A triangle has integer length sides. If two sides of the triangle are 16 and 21, how many possible lengths are there for the third side

For the given sentences, the algebraic expressions are:

a) N = 110*c - 300

b) N = 12*b

For the first statement:

A 3-digit number, where the tens digit is c, can be written as:

N = 100*a + 10*c + b

Then the hundreds digit is a, and here we know that is 3 less than the tens digit, then:

a = c - 3

The ones digit is b, here we know that it is 0, then b = 0.

Replacing that in our number we get:

N = 100*(c - 3) + 10*c = 110*c - 300

N = 110*c - 300

That is the algebraic expression.

b) A two-digit number can be written as:

N = b*10 + a

Where b is the tens digit and a is the ones digit.

Here we know that the units digit is twice as bit as the tens digit, then:

a = 2b

Replacing that we get:

N = b*10 + a = b*10 + 2b = 12*b

N = 12*b

That is the algebraic expression.

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The dimensions are 16  ft by 32 ft

The quadratic equation is w^2-256=0

We have given that,

Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. the shape of the backyard is rectangular, with the length twice as long as the width.

The area of a rectangle is equal to

A=WL

Where L is the long side of the rectangle

W is the width side of the rectangle

in this problem we have

A=512ft^2

S0,512=LW -----> equation A

L=2W ------> equation B

substitute equation B in equation A

512=2W(W)

512=2w^2

2w^2-512=0

W^2=512/2

W=\sqrt(256)

W=16

Find the value of L

L=2W

L=2(16)

L=32ft

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Answer:

C)512 = 2w2

Step-by-step explanation:

trust

The smallest possible length of the hypotenuse is 118

The given parameters are:

The non-degenerate implies that the right triangle has a positive area.

Since at least one length is 84, then both lengths can also be 84.

The hypotenuse is then calculated using the following Pythagoras theorem.

h^2 = 84^2 + 84^2

Evaluate the sum

h^2 = 14112

Take the square root of both sides

h = 118.8

Round down

h = 118

Hence, the smallest possible length of the hypotenuse is 118

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The quadratic equation is y = 1/2x^2 - 3x + 4

A quadratic equation is represented as:

y = ax^2 +bx + c

Using the values on the table, we have:

a(0)^2 + b(0) + c = 4 ---- when x = 0

a(2)^2 + b(2) + c = 0 ---- when x = 2

a(4)^2 + b(4) + c = 0 ---- when x = 4

Evaluate these equations

c = 4

4a + 2b + c = 0

16a + 4b + c = 0

Substitute c = 4

4a + 2b + 4 = 0

16a + 4b + 4 = 0

Divide through by 2 and 4

2a + b + 2 = 0

4a + b + 1 = 0

Subtract both equations

2a -1 = 0

Solve for a

a= 1/2

Substitute a= 1/2 in 4a + b + 1 = 0

4 * 1/2 + b + 1 = 0

Evaluate

2 + b + 1 = 0

Solve for b

b = -3

So, we have:

y = ax^2 +bx + c

This gives

y = 1/2x^2 - 3x + 4

Hence, the quadratic equation is y = 1/2x^2 - 3x + 4

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Step-by-step explanation:

The maximum data rate of that modem is doubled if the number of points in its constellation were doubled

According to statement

Modem has a data rate is 14,400 bps

we know that the data rate can be calculated by T=A/S

If a is Doubled then the data rate is also doubled.

Because A is directly proportional to the T and S is inversely proportional to T.

So, The maximum data rate of that modem is doubled if the number of points in its constellation were doubled

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Answer:

a: -13º

b: 83º

Step-by-step explanation:

- a: [tex]-27 + 14 = -13[/tex]º

- b: [tex]68 + 15 = 83[/tex]º

- the equation would originally be written as 68 - -15 but 2 negatives make a positive so -- becomes +

hope this helps :)

Answer:

A = 18 units²

Step-by-step explanation:

MNOP is a parallelogram whose area ( A) is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 6 and h = 3 , then

A = 6 × 3 = 18 units²

The standard form of the expression (6.8x10³)x(1.3x10⁻³) is 8.84 × 10⁰.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have:

Mathematical expression:

= (6.8x10³)x(1.3x10⁻³)

= 6.8x1.3

= 8.84

= 8.84 × 10⁰

Thus, the standard form of the expression (6.8x10³)x(1.3x10⁻³) is 8.84 × 10⁰.

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Answer: 33 degrees

Step-by-step explanation:

Angles inscribed in the same arc are congruent, so

[tex]13+4x=-7+8x\\\\20+4x=8x\\\\20=4x\\\\x=5\\\\\implies m\angle CDE=-7+5(8)=33^{\circ}[/tex]

Answer:

Step-by-step explanation:

Answer:

20% of the garden is in chillies.

Step-by-step explanation:

[tex] \frac{4.5 \times 2}{9 \times 5} = \frac{9}{45} = \frac{1}{5} = 20\%[/tex]

The experimental probability is 5/14.

Since, 4 appeared five times over the total, The experimental probability is 5/14.

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Answer:

307 paces

Step-by-step explanation:

First, lets convert Robert's pace to metres. (cm > m)

75cm = (75/100)m

= 0.75m

Number of Full Paces = Length of Bridge / 1 Full Pace

=

[tex] \frac{230m}{0.75m} \\ = 306 \frac{2}{3} paces[/tex]

See , we must have full paces, and in this case we are finding the minimum number of paces, so we will be looking at the lowest possible whole number, which in this case, is 307 paces.

Answer:

If you ever see a big word like greatest,biggest,largest,etc,that stands for Greatest Common Divisor(GCD) and therefore,you have to find prime numbers that can divide the two numbers each equally.

the greatest number of trees Abe can have in each row would be 9

3| 54|27

3 | 18| 9

3|. 6|3

you take the prime factors and multiply which would give you 9

Answer:

Option A

Step-by-step explanation:

Hello!

We can find the graph by finding the roots of the equation.

Since the equation is already in factored form, we can use the Zero Product Property to find the roots. The roots of an equation are the value(s) of x when y is 0 (x-axis).

The roots of the equation are 2 and 3. That means the graph intersects the x-axis at points 2 and 3. Looking at the graphs shown, the answer is Option A.

Answer:

6/5 or 1.2, they're the same value

Step-by-step explanation:

When it says "rate of change", it's really just asking for the slope. If you don't know what the slope is, essentially how much the y-value increases by whenever x increases by 1. This can be formally defined using the equation: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. The subtraction is finding the difference between the two numbers to see how much it's changed by. Btw the order doesn't matter, I could plug in (-3, -2) as (x2, y2) or I could plug it in as (x1, y1) as long as I make sure to input it in correctly. In this example I'll just say (-3, -2) = (x1, y1) and (2, 4) = (x2, y2). Plugging these values into the equation gives you: [tex]\frac{4- (-2)}{2- (-3)} = \frac{6}{5}[/tex] that's the rate of change

Answer:

$15

Step-by-step explanation:

Range is the difference of the highest and lowest data.

Based on the given $20 is the highest and $5 is the lowest.

$20 - $5 = $15

Answer:

15

Step-by-step explanation:

you can think of this table as a data set--and you could even write it out

5, 5, 5, 10, ......... 20, 20 {I did not write it out in full of course}

so, when thinking about the range, we can think of it as a range of our data set.

We find the range of a data set by finding the difference between the highest and lowest values

So, we know that our highest data value (amount) is 20, and the lowest is 5:

20 - 5 = 15

meaning that there is a range of $15 in this data set of allowance amounts

hope this helps!! have a lovely day! :)

360

Step-by-step explanation:

Let's take these problems step-by-step:

To solve these problem, simply plug in the values in parentheses in front of f:

 [tex]f(a) = 6a - 8\\\\f(a+h) = 6(a+h)-8=6a + 6h - 8\\\\\frac{f(a+h)-f(a)}{h} =\frac{(6a+6h-8)-(6a-8)}{h} =\frac{6a+6h-8-6a+8}{h} =\frac{6h}{6}=h[/tex]

Hope that helps!

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Using proportions, the coordinates of point R are given as follows: R(1.2, 0.4).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Segments pr and pq are partitioned in the ratio 3:2, hence:

[tex]PR = \frac{3}{5}PQ[/tex]

[tex]R - P = \frac{3}{5}(Q - P)[/tex]

The points are:

For the x-coordinate, we have that:

[tex]R - P = \frac{3}{5}(Q - P)[/tex]

[tex]x - 6 = \frac{3}{5}(-2 - 6)[/tex]

x - 6 = -4.8

x = 1.2.

For the y-coordinate, we have that:

[tex]R - P = \frac{3}{5}(Q - P)[/tex]

[tex]y + 5 = \frac{3}{5}(4 + 5)[/tex]

y + 5 = 5.4.

y = 0.4.

The coordinates are: R(1.2, 0.4).

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The correct statement is the distribution is unimodal.

A Stem plot is a table where each data value is split into a stem which is the first digit or digits and a leaf which is the last digit.

Mode refers to a value that appears most frequently in a data set. A unimodal data set is a distribution with one clear most frequent values. There are only one set of modes in the data. They are 76.

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Answer:

The club has 56 members

Step-by-step explanation:

We can set up a ratio problem to find the total number of kids in the club. There are two ways to do this, and I will show you both. The first way is to immediately set up a ratio between the number of boys and the number of total members in the club. Since the ratio of girls to boys is 6:2, the ratio of boys to members is 2:8 (add the number of girls and boys in the ratio to get the total number of people). Now, we can set up an equation, letting x equal the number of members total, and solve using cross multiplication:

[tex]\frac{2}{8}=\frac{14}{x}\\\\ 112=2x\\\\ x=56[/tex]

The other way to solve this problem would be to figure out the number of girls in the club if there are 14 boys and then add the two quantities together. If we let y be the number of girls in the club, we get the following solution:

[tex]\frac{6}{2}=\frac{y}{14}\\\\ 2y=84\\\\ y=42\\\\x+y=56[/tex]

Either way, we get that the total number of members is 56

The perimeter of the top of the basket is 20 in.

Perimeter of square is defined as addition the lengths of the  square's four sides.

Diagonal = 6

Let,  side of square = a

a²+a² = 6²

2a² = 36

a² = 18

a = 3√2

Perimeter of the square = 4 × side of square

Perimeter of the square = 4 × 3√2

Perimeter of the square = 12√2 ≈ 20 in

Hence, the perimeter of the top of the basket is 20 in.

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Answer: the attachment i put with this file

Step-by-step explanation:

to graph this linear function, you can use the mantra "rise and run" to plot the points on the graph, and draw a line through the points.

Answer:

Yes.

Step-by-step explanation:

It is a polynomial with degree 2 ( as it has x^2 as its highest power)

Hence, The value of x in the congruent triangles abc and dec is 1

the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.

The question implies that the triangles abc and dec are congruent triangles.

The congruent sides are,

ab = de

bc = ce = 4

ac = cd = 5

The congruent side ab = de implies that,

4x - 1 = x + 2

Collect like terms,

4x - x = 2 + 1

Evaluate the like terms,

3x = 3

Divide through by 3

x = 1

Hence, the value of x is 1

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