Please help me with this question

Answer:x>7

Step-by-step explanation:

Its saying a nuber greater than 7 and 3 plus 8 would be 11

The solution for the given equation will be x=7.8873 and x=0.112699.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Find the Solution for

9x²−72x+8=0

using the Quadratic Formula where

a = 9, b = -72, and c = 8

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{(-72)\pm\sqrt{(-72)^2-4(9)(8)}}{2(9)}[/tex]

x=   [tex]\dfrac{72\pm4896}{\sqrt{18}}[/tex]

The discriminant b2−4ac>0

so, there are two real roots. After solving for plus and then minus we will get two values as follows.

x=7.8873

x=0.112699

Therefore the solution for the given equation will be x=7.8873 and x=0.112699.

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i. Cube of any odd number is even. False

ii.  A perfect cube does not end with two zeros. True

iii.  If square of a number ends with 5, then its cube ends with 25. False

iv. There is no perfect cube which ends with 8. False

v. The cube of a two digit number may be a three digit number. False

vi.  The cube of a two digit number may have seven or more digits. False

vii. The cube of a single digit number may be a single digit number. True

i.  Cube of any odd number is even. This statement is false because the cube of odd numbers are also odd

ii.  A perfect cube does not end with two zeros. This statement is True because the cube of a two digit number cannot be a 3 digit number and therefore cannot end with two zeros.

iii.  If square of a number ends with 5, then its cube ends with 25. This statement is False

Using the illustration

35^2 = 35 x 35= 1225 , its square ends with 5

35^3= 35 x 35 x 35= 42875 which ends with 75

iv.  There is no perfect cube which ends with 8. This statement is False.

Using the illustration, the cube of 2 is given thus

2 * 2 * 2 = 8

The cube of 2 ends with 8

v. The cube of a two digit number may be a three digit number. This statement is False.

Using the illustration, 10 is a two digit number

10 * 10 * 10 = 1000

The cube of 10 which is a two digit number is not a three digit number and same applies to all two digit numbers

vi  The cube of a two digit number may have seven or more digits. This statement is False because the cube of a two digit number can only be a four digit number.

vii. The cube of a single digit number may be a single digit number. This statement is True because the cube of a single digit number can be a single, two or three digit number.

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Using it's concept, it is found that Brandon's net yardage for the game was of 26.

The total net yardage is the sum of all the yardage they gain, that is, the positive gains are added with a plus signal, while the negative gains are added with a negative signal.

Hence, his net yardage, considering that he gained 20 yards on his last 7 carries, is given by:

6 + 20 = 26.

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Answer:

n = 250

See solution and check blow.

Step-by-step explanation:

Solution:

-17 + n/5 = 33

Add 17 to both sides.

-17 + 17 + n/5 = 33 + 17

n/5 = 50

Multiply both sides by 5.

n/5 × 5 = 50 × 5

n = 250

Check:

-17 + n/5 = 33

Since we found out that n = 250, substitute 250 for n in the equation.

-17 + 250/5 = 33

Simplify the left side. Divide 250 by 5.

-17 + 50 = 33

Add on the left side.

33 = 33

Since 33 = 33 is a true statement, the solution n = 250 is correct.

Answer:

There are 240 students in the school

Step-by-step explanation:

Givens

55% of the total number of students in a school are girls.

Equation

55/100 * x = 132

Solution

Multiply both sides of the equation  by 100

55/100x * 100  = 132 * 100

55x = 13200                          Divide by 55

55x/55  = 13200/55

x = 240

Answer:

No. There should be 210 small triangles

Step-by-step explanation:

The number of small triangles in these figures forms a sequence

Fig         No Small Triangles
1             1
2            3  (1+2)
3            6  (1+2+3)

So the nth figure should have 1+2+3+.....+(n-1)+ n

1+2+3+.....+(n-1)+ n = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210

Answer:

240

Step-by-step explanation:

Using the straight line formula; y=mx+c, take two points, for example, (4, 80) and (5, 100)

m=change in y/change in x, so;

m=(100-80)/(5-4)= 20

Take point (4, 80)

80=20×4 + c

80-80=c=0

so y=20x

y=20×12=240

The line is drawn at point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.

It is defined as the line which will make exactly two halves with similar shape and size in geometry. For a two-dimensional shape, there is a line of symmetry, and for three-dimensional shapes, there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.

We have given a figure in the picture.

The figure is a quadrilateral(a kite)

As we know, lines of symmetry make exactly two halves with similar shapes and sizes.

IF we draw a line from Point A to Point C we will get two similar and figures in size and shape.

Thus, the line is drawn point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.

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Answer:

point C

Here is a step-by-step explanation of the statement:

1. Draw a point B and a point C on a piece of paper or a computer screen.

2. Draw a straight line that goes through both point B and point C.

3. Fold the paper along the line you just drew, so that the line is the fold line.

4. Notice that if you were to fold the paper exactly in half along the line, point B would match up with its reflection on the other side of the line, and point C would match up with its reflection on the other side of the line.

5. This means that the line you drew is a line of symmetry, because it divides the paper into two identical halves that can be folded together.

6. Therefore, the statement "A line drawn through point B and point C is a line of symmetry" is true.

Answer: Quadrant III

Step-by-step explanation:

The slope is negative and the y-intercept is positive.

This means that it is impossible for both x and y to be negative, and thus it does not pass through Quadrant III

£36

20+25=45          Take away 13 and it's 32.   32+4 (the shipping charge) is 36. So Ruth pays 36 pounds.

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Answer:  [tex]\textsf{Option A, (-2, 4)}[/tex]

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Given:  [tex]\textsf{f(x) = x + 6}[/tex]

Find:  [tex]\textsf{f(-2)}[/tex]

Solution:  We need to plug in the value -2 into every variable x that we have in the expression and simplify to get the solution.

Plug in the values

Simplify

Therefore, the ordered pair that would match would have a x-coordinate of -2 and a y-coordinate of 4 producing (-2, 4) which matches option A.

Answer:

Step-by-step explanation:

30 is an opposite angle (2 angles of 30°)

sum of all angles = 360°

360 - 90 -30 - 150 - 30 = 60°

check

60 + 30 + 150 + 30 + 90 = 360°

the answer is good

Answer:

b = 60

Step-by-step explanation:

A straight line is 180 degrees

30+90+b = 180

Combine like terms

120 +b = 180

b =180-120

b = 60

Answer:

Yes

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

4 + -x ==> 4 - x

Example

x = 3; 4 + (-3) = 4-3 =1

Answer:

A

Step-by-step explanation:

I assume that the whole expression a⁸a³ is under the square root.

then remember 2 things :

1. when multiplying the same base variable (or constant) the result is that single base variable (or constant) to the power of the sum of the exponents.

e.g. x³x² = x⁵ because

x×x×x × x×x = x×x×x×x×x = x⁵

2. a square root as exponent is 1/2.

a cubic root is 1/3 and so on.

therefore

sqrt(a⁸a³) = sqrt(a¹¹) = a^11/2

Answer:

x = 3

y = 2

Step-by-step explanation:

3x + 2y = 12

-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2

2 * 3x + 2y = 12

6x + 4y = 24

3 * -2x + 3y = 5

-6x + 9y = 15  now find the sum of both equation:

6x + 4y  -6x + 9y = 24 + 15 add like terms

13y = 39 divide both sides by 13

y = 3 now that we found the value of y we can use this to calculate the value of x

3x + 2y = 12 replace y with 3

3x + 2*2 = 12

3x + 4 = 12 subtract 4 from both sides

3x = 9 divide both sides by 3

x = 3

[tex] \frac{ - n}{5} + 7 = 2 \\ \\ \frac{ - n + 35}{5} = 2 \\ \\ - n + 35 = 10 \\ \\ - n = 10 - 35 \\ \\ - n = - 25[/tex]

cancel (-) sign both sides ,

[tex]n = 25.[/tex]

The vertex form of the give quadratic equation is f(x) = (x+1)² + 2

The standard vertex form of a quadratic equation is expressed as

y = a(x -h)² + k

where (h, k) is the vertex

Given the quadratic equation

f(x) = x^2 + 2x + 3

Complete the question

f(x) = (x^2+2x) + 3

f(x) = (x^2+2x+1)-1 + 3

f(x) = (x+1)² + 2

Hence the vertex form of the give quadratic equation is f(x) = (x+1)² + 2

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The values of k and r are given by 5 and 3 respectively.

Here in this problem it is given that,

General formula for the sequence is given by,

[tex]U_{n+1}=kU_n+r[/tex]

First term of the sequence, [tex]U_1=37[/tex]

Second term,

[tex]U_2=188[/tex]

[tex]U_{1+1}=188[/tex], rearranging

[tex]kU_1+r=188[/tex], applying general formula

[tex]37k+r=188[/tex]..........(1)

Third term,

[tex]U_3=943[/tex]

[tex]U_{2+1}=943[/tex], rearranging

[tex]kU_2+r=943[/tex], applying general formula

[tex]188k+r=943[/tex]..........(2)

Now (2) - (1) we get,

188k+r-37k-r = 943-188

151k = 755

k = 755/151 = 5

Hence the value of k is 5.

Substituting the value of k in (1) we get,

37*5+r = 188

185+r = 188

r = 188-185 = 3

Thus the value of r is 3.

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Answer:

[tex]12z^{2} -10z -12[/tex]

Step-by-step explanation:

Let the number be z

2 more than 3 times z ==> 3z + 2

6 less than 4 times z ==> 4z - 6

Product of the above two is
[tex](3z + 2) (4z - 6) \\= (3z)(4z) + (3z)(-6) + (4z)(2) + (2)(-6)\\= 12z^{2} -18z + 8z - 12\\= 12z^{2} -10z -12[/tex]

Answer:

The choice D.

[tex]f(x) = 3 {(0.2)}^{x} [/tex]

Answer:

D

Step-by-step explanation:

Order of elimination:

1. the graph is going down exponentially. This means that the base is less than 1.

A and C are eliminated.

2. When x is equal to 0, f(x) = 3.

Substitute x for 0, and you'll find out that the only one possible is D.

Answer:

9. 15b + 4

10. 4y + 6

11. 15r+72

12. 130n + 20

Step-by-step explanation:

9. Combine Like terms

10. Combine Like terms

11. Distribute the 8 into (r + 9) then combine like terms

12. Distribute 10 into (3n + 2 + 10n) then combine like terms

Answer:

[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]

Step-by-step explanation:

[tex]\textsf {Question 9}[/tex]

[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]

[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]

[tex]\mathsf {15b + 4}[/tex]

[tex]\textsf {Question 10}[/tex]

[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]

[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]

[tex]\mathsf {4y + 6}[/tex]

[tex]\textsf {Question 11}[/tex]

[tex]\mathsf {8(r + 9) + 7r}[/tex]

[tex]\mathsf {8r + 8(9) + 7r}[/tex]

[tex]\mathsf {8r + 7r + 72}[/tex]

[tex]\mathsf {15r + 72}[/tex]

[tex]\textsf {Question 12}[/tex]

[tex]\mathsf {10(3n + 2 + 10n)}[/tex]

[tex]\mathsf {10(13n + 2)}[/tex]

[tex]\mathsf {10(13n) + 10(2)}[/tex]

[tex]\mathsf {130n + 20}[/tex]

Answer:

.

Step-by-step explanation:

Step-by-step explanation:

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Answer:

Step-by-step explanation:

The quadratic expression having repeated root is 8x² - 32x + 32.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

We have to find the root of each quadratic expression.

x² - 18x - 81 = 0

Discriminant = [tex]\sqrt{(-18)^2-(4*-81)}[/tex] = [tex]\sqrt{648}[/tex]

x = (18 + √648) / 2 or x = (18 - √648) / 2

Distinct roots

x² - 2x + 3

Discriminant = [tex]\sqrt{(-2)^{2}-(4*3) }[/tex] = [tex]\sqrt{-8}[/tex]

x = (2 + [tex]\sqrt{-8}[/tex]) / 2 or x =  (2 - [tex]\sqrt{-8}[/tex]) / 2

Distinct roots

8x² - 32x + 32

Discriminant = [tex]\sqrt{(-4)^{2}-(4*4) }[/tex] = 0

x = (4 + 0)/ 2 or x = (4 - 0) / 2

x = 2 or x = 2

Repeated roots

Hence the quadratic expression having repeated roots is 8x² - 32x + 32.

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Answer:

A fraction equivalent to [tex]\frac{1}{2}[/tex] on the number line is [tex]\frac{3}{6}[/tex].

Drag the dot to [tex]\frac{3}{6}[/tex] on the number line.

Step-by-step explanation:

3 is half of 6. To check if this is correct multiply [tex]\frac{1}{2}[/tex] and 3.

[tex]\frac{1}{2}*3=\frac{3}{6}[/tex]

Hope this helps!

If not, I am sorry.

Answer:

y = 16.5 ft

Step-by-step explanation:

• in the right triangle BCD :

cos(∠BCD) = 8/14

________

• In the right triangle ABC :

cos(∠BCA) = 14/(8+y)

________

Since ∠BCD and ∠BCA are the same one

then

cos(∠BCD) = cos(∠BCA)

Therefore

[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]

[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]

[tex]\Longleftrightarrow 8y+64=196[/tex]

[tex]\Longleftrightarrow 8y=196-64[/tex]

[tex]\Longleftrightarrow 8y=132[/tex]

[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]

[tex]\Longleftrightarrow y=16.5[/tex]

Answer:

Step-by-step explanation:

Comment

x and 133 sit on the the same straight line with MO in common. Therefore they are supplementary which means that the add to 180o.

Equation

x + 133 = 180

Solution

Subtract 133 from both sides

x + 133 = 180                    

x + 133 - 133 = 180 - 133

x = 47 degrees.

Answer

x = 47