Expand and simplify (y + 3)(y + 7)

Answer:

60 weeks.

Step-by-step explanation:

10 and 12 both are divisible by 60, thus itll be 60 weeks before she visits them both in the same week again

The values of x and y in the system of equations are x = 1 and y = 2

Linear equations are equations that have constant average rates of change.

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

4x + 3y = 10

y - x = 1

Make y the subject in the second equation, by adding x to both sides of the equation

y - x + x = x + 1

This gives

y = x + 1

Substitute y = x + 1 in 4x + 3y = 10

4x + 3(x + 1) = 10

4x + 3x + 3 = 10

Evaluate the like terms

7x = 7

This gives

x = 1

Substitute x = 1 in y = x + 1

y = 1 + 1

Evaluate

y = 2

Hence, the solution for the system of linear equations 4x + 3y = 10 and y - x = 1 are x = 1 and y = 2

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Possible question

Solve for x and y in the following system of equations

y - x = 1

4x + 3y = 10

Answer:

Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.

Midpoint = [(3+5)÷2, (-8+(-2.5))÷2]

= (8÷2, -10.5÷2)

= (4, -5.25)

The value of the equation illustrated as 2(x + 3) is 2x + 6.

In Mathematics, an equation simply illustrates the relationship that the variables have. This can be replaced with letters to express the information.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same values.

In this case, it should be noted that the expression for 2(x + 3) will be:

= 2(x + 3)

Open the bracket

= 2x + 6

The value of the expression is 2x + 6.

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The number which is an irrational number as required to.ve identified among the answer choices given is; Choice B; √19.

What is an irrational number?

An irrational number, as the name implies is any real number that cannot be expressed as the quotient of two integers (fraction). It follows that such a number cannot be expressed , a/b, where a and b are both integers.

On this note, the number which cannot be expressed in such form is; Choice B; √19.

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Answer:

9

Step-by-step explanation:

So we'll need to add both angles to make it equal to the total angle. Then we can find X by solving an equation.

(4x + 12) + (12x - 8) = 148

16x + 4 = 148

16x = 144

x = 9

If a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75

The original price of the item = $825

The off offered by the store = 1/4

The off offered by the coupon = 1/5

Total off = 1/4 + 1/5

= 9/20

Then the selling price = The original price of the item - The original price of the item× (9/20)

= 825 - 825×9/20

= 825-371.25

= $453.75

Hence, if a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75

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Solution :-

2x - 9y = -1

2x = 9y - 1

x = 9y - 1 / 2 _________ (1)

Now, substitute it here!

-4x - 3y = - 19

-4 (9y - 1 /2) - 3y = -19

(-36y + 4 - 6y / 2) = -19

(-42y + 4 / 2) = -19

-42y + 4 = -38

-42y = -38 - 4

-42y = -42

y = 1

Value of x :

Substituting the value of y that is 1 in this equation. x = 9y - 1 / 2

x = 9(1) - 1 / 2

x = 9 - 1 / 2

x = 8 / 2

x = 4

The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The inequality is:

Let the number is x:

-0.96 ≥ 0.3x

0.3x ≤  -0.96

x ≤ -0.96 /0.3

x ≤ -3.2

x ∈ (-∞, -3.2]

As we know, the number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.

The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x

Thus, the number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) is correct.

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Answer:

70 square units

Step-by-step explanation:

Since it is half a big rectangle, (10*14)/2=70

Answer:

7

Step-by-step explanation:4*7=28

Therefore 5*7=35

28:35= 4:5

His grades improved by 2.2 %

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given: Original grades = 75, 85, 90, 90,

100, 75, 80, 100, 90.

And grades after the retake = 85, 85, 100, 90, 100, 85, 80, 100, 90.

So the sum of the original scores = 785.

Thus the percentage can be calculated by 785/ total marks

= 785/ 900 × 100 = 87.2 %

And the sum of the grades after retake= 805

Thus the percentage will become = 805/900 × 100 = 89.4 %

The mean of the first set is 87 and the mean of the second set is 89.

Thus the difference between the two is 2.

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Answer:

number is - 2

Step-by-step explanation:

let the number be n then 7 times the number is 7n and 3 times the number is 3n, so

4 - 7n = 12 - 3n ( add 3n to both sides )

4 - 4n = 12 ( subtract 4 from both sides )

- 4n = 8 ( divide both sides by - 4 )

n = - 2

We can identify vertical lines by seeing if two points that fall on the line have the same x-coordinate.

If they do, then it is a vertical line.

The slope of vertical lines are always undefined.

We're given the following points:

These points have the same x-coordinate, revealing that this is a vertical line. Therefore, it has an undefined slope.

Undefined

If jimmys saving account makes 0.7% interest every month if he puts 200 in the account 2 months ago, then 202.81  is in therenow round to the nearest cent

Percentage, a relative value indicating hundredth parts of any quantity.

Given

jimmys saving account makes 0.7% interest every month.

The initial deposit is 200 in the account

After two months of time, we need to the find the total amount in account.

0.7% is converted to decimal

0.7/100=0.007

So after two months

A is amount after two months

r is rate of interest

t is time period

[tex]A=P(1+r)^{t}[/tex]

=200(1+0.007)²

=200(1.007)²

=202.8

Hence 202.8  is there now in Jimmys savings accout

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The zeros in the equation  y = 2(x+3)(x+3)-1

[tex]x=-\frac{6-\sqrt{2}}{2},-\frac{6+\sqrt{2}}{2}[/tex]

This is further explained below.

2(x+3)(x+3)-1

Set 2(x+3)(x+3)-1 equal to 0 .

2(x+3)(x+3)-1=0

Solve for x.

Simplify [tex]2(x+3)(x+3)-1[/tex]

[tex]$2 x^2+12 x+17=0$[/tex]

Use the quadratic formula to find the solutions.

[tex]\frac{-b \pm \sqrt{b^2-4(a c)}}{2 a}[/tex]

Substitute the values a=2, b=12, and c=17 into the quadratic formula and solve for x.

[tex]\frac{-12 \pm \sqrt{12^2-4 \cdot(2 \cdot 17)}}{2 \cdot 2}[/tex]

Simplify.

[tex]x=\frac{-6 \pm \sqrt{2}}{2}[/tex]

In conclusion, The final answer is the combination of both solutions.

[tex]x=-\frac{6-\sqrt{2}}{2},-\frac{6+\sqrt{2}}{2}[/tex]

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Yes, a triangle that has sides with lengths of 9 feet, 12 feet, and 15 feet is a right-angled triangle

A right-angled triangle can be defined as a type of triangle, having one of its interior angles equivalent to 90 degrees.

The properties of right angled triangles include;

From the information given, we have;

Hypotenuse side = 15 feet

Opposite side = 12 feet

Adjacent side = 9 feet

We can see that the properties of a right-angles triangle submits to the parameters given.

Hence, it is a right-angled triangle

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Answer: Corresponding angles

Step-by-step explanation:

True by the definition of corresponding angles.

Answer:

35/7

Step-by-step explanation:

All of the translations describes the same inclination for a straight line because the they all have a pitch (slope) of 2/5.

Mathematically, the pitch (slope) of a geometric figure or straight line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the information provided, the pitch (slope) of this line is given by:

Pitch (slope) = Up 2/Right 5 = 2/5

Pitch (slope) = Up 4/Right 10 = 2/5

Pitch (slope) = Down 42/Left 5 = 2/5

Pitch (slope) = Up 1/Right 5/2 = 2/5

Pitch (slope) = Down 2/5/Left 1 = 2/5

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Answer:

20

Step-by-step explanation:

The sum of a number and its half is thirty. Find the number​:

the formula would be:

1.5x = 30

divide both sides by 1.5:

1.5x/1.5 = 30/1.5

x = 20

check:

20 = 20

1/2 of 20 = 10

20 + 10 = 30

Answer:

x+0.5x=30

1.5x=30

x=20

Answer:

Either A or B.

Step-by-step explanation:

Each number in the sequence is being added by 6.

So you can use the equation: x+6

The ninth term in the sequence would be 36 because 30+6=36

Answer:

0%

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 10*9 ways of selecting two biscuits (in order 1,2)

Of these 90 possible orders

2 digestives can be picked in 5*4 ways =20

2 chocolate can be picked in 2*1 ways = 2

2 ginger can be picked in 3*2 ways =6

Digestive then chocolate can be selected 5*2 ways =10

Chocolate then Digestive can be selected 2*5 ways = 10

Digestive then ginger can be selected 5*3 ways ways = 15

Ginger then digestive can be selected 3*5 ways ways = 15

Chocolate then Ginger can be selected 2*3 ways =6

Ginger then chocolate can be selected 3*2 ways = 6

I have done this the ‘long’ way to demonstrate that all 90 possible outcomes are covered. (Double check)

Probability of taking two different is then the total of the last 6 options divided by the total number of options = 2*(10+15+6)/90 = 31/45 = 68.89% (Approx.)

The area of the rectangle will be 512[tex]cm^{2}[/tex] .

let the longer side of the rectangle be "l" and the shorter side of the rectangle be "b".

Hence, the perimeter of rectangle = 2(l+b)

we are given the perimeter =96cm

thus, 2(l+b)=96

l+b = 96/2

l+b =48

also, we are given the condition that the longer side of the rectangle is two times the length of the Shorter side.

Thus, l=2b, substituting this in l+b=48 we get

2b+b=48

3b=48

b=48/3

b=16cm, now substituting this in l=2b,

l=2(16)

l=32cm

area of the rectangle = length x breadth

=l x b

=32 x 16

= 512[tex]cm^{2}[/tex]

What is the difference between perimeter and area?

Area and perimeter are two crucial characteristics of two-dimensional shapes in mathematics. The area of a shape describes the space it occupies, whereas the perimeter describes how far the shape's boundary extends.

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The equation of line passing through point (6,0) and having a slope of -5/6 is y = -(5/6)x + 5

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point: (6,0)

First, we determine the y-intercept by substituting the given values into the equation of line formula and solve for b.

y = mx + b

0 = (-5/6)6 + b

0 = -5 + b

b = 5

Now that the values of slope m ( -5/6 ) and y-intercept b ( 5 ) is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (-5/6)x + 5

y = -(5/6)x + 5

Therefore, the linear equation of the line is y = -(5/6)x + 5.

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Answer:

Step-by-step explanation:

Find the dividend. ___ ÷ 22 = 1.9

4,180

418

41.8

4.18

x : 22 = 1.9

x = 22 * 1.9

x = 41.8

Answer:

x = 41.8

Step-by-step explanation:

The range of the function  f(x) = |x| − 5 is −5 ≤ y < ∞.

Given the function is  f(x) = |x| − 5

we know the domain is (−∞,∞)

therefore from the domain we calculate the range as:

−5 ≤ y < ∞.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

All real numbers are defined by the function y=|ax+b|. Consequently, the set of all real numbers is the domain of the absolute value function. Every time a number has an absolute value, it has a positive value. The range of an absolute value function with the form y= |ax+b| is hence y R | y 0.

Hence we get the required range if the function.

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Answer:

hello Your answer is down below

Step-by-step explanation:

The Question given "What is the range of f(x) = |x| − 5?"

The answer choices:

−∞ < y ≤ −5

−5 ≤ y < ∞

0 ≤ y < ∞

5 ≤ y < ∞

So what do we know? hmm: The definition of Function range is: "The set of values of the dependent variable for which a function is defined".

So the range of: [tex]\mathrm{Range\:of\:}\left|x\right|-5\\[/tex]  is f(x) ≥ -5.

Which would mean the Interval Notation                Oh yeah btw the answer is −5 ≤ y < ∞

is [-5, [tex]\:\infty[/tex])

So based of that we can infer the answer is gonna have -5 in it.

As a graph it would look like this

SO from the graph we can see the answer is −5 ≤ y < ∞

Answer:

1. B

2. D

Step-by-step explanation:

2. 26(2)-2

26(2)=52

52-2=50

The plane was flying at a height of 706.32 m .

The fundamentals of an object's motion, such as its position, velocity, or acceleration over time, are defined by kinematics equations of motion. An object's motion in one, two, and three dimensions is determined by these three equations of motion. One of three equations of motion can be used to calculate components like displacement (s), velocity (initial and final), time (t), and acceleration (a). The following are the three motion equations:

Initial formula: v = u + at

The second formula is s = ut + 0.5at2.

The third formula is v2 = u2 + 2as.

Let t stand for the package's flight time, s for the plane's altitude, and u for the packet's initial vertical velocity since it is simply dropped.

Given: t = 12 seconds for the delivery to arrive to the ground

With t = 12 and u = 0 in the second equation of motion, we so obtain

s = 0*t + 0.5*9.81*12² = 706.32 m

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1; basically the therom states that 90 + 36 = 126 = 5n + 1;

126 = 5n + 1;

125 = 5n

25 = n