(03.01 MC) The length of a rectangle is 5 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle? O 5 units ( 03.01 MC ) The length of a rectangle is 5 units and its width is 4 units . What is the approximate length of the diagonal of the rectangle ? ​

Answer:

$63422.42

Step-by-step explanation:

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Answer:

A.28 minutes

B.40 minutes

C.56 minutes

D.70 minutes

Step-by-step explanation:

Answer:

the third option

Step-by-step explanation:

Our equation is

[tex] {y}^{2} = 36(x - 10)[/tex]

Equation of a vertical parabola is

[tex]( {y - k)}^{2} = 4p(x - h)[/tex]

where (h,k) is the center

The focus is

(h+p, k)

Equation of directrix is

x= h-p,

Here the center is (10,0)

Next, we factor out 4 in the original equation

[tex]4(9)[/tex]

So we have

[tex] {y}^{2} = 4(9)(x - 10)[/tex]

So our p=9,

So our focus is

(10+9,0) or (19,0)

The third option is the answer

The location of the light bulb is at point A. (10, 0).

Option A is the correct answer.

We have,

To find the location of the light bulb, we need to identify the coordinates (x, y) at which the light bulb is located.

In the given parabolic mirror equation, y² = 36(x - 10), the vertex form of the equation for a parabola with a vertical axis is (h, k), where h is the

x-coordinate of the vertex and k is the y-coordinate of the vertex.

Comparing the given equation with the standard form

(y - k)² = 4a(x - h),

we can see that h = 10 and k = 0.

So, the location of the light bulb is at the point (10, 0).

Therefore,

The location of the light bulb is at point A. (10, 0).

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A searchlight uses a parabolic mirror to cast a beam of light in parallel rays where the light bulb is located at the focus of the parabola in order to give the best illumination.

The mirror is modeled by y² = 36 (x-10), where the measurements are in cm.

What is the location of the light bulb?

A. (10, 0)

B. (14, 0)

C. (19, 0)

D. (36, 0)

Answer:

False

Step-by-step explanation:

I'm not a 100 percent though

The graph is in a reciprocal relationship with Option C

A function is a mathematical statement used to relate a dependent and n independent variable.

The function is represented by the graph

The nature of the graph is exponential

and the equation is determined by the points on the graph

( 1,1) ( 2,4) '

The equation is

y = ( 1/4) 4ˣ

The inverse of the function will be found by replacing the y variable with x and vice versa and then solving to bring the function into the form of x.

x = ( 1/4) [tex]\rm 4^y[/tex]

Plotting this gives the answer as Option C

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Answer:

x = 69 v = 103

Step-by-step explanation:

Angles in a triangle add up to 180 degrees:

34 + 77 + x = 180

x = 69

Angles on a straight line add up to 180:

77 + v = 180

v = 103

Answer:

Step-by-step explanation:

the sum of the interior angles in a triangles is 180°, take away from 180 the know angles (34° and 77°) and you will have your answer

180 - 34 - 77 = 69°

Now we find angle V

The angle V and the angle of 77 ° are on a straight line, so the sum is 180°, from 180° you subtract 77 ° and you have the value of V

180 - 77 = 103 °

Answer: D. It is the graph of f translated 3 units up and 7 units to the right

Step-by-step explanation:

the +3 part of the equation makes the function translated vertical 3 units

then the x - 7 part makes it translate horizontal to the right 7 units (always the opposite of the sign)

because when

x-7=0,

x=7

Answer:

24 unit²

Step-by-step explanation:

use Pythagoras to calculate the height of triangle

which gives you 6 √100-64

then half hight x base

The question posed in the task content is a goal seeking analysis type of question.

How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes is a goal seeking analysis question.

A goal seeking analysis question is a type of question which helps to determine the efficient and effective measure of achieving a goal either individually or in a group.

The question will help the manager of the restaurant to determine how many servers is needed in order to reduce the waiting time of customers.

Complete question:

The question "How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes?" is a type of

a. goal-seeking analysis.

b. what-if analysis.

c. sensitivity analysis.

d. utility modeling.

a. goal-seeking analysis.

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Solving a linear equation, we will see that the 3 numbers are:

48, 49, and 50.

3 consecutive integers can be written as:

x, x + 1, x + 2

Here we know that 2 times the largest number minus 3 times the smallest one is -44, then:

2*(x + 2) - 3x = -44

We can solve that linear equation for x:

2x + 4 - 3x = -44

(2 - 3)x = -44 - 4

-x = -48

x = 48

Then the 3 numbers are:

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Answer:

89

Step-by-step explanation:

[tex] \sqrt{ {80}^{2} + {39}^{2} } = 89[/tex]

The distance between the top of the pillar and the foot of the shadow is  80 meters.

Let's call the distance we want to find "x".

In particular, set up the following proportion:

pillar height / shadow length = distance / shadow length

Plugin the given values

80 / 39 = x / 39

Simplifying and solving for x

x = (80 / 39) * 39

x ≈ 80

Therefore, the distance between the top of the pillar and the foot of the shadow is  80 meters.

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Answer:

A. (3, 8) and [tex]2\sqrt{2}[/tex]

B. (2, 4) and [tex]2\sqrt{10}[/tex]

Step-by-step explanation:

Midpoint formula: [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2})[/tex]

Distance formula: [tex]\sqrt{(x_{2}-x_{1}) ^2+(y_{2}-y_{1}) ^2 }[/tex]

A. plug in the points in the formulas

(4, 7) and (2, 9)

Midpoint:

[tex](\frac{4 + 2}{2} , \frac{7+9}{2} )=6/2, 16/2 = (3,8)[/tex]

Length:

[tex]\sqrt{(2-4)^2+(9-7)^2}=\sqrt{4+4} =\sqrt{8} =2\sqrt{2}[/tex]

B.

(5, 5) and (-1, 3)

Midpoint:

[tex](\frac{5-1}{2} , \frac{5+3}{2} )=4/2,8/2=(2,4)[/tex]

Length:

[tex]\sqrt{(-1-5)^2+(3-5)^2} =\sqrt{-6^2+-2^2} =\sqrt{36+4} =\sqrt{40} = 2\sqrt{10}[/tex]

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The equation of the perpendicular line to the given line is: y = -5/4x - 30.

The slope values of two perpendicular lines are negative reciprocal of each other.

Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.

Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.

Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:

20 = -5/4(-40) + b

20 = 50 + b

20 - 50 = b

b = -30

Substitute m = -5/4 and b = -30 into y = mx + b:

y = -5/4x - 30

The equation of the perpendicular line is: y = -5/4x - 30.

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Answer:

m=months

clark= 10000-105m

lois= 7500-50m

10000-105m=7500-50m

+50m

10,000-55m=7500

-10000

-55m=-2500

simplify

55m=2500

divide by 55

m=45.45

so i would say b

Hope This Helps!!!

The margin of error for a 95% confidence interval for the population proportion is 0.0815.

Given sample size=60 and confidence interval of 95%.

We have to calculate margin of error for a confidence interval of 95%.

Margin of error is the difference between actual values and calculated values. Margin of error is a part of z test.

We have been given sample size=60.

8 people have received help from their parents from the sample.

p=8/60=0.13

which is sample proportion.

z=1-0.13

=0.87

To calculate standard error=[tex]\sqrt{p*z/n}[/tex]

=[tex]\sqrt{0.13*0.8/60}[/tex]

=0.0416

at 95% confidence interval

z(α/2)=1.96

therefore margin of error=1.96*0.0416

=0.081536

=0.0815

Hence the margin of error for 95% confidence interval is 0.0815

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Answer:

-1/3

Step-by-step explanation:

When x is 1, y is 5

When x is 4, y is 4

5-4=1

1-4=-3

1/-3=-1/3

Answer:

14

Step-by-step explanation:

when two lines intersect, the opposite angles are equal: vertical angles rule

this means that 88 and 6x + 4 are the same, therefore we get the equation 6x+4 = 88.

subtracting 4 from both sides, we find that 6x = 84

we get our final answer by dividing each side of the equation by 6:

x = 14

From the given information, the original number is 180. 02

Let the unit digit be x

The unit in tens is x+ 5

The original number = 10(x+5) + x = 11x + 50

The reversed number = 10x+ (x+5) = 11x+5

From the information given, we have that

(11x + 50) - (11x + 5) = 1/4 (11x + 50)

Expand the expression

11x + 50 - 11x - 5 = 1/ 4(11x + 50)

Collect like terms

11x - 11x + 50 - 5 = 1/ 4 (11x + 50)

45 = [tex]\frac{11x + 50}{4}[/tex]

Cross multiply

45 * 4 = 11x + 50

180 = 11x + 50

11x = 180 -50

11x = 130

x = 130/11

x = 11. 82

To find the original number, we have

Original number = 11x + 50

Substitute the value of x

Original number = 11(11.82) + 50

Original number = 130. 02 + 50

Original number = 180. 02

Therefore, the original number is 180. 02

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Answer:

e) 55°

Step-by-step explanation:

use the tangente ratio

[tex]tan\alpha =\frac{10}{7} =1.42857[/tex]

[tex]angle(?)=tan^{-1} (1.42857)=55^{0}[/tex]

Hope this helps

Answer:

55 degrees (e)

Step-by-step explanation:

This is a trigonometry problem. We are given a right triangle with an unknown angle in which the opposite and adjacent sides of the angle are known (10 and 7). We also know that the tangent of any angle is the length of the opposite divided by the length of the adjacent. If we let the unknown angle be Ф, we can say that tan(Ф) = 10/7. To isolate Ф, all we have to do is take the inverse. In other words, Ф = arctan(10/7). Using a graphing calculator, we find that arctan(10/7) is approximately 55 degrees.

Answer:

33.55

Step-by-step explanation:

Answer:

α = 33.56°  (nearest hundredth)

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

As all sides of the right triangle have been given, any of the trigonometric ratios can be used to find α.

Sine Ratio

[tex]\begin{aligned}\sf \sin(\alpha) & = \sf \dfrac{\sqrt{11}}{6}\\\implies \alpha & = \sf \sin^{-1}\left(\dfrac{\sqrt{11}}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]

Cosine Ratio

[tex]\begin{aligned}\sf \cos(\alpha) & =\sf \dfrac{5}{6}\\\implies \alpha & = \sf \cos^{-1}\left(\dfrac{5}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]

Tangent Ratio

[tex]\begin{aligned}\sf \tan(\alpha) & =\sf \dfrac{\sqrt{11}}{5}\\\implies \alpha & = \sf \tan^{-1}\left(\dfrac{\sqrt{11}}{5}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]

Therefore, α = 33.56°  (nearest hundredth)

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Answer:

[tex]a = (h)(2h - 5)[/tex]

Answer:

Area of the rectangle = 2h² - 5

Step-by-step explanation:

• base length l = 5 less than twice the height h

                        = 2h - 5

• height = h

Area of rectangle = base × height

                             ⇒ l × h

                             ⇒ (2h - 5)(h)

                              ⇒ 2h² - 5

Answer:

6

Step-by-step explanation:

9 x 2/3

9/1   x 2/3 =   18 / 3  = 6

Question 4

1) [tex]\overline{BD}[/tex] bisects [tex]\angle ABC[/tex], [tex]\overline{EF} \perp \overline{AB}[/tex], and [tex]\overline{EG} \perp \overline{BC}[/tex] (given)

2) [tex]\angle FBE \cong \angle GBE[/tex] (an angle bisector splits an angle into two congruent parts)

3) [tex]\angle BFE[/tex] and [tex]\angle BGE[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle BFE[/tex] and [tex]\triangle BGE[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\overline{BE} \cong \overline{BE}[/tex] (reflexive property)

6) [tex]\triangle BFE \cong \triangle BGE[/tex] (HA)

Question 5

1) [tex]\angle AXO[/tex] and [tex]\angle BYO[/tex] are right angles, [tex]\angle A \cong \angle B[/tex], [tex]O[/tex] is the midpoint of [tex]\overline{AB}[/tex] (given)

2) [tex]\triangle AXO[/tex] and [tex]\triangle BYO[/tex] are right triangles (a triangle with a right angle is a right triangle)

3) [tex]\overline{AO} \cong \overline{OB}[/tex] (a midpoint splits a segment into two congruent parts)

4) [tex]\triangle AXO \cong \triangle BYO[/tex] (HA)

5) [tex]\overline{OX} \cong \overline{OY}[/tex] (CPCTC)

Question 6

1) [tex]\angle B[/tex] and [tex]\angle D[/tex] are right angles, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex] (given)

2) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

3) [tex]\angle BAC \cong \angle CAD[/tex] (an angle bisector splits an angle into two congruent parts)

4) [tex]\triangle BAC[/tex] and [tex]\triangle CAD[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle BAC \cong \triangle DCA[/tex] (HA)

6) [tex]\angle BCA \cong \angle DCA[/tex] (CPCTC)

7) [tex]\overline{CA}[/tex] bisects [tex]\angle ACD[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)

Question 7

1) [tex]\angle B[/tex] and [tex]\angle C[/tex] are right angles, [tex]\angle 4 \cong \angle 1[/tex] (given)

2) [tex]\triangle BAD[/tex] and [tex]\triangle CAD[/tex] are right triangles (definition of a right triangle)

3) [tex]\angle 1 \cong \angle 3[/tex] (vertical angles are congruent)

4) [tex]\angle 4 \cong \angle 3[/tex] (transitive property of congruence)

5) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

6) [tex]\therefore \triangle BAD \cong \triangle CAD[/tex] (HA theorem)

7) [tex]\angle BDA \cong \angle CDA[/tex] (CPCTC)

8) [tex]\therefore \vec{DA}[/tex] bisects [tex]\angle BDC[/tex] (definition of bisector of an angle)

[tex]f( - 1) = - 3[/tex]

[tex]f(x) = 0 \\ for \: x = 2 \: or \: x = - 2[/tex]

The values of a, b, and c are -4,0 and 0 and the parabola opens downward with y-intercept (0,0).

we have

y=-4x^2

The quadratic equation in standard form is equal to

ax^2+bx+c=0

So,In this problem

a=-4, b=0 and c=0

The y-intercept is the value of y when the value of x is equal to zero

y=-4(0)^2=0

The y-intercept is the point (0,0)

The coefficient a is negative, therefore the parabola opens down.

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