Find the area of the triangle on problem #7 and what statement in true for the triangle on #8

Answer:

{15, 16} or {-15, -16}

Step-by-step explanation:

Quick solution:

take half of the sum (approx. 240), sqrt(240)=15.5

So the numbers are 15 and 16.  and also the negative equivalents since squares are always positive.

Exact method:

Let

x=smaller integer,

x+1 = next integer.

sum:

x²⁺(x+1)^2 = 481

2x^2 + 2x + 1 = 481

2x^2 + 2x - 480 = 0

x^2 + x -240 = 0

x = 15 or x = -16

so the integers are

either

{15, 16} or {-15, -16}

The sum of the squares of two consecutive integers is 481 will be -15 & -16 and 15 and 16.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Successive numbers are those that follow one another continually, from lowest to biggest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.

Assume 'x' is the number and the successive number is (x + 1).

The sum of the square of the consecutive number is 481. Then the equation of the number is given as,

x² + (x + 1)² = 481

Simplify the equation, then we have

x² + (x + 1)² = 481

x² + x² + 2x + 1 = 481

2x² + 2x - 480 = 0

x² + x - 240 = 0

x² + 16x - 15x - 240 = 0

x(x + 16) - 15(x + 16) = 0

(x + 16)(x - 15) = 0

x = 15, -16

Then the successive numbers are given as,

x + 1 = 15 + 1

x + 1 = 16

x + 1 = - 16 + 1

x + 1 = - 15

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Answer:

One of the altitude formed from the vertex to the base and its magnitude given as 12cm

There is also a hypotenuse whose length is 15cm

By pythagorean theorem b^2 +a^2= c^2

so 12^2+a^2 = 15^2

=> 144+a^2 = 225

=> a^2 = 225-144

=> a^2 = 81

so the length of a = √81 = 9 cm (ans)

Hope it helps

Answer:

c

Step-by-step explanation:

Answer:

Solution given:

perpendicular[p]=x

base[b]=11.6m

hypotenuse[h]=19.2m

by using Pythagoras law

h²=p²+b²

19.2²-11.6²=x²

x=[tex]\sqrt{234.08}[/tex]

x=15.3m

option

a.

15.3 m

Answer:

15.3 m

Step-by-step explanation:

c refers to the longest side (hypotenuse) whereas a and b referes to the two other smaller sides of atriangle.

pythagoras theorem

a^2 + b^2 = c^2

11.6^2 + x^2 = 19.2^2

134.56 + x^2 = 368.64

x^2 = 368.64 - 134.56

x^2 = 234.08

x=[tex]\sqrt{234.08[/tex]

x=15.29

x=15.3 m

Answer:

Most of the question is missing. If you could type out the rest, we might be able to help you.

Step-by-step explanation:

answer is 0

because x= 2 and y =3 make a circle

Answer:

192

Step-by-step explanation:

The ratio of pineapple to tomato to cherry is 3 to 5 to 4.

That means for some number x,

we have 3x pineapple, 5x tomato, and 4x cherry.

We are asked to find the total number which is 3x+5x+4x which is equal to 12x.

We are given that there are 80 tomato and we also have 5x tomato. These two expressions are therefore equal and we need to solve 80=5x which leads to x=80/5=16.

So the total amount is 12x=12(16)=192.

Answer:

I'm not the best at explaining but I'll try my best. The x value to the bottom right is 61 degrees because the two sides are equal. Knowing that, there are 180 degrees in a triangle and 61 degrees plus 61 degrees adds up to 122. So, the value for x at the top is 58 degrees.

Answer:

x = 5/26

Hope this helps! GL!

Answer:

I'll setup the problem and you can do the calculations

Step-by-step explanation:

Total length of straw - L

Length of piece 1 - x

Length of piece 2 - y

Length of piece 3 - z

What's given and the answer to (i)

y = x - 3

z = 2x

(ii) L = x + y + z = x + x - 3 + 2x

L = 4x-3

(iii) x = (21+3)/4 = 24/4

leaving you to calculate x

then substitute x into expressions for y & z above and you will have the answer

comment if you have questions

Answer:

The duration of the flight is 1 hour

Step-by-step explanation:

Since average speed = distance traveled / time

Let the duration of the flight be in z hours

So, (600km/z hours) - (600km/ z hours + (1/2)) = 200km/hr

Note: 1/2 is used as a result of 30 minutes increased in time which is half an hour.

200 = (600/z ) - (600/z + (1/2))

Multiply 2 through on (600/z + (1/2))

200 = (600/z ) - (1200 / (2z + 1))

Divide through by 200

= z(2z + 1) = 3

convert to quadratic equation

2z² + z = 3

2z² + z - 3 = 0

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

z-1 = 0

z = 1 hour

Answer: It is a 3% chance

Answer:

d

Step-by-step explanation:

dddddddddddddddddddd

Step-by-step explanation:

diamonds and hearts are red cards

spades and clubs are black cards

15+11=26

26/52 is the probability of selecting a black card, 50%

Answer:

4 – 5x = 59, x = -11

Step-by-step explanation:

The given equations is :

4 – 5x = 59

Subtracting 4 both sides,

4 – 5x -4 = 59-4

-5x = 55

Dividing both sides by -5.

x = -11

So, the answer of the given equation is -11.

Answer:

x ≈ 7.7

Step-by-step explanation:

Using the sine ratio in the right triangle

sin69° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{7.2}{x}[/tex] ( multiply both sides by x )

x × sin69° = 7.2 ( divide both sides by sin69° )

x = [tex]\frac{7.2}{sin69}[/tex] ≈ 7.7 ( to the nearest tenth )

Answer:

[tex]2 {x}^{2} + 5x - 3 = 0 \\ 2( {x}^{2} + \frac{5}{2} x - \frac{3}{2} ) = 0 \\ 2( {x}^{2} + \frac{5}{2} x + {( \frac{5}{4} )}^{2} ) - \frac{3}{2} - {( \frac{5}{4} )}^{2} ) = 0 \\ ( {(x + \frac{5}{4} )}^{2} = \frac{49}{16} \\ x + \frac{5}{4} = ± \frac{7}{4} \\ x = 0.5 \: \: and \: \: 3[/tex]

Answer:

x= [tex]\frac{1}{2}[/tex]     or     x= -3

Step-by-step explanation:

[tex]\boxed{x^{2} +kx=(x+\frac{k}{2})^{2} -(\frac{k}{2})^{2} }[/tex]

First ensure that the coefficient of x² is 1.

x² +[tex]\frac{5}{2}[/tex]x -[tex]\frac{3}{2}[/tex]= 0

[x +([tex]\frac{5}{2}[/tex] ÷2)]² -([tex]\frac{5}{2}[/tex] ÷2)² -[tex]\frac{3}{2}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])² -([tex]\frac{5}{4}[/tex])² -[tex]\frac{3}{2}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])²- [tex]\frac{25}{16}[/tex] -[tex]\frac{3}{2}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])² -[tex]\frac{49}{16}[/tex]= 0

(x +[tex]\frac{5}{4}[/tex])²= [tex]\frac{49}{16}[/tex]

x +[tex]\frac{5}{4}[/tex]= [tex]\sqrt{\frac{49}{16} }[/tex]                (square root both sides)

x +[tex]\frac{5}{4}[/tex]= ±[tex]\frac{7}{4}[/tex]

x= -[tex]\frac{5}{4}[/tex] +[tex]\frac{7}{4}[/tex]       or       x= -[tex]\frac{5}{4}[/tex] -[tex]\frac{7}{4}[/tex]

x= [tex]\frac{1}{2}[/tex]             or       x= -3

Answer:

6. Base

Step-by-step explanation:

In Mathematics, a power involves the multiplication of factors repeatedly. Thus, it's simply a multiplication (product) of repeated factors.

The base of a power is the common factor. When working with a power, the base is the number that is the common factor.

For example;

10⁴ = 10 * 10 * 10 * 10

Therefore, the base in the above expression is 10.

Additionally, the exponent is 4 and it represents the number of times the base "10" was used as a factor.

Answer:

Step-by-step explanation:

Adding two rational numbers results in a positive sum.

Answer:

x=ln 24

Step-by-step explanation:

e^x=24

If we take the ln of both sides

ln e ^x= ln 24

x=ln 24

Answer:

$5.25 for 2lbs

Step-by-step explanation:

C=total cost

C=4p-2.75

---

C=4(2)-2.75

C=$5.25

Answer:

$5.25 the expression is $4p-2.75

answer right 2, up 3

any function with the following form is a transformation from f(x) = x²

g(x) = (x – a)² + b

were a moves the function to the right when a is a positive number and to the left when its a negative number, and b moves the function up when b is positive and down when its negative.

then for a=2 positive and b=3 positive, we have

right 2, up 3

Answer:

answer right 2, up 3

Step-by-step explanation:

Me too. It's the third option. :)

Answer:

I think its the third bubble. Hopefullly this helps. im pretty sure its correct.

Step-by-step explanation:

1st. add rt to both sides so that it cancels out. That should give you xy= s+rt.

2nd. Then divide x from both sides to single out the y. since x is multiplying with y you must use the inverse operation and divide by X. This should leave you with y= (s+rt)÷x

answer is 4

it is the cube root of 4

4×4×4 = 64

The answer of value is 4.

Answer:

(1,1)

Step-by-step explanation:

Graph: y = -x^2 + 2x

Answer:

Step-by-step explanation:

Do this by making this 2-part function into one all-in. Do this by finding a common denominator and then writing the function as one, over the common denominator, x. When we do this we get the function:

[tex]y=\frac{3x^3-2}{x}[/tex] and we will use the rule for quotients, which is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the denominator squared. For us, that is, in steps:

[tex]y'=\frac{x(9x^2)-(3x^3-2)(1)}{x^2}[/tex] which simplifies to

[tex]y'=\frac{9x^3-3x^3+2}{x^2}[/tex] which simplifies finally to

[tex]y'=\frac{6x^3+2}{x^2}[/tex]. Nothing else you do can make this any more simplified.

Given :

Δ  Area of the Triangle is 96 square units

Δ  Height of the Triangle is 9.6 units

We know that:

[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]

[tex]\implies \sf{\dfrac{1}{2} \times Base \times 9.6 = 96}[/tex]

[tex]\implies \sf{\dfrac{1}{2} \times Base = \dfrac{96}{9.6}}[/tex]

[tex]\implies \sf{\dfrac{1}{2} \times Base = \dfrac{960}{96}}[/tex]

[tex]\implies \sf{\dfrac{1}{2} \times Base = 10}[/tex]

[tex]\implies \sf{Base = 20 \ units}[/tex]

Answer:

David is six times older than Janet. If David is 48 years old, how old is Janet? Janet is 8 years old.

Step-by-step explanation:

48÷6=8

Answer:

ST is 12 meters

Step-by-step explanation:

The given triangle ΔRST = An equilateral triangle

The altitude of ΔRST = SV

The length of segment RV = 6 meters

Given that ΔRST is an equilateral triangle, the base angles of the triangles = 60°, therefore, in the formed triangles, ΔRSV, and ΔTSV, ∠RSV = ∠TSV = 90° - 60° = 30°

∴ ΔRSV, and ΔTSV are congruent, based on ASA rule of congruency

∴ Side VT in ΔTSV is congruent to side RV in triangle ΔRSV  

The midpoint of side ST

VT ≅ RV

Therefore, VT = RV = 6 meters

RT = RV + VT = 6 + 6 = 12 By segment addition property

In equilateral triangle, ΔRST, all the sides are equal, therefore;

RT = RS = ST = 12 m

ST = 12 meters.

Answer:

(-12x - 25) / (x + 3) (x - 5)

Step-by-step explanation:

1 - 2x/(x+3) + (x+3)/(x - 5)

= {(x + 3)(x - 5) - 2x(x - 5) + (x + 3)(x - 3)} / (x + 3) (x - 5)

= {(x² -5x + 3x - 16) - (2x² + 10x) + (x² - 3x + 3x - 9)} / (x + 3) (x - 5)

= x² - 2x - 16 - 2x² - 10x + x² - 9 / (x + 3) (x - 5)

= x² - 2x² + x² - 2x - 10x - 16 - 9 / (x + 3) (x - 5)

= (-12x - 25) / (x + 3) (x - 5)