A study found that healthy eating can help to cut the risk of heart disease. Therefore, a person can conclude that if they eat healthy they definitely will not have any heart issues.

True or false?

The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

Given the equation

[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2

We know that,

xlogb = log[tex]b^{x}[/tex]

So,

2[tex]log_{8}[/tex](x) = logx²

For the same base

logA + logB = log(AB)

So,

[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2

[tex]log_{8}[/tex](16x²) = 2

We know that

[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]

so,

[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²

x = 2 hence x = 2 will be correct answer.

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Answer:

259 ft.

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles. scalene, equilateral, acute, obtuse and right angled triangle.

A right angled triangle is a triangle in which one of the angles is 90 degrees. Trigonometric ratios show the relationship between the angles of a right angle triangle and its sides.

Let h represent the height of the house above water, hence using trigonometric ratios:

tan(26) = h / 531

h = 531 * tan(26)

h = 259 ft.

Answer:

range{-5,4)

Step-by-step explanation:

3(-1)-2= -5

3(2)-2=4

Answer:

write question in short form

Step-by-step explanation:

Answer:

30 degrees.

Step-by-step explanation:

Let the acute angle be x.

Then as the 2 acute angles in a right triangle sum to 90 degrees,

x = 90 - 60

= 30.

We used the information we know to give us this equation.

90°+60°+x=180°

We add 90° and 60° to give 150°

150°+x=180°

Answer:

80%

Step-by-step explanation:

Change is (45-25)/25*100=(20/25)*100=80%

Answer:

a) 81-6

b) 10.4

Step-by-step explanation:

a) assuming that the VAT is 20% of the 68 pounds,

you calculate 120% of 68 (convert percentage to decimal)

= 1,20 * 68 = 81.6 pounds

or

calculate 20% of 68 pounds and add the answer to 68 pounds:

(0.2 * 68) + 68 = 81.6 pounds

b) 20% of 52

first convert the percentage to decimals:

0.2 * 52 = 10.4 pounds

Answer:

p = 1

Step-by-step explanation:

7 = 8 - p

7 + p = 8

p = 8-7

p = 1

Answered by Gauthmath

Answer:

(x+2)(2x+2) = 130

x=6.58m

Step-by-step explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

(2+2x)(2+x)= 130

(x+2)(2x+2) = 130

Expand the bracket:

[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]

Divide through by 2

[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]

Complete the square by adding the square of the half of the coefficient of x to both sides:

[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]

[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]

Take the square root of both sides

[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]

Hence the value of x is 6.58m

Answer:

m∠DAB+m∠ADC=180

115+ 29 + m∠ADB=180

m∠ADB=180 - 115 -29

= 36°

Answer:

a +73°=90°

a= 90°-73°

a =17°

d+18°=90°

d=90°-18°

d =72 °

Mistake in Line 2 : Was in the determining the values for a ,b,c

Mistake in Line 4 : Not taking the square roots of both sides.

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

First Mistake : Line 2

[tex]a = x \\ b = 6 \\ c = 10[/tex]

Second Mistake : Line 4

[tex]136 = {x}^{2} \\ not \\ 136 = x[/tex]

Correct Solution :

[tex] {x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ {x}^{2} = 100 - 36 \\ [/tex]

[tex] {x}^{2} = 64 \\ \sqrt{ {x}^{2} } = \sqrt{64} \\ x = 6[/tex]

Answer:

c = 21

Step-by-step explanation:

**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**

If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.

PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.

With that in mind, we can apply this ratio to find WX.

We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.

c = 21

Hope this helps (●'◡'●)

Answer:

54

Step-by-step explanation:

Surface area of a cube = 6a²

Where,

a = edge = 3

Surface area of a cube = 6a²

= 6 * (3)²

= 6 * (3 * 3)

= 6 * 9

= 54

Therefore,

The Surface area of the cube = 54

Answer:

B) To the left five units, down three units

Answer:

( B ) To the left five units, down three units.

Answer:

(-2,-2)

Step-by-step explanation:

x^2 + y^2 = 9

A circle has an equation of the form

(x-h)^2 + (y-k)^2 = r^2

where the center is at ( h,k) and the radius is r

The circle is centered at (0,0) and has a radius 3

The only point entirely within the circle must have points less than 3

(-2,-2)

Answer:rrrrrrrr

rrrrrrrrrr

Step-by-step explanation:

rrrrrrrrrrrrrrr

The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the first number:

The other numbers are:

x+1, x+2

The sum of three consecutive numbers is 117:

x + x+1 + x+2 = 117

3x + 3 = 117

3x = 114

x = 38

x+ 1 = 38+1 = 39

x+2 = 38+2 = 40

Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

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Step-by-step explanation:

1/5=1/5×1000=200

1/2 of 200

1/2×200=100

Answer:

-3/5

Step-by-step explanation:

Pythagorean formula :

x^2 + y^2 = r^2

(-8)^2 + (-6)^2 = r^2

64 + 36 = 100

r^2 = 100

r= 10

sin is the y coordinate over the radius :

-6/10

-3/5

Answer:

[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151

then 180-151=29

Answer:

14

Step-by-step explanation:

The a value is from the center to the maximum

We want from minimum to max so we need 2 times the amplitude

a = 7

2 *7 = 14

Answer:

-6

Step-by-step explanation:

A parabola is vertex form is written as

y = a(x-h)^2 +k  where (h,k) is the vertex

Substituting in the vertex

y = a(x-5)^2 +5

We know a point on the parabola so we can find a

-1 = a( 6-5)^2 +5

-1 =a(1)^2+5

-1 = a +5

Subtract 5 from each side

-1-5 = a

-6 =a

Answer:

Choice C.

[tex]y + 1 = - 2(x - 2)[/tex]

Step-by-step explanation:

When converting to

[tex]y = mx + b[/tex]

We are left with:

[tex]y = - 2x + 3[/tex]

Which fits both the x-intercept and y-intercept.

Answer:

42.78⁹, 137.22⁹.

Step-by-step explanation:

sine Ф=0.6792

Angle Ф in the first quadrant = 42.78 degrees.

The sine is also positive in the second quadrant so the second solutio is

180 - 42.78

= 137.33 degres.

Answer:

$7, 657

Step-by-step explanation:

Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

Answer:  13.46 km/h

Step-by-step explanation:

7 1/2 hr= 450 min

6057/450= 13.46

Answer:

5, 12, 19, 26, 33

Step-by-step explanation:

Using the recursive rule and a₁ = 5 , then

a₂ = a₁ + 7 = 5 + 7 = 12

a₃ = a₂ + 7 = 12 + 7 = 19

a₄ = a₃ + 7 = 19 + 7 = 26

a₅ = a₄ + 7 = 26 + 7 = 33

The first 5 terms are 5, 12, 19, 26, 33