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3 years ago

What is the expanded form of 4(y+6) ?

Mathematics

1 answer:

emmainna [20.7K]3 years ago

8 0

Answer: 4y + 24

Step-by-step explanation: In this problem, the 4 distributes

through the parentheses, multiplying by each of the terms inside.

So we have 4(y) + 4(6) which simplifies to 4y + 24.

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The interior angles of a triangie have measures 100° (4y + 25) ° , and (3y + 20) What is the value of y?

Mama L [17]

Answer:

since the sum of all angles of a triangle is 180°

Step-by-step explanation:

so 100°+4y+25°+3y+20=180°

145°+7y=180°

7y=180°-145°

7y=35°

y=5°

4 0

2 years ago

Match the reasons with the statements. GIVEN: x2 + 6x + 2x + 12 = 0 TO PROVE: x = -6 or x = -2 1. x2 + 6x + 2x + 12 = 0 Subtract

mestny [16]

Given: $x^2 + 6x + 2x + 12 = 0.$

1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):

$x^2+(6x+2x)+12=0,\\\\x^2+8x+12=0.$

2. Distributive postulate:

$x^2+8x+12=(x+6)(x+2).$

The equation is

$(x+6)(x+2)=0.$

3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):

$x+6=0 \text{ or } x+2=0.$

4. Subtraction property of equality:

a) subtract 6 from the first equation:

$x+6=0\Rightarrow x+6-6=-6, \ x=-6.$

b) subtract 2 from the second equation:

$x+2=0\Rightarrow x+2-2=-2, \ x=-2.$

6 0

3 years ago

Read 2 more answers

A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven

a_sh-v [17]

Answer:

$(17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745$

$(17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255$

Step-by-step explanation:

For this case we have the following info given:

Treatment: 12 13 15 19 20 21 24

Control: 18 23 24 30 32 35 39

We can find the sample mean and deviations with the the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}$

And repaplacing we got:

$\bar X_T = 17.714$ the sample mean for treatment

$\bar X_C = 28.714$ the sample mean for treatment

$s_T= 4.461$ the sample deviation for treatment

$s_C= 7.387$ the sample deviation for control

$n_T= n_C= 7$ the sample size for each sample

The degrees of freedom are given by:

$df= 7+7-2= 12$

The confidence interval for the difference of means is given by:

$(\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}$

The confidence is 98% so then the significance is $\alpha=0.02$ and $\alpha/2 =0.01$ . Then the critical value would be:

$t_{\alpha/2}=2.681$

And replacing we got:

$(17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745$

$(17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255$

4 0

4 years ago

13) A cell phone plan cost $200 to start. Then there is a $50 charge each month. What is the total cost for x months? (Hint: Wri

slamgirl [31]

Answer:

50x + 200

Step-by-step explanation:

50 dollars each month (for x months) is 50x, and the initial cost is 200 (flat fee) which means that the expression is 50x+200

7 0

2 years ago

Read 2 more answers

Which expression is equivalent to (2^3)^-5

34kurt

$\text{Use:}\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\dfrac{1}{a^n}\\\\\left(2^3\right)^{-5}=2^{3\cdot(-5)}=2^{-15}=\dfrac{1}{2^{15}}$

6 0

4 years ago

Read 2 more answers