Drag the tiles to the correct boxes to complete the pairs.
Using the properties of integer exponents, match each expression with the correct equivalent expression.

Answer:

Step-by-step explanation:

[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\============================[/tex]

[tex]\text{We have the points:}\ (-1,\ 2)\ \text{and}\ (3,1).\\\\\text{Substitute:}\\\\m=\dfrac{1-2}{3-(-1)}=\dfrac{-1}{4}=-\dfrac{1}{4}\\\\y-2=-\dfrac{1}{4}(x-(-1))\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{convert to the standard form}\ Ax+By=C\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{multiply both sides by 4}\\\\4y-8=-(x+1)\\\\4y-8=-x-1\qquad\text{add 8 to both sides}\\\\4y=-x+7\qquad\text{add x to both sides}\\\\x+4y=7[/tex]

The equation of a line passing through points (-1, 2) and (3, 1) can be determined using the slope formula, which is (y2 - y1)/(x2 - x1). The resulting slope is -1/4 or -0.25. Unfortunately, none of the provided options match this description.

The subject of the question is about finding the equation of a line that passes through the points (-1,2) and (3,1). To find the correct equation, we need to use the formula for the slope of a line which is: (y2 - y1) / (x2 - x1). Plugging in the coordinates (-1,2) and (3,1) will give us a slope of -1/4 or -0.25. This slope should be the coefficient of 'x' in the correct equation. None of the provided choices A, B, C, D have a coefficient of -0.25 for x, therefore, unfortunately, none of these equations represent a line that passes through the points (-1,2) and (3,1).

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Answer:

Step-by-step explanation:

[tex]a\ \vee\ b\ \text{is true if }\ a=T\ \text{or}\ b=T.\\\\\text{Therefore}\ p\ \vee\ (q\ \wedge\ r)\ \text{is\ true,\ if}\ p=T\ \text{or}\ (q\ \wedge\ r)=T.\\\\\text{We have}\ p=F.\ \text{Therefore}\ p\ \vee\ (q\ \wedge\ r)\ \text{is true, if}\ (q\ \wedge\ r)=T.[/tex]

Answer:

The area of the circle is [tex]A=6.25\pi\ units^{2}[/tex]

Step-by-step explanation:

step 1

Find the diameter of circle

we know that

The diameter of the circle is equal to the distance AB

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

[tex]AB=\sqrt{(5-1)^{2}+(5-2)^{2}}[/tex]

[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]

[tex]AB=\sqrt{25}[/tex]

[tex]AB=5\ units[/tex]

therefore

the diameter of the circle is

[tex]D=5\ units[/tex]  

step 2

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

[tex]r=5/2=2.5\ units[/tex]  ----> the radius is half the diameter

substitute

[tex]A=\pi (2.5)^{2}[/tex]

[tex]A=6.25\pi\ units^{2}[/tex]

Answer:

r(-1) = 6.31 and r(2) = -16.88

Step-by-step explanation:

* Lets read the problem and solve it

- Evaluate means find the value, so evaluate r(x) means find the value

 of it at the given values of x

∵ r(x) = -0.21x³ + x² - 8.1x - 3

∵ x = -1 and x = 2

- Then find r(-1) by substitute x by -1 and find r(2) by substitute x by 2

# At x = -1

∴ r(-1) = -0.21(-1)³ + (-1)² - 8.1(-1) - 3  

∴ r(-1) = -0.21(-1) + (1) - 8.1(-1) - 3

∴ r(-1) = 0.21 + 1 + 8.1 - 3

∴ r(-1) = 6.31

# At x = 2

∴ r(2) = -0.21(2)³ + (2)² - 8.1(2) - 3  

∴ r(2) = -0.21(8) + (4) - 8.1(2) - 3

∴ r(2) = -1.68 + 4 - 16.2 - 3

∴ r(2) = -16.88

* r(-1) = 6.31 and r(2) = -16.88

Answer:

7

Step-by-step explanation:

This operation is identical to subtracting 6 from 13.  The correct result is 7.

Answer:

Adjacent angles must share a vertex.

Step-by-step explanation:

we know that

Two angles are Adjacent when they have a common side and a common vertex

therefore

Adjacent angles must share a vertex.

Answer:

Adjacent angles must share a vertex.

Im so sorry I am so late on answering this question....

Hope the answer (my answer) helps!

Step-by-step explanation:

9.02

remember when dealing with decimals:

0.(tenth)(hundredths)(thousandths)

Nine and two hundredths as a decimal is 9.02.

The question asks for the decimal representation of nine and two hundredths. In the decimal number system, 'and' corresponds to the decimal point. So, the answer to the question is 9.02. This is because the 'nine' is in the whole number part before the decimal point and 'two hundredths' is represented by '02' after the decimal point.

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namely, how many times does 3/4 go into 3½?  Let's firstly convert the mixed fraction to improper fraction.

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\div \cfrac{3}{4}\implies \cfrac{7}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]

Answer:

Danika signed up to work for 3.5 hours at the science fair, if each work shift is 3/4 hour = 0.75 hours, the amount of shifts will be:

Shifts = 3.5/0.75 = 4,66 ≈ 5 shifts. Given that shifts have to be an integer number, we need to round the result to the nearest integrer.

Therefore, Danika will work 5 shifts.

Answer:

2.2

2.20

Explanation

You can add zeros or take them away and the number will still have the same value.

Answer:

rotate 180 degrees ccw from (0,0)

Answer:

We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.

Step-by-step explanation:

We are given a graph which Rectangle ABCD and A'B'C'D'

To find : Set of transformation

From the graph,

Vertex of the Rectangle ABCD,

A( -4 , 2 ) , B ( -4 , 1 ) , C ( -1 , 1 ) and D ( -1 , 2 )

Vertices of Rectangle A'B'C'D'

A( 4 , -2 ) , B ( 4 , -1 ) , C ( 1 , -1 ) and D ( 1 , -2 )

Clearly from above,

we get that coordinates of the vertices of Rectangle A'B'C'D' is negative of the coordinates of the vertices of Rectangle ABCD .

That is if Coordinates of A( x , y ) then A'( -x , -y )

This transformation is done when we rotate the given figure by 180° about origin.

Therefore, We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.

it's r because it does not sit on the same plane as the rest of the points that are given.when looking at the diagram c,d and e are all connected to the square on the bottom of the pyramid. The same goes for points u,s and a. The point R is different by sitting on one of the triangles of the pyramid.

The point R is not coplanar with C, D, and E. This is because point R is not lying in the plane of C, D, and E.

The points which lie on the same plane are said to be coplanar points.

The given points are R, A, S, and U

The considered pane is w.r.t the points C, D, and E.

So, point A is forming a square with the points C, D, and E. So, it is coplanar with these points.

Point S is on the surface of the plane formed by ACDE. So, it is coplanar.

Point U is also in the plane w.r.t point C, D, and E. So, it is a coplanar point.

But point R does not lie in the plane w.r.t C, D, and E. So, it is not coplanar with points C, D, and E.

Learn more about coplanar points here:

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The congruence theorems that will be used to prove that both triangles are congruent are: C. LL E. SAS.

The LL theorem is a triangle congruence theorem that states that if the two pairs of legs of two right triangles are congruent, then the triangles are congruent.

The SAS theorem is a triangle congruence theorem that states that if the two pairs of sides and a pair of included angles of two triangles are congruent, then the triangles are congruent.

Based on the information given, the theorem that can be used to show both triangles are congruent are: C. LL E. SAS

Learn more about the LL and SAS theorems on:

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Triangle DEF can be proven congruent to triangle KLM using the Leg-Leg (LL) Theorem, Side-Angle-Side (SAS) Theorem, and Hypotenuse-Leg (HL) criterion .

The correct answer is option B, C and E.

In geometry, a congruence theorem is a statement that two geometric figures are congruent, meaning that they have the same size and shape. There are many different congruence theorems, but the most common ones are the Side-Angle-Side (SAS) Theorem, the Angle-Side-Angle (ASA) Theorem, and the Leg-Leg (LL) Theorem.

The LL Theorem is a special congruence theorem that applies to right triangles. It states that if two right triangles have two congruent legs, then the triangles are congruent. This means that all of their corresponding sides and angles are congruent.

In the diagram provided, we have two right triangles, DEF and KLM. We are given that DE = KL and DF = LM. Since these are the legs of the two triangles, we can use the LL Theorem to conclude that DEF = KLM.

Hypotenuse-Leg (HL): This criterion applies specifically to right-angled triangles. If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. Here, the right angles at D and K establish the triangles as right triangles, and the equal side lengths ED = KL and DF = KM complete the congruence conditions.

We cannot use the HL Theorem because the diagram does not explicitly show that the two triangles are right triangles.

Therefore, from the given options the correct one is B , C and E.

For more such information on: congruent

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Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 2 and (a, b) = (10, - 9), hence

y - (- 9) = - 2(x - 10), that is

y + 9 = - 2(x - 10) ← in point- slope form

Answer: [tex]y+9=-2(x-10)[/tex]

Step-by-step explanation:

We know that the equation of a line in point slope form passing through point (a,b) and having slope 'm' is given by :-

[tex](y-b)=m(x-a)[/tex]

Given : Point : (10,-9)

Slope :  m=-2

Then , the equation of a line in point slope form passing through point (10,-9) and having slope '-2' is given by :-

[tex](y-(-9))=-2(x-10)\\\\\Rightarrow\ y+9=-2(x-10)[/tex]

x-3y= 1

The equation needs to be rewritten in proper Slope intercept form ( y = mx+b) where m is the slope and b is the y-intercept.

x-3y = 1

Subtract x from each side:

-3y = 1-x

Divide both sides by -3:

y = 1/-3 - x/-3

Simplify:

y = 1/3x - 1/3

The slope is 1/3

Answer:

x is equal to 20, or the answer A

Step-by-step explanation:

They are opposite angles so they are equal to each other. When you set up the equation (x+40)=3x, you get the answer to be 20. hope this helped!

For this case we have to define by opposite angles the vertex that:

[tex]x + 40 = 3x[/tex]

Subtracting 3x on both sides of the equation:

[tex]x-3x + 40 = 0\\-2x + 40 = 0[/tex]

Subtracting 40 from both sides of the equation:

[tex]-2x = -40[/tex]

Dividing between -2 on both sides of the equation:

[tex]x = \frac {-40} {- 2}\\x = 20[/tex]

So, we have that [tex]x = 20[/tex]

ANswer:

[tex]x = 20[/tex]

Answer:

the answers are A B AND D

Step-by-step explanation:

To find perpendicular lines you take the slope and change the sign and find the reciprocal. after doing that you set it up as a new equation that you will use to find b using the point.

in this case

y= - 2/5x +b

plug in the x and y values of the point (5, -4) to find b

b= -2

you put that together to get the equation

The equation of the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4) is y = -0.4x - 2.

The given equation is 5x - 2y = -6. First step is to convert this to the slope-intercept form (y = mx + b) to find the slope. To do this, solve for y in terms of x, which looks like y = 2.5x + 3. The perpendicular line would have a slope that is the negative reciprocal this slope (m = -1/2.5 or -0.4).

Next, apply the point-slope formula (y - y1 = m(x - x1)) where m is the slope and (x1, y1) is the point that the line passes through. In this case, (x1, y1) is (5, -4), and slope m is -0.4. Then, y - (-4) = -0.4(x - 5), results to y + 4 = -0.4x + 2, finally gives y = -0.4x - 2 as the equation of the line that is perpendicular to 5x - 2y = -6 and passes through the point (5, -4).

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Answer:

0.2

Step-by-step explanation:

[tex]\text{f(x) = }\dfrac{90}{9+\frac{50}{e^x}}[/tex]

[tex]\text{f(-2) = }\dfrac{90}{9+\frac{50}{e^{-2}}}[/tex]

[tex]\text{f(-2) =} \dfrac{ 90 }{9 + 50*e^2}[/tex]

Now we can work out the denominator separately.

9 + 50*e^2

9 + 50*7.389

9 + 369.45

378.45

Now use this number to get the final answer.

f(-2) = 90 / 378.45

f(-2) = 0.237   To the nearest tenth

f(-2) = 0.2

There was a lot of movement for that e^x factor make sure you study carefully how that moved around and why. It's a good question. Get what you can from it.

Answer:

Yes

Step-by-step explanation:

Think simple.

The picture has already provided us with the information that ∠EFT ≅ ∠LKM, and we also have:

∠EFT ≅ ∠GFH (opposite angles)

∠LKM ≅ ∠JKN (opposite angles as well)

Therefore ∠JKN ≅ ∠GFH

Answer:

10

Step-by-step explanation:

x=2

f(2)=5x3-2=15-2=13/2=6.5=f

g(2)=2+1=3/2=1.5=g

(6.5-1.5)(2)=(13-3)=10

Answer:

5x³ - x - 3

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 5x³ - 2 -(x + 1) = 5x³ - 2 - x - 1 = 5x³ - x - 3

Answer:

d) 1⃣

Step-by-step explanation:

Multiply -5 by -2 to get , then deduct 7 to get 3. So, you now know that 3 = 3a; 1 = a.

Answer:

slope = [tex]\frac{7}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (2, 7)

m = [tex]\frac{7-0}{2+3}[/tex] = [tex]\frac{7}{5}[/tex]

Hello!

Hint: ⇒ Slope formula: ⇒ [tex]\frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]Y_2=7\\ Y_1=0\\\\X_2=2\\X_1=-3[/tex]

[tex]\frac{7-0}{2-(-3)}=\frac{7}{5}[/tex]

[tex]\boxed{\frac{7}{5}}\checkmark[/tex]

[tex]\boxed{\frac{7}{5}}[/tex], which is our correct answer.

Hope this helps you!

Have a great day! :)

Check the picture below.

Answer:

L=9 ft

W=28 ft

Step-by-step explanation:

LW=252

L=10+2W

Plug 2nd into 1st

(10+2W)W=252

Distribute

10W+2W^2=252

Divide both sides by 2

5W + W^2=126

Reorder using commutative property

W^2+5W =126

Subtract 126 on both sides

W^2+5W-126=0

What are two numbers multiply to be -126 and add to be 5?

My scratch paper:

-126=-2(63)

-126=-2(7)(9)

-126=-14(9)

So 14(-9) is -126 and 14+(-9)=5 so these are our magic numbers

(W+14)(W-9)=0

W=-14 or W=9

So W=9 is what makes sense here sense length can't be negative

Now let's go back and find L...

L=10+2W=10+2(9)=10+18=28

The problem can be solved by setting up a quadratic equation based on the given information. By solving the equation, we find that the width is 7 feet, and the length is 24 feet.

In this problem, we are given that the area (A) of the rectangular wall is 252 square feet, and the length (L) of the wall is 10 feet longer than twice its width (W). We need to find both the length and width of the barn. The formula for the area of a rectangle is A = L × W.

From the problem, we know that L = 2W + 10. Substituting this into the formula gives us A = W × (2W + 10). Set this equal to 252 to get 252 = W × (2W + 10). Solving this quadratic equation, we find that the width of the barn is 7 feet. Substituting this value into L = 2W + 10, the length of the barn is 24 feet.

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[tex]9-(4^2-(3+20)=9-(16-23)=9-(-7)=16[/tex]

Answer:

A.

(x - 3)(x - 3)

Step-by-step explanation:

x^2 – 6x + 9

What 2 numbers multiply to 9 and add to -6

-3*-3 =9

-3+-3 = -6

(x-3) (x-3)

Answer:

C. $150 :)

Step-by-step explanation:

If Annabell works 4 hours and earns $100 that means for every hour she earns $25 so 25×4=100 so then multiply 25×6=15]

Answer:  C. $150.

Step-by-step explanation:

When two quantities x and y are directly proportional ,then the equation of direct proportion is given by :-

[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

Given : Annabelle's total pay varies directly with the number of hours she works. If she works 4 hours, she earns $100.

Let [tex]x_1=100\ ;\ y_1=4 \ :\ x_2=x,\ y_2=6[/tex], then we ahve

[tex]\dfrac{100}{4}=\dfrac{x}{6}\\\\\Rightarrow\ x=\dfrac{100\times6}{4}=150[/tex]

Hence, Annabelle earns $150 if she works 6 hours.

Answer:

[tex]\large\boxed{x=-\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]f(x)=9x^2+6x+1\\\\\text{The zeros are for}\ f(x)=0\\\\9x^2+6x+1=0\\\\9x^2+3x+3x+1=0\\\\3x(3x+1)+1(3x+1)=0\\\\(3x+1)(3x+1)=0\\\\(3x+1)^2=0\iff3x+1=0\qquad\text{subtract 1 from both sides}\\\\3x=-1\qquad\text{divide both sides by 3}\\\\x=-\dfrac{1}{3}[/tex]

For this case we have that by definition, a quadratic equation is of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Its roots are given by:

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

By definition, the discriminant is given by:

[tex]D = b ^ 2-4 (a) (c)[/tex]

According to the given equation we have to:

[tex]a = 5\\b = 3\\c = -5[/tex]

Substituting:

[tex]D = 3 ^ 2-4 (5) (- 5)\\D = 9 + 100\\D = 109[/tex]

Answer:

The discriminant is 109

Answer:

your answer is A// -37

Step-by-step explanation:

1 shirt=$6

5 shirts= 5 × $6

=$30

lunch= $7

So in total she spent:

$30 + $7= $37

And from what we are given above; the balance in her account is

5(-6) + (-7)

= -30 - 7= -37

Answer:

103

Step-by-step explanation:

Evaluate 4k2 + 3

To evaluate 4k² + 3, when k = 5, which means when you sees k, put 5 in replacement

4k² + 3 = 4(5)² + 3

4(5×5) + 3

4(25) + 3

open the bracket

4 × 25 = 100

∴ 100 + 3 = 103

Please mark me brainliest  

[tex]\text{Hey there!}[/tex]

[tex]\text{If k = 5 the replace the 'k' value with 5}[/tex]

[tex]\text{4(5)}^2+3[/tex]

[tex]\text{(5)}^2=5\times5=25[/tex]

[tex]\text{4 (25)+ 3 = ?}[/tex]

[tex]\text{4 (25) = 25 + 25 + 25 + 25 = 100}[/tex]

[tex]\text{100 + 3 = 103}[/tex]

[tex]\boxed{\boxed{\bf{Your\ answer: 103}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]