Can someone help me find the value of x

Answer:

x = 16

z = 90°

Step-by-step explanation:

The angle with the measure (10x - 70) and the angle with measure (5x+10) are supplementary angles and their sum is equal to 180 so it's safe to write the following equation:

10x - 70 + 5x + 10 = 180 add like terms

15x - 60 = 180 add 60 to both sides

15x = 240 divide both sides by 15

x = 16

The angle represented with z and the angle with measure (10x - 70) are also supplementary because they are on a straight line so we can write the following equation to find the value of z:

z + (10*16-70) = 180 calculate inside the parenthesis

z + 90 = 180 subtract 90 from both sides

z = 90°

The contrapositive of the statement will be :  if it is not obtuse, then an angle does not measure greater than 90° .

We need to know about conditional and contrapositive statement to solve this problem.

A conditional statement takes the form "If p, then q" where p is the hypothesis while q is the conclusion. So, here in this problem p is 'an angle measures greater than 90° and q is it is obtuse.

The Contrapositive of a Conditional Statement is obtained by supposing that you have the conditional statement p→ q. Now, we first find the inverse of the given conditional statement then swap the roles of hypothesis (p) and  conclusion (q) . Therefore, the contrapositive of the conditional statement p→ q is  ~q → ~p.

Thus, contrapositive of the statement : If an angle measures greater than 90°, then it is obtuse will be if it is not obtuse, then an angle does not measure greater than 90° .

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Triangle XYZ with vertices X(-3 , -2), Y(-1 , 0), and Z(0 , -1) is a right triangle.

First, using the distance formula, find the length of each side of the triangle: side XY, side XZ, and side YZ.

d = √(x2 - x1)^2 + (y2 - y1)^2

side XY : d = √(-1 - -3)^2 + (0 - -2)^2 = √4 + 4 = 2√2

side XZ : d = √(0 - -3)^2 + (-1 - -2)^2 = √9 + 1 = √10

side YZ : d = √(0 - -1)^2 + (-1 - 0)^2 = √1 + 1 = √2

Next, check if it follows the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = XY = 2√2, b = XZ = √10, and c = YZ = √2

a + b > c     2√2 + √10 > √2     5.99 > 1.41     True

a + c > b     2√2 + √2 > √10     4.24 > 3.16     True

b + c > a     √10 + √2 > 2√2     4.58 > 2.83     True

Lastly, to know what type of triangle based on the length of its side,

1. Take the sum of the squares of the two smaller sides.

(√2)^2 + (2√2)^2 = 10

2. Compare it to the square of the largest side.

(√10)^2 = 10

10 = 10

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle.

if they are smaller, then it is an obtuse triangle.

Hence, triangle XYZ is a right triangle.

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The value of q for the given relation will be 32.

A sort of proportionality known as "direct variation" occurs when one quantity immediately changes in response to a change in another variable.

This suggests that if one number increases, the other quantity will also rise proportionately. Similar to the last example, if one quantity declines, the other amount likewise declines. The link between direct variation and the graph will be linear, resulting in a straight line.

As q varies jointly with v and s,

It implies that

q = k v s

Given,

q=24 when v=2 and s=3

24 = k × 2 × 3

k = 24 / 2 × 3

k = 4

When we put v = 4 and s = 2

⇒ q = 4 × v × s

⇒ q = 4 × 4 × 2

⇒ q = 32

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Answer:

x = -3

Step-by-step explanation:

6(3x-4) + 54 = -3(x+11)

18x-24+54 = -3x-33       Multiply 3x and -4 by 6 this means distributive  

                                          property. Next, multiply x and 11 by -3.

18x+30 = -3x-33            Next, combine -24 and 54 which equals 30.

     -30          -30       Next, subtract 30 from both sides to leave 18x by itself.

18x = -3x-63

+3x   +3x                   Next, add 3x to both sides to leave -63 by itself.

21x = -63

/           /

21       21                 Divide 21 on both sides to leave x by itself.

x = -3

The correct answer is 1.19×10³ lbs.

The weight of first animal = 5.12×10² lbs

Performing multiplication to get the complete weight of first animal

The weight of first animal = 512 lbs

The weight of second animal = 6.8×10² lbs

Performing multiplication to get the complete weight of second animal

The weight of second animal = 680 lbs

Now, performing addition to find the approximate weights of two animals-

Final answer = 512 + 680

Performing addition to find the approximate weights of two animals

Final answer = 1192 lbs

Now, converting the number in scientific notation -

Final answer = 1.19×10³ lbs

Hence, the final answer in significant digits is 1.19×10³ lbs.

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You can either form no triangles or an endless number of triangles when you are given three angles.

For Example -

How many distinct triangles can you construct using angles of 30, 60, and 90 degrees?

Use a protractor to create one of the angles needed to form a triangle. You can adjust the side lengths to your desired length. Make another angle at the end of one of the sides, then link the sides together. You've constructed a triangle.

You should note that you chose the side lengths. This implies that you might choose differently. This allowed you to create an infinite number of distinct triangles using the same angles.

Hence, we can form infinite number of triangles when only the measurements of three angles is given

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Answer: f(-1)=-13

Step-by-step explanation:

f(0) = -5

f(n) = f(n - 1) + 8

f(0) = f(0 - 1) + 8

-5 =f(-1) + 8

f(-1)=-13

Answer:

Eli has the faster speed than Jess.

Answer:

115 ≤ 25a+15

-15. -15

100 ≤ 25a

100/25 ≤ 25/25 a

4≤a

Answer:

    25x + 15 > 115

Step-by-step explanation:

Subtract 15 from both sides

25x+15-15 > 115-15

Simplify

25x > 100

Divide both sides by 25

25x/25 > 100/25

Simplify

x > 4

Sorry if it doesn't help

Answer:

x ≥ 8

Step-by-step explanation:

  x

-------  ≥  4(2)

  2(2)

x ≥ 8

[8, ∞)

I hope this helps!

The area of the parallelogram is 54 square units.

In this question we have been given a parallelogram

We need to find the area of the parallelogram.

Here, the slant height of the parallelogram is 8 units.

the base of the parallelogram is 9 units.

And the height of the parallelogram is 6 units.

We know that the area of the parallelogram is,

A = base × height

⇒ A = 9 × 6

⇒ A = 54 square units

Therefore, the area of the parallelogram is 54 square units.

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The algebraic expression models for the word phrase two times the sum of a and b is 2(a+b)

Given,

The word phrase : Two times the sum of a and b.

Sum of a and b = a+b

2 times the sum of a and b = 2(a+b)

Hence, the algebraic expression models for the word phrase two times the sum of a and b is 2(a+b)

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Answer: 1st image: option 2

2nd image: (x, y) ==> (x+4, y-9) ==> option 4

Step-by-step explanation:

1st image: Reflection over the y-axis means that all x-coordinates are negated while the y-coordinates remain the same.

A: (2, -2) ==> A' (-2, -2)

B: (-2, 5) ==> B' (2, 5)

C: (-4, 2) ==> C' (4, 2)

Answer: option 2

A to A', B to B', C to C'

Purple to Blue

2nd image: 1st, the purple triangle moves 4 units to the right (x ==> x+4)

Then, the purple triangle moves 9 units down to become the blue triangle (y ==> y-9)

(x, y) ==> (x+4, y-9) ==> option 4

Answer: its b

Step-by-step explanation:

The orthocenter of a triangle is the point at which the perpendicular lines drawn from the vertices to the opposite sides of the triangle intersect. The coordinates of the orthocenter of ΔJKL is (5, -1).

The orthocenter of a triangle is the point at which the perpendicular lines drawn from the vertices to the opposite sides of the triangle intersect. The orthocenter of an acute angle triangle is located within the triangle. The orthocenter of the obtuse angle triangle is located outside the triangle.

The slope of JK is (6+2)/(5-3) or 4.

So, the slope of the altitude, which is perpendicular to JK is -1/4.

Now, the equation of the altitude from L to JK is:

y + 2 = -1/4 (x - 9)

y = -1/4x + 1/4

Use the same method to find the equation of the altitude from J to KL. That is, y + 2 = 1/2 (x - 3) or y = 1/2x - 7/2.

Solve the equations to find the intersection point of the altitudes.

-1/4x + 1/4 = 1/2x - 7/2

simplifying the above equation, we get

-1/4x - 1/2x = - 7/2 - 1/4

-3/4x = - 15/4

x = 5

y = -1/4(5) + (1/4)

simplifying the above equation, we get

= -4/4

y = -1

Therefore, the coordinates of the orthocenter of ΔJKL is (5, -1).

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By the definition of supplementary angles, angle 1 + angle 2 = 180° and angle 2 + angle 3 = 180°. Then angle one + angle 2 = angle 2 + angle 3 = 180°. Subtract angle 2 from each side. You get angle 1 = Angle 3 or angle 1 ≅ angle 3.

It should be noted that supplementary angles are the angles that their sum equals to 180°.

Therefore, angle 1 + angle 2 = 180° .... i

angle 2 + angle 3 = 180° .... ii

Equate equation i and ii and subtracting angle 2 from both sides will illustrate that angle 1 = angle 3.

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Complete the paragraph proof.

Given: angle 1 and angle 2 are supplementary, and angle 2 and angle 3 are supplementary.

Prove: angle 1 ≅ angle 3

By the definition of supplementary angles, angle 1 + angle 2 = _____(a) and angle 2 + angle 3 = ____ (b). Then angle one + angle 2 = angle 2 + angle 3 ______(c). Subtract angle 2 from each side. You get angle 1 = ______(d), or angle 1 ≅ ______(e).

Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

6.2 + 13.8 > 20

13.8 + 20 > 6.2

20 + 6.2 > 13.8

Hence, these set of numbers can be the measures of the sides of a triangle.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if [tex]a^{2} + b^{2} < c^{2}[/tex]

obtuse if  [tex]a^{2} + b^{2} > c^{2}[/tex]

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

∴The longest side is 20.

Hence, a = 6.2, b = 13.8 and c = 20;

Consider [tex]a^{2} + b^{2}[/tex]  :

= [tex]6.2^{2} + 13.8^{2}[/tex]

= 228.88.

Now consider [tex]c^{2}[/tex] :

= [tex]20^{2}[/tex]

= 400.

Thus,  [tex]a^{2} + b^{2} < c^{2}[/tex].

Hence, the triangle is acute.

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The common ratio of the geometric sequence can be determined by finding the dividing any of the given term in the geometric sequence, n by the preceding term n-1.

The geometric sequence from part a is 2,4,8,…

Geometric sequence is a series of number that increases or decreases by a constant ratio called a common ratio. Each term in the sequence is the product of the common ratio and the previous term.

Hence, common ratio r = nth term/n-1 term

For the given geometric sequence,

r=2nd term/1st term=3rd term/2nd term

r=4/2=2 or

r=8/4=2

The common ratio of the geometric sequence 2,4,8,… is 2

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The value of Slope is undefined for given points.

A Line's Slope

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks.

The formula to calculate the slope is

Slope of the line passing through 2 points is y₂ - y₁ / x₂ - x₁

points given are  (9,3) and (9,-4)

after putting it in the formula,

⇒ -4 - 3 / 9 - 9

It implies that the slope is undefined.

Line is parallel to y axis, x = 9

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Answer:

Step-by-step explanation:

Step-by-step explanation:

it is simple for such a line.

x goes to -infinity, and therefore y (or f(x)) also goes to -infinity.

x goes to +infinity, and therefore y (or f(x)) also goes to +infinity.

the difference between x and y values is just a constant factor (the slope). that constant factor becomes irrelevant, when the values approach infinity anyway. only the sign is relevant.

but in our case the slope is +1/+2 (the y value increases by +1 for every increase of x by +2).

so, the line (as we can see in the graph) is

y = 1/2 × x - 1

when x goes to +infinity, "-1" is irrelevant, and

1/2 × +infinity = +infinity.

when x goes to -infinity, again, "-1" is irrelevant, and

1/2 × -infinity = -infinity

The probability that a family vacations in the mountains is 0.3

A Venn diagram is a diagram that uses circles to depict the relationships between things or finite collectives of things. Circles that overlap share characteristics, whereas circles that don't overlap do not.

Refer the Venn diagram.

The probability of a family vacationing at the beach is P(B) [the a whole blue circle] = 0.6,

The probability of a family vacationing at both locations is P(B∩M) [the red/blue overlapping intersection of a two circles] = 0.2.

P(only B) [the blue just background] = 0.6 - 0.2 = 0.4 is the probability which a family vacationed only on the beach.

P(neither) [a white background] = 0.1 is the possibility that a family vacationed at none of location.

Remember that the probability sum is 1.

P(M) [a entire red circle] = 1 - 0.1 - 0.4 = 0.5 is the probability which a family vacationed with in mountains.

As a result, the probability of a family vacationing only in the mountains is P(only M) [a red only background] = 0.5 - 0.2 = 0.3.

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Answer: x<-5

Step-by-step explanation:

[tex]2.5 < (-0.5)(x)\\2.5 < -0.5x\\[/tex]

Multiply both parts of the equation by 2:

[tex]5 < -x\\5+x < -x+x\\5+x < 0\\5+x-5 < 0-5\\x < -5[/tex]

Answer:

d

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

i got it from that little mathemetician

Answer:

The answer is 40. If you divide 4000 by 100 you get 40. Hopefully this is what you were looking for.

Step-by-step explanation:

4000/100=40

Answer:

_00 x 10 = _000 (100 x 10 = 1000 basically).

40 x 100 = 4000

so..

40 hundreds is the same as 4 thousands.