A ladder resting against a wall makes an
angle of 63° with the ground. The foot of
the ladder is 4.7 m from the wall.
Calculate the height of the top of the
ladder above the ground​

The multiplication shows that the answers will be:

1. 3744

2. 8244

3. 3630

4. 2616

5. 20772

6. 7820

7. 3916

8. 3521

9. 21285

10. 54162

11. 4548

12. 2091

13. 17128

14. 55692

15. $895

16. 4300 miles

1. 416 × 9 = 3744

2. 1374 × 6 = 8244

3. 726 × 5 = 3630

4. 872 × 3 = 2616

5. 2308 × 9 = 20772

6. 1564 × 5 = 7820

7. 4 × 979 = 3916

8. 503 × 7 = 3521

9. 5 × 4257 = 21285

10. 6018 × 9 = 54162

11. 758 × 6 = 4548

12. 3 × 697 = 2091

13. 2141 × 8 = 17128

14. 7 × 7956 = 55692

15. From the information given, the cost of each ticket is $179. Also, there are 5 people that are flying.

Therefore, the total cost will be:

= $179 × 5

= $895

16. Also, for the second question, since the distance between the two cities is 2150 miles. The exact distance will be:

= 2150 × 2

= 4300 miles.

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The exponential function represented on the graph is defined by the following rule:

[tex]y = 3 \times 2^x[/tex]

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

From the graph, we get that when x = 0, y = 3, hence the initial value is of a = 3. Then the temporary definition is:

[tex]y = 3b^x[/tex]

Also from the graph, when x = 1, y = 6, hence we can apply to the definition to find b.

[tex]6 = 3b^1[/tex]

3b = 6

b = 2.

Hence the function is:

[tex]y = 3 \times 2^x[/tex]

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1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.

2. The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists at 0.531.

Let the number of the person who is older than 35 years have a hemoglobin level between 9 and 11 be x.

From the given table it is clear that the total number of the person who is older than 35 years exists 162.

75+x+40 = 162

x+116 = 162

x = 162-116

x = 46

The number of people who are older than 35 years has a hemoglobin level between 9 and 11 exists at 46.

1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists

P = Probability who is older than 35 years has a hemoglobin level                                                              

     between 9 and 11 / Person who exists older than 35

P = 46/162 = 0.284

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.

2. Person who is older than 35 years has a hemoglobin level of 9 and above exists 46 + 40 = 86.

The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists

P = Probability who is older than 35 years has a hemoglobin level  

       between 9 and above / Person who is older than 35

P = 86/162 = 0.531.

The probability that a person who is older than 35 years has a hemoglobin level of 9 and above exists at 0.531.

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The area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].

Given the sides of trapezium be 16 cm, 15 cm, 30 cm, 13 cm.

We are required to find the area of adjoining trapezium.

Draw two perpendiculars on AD and the points will be E and F.

From triangles ABE and CFD.

let the length of AE=x, FD=30-16-x=14-x.

BE=[tex]\sqrt{169-x^{2} }[/tex], CF=[tex]\sqrt{225-(14-x)^{2} }[/tex]

BE=CF

[tex]\sqrt{169-x^{2} }[/tex]=[tex]\sqrt{225-(14-x)^{2} }[/tex]

Squaring both sides.

169-[tex]x^{2}[/tex]=225-196-[tex]x^{2}[/tex]+28x

140=28x

x=5 cm.

Put in BE=[tex]\sqrt{169-x^{2} }[/tex]

BE=[tex]\sqrt{169-25}[/tex]

=[tex]\sqrt{144}[/tex]

=12 cm.

Area of trapezium=1/2 (sum of parallel sides)*height

=1/2 (30+16)*12

=23*12

=276 [tex]cm^{2}[/tex]

Hence if the sides of trapezium are 16 cm, 15 cm, 30 cm, 13 cm then the area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].

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Answer:

10

Step-by-step explanation:

f(x) = 3x + 1

f^-1 = x-1/3 , it is known as inverse function.

f(3)= 3*3 +1

=9+1

=10

To find inverse,

x=3x + 1

y=3x+1

Exchanging the position or x and y

x=3y+1

x-1=3y

.•. y=x-1/3

109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade. This can be obtained by forming the algebraic expression for the given conditions.

Given that,

A parent made x cupcakes for each of the 109 students in the fourth grade.

The total number of students in the class = 109

The number of cupcakes one student gets = 1 × x = x

⇒ The number of cupcakes 109 student gets = 109 × x = 109x

Hence 109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade.

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1) [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{AB} \parallel \vec{CE}[/tex] (given)

2) [tex]\angle A \cong \angle B[/tex] (base angles theorem)

3) [tex]\angle A \cong \angle 1[/tex] (corresponding angles theorem)

4) [tex]\angle B \cong \angle 2[/tex] (alternate interior angles theorem)

5) [tex]\angle 1 \cong \angle 2[/tex] (transitive property of congruence)

6) [tex]\vec{CE}[/tex] bisects [tex]\angle BCD[/tex] (if a ray splits an angle into two congruent parts, it is a bisector)

Answer:

D) 3

Step-by-step explanation:

22 * 2 = 44

To have a remainder 3, the number should be 44 + 3 = 47

47 ÷ 22 , leaves a remainder 3.

47 +22 = 69

69 ÷ 3  leaves a remainder 3.

69 +22 = 91

91 ÷ 3 leaves a remainder 3.

Answer: 47 , 69 , 91

Answer:B:1

Step-by-step explanation:

Write each number out and divide by 22 until you get one that’s answer is 3

Answer:

Step-by-step explanation:

1. $135

2. a. no

    b. $340

3. a. 33

   b. $135*33= $4455+340= $4795

4. a. $7630 = 135v + 340

     b. 135v + 340 = 7630

          135v = 7290

              v = 54 vacuums        

Answer:

  3

Step-by-step explanation:

The quadratic formula is used to solve a quadratic equation in standard form, based on the values of the coefficients.

The standard-form quadratic ax² +bx +c = 0 has solutions given by the quadratic formula:

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

For the quadratic 3x² +4x -2 = 0, we have a=3, b=4, c=-2 and the formula gives ...

  [tex]x=\dfrac{-4\pm\sqrt{4^2-4(3)(-2)}}{2(3)}=\dfrac{-4\pm\sqrt{16+24}}{6}\\\\x=\dfrac{-4\pm 2\sqrt{10}}{6}=\dfrac{-2\pm\sqrt{10}}{3}[/tex]

The denominator in the solution is 3.

Answer:

The answer is x=(-2±√10)/3

Step-by-step explanation:

The value of the x from the given equation is 1 and 6/7.

According to the statement

we have given that the quadratic equation and we have to find the solve for the value of the x.

So, For this purpose we know that the

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers.

So, The given equation is

7x^2 -x -6 =0

Find the factors of the equation

7x^2 -7x + 6x -6 =0

7x(x-1) -6(x-1) = 0

(x-1)(7x-6) =0

here the values of x becomes 1 and 6/7.

So, The value of the x from the given equation is 1 and 6/7.

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Answer:

36

Step-by-step explanation:

12 times 2 which is 24 then u add 12 cause it's the amount they have together so you get 36

idrk but I hope you have a good day and good luck with ur answer

Answer:

  9.08

Step-by-step explanation:

To find the predicted value of y, put the x-value where x is in the equation and do the arithmetic.

  [tex]\hat{y}=134.63-2.79x\qquad\text{given}\\\\\hat{y}=134.63-2.79(45) = 134.63-125.55\qquad\text{use 45 for x}\\\\\boxed{\hat{y}=9.08}\qquad\text{simplify}[/tex]

Answer: x = 3.5

Step-by-Step Solution:

Let us first label the figure.

Let the Triangle be ABC with a line DE || BC.

Now, in ∆ABC,

DE || BC (given)

=> AD/DB = AE/EC (by B.P.T)

Substituting the given values,

AD/DB = AE/EC

2/4 = x/7

1/2 = x/7

2x = 7

x = 7/2

=> x = 3.5

Therefore, x = 3.5

Answer: False

Step-by-step explanation:

The base is more than 1, so the function is increasing.

Using the law of cosines, the ship turned 72 degrees northwest when it changed direction.

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 94, b = 119, c = 173.

Hence the internal angle C is found as follows:

c² = a² + b² - 2abcos(C)

173² = 94² + 119² - 2 x 94 x 119cos(C)

22327cos(C) = -6932

cos(C) = -6932/22327

C = arccos(-6932/22327)

C = 108º.

The turning angle is the outside angle, which is supplementary with C, hence:

T = 180 - C = 180 - 108 = 72º.

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The information given that A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle.

It should be noted that an equilateral triangle simply means the triangle tht had equal shape and angles. Here, since A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle. On such triangle, two out of the three sides are equal.

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Step-by-step explanation:

since the 2 arc angles cover the full circle, we know their sum must be 360°.

so,

23x - 5 + 37x + 5 = 360

60x = 360

x = 6

and so the angle at V = 5×6 + 17 = 30+17 = 47°

Answer:

Step-by-step explanation:

Set it up like an equation first:

[tex]\frac{\frac{-7}{25} }{x}=-\frac{1}{15}[/tex] and then bring up the lower fraction, flip it, and multiply:

[tex]-\frac{7}{25}*\frac{1}{x}=-\frac{1}{15}[/tex]

Simplify to

[tex]-\frac{7}{25x}=-\frac{1}{15}[/tex] and cross multiply to get

-25x = -105 and divide both sides by -25 to get that

[tex]x=\frac{105}{25}=\frac{21}{5}[/tex]

Answer:

336 ways

Step-by-step explanation:

Use nPk which is [tex]\frac{n!}{(n-k)!}[/tex]. This is [tex]\frac{8!}{5!}[/tex]. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.

Total number of possible 3-topping pizzas are 336 ways.

In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!

Given that,

Total number of items n = 8

number of picking item k = 3

Now,

p(n,k) = [tex]\frac{n!}{(n -k)!}[/tex]

p(8,5) =  [tex]\frac{8!}{(8 -3)!}[/tex]

         = [tex]\frac{8!}{5!}[/tex]

         = [tex]\frac{8.7.6.5! }{5! }[/tex]

         = 8 × 7 ×6

p(8,5) = 336 ways

Hence, Total number of possible 3-topping pizzas are 336 ways.

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The expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].

What is an expression?

To find which expression correctly sets up the quadratic formula to solve the equation:

Theory of quadratic equation - A quadratic equation is defined as any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

An example of a quadratic equation in x is [tex]-4x^{2} +4=9x[/tex].

How to solve any quadratic equation using the Sridharacharya formula?

Let us represent a general quadratic equation in x, [tex]ax^{2} +bx+c=0[/tex] where a, b and c are coefficients of the terms.

According to the Sridharacharya formula, the value of x or the roots of the quadratic equation is -

[tex]x=\frac{-b+-\sqrt{(b)^{2}-4(a)(c) } }{2a}[/tex]

The given equation is [tex]x^{2} -4x+3=0[/tex]

Comparing with the general equation of quadratic equation, we get a = 1, b = -4 , c = 3.

Putting the values of coefficients in the Sridharacharya formula,

[tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex]  which is (A).

Therefore, the expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].

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The complete question is shown below:

Consider this quadratic equation. x^2+3=4x. Which expression correctly sets up the quadratic formula to solve the equation?

The graph of the function has no asymptotes.

The function is given as:

c(t) = 5t - t² + 1

When t = 1, 2, 5, 10;

We have:

c(1) = 5(1) - 1² + 1 = 5

c(2) = 5(2) - 2² + 1 = 7

c(5) = 5(5) - 5² + 1 = 1

c(10) = 5(10) - 10² + 1 = -49

So, the table of values is

t        c(t)

1         5

2        7

5        1

10      -49

See attachment for the graph of the function

The domain

From the question, we understand that t represents time.

So, the domain is 0 ≤ t ≤ 5.2

The range

From the graph, the maximum of the graph is 7.25

So, the range is 0 ≤ f(t) ≤ 7.25

Asymptotes

From the graph, we can see that the graph has no asymptotes.

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Answer: 12 cm

Step-by-step explanation:

[tex]\mathtt{Using\ the \ pythagorean \ theorem: \\}[/tex]

[tex]a^2+b^2=c^2, \\\ we\ can\ plug\ in\ values\ for\ a,\ b,\ and\ c[/tex]

[tex]L=a\ and\ M=b\ and\ N=c[/tex]

Therefore,

[tex]L^2+35^2=37^2\\L^2+1225=1369\\L^2=144\\\sqrt{L^2} =\sqrt{144} \\L=\pm12\\Taking\ only\ the\ positive\ answer,\ we\ get:\\\large\boxed{L = 12cm}[/tex]

We have: L² + M² = N²

=> L² = N² - M² = 37² - 35² = 144 = 12²

=> L = 12

ANSWER: B.12

OK done. Thank to me :3

Answer:

E. >

Because 65 is greater than 56.

The average view of the dress code is that this dress is not good

For Rashad's sample to be a random sample gotten from the population, the following must be considered.

To do this, we simply create a bar graph.

The response would go into the x-axis, while the number of people would go into the y-axis

See attachment for bar graph

The average view of the dress code is that this dress is not good

It is considered the average view of the dress code because it is the opinion with the most frequency

The number of students that do not like the dress as:

210 + 206 + 770 = 1186

Their percentage is

Percentage = 1186/(210 + 206 + 770 + 358)

Percentage = 77%

This means that

Yes, the dress will change

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The time it takes them working together to paint the room is 3.08 hours

Rational expression are equation written as a ratio of two expressions or equations.

If Wes can paint a certain room in 8 hours, she can paint 1/8 of the room in 1 hr

Similarly, if Sally can paint the same room in 5 hours, , she can paint 1/5 of the room in 1 hr

Determine the time it takes them to paint the room altogether.

Time together = x

Using the expression below to determine the value of x

1/x = 1/8 + 1/5

1/x = 5+8/40

1/x = 13/40
x = 40/13

x = 3.08

Hence the time it takes them working together to paint the room is 3.08 hours

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