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3 years ago

7th grade math help me plzzz

Mathematics

1 answer:

sp2606 [1]3 years ago

4 0

Answer:

4 + (-10)

Step-by-step explanation:

for the answer you are taking adding TEN negatives from a non negative number. So we subtract 4 - 10 this equals -6 which is the same as -10 - (-4)

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Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

3 years ago

Jessica works between 12h and 18h per week at her part-time job. She earns $9.25 per hour. The function p(h) = 9.25h models the

Tpy6a [65]

D. All real numbers between 111 and 166.5 inclusive.

3 0

3 years ago

Solve the system using substitution. y - 3x = 1 2y - x = 12 ([?], [])

anyanavicka [17]

Answer:

(2, 5)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

y - 3x = 1

2y - x = 12

Step 2: Rewrite Systems

y - 3x = 1

Add 3x on both sides: y = 3x + 1

Step 3: Redefine Systems

y = 3x + 1

2y - x = 12

Step 4: Solve for x

Substitution

Substitute in y: 2(3x + 1) - x = 12
Distribute 2: 6x + 2 - x = 12
Combine like terms: 5x + 2 = 12
Isolate x term: 5x = 10
Isolate x: x = 2

Step 5: Solve for y

Define equation: 2y - x = 12
Substitute in x: 2y - 2 = 12
Isolate y term: 2y = 10
Isolate y: y = 5

4 0

2 years ago

Given that 8 bolts and 6 nuts weigh 138grams and 3 bolts and 5 nuts weigh 71 grams. Find the weight of;(a)one bolt and one nut (

Viktor [21]

Answer:

(a) Weight of a bolt = 12 grms and weight of a nut is 7 gms. Weight of one bolt and one nut = 12 + 7 = 19 gms

(b) 69 gms

Step-by-step explanation:

This problem relates to solution of 2 unknowns using simultaneous equations.

Let B be the weight of a single bolt and N be the weight of a single nut

Since 8 bolts and 6 nuts weigh 138 grams we get one of the equations as

8B + 6N = 138 (1)

The second equation in the unknowns is

3B + 5N = 71 (2)

To solve, we eliminate one of the unknowns by making its coefficients the same and subtracting one from the other

Multiplying (1) by 5 ===> 40B + 30N = 690 (3)

Multiplying (2) by 6 ===> 18B + 30N = 426 (4)

(3) - (4) eliminates the N variables and yields

22B = 264 ==> B = 264/22 ==> B = 12

So the weight of a single bolt is 12 grams

We can find the weight of a single nut by substituting this value of B into any of the equations (1), (2), (3) or (4) and solving for N. Let's use equation (2)

3(12) + 5N = 71 ==> 36 + 5N = 71 ==> 5N = 71-36 = 35 ==> N= 7

So the weight of a single nut is 7 grams

Weight of one bolt and one nut is the sum of the above individual weights = 12 + 7 = 19 gms

To solve (b) and (c) we could set up two other equations and plug in values for B and N

(b) 4B + 3N = 4.12 + 3.7 = 69
However, an alternate way is to perceive that 4B + 3N is exactly half of 8B + 6N so the value of that must be 138/2 = 69

11B + 11N = 138 + 71 = 209 which is the equation for the total weight of 11 bolts and 11 nuts

5 0

1 year ago

nikita wrote the expression 72 + 26. Bettina wrote the expression 4(72+26). Which sentence is true about the value of their expr

katen-ka-za [31]

Nikita's value is 4 times less than Bettina's value. I believe this is the answer.

8 0

3 years ago