On the following composite figure, all angles are right angles. All short edges of the figure have a measure of 1.5 centimeters. All long edges have a measure of 3 centimeters. Find the area of the figure. Explain or show how you got your answer.

Answer:

Applying Heron's Formula

[tex]s=\frac{2.89+4.3+6.81}{2}[/tex]

[tex]s_1=7[/tex]

[tex]A_1=\sqrt{7(7-2.89)(7-4.3)(7-6.81)}[/tex]

[tex]A_1=10.56[/tex]

Now, [tex]s_2=\frac{6.81+8.59+7.58}{2}[/tex]

[tex]s_2=11.49[/tex]

[tex]A_2=\sqrt{11.49(11.49-6.81)(11.49-8.59)(11.49-7.59)}[/tex]

[tex]A_2=24.69[/tex]

Total Area:

[tex]10.56+24.69[/tex]

[tex]=35.25[/tex]

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Answer:

17.02939

Step-by-step explanation:

f(x+1)=3x+4

[tex]\\ \sf\longmapsto f(y)=3(y-1)+4[/tex]

[tex]\\ \sf\longmapsto f(y)=3y-3+4[/tex]

[tex]\\ \sf\longmapsto f(y)=3y+1[/tex]

[tex]\\ \sf\longmapsto f(x)=3x+1\checkmark[/tex]

[tex]\\ \sf\longmapsto f(3)[/tex]

[tex]\\ \sf\longmapsto 3(3)+1[/tex]

[tex]\\ \sf\longmapsto 9+1[/tex]

[tex]\\ \sf\longmapsto 10[/tex]

Answer:

70 feet

Step-by-step explanation:

If the miniature model has size of 1 inch, the real statue will be 10 feet in size. So if the model is 7 inch in size, the real statue will be 70 feet in size.

Answer:

Its 2.5 percent ladd enjoy

Step-by-step explanation:

Answer:

2 per team and 2 left

Step-by-step explanation:

10 can't split into 4 evenly so, you can only give 2 to each team causing there to be 2 left.

4*2 = 8

10-8 = 2

=========================================================

Work Shown:

SA = surface area of the rectangular prism (aka block or box)

SA = 2*(LW + LH + WH)

SA = 2*(8*3 + 8*1 + 3*1)

SA = 2*(24 + 8 + 3)

SA = 2*(35)

SA = 70 square feet

This is the amount of wrapping paper you would need to cover all six sides of the box. This assumes that there are no gaps or overlaps.

Answer:

f(x +1 ) =14

Step-by-step explanation:

12= f(x +1) -2

f(x +1) = 12 +2

f (x+1 ) = 12

Answer:

-14

Step-by-step explanation:

12mn-8mt+9t²-6mt

12mn+9t²-14mt

the coefficient of mt is -14

The coefficient of the given expansion 4m(3n-2t)+3t(3t-2m)​ will be -14.

Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.

When a mathematical object is increased by a multiplier that is bigger in actual values than one, an expansion follows.

In another word, if you solve a factor by opening the bracket then you will go to get on some expanded term called expansion.

In mathematics, all real-life problems can be converted into equations which are sometimes in form of factors and we need to expand them to create solutions.

Given that

⇒ 4m(3n-2t)+3t(3t-2m)​

⇒  12mn -8mt + 9t² - 6mt

⇒  12mn + 9t² + 14 mt

Hence it's clear that the coefficient of mt will be -14.

For more information about the expansion

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9514 1404 393

Answer:

  8

Step-by-step explanation:

The matrix being multiplied is the same in all cases, so we can "collect terms" in the usual way.

  3A +5A = (3+5)A = 8A . . . . . . where A represents the 2×2 matrix

The missing number is 8.

Answer:

Step-by-step explanation:

Let the number is in the form of aabb.

We can put it as:

The number is a perfect square so it must be divisible by 11.

It is divisible by 11 if (a + b) is divisible by 11..

On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.

Also, both a and b must be within (0,9) interval.

Considering the above conditions we have options:

The numbers are:

By testing we confirm only one of them is a perfect square:

Answer:

85 minutes

Step-by-step explanation:

425/50=8.5 10 minute increments

8.5*10= 85 minutes

Answer:

Step-by-step on:ơ

Answer:

b. 8/9

Step-by-step explanation:

step by step explanation

Answer:

A

Step-by-step explanation:

Because if you were to out each fraction into a calculator you see that b,c, and d have a never ending decimal. The only fraction that does end in option A, therefore ur answer is option a

Answer: 4 8/10m

Explanation:

Total Ribbon = 24m

Total children = 5

Ribbon each student gets = 24÷5

= 4.8

Now 4.8 = 48/10

4 8/10m is the mixed fraction

So each child will get 4 8/10m ribbon

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If five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

A division is a process of splitting a specific amount into equal parts.

Given that five children share 24m of ribbon equally.

We have to find the amount of ribbon each children gets.

To find this we have to divide the length of the ribbon with the number of children.

Twenty four divided by five.

24 is the dividend and five will be the divisor

24/5

Now we have to write this in mixed fraction

[tex]4\frac{4}{5}[/tex]

Hence, if five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

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Answer: quadrant 1

Step-by-step explanation:

the triangle will make 5 360° rotations and then one 180° rotation. we know this because 1980/360=5.5

alright I can help!

so to find the two values of x that are roots of the equation we need to put the variables all on one side so that we can set up the quadratic formula.

3x^2+2x-5=0 (the -3x^2 becomes positive when moved across the equal sign)

now we can set up the quadratic formula. the equation is x= (-b+-(sqrt of b^2 -4ac))/ 2a

so now we just plug in our variables.

x= (-2+-(sqrt of 2^2 -4×3×-5))/ 2×3

x= (-2+-8)/6

now we just seperate the equations so that we have the two roots. and then just solve!

x= (-2-8)/6 -> x= -5/3

x= (-2+8)/6 -> x=1

hope this helps! best wishes and best of luck!!

Answer:

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Step-by-step explanation:

Answer:

I'm not sure about the answer.

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Hope this helps you ^^

Answer:

$962.00

Step-by-step explanation:

We can start from the first sentence of the word problem and work from there.

First, the employee is working for 40 hours at $18.50 per hour. This means that for each hour, the employee is gaining $18.50 . This can be represented as $18.50 * 40 = $740 for their base pay.

Next, the employee works 8 hours of overtime at 1.5 * base pay (18.50). For each hour of overtime they work, they earn 1.5 * 18.50 = $27.75 dollars. Their earnings from overtime work for the week can be represented as

8 * 27.75 = $222

Because all the employee's hours are encompassed in overtime and base pay, we can add the two together to get

740 + 222 = $962.00 for their total pay for the week

Answer:

136+(4n-8)=180

136+4n-8=180

4n+128=180

4n=52

n=13

Step-by-step explanation:

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Answer:

x ≈ 13.7

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos70° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )

40 × cos70° = x , then

x ≈ 13.7 ( to the nearest tenth )

Answer:

see explanation

Step-by-step explanation:

The area (A) of a rectangle is calculated as

A = length × breadth

   = (2 + [tex]\sqrt{2}[/tex] )(4-2[tex]\sqrt{2}[/tex] ) ← expand using FOIL

   = 8 - 4[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{2}[/tex] - 4 ← collect like terms

   = 4 units²

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

The opposite sides of a rectangle are congruent , so

perimeter = 2(4 - 2 [tex]\sqrt{2}[/tex]) + 2(2 + [tex]\sqrt{2}[/tex] ) ← distribute parenthesis

                 = 8 - 4[tex]\sqrt{2}[/tex] + 4 + 2[tex]\sqrt{2}[/tex] ← collect like terms

                 = 12 - 2[tex]\sqrt{2}[/tex] units

Answer:

Step-by-step explanation:

Rolling two dice, there are 6*6 = 36 outcomes

The outcomes with the difference of 4:

Required probability:

Correct choice is b

Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2

Answer:

A

Step-by-step explanation:

Divide both sides with -16. ALWAYS remember that if you divide any number with a negative number, this "< ≤ > ≥" symbols have to change to the opposite direction

Answer:

1

Step-by-step explanation:

Once you have two sides and the included angle, there is only one triangle.

Answer: 1

Answer:

The answer is B. 1

Step-by-step explanation:

I hope I helped

Answer:

We know that an isosceles triangle has 2 of its sides being equal

With R, being the midpoint of PS, we can say that

PR=RS

Noting that, with R as midpoint, we can conclude that RT is a straight line which divides angles TPR and TSR into 2 right angle triangles

Step-by-step explanation:

therefore angle at P is 45°. Angle at S also 45°

Therefore PT = TS

This is because T is 45 degrees as well as P which is also 45 degrees

angle in triangle PTS is 180 degrees

R is 90 degrees, P is 45 degrees and the whole of T is also 45 degrees(which has been split into 2)