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gregori [183]
3 years ago
6

Factor the expression. 8g3 + 10g2 – 12g – 15

Mathematics
1 answer:
IrinaVladis [17]3 years ago
6 0
The correct answer is (2g2 - 3) • (4g + 5)
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The quotient of y and 27
valina [46]
Quotient means to Divide so we are gonna divide y and 7.
The Answer is Y/7.
5 0
3 years ago
In an arithmetic sequence, t4 + t5 + t6 = 300, and t15 +t16+ t17 = 201. Find t18.
stiks02 [169]
In an arithmetic sequence:
Tn=t₁+(n-1)d

t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d

t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d

Therefore:
3t₁+12d=300    (1)


t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d

t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d

Therefore:
3t₁+45d=201    (2)

With the equations (1) and (2) we make an system of equations:

3t₁+12d=300
3t₁+45d=201

we can solve this system of equations by reduction method.

  3t₁+12d=300
-(3t₁+45d=201)
-----------------------------
       -33d=99      ⇒d=99/-33=-3

3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112

Threfore:

Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n

Now, we calculate T₁₈:

T₁₈=115-3(18)=115-54=61

Answer: T₁₈=61




5 0
3 years ago
In right triangle KLM, KL =14 and angle L=30° and angle M=90°. Find KM. Leave your answer in the simplest radical form.
salantis [7]

Answer:

KM = 7 Units

Step-by-step explanation:

In the given structure ΔKLM

∠KLM = 30° and side KL = 14 and ∠KML = 90°

and we have to find the measurement of KM.

From right angle triangle KLM

Side Sin30° = KM/KL = KM/14

KM = 14×sin30° = 14×1/2 = 7

So the answer is KM = 7 Units

5 0
3 years ago
What is the slope<br> 19,-16<br> -7,-15
zubka84 [21]
\bf \begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%   (a,b)&#10;&({{ 19}}\quad ,&{{ -16}})\quad &#10;%   (c,d)&#10;&({{ -7}}\quad ,&{{ -15}})&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope = {{ m}}= \cfrac{rise}{run} \implies &#10;\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-15-(-16)}{-7-19}\implies \cfrac{-15+16}{-7-19}&#10;\\\\\\&#10;\cfrac{1}{-26}\implies -\cfrac{1}{26}
5 0
4 years ago
. A survey of 30 students is taken. 11 students say that mathematics is their favorite subject. Based on this survey, how many s
Sveta_85 [38]
Ok, so based on a survey - you know that out of 30 students, 11 said that their favourite subject is mathematics. :-)

This means that:

11/30 of these students think mathematics if their favourite subject.

Now, in order to answer your question, we are going to have to change the denominator of the fraction above to 1000. Whatever we do to the denominator of this fraction, we must do to the numerator of this fraction.

Example:

\frac { 11 }{ 30 } \times \frac { \frac { 1000 }{ 30 }  }{ \frac { 1000 }{ 30 }  } \\ \\ =\frac { \frac { 11000 }{ 30 }  }{ 1000 } \\ \\ =\frac { 366.\dot { 6 }  }{ 1000 }

This means that rounded to the nearest ten, theoretically speaking, 370 students out of 1000 would say that mathematics is their favourite subject.
7 0
4 years ago
Read 2 more answers
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