9
Question 4 (5 points)
Evaluate the expression: 230 - 151 + 180 + (43 - 12).
A) 46
OB) -44
C) 18
D) 57​

Answer:

54 = 2 x 27

the cube root of 27 is 3.

the answer is C

Step-by-step explanation:

Answer:

The perfect cube is 27 and the perfect cube root is 3

Step-by-step explanation:

( 54) ^ 1/3

( 27*2) ^ 1/3

(27) ^1/3 * (2)^1/3

3 * (cube root of 2)

The perfect cube is 27 and the perfect cube root is 3

Answer:

[tex]a = 30[/tex]

[tex]b = 40[/tex]

Step-by-step explanation:

Given

The attached triangle

Such that K is parallel to L

Required

Find the value of a and b

From the properties of parallel triangles;

Provided that k is parallel to l, then

[tex]\frac{a}{40} = \frac{a+15}{60}[/tex]

Multiply both sides by (60)(40)

[tex](60)*(40)*\frac{a}{40} = (60)*(40)*\frac{a+15}{60}[/tex]

[tex]60a = 40(a+15)[/tex]

Open Bracket

[tex]60a = 40*a+40*15[/tex]

[tex]60a = 40a+600[/tex]

Subtract 40a from both sides

[tex]60a - 40a = 40a - 40a + 600[/tex]

[tex]20a = 600[/tex]

Divide both sides by 20

[tex]\frac{20a}{20} = \frac{600}{20}[/tex]

[tex]a = \frac{600}{20}[/tex]

[tex]a = 30[/tex]

Similarly;

[tex]\frac{b}{40} = \frac{b+20}{60}[/tex]

Multiply both sides by (60)(40)

[tex](60)*(40)*\frac{b}{40} = (60)*(40)*\frac{b+20}{60}[/tex]

[tex]60b = 40(b+20)[/tex]

Open Bracket

[tex]60b = 40*b+40*20[/tex]

[tex]60b = 40b+800[/tex]

Subtract 40b from both sides

[tex]60b - 40b= 40b - 40b + 800[/tex]

[tex]20b= 800[/tex]

Divide both sides by 20

[tex]\frac{20b}{20} = \frac{800}{20}[/tex]

[tex]b = \frac{800}{20}[/tex]

[tex]b = 40[/tex]

Answer:

The lowest number that is a multiple of 6 and 8 is 24.

Step-by-step explanation:

6, 12, 18, 24.

8, 16, 24.

Out of the given numbers, 24 is the multiple of 6 and 8. Hence, the option (3) is correct.

Let's check for all the given options:

1) 3: 3 is divisible by neither 6 nor 8 hence it is not a multiple of both.

2) 18 : 18 is divisible by 6 but not divisible by 8. Hence, this option is not correct. Since we have to find a number which is divisible by 6 as well as by 8.

3) 24: 24 is divisible by 6 as well as by 8. Hence, this option is correct.

4) 2: 2 is neither divisible by 6 nor by 8. Hence, this option is not correct.

Hence, the correct option is (3).

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Answer:

a) is -7

Step-by-step explanation:

8=2048[tex](2)^{n-1}[/tex]

[tex]\frac{8}{2048} =\frac{2048^{n-1} }{2048}[/tex]

8/2048=0.00390625 = [tex](2)^{n-1}[/tex]

[tex]2^{-8}[/tex] = 0.00390625

-8-1=-7

and do the rest with the same equation which is tn=a[tex]r^{n-1}[/tex]

Answer:

[tex]g(x) = \frac{1}{9} \,x^2[/tex] which agrees with option A in the list of possible answers

Step-by-step explanation:

A vertical compression by a factor 9 is represented by the transformation:

[tex]\frac{1}{9} \,f(x) = \frac{1}{9} \,x^2[/tex]

Therefore the answer to the problem is:

[tex]g(x) = \frac{1}{9} \,x^2[/tex]

Answer:

5/14

Step-by-step explanation:

Multiply.

(-5 × -1 × 4) / (7 × 8)

20/56

Simplify.

5/14

Answer:

The answer is [tex]\frac{5}{14}[/tex].

Step-by-step explanation:

1. -5 × [tex]\frac{-1}{7}[/tex] =  [tex]\frac{5}{7}[/tex]

2.  [tex]\frac{5}{7}[/tex] · [tex]\frac{4}{8}[/tex] = [tex]\frac{20}{56}[/tex]

3. Simplify:

[tex]\frac{20}{56}[/tex]  = [tex]\frac{5}{14}[/tex]

Answer:

The answer is c. (0,-1)

Step-by-step explanation:

So the unit circle is derived from a right triangle.

Answer:

113.1 square mm

Step-by-step explanation:

A=πr2=π·62≈113.09734

Answer:

[tex]= 36\pi \: {mm}^{2} \\ [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = \pi \times 6 \times 6 \\ = 36\pi \: {mm}^{2} [/tex]

Answer:

Yes the new method if sample size was less than 20 than that of old method or identical sample numbers of old and new the differences still prove the new operation is better. As 88 patients minus 1% still shows us 76.7475 significance of  old method being low point 67.5 = 30% of 225 and proved a 65.25 low point and 69.75 high point which is also a 20% jump to new methods low point significance.

You cna show this as workings to prove or follow any of the below statements.

Where new method of 88 patients -0.01 significance rate stands at 76.7475. This figure has reduced by 11.2525 from 88 patients to 76.7 we compare this to the old method if reversing significance we find  = 62.5 and it's 30% standing value of 67.5  as +1% increase shows us 31% = 69.7  ( 0.31 x 225 = 69.74)

Step-by-step explanation:

88/225  = 0.39111111111 = 39.11%%

P value 01 = 1%  =  225.225 or 5% range of alternative hypotheses.

To graph the P value we take the distance between the sample mean and the null hypothesis value (225 + 1% of sample - x nhv) = y ). We can graph the probability of obtaining a sample mean  (225 +/- ( x +1% of sample) where nhv has a decimal if needed to utilize the 1% added). we would replace nvp in this example with  Ha or H1 which means the alternative hypotheses as the data shows less than or equal to.

We can then show 225.225 -  Ha or H1  then graph the probability of obtaining a sample mean that is at least extreme in both tails  Ha or H1

However it would be the other way round where you take the first set of data and use the sample as the 30% significance of that sample indicates it may be a larger sample or a higher significance. Therefore this would be used in the graphing - 1%

We prove that 30-1 =29  where 29% of 225 = 225 x 0.29 = 65.25

this way we have proved that the new set of data being equal to 88 patients regaining their eyesight is <23 and can be written like this 65.25< x <88

This means that sample mean has taken the 1% to show on the graph we can show 225> 33.11 +1 .

We can prove that both indifference of significance would reduce when 1% is added and close based on being a higher percentage to begin with.

34.11 = 0.3411 x 225 = 76.7475 for second surgeon = 33.11% +1

Where as shown

30 = 0.3 x 225 = 67.5

76.5475 - 67.5 = 9.04 difference when comparing old method = +1%

where new method stands at 76.7475 has reduced by 11.2525 from 88 patients and where old method if reversing = 62.5 and has reduced from 67.5  as +1% and 31% = 69.7  ( 0.31 x 225 = 69.74)

You would therefore graph each higher methods first if comparing both by 0.01 or show 88 on graph and 76.7475 = +1%

NB/ if sample size was 20 more in the old data then 225+20 = 245 x 0.29 = 71.05 and would still be lower than new data. = 2.0 increase level of significance and not relevant unless you are looking for the decrease which means new is greater than 20% success than that of old method findings where 30% = 67.5.

Answer:

Proved: PM ≅ ON

Step-by-step explanation:

A parallelogram is a quadrilateral with two opposite sides equal and parallel.

Find attached the diagram obtained from the information

From the above definition, quadrilateral MNOP is a parallelogram if:

Line MN is parallel to Line OP

Line ON is parallel to Line PN

From the diagram

Line MN is parallel to Line OP

Side MN is = side OP

Line ON is parallel to Line PN

Side ON is = side PN

Since the geometric size is equivalent

PM ≅ ON

Where ≅ means congruent to

Proved.

Answer:

240; 24

Step-by-step explanation:

Given that:

Sum of two numbers = 264

One number ends with '0'

Second number = first number without '0'

Let the first number be 'a'

Since the second number is the first number with '0' erased, then,

Second number = (a ÷ 10)

Therefore, the expression becomes :

a + a/10 = 264

Multiply the equation by 10

10a + a = 2640

11a = 2640

a = 2640/11

a = 240

Therefore ;

a = 240 ;

a/10 = 240/10 = 24

The numbers are 240 and 24

Answer:

The A) ΔABC ≅ ΔEDC

Step-by-step explanation:

The AAS congruence method requires 2 angles and their un-included side to be congruent. ∠A ≅ ∠E due to the markings, ∠C ≅ ∠C because they are vertical angles, and AB ≅ ED due to the markings. 2 angles and their un-included side are congruent.

As for the congruence statement, A is the correct answer because ∠A ≅ ∠E, ∠B ≅ ∠D, and ∠C ≅ ∠C. The order of the naming of the triangles aligns to the angle's congruence.

Answer:

A) triangle ABC is congruent to triangle EDC

Step-by-step explanation:

The AAS method of proving congruence of triangles uses two angles and a non-included side of the triangle. If two angles and the non-included side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Let's see what we have in this problem:

<ACB and <ECD are congruent since they are vertical angles.

<A and <E are congruent by given.

Sides AB and ED are non-included sides and are congruent.

Since we have two angles and a non-included side of a triangle and the corresponding parts of another triangle, the triangles are congruent by AAS.

Now we need the statement of congruence.

Angles ACB and ECD are corresponding angles, so the letter C must appear in both triangles in the same position.

Angles A and E are corresponding angles, so the letters A and E must appear in both triangles the same position.

We already have CA and CE. The last angles left are corresponding angles B and D, so we get triangle CAB and triangle CED. Since a triangle may be named using any order of the vertices, we can rename the triangles ABC and EDC and maintain the same corresponding vertices.

Answer: A) triangle ABC is congruent to triangle EDC

Answer:

62.363°

Step-by-step explanation:

The decimal form of degree is 62.363°.

Geographic coordinates for latitude and longitude can be expressed as decimal fractions of a degree using the notation decimal degrees (DD). Many geographic information systems (GIS), web mapping tools like OpenStreetMap, and GPS units all employ DD.

Latitudes that are positive are north of the equator and those that are negative are south of the equator. Longitudes that are positive are east of the Prime Meridian and those that are negative are west of the Prime Meridian.

Given 62°21'47"

A DMS value is converted to decimal degrees using the formula:

[tex]{\displaystyle \mathrm {D} _{\text{dec}}=\mathrm {D} +{\frac {\mathrm {M} }{60}}+{\frac {\mathrm {S} }{3600}}}[/tex]

D = 62°

M = 21'

S = 47"

substitute the values,

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62 + 21/60 + 47/3600

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62 + 0.35 + 0.01305

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62.3630

[tex]{\displaystyle \mathrm {D} _{\text{dec}}[/tex] = 62.363°

Hence the decimal form is 62.363°.

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Answer:

The first one!

Step-by-step explanation:

the others don't work since there could be more possibilitys than just b and c.

D is just wrong (as you creati)

I seriously cited the sources you fool>;/

plagiarism, what joke is that! is it a joke? don't be crazy please! thanks!

Answer:

25.12

Step-by-step explanation:

round pi to first 2 digits after decimal point.

3.14 x 8 =25.12

Answer:

7/4 + 9/-5 =

Since the denominator of the second fraction is negative the sign will change from negative to positive

We will get

7/4 - 9/5

First find the LCM

LCM of 4 and 5 is 20

7/4 - 9/5 = 5(7) - 4(9)/ 20

Simplify

We get

35 - 36/20

= -1/20

Hope this helps

Answer:

-1/20

Step-by-step explanation:

7/4 + -9/5

We need a common denominator, which is 20

7/4 *5/5   + -9/5 *4/4

35/20  + -36/20

Add the numerators together

-1/20

Answer:

Step-by-step explanation:

For greater clarity, graph this triangle.  If this triangle is reflected about the y-axis, the point C(0, 2) remains a vertex.  The point B(3, -3) becomes D(-3, -3).  Finally, the point A(4, -1) becomes E(-4, -1).

Answer:

A(4,-1)-> A'(-4,-1) .   B(3,-3)->B'(-3, -3) .  C(0,2) -> C' (0,2)

Step-by-step explanation:

Answer:

Approximately 43.30 miles

Step-by-step explanation:

We use the given formula:

[tex]d=\sqrt{1.5\,h}[/tex]

replacing "h" with the value of the height of the Empire State Building (1250 feet):

[tex]d=\sqrt{1.5\,*1250} \\d= 43.30 \,\,\,miles[/tex]

Answer:

I think there is an error in the question because

(f-g) = -4

(f-g) (7) = NO SOLUTION

Step-by-step explanation:

[tex]f(x) = -9x + 2 \\g(x) = -9x + 6\\(f - g)(7)\\(f - g) = -9x + 2 - (-9x+6)\\(f - g) = -9x +2 +9x-6\\(f - g) = -9x +9x+2-6\\(f - g) = -4[/tex]

Answer:

Step-by-step explanation:

d = √(x₂ - x₁)² + (y₂ - y₁)²

x₂ = 1

x₁ = - 2 1/2 = - 5/2

y₂ = - 3

y₁ = - 3

d = √( 1 + 5/2)² + (- 3 + 3)²

= √(2/2 + 5/2) + 0

= √(7/2)²

= 7/2

= 3  1/2

Answer:

D

Step-by-step explanation:

(-2 1/2, -3) = (-5/2 , -3)    &  (1, -3)

[tex]Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(1-[\frac{-5}{2}])^{2}+(-3-[-3])^{2}}\\\\ =\sqrt{(1+\frac{5}{2})^{2}+(-3+3)^{2}}\\\\ =\sqrt{(\frac{7}{2})^{2}} \\\\=\frac{7}{2}\\\\=3\frac{1}{2}[/tex]

Answer:

x= 70

Step-by-step explanation:

This question needs an attachment; see attached

Given

ABD = 55

Required

Find x?

In the figure shown in the attachment, angle b and ABD are alternate interior angles;

From parallel and perpendicular line theorems; alternate interior angles are equal.

This implies that <b = 55

Also; when a rectangle is divided by two diagonals, the resulting triangles are isosceles triangles;

where 2 sides and 2 angles are equal;

This implies that <b = <c = 55

Sum of angles in a triangle  = 180;

So,

<x + <b + <c = 55

x + 55 + 55 = 180

x + 110 = 180

Subtract 110 from both sides

x + 110 - 110 = 180 - 110

x = 180 - 110

x = 70

Answer:

n(n +1) is the Total number of seats in the corner section.

Step-by-step explanation:

We are given that:

Number of seats in first row = 2

Number of seats in second row = 4

Number of seats in third row = 6

:

Number of seats in [tex]n^{th}[/tex] row = [tex]2n[/tex]

We can clearly see that it is an Arithmetic progression with

First term, a = 2

Common Difference, d = 2

[tex]n^{th}[/tex] term, [tex]a_n=2n[/tex]

To find: Total number of seats in corner sections with n rows.

i.e. Sum of n terms of above AP.

Formula for sum of n terms of an AP:

[tex]S_n=\dfrac{n}{2}(2a+(n-1)d)\\[/tex]

Putting the values:

[tex]\Rightarrow \dfrac{n}{2} ({2 \times 2 +(n-1)2})\\\Rightarrow \dfrac{n}{2} (4 +2n-2)\\\Rightarrow \dfrac{n}{2} (2n +2)\\\Rightarrow \dfrac{n}{2} \times 2(n +1)\\\Rightarrow n(n +1)[/tex]

n(n +1) is the Total number of seats in the corner section.

Answer:

Both lines are equal (they are the same)

Step-by-step explanation:

Given

[tex]3y - 8 = -5x[/tex]

[tex]6y = -10x + 16[/tex]

Required

What is true about graph of both lines

Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check  if both lines are either parallel or perpendicular

To do this,

The first thing to do is to calculate the slope of both lines

[tex]3y - 8 = -5x[/tex]

Add 8 to both sides

[tex]3y - 8 + 8 = -5x + 8[/tex]

[tex]3y = -5x + 8[/tex]

Divide both sided by 3

[tex]\frac{3y}{3} = -\frac{5x}{3} + \frac{8}{3}[/tex]

[tex]y = -\frac{5x}{3} + \frac{8}{3}[/tex]

The slope of the line is the coefficient of x;

[tex]Slope = -\frac{5}{3}[/tex]

Solve for the y intercept; Let x = 0

[tex]y = -\frac{5 * 0}{3} + \frac{8}{3}[/tex]

[tex]y = 0 + \frac{8}{3}[/tex]

[tex]y = \frac{8}{3}[/tex]

Solve for the x intercept; Let y = 0

[tex]0 = -\frac{5x}{3} + \frac{8}{3}[/tex]

Subtract [tex]\frac{8}{3}[/tex] from both sides

[tex]0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}[/tex]

[tex]- \frac{8}{3} = -\frac{5x}{3}[/tex]

Subtract both sides by [tex]-\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = x[/tex]

[tex]\frac{3}{5} * \frac{8}{3} = x[/tex]

[tex]\frac{8}{5} = x[/tex]

[tex]x = \frac{8}{5}[/tex]

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

[tex]6y = -10x + 16[/tex]

Divide both sides by 6

[tex]\frac{6y}{6} = -\frac{10x}{6} + \frac{16}{6}[/tex]

[tex]y = -\frac{10x}{6} + \frac{16}{6}[/tex]

Simplify fractions to lowest term

[tex]y = -\frac{5x}{3} + \frac{8}{3}[/tex]

The slope of the line is the coefficient of x;

[tex]Slope = -\frac{5}{3}[/tex]

Solve for the y intercept; Let x = 0

[tex]y = -\frac{5 * 0}{3} + \frac{8}{3}[/tex]

[tex]y = 0 + \frac{8}{3}[/tex]

[tex]y = \frac{8}{3}[/tex]

Solve for the x intercept; Let y = 0

[tex]0 = -\frac{5x}{3} + \frac{8}{3}[/tex]

Subtract [tex]\frac{8}{3}[/tex] from both sides

[tex]0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}[/tex]

[tex]- \frac{8}{3} = -\frac{5x}{3}[/tex]

Subtract both sides by [tex]-\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}[/tex]

[tex]-\frac{3}{5}*- \frac{8}{3} = x[/tex]

[tex]\frac{3}{5} * \frac{8}{3} = x[/tex]

[tex]\frac{8}{5} = x[/tex]

[tex]x = \frac{8}{5}[/tex]

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

By comparing the slope, x intercept and y intercept of both lines;

It'll be observed that they have the same slope, x intercept and y intercept

This implies that both lines are equal; in other words, they are the same.

Answer:

a) 5.83 cm

b) 34.4 deg

Step-by-step explanation:

a)

AC is the hypotenuse of a right triangle with legs measuring 3 cm and 5 cm.

c^2 = a^2 + b^2

c^2 = 3^2 + 5^2

c^2 = 9 + 25

c^2 = 34

c = sqrt(34) cm = 5.83 cm

b)

Triangle ACD is a right triangle with right angle DAC.

AD = 4 cm

AC = 5.83 cm

tan <ACD = opp/adj

tan <ACD = AD/AC

tan <ACD = 4/5.83

m<ACD = tan^-1 (0.68599)

m<ACD = 34.4 deg

The side length AC is 5.83 cm and angle ACD is 34.5 degrees

(a) Length AC

To do this, we make use of the following Pythagoras theorem in triangle ABC

[tex]\mathbf{AC^2 = AB^2 + BC^2}[/tex]

So, we have:

[tex]\mathbf{AC^2 = 3^2 + 5^2}[/tex]

[tex]\mathbf{AC^2 = 9 + 25}[/tex]

[tex]\mathbf{AC^2 = 34}[/tex]

Take square roots

[tex]\mathbf{AC = 5.83}[/tex]

(b) Angle ACD

To do this, we make use of the following tangent ratio

[tex]\mathbf{tan(C) = \frac{AD}{AC}}[/tex]

So, we have:

[tex]\mathbf{tan(C) = \frac{4}{5.83}}[/tex]

[tex]\mathbf{tan(C) = 0.6861}[/tex]

Take arc tan of both sides

[tex]\mathbf{C= 34.5}[/tex]

Hence, side length AC is 5.83 cm and angle ACD is 34.5 degrees

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Answer:

yes their parallel

Step-by-step explanation:

their the same equation just one is negative they go the go next to each other but never touch

Answer:

Step-by-step explanation:

$11/ 47 pound = $0.234 for 1 pound

the cost of buying 47 pound for 11 dollars is cheaper than to buy individual 1 pound bag for 0.45.

Answer:

First, let's find the unit price.

$11 ÷ 47 = $0.23 per pound.

$0.45 ÷ 1 = $0.45 per pound.

As you can see here, the 1 pound bag(smaller bag) clearly costs more per pound. The 47 pound bag(larger bag) costs less.

We can also put the values on a number line to compare.

          $0.23               $0.45

      (larger bag)    (smaller bag)

<-|---------o---------------------o---------|------------------------------------------|->

$0                                         $0.50                                           $1

As you can see, the larger bag is closer to zero.

Hope this helped!

-Emma

Answer:

I'm pretty sure its c

Answer:

D

Step-by-step explanation:

Perfect square trinomials can be written as (a + b)² = a² + 2ab + b². In this case, we know that a = x so we can write this as x² + 2bx + b². Since we know that 2bx = 24x we can conclude that b = 12, so that means b² = 12 * 12 = 144.

Answer:

Answer D

Step-by-step explanation:

Take half of the coefficient of x:  Take half of +24, obtaining 12.  Now square this 12, obtaining 144.  This is the desired value.  Answer D is correct.

Answer:

function 18/y is defined for all values of y such that [tex]y \in R, y\neq 0[/tex]

Step-by-step explanation:

given data

number = 18/y

solution

in given value 18/y

If y=0, the function will be Undefined.

Because, the function is undefined if its denominator = 0

so that if we determine the function is defined, we will find out for what values the function is undefined and remove it

so, the function 18/y is defined for all values of y such that

[tex]y \in R, y\neq 0[/tex]