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3 years ago

Use the expression 5x + 23 to match the following vocabulary words.

Mathematics

1 answer:

andriy [413]3 years ago

6 0

From the expression 5x^23, we identify the terms as follows:

5 = coefficient

x = variable

23 = exponent

x = base

The coefficient is the constant in the term, the variable is any letter in a term, the exponent is the the number of times a number is being multiplied by itself in a power and the base is the number being multiplied in a power.

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In the figure below, segment CD is parallel to segment EF and point H bisects segment DE :

Grace [21]

Answer:

See explanation

Step-by-step explanation:

In the figure below, segment CD is parallel to segment EF, DE is a transversal, then angles DIH and HGI are congruent as alternate interior angles when two parallel lines are cut by a transversal.

Consider triangles DIH and EGH. In these triangles,

$\angle DIH\cong \angle EGH$ as alternate interior angles;
$\angle DHI\cong \angle GHE$ as vertical angles;
$DH\cong HE$ because point H bisects segment DE (given).

Thus,

$\triangle DIH\cong \triangle EGH$ by AAS postulate

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3 years ago

A 5-gallon jug of cleaning solution contains 6% bleach. How much pure water should be added to it to dilute to 4% bleach?

mihalych1998 [28]

Let's bear in mind that 5 gallons with a solution of 6% bleach, contains some water plus some bleach, how much bleach? well, is just 6% of 5 gallons or namely (6/100) * 5 gallons, or 0.30 gallons.

if we use "x" gallons of water, well pure water has no bleach, so is 0% bleach, and it has a (0/100) * x or 0x gallons of bleach.

the mixture will be say "y" gallons, and is 4% bleach, so (4/100) * y is 0.04y gallons in the mixture of bleach.

$\bf \begin{array}{lcccl}
&\stackrel{gallons}{quantity}&\stackrel{\textit{\% of bleach}}{amount}&\stackrel{\textit{gallons of bleach}}{amount}\\
&------&------&------\\
\textit{pure water}&x&0.00&0x\\
\textit{6\% solution}&5&0.06&0.3\\
-----&------&------&------\\
mixture&y&0.04&0.04y
\end{array}
\\\\\\
\begin{cases}
x+5=\boxed{y}\\
0x+0.3=0.04y\\
---------\\
0.3=0.04\left( \boxed{x+5} \right)
\end{cases}
\\\\\\
0.3=0.04x+0.2\implies 0.1=0.04x\implies \cfrac{0.1}{0.04}=x\implies 2.5=x$

3 0

3 years ago

Find the value of 1415×211 Although these numbers aren't quite as nice as the ones from the example, the procedure is the same,

BabaBlast [244]

Answer:

298565

Step-by-step explanation:

Given problem,

1415 × 211

∵ Direct multiplication is quite tough so we can split the number into smaller one for making the multiplication easier,

= (1400 + 15) × (210 + 1)

By using distributive property,

= 1400 × (210 + 1) + 15(210 + 1)

Again by distributive property,

= 1400 × 210 + 1400 + 15 × 210 + 15

Simplifying,

= 294000 + 1400 + 3150 + 15

= 298565

Hence, 1415 × 211 = 298565

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3 years ago

Which of the following statements is true? a. A 30 year fixed mortgage will always result in the lowest payment. b. You must hav

saw5 [17]

Answer:

The correct answer is option C.

Step-by-step explanation:

The lower your interest rate is, the lower your monthly payments are. This is true. The interest rate is directly proportional to monthly or yearly payments. If the rates are high, the installments are high and if the rate of interest is low, the installments are lower.

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2 years ago

Read 2 more answers

What is the answer to 8 3n/12=13?

Greeley [361]

Does this say 8 × 3n/12=13? I want to be sure so I don't give you the wrong answer.

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3 years ago