Select the correct answer.

If function f has zeros at -3 and 4, which graph could represent function f?

A.
the graph of a quadratic function y = (1/4)(x+3)(x-4)
B.
the graph of a quadratic function y = -(1/4)(x-3)(x+4)
C.
the graph of a quadratic function y = -(x+3)(x+4)
D.
the graph of a quadratic function y = (x-3)(x-4)

Answer:

S = {1, 2, 3, . . . 49, 50}, n(S) = 50 (i) Condition for event A : number is divisible by 6. A = {6, 12, 18, 24, 30, 36, 42, 48} n(A) = 8 (ii) Condition for event B : the number on the card is a complete square. B = {1, 4, 9, 16, 25, 36, 49} n(B)

Step-by-step explanation:

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Answer:

(8,-9)

Step-by-step explanation:

solve the equation for x

x=13/5-3/5y

7x+8y=-16

substitute the given value of x into the equation 7x+8y= -16

7(13/5-3/5y)+8y= -16

solve the equation for y

7(13/5-3/5)+8y= -16

y= -9

substitute the given value of y into the equation x=13/5-3/5y

x=13/5-3/5x(-9)

solve for x

x=8

the ordered pair is (8,-9)

Answer:

The solution to this system of equations is x = 8, and y = -9

Step-by-step explanation:

Firstly we need to use the first equation to represent "x" in terms of "y", so we do the following...

[tex]5x + 3y = 13\\5x = 13 - 3y\\x = \frac{13}{5} - \frac{3}{5}y[/tex]

Now we take the second equation and replace "x" with an equal value in terms of "y" which we know from the previous equation, and just solve for "y".

[tex]7x + 8y = -16\\7(\frac{13}{5} -\frac{3}{5} y) + 8y = -16\\\\18\frac{1}{5} - 4\frac{1}{5} y + 8y = -16\\\\3\frac{4}{5}y = -34\frac{1}{5} \\\\y = -34\frac{1}{5} / 3\frac{4}{5} \\y = -9[/tex]

After we found the value of "y" we can find the value of "x" by using any of the two equations, we just have put "-9" instead of "y". For example...

[tex]5x + 3y = 13\\5x + 3(-9) = 13\\5x - 27 = 13\\5x = 13 + 27\\5x = 40\\x = 40 / 5\\x = 8[/tex]

Now we know that the solution to this system of equations is x = 8, and y = -9

Answer:

(x+5)(x-2)

Step-by-step explanation:

x^2 +3x-10

What two numbers multiply to -10 and add to 3

5*-2 = -10

5+-2 = 3

(x+5)(x-2)

Answer:

∠1 = 90°

∠2 = 66°

∠3 = 24°

∠4 = 24°

Step-by-step explanation:

Usually the diagonals of a rhombus bisect each other at right angles.

Thus; ∠1 = 90°

Since they bisect at right angles, then;

∠R1S = 90°

Now, sum of angles in a triangle is 180°

Thus;

66° + 90° + ∠4 = 180°

156 + ∠4 = 180

∠4 = 180 - 156

∠4 = 24°

Now, also in rhombus, diagonals bisect opposite angles.

Thus; ∠4 = ∠3

Thus, ∠3 = 24°

Similarly, the diagonal from R to T bisects both angles into 2 equal parts.

Thus; ∠2 = 66°

Answer:

There are two types of similar triangle problems; these are problems that require you to prove whether a given set of triangles are similar and those that require you to calculate the missing angles and side lengths of similar triangles. Subtract both sides by 130°. Hence; By Angle-Angle (AA) rule, ΔPQR~ΔXYZ.

Step-by-step explanation:

Answer:

...........................I would be I don't know

Answer:

1/3

Step-by-step explanation:

3x -9y =4

To find the slope get the equation in slope intercept form ( y= mx+b where m is the slope and b is the y intercept)

Subtract 3x from each side

-9y = -3x+4

Divide each side by -9

-9y/-9 = -3x/-9 +4/-9

y = 1/3x -4/9

The slope is 1/3 and the y intercept is -4/9

Here,

3x -9y =4

To find the slope get the equation in slope intercept form ( y= mx+b where m is the slope and b is the y intercept)

Subtract 3x from each side

-9y = -3x+4

Divide each side by -9

-9y/-9 = -3x/-9 +4/-9

y = 1/3x -4/9

The slope is 1/3 and the y intercept is -4/9

[tex] \\ [/tex]

Answer:

43 units^2

Step-by-step explanation:

Area of a rectangle is

A = l*w

The bottom rectangle is 3 by 11 for an area of 33

The top rectangle is  2 by 5 for an area of 10

Add the areas together

33+10 = 43

Answer:

2) slope=2

y intervept=2

3) slope=1/2

y intercept=-6

4)slope=2

y intercept=4

Answer:

Step-by-step explanation:

Apply the Distributive Property of Multiplication.  Multiply each of the three terms inside parentheses by -(1/2):

(3/4)x - 3x - (1/2) - 3x, or

(3/4)x - 6x - 1/2

The first two terms can be combined, to obtain:

(-5 1/4)x - 1/2, or (-21/4)x - 1/2

Step-by-step explanation:

Solve the inequality:

[tex]3x - 11 > 7x + 9[/tex]

Rearrange unknown terms to the left side of the equation:

[tex]3x - 7x > 9 + 11[/tex]

Combine like terms:

[tex] - 4x > 9 + 11[/tex]

Calculate the sum or difference:

[tex] - 4x > 20[/tex]

Reduce the greatest common factor for both sides of the inequality:

[tex] - x > 5[/tex]

Divide both sides of the inequality by the coefficient of variable:

[tex]x < - 5[/tex]

2: plot:

[tex]x < - 5[/tex]

Graph on number line:

The solution inequality that represents the solution of the given expression inequality is → x < - 5.

Given is the inequality as follows -

3x – 11 > 7x + 9

The inequality is given as -

3x – 11 > 7x + 9

3x > 7x + 9 + 11

3x - 7x > 9 + 11

- 4x > 20

x < - 5

Therefore, the solution inequality that represents the solution of the given expression inequality is → x < - 5.

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Answer:

False

Step-by-step explanation:

Step-by-step explanation:

YOU ARE CORRECT

[tex] {7}^{(1 \times 9)} = {7}^{5 + 5} \\ {7}^{9} \: \: \: \: \: \: \: \: \: \: \: {7}^{10} [/tex]

the equation is false

Answer:

x - 3

Step-by-step explanation:

Jenna picked x.

Josh picked 2x - 3.

The difference is:

2x - 3 - x

which simplifies to

x - 3

Answer: x - 3

Answer:

24 cm

Step-by-step explanation:

Answer:

24cm

Step-by-step explanation:

V= 4/3πr³

or, r³= 3/4π ×V= 3/4π× 18432π= 13824

or, r= (13824)^1/3= 24cm

Answer:

-5

Step-by-step explanation:

4+2(x-4) = -7(x+7)

First, work out parenthesis: 4+ 2x-8 = -7x -49

Combine like terms: 2x-4= -7x-49

now isolate x by first adding 49 to each side: 2x+45= -7x

Then subtract 2x from each side: 45= -9x

Last, divide both sides by -9:

x= -5

Answer:

The answer is negative five or -5.

Step-by-step explanation:

First, you need to distribute your equation and at the end, the -4 should be just 2x - 8.

Second, subtract the numbers 4 and -8, which will equal to -4.

Third, rearrange your terms. Those terms would be -4 + 2x, so it should be 2x - 4.

Fourth, distribute again but with -7(x + 7) and you should get -7x - 49.

Fifth, add four to both sides of your equation. It should be like 2x - 4 + 4 = -7x - 49 + 4.

Sixth, add the numbers for the both sides. Therefore, you have 2x = -7x - 45.

Seventh, add 7x to both sides of the equation. You add it to 2x and -7x - 45 + 7x.

Eighth, simplify by combining like terms which you get 9x = -45.

Ninth, divide both of the sides of your equation by the same term. Your number to use when diving is 9.

Tenth, simplify but cancel terms that are both the numerator and denominator. Then you divide the numbers and get -5.

Answer:

-9

Step-by-step explanation:

Find the common ratio by dividing one of the numbers in the sequence by the previous number:

117/-13

= -9

So, the common ratio is -9.

Answer:

(C).

[tex]height = \sqrt{ {29}^{2} - {21}^{2} } \\ = \sqrt{400} \\ = 20 \: units[/tex]

Answer:

62.5

Step-by-step explanation:

Because there are 5 prime numbers so you have to divide 100 by 8 and then multiply by 5 so the answer is 62.5

Answer:

[tex]{ \tt{let \: one \: side \: be \: s}} \\ { \bf{perimeter = 4s}} \\ 56 = 4s \\ s = \frac{56}{4} \\ { \tt{s = 14 \: cm}} \\ \\ { \bf{area = {s}^{2} }} \\ = {14}^{2} \\ { \boxed{ \tt{area = 196 \: {cm}^{2} }}}[/tex]

Answer:

A =196 cm^2

Step-by-step explanation:

The perimeter of a square is

P = 4s where s is the side length

56 = 4s

Divide by 4

56/4 = 4s/4

14 =s

The area is given by

A =s^2

A =14^2

A =196 cm^2

Answer:

y = 9x + (-7) should be the answer

Step-by-step explanation:

answer is in the photo above

Answer:

[tex]\displaystyle p = \frac{16}{q + 1}[/tex].

Step-by-step explanation:

Factor out the coefficient of [tex]x^{2}[/tex]:

[tex]\displaystyle \frac{1}{q + 1}\, [(q + 1)\, x^2 - 8\, x + p] = 0[/tex].

[tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex].

Let [tex]m[/tex] denote the real root of this equation. By the Factor Theorem, this equation would have the factor [tex](x - m)[/tex] repeated for two times in total:

[tex](x - m)^{2} = 0[/tex].

Expand to obtain: [tex]x^2 - 2\, m\cdot x + m^{2} =0[/tex].

Compare this expression with [tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex]:

[tex]\displaystyle -\frac{8}{q + 1} = -2\, m[/tex] (for the coefficient of [tex]x[/tex].)

[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex] (for the constant.)

Rewrite the first equation to find an expression for [tex]m[/tex] in terms of [tex]q[/tex]:

[tex]\displaystyle m = \frac{4}{q + 1}[/tex].

Substitute this expression for [tex]m[/tex] into the second equation to find an expression for [tex]p[/tex] in terms of [tex]q[/tex]:

[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex].

[tex]\displaystyle \frac{p}{q + 1} = \frac{4^2}{(q+1)^{2}}[/tex].

[tex]\displaystyle p = \frac{16}{q + 1}[/tex].

Verify that this expression for [tex]p[/tex] satisfies the requirements:

[tex]\displaystyle (q + 1) \, x^{2} - 8\, x + \frac{16}{q + 1} = 0[/tex].

[tex]\displaystyle x^2 - \frac{8}{q + 1} + \frac{16}{(q+1)^2} = 0[/tex].

[tex]\displaystyle x = \frac{4}{q + 1}[/tex] is the (repeated) real root of this quadratic equation.

Answer:

Part A: x = y+45

Part B: 40 125-45 = 80, 80÷2 = 40

Part C: Yes, because 80+45 adds up to 125.

Hope this helps! :)

Answer:

y=80

Step-by-step explanation:

when solve y-intercept let x=0

y= -16(0)2+64(0)+80

y=0+0+80

y=80

(0;80)

Answer:

just subtract

Step-by-step explanation:

first go number by number and then subtract them and see the average rate of change and input that number

Answer:

The final speed after collision of the first ball that weighs 4 kg will be 8.5 m/s.

Step-by-step explanation:

M1 = 4

M2 = 2

V1 = 8

V2 = 6

V2f = 5

V1f = ?

Rep. Situation with Momentum formula:

M1*V1+M2*V2 = M1*V1f+M2*V2f

Rearrange:

((M1*V1+M2*V2)-M2*V2f) / M1 = V1f

Calculate:

((44) - 10) / 4 = V1f

V1f = 8.5

Answer:

It's actually 13 groups

4 students will be left over

Step-by-step explanation:

Add all the students together

134

Divide 10

13 and remainder 4

Answer:

13 ; 4

Step-by-step explanation:

Total students = 24 + 21 + 33 + 36 + 20 = 134

grups that will be made = 134 : 10 = 13,4 = 13

13 x 10 = 130

Students that will be left overs = 134 - 130 = 4

Answer:

B.  2(x+2)(x+1)

Step-by-step explanation:

[tex]\sf\purple{B. \:2(x + 2)(x+1) }[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]2 {x}^{2} + 6x + 4[/tex]

Taking 2 as common factor, we have

[tex] = 2 \: ( {x}^{2} + 3x + 2) \\ =2 \: ( {x}^{2} + 2x + x + 2)[/tex]

Taking [tex]x[/tex] as common from first two terms and 1 from last two terms, we have

[tex] = 2 \:[x(x + 2) + 1(x + 2)][/tex]

Taking the factor [tex](x+2)[/tex] as common,

[tex] = 2(x + 2)(x + 1)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]