Write the following as an expression and evaluate . The sum of -6 and the quotient of -36 and 6

Answer:

B.

Step-by-step explanation:

This is only true if it is an isosceles trapezium so B is false.

Final answer:

The false statement is that the perpendicular bisector of the base of any trapezoid is always a line of symmetry. This is incorrect as only isosceles trapezoids, which have two non-parallel sides of equal length, are symmetrical in this way.

Explanation:

The statement that is FALSE is: B) The perpendicular bisector of the base of any trapezoid is always a line of symmetry. This statement is incorrect because a trapezoid, by definition, has only one pair of parallel sides, and not all trapezoids are symmetrical unless specified as an isosceles trapezoid. For instance, in irregular trapezoids where the non-parallel sides are of different lengths, the perpendicular bisector of the base does not act as a line of symmetry.

Moreover, statement C, which is true, specifies the conditions under which the perpendicular bisector of the base can be a line of symmetry - that is, in the case of an isosceles trapezoid. An isosceles trapezoid is specifically designed to be symmetrical along the perpendicular bisector of its bases, given its two non-parallel sides are equal in length, unlike general trapezoids.

Answer:

B = 26.407 degrees

C = 73.593 degrees

c = 30.196 units

Step-by-step explanation:

Use the law of sines

sin(B) / 14 = sin(80) / 31

B = sin-1( sin(80) / 31 x 14)

B = 26.407

C = 180 - 80 - 26.407

C = 73.593

c / sin(73.593) = 31 / sin(80)

c = 31 / sin(80) x sin(73.593)

c = 30.196

Answer:

7.5% < 7.49 <  [tex]7\frac{49}{50}[/tex]

Step-by-step explanation:

To make this easier to look at, first you change them into the same form. Let us make them all into fractions and compare:

7.49 as a fraction is [tex]7\dfrac{49}{100}[/tex]

[tex]7\dfrac{49}{50}[/tex] is already a fraction so let's leave it first.

7.5% in fraction form is [tex]\dfrac{75}{1000}[/tex]

Now knowing this, we can already say that 7.5% is already the least comparing it to the others.

Now we compare the two:

[tex]7\dfrac{49}{100} < 7\dfrac{49}{50}[/tex]

If we make them into similar fractions:

[tex]7\dfrac{49}{50} = 7\dfrac{98}{100}\\\\Then\\\\7\dfrac{49}{100}<7\dfrac{98}{100}[/tex]

The equation for this would be 6x=42

Here's an explanation.

You have 6 sheets of paper, and you draw some number of stars on each paper. The number of stars are the same. Let's put the stars one each paper as x. Now it's also given that the total number of stars are 42. Since there are x stars on each paper, then 6 times x would be the total number of stars, which is 42. So 6x=42, and x=7

Answer:

X=-4+ 41/2 SQUARED

Or

X=-4- 41/2 SQUARED

The zeroes of the quadratic equation are -

[tex]\frac{-8-\sqrt{82} }{2}[/tex]  and  [tex]\frac{-8+\sqrt{82} }{2}[/tex].

We have the following quadratic equation -

f(x) = [tex]2x^{2} +16x-9[/tex]

We have to find the zeroes of this quadratic function.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2} +bx+c[/tex] , where a and b are the coefficients, x is the variable, and c is the constant term.

According to the question, we have a quadratic equation -

f(x) = [tex]2x^{2} +16x-9[/tex]

In order to find its zeroes, we will equate f(x) = 0. Therefore -

[tex]2x^{2} +16x-9 = 0[/tex]

Using the quadratic formula -

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

Where a = 2, b = 16 and c = -9.

Substituting the values, we get -

x = [tex]\frac{-16\pm\sqrt{(16)^2-4(2)(-9)}}{2(2)}[/tex]

x = [tex]\frac{-8\pm\sqrt{82} }{2}[/tex]

Hence, the zeroes of the quadratic equation are -

[tex]\frac{-8-\sqrt{82} }{2}[/tex]  and  [tex]\frac{-8+\sqrt{82} }{2}[/tex].

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Step-by-step explanation:

(3 × 70) + (3 × 2)

210 + 6 = 216

Answer:

should be D.

Step-by-step explanation:

hopefully that helps u out!

Answer:

This might be late but D I think

The interest earned is $32.

What is interest?

Interest is the price you pay to borrow money or the cost you charge to lend money.

Given that, Principal $400 Rate = 8% and Time = 1 year

SI = PRT/100

= 400x8x1/100

= 32

Hence, interest earned is $32.

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Answer:

u

Step-by-step explanation:

the endpoint will be the last one to the right

92.004 = 92 + .004 = 92 + 4 = 92 + 1 = 92 1

                                            --            --      -----

                                         1,000       250   250

Answer:

[tex]\large\boxed{92.004=92\dfrac{4}{1000}=92\dfrac{1}{250}}[/tex]

Step-by-step explanation:

[tex]92.004=92+0.\underbrace{004}_{3}=92+\dfrac{4}{1\underbrace{000}_3}=92\dfrac{4}{1000}=92\dfrac{4:4}{1000:4}=92\dfrac{1}{250}[/tex]

Answer:

0.54

Step-by-step explanation:

In Probability "OR" means "ADDITION" and "AND" means "MULTIPLICATION"

Here, we want probability of Jack "OR" Red, so we find individual probabilities and then "ADD" them.

There are 26 cards that are RED, half of the deck. So probability of RED CARD is:

P(red) = 26/52 = 1/2

Now, there are 4 Jacks in the whole deck, 2 red Jack and 2 black Jack. We already accounted for the 2 red jacks, so we have 2 black Jacks at hand. So

P(Jack) = 2/52 = 1/26

Now, we add the 2 probabilities:

P(jack or red) = 1/2 + 1/26 = 13/26 + 1/26 = 14/26 = 0.54 (rounded to 2 decimal places)

Answer: Junior is 3 3/10 feet tall .

Step-by-step explanation:

As given

Junior's brother is 5 1/2 feet tall

i.e

Junior's brother is 11/2 feet tall

Junior is 3/5 of his brother's height

Thus

Junior's heights = 3/5 times his brother's height

Putting all the values in the formula

Junior's Height = 3/5 X 11/2

Junior's height = 33/10

Junior's height = 3 3/10 feet

Therefore Junior is 3 3/10 feet tall .

Junior's height is calculated by taking 3/5 of his brother's height, which is 5.5 feet. Multiplying these, we find out that Junior is 3.3 feet tall.

The student is asking to solve a problem involving fractions and proportions to find out how tall Junior is compared to his brother. Junior's brother is 5 1/2 feet tall, which is equivalent to 5.5 feet. Junior is 3/5 of his brother's height. To find out Junior's height, we multiply the brother's height by 3/5:

To find Junior's height, we need to multiply his brother's height by \( \frac{3}{5} \). If Junior's brother is 5 1/2 feet tall, we can first express this height as an improper fraction:

\[ \text{Brother's height} = 5 \frac{1}{2} = \frac{11}{2} \text{ feet} \]

Now, we can find Junior's height by multiplying his brother's height by \( \frac{3}{5} \):

\[ \text{Junior's height} = \frac{3}{5} \times \frac{11}{2} \]

Multiplying the numerators and denominators:

[tex]\[ \text{Junior's height} = \frac{33}{10} \text{ feet} \][/tex]

To express this as a mixed number:

[tex]\[ \text{Junior's height} = 3 \frac{3}{10} \text{ feet} \][/tex]

Therefore, Junior is 3 feet 3 inches tall, or 3.3 feet, which is [tex]\( \frac{3}{10} \)[/tex]than 3 feet.

Height of Junior = 5.5 feet x 3/5

Height of Junior = 3.3 feet

Therefore, Junior is 3.3 feet tall.

Answer:

C)  It will take  14 weeks for Edurado to make a profit.

Step-by-step explanation:

The money spent on obtaining the merchandise = $ 7500

The general expense per week = $300

Let us assume Eduardo has to work for N weeks to break Even.

So, the general expense in N weeks  = N x( Expense per week)

=  N x ( $300)  = 300 N

So, the total expense in N weeks  =  Money spent on merchandise + general expense

or, the TOTAL EXPENSE =  $ 7500 +  300 N     .... (1)

Now, the earning per week = $850

So, the total earning in N weeks = N x ( Earning in 1 week) =  N x ( $850)

or, the TOTAL EARNING  =  850 N    .... (2)

Now, for N weeks ,

TOTAL EXPENSE  = TOTAL EARNING

⇒ $7500 +  300 N = 850 N

or, 7500 = 850 N -  300 N = 550 N

⇒ N  = 7500/550 = 13.63

So, number of weeks should at least be 13.63

Among the given options, N = 14 weeks is the most feasible answer.

Hence, it will take  14 weeks for Edurado to make a profit.

To minimize the cost, the packaging that should be used is the rectangular prism boxes.

From the complete information, the pencils needed is 2400. The prism can hold 60 pencils. Therefore, the number of prisms needed will be:

= 2400/60 = 40 prisms

The total cost for the prism will be:

= $0.50 × 40

= $20

The cylinder can hold 80 pencils. Therefore, the numbers needed will be:

= 2400/80

= 30

The cost of the cylinders will be:

= 30 × $0.75

= $22.50

Therefore, it implies that to minimize the cost, the packaging that should be used is the rectangular prism boxes.

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The company should use rectangular prism boxes, as they require fewer units and incur lower total cost.

To minimize cost, we need to find out which packaging option, between the rectangular prism box and the cylindrical container, requires fewer units and hence incurs lower total cost.

First, let's calculate how many units of each packaging option are needed to package 2,400 pencils:

1. **Rectangular Prism Box:**

  Each box holds 60 pencils.

  Number of boxes needed [tex]\(= \frac{2400}{60} = 40\)[/tex]

2. **Cylindrical Container:**

  Each container holds 80 pencils.

  Number of containers needed [tex]\(= \frac{2400}{80} = 30\)[/tex]

Now, let's calculate the total cost for each option:

1. **Cost for Rectangular Prism Boxes:**

  Number of boxes: 40

  Cost per box: $0.50

  Total cost: [tex]\(40 \times \$0.50 = \$20\)[/tex]

2. **Cost for Cylindrical Containers:**

  Number of containers: 30

  Cost per container: $0.75

  Total cost: [tex]\(30 \times \$0.75 = \$22.50\)[/tex]

Comparing the total costs, we can see that using the rectangular prism boxes incurs a lower cost $20 compared to using the cylindrical containers $22.50.

The reason for the lower cost with rectangular prism boxes is that each box holds fewer pencils (60) compared to cylindrical containers (80). Therefore, even though the cost per unit for the cylindrical containers is lower ($0.75) compared to the rectangular prism boxes ($0.50), the higher number of units required for cylindrical containers results in a higher total cost.

Therefore, to minimize cost, the company should use the rectangular prism boxes for packaging the pencils.

Answer:

[tex]x^{4}[/tex] - 256

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x² - 16) + 16(x² - 16) ← distribute both parenthesis

= [tex]x^{4}[/tex] - 16x² + 16x² - 256 ← collect like terms

= [tex]x^{4}[/tex] - 256

Answer:

Step-by-step explanation:

(x²+16)(x²-16) = (x²)² - 16² = x^4 - 256 use identity a²-b² = (a-b)(a+b)

Live Fund receive [tex]\bold{\$2500 A}[/tex] it they sold half thier holding in Marks Brothers.

Solution:

Given: Sale price of Live Fund holding = 5000 dollar

To find: Amount that Live Fund will get if they sell half of their holding in Marks Brothers.

Assume the total number of shares held by Live Fund in Marks Brothers as A

Therfore, half the holdings (or half the number of shares) of Live Fund will be [tex]\frac{A}{2}[/tex].

Thus, if each share is valued at [tex]\$5000[/tex], then the total value of the number of shares sold will be as follows,

[tex]\Rightarrow5000\times\frac{A}{2}\text{ dollars }\rightarrow\frac{5000\times A}{2}\text{ dollars }[/tex]

[tex]\Rightarrow2500 A\text{ dollars }[/tex]

Hence, Live Fund will receive [tex]\$2500 A[/tex]

The asymptotes of the function f(x) = 7/(x^2 - 2x - 24) are located at x = 6 and x = -4.

The function f(x) is a rational function, which means it's a fraction of two polynomials. The function has vertical asymptotes where the denominator (x^2 - 2x - 24) equals zero.

To find the asymptotes, set the denominator equal to zero and solve for x:

x^2 - 2x - 24 = 0

Factor the equation: (x - 6)(x + 4) = 0

Therefore, x = 6 and x = -4 are the roots of the denominator.

Since the denominator becomes zero at x = 6 and x = -4, these points represent vertical asymptotes where the function approaches positive or negative infinity.

Therefore, the function f(x) has asymptotes at x = 6 and x = -4.

Answer: 13y-5

Step-by-step explanation: Remove parentheses.

4y-5+9y4y−5+9y

2 Collect like terms.

(4y+9y)-5(4y+9y)−5

Answer:

A u B = {3,5,6,7,8,11,12}

Step-by-step explanation:

A = {3,6,7,11}

B = {3,5,7,8,12}

A u B = {3,5,6,7,8,11,12}

One adult ticket costs £11 and one child ticket costs £8.5

Step-by-step explanation:

Let,

Adult ticket = a

Child ticket = c

According to given statement;

3a+4c=67   Eqn 1

5a+6c=106   Eqn 2

Multiplying Eqn 1 by 5;

[tex]5(3a+4c=67)\\15a+20c=335\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 3;

[tex]3(5a+6c=106)\\15a+18c=318\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 4 from Eqn 3

[tex](15a+20c)-(15a+18c)=335-318\\15a+20c-15a-18c=17\\2c=17\\[/tex]

Dividing both sides by 2

[tex]\frac{2c}{2}=\frac{17}{2}\\c=8.5[/tex]

Putting c=8.5 in Eqn 1

[tex]3a+4(8.5)=67\\3a+34=67\\3a=67-34\\3a=33[/tex]

Dividing both sides by 3;

[tex]\frac{3a}{3}=\frac{33}{3}\\a=11[/tex]

One adult ticket costs £11 and one child ticket costs £8.5

Keywords: Linear equation, subtraction

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Answer:

4x+9

Step-by-step explanation:

x^2+8x+9-(x^2+4x)

x^2-x^2+8x+9-4x

8x-4x+9

4x+9

Answer:

I think A=8 and B would = 2(where the curve is)

hope this helps you!

(p.s;please mark me as brainlyest)

Step-by-step explanation:

ask me if you want/need the explanation

Answer:

The price of the glove is $8.5 and the price of the hat is $6.5.

Step-by-step explanation:

2x+4y=43

2x+2y=30

---------------

2x+4y=43

x+y=15

--------------

x=15-y

2(15-y)+4y=43

30-2y+4y=43

30+2y=43

2y=43-30

2y=13

y=13/2

x+13/2=15

x=15-13/2

x=30/2-13/2=17/2

x=17/2, y=13/2.

The price of the glove is $8.5 and the price of the hat is $6.5.

Answer:

4 + x = 16

Step-by-step explanation:

In general, if we have an equation that has just one variable, such as x, then "solving the equation" means finding the set of all values that can be substituted for the one variable to produce a valid equation.

Isolate "x" on one side of the algebraic equation by adding the negative number that appears on the same side of the equation as the "x." For example, in the equation "x - 5 = 12", rewrite the equation as "x = 12 + 5" and solve for "x."

Answer:

The number is -16.

Step-by-step explanation:

3/4x=-12

x=-12/(3/4)

x=(-12/1)(4/3)

x=-48/3

x=-16

Answer:

11.3%

Step-by-step explanation:

[tex]\%\ increase=\frac{final-initial}{initial} \times 100\%\\\%\ increase=\frac{69-62}{62} \times 100\%\\\%\ increase=\frac{7}{62} \times 100\%\\\%\ increase=11.3\%[/tex]

Answer:

16.1%

Step-by-step explanation:

Answer:

4. 24.39°

5. 27.29°

6. 38.21°

Step-by-step explanation:

Given:

Δ ABC is right angle at A

Δ PQR is right angle at Q

Δ XYZ is right angle at X

To find:

∠ C = ?

∠ P = ?

∠ Z = ?

Solution:

For 4.)

We Know the Identities,

[tex]\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}  \\[/tex]

∴ [tex]\sin C=\frac{AB}{BC} \\\sin C =\frac{19}{46} \\\sin C =0.413\\\therefore C= sin^{-1}(0.413)\\ \angle C=24.39\°[/tex]

For 5.)

[tex]\tan P = \frac{\textrm{side opposite to angle P}}{\textrm{side adjacent to angle P}}\\\tan P = \frac{QR}{QP}\\\tan P = \frac{16}{31}\\\tan P = 0.5161\\\angle P=\cos^{-1}(0.5161)\\\angle P=27.29\°[/tex]

For 6.)

[tex]\cos Z = \frac{\textrm{side adjacent to angle Z}}{Hypotenuse}\\\cos Z = \frac{XZ}{YZ}\\\cos Z = \frac{11}{14}\\\cos Z = 0.7857\\\angle Z= \cos^{-1}(0.7857)\\\angle Z= 38.21\°[/tex]

Law of Sines

[tex]\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a} \\ \\ \frac{sin\:40°}{5} = \frac{sin∠C}{7} → \frac{7sin\:40°}{5} = sin∠C → 0,8999026535... = sin∠C → 64,14527443...° = sin^{-1}\:0,8999026535... \\ \\ 64° ≈ m∠C[/tex]

As you can see, the inverse function had to be used towards the end, or the answer would have been thrown off.

I am joyous to assist you at any time.

Answer:

[tex]59.19 ft^2[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=7.2\ ft[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(7.2)^{2}[/tex]

[tex]A=162.78\ ft^2[/tex]

step 2

we know that

The area of a circle subtends a central angle of 2π radians

so

using proportion

Find out the area of a sector with a central angle of 8 π/11 radians

[tex]\frac{162.78}{2\pi }\frac{ft^2}{rad} =\frac{x}{(8\pi/11)}\frac{ft^2}{rad} \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2[/tex]

Final answer:

The area of a sector with a central angle of 8π/11 radians and a radius of 7.2 ft, using 3.14 for π, is approximately 78.60 ft² when rounded to the nearest hundredth.

Explanation:

To calculate the area of a sector of a circle, we use the formula ½ θr², where θ is the central angle in radians, and r is the radius of the circle. For a sector with a central angle of ₈π/₁₁ radians and a radius of 7.2 ft, substituting 3.14 for π, we can find the area as follows:

Use the formula: Area = (½)(θ)(r²).

Substitute the given values to get: Area = (½)(₈π/₁₁)(7.2 ft)².

Calculating using 3.14 for π we get: Area = (0.5)*(8*3.14/11)*(7.2 ft)².

Simplify and calculate the result which gives us: Area = 78.5952 ft².

Round the final answer to the nearest hundredth: Area = 78.60 ft².