√6

B. 2√3

C.6√2

____

√3

D.6√3

### Answers

6√2 /√3 Rationalize the surd.

(6√2 /√3) * (√3 /√3)

= (6√2*√3) /(√3 *√3)

= 6√6/3

= 2√6

Option A.

Concept maps work because they _______.

### Answers

Showing the relationships among concepts.

Help to tie the relationship between different subject areas.

The hypotenuse of an isosceles triangles measures 10 inches long. What is the length of one leg of the triangle?

### Answers

Let one leg be x. Hypotenuse = 10

x² + x² = 10²

2x² = 10²

2x² = 100

x² = 100/2

x² = 50

x =√50

x =√(25 *2)

x =√25 *√2 = 5√2

x = 5√2≈ 5*1.414 = 7.07

Length of each leg≈ 7.07

The leg sides are or at least one is (10 in.)/√(2) = 10√(2)/2 in. = 5√(2) long.

When solving a word problem, what step should you always do after reading the problem, but prior to writing the equation?

### Answers

Be sure to understand to understand it. And write out the given parameters from the question.

if the principal and the amount of interest for one year are known, the rate of interest of interest can be found

### Answers

For SimpleInterest, I = PRT/100

Time = 1 year.

I = P*R*1/100

100*I = PR

100I / P = R

The formula for the Rate, R = 100I / P.

The following table shows the frequency of outcomes when two distinguishable coins were tossed 4000 times and the uppermost faces were observed. Outcome HH HT TH TT

Frequency 1,100 950 1200 750

what is the relative frequency that the first coin lands with heads up?

### Answers

In probability , 0.8125 is the relative frequency that the first coin lands with heads up.

What is probability explain?

- Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.
- The range of the value is 0 to 1. To forecast how likely occurrences are to occur, probability has been introduced in mathematics.

the frequency of outcomes when two distinguishable coins were tossed

= 4000 times

outcome frequency = 1,100 950 1200 750

relative frequency = frequency of a particular outcome/total no of experiments

= 1100 + 950/ 4000

= 2050/4000

= 0.8125

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So in this case we get:

which can be simplified.

A cafe sells puffs. 5/9 are beef and 1/3 are chicken. The remaining 18 are tuna. Calculate 1. What fraction of the puffs are tuna and 2. How many puffs are there in all. I really need to see the working for this.

### Answers

Let n be the total number of puffs. Now we can write:

Adding the fractional value of n, we get:

Simplifying and rearranging gives us:

Therefore we can simplify to get:

and finally

The fraction of the puff that are tuna is found from:

5/9 + 1/3 + tuna = 1

tuna = 1 - 5/9 - 1/3. LCM = 9

tuna = 9/9 - 5/9 - 3/9 = (9 - 5 - 3)/9 = 1/9

Fraction of tuna = 1/9

Let all the puffs be x. Recall there are 18 tuna

(1/9)x = 18

x/9 = 18

x = 9*18

x = 162

There are 162 puffs in all.

If the player moves the knight from (5, 1) to (6, 3), the translation made is

### Answers

X increases by one

y increases by 2

(5, 1) - > (x + 1, y + 2) -> (6, 3)

A newly married couple took out a 5-year $30,000 loan for their wedding. After 5 years, they paid a total of $32,800 back to the bank. What was the interest rate on the loan?

### Answers

Interest = Future value - Principal

I= $32800 - $30000 = $ 2800

Interest at the end of 5 years. Time = 5 years, Principal = $30000

I = 32800 - 30000 = 2800.

Assuming simple interest.

I = PRT

2800 = 30000*R * 5

30000*R * 5 = 2800

R = 2800 /(30000*5)

R ≈ 0.018667

R ≈ 1.8667 %

Interest ≈ 1.8667% per year.

Which of these figures must be a rectangle? A.) aParallelogram with four congruent sides.

B.) a trapezoid with at least one right angle

C.) a trapezoid with two congruent sides

D.) a Parallelogram with at least one right angle

### Answers

A Parallelogram with at least one right angle

What is rectangle?

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°. Observe the rectangle given below to see its shape, sides and angles.

Properties of a Rectangle

A rectangle is a closed figure which has four sides and the angle formed by adjacent sides is 90°. A rectangle can have a wide range of properties. Some of the important properties of a rectangle are given below.

- A rectangle is a quadrilateral.
- The opposite sides of a rectangle are equal and parallel to each other.
- The interior angle of a rectangle at each vertex is 90°.
- The sum of all interior angles is 360°.
- The diagonals bisect each other.
- The length of the diagonals is equal.
- The length of the diagonals can be obtained using the Pythagoras theorem. The length of the diagonal with sides a and b is, diagonal = √( a2 + b2).
- Since the sides of a rectangle are parallel, it is also called a parallelogram.
- All rectangles are parallelograms but all parallelograms are not rectangles.

A parallelogram have opposite side equal and parallel.

Also, if a parallelogram have one of its angle right angle then it can show the property of rectangle.

Hence, the Parallelogram with at least one right angle can be rectangle.

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Answer: A parallelogram with at least one right angle

Step-by-step explanation:

Is y=2x+5 a function?

### Answers

It is a function... it would not be a function if it is 2x squared

a cashier has a total of 26 bills made up of tens and hundreds the total value is 1610 how many hundreds and tens does she have?

### Answers

Let the tens be x.

Therefore the hundreds will be (26 - x).

Since they both total to 26.x + (26 - x) = 26

10*x + 100*(26 - x) = 1610

10x + 2600 - 100x = 1610

10x - 100x = 1610 - 2600

-90x = -990

x = -990/-90

x = 11.

So the 10s are x =11, the 100s are (26 -11) = 15

11 tens bills and 15 hundred bills.

How many acres are in a rectangular field that measures 2310 ft by 535 ft?

### Answers

Area = 2310 ft * 535 ft = 1 235 850 ft²

43560 ft² = 1 acre.

1 235 850 ft² = 1 235 850/43560≈ 28.371 acres.

State how many tens there are in 5463 than in 3746?

### Answers

There are 162 tens but if you want to be exact, there are 162.7

Tens in 5463 = 5463/10 = 546.3

Tens in 3746 = 3746/10 = 374.6

Many more?

546.3 - 374.6 = 171.7

171.7 more.

A saleswomen sells a dried fruit mixture for $5.7 per pound and nuts for $14.55 per pound. She wants to blend the two to get a 10 pound mixture that she will sell for $9.24 per pound. How much should she use? to get a 10 pound mixture she should use __ lb of fruit mixture and __ lb of nuts.

### Answers

Let the fruit mixture of $5.7 per poundbe for x pounds.

The nut of $14.55 per pound would then be: (10 -x).

Since the total blend of both = 10 pounds,selling for $9.24 per pound.

cost of 1st type + cost of second type = Total cost of blend mixture

5.7*x + 14.55*(10 - x) = 9.24*10

5.7x + 145.5 - 14.55x = 92.4

5.7x - 14.55x = 92.4 - 145.5

-8.85x = -53.1

x = -53.1/-8.85

x = 6

The other will be (10 -x) = 10 - 6 = 4.

She should use 6 lb of fruit mixture and 4 lb of nuts.

A cylindrical water trough has a diameter of 6 feet and a height of 2 feet. It is being filled at the rate of 4 ft^3/min. How fast is the water level rising when the water is 1 foot deep?

### Answers

Volume of Cylinder V =πr²h

diameter = 6 feet, radius = 6/2 = 3 feet

dV/dt = (dV/dh) * (dh/dt)by change rule.

V =πr²h

dV/dh = πr² =π*3² = 9π ft²

dV/dt = 2 ft³/min

dV/dt = (dV/dh) * (dh/dt)

2 ft³/min = 9π ft² * (dh/dt)

9π ft² * (dh/dt) =2 ft³/min

(dh/dt) = (2 ft³/min)/(9π ft²)

(dh/dt) = (2/9π) ft/min

So the water level is rising at (2/9π) ft/min.

An interior designer purchased 4 1/2 yards, 6 2/3 yards and 9 1/4 yards of fabric to make curtains How many yards of fabric did they purchase?

### Answers

Simply add up all.

4 1/2 + 6 2/3 + 9 1/4

(4 + 6 + 9) + 1/2 + 2/3 + 1/4

19 6/12 + 8/12 + 3/12 = (6+8+3)/12 = 17/12

19 17/12

19 1 5/12

19 + 1 5/12

= 20 5/12

20 5/12 yards was purchased.

after 1 second the ball is 76 feet in the air: after 2 seconds it is 144 feet in the air. Find the height of the function. h(x)= ?

### Answers

General equation for height, h

h = ut + 0.5gt^2

at t=1s, h = 76 feet

76 = u*1 + 0.5*a*1^2

76 = u + 0.5a

at t=2s, h = 144 feet

144 = u*2 + 0.5*a*2^2

144 = 2u + 2a

72 = u + a

Subtract 2 equations

0.5a = -4

a = -8

u = 80

So the equation,

h(x) = 80t + 0.5*(-8) t^2

h(x) = 80t - 4t^2

## FAQs

### How many solutions does the equation y 3x 4 have? ›

Answer and Explanation: The equation y=3x−4 y = 3 x − 4 is a linear equation with an **infinite number of solutions** as there is a new value of y every time we change the...

**What ordered pair is a solution of the equation y =- 3x 4? ›**

Hence (x, y) is the notation used to express ordered pairs for the equation y = 3x - 4. The specifice ordered pairs from the values above which satisfy the equation are **(1, -1), (0, -4), (3, 5), and (-2, -10)**.

**What is Y =- 3x 4 in standard form? ›**

Example. Equation: y=3x+4 You must subtract 3x from both sides. The standard form will be **-3x+y=4**.

**What is the y-intercept of Y =- 3x 4? ›**

Answer and Explanation: The x-intercept of y = 3x - 4 is the point (4/3, 0), and the y-intercept of y = 3x - 4 is the point **(0, -4)**.

**What is the answer slope of y 3x 4? ›**

Using the slope-intercept form, the slope is **−3** .

**How do you find a solution to the equation? ›**

Determine whether a number is a solution to an equation.

**Substitute the number for the variable in the equation.** Simplify the expressions on both sides of the equation. Determine whether the resulting equation is true. If it is true, the number is a solution.

**How do you find the ordered pair of solutions of an equation? ›**

To determine if an ordered pair is a solution to a system of two equations, we **substitute the values of the variables into each equation**. If the ordered pair makes both equations true, it is a solution to the system.

**What are the four solutions of the equation 2 3x y 4? ›**

Therefore, **6 , 0 , 0 , - 4 , 3 , - 2 , 9 2 , - 1** are four solution of equation 2 3 x - y = 4 .

**Is Y =- 3x 4 a function? ›**

Some authors define such function as "affine-linear". **y=3x+4 is a linear equation** as all components are linear in terms of x (i.e. the only exponents of x are 0 or 1).

**What is the dependent variable in y 3x 4? ›**

In the linear equation $y = 3x - 4$, the independent variable is the one that can be freely chosen, while the dependent variable is determined by the independent variable. In this case, $x$ is the independent variable, and **$y$** is the dependent variable.

### How do you find all solutions to a system of equations? ›

**How do I solve systems of linear equations by substitution?**

- Isolate one of the two variables in one of the equations.
- Substitute the expression that is equal to the isolated variable from Step 1 into the other equation. ...
- Solve the linear equation for the remaining variable.

**How many solutions does the equation y 0 and y =- 5 have? ›**

Explanation: Since, given variable y has different values so, The pair of equations y=0 and y=−5 has **no solution**.

**How many solutions does 3 have? ›**

When a problem has **infinite solutions**, you'll end up with a statement that's true no matter what. For example: 3=3 This is true because we know 3 equals 3, and there's no variable in sight. Therefore we can conclude that the problem has infinite solutions.

**How many solutions can a equation have? ›**

An equation can have **infinitely many solutions** when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

**Which equation has no solution? ›**

The last type of equation is known as a contradiction, which is also known as a No Solution Equation. This type of equation is never true, no matter what we replace the variable with. As an example, consider **3x + 5 = 3x - 5**. This equation has no solution.

**What is the slope y-intercept for y 3x 4? ›**

Answer: The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is −3 .

**What is the slope and y-intercept of 3x 4? ›**

Answer and Explanation: We write the slope-intercept form for a line with slope m and the y-intercept c as the equation y=mx+c y = m x + c . Thus, **the slope is 3 and the y-intercept is −4 units**.

**What are the slope and the y-intercept of the line y 3x 4? ›**

y=3x+4 Geometric figure: Straight Line **Slope = 6.000/2.000 = 3.000 x-intercept = 4/-3 = -1.33333 y-intercept = 4/1 = 4.00000** Rearrange: Rearrange the equation by subtracting what is ...

**What is the slope of y 3x 4 that is perpendicular? ›**

The slope of y = –3x – 4 is **–3**. The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite: in this case to 3. Then find the reciprocal by switching the denominator and numerator to get 1/3; therefore the slope of the perpendicular line is 1/3.

**How do you find the y-intercept? ›**

Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y. On a graph, the y-intercept can be found by **finding the value of y when x=0**. This is the point at which the graph crosses through the y-axis.

### What is the slope of 2y 3x =- 4? ›

Hence, the slope of the line parallel to the line 2y−3x=4 is **m=23**.

**What is the domain and range of y 3x 4? ›**

Summary: The range of the function y = 3x -4 when domain is {-3,-1,4}, is **{-13, -7, 8}**.

**How do you solve for y in inverse? ›**

How do you find the inverse of a function? To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

**What are the three 3 possible solutions to an equation? ›**

There are three ways to solve systems of linear equations: **substitution, elimination, and graphing**.

**What are the 3 types of solutions you can have in an equation? ›**

**They are:**

- Unique Solution.
- No Solution.
- Infinitely Many Solutions.

**What are the 4 steps to solving an equation? ›**

We have 4 ways of solving one-step equations: **Adding, Substracting, multiplication and division**.

**What is the ordered pair calculator? ›**

An 'Ordered Pair Calculator' is **a free online tool that calculates the ordered pairs for a given equation**. In this calculator, you can enter the equation and the ordered pairs will be calculated within a few seconds.

**How many solutions is an ordered pair? ›**

Ordered pairs (x,y) that work in both equations are called solutions to the system of equations. They represent the intersection points of the two lines. Thus a system has one solution, no solutions, or infinitely many solutions. **If an ordered pair is a solution, it must work in both equations**.

**Which ordered pair is a solution of the equation 3x 4y 14? ›**

Instant Text Answer

y = (3/4)(0) + 7/2 y = 0 + 7/2 y = 7/2 So, one ordered pair is **(0, 7/2)**.

**Which is a solution of 3x 4y 2? ›**

Thus, **(x = 2, y = -1)** is the solution.

### What are two solutions for 3x 4y 7? ›

Therefore, **1 , 1 , 2 , 1 4 , - 3 , 4 , - 1 , 5 2** are four solution of equation 3 x + 4 y = 7 .

**What are two solutions for the equation 3x 4y 12? ›**

Therefore, **0 , 3 , 4 , 0** are two solution of equation.

**What is the graph of the function y 3x 4? ›**

Your graph will be **a straight line**. You can set values for x and evaluate the correspondent y to find the point(s) used to plot your line.

**Is a function a solution of an equation? ›**

A solution is **a function y=f(x) that satisfies the differential equation when f and its derivatives are substituted into the equation**. The order of a differential equation is the highest order of any derivative of the unknown function that appears in the equation.

**How to find the slope? ›**

Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: **Slope =riserun** Slope = rise run .

**What are dependent equations in 3 variables? ›**

Systems of equations in three variables that are dependent **could result from three identical planes, three planes intersecting at a line, or two identical planes that intersect the third on a line**.

**What is the equation of dependent variable? ›**

The dependent variable is the one that depends on the value of some other number. If, say, **y = x+3**, then the value y can have depends on what the value of x is. Another way to put it is the dependent variable is the output value and the independent variable is the input value.

**What are the dependent equations? ›**

A dependent system of equations is **when the same line is written in two different forms so that there are infinite solutions**. These two situations occur when trying to solve for a system of equations.

**What is standard form math 8th grade? ›**

The standard form for linear equations in two variables is **Ax+By=C**. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

**What does standard form mean in 7th grade math? ›**

**Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10**, is said to be in standard form.

### What are the three forms in math? ›

There are three major forms of linear equations: **point-slope form, standard form, and slope-intercept form**.

**How do you know how many solutions a quadratic equation will have? ›**

**If b ^{2} - 4ac is positive (>0) then we have 2 solutions**. If b

^{2}- 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/2a. So x = -b/2a, giving only one solution. Lastly, if b

^{2}- 4ac is less than 0 we have no solutions.

**How many solutions does y 2x 4 have? ›**

Use the x x and y y values to form the ordered pair. These are **three** possible solutions to the equation.

**How do you know how many solutions a polynomial has? ›**

Recall from the Quadratic Functions chapter, that every quadratic equation has two solutions. The degree of a quadratic equation is 2, thus leading us towards the notion that it has 2 solutions. **The degree will always tell us the maximum number of solutions a polynomial has**.

**How many solutions do exponential equations have? ›**

Exponential functions have a one-to-one property which means each input, x, value gives one unique output, y, value. Each x gives only one y, and each y gives only one x. This means exponential equations have **only one solution**.

**What are the three possible number of solutions for a quadratic equation? ›**

As we have seen, there can be **0, 1, or 2** solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b^{2} - 4ac), is positive, negative, or zero.

**What are the solutions of this quadratic equation? ›**

The solutions to the quadratic equation are **the values of the unknown variable x, which satisfy the equation**. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

**What is a solution in a polynomial? ›**

A solution of a polynomial system is **a tuple of values of (x _{1}, ..., x_{m}) that satisfies all equations of the polynomial system**. The solutions are sought in the complex numbers, or more generally in an algebraically closed field containing the coefficients.

**How many solutions are there in two variables? ›**

Further, a linear equation in two variables has **infinitely many solutions**. The graph of every linear equation in two variables is a straight line and every point on the graph (straight line) represents a solution of the linear equation.