Which is a correct way to name the line in this picture?

A. line p
B. ph
C. line h
D. hp

Answer:

25

Step-by-step explanation:

3x+2x+55=180

5x+55=180

5x=180-55

5x=125

X=125/5

X=25

So the value of X is 25

Answer:

\( \boxed{ \bold{ \boxed{ \sf{f( - 4) = 1}}}}\)

Step-by-step explanation:

Given, f ( x ) = - x - 3

Let's find the value of f ( - 4 )

\( \sf{f( - 4) = - ( - 4) - 3}\)

We know that , \(( - ) \times ( - ) = ( + )\)

⇒\( \sf{ 4 - 3}\)

Subtract 3 from 4

⇒\( \sf{1}\)

Hope I helped!

Best regards!!

The value of the angle θ is approximately 24.2 degrees to 1 decimal place.

In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Given that tan θ = 23/52, we can find the value of the angle θ.

To find the value of θ, we can use the inverse tangent or arctan function. Taking the inverse tangent of both sides of the equation, we have:

θ = arctan(23/52)

Using a calculator or trigonometric tables, we can evaluate the inverse tangent of 23/52. The result is approximately 24.2 degrees.

Note that in the context of a right-angled triangle, the tangent function is defined for acute angles (less than 90 degrees). Since 0 degrees is the smallest possible angle, it is considered an acute angle in this case.

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Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Answer:

Width = 8 m

Length = 32 m

Step-by-step explanation:

Width = w

Length = 4w

Perimeter = 80 m

2*(length +width) = 80

2 *(4w +w ) = 80

       2* 5w  = 80

           10w = 80

               w = 80/10

                w = 8 m

Width = 8 m

Length = 4 * 8 = 32 m

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

center:(0,0)

Radius:7

Step-by-step explanation:

the equation of circle:

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

the point h and k are the center of the circle
(h,k)  ———-> (0,0)

since r^2 =49

So, the radius will be the square root of that number
\(r^{2} =49\)

\(\sqrt{r^{2} } =\sqrt{49}\)

\(r=7\)

The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

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

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720

Answer:

60

Step-by-step explanation:

\(45 \div \dfrac34=\dfrac{45}{1} \div \dfrac34=\dfrac{45}{1} \times \dfrac43=\dfrac{45\times 4}{1\times 3} =\dfrac{180}{3}=60\)

Answer:

60

Step-by-step explanation:

45:3/4=x:1

\(x = \frac{45 \times 1} { \frac{3}{4} } \\ x = 45 \times \frac{4}{3} \\ x = 60\)

The probability of randomly selecting a blue jelly bean from the first bag and then randomly selecting a green jelly bean from the second bag is 1/15 (option a).

Firstly, we need to determine the total number of jelly beans in both bags.

The first bag contains 15 jelly beans (3+5+2+5) and the second bag contains 10 jelly beans (1+7+2).

Therefore, the total number of jelly beans in both bags is 25.

Next, we need to determine the probability of randomly selecting a blue jelly bean from the first bag.

Since there are 5 blue jelly beans out of a total of 15 jelly beans in the first bag, the probability of selecting a blue jelly bean is 5/15 or 1/3.

After selecting a blue jelly bean from the first bag, we move on to the second bag to select a green jelly bean.

Since there are 2 green jelly beans out of a total of 10 jelly beans in the second bag, the probability of selecting a green jelly bean is 2/10 or 1/5.

To determine the probability of both events occurring, we use the multiplication rule of probability.

Therefore, the probability of randomly selecting a blue jelly bean from the first bag and then randomly selecting a green jelly bean from the second bag is (1/3) x (1/5) = 1/15.

Hence, the answer is option (a) 1/15.

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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The number of grams of cocoa is 50.9 grams

This is the mass of an object

Since we have that a chocolate bar contains 53% cocoa and the weight of the chocolate bar is 96 grams.

Let

So, we have that

x = pW

Given that

Substituting the values of the variables into the equation, we have that

x = pW

x = 0.53 × 96 grams

x = 50.88

x ≅ 50.9 grams

So, the number of grams of cocoa is 50.9 grams

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9514 1404 393

Explanation:

1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.

If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)

__

2. The general form of the equation of a circle is ...

  Ax² +Ay² +Dx +Ey +F = 0

Any equation of a circle can be put in this form. If we divide by A, this can be written as ...

  x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A

and the equation can be further transformed to the standard form ...

  (x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c

The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.

__

3. Again refer to the attached diagram.

a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.

b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.

c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.

d) A secant is a line containing two points of the circle. Lines CG and CE are secants.

e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.

f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).

Answer:

3 x 21.50= 64.50

3 x 7.96= 23.88

3 x 14.99= 44.97

Altogether equals  133.35

400-133.35= 266.65

Answer:

3 x 21.50= 64.50

3 x 7.96= 23.88

3 x 14.99= 44.97

Altogether equals  133.35

400-133.35= 266.65

If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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The quadratic model for the large cables follows the equation;

f(x) = (¹²/₁₄₃₆₄₁)x² + 2

If we assume that the cable is of constant density, then it means that the positioning in the cable can be said to behave like the deflection of a beam with a point load at the center.

Thus, we can say that the maximum deflection will take place at the middle of the span where the height is 2. Therefore, we will say that this structure is symmetric, because a symmetric structure will transfer the loads better.

If we imagine this deflection like a graph, it means that at the left we have the point (0,50) and on the right we have (1516, 50).

Let us use the general form of the parabola to get;

f(x) = ax² + c

We have two points on the parabola known as;

(0, 2) and (758, 50)

At f(0) = 2, we have;

f(0) = a(0)² + c = 2

c  = 2

Thus;

f(x) = ax² + 2

At f(758) = 50, we will have a = 12/143641

Thus, the quadratic model for the large cables is;

f(x) = (¹²/₁₄₃₆₄₁)x² + 2

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Answer:

\(\huge\boxed{\bf\:r > -4 }\)

Step-by-step explanation:

\(3(r+1)+2 > -7\)

Use the distributive property to solve 3 (r + 1).

\(3r+3+2 > -7 \\3r + 5 > -7\)

Now, bring 5 to the right hand side of the inequality .

\(3r > -7-5 \\3r > -12\)

Divide both sides of the inequality by 3.

\(r > \frac{-12}{3} \\\boxed{\bf\:r > -4 }\)

\(\rule{150pt}{2pt}\)

Answer:

1:quadrant 1

2:quadrant 1

3:quadrant 2

4:quadrant 3

5:quadrant 1

6:quadrant 4

7:Z and quadrant 2

8: F and quadrant 1

9:A and quadrant 4

10: R and quadrant 4

11: N and quadrant 2

12: Q and quadrant 3

13a:the clock

13b:wonder wheel

13c:big coaster

13d: -1,2

Good luck

Answer:

See explaination and answer below

Step-by-step explanation:

Absolute Error:

ae = | E - A |

ae = | 35ft - 33ft|

ae = 2 ft

Percent Error:

pe = 100% * | E - A | / A

pe = 100% * | 35ft - 33ft | / 33ft

pe = 6.06% error

EDIT: 6.1% if asked to the nearest tenth.

Please mark brainliest if this helped!

Please mark brainliest if this helped!

9514 1404 393

Answer:

  $41,977.60

Step-by-step explanation:

Allison's average salary for the last 5 years is ...

  (70 +73.1 +75.2 +77.5 +79)/5 = 74.96 . . . . thousand dollars

Then her annual pension is ...

  1.75% × $74,960 × 32 = $41,997.60

Answer:

Your answer is: 6

84/7=12-6= 6

6 is your answer

The height of the kite off the ground is approximately 17.87 feet rounded to two decimal places.

To solve the problem can use similar triangles.

Let's draw a diagram:

     A

      |\

      | \

   h |   \   x

      |      \

      |____\

       d   B

Point A represents the kite, point B represents the tip of the kite's shadow on the ground and point D represents the point directly below the spool of string on the ground.

The height of the kite represented by h.

The length of the string is 42.9 feet so the distance from point A to point D is also 42.9 feet.

The distance from point B to point D is 16.5 feet.

These two lengths to find the length of segment AB:

AB/AD = BD/AD

AB/42.9 = 16.5/42.9

AB = 16.5

So AB is 16.5 feet.

Now we can use the similar triangles to find h.

We have:

h/x = AB/AD

h/x = 16.5/42.9

h = x × 16.5/42.9

We need to find x.

The spool of string is 3.4 feet above the ground and we know that the kite is directly above the spool when it is at its highest point in the sky.

So the height of the kite above the ground is the same as the height of the spool above the ground plus the length of string that has been let out:

x = 3.4 + 42.9

= 46.3

Now we can substitute this value of x into the previous equation to find h:

h = 46.3 × 16.5/42.9

= 17.87

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Answer: i think it's 942,480

Step-by-step explanation:

i just multiplied all of the numbers but i'm probably wrong srry

Answer:

7986m^2

Step-by-step explanation:

140-102=38

area of triangle:

(38*66)/2=1254m^2

area of rectangle:

66*102=6732m^2

total area:

1254+6732=7986m^2

I’m very sorry but I don’t understand

Step-by-step explanation:

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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