Triangle TQRS Find the value of x.
O x = 2
O x = 3
O x= 33
O x= 52

From top to bottom, the answers are

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

Explanation:

The first system of equations has each equation with the same slope 2, but different y intercepts. This indicates we have parallel lines. Parallel lines never cross, so there are no solutions. A solution is where the two lines cross.

The second system of equation has one solution where the two lines cross. This is because the slopes are different

The third system has infinitely many solutions. We have the same line graphed out twice. One line is directly on top of the other to yield infinitely many intersection points.

The fourth system is similar to the second system. Different slopes lead to exactly one solution. The y intercept doesn't affect the number of solutions (whether its 0, 1 or infinitely many)

For each equation shown, they are in the form y = mx+b with m as the slope and b as the y intercept.

There's a bit of ambiguity in your question...

We know that [tex]f^{-1}(-15)=7[/tex], which means [tex]f(7)=-15[/tex].

I see three possible interpretations:

• If [tex]f(x)=k\sqrt2+x[/tex], then

[tex]f(7)=-15=k\sqrt2+7\implies k\sqrt2=-22\implies k=-\dfrac{22}{\sqrt2}=11\sqrt2[/tex]

• If [tex]f(x)=k\sqrt{2+x}[/tex], then

[tex]f(7)=-15=k\sqrt{2+7}\implies -15=3k\implies k=-5[/tex]

• If [tex]f(x)=\sqrt[k]{2+x}[/tex], then

[tex]f(7)=-15=\sqrt[k]{2+7}\implies-15=9^{1/k}\implies\dfrac1k=\log_9(-15)[/tex]

which has no real-valued solution.

I suspect the second interpretation is what you meant to write.

Answer:

a) [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] or [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex], b) The magnitude of segment PQ is approximately 11.489, c) The two unit vectors associated to PQ are, respectively: [tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]

Step-by-step explanation:

a) The vectorial form of segment PQ is determined as follows:

[tex]\overrightarrow {PQ} = \vec Q - \vec P[/tex]

Where [tex]\vec Q[/tex] and [tex]\vec P[/tex] are the respective locations of points Q and P with respect to origin. If [tex]\vec Q = (13,13,3)[/tex] and [tex]\vec P = (5,5,1)[/tex], then:

[tex]\overrightarrow{PQ} = (13,13,3)-(5,5,1)[/tex]

[tex]\overrightarrow {PQ} = (13-5, 13-5, 3 - 1)[/tex]

[tex]\overrightarrow{PQ} = (8,8, 2)[/tex]

Another form of the previous solution is [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex].

b) The magnitude of the segment PQ is determined with the help of Pythagorean Theorem in terms of rectangular components:

[tex]\|\overrightarrow{PQ}\| =\sqrt{PQ_{x}^{2}+PQ_{y}^{2}+PQ_{z}^{2}}[/tex]

[tex]\|\overrightarrow{PQ}\| = \sqrt{8^{2}+8^{2}+2^{2}}[/tex]

[tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex]

The magnitude of segment PQ is approximately 11.489.

c) There are two unit vectors associated to PQ, one parallel and another antiparallel. That is:

[tex]\vec v_{1} = \vec u_{PQ}[/tex] (parallel) and [tex]\vec v_{2} = -\vec u_{PQ}[/tex] (antiparallel)

The unit vector is defined by the following equation:

[tex]\vec u_{PQ} = \frac{\overrightarrow{PQ}}{\|\overrightarrow{PQ}\|}[/tex]

Given that [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] and [tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex], the unit vector is:

[tex]\vec u_{PQ} = \frac{(8,8,2)}{11.489}[/tex]

[tex]\vec u_{PQ} = \left(\frac{8}{11.489},\frac{8}{11,489},\frac{2}{11.489} \right)[/tex]

[tex]\vec u_{PQ} = \left(0.696, 0.696,0.174\right)[/tex]

The two unit vectors associated to PQ are, respectively:

[tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]

Answer:

The coordinate of the point is (-5, 4)

Step-by-step explanation:

In a regular two dimensional graph, the abscissa is the horizontal or x - axis while the y-axis which is the vertical axis is referred to as the ordinate

Abscissa and ordinate are used in mathematics to indicate the coordinate of a point in a two dimensional coordinate system, where the abscissa and ordinate are placed in between a parenthesis, with the abscissa being on the left and the ordinate on the right separated by a comma.

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

Explanation:

List out the multiples of 25 to get {25, 50, 75, 100, 125, 150, 175, 200}

Do the same for the multiples of 40 to get {40, 80, 120, 160, 200}

We see that the lowest common multiple (LCM) is 200

---------

Another way to get the LCM is to multiply 25 and 40 to get 25*40 = 1000. Then divide this over 5 as this is the GCF between the two original numbers. We end up with the same LCM since 1000/5 = 200.

--------

There's a third way to get the LCM

List out the prime factorization of each value

25 = 5*5

40 = 2*3*5

Note how we have the unique factors of 2, 3 and 5. Circle the unique factors such that we highlight the ones that occur the most. We have 2 occur once, 3 occur once, and 5 occurs twice. We have circled one 2, one 3, and two 5's. They multiply out to 2*3*5*5 = 8*25 = 200

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

Whichever method works for you, the LCM is 200. This means that every 200 minutes, we have bus A and bus B arrive at the depot at the same time. Their cycles line up at the 200 minute mark.

Convert this to hours,minutes format.

200 minutes = 180 minutes + 20 minutes

200 minutes = 3 hours + 20 minutes

200 minutes = 3 hrs, 20 min

We can represent "3 hrs, 20 min" in 12-hour clock notation by writing 3:20

Add this onto 7:00, which is 7 AM and we get

(7:00) + (3:20) = (7+3):(00+20) = 10:20 AM

We have started at 7 AM and fast forwarded 3 hours and 20 minutes to arrive at 10:20 AM.

Answer:

Hey there!

These triangles can be proved congruent by the HL Theorem.

Hope this helps :)

Hey Mate!!

Your answer will be HL Theorem.

Because, Since the triangles overlap, their hypotenuses are the same side and therefore congruent by the reflexive property. This means the triangles are congruent by a hypotenuse, leg and right angle. This is known as HL.

☆ Good Luck ☆

♡ Comments down ♡

By ◇~Itsbrazts ◇~

Answer:

a) [tex]a_n=3\,n-11[/tex]

b) [tex]a_{20}=49[/tex]

c) term number 17 is the one that gives a value of 40

Step-by-step explanation:

a)

The sequence seems to be arithmetic, and with common difference d = 3.

Notice that when you add 3 units to the first term (-80, you get :

-8 + 3 = -5

and then -5 + 3 = -2 which is the third term.

Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:

[tex]a_n=a_1+(n-1)\,d[/tex]

That in our case would give:

[tex]a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11[/tex]

b)

Therefore, the term number 20 can be calculated from it:

[tex]a_{20}=3\,(20)-11=60-11=49[/tex]

c) in order to find which term renders 20, we use the general form we found in step a):

[tex]a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17[/tex]

so term number 17 is the one that renders a value of 40

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

Where m is the slope

c is the y intercept

From the question the y intercept is 3

and the slope is 2

Substituting the values into the above equation

We have

Hope this helps you

The equation of a line that passes through [tex](0,3)[/tex] and a slope [tex]2[/tex] is [tex]y=2x+3[/tex].

The equation of a line that passes through a point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is:

[tex](y-y_1)=m(x-x_1)[/tex]

Here, the point is [tex](0,3)[/tex] and the [tex]slope[/tex] is [tex]2[/tex].

So, [tex]x_1=0, y_1=3[/tex] and [tex]m=2[/tex].

So, the equation of the line is

[tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-3)=2(x-0)[/tex]

[tex]y-3=2x-0[/tex]

[tex]y=2x+3[/tex]

So, option B is correct.

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Answer:

sqrt(68) is the length.

Step-by-step explanation:

For this you will use the distance formula, sqrt((x2-x1)^2+(y2-y1)^2)

So for this it is sqrt((5+3)^2+(-2+4)^2)

sqrt(64+4)

sqrt(68)

8.246

Answer:

B. 2

Step-by-step explanation:

ed2020

If Y bracelet is chosen first then there will be only two ways to give out the bracelets.

When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.

The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.

Given that Jillian has three bracelets

X, Y, and Z

Said that Y has chosen first

The remaining bracelets are X and Z

Number of ways

It means there are only two ways to give out bracelets.

Hence "If Y bracelet is chosen first then there will be only two ways to give out the bracelets".

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Answer:

1. 2⁶

2. 6⁷

3. 14⁵

Step-by-step explanation:

We assume and apply the laws of logarithms and indices in the problems above.

1. Product Rule Law: which states that

loga (MN) = loga M + loga N

Where 2² X 5⁵  = 2²+⁵ = 2⁷

2. The Power rule: in which (6⁵)² = 6⁵+² = 6⁷

3. (2x7)⁵ = (14)⁵ or 5 log 14

Answer: Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Step-by-step explanation:

Given that;

U = 75

X = 78

standard deviation α = 10

sample size n = 20

population is normally distributed

PROBLEM is to test

H₀ : U = 75

H₁ : U ≠ 75

TEST STATISTIC

since we know the standard deviation

Z =  (X - U) / ( α /√n)

Z = ( 78 - 75 ) / ( 10 / √20)

Z = 1.3416 ≈ 1.342

Now suppose we need to test at ∝ = 0.05 level of significance,

Then Rejection region for the two tailed test is Zc = 1.96

∴ Reject H₀ if Z > Zc

and we know that Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

At the null hypothesis, we test if the mean is of 75, that is:

[tex]H_0: \mu = 75[/tex]

At the alternative hypothesis, we test if the mean is different of 75, that is:

[tex]H_1: \mu \neq 75[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

For this problem, we have that:

[tex]X = 78, \mu = 75, \sigma = 10, n = 20[/tex]

The value of the test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}[/tex]

[tex]z = 1.34[/tex]

Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.

Looking at the z-table, z = -1.34 has a p-value of 0.0901.

2(0.0901) = 0.1802

The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

A similar problem is given at https://brainly.com/question/15535901

f-g means to subtract g from f:

(4^x - 8) - (5x+6)

Remove the parenthesis and change the equations sings for g:

4^x-8 -5x -6

Combine like terms:

4^x - 5x - 14

The answer is A.

Answer:

+3, 0

Step-by-step explanation:

y-intercept for f(x) is when x = 0, so it is +1, 0

y-intercept for g(x) is when x = 0, so it is +3, 0

y-intercept for h(x) is when x = 0, so it is -2, 0

The y-intercept of a function is the point where x = 0.

The ordered pair that represents the greatest y-intercept is (0,3)

The functions are given as:

[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]

[tex]\mathbf{g(x) = (x + 3)}[/tex]

[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]

Set x = 0, and solve the functions

[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]

Substitute 0 for x

[tex]\mathbf{f(0) = |0 - 1| + 2}[/tex]

[tex]\mathbf{f(0) = |- 1| + 2}[/tex]

Remove absolute brackets

[tex]\mathbf{f(0) = 1 + 2}[/tex]

[tex]\mathbf{f(0) = 3}[/tex]

[tex]\mathbf{g(x) = (x + 3)}[/tex]

Substitute 0 for x

[tex]\mathbf{g(0) = (0 + 3)}[/tex]

[tex]\mathbf{g(0) = 3}[/tex]

[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]

Substitute 0 for x

[tex]\mathbf{h(0) = (0 + 1) - 3}[/tex]

[tex]\mathbf{h(0) = 1 - 3}[/tex]

[tex]\mathbf{h(0) = - 2}[/tex]

Hence, the ordered pair that represents the greatest y-intercept is (0,3)

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Answer:

8 cans

Step-by-step explanation:

[tex]V=lwh\\l=40\\w=25\\h=8\\V=(40)(25)(8)\\V=(1000)(8)\\V=8000^3\\\frac{8000^3}{1000^3} =8[/tex]

Since the volume is 8000 cm³ and 8000 cm³ divided by 1000 cm³ is equal to 8, the total cans it will take to fill up the go cart is 8 cans.

Note:

I know this is really late but this to help people for future references

Answer:

Δ BEC ≅ Δ AED

Step-by-step explanation:

Consider triangles BCA and ADB. Each of them share a common side, AB. Respectively each we should be able to tell that AD is congruent to BC, and DB is congruent to CA, so by SSS the triangles should be congruent.

_________

So another possibility is triangles BEC, and AED. As you can see, by the Vertical Angles Theorem m∠BEC = m∠ADE, resulting in the congruency of an angle, rather a side. As mentioned before AD is congruent to BC, and perhaps another side is congruent to another in the same triangle. It should be then, by SSA that the triangles are congruent - but that is not an option. SSA does is one of the exceptions, a rule that is not permitted to make the triangles congruent. Therefore, it is highly unlikely that triangles BEC and AED are congruent, but that is what our solution, comparative to the rest.

Δ BEC ≅ Δ AED .... this is our solution

Answer:

Step-by-step explanation:

eq. of line parallel to y=34x-9 is y=34 x+k

∵ it passes through (-8,-18)

∴-18=34×-8+k

k=-18+272

k=254

so reqd. eq. is y=34 x+272

Answer:

No answer can be found

Step-by-step explanation:

There isn't any value to find and express in simplest form lol.

Answer:

AC = 20°

Step-by-step explanation:

180° (total angle amount of a triangle) - 70° + 90° (right angle) = ac

AC = 20°

Hope this helps!

Answer:

x = 64

Step-by-step explanation:

∠ HIA and ∠ LJK are corresponding angles and congruent, thus

∠ HIA = 60°

The sum of the 3 angles in Δ HIA = 180° , thus

x = 180 - (60 + 56) = 180 - 116 = 64

Answer:

Correct answer:

A. I and II

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with [tex]f^{-1}(x)[/tex]

Given that:

[tex]I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3[/tex]

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = [tex]a^{-1}(x)[/tex] = [tex]a(x)[/tex]  Hence, I is true.

II. [tex]y =\dfrac{1}{x}[/tex]

Replacing y with and x with y:

[tex]x =\dfrac{1}{y}[/tex]

[tex]x=\dfrac{1}{a^{-1}(x)}[/tex]

[tex]\Rightarrow a^{-1}(x) = \dfrac{1}{x}[/tex]

[tex]a^{-1}(x)[/tex] = [tex]a(x)[/tex]  Hence, II is true.

III. [tex]y =x^{2}[/tex]

Replacing y with and x with y:

[tex]x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)[/tex]

 Hence, III is not true.

IV. [tex]y =x^{3}[/tex]

Replacing y with and x with y:

[tex]x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)[/tex]

Hence, IV is not true.

Correct answer:

A. I and II

Answer:

A:

9×1=9

9×2=18

9×3=27

9×4=36

9×5=45

9×6=54

9×7=63

9×8=72

9×9=81

9×10=90

B:

It goes down by 1 after multiplying a bigger number.

C:

It goes up by 1 after multiplying a bigger number.

Step-by-step explanation:

hope this helps you and have a great day

Answer: The length is 15 yards so the answer is A.

Step-by-step explanation:

If  the length is 3 more than the width  the we will represent it by the equation L = w+3    where w is the width and to find the area of a rectangle, we need to multiply the length by the width. so the length is w+3 and the width is w so

w(w+3) = 180   solve for the w

w^2 + 3w = 180     subtract 180 from both sides

w^2 + 3w -180 = 0    find two numbers that their product is -180 and add to 3.

  the number 12 and -15 works out because -12*15= -180  and -15+ 12 =3

We will now have a new quadratic equation as

w^2 - 12w + 15w - 180 = 0  factor by grouping

w(w-12) 15(w-12)= 0     factor out w-12

(w-12)(w+15) = 0    set them both equal  zero.

w -12 = 0      or  w+15= 0  

w =  12      or  w = -15

Since we know that -15 can't represent a distance, then 12 is the width .  

So if we are to find the length and it gives us the information that the length is 3 yards more that the width then we will add 3 to the width to equal the length.

L= 12 +3

L = 15

The length of the rectangular playground is 15 yards. The correct answer would be an option (A).

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

Since the length is 3 more than the width

So, we will represent it by the equation L = W+3  ...(i)

A rectangular playground has an area of 180 square yards

So, L × W = 180

Substitute the value of equation (i), and we get

W(W+3) = 180

W² + 3W = 180

W² + 3W -180 = 0  ...(i)

Solving the above quadratic equation, we get the values of W :

W = 12 and W = -15

Take positive value because dimensions can't be negative.

Substitute the value of W = 12 in equation (i), and we get

L = 12 + 3 = 15

Therefore, the length of the playground is 15 yards.

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Answer:

Project A : $58,000

Project B: $52800

Project A should be selected as it has a higher expected profit value than project B

Step-by-step explanation:

Given the following:

PROJECT A:

Profit : ---------50000--90,000--10,000

Probability: ----0.6-------0.3--------0.1

PROJECT B:

Loss of 20,000 = -20,000 in profit terms

Profit : -----100,000--64,000--(-20,000)

Probability: ----0.1-------0.7--------0.2

Expected profit:

Profit value * probability of profit

Expected profit on project A:

[(50000*0.6)+(90000*0.3)+(10000*0.1)

30000 + 27000 + 1000 = $58000

Expected profit on project B:

[(100000*0.1)+(64000*0.7)+(-20000*0.2)

10000 + 44800 - 4000 = $50800

Project A should be selected as it has a higher expected profit value than project B

Answer:

e = -2

Step-by-step explanation:

Well to solve for e in the following equation,

.75(8 + e) = 2 - 1.25e

We need to distribute and use the communicative property to find e.

6 + .75e = 2 - 1.25e

-2 to both sides

4 + .75e = -1.25e

-.75 to both sides

4 = -2e

-2 to both sides

e = -2

Thus,

e is -2.

Hope this helps :)

Answer:

[tex]\large \boxed{\sf \ \ 23 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]a_1=f(1)=3\\\\a_2=f(1)+4=3+4=7\\\\a_3=f(3)=a_2+4=7+4=11\\\\a_4=a_3+4=11+4=15\\\\a_5=a_4+4=15+4=19\\\\a_6=a_5+4=19+4=23[/tex]

So the answer is 23.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

a = 55° and b = 60°

Step-by-step explanation:

→ Remember 2 key points about angles

→ Angle a is alternate to 55° so using the 2nd point,

a = 55°

→ Remember the fact that angle in a triangle add up to 180°

55°  + 65° + b = 180°

→ Collect the whole numbers

120° + b = 180°

→ Minus 120° from both sides to isolate b

b = 60°

The solution is : the measures of angles A and B are:

A = 55° and B = 60°

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

We know that 55+ b+ other angle = 180 since they make a straight line

The other angle = 65 since they are alternate interior angles

55+ B+ 65 = 180

Combine like terms

120 + B = 180

B = 60

A + B + 65 = 180

interior angles of a triangle must equal 180 degrees

A +60+ 65 =180  

Combine like terms

A +125 = 180

A = 55

Hence, The solution is : the measures of angles A and B are:

A = 55° and B = 60°

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Answer:

x² - 20 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{( {b})^{2} - 4ac } }{2a} [/tex]

a = 1 b = 0 c = -20

So we have

[tex]x = \frac{ - 0 ± \sqrt{ {0}^{2} - 4(1)( -20)} }{2(1)} \\ \\ x = \frac{± \sqrt{80} }{2} \\ \\ x = \frac{±4 \sqrt{5} }{2} \\ \\ \\ x = ±2 \sqrt{5} \\ \\ \\ x = 2 \sqrt{5} \: \: \: or \: \: \: x = - 2 \sqrt{5} [/tex]

Hope this helps you.

Answer:

Correct Option: B

Step-by-step explanation:

Linear functions are the type of functions that are applied to model occurrences that rise or fall at a constant proportion. These sorts of functions are polynomial functions with a maximum exponent of one on the variable. The graphs of these kind of functions are in the form of a line.

Exponential functions are the type of functions that have the variable in exponent form. The growth rate or decline rate is either slow than quick or quick than slow.

Quadratic functions are of the form f (x) = ax² + bx + c. The graph of this function is in the form of a parabola. The graph first increases, hit a maximum, then decreases or decreases, hit a minimum, then increases.

From the provided graphs it can be seen that, the exponential function grows at approximately the same rate over the interval 0 ≤ x ≤ 1 as the quadratic function.

Answer:

bbb

Step-by-step explanation: