(SAT Prep) In the given figure, a║b. What is the value of x? A. 70° B. 45° C. 80° D. 65° I NEED THIS FAST PLZZZZZZ!!!!!!!!!!!!

Answer:

18.03 inches

Step-by-step explanation:

The cardboard is cut as shown below.

The line c cuts the rectangle into 2 right angled triangles.

To find the diagonal (hypotenuse), we have to apply Pythagoras Rule:

[tex]hyp^2 = opp^2 + adj^2\\\\=> c^2 = 10^2 + 15^2\\\\c^2 = 100 + 225 = 325\\\\[/tex]

=> c = 18.03" = 18.03 inches

The length of c, the diagonal, is 18.03 inches.

Answer:

(a) [tex]Q_1=36.5,M=Q_2=41,Q_3=46[/tex]

(b) [tex]IQR=9.5[/tex]

(c) 15

Step-by-step explanation:

The given data set is

41, 52, 37, 44, 42, 38, 41, 48, 43, 39, 36, 55, 42, 35, 15, 52, 39, 50, 29, 30

Arrange the data in ascending order.

15, 29, 30, 35, 36, 37, 38, 39, 39, 41, 41, 42, 42, 43, 44, 48, 50, 52, 52, 55

Divide the data in four equal parts.

(15, 29, 30, 35, 36), (37, 38, 39, 39, 41), (41, 42, 42, 43, 44), (48, 50, 52, 52, 55)

Now,

[tex]Q_1=\dfrac{36+37}{2}=36.5[/tex]

[tex]M=Q_2=\dfrac{41+41}{2}=41[/tex]

[tex]Q_3=\dfrac{44+48}{2}=46[/tex]

[tex]IQR=Q_3-Q_1=46-36.5=9.5[/tex]

Range for outlier is

[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[36.5-1.5(9.5),46+1.5(9.5)][/tex]

                           [tex]=[22.25,60.25][/tex]

Since, 15 lies outside the interval [22.25,60.25], therefore 15 is an outlier.

Answer:

<M = 78°

Step-by-step explanation:

The sum of angles in a kite is 360°.

One of the properties of a kite is that one pair of opposite angles are equal.

Since it is not <L and <N, it must be <O and <M

Therefore:

<O = <M = x

=> x + x + 130 + 74 = 360

2x + 204 = 360

2x = 360 - 204

2x = 156

x = 156/2 = 78°

This means that <M = 78°

Answer: 1/4≤x

Step-by-step explanation:

-5/(2x-3)≤2

Multiply by (2x-3)

-5≤4x-6

Add 6

1≤4x

1/4≤x

Hope it helps <3

Answer:

[tex]x \geq 1/4[/tex]

Step-by-step explanation:

=> [tex]\frac{-5}{2x-3} \leq 2[/tex]

Multiplying both sides by (2x-3)

=> [tex]-5 \leq 2(2x-3)[/tex]

=> [tex]-5 \leq 4x-6[/tex]

Adding 6 to both sides

=> [tex]-5+6 \leq 4x[/tex]

=> [tex]4x\geq 1[/tex]

Dividing both sides by 4

=> [tex]x \geq 1/4[/tex]

Answer:

I did my best with the information! The Man died at around 11:20 am.

Step-by-step explanation:

So due to the algus mortis process, after death, a body can stay at its regulated temperature for up to 2 to 3 hours postmortem. But after that, the body soon drops at about 1 degrees celsius each hour. 1 degrees celsius is about -33 . So he was found at 42 degrees fahrenheit, which means he died somewhere around 11 o-clock. We do not know how long the postmortem process had his temperature delayed, so it would be roughly I say around 11: 20 am.

Answer:

Perimeter = 54.6 cm

Area = 173 cm²

Step-by-step explanation:

sin 30 = x/20

x = 10

cos 30 = y /20

y = 17.3

perimeter = 10 + 17.3 + 10 + 17.3 = 54.6 cm

area = 10 * 17.3 = 173 cm²

Answer:

120

Step-by-step explanation:

Answer: 120

Hope that helped!(:

Answer:

11[tex]\sqrt{x6/4[/tex]

Given:

The triangle on the left ( triangle 1) has a 60º, a 90º, and a side that equals 11.

So we know the triangle on the right (triangle 2) has a 45º and a 90º angle.

Triangle 2

Since triangle angles always have a sum of 180º, we can solve for the third angle of triangle 2. 180 - (45 + 90) = 45. So the third angle of triangle 2 is 45º.

This is a special type of right triangle called a 45-45-90. An image of the leg/hypotenuse is uploaded below. Meaning, if we solve for the leg that joins the two triangles, we can solve for the hypotenuse.

Triangle 1

To solve for the middle leg, we work with the information we have. So first, find the third angle. 190 - (60 + 90) = 30. This brings us to a second type of special right triangle. An image of the leg/hypotenuse is uploaded below.

Given that we have a side angle of 11, we know that is 2x due to orientation. So 2x=11 simplifies to x=5.5. We then plug that back in to find the leg that we want: 5.5[tex]\sqrt{3}[/tex] .

Triangle 2

Now that we have a side length for the second triangle we can solve. x for this triangle is 5.5[tex]\sqrt{3}[/tex] so to find the hypotenuse we plug into x[tex]\sqrt{2}[/tex]. This turns into (5.5[tex]\sqrt{3}[/tex][tex]\sqrt{2}[/tex]) which simplifies into 5.5[tex]\sqrt{6}[/tex] = 13.47

Answers

The answers are not in the correct form. By going through and finding the decimal form of each, you find out that 11[tex]\sqrt{6/4}[/tex] is equivalent to 13.47, therefore your answer.

I suppose this is saying that 20%, 25% and 55% are each a whole number of science students.  The GCD is 5%, 1/20th, so minimum 20 people total.  55% are studying biology, that's 11.

Answer: C. 11

Answer:

18 is the first multiple of 3,6, and 9.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

We need to find the LCM (lowest common multiple) of 3, 6, and 9. Let's count by multiples of 3 to find it.

3 (not a multiple of 6 or 9), 6 (not a multiple of 9), 9 (not a multiple of 6), 12 (not a multiple of 9), 15 (not a multiple of 6 or 9), 18.

Since 18 is the first number that is a multiple of 3, 6, and 9, that is the answer.

Answer:

[tex]y_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]  ,  [tex]y_2 = \left[\begin{array}{ccc}5\\1\\-6\\-1\end{array}\right][/tex]

Step-by-step explanation:

[tex]x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]    and [tex]x_2 = \left[\begin{array}{ccc}7\\-7\\-6\\1\end{array}\right][/tex]

Using Gram-Schmidt process to produce an orthogonal basis for W

[tex]y_1 = x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]

Now we know X₁ , X₂ and Y₁

Lets solve for Y₂

[tex]y_2 = x_2- \frac{x_2*y_1}{y_1*y_1}y_1[/tex]

see attached for the solution of Y₂

Answer:

theres the screenshot of it

The solution to prove the sum of the interior angles of a triangle is 180° is

∠1 + ∠2 + ∠3 = 180°  ( angles in a straight line )

∠2 + ∠5 + ∠6 = 180°  ( interior angles of a triangle )

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the angles inside the triangle are ∠2 , ∠5 and ∠6

Now , the lines l₁ and l₂ are two parallel lines

From the figure ,

The measure of ∠1 = The measure of ∠5 ( alternate interior angles )

The measure of ∠3 = The measure of ∠6 ( alternate interior angles )

Now , for a straight line , the measure of angle = 180°

So , ∠1 + ∠2 + ∠3 = 180°  ( angles in a straight line ) ( angle addition )

And , the sum interior angles of a triangle is 180°

So , ∠2 + ∠5 + ∠6 = 180°  ( interior angles of a triangle ) ( substitution )

Hence , the sum of the angles inside a triangle is 180°

To learn more about triangles click :

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Answer: Speed = 5.6 mph

              Oxygen consumption = 71.6 mL/lb/min

Step-by-step explanation: For the oxygen consumption to be the same, functions must be equal:

f(x) = g(x)

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x+10=11x+10[/tex]

Resolving:

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x - 11x =0[/tex]

[tex]\frac{5}{3}x^{2} + \frac{5}{3}x - \frac{33x}{3}=0[/tex]

[tex]\frac{5}{3}x^{2} - \frac{28x}{3}=0[/tex]

[tex]\frac{x}{3}(5x - 28)=0[/tex]

[tex]\frac{x}{3} = 0[/tex]

x=0

5x - 28 = 0

[tex]x = \frac{28}{5}[/tex]

x = 5.6

The speed when the oxygen consuption is the same is 5.6 mph.

For the level of oxygen consumption:

f(5.6) = g(5.6)

g(5.6) = 11*5.6 + 10

g(5.6) = 71.6

The level of oxygen consumption is 71.6 mL/lb/min

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption is 71.6 milliliter per pound per minute

The oxygen consumption for a person walking at x mph is given by,

             [tex]f(x)=\frac{5}{3} x^{2} +\frac{5}{3}x+10[/tex]

The oxygen consumption for a runner at x mph is approximated given by the function,

             [tex]g(x)=11x+10[/tex]

To be oxygen consumption same for both walker and runner, both function must be equal.

             [tex]f(x)=g(x)\\\\\frac{5}{3} x^{2} +\frac{5}{3}x+10=11x+10\\\\\frac{5}{3} x^{2} +\frac{5}{3}x-11x=0\\\\x(\frac{5}{3} x-\frac{28}{3} )=0\\\\x=0,x=28/5=5.6mph[/tex]

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption at that speed is,

             [tex]g(5.6)=11(5.6)+10=71.6[/tex]

Learn more:

https://brainly.com/question/6237128

[tex]\bold{Answer}:\quad \dfrac{24}{25}[/tex]

Step-by-step explanation:

There are 100 oranges.  4 of them are unripe which means 96 are ripe.

[tex]\dfrac{ripe}{total}=\dfrac{96}{100}\quad \div \dfrac{4}{4}=\large\boxed{\dfrac{24}{25}}[/tex]

Answer:

20%

Step-by-step explanation:

When you divide 40 by 8, you get 0.2. To convert a decimal into a percent, you multiply by 100 to get 20.

Hence,

8 is 20% of 40.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

The answer is option B.

Step-by-step explanation:

Let the percentage be x

We have

[tex] \frac{x}{100} \times 40 = 8 \\ \\ \frac{4}{10} x = 8 \\ \\ 4x = 80 \\ \\ x = \frac{80}{4} \\ \\ x = 20[/tex]

Hope this helps you

Answer:

A: y = (x − 4)^2 − 4

Step-by-step explanation:

vertex=(4.-4)

A: y = (x − 4)^2 − 4

y=x^2-8x+16-4

y=x^2-8x+12 (a=1,b=-8,c=12)

the y intercept is (0,12)

vertex ( h, k)

h=-b/2a ⇒ h=-(-8)/2=4

plug the value of h in the equation y=x^2-8x+12

k=4²-8(4)+12

k=16-32+12

k=-4

v(4,-4)

The required equation of the given graph in vertex form is y = (x − 4)² − 4. which is the correct answer would be option (A).

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c.

The parabola equation into the vertex form:

(y-k) = a(x-h)²

Where (h,k) are the x and y-coordinates of the vertex.

The vertex = (4, -4) is given in the shown graph.

As per option (A),

y = (x − 4)² − 4

y = x²-8x+16-4

y = x²-8x+12 (a=1,b=-8,c=12)

the y-intercept is (0,12)

vertex ( h, k)

h = -b/2a ⇒ h=-(-8)/2=4

Substitute the value of h in the equation y = x²-8x+12

k = 4²- 8(4) + 12

k =16 - 32 + 12

k = -4

Thus, the vertex is (4,-4)

Hence, the correct answer would be option (A).

Learn more about the parabola here:

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Answer:

[tex]y-4=2\,(x+1)[/tex]

which agrees with answer C in your list of possible answers.

Step-by-step explanation:

We can use the general point-slope form of a line of slope m and going through the point [tex](x_0, y_0)[/tex]:

[tex]y-y_0=m(x-x_0)[/tex]

which in our case, given the info on the slope (2) and the point (-1, 4) becomes:

[tex]y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)[/tex]

Answer:

123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134

Step-by-step explanation:

123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134

Answer: True

Step-by-step explanation:

The probability of an event occurring lies between zero and one. A probability of 0 means that the event has no chance of happening for example, rolling a die once and getting a number greater than 6 while a probability of 1 means the event will definitely happen for example, getting a number less than 7 when you roll a die once.

Every other probability falls in-between this range so probability can never be 154.

Answer: 0.0668

Step-by-step explanation:

Given the following :

Mean (m) Cost = RS385

Standard deviation (s) = RS110

Assume a normal distribution, Probability that domestic airfare is RS550 or more?

P(x > 550)

Find the z - score

Z - score = (x - m) / s

Where x = 550

Z = (550 - 385) / 110

Z = 165 / 110 = 1.5

P(Z > 1.5) = 1 - P(Z ≤1.5)

Using the z table : 1.5 = 0.9332

Therefore,

1 - P(Z ≤1.5) = 1 - 0.9332 = 0.0668

P(x > 550) = 0.0668

Answer:

x^2 +3

Step-by-step explanation:

f(x) = 2x^2 + 2

g(x) = x2 – 1,

find (f – g)(X).

f(x) - g(x) = 2x^2 + 2 -( x^2 – 1)

Distribute the minus sign

             = 2x^2 +2 -x^2 +1

             = x^2 +3

Answer:

viscosity is the state of being thick, sticky, and semifluid in consistency, due to internal friction.

"cooling the fluid raises its viscosity"

a quantity expressing the magnitude of internal friction, as measured by the force per unit area resisting a flow in which parallel layers unit distance apart have unit speed relative to one another.

plural noun: viscosities

"silicone oils can be obtained with different viscosities"

Step-by-step explanation:

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. hope this helps you :)

Answer:

O An oil's resistance to flow at different temperatures

Step-by-step explanation:

Internal friction of a moving fluid .

Answer:

There is no significant interaction between the number of sales calls and the miles driven.

Step-by-step explanation:

The variables are defined as follows:

Dependent (Y) = amount earned in commissions last month

Independent (X₁) = number of miles driven last month

Independent (X₂) = number of sales calls made last month

In this case we need to test whether there is a significant interaction between the number of sales calls and the miles driven.

The hypothesis can be defined as follows:

H₀: There is no significant interaction.

Hₐ: There is a significant interaction.

Assume that the significance level of the test is, α = 0.05.

Use the Data Analysis tool in Excel to form the regression equation.

For the regression equation, we need to compute the values of (X₁ × X₂).

Steps:

The output of the regression analysis is attached below.

The regression equation is:

[tex]Y=-455.07+3.128\cdot X_{1}+0.143\cdot X_{2}-0.001\cdot X_{1}X_{2}[/tex]

Consider the third table in the regression output.

The test statistic corresponding to the interaction term is:

t = -1.85

The p-value for the test of the interaction term is:

p-value = 0.078.

The p-value of the test is more than the significance value.

The null hypothesis will not be rejected.

Thus, concluding that there is no significant interaction between the number of sales calls and the miles driven.

Answer:

( 2A - kn) /k = m

Step-by-step explanation:

A = k/2(m+n)

Multiply each side by 2/k

2/k *A =2/k * k/2(m+n)

2A /k = m+n

Subtract n from each side

2A /k - n = m+n -n

2A /k - n = m

Getting a common denominator

2A/k - kn/k = m

( 2A - kn) /k = m

Answer:

Step-by-step explanation:

[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]

Answer:

1)  m = negative StartFraction 10 over 4 EndFraction

2) m = negative five-halves

3) m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]

Step-by-step explanation:

The given equation is:

=> [tex]\frac{3}{4} +m = -\frac{7}{4}[/tex]

Subtracting 3/4 to both sides

=> m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]

=> m = [tex]\frac{-10}{4}[/tex]

=> m = [tex]-\frac{5}{2}[/tex]

Answer:

-5/2 ye

cause ya do the math

Step-by-step explanation:

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

B = 26.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin B = 4/9

Take the inverse sin of each side

sin ^-1 sin ( B) = sin ^-1 ( 4/9)

B = 26.38779996

B = 26.4

Answer:

[tex]26.4\º[/tex]

Step-by-step explanation:

[tex]\theta=?[/tex]

[tex]$\sin(\theta)=\frac{opp}{hyp} = \frac{4}{9} $[/tex]

[tex]$\theta=\sin^{-1}\frac{4}{9} =\arcsin\frac{4}{9} \approx 26.4\º$[/tex]

Answer:

13°

Step-by-step explanation:

The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.

The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft

Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:

[tex] tan x = \frac{opposite}{adjacent} [/tex]

[tex] tan x = \frac{6}{26} [/tex]

[tex] tan x = 0.2308 [/tex]

x = tan-¹(0.2308)

x = 12.996

x ≈ 13° (to the nearest whole degree)

The angle of elevation of the sun = 13°

Answer:

[tex]1x=\frac{1\sqrt{129} }{8}[/tex]

Step-by-step explanation:

In between the 1 and the [tex]\sqrt{129}[/tex] goes this symbol: ±

hope this helps!