MATHEMATICS HIGH SCHOOL

Jack is now seven times as old as James. In 5 years, Jack will be five times as old as James. How old is James now?Answers: 70 55 10

Answers

Answer 1

Answer: the answer to this question 70, because jack would be 55

Answer 2

Answer:

Answer: 10

Step-by-step explanation:

James's age = x

Jack's age = y

y = 7x

y + 5 = 5(x + 5)

y = 7x

y + 5 = 5x + 25

7x - y = 0

5x - y = -20

7x - y = 0

-5x + y = 20

2x = 20

x = 10

James's age: x = 10

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A chef uses 12 cup of cheese for a small pizza. There are 6 grams of fat in 14 cup of cheese. Drag one expression next to each question. The correct expression for each row is a way to answer that question.
Write as a fraction and simplify. (use the symbol / for your answer)0.23333...I
Copy and complete the table for the sequence 3n-1 Term number Term 3n-1 1 2 3.
Which of the following is another way to express the equation 16 = -9 + z?

Knowing that 2i is one answer to the equation x^4 - 2x^3 + 6x^2 - 8x + m = 0, find the 'm' and the other possible answers.

Answers

ok so remember
if a+bi is a root, then a-bi is also a root

since 2i is a root, -2i is also a root
use synthetic division and the fact that when we divide by 2i and -2i, we have to get all real coeficients and end witha zero at the end
I will show the division in the attachment

we find m=8

we then find th resulting equation that is x^2-2x+2=0
quadratic formula
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$
x=1+i or 1-i

m=8 and the other roots are
x=-2i, 1+i, 1-i

Which answer is equal to ( sqrt 7)^3?
A.7 3/2
B.7 2/3
C.7 1/6
D.7 1/3

Answers

$(√(7))^(3)$
$√(7)√(7)√(7)$
$√(7 * 7 * 7)$
$√(49 * 7)$
$√(343)$
$√(49 * 7)$
$√(49)√(7)$
$7√(7)$
$(7)^{(3)/(2)}$

The answer is A.

Try D As your Answer.

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answers

1. The first theorem used is that vertical angles are congruent.
2. The next theorem used is that adjacent angles in a parallelogram are supplementary.
3. The definition of supplementary angles is then used for angle formed by intersecting lines.
4. The theorem on vertical angles is used again.
5. Finally, the definition of the transitivity property is used to prove that alternate exterior angles are congruent.

Using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Recall:

Alternate exterior angles are angles that lie outside the two lines that is cut across by a transversal but on opposite sides along the transversal.
Examples of alternate exterior angles are <2 and <7; <4 and <5 as shown in the figure attached below.

If we are given that $m \parallel n$ in the diagram attached below, the following are theorems and definitions we can use to prove that $\angle 4 \cong \angle 5$ (alternate exterior angles).

Statement 1: $\angle 4 \cong \angle 8$

Reason: Corresponding Angles Theorem

The corresponding angles theorem states that when two parallel lines (lines m and n) are intersected by a transversal line (line w), the two corresponding angles formed (e.g. <4 and <8) are congruent.

Statement 2: $\angle 8 \cong \angle 5$

Reason: Vertical Angles Theorem

The Vertical Angles Theorem states that the opposite vertical angles (e.g. <8 and <5) formed when two lines (lines n and w) intersect are congruent to each other.

Statement 3: $\angle 4 \cong \angle 5$

Reason: Transitive Property of Congruence

The Transitive Property of Congruence states that if a = b; and b = c; then a = c.

Therefore, using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Learn more here:

brainly.com/question/16182992

Graph the linear equation 3x=10

Answers

3x = 10
3x = 10
3 3
x = 3¹/₃

Find the complete factored form of the
polynomial:
-36a5-24b6

Answers

The factored form of the given polynomial (-36a⁵-24b⁶)is -3 × 12a⁵ + (-2 × 12b⁶).

What are polynomials?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
x² - 4x + 7 is an illustration of a polynomial with a single indeterminate x.
They are the cubic polynomial, the zero polynomial, the linear polynomial, and the quadratic polynomial.
The degree of polynomials should be a full number.
Polynomials are not expressions with negative exponents.

So, factor form of -36a⁵-24b⁶:

Now, factorize as follows:

-36a⁵-24b⁶
3 × 12a⁵ + 2 × 12b⁶
-3 × 12a⁵ + (-2 × 12b⁶) (Get common out)

Therefore, the factored form of the given polynomial is -3 × 12a⁵ + (-2 × 12b⁶).

Know more about polynomials here:

brainly.com/question/2833285

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A box contains 4 oranges, 9 apples, and 3 pears. Liliana selects a piece of fruit from the box at random.What is the probability that she selects an orange or a pear?

A.1 over 20

B.3 over 64

C.7 over 16

D.9 over 16

Answers

oranges+apples+pears = 4+9+3=16

oranges = 4/16
pears = 3/16
4/16 + 3/16 = 7/16

Answer:

7/16

Step-by-step explanation:

k12

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