What number should replace the question mark?

Answer: Length 132cm, Breadth 48cm

Explanation:

Perimeter = 360cm

Let the length and breadth be x

ATQ

2(11x + 4x) = 360

22x + 8x = 360

30x = 360

x = 360/30

x = 12

Length = 11×12

= 132 cm

Breadth = 4×12

= 48cm

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Answer:

m∠Q = 61°

m∠S = 61°

m∠R = 58°

Step-by-step explanation:

Since we have an isosceles triangle, we know that ∠Q and ∠S are congruent.

Step 1: Definition of isosceles triangle

2x + 41 = 3x + 31

41 = x + 31

x = 10

Step 2: Find m∠Q

m∠Q = 2(10) + 41

m∠Q = 20 + 41

m∠Q = 61°

Step 3: Find m∠S

Since m∠Q = m∠S,

m∠S = 61°

Step 4: Find m∠R (Definition of a triangle)

Sum of angles in a triangle adds up to 180°

m∠R = 180 - (61 + 61)

m∠R = 180 - 122

m∠R = 58°

Answer:

The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.

If it was just a number and no x then it would still be the coefficient.

The degree is 9 as it is the highest power shown.

Step-by-step explanation:

See attachment for examples

Answer:

b. steepest slope

Step-by-step explanation:

The cumulative relative frequency curve also known as Ogive is used for reading the median, upper quartile, lower quartile from the curve and calculating the semi-interquartile range when needed.

From the cumulative relative frequency curve, the interval with the highest proportion of measurements is the interval with the steepest slope. This is because the cumulative relative frequency curve always have a positive slope, and given that the interval has the highest proportion, then the slope will be steepest.

Answer:

Washer $735

Dryer $245

Step-by-step explanation:

If x is the cost of the washer, and y is the cost of the dryer, then:

x + y = 980

x = 3y

Solve with substitution.

3y + y = 980

4y = 980

y = 245

x = 735

Answer:

4 cups of flour is needed and 4/3 cups of sugar

Step-by-step explanation:

Given

2 dozen Muffins; 3 cups of flour and 1 cup of sugar

Required

Determine the cups of flour if 18 muffins is used

First, we have to determine the proportion of the number of muffins used previously and now;

Represent this with p;

[tex]p = \frac{2\ dozen}{18}[/tex]

[tex]p = \frac{2 * 12}{18}[/tex]

[tex]p = \frac{24}{18}[/tex]

[tex]p = \frac{4}{3}[/tex]

Multiply this to the previous cups of flours and sugars;

Cups of flour = p * previous cups of flour

[tex]Cups\ of\ flour = \frac{4}{3} * 3[/tex]

[tex]Cups\ of\ flour = 4[/tex]

Cups of Sugar = p * previous cups of sugar

[tex]Cups\ of\ sugar= \frac{4}{3} * 1[/tex]

[tex]Cups\ of\ sugar= \frac{4}{3}[/tex]

Hence, 4 cups of flour is needed and 4/3 cups of sugar

Step-by-step explanation:

what is the criteria for success ? how many questions must be right ? and how many must be wrong for failure ?

if success means all answers right, then she has 4 choices on the first question to pick one right answer. and then for each of those again 4 choices on the second question and so on.

so, all possible outcomes are 4²⁰.

that means the probability to guess all 20 right is

1/4²⁰

a tiny, tiny number.

and the probabilty to have all wrong ?

she has 4 choices to pick 1 of 3 wrong answers.

so, the probability is 3/4 to answer the first question wrong.

for that she has again then the same chance to get the second question wrong too.

so, it is 3/4 × 3/4 = 9/16

and so on.

the probability to guess all 20 wrong is then

(3/4)²⁰ ≈ 0.0032

that is still a small number but much, much larger than the probability to get everything right.

still, even the goal to truly get everything wrong is highly unlikely.

Answer:

3 and 2

Step-by-step explanation:

I can't see your orginal equation. But it's probably 3 cos x . Which the amplitude is 3 then. Vertical translation would be how I move this graph up or down compared to the y axis. So if I were to add a +2 to the end of 3cos(x) I will move the graph up 2 spaces. So my final equation is 3cos (x)+2.

Answer:

Sphere Volume = 4/3 * PI * radius^3

Sphere Volume = 4/3 * PI * 8^3

Sphere Volume = 4/3 * PI * 512

Sphere Volume = 2,144.7 cubic inches

Step-by-step explanation:

The measures of the angles between the peaks are;

m∠BSC = 22.5°

m∠ASB = 67.5°

The reason for arriving at the above angles is as follows:

The known values are;

The location of the surveyor = Point S

The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC

The measure of angle m∠ASC = A right angle = 90°

Required:

To find m∠ASB and m∠BSC

From the given diagram, we have;

m∠ASC = 90°

m∠ASC = m∠ASB + m∠BSC (angle addition postulate)

m∠ASB = 3 × m∠BSC

∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC

m∠ASC = 4 × m∠BSC = 90°

m∠BSC = 90°/4 = 22.5°

m∠BSC = 22.5°

m∠ASB = 3 × m∠BSC

∴ m∠ASB = 3 × 22.5° = 67.5°

m∠ASB = 67.5°

Learn more about angle addition postulate here:

https://brainly.com/question/4208193

9514 1404 393

Answer:

Step-by-step explanation:

-2 is 2 units in the negative direction (left on a number line). When that is added to 3, the result is 2 units from 3 in the negative direction.

Answer:

0.03 square meters

Step-by-step explanation:

1. convert 20 cm, 15 cm into m by dividing the number by 100 then you got 0.2 m and 0.15 m respectively

2. calculate the area by multiply 2 numbers together

0.2 × 0.15 = 0.03 square meter

Answer:

See below.

Step-by-step explanation:

From the graph, we can see that g(x)=3 is true only when x is between 3 and 5. However, note that when x=3, the point is a closed circle. When x=5, the point is an open circle. Therefore, the solution is between 3 and 5, and it includes 3 but not 5.

In set-builder notation, this is:

[tex]\{x|x\in \mathbb{R}, 3\leq x<5\}[/tex]

In interval notation, this is:

[tex][3,5)[/tex]

Essentially, these answers are saying: The solution set for g(x)=3 is all numbers between 3 and 5 including 3 and not including 5.

Answer:

The median would be 7.0.

Step-by-step explanation:

The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.

Answer:

  b.  $11,820

Step-by-step explanation:

The 'rule of 72' tells you the doubling time of this account is about ...

  (72 years)/(4.25) = 16.9 years

So, in 18 years, the amount will be slightly more than double the present value. That is, the present value is slightly less than half the future amount.

  $25,000/2 = $12,500

The closest answer choice is ...

  $11,820

__

The present value of that future amount is ...

  PV = FV×(1 +r)^-t = $25,000×1.0425^-18 ≈ $11,818.73

The present value is about $11,820.

Answer:

B

Step-by-step explanation:

9514 1404 393

Answer:

  A

Step-by-step explanation:

Vertical multiplication of polynomials is virtually identical to vertical multiplication of integers. The "place value" associated with a column is the power of the variable. When adding within a column, there is no "carry" to the next column the way there is with integers.

Here, the correct answer choice can be found by looking at the coefficients of x^2 and of x.

Answer:

A

Step-by-step explanation:

Answer:

1) 4T+T=125

2) Rhonda drove 25 miles

and Jamie drove 100 miles

Step-by-step explanation:

1) Rhonda drove = T

Jamie drove = 4T

4T+T=125

2) 5T=125

T=125/5

T=25

So Rhonda drove T = 25

And Jamie drove 4T = 100

Answer:

1). m° = 56.1°

2). X= 91.8 mm

Step-by-step explanation:

For angle m°

Using the sine rule

15.1/sin m= 18.2/sin 90

But Sin 90= 1

15.1/sin m= 18.2

15.1= 18.2*sin m

Sin m = 15.1/18.2

Sin m=0.8297

m= sin^-1(0.8297)

m= 56.06°

m° = 56.1°

For length of side x

Using sine rule

X/sin 61= 105/sin 90

But sin 90= 1

X/sin 61= 105

X = sin61 *105

X=0.8746*105

X= 91.833 mm

X= 91.8 mm

Answer:

(3, 0)

Step-by-step explanation:

x-intercept is where the line touches the x-axis

It is the point on the line where y=0

Answer:

3,0

Step-by-step explanation:

the point where the line cuts the x axis is the x-intecept

Answer:

D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)

(4, 0)

[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)

(0,-16)

[tex]c = -16[/tex] (Eq. 3)

Then,

[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)

[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)

[tex]a = 4 + 0.5\cdot b[/tex]

Then,

[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)

[tex]64 + 12\cdot b = 16[/tex]

[tex]12\cdot b = -48[/tex]

[tex]b = -4[/tex]

The remaining coeffcient is:

[tex]a = 4 + 0.5\cdot b[/tex]

[tex]a = 4 + 0.5\cdot (-4)[/tex]

[tex]a = 2[/tex]

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.

Answer:

D ƒ(x) = 2x2 – 4x – 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, please consider the following.

Question 1.

[tex]\dfrac{3^{2x+1}}{3^{3x-4}\cdot 3^{6-7x}}=27^x\\\\<=> 3^{2x+1}\cdot 3^{-3x+4}\cdot 3^{-6+7x}=3^{2x+1-3x+4-6+7x}=(3^3)^x=3^{3x}\\\\<=> 2x+1-3x+4-6+7x=3x\\\\<=> 6x-1=3x\\\\<=> 3x=1\\\\<=> \boxed{x=\dfrac{1}{3}}[/tex]

Question2.

[tex]2^{x+y}=8=2^3 <=>x+y=3\\\\3^{x-y}=1=3^0<=>x-y=0[/tex]

So, it gives (by adding the two equations) 2x = 3

[tex]\boxed{x=\dfrac{3}{2} \ \ and \ \ y = x = \dfrac{3}{2} }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]

Step-by-step explanation:

Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:

[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]

Answer:

72

Step-by-step explanation:

The formula for surface area is SA = 2lw + 2wh + 2lh

W = width

L= length

H = height

A = 2(wl + hl + hw)

2·(6·3+2·3+2·6)

Simplify that down to get the answer 72

Answer:

[tex]log_{10}[/tex] 10000 = 4

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Here b = 10, n = 4 and x = 10000, thus

[tex]log_{10}[/tex] 10000 = 4 ← in logarithmic form

that is [tex]10^{4}[/tex] = 10000 ← in exponential form

Answer:

Macroeconomics is a study that deals with the whole economy and everything pertaining to it.

Step-by-step explanation:

when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.

Answer:

[tex]\frac{7}{2}\sqrt{3}[/tex]

Step-by-step explanation:

the ratio of hypotenuse to longer leg of 30-60-90 triangle is 1 to sqrt(3)/2, and multiply by 7 to obtain answer

Answer:

342 m

Step-by-step explanation:

SIn(20) * 1000 = RS

342 = RS