Simplify (5√2-1)^2

10 √2+51
-10 √2+51
41 √2

Answer:

The distance from B to B’ is [tex]5\ units[/tex]

Step-by-step explanation:

we know that

In a translation the shape and dimensions of the figure are not going to change.

therefore

AA'=BB'=CC'=DD'

Find the distance AA'

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

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

[tex]A(1,5)\\A'(-2.1)[/tex]  

substitute the values

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

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

[tex]AA'=\sqrt{25}[/tex]

[tex]AA'=5\ units[/tex]

therefore

[tex]BB'=5\ units[/tex]

Answer:

(3 x - 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + x - 6

Factor the quadratic 12 x^2 + x - 6.

The coefficient of x^2 is 12 and the constant term is -6.

The product of 12 and -6 is -72. The factors of -72 which sum to 1 are -8 and 9.

So 12 x^2 + x - 6 = 12 x^2 + 9 x - 8 x - 6 = 3 (3 x - 2) + 4 x (3 x - 2):

3 (3 x - 2) + 4 x (3 x - 2)

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2):

Answer:  (3 x - 2) (4 x + 3)

The answer is (3 x - 2) (4 x + 3).

Polynomial exists an algebraic expression with terms divided utilizing the operators "+" and "-" in which the exponents of variables exist always nonnegative integers.

Factor the following:

[tex]$$12x^{2}+x-6$$[/tex]

Factor the quadratic

[tex]$12x^{2} +x-6$[/tex]

The coefficient  [tex]x^{2}[/tex] is 12 and the constant term is -6.

The product of 12 and -6 is -72.

The factors of -72 which sum to 1 exist at -8 and 9.

So

[tex]$12 x^{2} +x-6=12 x^{2} +9 x-8 x-6[/tex]

[tex]=3(3 x-2)+4 x(3 x-2)$[/tex]

[tex]$3(3 x-2)+4 x(3 x-2)$[/tex]

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2)

Hence, The answer is (3 x - 2) (4 x + 3).

To learn more about Polynomials refer to:

https://brainly.com/question/13769924

#SPJ2

Answer:

B and E

Step-by-step explanation:

By looking at the discriminant, which is [tex]b^2-4ac[/tex], you get that [tex]5^2-4*1*7=25-28=-3[/tex]. Therefore, the only two answers with a -3 inside the square root are B and E.

Answer:

B & E

Step-by-step explanation:

see attached

Answer:

a = sqrt(33)

Step-by-step explanation:

a^2 + 4^2 = 7^2

a^2 + 16 = 49

a^2 = 33

a = sqrt(33)

Answer:

Step-by-step explanation:

the nth term of the geometric sequence  is :  An =A1 × r^(n-1)

A1 = -10

r= -40/20=20/-10=-2

n =11

A11 = -10× (-2)^(11-1)

A11 = -10× (-2)^(10)

A11 = - 10240

Answer:

-10,240.

Step-by-step explanation:

This is a geometric sequence with common ratio 20/-10 = -40/20 = -2.

The nth term = a1r^(n-1)   where a1 = the first term and r = the common ratio, so the 11th term = -10 * (-2)^ (11-1)

= -10 * 1024

= -10,240.

Answer:

i think the answer is undefined

Step-by-step explanation:

Answer: 1. inconsistent, 2. infinite, 3. (4, -1), 4. exactly two solutions.

Step-by-step explanation: HOPE THIS HELPS. ;))))

Answer:

subtraction property of equality

Step-by-step explanation:

The equation in the question is incomplete, the complete equation is:

5 + x = 2

To solve this equation we have to use the subtraction property of equality, that is, if you subtract some number at both sides of the equal sign, the equation doesn't change. So:

5 + x - 5 = 2 - 5 (You must select a number which isolate x)

x = -3

And the answer is gotten.

d

ur welcome its right

You are on the right tracks.

Since angle ABC is a right angle, that means lines AB and BC are perpendicular.

Therefore the gradient of BC = the negative reciprocal of the gradient of AB. We can use this to form an equation to find what K is.

You have already worked out the gradient of AB ( 1/2)  (note it's easier to leave it as a fraction)

Now lets get the gradient of BC:

[tex]\frac{5-k}{6-4}= \frac{5-k}{2}[/tex]

Remember: The gradient of BC = the negative reciprocal of the gradient of AB. So:

[tex]\frac{5-k}{2} =negative..reciprocal..of..\frac{1}{2}[/tex]

So:

[tex]\frac{5-k}{2}=-2[/tex]           (Now just solve for k)

[tex]5-k=-4[/tex]

[tex]-k=-9[/tex]                          (now just multiply both sides by -1)

[tex]k = 9[/tex]

That means the coordinates of C are: (4, 9)

We can now use this to work out the gradient of line AC, and thus the equation:

Gradient of AC:

[tex]\frac{1-9}{-2-4} =\frac{-8}{-6} = \frac{4}{3}[/tex]

Now to get the equation of the line, we use the equation:

y - y₁ = m( x - x₁)                            

Let's use the coordinates for A (-2, 1), and substitute them for y₁  and x₁  and lets substitute the gradient in for m:

y - y₁ = m( x - x₁)    

[tex]y - 1=\frac{4}{3}(x +2)[/tex]           (note: x - - 2 = x + 2)

Now lets multiply both sides by 3, to get rid of the fraction:

[tex]3y - 3 = 4(x+2)[/tex]             (now expand the brackets)

[tex]3y - 3 = 4x+8)[/tex]              

Finally, we just rearrange this to get the format: ay + bx = c

[tex]3y - 3 = 4x+8[/tex]              

[tex]3y = 4x+11[/tex]

[tex]3y - 4x = 11[/tex]          

And done!:

________________________________

Answer:

The equation of a line that passes through point A and C is:

[tex]3y - 4x = 11[/tex]        

Answer:

Out of the four, the only statement true about the parent and the transformed function is:

"The domain of the transformed function and the parent function are all real numbers."

Step-by-step explanation:

Parent function:

f(x) = |x|

Applying transformations:

1. Stretched by a factor of 0.3:

f(x) = 3|x|

2. Translated down 4 units:

f(x) = 3|x| - 4

Transformed function:

f(x) = 3|x| - 4

We can see that:

Range of the parent function = All real numbers greater than or equal to 0.

Range of the transformed function = All real numbers greater than or equal to -4.

Domain of the parent and the transformed function is same and equal to all real numbers.

Hence, the first three statements are wrong and the fourth one is true.

Answer:

The domain of the transformed function and the parent function are both all real numbers.

Step-by-step explanation:

Stretching a function by any factor doesn't change either its domain nor its range.

Translating up or down a function changes its range. In this case, the lowest value the parent function can take is 0 when x=0; after translation, for x = 0 then f(x) = -4. Therefore,

f(x) = |x|  

domain = all real numbers

range = [0, infinity)

f(x) = 0.3*|x| - 4

domain = all real numbers

range = [-4, infinity)

ANSWER

The radius is 4

EXPLANATION

The given equation is:

[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]

We complete the square to get the expression in standard form:

[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]

[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]

We factor using perfect squares to get:

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]

This implies that,

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]

Comparing to

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

The radius is r=4

Answer:

Step-by-step explanation:

6,-5 ON APEXXXXX

Answer: (6, -5)

Step-by-step explanation:

The general equation of a circle is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is center and r is radius of the circle.

Given : The equation of a circle : [tex](x-6)^2+(y+5)^2=15^2[/tex]

[tex]\Rightarrow\ (x-6)^2+(y-(-5))^2=15^2[/tex]

Comparing to the general equation of circle , we get

[tex](h,k)=(6, -5)[/tex]

Hence, the coordinates of the center of the circle = (6, -5)

[tex]x^2-5\leq0\\x^2\leq5\\x\leq \sqrt5 \wedge x\geq-\sqrt5\\x\in\left\langle-\sqrt5,\sqrt5\right\rangle[/tex]

For this case we must indicate the solution of the following inequality:

[tex]x ^ 2-5 \leq0[/tex]

Adding 5 to both sides of the inequality:

[tex]x ^ 2\leq5[/tex]

We apply square root on both sides of the inequality to eliminate the exponent:

[tex]x \leq\pm \sqrt {5}[/tex]

So, we have two solutions:

[tex]x\leq \sqrt {5}[/tex]

Since it is an inequality, the sign for the negative portion is changed:

[tex]x\geq- \sqrt {5}[/tex]

Answer:

[tex]x\leq \sqrt {5}\\x\geq-\sqrt {5}[/tex]

Answer:

[tex]\large\boxed{\dfrac{50}{3}}[/tex]

Step-by-step explanation:

If the polygons are similar, then the corresponding sides are in proportion:

[tex]\dfrac{z}{10}=\dfrac{20}{12}[/tex]        cross multiply

[tex]12z=(10)(20)[/tex]

[tex]12z=200[/tex]         divide both sides by 12

[tex]z=\dfrac{200}{12}\\\\z=\dfrac{200:4}{12:4}\\\\z=\dfrac{50}{3}[/tex]

Answer:

25

Step-by-step explanation:

look B=C

so,

A+B+C=180 Sum of all <s of Tri

x+5+3x+3x=180

7x=175

x=175÷7

x=25

Answer: A or 25

Step-by-step explanation:

did the exam on edge 2020

[tex]19 + 6 = 25 \div 2 = 12.5[/tex]

Answer:

12.5

Step-by-step explanation:

19+6=25 , 25÷2= 12.5

Answer:

Slope is 1

Step-by-step explanation:

Rise over Run.  Delta y over Delta x.  -8-2/-5-5 = -10/-10 = 1

9 x 5 = 45 -> total $ on Friday

99 - 45 = 54 -> total $ on Saturday

54 ÷ 9 = 6 hours

Answer:

A, B.

Step-by-step explanation:

If Matt charges $9 an hour, and he worked for 5hrs on Friday night, then that means we have to do multiplication.

So, $9x5=$45.

And then it says he babysat again on Saturday, and in TOTAL, he earned $99.

So, if he already made $45, and he has a total of $99, then we need to work backwards to figure out how much he made on Saturday.

$99-$45=$54

So, he made $45 on Friday and $54 on Saturday.

Now, we continue to work backwards and divide how much he made on Saturday ($54), by how much he charges per hour.

$54/9=6

So, Matt worked a total of 6hrs on Saturday.

Answer:

The solution of the inequality is a < 0.2870

Step-by-step explanation:

* Lets talk about the exponential function

- the exponential function is f(x) = ab^x , where b is a constant and x

 is a variable

- To solve this equation use ㏒ or ㏑

- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)

* Lets solve the problem

∵ 13^4a < 19

- To solve this inequality insert ㏑ in both sides of inequality

∴ ㏑(13^4a) < ㏑(19)

∵ ㏑(a^n) = n ㏑(a)

∴ 4a ㏑(13) < ㏑(19)

- Divide both sides by ㏑(13)

∴ 4a < ㏑(19)/㏑(13)

- To find the value of a divide both sides by 4

∴ a < [㏑(19)/㏑(13)] ÷ 4

∴ a < 0.2870

* The solution of the inequality is a < 0.2870

Answer:

a < 0.2870

Step-by-step explanation:

We are given the following inequality which we are to solve, rounding it to four decimal places:

[tex] 1 3 ^ { 4 a } < 1 9 [/tex]

To solve this, we will apply the following exponent rule:

[tex] a = b ^ { l o g _ b ( a ) } [/tex]

[tex]19=13^{log_{13}(19)}[/tex]

Changing it back to an inequality:

[tex]13^{4a}<13^{log_{13}(19)}[/tex]

If [tex]a > 1[/tex] then [tex]a^{f(x)}<a^{g(x)}[/tex] is equivalent to [tex]f(x)}< g(x)[/tex].

Here, [tex]a=13[/tex], [tex]f(x)=4a[/tex] and [tex]g(x)= log_{13}(19)[/tex].

[tex]4a<log_{13}(19)[/tex]

[tex]a<\frac{log_{13}(19)}{4}[/tex]

a < 0.2870

Answer:

[tex]\large\boxed{f(x)=x+4}[/tex]

Step-by-step explanation:

[tex]y-8=(x-4)\\\\y-8=x-4\qquad\text{add 8 to both sides}\\\\y-8+8=x-4+8\\\\y=x+4\to f(x)=x+4[/tex]

Answer:

24x - 20

Step-by-step explanation:

4(6x-5)

= 4(6x) - 4(5).............. (Distributive property)

= 24x - 20 (Ans)

Hello There!

The answer would be (24x-20)

We use order of operations so first we would multiply 4 by 6 and get 24x

then, we would multiply 4 by -5 and get -20

Your answer would be 24x - 20

Answer: [tex]945\ pixels[/tex]

Step-by-step explanation:

We know  that the original photo was 800 pixels wide and the new photo will be 1,260 pixels wide. Therefore,  we can find the scale factor.

Divide the width of the new photo by the width of the original photo. Then the scale factor is:

[tex]scale\ factor=\frac{1,260\ pixels}{800\ pixels}\\\\scale\ factor=\frac{63}{40}[/tex]

The final step is to multiply the height of the original photo by the scale factor calculated.

Therefore the height of the new photo will be:

[tex]h_{new}=(600\ pixels)(\frac{63}{40})\\\\h_{new}=945\ pixels[/tex]

Answer:

Step-by-step explanation:

Givens

First, we need to find the scale factor by dividing

[tex]s=\frac{1260}{800}=1.575[/tex]

Then, we multiply the height by the scale factor

[tex]600 \times 1.575 = 945[/tex]

Therefore, the new height is 945 pixels.

Answer:

(x-8) (x+5)

Step-by-step explanation:

x^2-3x-40

What 2 numbers multiply to -40 and add to -3

-8 *5 = -40

-8+5 = -3

(x-8) (x+5)

Answer:

7/2

Step-by-step explanation:

Round 6 3/4 to 7

Round 1 1/2 to 2

7 divided by 2

=7/2

Answer:

They would be perpendicular because the lines intersect at a ninety degree angle. Hope this helps! Please mark brainliest!

Step-by-step explanation:

Follow below steps:

The term that describes lines that intersect at 90-degree angles is perpendicular. Lines that are perpendicular to each other form four angles at the point of intersection. Each of these angles is a right angle, which measures 90 degrees. This is a fundamental concept in geometry, which is a branch of mathematics dealing with properties and relations of points, lines, surfaces, solids, and higher dimensional analogues.

For example, in the context of a coordinate plane, the x-axis and y-axis are perpendicular to each other. Moreover, theorems in geometry further explain the properties of perpendicular lines, such as the fact that if a line segment is drawn joining the extremities of two equal lines which are perpendicular to a given line, the joining segment is bisected at right angles by a third perpendicular line.

Check the picture below.

let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.

[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]

Answer:

Δ TUW ≅ ΔVWU ⇒ by AAS case

Step-by-step explanation:

* Lets revise the cases of congruent for triangles

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ  

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

 and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

 leg of the 2nd right angle Δ

* Lets solve the problem

- There are two triangles TUW and VWU

- ∠T and ∠V are right angles

- LINE TW is parallel to line VU

∵ TW // VU and UW is a transversal

∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)

- Now we have in the two triangles two pairs of angle equal each

 other and one common side, so we can use the case AAS

- In Δ TUW and ΔVWU

∵ m∠T = m∠V ⇒ given (right angles)

∵ m∠TWU = m∠VUW ⇒ proved

∵ UW = WU ⇒ (common side in the 2 Δ)

∴ Δ TUW ≅ ΔVWU ⇒ by AAS case

Answer:

Step-by-step explanation:

Given ∠T and ∠V are right angles.

TW ║ UV

To prove ⇒ ΔTUW ≅ ΔVWU

Proof ⇒ In ΔTUW and ΔVUW,

∠T ≅ ∠ V ≅ 90° (given)

Side UW ≅ UW ( Common in both the triangles )

TW ║ UV

and UW is a transverse.

So ∠TWU ≅ ∠WUV [alternate interior angles]

Since Angle = Angle = side are equal

Therefore, ΔTUW ≅ ΔVWU

Answer:

15 ounces

Step-by-step explanation:

If there is 165 ounces in 11 boxes then divide the ounces by the boxes to get the amount of ounces in one box.

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\sqrt[3]{y}=4\qquad\text{cube of both sides}\\\\(\sqrt[3]{y})^3=4^3\\\\y=64\\\\\bold{METHOD\ 2:}\\\\\text{Use the de}\text{finition of cube root}:\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\sqrt[3]{y}=4\iff 4^3=y\to y=64[/tex]

Mapping A shows x--->y. A is the answer. Exactly one x value is matched to exactly one y value.