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zloy xaker [14]

2 years ago

9

The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers.

1 answer:

umka21 [38]2 years ago

3 0

Answer:

The two numbers are <u>15</u> and <u>6</u>.

Step-by-step explanation:

Given:

The difference between two numbers is 9.

The first number plus twice the other number is 27.

Now, to find the two numbers.

Let the first number be $x.$

And the other number be $y.$

So, the difference between two numbers is 9.

$x-y=9$

$x=9+y$ ............(1)

As, given the first number plus twice the other number is 27.

According to question:

$x+2y=27$

Substituting the value of $x$ from equation (1):

$(9+y)+2y=27\\9+y+2y=27\\9+3y=27$

<em>Subtracting both sides by 9 we get:</em>

$3y=18$

<em>Dividing both sides by 3 we get:</em>

$y=6.$

The other number = 6.

Now, substituting the value of $y$ in equation (1):

$x=9+y\\x=9+6\\x=15.$

The first number = 15.

Therefore, the two numbers are 15 and 6.

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2 years ago

Evaluate \dfrac14c+3d

Crank

Answer: $\frac{45}{2}$

Step-by-step explanation:

<h3> The exercise is: " Evaluate $\frac{1}{4}c + 3d$ when $c = 6$ and $d = 7$ </h3>

Given the following expression:

$\frac{1}{4}c + 3d$

You can follow these steps in order to evaluate it:

1. Substitute $c = 6$ and $d = 7$ into the expression provided in the exercise:

$\frac{1}{4}(6) + 3(7)$

2. Solve the multiplications. Remember that:

$\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}$

Then:

$=\frac{6}{4} +21$

3. Reduce the fraction. Notice that the numerator 6 and the denomiantor 4 can be both divided by 2. Then:

$=\frac{3}{2} +21$

4. Solve the addition:

$=\frac{3}{2} +\frac{21}{1}$

Since the number 21 has a denominator 1, the Least Common Denominator is:

$LCD=2$

Then, the sum is:

$=\frac{3+42}{2}=\frac{45}{2}$

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2 years ago

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disa [49]

Answer:

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2 years ago

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In ΔGHI, the measure of ∠I=90°, IG = 6.8 feet, and HI = 2.6 feet. Find the measure of ∠G to the nearest degree.

Luda [366]

Answer:

$\angle G=20.8\approx 21^{\circ}$

Step-by-step explanation:

Given: In ΔGHI, $\angle I$ =90°, IG = 6.8 feet, and HI = 2.6 feet

To find: $\angle G$

Solution:

Trigonometry defines relationship between the sides and angles of the triangle.

For any angle $\theta$ ,

$tan\theta$ = side opposite to $\theta$ /side adjacent to $\theta$

In ΔGHI,

$tan G=\frac{HI}{GI}$

Put $HI=2.6 \,\,feet\,,\,GI=6.8\,\,feet$

So,

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2 years ago

A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-

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Answer:

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Step-by-step explanation:

The confidence interval formula for mean difference for a paired data is as follows:

$CI=\bar x_{d}\pm t_{\alpha/2, (n-1)}\times \frac{s_{d}}{\sqrt{n}}$

Here,

$\bar x_{d}$ = sample mean of the difference,

$s_{d}$ = sample standard deviation of the difference,

<em>n </em>= sample size (both samples are of same size).

$t_{\alpha/2, (n-1)}$ = critical value of <em>t</em>

(<em>n</em> - 1) = degrees of freedom

The information provided is:

<em>n</em> = 5

Confidence level = 95%

The critical value of <em>t</em> is:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (5-1)}$

$=t_{0.025, 4}$

$=2.776$

*Use a <em>t</em>-table for the critical value of <em>t</em>.

Thus, the <em>t</em>-value used for the 95% confidence interval of paired data is 2.776.

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2 years ago