True or false a circle could be circumscribed about the quadrilateral below

The dimensions of playing card is L = 10 centimeter and W=5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.

Step-by-step explanation:

The given is,

                  Playing card has an area of 50 square centimeters

                  A perimeter of 30 centimeters

Step:1

                 A playing card is in the shape of rectangle,

                 Formula for perimeter of rectangle is,

                                      [tex]Perimeter, P = 2(l+w)[/tex] .........................(1)

                 Formula for area of rectangle is,

                                             [tex]Area, A= lw[/tex]......................................(2)

                  Where, l - Length of rectangle

                             w - Width of rectangle

Step:2

                From the given values equation (1) becomes,

                                                       [tex]30 = 2(l+w)[/tex]              

                                                       [tex]\frac{30}{2}=(l+w)[/tex]      

                                                       [tex]15 =(l+w)[/tex]

                                                       [tex]w=15-l[/tex]  .............................(3)

                Width value in terms of length is calculated.

Step:2

                Equation (2) becomes,

                                                      [tex]50 = (15-l)(l)[/tex]

                                                      [tex]50= 15l -l^{2}[/tex]

                                      [tex]l^{2}-15l+50=0[/tex]

              Solving the above equation,

                                                          [tex]=10[/tex]

                                                       [tex]l=10 cm[/tex]

Step:3

                 Equation (3) becomes,

                                                       [tex]w=15-l[/tex]

                                                           [tex]=15-10[/tex]

                                                           [tex]=5[/tex]

                                                     w = 5 cm

Result:

           The dimensions of playing card is L = 10 centimeter and W = 5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.

Final answer:

By creating an equation system using the area and perimeter formulas for a rectangle, the dimensions of the playing card are found to be either 5 cm by 10 cm or 10 cm by 5 cm.

Explanation:

To determine the dimensions of a playing card given its area and perimeter, we need to set up an equation system based on the properties of a rectangle. Let's call the length L and the width W. The area (A) of a rectangle is A = L × W, which in this case is 50 sq cm. The perimeter (P) is P = 2(L + W) and is given as 30 cm.

From the perimeter, we can rearrange this to find L in terms of W:
30 cm = 2(L + W)
15 cm = L + W
L = 15 cm - W

Now, substituting L in the area equation gives us:
50 cm² = (15 cm - W) × W
This can be rearranged to form a quadratic equation:

0 = W² - 15W + 50

Factoring, we find:
0 = (W - 5)(W - 10)
So we have two solutions, W = 5 cm or W = 10 cm.

If we take W as the width, then L (the length) would be the other dimension, which would be 15 cm - W. So, we have two possible dimension pairs based on the standard card size: (5 cm by 10 cm) or (10 cm by 5 cm).

Answer:

option 1

Step-by-step explanation:

step 1

Find the arc length of the complete circle

The circumference of the circle ios given by

[tex]C=2\pi r[/tex]

we have

[tex]r=10\ in[/tex]

substitute

[tex]C=2\pi (10)[/tex]

[tex]C=20\pi\ in[/tex]

step 2

Find the arc length for a sector with a cenytral angle of 30 degrees

we know that

The complete circle subtends a central angle of 360 degrees

so

using proportion

[tex]\frac{20\pi}{360^0}=\frac{x}{30^o}\\\\x=20\pi(30)/360\\\\x=\frac{5}{3} \pi\ in[/tex]

Answer:

When x = 4

Step-by-step explanation:

Division by zero is undefined. With real numbers, you are not allowed to divide by zero. Any value of x that causes the denominator to have a value of zero is not allowed. We need to find out which values of x cause the denominator to equal zero.

To do that, we set the denominator equal to zero and solve for x.

2x - 8 = 0

Add 8 to both sides.

2x = 8

Divide both sides by 2.

x = 4

Answer: The rational expression is undefined when x = 4

Check:

Let x = 4, and evaluate the denominator of the fraction.

2x - 8 = 2(4) - 8 = 8 - 8 = 0

By letting x = 4 in the denominator, the denominator does evaluate to zero causing an undefined value in the division. Therefore, our answer above is correct.

Answer:

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited or borrowed.

Answer:

6.25? is that even possible?

Step-by-step explanation:

Answer: 400

Step-by-step explanation:

25÷4=6.25

2500÷6.25=400

Based on the random sample of 25 iPhones in which 4 were found to be defective, it is projected that approximately 400 iPhones in the total shipment of 2,500 would be defective.

The question is essentially asking for a projection based on a statistical sample. In this case, the sample is 25 iPhones, out of which 4 were found to be defective. This implies that, out of every 25 iPhones, we can expect approximately 4 to be defective.

To project this onto the entire shipment of 2,500 iPhones, we can use the proportion found in the sample. Divide the total number of iPhones by the sample size to find the number of 'samples' in the shipment: 2500 ÷ 25 = 100. Then multiply this by the number of defective iPhones found in the sample: 100 x 4 = 400.

So based on the sample, the manager can expect approximately 400 iPhones in the shipment to be defective.

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The answer to your question would be:

B-  f(x) has the greatest maximum.  

C-  All three functions have a y-intercept.

(I know this question is old but I hope it helps someone else.)

:)

Answer:

[tex]12[/tex]

Step-by-step explanation:

Step 1:  Set x to 3 and solve

[tex]4x[/tex]

[tex]4(3)[/tex]

[tex]4 * 3[/tex]

[tex]12[/tex]

Answer:  [tex]12[/tex]

Answer:

A. 212.7

Step-by-step explanation:

To find the score that separate the lower 60% from the top 40% , we need to know the z value that satisfy:

P(Z<z) = 0.6

So, using the standard normal table, we know that the z value is equal to 0.2533

Then, the score x that is equivalent to the z value 0.25 can be calculate as:

[tex]z=\frac{x-m}{s}\\x=(z*s)+m[/tex]

Where m is the mean and s is the standard deviation. Therefore, replacing z by 0.25, m by 200 and s by 50, we get:

[tex]x=(0.2533*50)+200\\x=212.7[/tex]

Answer:

(-2+-5) equals -7.

Because the signs are the same, we dont change it.

(3+5) equals 8. Same like the other equation, the signs are the same so we do not change it.

Now we do (-7+8) The answer will be 1. Lets use a little graph since its hard to explain.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Mark -7 anyway you want. (Circle it, draw a line under it, what ever you want.)

Now Move the line 8 times.

When you do that your line will stop at 1.

And thats how you do it.

Step-by-step explanation:

Answer:

All you have to do is Subtract the first number of both equation so 2-3= 1.

Step-by-step explanation:

Answer:

Can i have brainliest

The second one

The third one

and the last ones

Step-by-step explanation:

The x values are opposite

and the y stay the same

Answer:

y = f(x − 2) + 4

Shifts 2 units right, 4 units up.

y = −f(x − 3)

Shifts 3 units right, reflects in x-axis.

y = f(x + 5)

Shifts 5 units left

Step-by-step explanation:

Let the initial function be y = f(x)

Then,

y = f(x − 2) + 4 is obtained by translating the function 2 units towards right and 4 units up

y = -f(x - 3) is obtained by translating the graph 3 units towards right and then reflection along the x-axis

y = f(x + 2) is obtained by translating the graph 2 units towards left

Step-by-step explanation:

log 47.2 in four decimal places

= 1.6739

Final answer:

To find log 47.2 to four decimal places, use the logarithmic function. The result is approximately 1.6739

Explanation:

To find log 47.2 to four decimal places, we need to use the logarithmic function. The logarithm function is the inverse of exponentiation. In this case, we are looking for the logarithm of 47.2.

Using a scientific calculator or logarithmic tables, we can find that log 47.2 ≈ 1.6739 to four decimal places.

The four decimal places are determined by the precision of the logarithm function and the number of significant figures in the input value (47.2 has four significant figures).

Answer:

Area of the circle = [tex]113.04\;units^2[/tex]

Step-by-step explanation:

Circumference = [tex]37.68\;units[/tex]

Circumference of the circle = [tex]2\times \pi \times r[/tex]

As,

    [tex]\pi =\dfrac{22}{7}=3.14[/tex]

                        [tex]37.68=2\times \pi \times r\\\\37.68=2\times 3.14 \times r\\\\37.68=6.28\times r\\\\r=\dfrac{37.68}{6.28} \\\\r=6\;units[/tex]

Area of a circle = [tex]\pi \times r^2[/tex]

                       [tex]=3.14\times (6\times 6)\\\\=3.14\times 36\\\\=113.04\;units^2[/tex]

Answer:

113.04 units²

Step-by-step explanation:

A = πr2 = π(d2)2 A = C24π π = 3.1415 A = area C = circumference or perimeter r = radius, d = diameter

Hope this helps

Answer:

4 lines

Step-by-step explanation:

40 + 10x = 20x

40 = 10x

4=x

Answer:

[tex]v = {210cm}^{3} [/tex]

Step-by-step explanation:

Formula for finding the volume of a triangular prism is given as:

[tex]v = \frac{1}{2} \times b \times h \times l[/tex]

where,

b = breadth = 7cm

h = height = 6cm

l = length = 10cm

Thus,

[tex]v = \frac{1}{2} \times 7cm \times 6cm \times 10cm[/tex]

[tex]v = \frac{1}{2} \times 420 {cm}^{3} [/tex]

[tex]v = \frac{ {420cm}^{3} }{2} [/tex]

[tex]v = {210cm}^{3} [/tex]

Answer:

A) The expression is a trinomial.

Step-by-step explanation:

If the degree is 2, the expression would be a binomial, not a trinomial. If this answer is correct, please make me Brainliest!

Answer:

m<1 = 135°, m<2 = 45°, m<3 = 135°, m<4 = 45°, m<5 = 135°, m<6 = 45°, m<7 = 135°

Step-by-step explanation:

We know that a straight line always gives us a measure of 180° total. This would mean 180° = m<8 + m<7. So, if we plug in the real value of m<8, we get 180 = 45 + m<7. From there, we can subtract 180 by 45, and we get 135° = m<7.

We know that vertical angles are congruent - so m<5 is the same as m<7 - making m<5 = 135° as well. This could also apply to m<8 and m<6, so m<6= 45°.

From there, we can also say that alternate interior angles are congruent to each other - meaning m<5 = m<3, and m<6 = m<4. So, m<3 = 135° and m<4 = 45°.

Alternate exterior angles are congruent too, which means m<8 = m<2, and m<7 = m<1. So, m<2 = 45° and m<1 = 135°.

In summary,

m<7 = 135° because angle subtraction.

m<5 = 135° and m<6= 45° because vertical angles are congruent.

m<3 = 135° and m<4 = 45° because alternate interior angles are congruent.

m<1 = 135° and m<2 = 45° because alternate exterior angles are congruent!

Hope this makes sense! Not sure if I explained it well.

Answer:

Tj hit 85% of the balls pitched to him

Step-by-step explanation:

Final answer:

Both vendors cost about the same for 20 pairs of soccer shoes.

Explanation:

For Sports Shoe Warehouse, the cost for 11 pairs is $1100, and each additional pair costs $66. So, the total cost for x additional pairs would be $1100 + $66x.

For Winning Team Shoes, the cost for 11 pairs is $825, and each additional pair costs 6% more than the previous pair. So, the total cost for x additional pairs would be $825 + 0.06(825)x.

To find when both vendors cost the same, we set their expressions equal: $1100 + $66x = $825 + 0.06(825)x. Solving for x gives x = 20. Therefore, both vendors cost about the same for 20 pairs of soccer shoes.

Answer:

we need the question

Step-by-step explanation:

Answer:

The answer is 43 minutes I'm pretty sure.

Answer:

43 mins

Step-by-step explanation: All you have to do is subtract 57 from 14 then you will get your amount of time. And that is all you have to do

Answer:

14 -2i

Step-by-step explanation:

9 + sqrt(-4) - ( -5 + sqrt(-16))

We know the sqrt of a negative number is i * sqrt(number)

9 + isqrt(4) - ( -5 + isqrt(16))

9 + 2i - (-5 + 4i)

Distribute the negative sign

9+2i +5 -4i

Combine like terms

14 -2i

Answer:

100 pi (314.16)

Step-by-step explanation:

Because the diameter is 20 in, that makes the radius = 20/2 inches = 10 inches.

10^2 * pi = area

100 pi =  area

314.16 is approx. area.

Answer:

It should be 1,256.6 in square inches

Step-by-step explanation:

Answer:

-1500

Step-by-step explanation:

"descends," means to go down (ascend means to go up), so the number would be negative. The number given is 1500, so we use that, and get -1500.

Answer:

-1500

Step-by-step explanation: Descending means "going down" negative numbers are below normal. They had descended  from the normal numbers.

Answer:

11 1/4 or 11.25.

Step-by-step explanation:

9514 1404 393

Answer:

  1278 × 4

Step-by-step explanation:

Apparently, a 4-digit number is being multiplied by a 1-digit number. We expect that the partial products are the result of multiplying single digit numbers with different place values.

So, 4000 = 1000 × 4 or 500 × 8

  800 = 200 × 4 or 100 × 8

We don't think 8 is the multiplier, because 500 and 100 have digits with the same place value multiplier (100).

Continuing, ...

  280 = 70 × 4

  32 = 8 × 4

The numbers being multiplied seem to be 1278 × 4.

Answer:B

Step-by-step explanation:

The x-intercept of the mathematical function f(x) = 3x(x – 1) will be at (0, 0) and (0,1).

The roots of the function are equal to 2 or less than 2.

The mathematical function is given below.

f(x) = 3x(x – 1)

Then the roots of the function will be

3x = 0

 x = 0

And x – 1 = 0

             x = 1

Then the x-intercept of the function f(x) = 3x(x – 1) will be at (0, 0) and (0,1)

More about the roots of the function link is given below.

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Given:

[tex]\cos 15^{\circ}[/tex]

To find:

The exact value of cos 15°.

Solution:

[tex]$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}[/tex]

Using half-angle identity:

[tex]$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}[/tex]

[tex]$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}[/tex]

Using the trigonometric identity: [tex]\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}[/tex]

            [tex]$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}[/tex]

Let us first solve the fraction in the numerator.

            [tex]$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}[/tex]

Using fraction rule: [tex]\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}[/tex]

            [tex]$=\sqrt{\frac {2+\sqrt{3}}{4}}[/tex]

Apply radical rule: [tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]

           [tex]$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}[/tex]

Using [tex]\sqrt{4} =2[/tex]:

           [tex]$=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

[tex]$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

The remainder when the 100th term of the Fibonacci sequence is divided by 8 is 3.

The Fibonacci sequence is a sequence where each term is the sum of the previous two terms. The sequence starts with 1, 1, and then continues with 2, 3, 5, and so on. To find the remainder when the 100th term of the sequence is divided by 8, we can calculate the terms of the sequence modulo 8 until we reach the 100th term.

We can see from the pattern that the terms modulo 8 repeat every 6 terms. Therefore, to find the remainder when the 100th term is divided by 8, we can calculate the remainder when 100 is divided by 6. 100 mod 6 = 4. So, the remainder when the 100th term of the Fibonacci sequence is divided by 8 is the same as the remainder when the 4th term is divided by 8, which is 3.