The diagonal of a square measured 7 square root of 2 cm. Find the length of a side of the square

Answer:

(8, -2)

Step-by-step explanation:

(8, 2) becomes (8. -2)

Answer:

(8 -2)

Step-by-step explanation:

If c is the longest side, then c must be equal to 10 in order to have a right triangle. This is due to the pythagorean theorem

a^2+b^2 = c^2

6^2+8^2 = c^2

36+64 = c^2

100 = c^2

c^2 = 100

sqrt(c^2) = sqrt(100) ... apply square root to both sides

c = sqrt(100)

c = 10

-----------------

So if we know that c = 10, then the side lengths 6,8,c form a right triangle.

Part A

h(d) = (-1/5)d^2 + 2d is the same as h(d) = -0.2d^2 + 2d because -1/5 = -0.2

I'll use x in place of d, and y in place of h(d) to get this equivalent equation: y = -0.2x^2 + 2x

Let's find the vertex of y = -0.2x^2 + 2x

Note how y = -0.2x^2 + 2x is in the form y = ax^2+bx+c with

a = -0.2

b = 2

c = 0

So the x coordinate of the vertex is

h = -b/(2a)

h = -2/(2(-0.2))

h = 5

Plug this value into the h(d) function to compute the corresponding y coordinate

h(d) = -0.2d^2 + 2d

h(5) = -0.2(5)^2 + 2(5)

h(5) = 5

Coincidentally, the x and y coordinates of the vertex are both the same. This wont be the case in general.

-----------------

Answers:

The vertex is located at (5,5)

The interpretation is that the highest the dolphin can get is 5 feet off the surface of the water and this occurs 5 horizontal feet away from the starting point. Imagine a parabola that opens downward to have a highest point at the vertex mentioned.

====================================

Part B

From part A above, we found x = 5 to be the x coordinate of the vertex. Simply double this value to get 10 as the answer. The reason why this works is because x = 0 is the starting x intercept, or the starting point which the dolphin jumps from. Also, its because of the hint given how the vertex is between each x intercept.

If the dolphin started from any other point on the x axis, then this trick of "double the result from part A" wouldn't apply.

Part C below shows that x = 0 and x = 10 are the two x intercepts. This helps confirm the proper range.

-----------------

Answer: 10 feet

====================================

Part C

h(d) = y = height of dolphin

we want to find the two x values that make y = 0, which help us figure out when the dolphin jumps out of the water and when it lands back in the water

--------

Plug y = 0 into the equation y = -0.2x^2 + 2x and solve for x

y = -0.2x^2 + 2x

-0.2x^2 + 2x = y

-0.2x^2 + 2x = 0

x(-0.2x + 2) = 0 .... factor out x

x = 0 or -0.2x + 2 = 0 .... zero product property

x = 0 or -0.2x = -2

x = 0 or x = -2/(-0.2)

x = 0 or x = 10

-----------------

Answer:

The two x intercepts are x = 0 and x = 10

This means the parabola crosses the x axis at the locations (0,0) and (10,0).

Answer:

234 ÷ g

Step-by-step explanation:

Convert "234 divided by g" into algebraic form, which is:

234 ÷ g

It can also be written as 234/g.

An expression is has no equal sign, as opposed to an equation, which has an answer.

Answer:

82.28 in

Step-by-step explanation:

Answer: 11

Step-by-step explanation:

plug in 4 any instance you see "x"

f(x) = 3x - 1​

f(4) = 3(4) - 1 = 11

Functions are mappings who map inputs to at max one corresponding outputs. The value of function at x=4 is: [tex]f(4) = 11[/tex]

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

For given case, we have:

[tex]f(x) = 3x - 1[/tex]

Taking x = 4, we get:

[tex]f(4) = 3(4) - 1 = 3 \times 4 - 1 = 12 - 1\\f(4) = 11[/tex]

Thus, The value of function at x=4 is: f(4) = 11

Learn more about evaluating functions here:

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Answer:

x=15

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

4x+10=x+5+50

4x+10=x+55

4x-x+10=55

3x+10=55

3x=55-10

3x=45

x=45/3

x=15

Answer:

The Proceeds of maturity after 10 years is $1613.4

Step-by-step explanation:

Given as :

The maturity value = $ 6000

The rate applied at 6 % compounded quarterly

The Time period = 4 years

Now,

Amount = Principal × [tex](1+\dfrac{\textrm Rate}{4\times 100})^{\textrm 4\times Time}[/tex]

Or, Amount = 6000  × [tex](1+\dfrac{\textrm 6}{4\times 100})^{\textrm 4\times 4}[/tex]

Or, Amount = 6000 × [tex](1.015)^{16}[/tex]

Or,  Amount = 6000 × 1.2689

∴  Amount = $ 7613.4

So, The proceeds after 10 years = $ 7613.4 - $ 6000 = $ 1613.4

Hence The Proceeds of maturity after 10 years is $1613.4   Answer

Answer:

Below.

Step-by-step explanation:

No - because the length of any one side must not be equal or greater than the sum of the other 2 sides.

Here 7 = 3 + 4 so they can't form a triangle.

Answer:

no

Step-by-step explanation:

as 3+4 = 7 and the sum of the first 2 sides is supposed to be greater than the third side and 7 is the sum of the first 2 side and the third side is also 7

Answer:

Law of cosines

Step-by-step explanation:

In this problem i need to use the law of cosines, because the angles are unknown.

we know that

The formula of the law of cosines is equal to

[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]

where

[tex]a=7\ units\\b=8\ units\\c=10\ units\\C=\theta[/tex]

substitute in the formula

[tex]10^2=7^2+8^2-2(7)(8)cos(\theta)[/tex]

[tex]100=49+64-112cos(\theta)[/tex]

[tex]100=113-112cos(\theta)[/tex]

[tex]112cos(\theta)=113-100[/tex]

[tex]112cos(\theta)=13[/tex]

[tex]cos(\theta)=\frac{13}{112}[/tex]

using a calculator

[tex]\theta=cos^-1(\frac{13}{112})[/tex]

[tex]\theta=83.33\°[/tex]

Answer:

The answer is C , 5^(1/3)

Answer:

$10

Step-by-step explanation:

$45 x 5 = 225

$225 + $10 = $235

Answer:

They will need $10 more dollars

Step-by-step explanation:

So 45 times 5 is 225 so what that means is that for each week they raised 45 dollars multiply that by 5 weeks and they made $224 dollars then subtract that from 235 so (235-225=10)

They will need $10 more dollars

Answer:

d)  Mr.Wallace can use the following equations:

    a + b = 9

   2 a + 3 b = 23

Step-by-step explanation:

Here, the total number of students = 23

Number of groups = 9

Each group can have 2 or 3 students.

a is the number of  groups of 2.

⇒ Total students in a groups  = a x (Number of  student in each group)

= a x 2 = 2 a

b is the number of groups of 3

⇒ Total students in b groups  = b x (Number of  student in each group)

= b x 3 = 3 b

So, according to the question:

Total number of groups formed = 9

⇒ a + b = 9

Total number of students  = 23

or Number of students in  ( a  group + b group ) = 23

⇒ 2 a + 3 b = 23

Hence, Mr.Wallace can use the following equations:

a + b = 9

2 a + 3 b = 23

Answer:

The equation is [tex]0.3x\leq 180[/tex] and  consuela can drive maximum  600 miles.

Step-by-step explanation:

Given:

Consuela Budget= [tex]\$250[/tex]

Rental Company Charges = [tex]\$10 \ per\ day[/tex]

Additional Cost = 30 cents per mile = $0.3 per miles.

Number of days for vacation = 7

We need to find the number of miles Consuela can drive and still be in budget.

Let number of miles she can drive be [tex]x[/tex]

Rental Company Charges for per day [tex]\times[/tex] number of days + Additional Cost per mile [tex]\times[/tex] Number of miles she can drive sholud be less than or equal to Consuela Budget

Now the equation will be.

[tex]10\times 70 +0.3x \leq 250\\70 +0.3 x\leq 250\\0.3x\leq 250-70\\0.3x\leq 180\\x\leq \frac{180}{0.3}\\\\x\leq 600 \ miles[/tex]

Hence Consuela can drive maximum of 600 miles to stay within her budget.

Answer:

2x^3 + 3x^2 - 11x - 6.

Step-by-step explanation:

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

= (2x + 1)[x(x + 3)-2(x + 3)]

= (2x + 1)(x^2 + x - 6)

= 2x(x^2 + x - 6) + 1(x^2 + x - 6)

= 2x^3 + 2x^2 - 12x + x^2 + x - 6

= 2x^3 + 3x^2 - 11x - 6.

Good morning,

Answer:

Step-by-step explanation:

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

= (2x+1) [(x-2) (x+3)]

= (2x+1) [x²+3x-2x-6]

= (2x+1) [x²+x—6]

= 2x³+2x²-12x+x²+x-6

=2x³+3x²-11x-6.

:)

Answer:

commutative property is C+2+0=C+2

(As a+b=b+a is the law of commutative property of addition )

Ms. Mundo can fill 5 full glasses with 40 ounces of tropical punch, with 5 ounces remaining. This remaining amount fills 2/3 of the last glass.

Ms. Mundo made 40 ounces of tropical punch to pour into glasses that each holds 7 1/2 ounces. To find out what fraction of the last glass is full of punch, we first need to determine how many full glasses can be poured from the 40 ounces.

Since each glass holds 7.5 ounces (which is the same as 7 1/2 ounces), we divide 40 by 7.5 to find the number of full glasses:

 40 ÷ 7.5 = 5 remainder 5

This means that 5 full glasses can be filled, with 5 ounces of punch remaining. Now, to find out what fraction of the last glass the remaining punch fills, we divide the leftover ounces by the capacity of one glass:

 5 ÷ 7.5 = 2/3

The fraction of the last glass that is full of punch is 2/3.

Answer:

[tex]\sin A = \frac{a}{b}[/tex]

Step-by-step explanation:

Given:

We took here a Right Angle Triangle,Δ ABC at angle B as 90°

Side opposite to angle A = a

Side opposite to angle B = b = Hypotenuse

Side opposite to angle C = c

To Find:

Sin A = ?

Solution:

Property of a Sine rule for a Right Angle Triangle.

[tex]\sin A =\frac{\textrm{side opposite to angle A}}{Hypotenuse}\\\sin A =\frac{a}{b}[/tex]

∴ [tex]\sin A = \frac{a}{b}[/tex]

Answer:

Step-by-step explanation:

[tex]1010-n=101\qquad\text{subtract 1010 from both sides}\\\\1010-1010-n=101-1010\\\\-n=-909\qquad\text{change the signs}\\\\n=909[/tex]

Steps to solve:

1010 - n = 101

1010 + (-n) - 1010 = 101 - 1010

-n = -909

-n/-1 = -909/-1

n = 909

_______

Best Regards,

Wolfyy :)

Answer:

The answer would be 22.

Step-by-step explanation:

Since we have 2 bases one being 5 and the other 10, if you multiply the base of the smaller triangle by 2 you get 10. Whatever the sides are for the smaller triangle multiply those by 2. ONce you get all the numbers for the large triangle add them all to get the perimeter.

[tex]\bf \stackrel{\textit{\Large Similar Triangles}}{\cfrac{\stackrel{base}{5}}{\underset{perimeter}{11}}=\cfrac{\stackrel{base}{10}}{\underset{perimeter}{x}}}\implies 5x=110\implies x=\cfrac{110}{5}\implies x=22[/tex]

Answer:

S₈ = 296

Step-by-step explanation:

Given: 2 + 12 + 22 + 32 + .... + (10n - 8) = [tex]$5n^2 - 3n $[/tex]

To prove [tex]$ S_8 $[/tex] is true, substitute [tex]$ n = 8 $[/tex] and compare LHS and RHS

n = 8:

[tex]10n - 8 = 10(8) - 8[/tex]

[tex]$ \implies 72 $[/tex]

[tex]$ \therefore LHS = 2 + 12 + 22 + 32 + 42 + 52 + 62 + 72 $[/tex]

[tex]$ = 296 $[/tex]

Now, Substituting n = 8 in RHS, we get:

[tex]$ 5n^2 - 3n = 5(8)^2 - 3(8) = 5(64) - 24 $[/tex]

[tex]$ = 296 $[/tex]

Therefore, RHS  = 296

We see, LHS = RHS

Hence, we can conclude that [tex]$ S_8 $[/tex] is correct.

Answer:

0.75°C

Step-by-step explanation:

Person A     Person B          Person C

-3                   4                      8

-1                   -4                     -2

0                    2                      5

2                     -3                   1

To get Fatima mean value, we have to add all the given values together  

= - 3 + 4 + 8 - 1 - 4 - 2 + 0 + 2 + 5  +  2  - 3  + 1

= 9  

Estimate is 9 deg above Actual Temperature in 12 readings

The formula for our Mean Value will be, the added values divided by actual temperatures  

Added values = 9  

Actual temperature = 12  

Mean value = 9 ÷ 12 = 0.75°C above actual Temperature

Answer:

y = 3x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

12x - 4y = - 8 ( subtract 12x from both sides )

- 4y = - 12x - 8 ( divide all terms by - 4 )

y = 3x + 2 ← in slope- intercept form

if a line is perpendicular to another line with slope m, the perpendicular line's slope is always -1/m. Since the slope of the given line is -4, the perpendicular slope would be 1/4 (-1/-4 = 1/4). Our line right now is y = (1/4)x + b. Now substitute the given point in for x and y to solve b. In this case b = -1, so your line would be  y = (1/4)x + -1.

Answer:

Explanation:

The expression that you want to simplify is:

This is the simplification step-by-step:

1. Mulitply the expressions on the numerator among them and the expressions on the denominator among them:

[tex]5x\times \frac{1}{x^{-7}}\times x^{-2}=\frac{5x\cdot x^{-2}}{x^{-7}}[/tex]

2. For equal bases that are multiplying, add the exponents:

[tex]\frac{5x\cdot x^{-2}}{x^{-7}}=\frac{5x^{1-2}}{x^{-7}}=\frac{5x^{-1}}{x^{-7}}[/tex]

3. Pass the power on the denominator to the numerator by changing its sign (negative exponents become positive when inverted)

[tex]\frac{5x^{-1}}{x^{-7}}=5x^{-1}x^{7}[/tex]

4. Simplify adding the exponents with the same base:

[tex]5x^{-1}x^{7}=5x^{-1+7}=5x^6[/tex]

And that is the final expression in its most simple form.

When dividing 117 into equal groups of 3, we find that there are 39 groups, and each group contains 3 items. This calculation involves finding the quotient of the division, which tells us how many groups of 3 can be formed with a total of 117 items.

When dividing 117 into equal groups of 3, we are essentially finding how many groups of 3 can be formed with a total of 117 items. This can be visualized as distributing 117 items equally into 3 groups.

Step 1: Perform the division:

117 ÷ 3 = 39

Step 2: Interpret the result:

The quotient 39 represents the number of equal groups of 3 that can be formed using 117 items. Each group will have 3 items.

Step 3: Final answer:

117 can be divided into 3 equal groups, and each group will have 39 items.

In summary, when dividing 117 into equal groups of 3, we find that there are 39 groups, and each group contains 3 items. This calculation involves finding the quotient of the division, which tells us how many groups of 3 can be formed with a total of 117 items.

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Gain percentage made by Mr William by selling the table at Rs. 1050 is 12.30%.

Given that  

Mr. William bought an old table for RS 850

Mr. William spent 1/10 of the cost price on its repairs.

Mr. William sold the table for Rs 1050.

Need to determine gain or loss percent.

Let’s first calculate total money spent by Mr William on Table

Total money spent by Mr William on Table = Amount at which Mr. William bought an old table + amount spent on repairs

[tex]=\text { Cost price }+\frac{1}{10} \text { of the cost price }=850+\frac{1}{10} \text { of } 850=850+85=935[/tex]

So Total money spent by Mr William on Table = 935

Money generated by selling the table = Rs 1050

As Money generated by selling the table is more that Total money spent by on Table so there is a gain.

Gain by selling the table = Money generated by selling the table - Total money spent by Mr William on Table

= 1050 – 935 = 115

[tex]\text { Gain percentage }=\frac{\text { gain amount }}{\text { Money spent on table }} \times 100[/tex]

[tex]=\frac{115}{935} \times 100=12.299 \approx 12.30 \%[/tex]

Hence gain percentage made by Mr William by selling the table at 1050 is 12.30%.

Answer:

x=3, y=1. (3, 1).

Step-by-step explanation:

x+3y=6

4x-6y=6

------------

simplify 4x-6y=6 into 2x-3y=3

------------------------

x+3y=6

2x-3y=3

--------------

3x=9

x=9/3

x=3

3+3y=6

3y=6-3

3y=3

y=3/3

y=1

Answer: 77

Step-by-step explanation: Based on the order of operations or PEMDAS, parentheses are always done first.

So our first step in this problem is to simplify (9 + 2) to get 11.

So we now have (7) (11) which is 77.