david study table is 20 inches long. if the diagonal measures 25 inches, find the width of david study table

David Study Table Is 20 Inches Long. If The Diagonal Measures 25 Inches, Find The Width Of David Study

Answers

Answer 1

Answer:

15 inches

Step-by-step explanation:

Since we know diagonal and a side of a right triangle, we can use the Pythagorean theorem to solve.

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

20 ^2 + b^2 = 25^2

400+b^2 =625

b^2 =625 -400

b^2 =225

Taking the square root of each side

sqrt(b^2) = sqrt(225)

b= 15

Answer 2

Answer:

15

Step-by-step explanation:

You can use Pythagorean theorem or if you draw it out and label the given information you may recognize that the triangle created is a 3 - 4 - 5 triangle.

[tex]25^{2}[/tex] = [tex]20^{2}[/tex] + [tex]x^{2}[/tex]             [tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]

625 = 400 + [tex]x^{2}[/tex]        

225 = [tex]x^{2}[/tex]                     Square root both sides

15 = x

A special right triangle has a leg that measures 3, another leg that measures 4. and a hypotenuse that measures 5.

The given triangle in this problem has a leg that measures 20 and a hypotenuse that measures 25. If you divide each measure by 5, you will have a leg that is 4, and a hypotenuse that is 5. That means the last leg must be 15.

Why? Because 3 x 5 = 15. or 15/5 = 3

This comes up very often when working with triangles.


Related Questions

Find the values of x and y.

Answers

Answer:

I think it's 43 and 43 degrees. I just subtracted 180-94, got 86, and divided it so yea.

the length of a rectangular box is 8cm. If its diagonal is 10cm. Find its width​

Answers

Answer:

Step-by-step explanation:

The diagonal of this rectangular box serves as the hypotenuse of the 2 right triangles that exist within this rectangle. The length is one leg, the hypotenuse is...well, the hypotenuse, so we need to use Pythagorean's Theorem to find the missing leg.

[tex]10^2=8^2+x^2[/tex] and

[tex]100-64=x^2[/tex] and

[tex]x^2=36[/tex] so

x = 6. The width is 6.

can someone help me out

Answers

5.6 cm sry if i got it wrong

What is the axis of symmetry for y = 3x^2 + x - 2

Answers

Axis of Symmetry:
x= -1/6

Tell whether the line for x = -5 is horizontal, vertical, or neither.

Answers

Answer:

vertical

Step-by-step explanation:

The line x = -5 includes all points where the value of x is -5, regardless of the value of y. This can be graphed as a vertical line going through (-5, 0), as the line represents the only place where x is the value -5.

How do you calculate percentage or find the per cent value

Answers

Answer:

Divide the number you want to find the percentage for by the total amount of items in that group. Then, multiply that value by 100.

Step-by-step explanation:

Ex. There are 3 boys in a group of 4. What percentage of the group are boys?

[tex]\frac{3}{4} =0.75[/tex]

[tex]0.75*100=75[/tex]

75% of the group are boys

X+3y=2 and y=2x+3
Please explain using substitution method.

Answers

- X + 3Y = 2  (*)

⇔X = 2 - 3Y  (1)

- Y = 2X + 3   (2)

(1),(2)⇒ Y = 2(2 - 3Y) +3

       ⇔ Y = 4 - 6Y + 3

       ⇔ Y = 1  (**)

(*),(**)⇒ X + 3×1 =2

       ⇔ X = -1

. Error Analysis Describe and correct the error
a student made when ordering numbers from
least to greatest.



HELP ASAP

Answers

Answer:

Step-by-step explanation:

[tex]\sqrt{144} = 12[/tex]

the error was in not take the root of the number correctly

the student assumes that the root of 144 was equal to 72

please ans this question pleaseee​

Answers

Answer:

[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]

PLS HELP ME!!!
A sample is generated from a population of 20 items. Each of the 20 items are given a label, and a 20-sided die is rolled 3 times to determine which 3 items are in the sample. This is an example of a __________.

A. systematic sample

B. random sample

C. convenience sample

D. self-selecting sample

Answers

Answer:

Option B, random sample

That should be the answer

Given an arithmetic progression 17,13,9,..... find the number of terms required so that its sum is - 33 .

Answers

Answer:

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]

Simplify:

[tex]-66 = k(17 + x_k)[/tex]

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

[tex]x_ n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]

Then the last term is given by:

[tex]x_k = 17 - 4(k-1)[/tex]

Substitute:

[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Answer:

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]

[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]

Given: The equation of a parabola is x2 = 8y.

Step 3: Where does the directrix for the given parabola lie? Enter the equation for the directrix line. Use your keyboard and the keypad to enter your answer. Then click Done.

Answers

Answer:

x=-2

Step-by-step explanation:

Answer:

Since a = 2, the equation for the directrix line will be y = −2.

Step-by-step explanation:

The polygons in each pair are similar. Find the missing side length.

Answers

Answer:

12

Step-by-step explanation:

We can say that two polygons are similar to each other if both of the polygons have the same shape and their corresponding sides are in the same proportion, hence the ratio of their corresponding sides are equal to each other.

As we can see from the problem since both of the polygons are similar, hence the ratio of their corresponding sides are in the same proportion, therefore let x represent the missing length, hence:

[tex]\frac{x}{15} =\frac{32}{40} =\frac{32}{40} \\\\\frac{x}{15} =\frac{32}{40} \\\\x=\frac{32*15}{40} \\\\x=12[/tex]

b) 2x (x - y) + 3y (x - y)​

Answers

Use distributive law

[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]

Now

[tex]\\ \sf\longmapsto 2x(x-y)+3y(x-y)[/tex]

[tex]\\ \sf\longmapsto 2x^2-2xy+3xy-3y^2[/tex]

[tex]\\ \sf\longmapsto 2x^2-3y^2-2xy+3x^2[/tex]

[tex]\\ \sf\longmapsto 2x^2-3y^2+xy[/tex]

Taking common

Answer: 2x (x-y) + 3y (x-y)

             = ( x-y ) ( 2x-3y )

Anyone could please answer this??​

Answers

Answer:

Ans no. 1 = 14/15

Ans no. 2= 1/192

What is the slope, in its most simplified form, of the line that contains (1, 3) and (5, 9)

Answers

Answer:

The slope is 3/2

Step-by-step explanation:

Use the Slope-Formula to identify the slope

Slope = change in y/change in x

Slope = (y2 - y1)/(x2 - x1)

Points: (1, 3) and (5, 9)

Slope = (9 - 3)/(5 - 1)

Slope = 6/4

Slope = 3/2

Which angles are supplementary to each other?

Angle 4 and Angle 2
Angle 5 and Angle 2
Angle 4 and Angle 3
Angle 2 and Angle 7​

Answers

Answer:

The answer is Angle 4 and Angle 3.

Answer:

It's answer is angle 4 and angle 3

Adding the fractions

3/14+2/21+1/6

Answers

Answer:

[tex]\frac{10}{21}[/tex]

Step-by-step explanation:

The LCM of 14, 21 and 6 is 42

We require to change the fractions to fractions with a denominator of 42

[tex]\frac{3(3)}{14(3)}[/tex] + [tex]\frac{2(2)}{21(2)}[/tex] + [tex]\frac{1(7)}{6(7)}[/tex]

= [tex]\frac{9}{42}[/tex] + [tex]\frac{4}{42}[/tex] + [tex]\frac{7}{42}[/tex] ← add the numerators, leaving the denominator

= [tex]\frac{9+4+7}{42}[/tex]

= [tex]\frac{20}{42}[/tex] ← divide both values by 2

= [tex]\frac{10}{21}[/tex] ← in simplest form

Help please Algebra 1
Simplify 4y-6yx+y

Answers

I hope you will like my answer

The expression 13.25×5+6.5 gives the total cost in dollars of renting a bicycle and helmet for 5 days. The fee for the helmet does not depend upon the number of days.

Answers

Answer:

13.25×5+13, cost per day with a helmet.

Step-by-step explanation:

Numerical Expressions • Practice

Answer:

13.25×5+13, Per day without a helmet

Step-by-step explanation:

It took francisco 60 minutes to walk from his house to his grandmother’s house. what is 60 written as a product of factors greater than 1? each factor can have only 1 and itself as factors.

Answers

Answer:

2 × 2 × 3 × 5

Step-by-step explanation:

Given that,

The number = 60

To find,

Factors of 60 greater than 1 = ?

Procedure:

As we know,

Any of various numbers multiplied together to form a whole.

To find the factors of a number, we will have to do its prime factorization.

So,

The prime factorization of 60:

1 * 2 * 2 * 3 * 5 = 60

Since the factors greater than 1 are asked, the factors would be;

2 * 2 * 3 * 5

Thus, 2 * 2 * 3 * 5 is the correct answer.

help please tries 2 times

Answers

Answer:

(2,1)

Step-by-step explanation:

2x - 2y = 2

5x + 2y = 12

again just add them in this case

7x = 14

x = 2

4 - 2y = 2

-2y = -2

y = 1

Product of the zeroes of polynomial 3x²-2x-4 is ? No spam ❌ Want accurate answers ✔ No spa.

full explain​

Answers

9514 1404 393

Answer:

  -4/3

Step-by-step explanation:

Quadratic ax² +bx +c can be written in factored form as ...

  a(x -p)(x -q)

for zeros p and q. The expanded form of this is ...

  ax² -a(p+q)x +apq

Then the ratio of the constant term to the leading coefficient is ...

  c/a = (apq)/a = pq . . . . the product of the zeros

For your quadratic, the ratio c/a is -4/3, the product of the zeros.

_____

Additional comment

You will notice that the sum of zeros is ...

  -b/a = -(-a(p+q))/a = p+q

Answer:

[tex] \green{ \boxed{ \bf \: product \: of \: the \: zeros \: = - \frac{4}{3} }}[/tex]

Step-by-step explanation:

We know that,

[tex] \sf \: if \: \alpha \: and \: \beta \: \: are \: the \: zeroes \: of \: the \: \\ \sf \: polynomial \: \: \: \pink{a {x}^{2} + bx + c }\: \: \: \: then \\ \\ \small{ \sf \: product \: of \: zeroes \: \: \: \alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} } } \\ \\ \sf \implies \: \pink{ \boxed{\alpha \beta = \frac{c}{a} }}[/tex]

Given that, the polynomial is :

[tex] \bf \: 3 {x}^{2} - 2x - 4[/tex]

so,

constant term c = - 4coefficient of x^2 = 3

[tex] \sf \: so \: product \: of \: zeroes \: \: = \frac{ - 4}{3} = - \frac{4}{3} [/tex]

I really need this answered!

Answers

Answer:

Its AA similaroty theorem

Triangle Q R S is shown. Line R Q extends through point P. Angle Q S R is 35 degrees. Angle S R Q is 58 degrees. Exterior angle S Q P is x degrees. What is the value of x?

Answers

The triangle is missing and so i have attached it.

Answer:

x = 93°

Step-by-step explanation:

From the triangle attached, we can say that;

<SQP + <SQR = 180°

This is because sum of angles on a straight line equals 180°.

Secondly, we know that sum of angles in a triangle also equals 180°.

Thus;

<SQR + <QSR + <SRQ = 180

From the attached triangle, we see that;

<QSR = 35°

<SRQ = 58°

Thus;

<SQR + 35° + 58° = 180°

<SQR + 93° = 180°

<SQR = 180° - 93°

<SQR = 87°

From earlier on, we saw that;

<SQP + <SQR = 180°

Plugging in <SQR = 87°, we have;

<SQP + 87° = 180°

<SQP = 180° - 87°

<SQP = 93°

We are told in the question that <SQP is denoted by x.

Thus;

x = 93°

Answer:

The value of x is answer D: 93

A person walks on average 4000 steps per day. If one step is about 2 feet long, how much would the average person walk per week? HELP

Answers

Answer:

56000 ft

Step-by-step explanation:

4000 steps a day.

7 days in a week.

2 ft per step

so, we calculate how many steps in a week

4000 × 7 = 28000

and then we calculate the distance by saying each of these steps is 2 ft

so,

28000 × 2 = 56000 ft

as a little extra thought :

there are 5280 ft in a mile.

so, the person walks

56000 / 5280 miles = 10.61 miles

in a week.

Help me come up with a YT name plz. I’m looking for something that POPS, but I keep coming up with the same names/words.

Answers

ACEMaster52 u like that I made it up

2. Find 3 rational number between:
1) -5 and -6 2) ( -1/7) and (1/8)
i need steps
explanation also pls guys

Answers

Step-by-step explanation:

between -5 and -62

-7,-10,-60...so..on

between -1/7 and 1/8

Multiply any number by number with both the numbers but it should be multiplied by both the numbers:

for example:

-1/7×3/3= -3/21 ; 1/8×3/3= 3/24

So,

-2/21,2/24,1/24

hope it helps

Emily puts away basketballs after the gym class. there are 15 basketballs, and each rack holds 4 basketballs. how many racks does Emily completely fill? How many basketballs are left?

Answers

Emily would completely fill 3 racks of baskets balls and she would have 3 basketballs left over.

4(number of basketballs each rack can hold) multiplied by 3 is equal to 12. Meaning 12 of the 15 basketballs will be able to go on a rack, and there would be 3 left over.(subtract 15-12 and you will get 3)

Answer:

emily fills 3 racks

3 basketballs are Left!

Step-by-step explanation:

15/4 = 3.3

how many degrees does a unit angle measure a 10° B 90° c 180 degrees d 100 degrees​

Answers

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