thirty-five times the sum of eight and x

Answer:

Value of x = 11 ° , ∠B = 108° ,∠C = 36° ,∠D = 36°

Step-by-step explanation:

Given :

In ΔBCD , BC = BD And ∠B= (13x-35)° , ∠C= (5x-19)° ,∠D=(2x+14)°

To Find :

value of x and ∠D , ∠B and ∠C

Solution:

∵ BC=BD , So ∠C = ∠D

Therefore 5x-19 = 2x+14

3x = 33 , ∴ x=11°

So, ∠B = (13×11) - 35 = 108°

∠C = (5×11)-19 = 36°

∠D= (2×11) +14 =36°

Therefore , the solution of the given problem of angles comes out to be Greeks failed to demonstrate that tripling a square with only a straight edge and compass was also unachievable.

The highest and lowest walls of a skew are used to split the curved lines that make up its ends using Cartesian measurements. A collision between two poles at an intersection is a potential. Angle is another outcome of two things interacting. They resemble dihedral forms the most closely. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.

Here,

The Greeks were unable to trisect a line section using only a straight edge and compass.

The Greeks proved that using only a straight edge and compass, it is impossible to trisect any angle or double a cube.

The Greeks failed to demonstrate that tripling a square with only a straight edge and compass was also unachievable.

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Answer:

write the question properly-_-

Answer:

The answer is A&C

Step-by-step explana

Answer:

11/100, 0.21, 0.35, 0.6, 7/10, 0.9

Step-by-step explanation:

Answer:

For parallel:

gradient is 1/5

\(y = mx + c\)

consider (5, -2):

\( - 2 = ( \frac{1}{5} \times 5) + c \\ - 2 = 1 + c \\ c = - 3\)

\({ \boxed{ \bf{equation : y = \frac{1}{5}x - 3 }}}\)

For perpendicular:

gradient, m1:

\(m _{1} \times m_{2} = - 1 \\ m _{1} \times \frac{1}{5} = - 1 \\ \\ m _{1} = - 5\)

gradient = -5

\(y = mx + c \\ - 2 = (5 \times - 5) + c \\ - 2 = - 25 + c \\ c = 23\)

\({ \boxed{ \bf{equation :y = - 5x + 23 }}}\)

Answer:

Parallel: \(y=\displaystyle \frac{1}{5}x-3\)

Perpendicular: \(y=-5x+23\)

Step-by-step explanation:

Hi there!

What we must know:

Finding the Parallel Line

\(y=\displaystyle \frac{1}{5} x-3\)

Given this equation, we can identify that its slope (m) is \(\displaystyle \frac{1}{5}\). Because parallel lines always have the same slope, the slope of the line we're currently solving for would be \(\displaystyle \frac{1}{5}\) as well. Plug this into \(y=mx+b\):

\(y=\displaystyle \frac{1}{5}x+b\)

Now, to find the y-intercept, plug in the given point (5,-2) and solve for b:

\(-2=\displaystyle \frac{1}{5}(5)+b\\\\-2=1+b\\-2-1=b\\-3=b\)

Therefore, the y-intercept is -3. Plug this back into \(y=\displaystyle \frac{1}{5}x+b\):

\(y=\displaystyle \frac{1}{5}x+(-3)\\\\y=\displaystyle \frac{1}{5}x-3\)

Our final equation is \(y=\displaystyle \frac{1}{5}x-3\).

Finding the Perpendicular Line

\(y=\displaystyle \frac{1}{5} x-3\)

Again, the slope of this line is \(\displaystyle \frac{1}{5}\). The slopes of perpendicular lines are negative reciprocals, so the slope of the line we're solving for would be -5. Plug this into \(y=mx+b\):

\(y=-5x+b\)

To find the y-intercept, plug in the point (5,-2) and solve for b:

\(-2=-5(5)+b\\-2=-25+b\\-2+25=b\\23=b\)

Therefore, the y-intercept is 23. Plug this back into \(y=-5x+b\):

\(y=-5x+23\)

Our final equation is \(y=-5x+23\).

I hope this helps!

Answer:

Y intercept = (0;6)

X intercept = (42/5;0)

Answer:

36.5 degrees

Step-by-step explanation:

draw a line from B to H then you'll notice that  all the angles on the base are right angles as its a rectangle;e so when you connect BH and AH it makes a right triangle whose base can be found by using 23^2+21^2=c^2

and c=31.1cm so now you have a right triangle with two sides BA=23cm and AH=31.1cm so do tan^-1(23cm/31.1cm) which is equal to 36.5 degrees( correct to 1 d.p.)

Answer:

Step-by-step explanation:

To find the angle between the line BH and plane AEHD, we first need to identify these two elements in the given cube.

From the description of the cube, we can see that the line BH lies on the front plane of the cube, which is formed by the lines AB, BC, CD, and AD.

Also, the plane AEHD is the base plane of the cube, which is formed by the lines AE, EH, HD, and AD.

Therefore, to find the angle between line BH and plane AEHD, we need to determine the direction vectors of both BH and the plane AEHD.

Let's start with BH:

The line BH passes through points B and H. To find the direction vector of BH, we can subtract the position vectors of B and H:

BH = vector(H) - vector(B)

To do this, we need to find the position vectors of B and H with respect to some chosen origin. We can use the vector AD as one of the basis vectors for our coordinate system, and choose A as the origin.

The position vector of B is:

vector(B) = vector(A) + vector(AB)

= (0, 0, 0) + (7, 0, 0)

= (7, 0, 0)

The position vector of H is:

vector(H) = vector(A) + vector(AD) + vector(AE) + vector(AH)

= (0, 0, 0) + (0, 0, 21) + (7, 0, 0) + (0, 23, 0)

= (7, 23, 21)

Therefore, the direction vector of BH is:

BH = vector(H) - vector(B)

= (7, 23, 21) - (7, 0, 0)

= (0, 23, 21)

Next, let's find the normal vector of the plane AEHD:

The plane AEHD is the base plane of the cube, which means it is parallel to the X-Y plane. Therefore, its normal vector is in the Z direction.

To find the normal vector of the plane AEHD, we can take the cross product of two vectors lying in the plane, such as AE and AD:

normal vector = AE x AD

= (7, -23, 0) x (0, 0, 21)

= (-483, -147, 0)

(Note: We could also take the cross product of other pairs of vectors lying in the plane, such as EH and HD, to get the same normal vector.)

Now that we have the direction vector of BH and the normal vector of the plane AEHD, we can find the angle between them using the dot product:

cos(angle) = (BH . normal vector) / (|BH| |normal vector|)

where BH . normal vector is the dot product of BH and the normal vector, and |BH| and |normal vector| are the magnitudes of BH and the normal vector, respectively.

BH . normal vector = (0, 23, 21) . (-483, -147, 0)

= 0 - 3393 + 0

= -3393

|BH| = sqrt(0^2 + 23^2 + 21^2) = sqrt(1102)

|normal vector| = sqrt((-483)^2 + (-147)^2 + 0^2) = sqrt(234018)

Therefore,

cos(angle) = -3393 / (sqrt(1102) * sqrt(234018))

= -0.0662

Finally, we can find the angle between BH and the plane AEHD by taking the inverse cosine. cos(angle) = -0.0662

To find the angle, we take the inverse cosine of both sides:

angle = arccos(-0.0662)

Using a calculator, we get:

angle ≈ 1.649 radians ≈ 94.53 degrees

Therefore, the angle between the line BH and plane AEHD is approximately 94.53 degrees.

Answer:c

Step-by-step explanation:

cccccccccc

Answer:

1500

Step-by-step explanation:

i did the test

The Greatest Common Factor is \(b^{2}\) Option B

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers

Find the common factors of each term in order to find the greatest common factor (GCF).

The Prime Factors of:

\(b^{5}\) = \(b^{5}\)

2\(b^{4}\) = 2\(b^{4}\)

\(3b^{3}\) = \(3b^{3}\)

\(b^{2}\) = \(b^{2}\)

From the common factors, the greatest common factors is \(b^{2}\)

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The graph that most effectively displays the distance covered by the waves would be:

C). Circle above the x-axis.  

Given that,

Location of the earthquake = across the Pacific Rim

Also

The distance that the waves covered is signaled by r(miles) = 15sin(θ)

Since 15sin(θ) is the distance, the circle above to the x-axis would be the correct representation.

Thus, option C is the correct answer.

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Answer:

2.83

Step-by-step explanation:

36 pi = pi×r×r×h

36=r×r×h

h= 4

36= r×r×4

8=r×r

\( \sqrt{8} = x\)

r= 2.83

Answer:

-136.5

Sn=A1+An/2*n

Step-by-step explanati

d=-2-5=-7

A1=5   An=-44   n=-49/7=7

S7=5+(-44)/2*7=19.5*7=-136.5

Answer:

41%

Step-by-step explanation:

adding percentages is just regular adding so 15 + 14 + 12 = 41

Answer:

0.41

Hope this helped you

Answer:

the probability of rolling a 6 on one die is 1/6 or 16.7 %

the same could be said about rolling a 4 on a similar die.

The inequality that represent each situations are:

a. 6(n + 3) ≥ 42.

b. 6(n + 3) ≤ 42

c. 6(n + 3) < 42

d. 6(n+3) > 42.

To write the inequality for each of the situations, translate each statement into algebraic expressions and use the appropriate inequality sign where necessary.

Thus, let the unknown number be represented as n.

a. The statement, "at least 42" means not less 42, which is the same as "greater than or equal to 42".

Therefore, the first statement is represented by the inequality, 6(n + 3) ≥ 42.

b. "6 times n and 3 is at most 42" is written as, 6(n + 3) ≤ 42

c. "6 times n and 3 is less than 42" would be translated as: 6(n + 3) < 42

d. "6 times n and 3 is more than 42" would be, 6(n+3) > 42.

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Step-by-step explanation:

6(n+3)>42

this is your answer

arlynn

Answer:

7lm - 21lmn

taking common

7lm(1-3n)

Answer:

$136.50

Step-by-step explanation:

Time and a half = 13.00 + (13 × 1/2)

Time and a half = 13.00 + 6.50

Time and a half = $19.50

If he works 7 hours of overtime, and overtime means getting paid time and a half, we would multiply 7 hours by $19.50 to find the total amount he was paid

7 × 19.50 = 136.50

In overtime, he was paid $136.50

A plane can be defined by three non-collinear points statement is true about the points and planes .

However, in general, some true statements about points and planes include:

A plane can be defined by three non-collinear points, meaning three points that are not on the same line. This is known as the point-normal form of the equation of a plane.

If a point lies on a plane, then any line passing through that point and parallel to the plane lies entirely within the plane.

If two planes intersect, their intersection is a line. The line of intersection is perpendicular to the normal vectors of both planes.

If three or more points lie on the same plane, the plane is uniquely defined by those points, and any additional point on the plane can be found using the point-normal form equation.

Again, without additional information or context, it is difficult to determine which of these statements, if any, is applicable to the specific scenario or diagram in question.

A plane can be defined by three non-collinear points, meaning three points that are not on the same line. This is known as the point-normal form of the equation of a plane.

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It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

Answer:

16

Step-by-step explanation:

eighths are 1/8 therefore there are 8 eighths in one,

1 x 2 is 2

8 x 2 is 16

therefore there are 16 eighths in 2

Answer:

Step-by-step explanation:

1 pizza has 8 slices

2 pizzas has 16 slices

i think it is easier to remember like this

Answer:

8 for tens, 9 for hundredths and thousandths is 1

Step-by-step explanation:

you can find the number by looking at the place of the numbers if it is tens look at the tens place which is the number eight as tens are 2 digit numbers

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

it would become 61

Step-by-step explanation:

the tenths place (.9) is greater or equal to five. if it follows the rule, the tens place (0) would increase by one.

Answer:

tan

Step-by-step explanation:

take 19 degree as reference angle

using tan rule

tan 19=opposite/adjacent

0.34=14/x

x=14/0.34

x=41.17

x=41.2

Step-by-step explanation:

4(-3)-5y=12

-12-5y=12

-5y=12+12

-y= 24/5

y= -24/5

y= -4⅕

hope it helps