For the function f(x) = – 3x + 8, determine f(-5)

Answer:

y = -7,   y = -3

Step-by-step explanation:

(y - 3)² = 2y² + 4y + 30

expand:

y² - 6y + 9 = 2y² + 4y + 30

subtract 30 from both sides

y² - 6y + 9 - 30= 2y² + 4y + 30 - 30

simplify:

y² - 6y - 21 = 2y² + 4y

subtract 4y from both sides

y² - 6y - 21 -4y = 2y² + 4y - 4y

simplify:

y² - 10y - 21 = 2y²

subtract 2y² from both sides

y² - 10y - 21 - 2y² = 2y² - 2y²

simplify:

-y² - 10y - 21 = 0

solve y by quadratic equation

         - (-10) ± √ (-10² - 4(-1)(21)

y = --------------------------------------

               2(-1)

y = -7,   y = -3

Answer:

[tex]\Huge \boxed{y=-7 \ \ \mathrm{or} \ \ y=-3}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex](y-3)^2 =2y^2 +4y+30[/tex]

Expanding brackets.

[tex]y^2-6y+9=2y^2 +4y+30[/tex]

Subtracting (y² - 6y + 9) from both sides, then switching sides.

[tex]y^2 +10y+21=0[/tex]

Factoring left side.

[tex](y+3)(y+7)=0[/tex]

Setting factors equal to 0.

[tex]\Longrightarrow y+3= 0 \\\\\\ \Longrightarrow y=-3[/tex]

[tex]\Longrightarrow y+7=0 \\\\\\ \Longrightarrow y=-7[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

[tex](5x)^4=5x*5x*5x*5x=625x^4\\(-4xy)^2=-4xy*-4xy=16x^2y^2\\-4(xy)^2=-4*xy*xy=-4x^2y^2\\5x^4=5*x*x*x*x\\left~over -16x^2y^2[/tex]

Answer:

74 students would attend the assembly for third graders

Step-by-step explanation:

26 × 3 = 78

78 - 4 = 74

Answer:

34

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

18 × 2 - 4² ÷ 8

Step 2: Exponents

18 × 2 - 16 ÷ 8

Step 3: Multiply

36 - 16 ÷ 8

Step 4: Divide

36 - 2

Step 5: Subtract

34

Answer: B.) Quantitative data

Step-by-step explanation:

In the given statement, we do not have categories but the count of dogs as "four" in a group.

Hence, the given statement represents "Quantitative data" .

So, the correct option is B) .

Answer:

[tex]4 * p * 4 * p = 4^2p^2[/tex]

Step-by-step explanation:

Given

[tex]4 * p * 4 * p[/tex]

Required

Write as exponents

[tex]4 * p * 4 * p[/tex]

Rearrange to collect Like Terms

[tex]4 * 4 *p * p[/tex]

Group both items

[tex](4 * 4) *(p * p)[/tex]

Apply law of indices

[tex](4^{1+1})(p^{1+1})[/tex]

[tex](4^2)(p^2)[/tex]

Remove bracket

[tex]4^2p^2[/tex]

Hence:

[tex]4 * p * 4 * p = 4^2p^2[/tex]

Step-by-step explanation:

A repeating decimal is a recurring decimal. It has no end when divided.

9/3 is 3 so it is a terminating decimal.

Answer:

The single repeating digit is 3.

Step-by-step explanation:

Answer:

520

Step-by-step explanation:

To know what value should be placed in the box, let us calculate the carry out the operation.

Please see attached photo for explanation.

From the calculations made as shown in the attached photo, the value that should be placed in the box is 520

Answer: it flew 1883 miles and average speed was about 50 miles per hour

Step-by-step explanation: to get 1883 you just add up 1282+601

Answer:

-8

Step-by-step explanation:

6-(-8)= 14

Answer:

x = -8

Step-by-step explanation:

I hope this helps!

Answer:

3

Step-by-step explanation:

a^2+b^2=9

(a+b)^2=9

finding the square root on both sides of the equation

a+b=3

Answer:

x = 29

Step by step explantion:

Answer:

x = 29

Step-by-step explanation:

Distribute/ Multiply:

8x - 4 - 3 = 9x - 36

Rearrange the equation:

8x - 9x = -36 + 4 + 3

Combine like terms:

-1x = -29

Divide:

x = 29

Answer:

2.5 hours

Step-by-step explanation:

(380/50) x 20

7.6 x 20

152

The final answer wold be 152 minutes or 2.5 hours

Answer:

[tex]\boxed{\bold{\huge{\boxed{x = 4.0}}}}[/tex]

Step-by-step explanation:

[tex]\sf Cos\ \theta = \frac{Adjacent}{Hypotenuse}[/tex]

Where [tex]\theta[/tex] = 34° , Adjacent = x and Hypotenuse = 4.8

[tex]\sf Cos \ 34 = \frac{x}{4.8} \\0.829 = \frac{x}{4.8} \\x = 0.829*4.8\\x = 4.0[/tex]

Answer:

[tex]\Huge \boxed{x \approx 4}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trig functions to solve for the problem.

[tex]\sf \displaystyle cos (\theta) = \frac{adjacent}{hypotenuse }[/tex]

[tex]\sf \displaystyle cos (34) = \frac{x}{4.8 }[/tex]

Multiplying both sides by 4.8.

[tex]\sf \displaystyle 4.8 \cdot cos (34) = \frac{x}{4.8 } \cdot 4.8[/tex]

[tex]\sf x = 3.97938034[/tex]

The value of x is approximately 4.

[tex]\rule[225]{225}{2}[/tex]

Answer:

  the number of faces of a cube

Step-by-step explanation:

For an edge length of s, the area of one face of a cube is s^2. The area of all six faces of the cube, the total surface area, is 6s^2. The number 6 represents the number of congruent faces of a cube.

Answer:  the number of faces on the box

Step-by-step explanation:

Answer: -3/2

Step-by-step explanation:

There are two methods to find the slope

METHOD 1. Rise/Run

Rise: the y-axis value

Run: the x-axis value

In the graph, rise/run=3/2

The line is going down, so it should be negative

-3/2

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

g(1)=7 1/5

Step-by-step explanation:

vertex (-5,0) , y intercept(0,5)

the quadratic equation is in the form of a parabola: y=ax²+bx+c

y=a(x-h)²+k    find a and b and c

5=a(0-(-5))²+0

5=a(5)²+0

5=25a  ⇒ a=5/25 ⇒ a=1/5

-b/2a=h

-b=2ah ⇒=-b=2(1/5)(-5) ⇒ -b=-2⇒ b=2

y=c=5 ( when x=0, y intercept)

y=1/5x² + 2x + 5

g(1)=1/5(1)²+2(1)+5

g(1)=1/5+2+5

g(1)=7 1/5

A quadratic function has a degree of 2, and it is represented as: [tex]y = ax^2 + bx + c[/tex]. The value of g(1) is -7.2

Given that:

[tex](h,k) = (-5,0)[/tex] --- the vertex

[tex](x,y) = (0,-5)[/tex] --- the y-intercept

The quadratic function in vertex form is:

[tex]y = a(x - h)^2 + k[/tex]

Where:

[tex](h,k) = (-5,0)[/tex] --- the vertex

So, we have:

[tex]y = a(x - -5)^2 + 0[/tex]

[tex]y = a(x +5)^2[/tex]

Substitute [tex](x,y) = (0,-5)[/tex] to calculate the value of a

[tex]-5 = a(0 +5)^2[/tex]

[tex]-5 = a(5)^2[/tex]

[tex]-5 = a \times 25[/tex]

Divide both sides by 25

[tex]a = -\frac 15[/tex]

So, the quadratic equation is:

[tex]y = a(x +5)^2[/tex]

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

Rewrite as a function

[tex]g(x) = -\frac 15(x +5)^2\\[/tex]

To calculate g(1), we simply substitute 1 for x

[tex]g(1) = -\frac 15(1 +5)^2[/tex]

[tex]g(1) = -\frac 15(6)^2[/tex]

[tex]g(1) = -\frac 15 \times 36[/tex]

[tex]g(1) = -7.2[/tex]

Hence:

The value of g(1) is -7.2

Read more about quadratic functions at:

https://brainly.com/question/4119784

Answer:

y intercept is 10 and slope is 2

Step-by-step explanation:

Answer:

= 3xy + ( 5x + x) + 3y + ( 4 +2 )

= 3xy + 6x + 3y + 6

Answer:

3,000. You take 15,000 and multiply by .4 to get how much she spent on rent (6,000). They you subtract the rent money from her total pay to get her money that she spent on living expenses, clothes and entertainment in total (9,000). Since she spent her money in six parts (3+2+1), you divide 9,000 by 6 to get 1,500 to get each part. Since for entertainment she has two parts you multiply 1,500 by 2 to get 3,000.

372₁₀ = 2442₅

372 : 5 = 74 r 2

74 : 5 = 14 r 4

14 : 5 = 2 r 4

2 : 5 = 0 r 2 ↑

write down the remainders in the reverse order

372₁₀ = 2442₅

Answer:

6 liters.

Step-by-step explanation:

So we have a glass, a jar, and a pitcher and together, they hold 54 liters.

We are told that the jar has the same volume as 3 glasses and the pitcher has the same volume as 5 glasses. In other words, let g denote glasses, j denote jars, and p denote pitchers:

[tex]g+j+p=54[/tex]

Since  jar is the same as 3 glasses, this means that j=3g. And since the pitcher is the same as 5 glasses, this means that p=5g. Substitute:

[tex]g+(3g)+(5g)=54[/tex]

Combine like terms:

[tex]9g=54[/tex]

Divide both sides by 9. The left cancels:

[tex](9g)/9=54/9\\g=6[/tex]

Therefore, the volume of the glass is 6 liters.

Answer:

[tex]\Large \boxed{\sf 6 \ liters}[/tex]

Step-by-step explanation:

Let the volume of the glass be x.

Let the volume of the jar be y.

Let the volume of the pitcher be z.

[tex]\sf y = 3x \\\\z = 5x[/tex]

[tex]\sf x + y + z = 54[/tex]

Substitution method.

[tex]\sf x+3x+5x=54[/tex]

Combining like terms.

[tex]\sf 9x = 54[/tex]

Dividing both sides by 9.

[tex]\sf x = 6[/tex]

The volume of the glass is 6 liters.

Answer:

x = 9

Step-by-step explanation:

Calculate the slope m using the slope formula then equate to 2

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 8) and (x₂, y₂ ) = (x, 2 )

m = [tex]\frac{2+8}{x-4}[/tex] = [tex]\frac{10}{x-4}[/tex] = 2 ( multiply both sides by x - 4 )

2(x - 4) = 10 ( divide both sides by 2 )

x - 4 = 5 ( add 4 to both sides )

x = 9

Step-by-step explanation:

2x*2+10x + 8

=4x+10x+8

=14x+8

inverse of 14x+8

x-8/14

=14

Answer:

y vertex=2(-5/2)^2+10(-5/2)+8=-9/2

vertex=(-5/2, -9/2)

Answer:

it is so unclear to say . If any more information is given, then only it can be answered. I don't think 196 is so special to be classified.

Answer:

Rectangle

Step-by-step explanation:

According to this grapher that I am using it shows a rectangle using your coordinates

Please give brainliest

Answer:

Rectangle

Step-by-step explanation:

Opposite sides (1, 1), (4,1) and (1, 3), (4,3) are horizontal and have length 3.

Opposite sides (1, 1), (1, 3) and (4, 1), (4,3) are vertical and have length 2.

There two pairs of opposite sides that are congruent, so this is a parallelogram. Since not all sides are congruent, this is not a square or a rhombus.

In addition, vertical sides and horizontal sides form right angles, so this is a parallelogram with right angles. It is a rectangle.

Answer:

the answer is the last choice

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

The absolute value function always gives a positive value, that is

| a | = | - a | = a , thus

| - 34 | = 34

Answer:

2, 6, 10, 14

or

14, 10, 6, 2.

Step-by-step explanation:

Let the four consecutive numbers in A.P. be a - 3d, a - d, a + d, a + 3d

According to the first condition:

a - 3d + a - d + a + d + a + 3d =32

4a = 32

a = 32/4

a = 8

According to the second condition:

[tex] \frac{(a - 3d)(a + 3d)}{(a - d)(a + d)} = \frac{7}{15} \\ \\ \frac{ {a}^{2} - (3d)^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {a}^{2} - 9d^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {8}^{2} - 9d^{2} }{ {8}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ 64 - 9d^{2} }{ 64 - {d}^{2} } = \frac{7}{15} \\ \\ 15(64 - 9 {d}^{2} ) = 7(64 - {d}^{2} ) \\ \\ 960 - 135 {d}^{2} = 448 - 7 {d}^{2} \\ \\ 960 - 448 = 135 {d}^{2} - 7 {d}^{2} \\ \\ 512 = 128 {d}^{2} \\ \\ {d}^{2} = \frac{512}{128} \\ \\ {d}^{2} = 4 \\ \\ d = \pm 2 \\ \\ when \: d = 2 \\ a - 3d = 8 - 3 \times 2 = 8 - 6 = 2 \\ a - d = 8 - 2 = 6 \\ a + d = 8 + 2 = 10 \\ a + 3d = 8 + 3 \times 2 = 8 + 6 = 14 \\\\ when \: d = - 2 \\ a - 3d = 8 - 3 \times ( -2 ) = 8 + 6 = 14 \\ a - d = 8 -( - 2 )= 8 + 2 = 10 \\ a + d = 8 + ( - 2 )= 8 - 2 = 6\\ a + 3d = 8 + 3 \times ( - 2 )= 8 - 6 = 2 \\[/tex]

Thus the four consecutive numbers of the A. P. are 2, 6, 10, 14 or 14, 10, 6, 2.