Find the hypotenuse of each isosceles right triangle when the legs are of the given measure.

Given = [tex]3\sqrt{2}[/tex]

________ inches.

Answer:

True

m∠T = 40.4°

Step-by-step explanation:

We know all the sides of the triangle but we do not know any of its angles.

To find out if the angle T = 40.4 ° we use the cosine theorem.

According to the cosine theorem:

[tex]c^2=a^2 +b^2-2abcos(\alpha)[/tex]

Where [tex]\alpha[/tex] is the angle between a and b.

In this case:

[tex]\alpha = T\\\\a= 11\\\\b=13\\\\c= 8.5[/tex]

Then we clear α from the formula and verify that it is equal to 40.4 °

[tex]8.5^2 =11^2 + 13^2 -2(11)(13)cos(\alpha)\\\\8.5^2 -11^2 - 13^2= -2(11)(13)cos(\alpha)\\\\-8.5^2 +11^2 + 13^2= 2(11)(13)cos(\alpha)\\\\\frac{-8.5^2 +11^2 + 13^2}{2(11)(13)}=cos(\alpha)\\\\\alpha=arcos(\frac{-8.5^2 +11^2 + 13^2}{2(11)(13)})\\\\\alpha = 40.4\° =T[/tex]

Answer:

88 times

Step-by-step explanation:

The two comes up 20 out of 50 times

We don't know how many times 2 will come up if the die is rolled 220 times. We can, however, set up a proportion

20/50 = x/220                    Cross multiply

50x = 20 * 220                   Combine the right

50x = 4400                         Divide by 50

50x/50 = 4400/50             Do the division

x = 88   times.

Answer:

88

Step-by-step explanation:

George's earnings from typing forty-five regular pages are $67.50. To calculate his total earnings, the charge per page for thirty-six technical papers is needed, which is not provided in the question.

To calculate how much George will earn for typing papers, we must know the charge per page for both regular and technical papers. For regular term papers, the charge has been provided: $1.50 per page. However, the charge for technical papers has not been specified. Thus, additional information is needed: the rate George charges per page for technical papers. Without this rate, we cannot accurately calculate his total earnings.

Given that George types forty-five regular pages, his earnings from regular papers can be calculated as:
45 pages *$1.50 per page = $67.50

As for the technical papers, we must have the rate per page to calculate his earnings from the thirty-six technical pages he typed. Once we have this rate, it would be a similar calculation to the one done for regular papers.

3x-14=58

3x-14+14= 58+14

3x= 72

Divide by 3 for 3x=72

x= 24

check answer by using substitution method

3x-14=58

3(24)-14=58

72-18=58

58=58

Answer is C.(x=24)

Answer:  The correct option is (A) 58.

Step-by-step explanation:  We are given to find the length of JK in the given figure.

From the figure, we note that

JKLM is a parallelogram. So, the opposite sides of JKLM will be parallel and congruent.

Also, JK = 3x - 14  and  LM = 58.

Since JK and LM are the opposite sides of the parallelogram JKLM , so we must have

[tex]JK=LM\\\\\Rightarrow 3x-14=58\\\\\Rightarrow 3x=58+14\\\\\Rightarrow 3x=72\\\\\Rightarrow x=\dfrac{72}{3}\\\\\Rightarrow x=24.[/tex]

Therefore, the length of JK is given by

[tex]JK=3x-14=3\times24-14=72-14=58.[/tex]

Thus, the length of JK is 58 units.

Option (A) is CORRECT.

The intersecting secants theorem says

[tex]PQ\cdot PR=PS\cdot PT[/tex]

[tex]\implies8(8+x)=4(24+4)[/tex]

[tex]\implies64+8x=112[/tex]

[tex]\implies8x=48[/tex]

[tex]\implies x=6[/tex]

It's clear from the image that [tex]PT=28[/tex], so the first option is correct.

###

Same as in the first problem; the intersecting theorems says

[tex]NM\cdot NL=NO\cdot NP[/tex]

[tex]\implies5(5+x)=3(3+17)[/tex]

[tex]\implies25+5x=60[/tex]

[tex]\implies5x=35[/tex]

[tex]\implies x=7[/tex]

so the third option is correct.

Answer:

x = 6; PR = 14; PT = 28

Step-by-step explanation:

ur welcome

Answer:

Option C. [tex]y+3=5(x+2)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

In this problem we have

[tex]m=5[/tex]

[tex](x1,y1)=(-2,-3)[/tex]

substitute the given values

[tex]y+3=5(x+2)[/tex]

Final answer:

The equation of the line with slope 5 that contains the point (-2, -3) is y + 3 = 5(x + 2), which corresponds to answer choice C.

Explanation:

To find the equation of the line with a given slope that contains a specific point, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). In this equation, m is the slope and (x1, y1) is the point the line passes through. Given the slope is 5 and the point is (
-2, -3), we substitute these values into the formula: y - (-3) = 5(x - (-2)), which simplifies to y + 3 = 5(x + 2). Therefore, the correct answer is C.

this is the answer, I guess.

Answer: Last option

(42÷2) +5

Step-by-step explanation:

We know that Mr. Roberts drove 42 miles on Monday.

On Tuesday Mr. Roberts drove half of what he drove on Monday plus 5 miles.

If we want to know how many miles Mr. Roberts drove on Tuesday then we should divide 42÷2 to find half of 42.

[tex]\frac{42}{2} = 21[/tex]

Then we know that in addition to the 21 miles he drove 5 more miles. Then we add 21 +5 = 26 miles.

So the expression that gives us the number of miles that Mr. Roberts drove on Tuesday is:

(42÷2) +5

The answer is D trust me

Answer: The answer is D.

Step-by-step explanation: Considering that the dots represent people, all you have to do is count the dots. Graph D is the only plot that has three in both 6 and 8.

Hope this helps & Good Luck,

Melodii

The answer is D

The last chart that has three dots on the numbers 8 and 6

To find 3 people that sleep for 8 hrs, there should be 3 dots on top of the number 8...

And to find 3 people that sleep ofor 6 hrs, there should be 3 dots on top of the number 6 too

Hope this helped,

have a blessed day :-)

Answer:

[tex]\large\boxed{_6P_2=30}[/tex]

Step-by-step explanation:

[tex]_nP_k=\dfrac{n!}{(n-k)!}\\\\n!=1\cdot2\cdot3\cdot...\cdot n\\======================\\\\_6P_2=\dfrac{6!}{(6-2)!}=\dfrac{6!}{4!}=\dfrac{4!\cdot5\cdot6}{4!}\\\\\text{cancel}\ 4!\\\\=5\cdot6=30[/tex]

Answer:

$59.27

Step-by-step explanation:

It is exponential decrease.

After each year goes by its worth 100 - 0.13 = 0.87 of the previous value.

The equation of decrease  is V = 90(0.87)^t   where t = the number of years.

So after 3 years it is worth  90(0.87)^3

= $59.27.

Answer:

We have to determine the time it takes for carbon 14 to decay to 15% of its original amount.

The half life of carbon 14 is 5,730 years

elapsed time = half life * log (beginning amount / ending amount) / log 2

elapsed time = 5,730 * log (100 / 15) / log 2

elapsed time = 5,730 * 0.82390874094 / 0.30102999566

elapsed time = 5,730 * 2.7369655942

elapsed time = 15,683 years

= 15,700 years

Step-by-step explanation:

Solving the exponential equation, it is found that the painting is 15,679 years old.

The amount of carbon-14 after t years is modeled by the following equation:

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

It retains 15% of the original amount, thus:

[tex]A(t) = 0.15A(0)[/tex]

Solving for t, we find the age.

[tex]0.15A(0) = A(0)e^{-0.000121t}[/tex]

[tex]e^{-0.000121t} = 0.15[/tex]

[tex]\ln{e^{-0.000121t}} = \ln{0.15}[/tex]

[tex]-0.000121t = \ln{0.15}[/tex]

[tex]t = -\frac{\ln{0.15}}{0.000121}[/tex]

[tex]t = 15679[/tex]

The painting is 15,679 years old.

A similar problem is given at https://brainly.com/question/16725555

Answer:

simplify -1(3/5)÷(-2/3) = 9/10

=90/100

= .90 and there's your answer

Answer:

12/5 = 2  2/5

Step-by-step explanation:

Convert -1  3/5 into an improper fraction:  -8/5.

Next, divide -8/5 by (-2/3).  Equivalently, invert (-2/3), obtaining (-3/2), and multiply:

(-8/5)(-3/2) = 24/10 = 12/5 = 2  2/5

Answer:

PARABOLA

Step-by-step explanation:

The graph of a quadratic function is a PARABOLA.

The graph of a quadratic function is called a parabola.

A parabola is a U-shaped curve that is symmetric about a vertical line called the axis of symmetry. The vertex of the parabola is the point that is highest or lowest on the curve.

The number a determines the shape of the parabola. If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. The number h determines the horizontal shift of the parabola. The number k determines the vertical shift of the parabola.

Find out more on parabolas at https://brainly.com/question/9201543

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Answer:

there is no relation between millimeters and liters

4000 milliliters = 4 liters

Step-by-step explanation:

"milli-" is a prefix meaning 1/1000. So 1 milliliter = (1/1000) liter. Thus it takes 1000 milliliters to make 1 liters, hence 4000 milliliters to make 4 liters.

_____

A meter, and a millimeter, is a measure of distance. A liter, and a milliliter, is a measure of volume. There is no sensible conversion between linear (one-dimensional) distance and 3-dimensional volume.

Converting liters to millimeters directly isn't typical because they represent different types of measurement: volume and length. However, in the context of a container's dimensions, it's needed to know that a 1-liter volume takes up a cube that is 10 cm (or 100 mm) on each side, and a 4-liter volume would be a cube of approximately 15.92 mm on each edge.

To convert liters to millimeters, it's important to understand that these are units of different quantities: liters are a measure of volume, while millimeters are a measure of length. Therefore, converting between the two directly isn't possible or meaningful. However, if you have a container with a certain liter capacity and want to know its dimensions in millimeters, you could potentially do this if the shape of the container is known.

As a reminder, when dealing with volume in the metric system, one cubic decimeter (dm³) is equivalent to one liter. A cube with edge lengths of exactly one decimeter, therefore, would contain a volume of one liter. This works out to a cube that is 10 cm (or 100 mm) on each side to equal 1 liter of volume. So, for a 4-liter volume, considering a perfect cubic, each side would be the cubic root of 4000 mm³ which is approximately 15.92 mm.

https://brainly.com/question/35097419

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Step-by-step explanation:

20°

Half of 40°

x=20° answer

Answer:

x = 20°

Step-by-step explanation:

The inscribed angle x is half the central angle subtended by the same arc on the circle, hence

x = 0.5 × 40 = 20°

the answer is........ B

For this case we must factor the following expression:

[tex]x^{12}y{18}+1[/tex]

We rewrite [tex]x^{12}y^{18}[/tex]as [tex](x ^ 4y ^ 6) ^ 3:[/tex]

[tex](x ^ 4y ^ 6) ^ 3 + 1[/tex]

Being both perfect cube terms, it is factored by applying the cube sum formula:

[tex]a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2)[/tex]

Where:

[tex]a = x ^ 4y ^ 6\\b = 1[/tex]

So:

[tex](x ^ 4y ^ 6 + 1) ((x ^ 4y ^ 6) ^ 2-x ^ 4y ^ 6 + 1 ^ 2) =\\(x ^ 4y ^ 6 + 1) (x ^ {8} y ^ {12} -x ^ 4y ^ 6 + 1)[/tex]

Answer:

Option B

Answer:

see explanation

Step-by-step explanation:

36

Since triangle is isosceles then AB = BC

Equate the 2 sides, that is

4x - 21 = 2x - 7 ( subtract 2x from both sides )

2x - 21 = - 7 ( add 21 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7, hence

AB = 2x - 7 = (2 × 7) - 7 = 14 - 7 = 7

BC = 4x - 21 = (4 × 7) - 21 = 28 - 21 = 7

AC = x - 3 = 7 - 3 = 4

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

37

Since the triangle is equilateral then all 3 sides are equal.

Equate any 2 sides and solve for x

6x + 1 = 3x + 10 ( subtract 3x from both sides )

3x + 1 = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

HF = 6x + 1 = (6 × 3) + 1 = 18 + 1 = 19 = FG = HG

Answer:

William's age is 18 years old and Monica's age is 6 years old

Step-by-step explanation:

Let

x ----> William's age

y ----> Monica's age

we know that

x=3y ----> equation A

(x+6)=2(y+6) ----> equation B

Substitute equation A in equation B and solve for y

(3y+6)=2(y+6)

3y+6=2y+12

3y-2y=12-6

y=6 years

Find the value of x

x=3(6)=18 years

therefore

William's age is 18 years old

Monica's age is 6 years old

ANSWER

[tex]y ={x}^{2} + 2[/tex]

EXPLANATION

The equation of a parabola that has vertex at (h,k) is given by:

[tex]y = a {(x - h)}^{2} + k[/tex]

If the given parabola has vertex at (0,2), then h=0 and k=2.

Considering the possible answers, we must have a=1.

We substitute the values in to the formula to get:

[tex]y =1 {(x - 0)}^{2} + 2[/tex]

[tex]y ={x }^{2} + 2[/tex]

The first option is correct.

Check the picture below.

let's recall that the point of tangency  with the radius chord is always a right-angle.

Answer:

x = 9

Step-by-step explanation:

The angle formed by the tangent BC and the radius AB is right at B

Thus ΔABC is right with AC as the hypotenuse

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, hence

AC² = AB² + BC² ← substitute given values

(x + 6)² = x² + 12² ← expand squared parenthesis on left side

x² + 12x + 36 = x² + 144 ( subtract x² from both sides )

12x + 36 = 144 ( subtract 36 from both sides )

12x = 108 ( divide both sides by 12 )

x = 9

Answer:

1.

A) Graph the points (length is x, weight is y)

B) Find slope and substitute 75 for x value

c) the relationship between length and weight is... (define the slope)

d)

2.

a) draw line through (0,40) and (6,70)

b) First find the slope and put it into y=mx+b (i guess you know this). then put slope into slope int. form and yeah.

c) just put x as 18 and solve for y, monthly revenue.

Step-by-step explanation:

I was too lazy so i just gave instructions in the answer. Follow them and you should be fine. Good Night.

Answer:

At 1.5 seconds and 2.5 seconds

Step-by-step explanation:

Because this is parabolic motion, the object will reach the height of 68 feet when it's going up AND when it's coming down.  In order to find out those times, you set the h on the left side of the equation equal to 68, because h stands for height.

[tex]68=-16t^2+64t+8[/tex]

Set that equal to 0 and factor to solve for t:

[tex]-16t^2+64t-60=0[/tex]

Using the quadratic formula, we get t = 1.5 and t = 2.5

Answer:

±0.04

Step-by-step explanation:

From the Empirical Rule, we can estimate the range as being 6 standard deviations wide.  Therefore, the standard deviation is:

σ = (0.40 - 0.28) / 6

σ = 0.02

The margin of error is ±2σ, so:

ME = ±0.04

Answer:

x^4 + 4x^3 + 6x^2 + 7x +2

Step-by-step explanation:

Answer:

109 degrees is the answer

Answer:

96°

Step-by-step explanation:

The given quadrilateral is inscribed in a circle, so its opposite angles are supplementary, which means that the sum of their measures is 180∘.

The measures of the opposite angles in the quadrilateral are given as      (6m + 1 3)∘ and (4m + 7)∘.

Equate the sum of the given measures to 180∘.

6m + 13 + 4m + 7 = 180

Combine like terms.

10m + 20 = 180

Subtract 20 from both sides.

10m = 160

Divide both sides by 10.

m = 16

Substitute 16 for m into the expression given for the measure of angle M and simplify.

6m = 6(16)

=96∘

Therefore, m∠M = 96∘.

A parabola is U shaped.

Answer:

C

The answer is c

Hope it helps

1. Positive

2. Positive

3. Negative

4. Negative

5. Positive

6. Negative

When dividing, the only time you will get a negative answer is when only one of the numbers is negative

The identification of the rational numbers is as follows:

To identify whether the given rational numbers are positive or negative, we need to analyze each one based on the rules of sign with fractions. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers. In this context, if the numerator and denominator have the same sign, the fraction is positive. If they have different signs, the fraction is negative.

Let's evaluate each one:

+1/+7: Both the numerator (1) and the denominator (7) are positive, so this fraction is positive.
Result: Positive

+4/+4: Here too, both the numerator and denominator are positive, making this fraction positive.
Result: Positive

+4/-5: The numerator is positive (4) and the denominator is negative (-5), so this fraction is negative.
Result: Negative

+1/-7: Similar to the previous one, the numerator is positive (1) while the denominator is negative (-7), resulting in a negative fraction.
Result: Negative

-1/-7: Both the numerator (-1) and denominator (-7) are negative. Since a negative divided by a negative is positive, this fraction is positive.
Result: Positive

-4/+5: The numerator is negative (-4) and the denominator is positive (+5), making this fraction negative.
Result: Negative

Answer:

a x = 14.3 units

Step-by-step explanation:

The Pythagorean theorem is

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

x^2 + 14^2 = 20^2

x^2 +196 = 400

Subtract 196 from each side

x^2+196-196 = 400-196

x^2 =204

Take the square root of each side

sqrt(x^2) = sqrt(204)

x =14.28285686

To the nearest tenth

x = 14.3 units

Answer:

  0.5588

Step-by-step explanation:

The CDF of an exponential function with mean μ is ...

  CDF(x) = 1 - e^(-x/μ)

Then the probability that graduation will occur in 4.5 years or less is ...

  P(x<4.5) = 1 - e^(-4.5/5.5) ≈ 0.558767 ≈ 0.5588