What happens when you multiply a positive number by a positive number less than 1?

Answer:

SAS Postulate

Step-by-step explanation:

Answer:

option B  

Step-by-step explanation:

Given in the question are ∠x ≅ ∠y and ∠zwx ≅ ∠ ywz and wz is common in both.

These angles are adjacent angles of triangles.

We know theorem for congruence is Angle - Angle - Side

Therefore, for the congruence of these two triangles option B, AAS congruence theorem is the answer.

Final answer:

The dimensions of the rectangular plot of land, where the length is 10 yards more than its width and the area is 600 square yards, are 20 yards by 30 yards. We arrived at this by setting up a quadratic equation and solving for the width.

Explanation:

To find the dimensions of a rectangular plot of land where the length is 10 yards more than its width and the area is 600 square yards, we can set up an equation. Let w be the width of the plot. Then the length is w + 10 yards. The area of a rectangle is given by the formula length × width, which in our case is (w + 10) × w = 600.

Setting up the equation, we get:

w(w + 10) = 600

w^2 + 10w - 600 = 0

To solve the quadratic equation, we can factor it, use the quadratic formula, or complete the square. Factoring the equation, we find that:

(w - 20)(w + 30) = 0

Thus, the width w can be either 20 yards or -30 yards. Since a width cannot be negative, we take w = 20 yards. Then, the length is:

w + 10 = 20 + 10 = 30 yards

The dimensions of the rectangular plot of land are 20 yards by 30 yards.

To find f(a) for the given function, substitute a for x in the function and simplify the expression.

Given the function f(x) = 5x0 + 4x-3, we need to find f(a). To find f(a), we substitute a for x in the function. Plugging in a, we get f(a) = 5a0 + 4a-3. Since any number raised to the power of 0 is equal to 1, we have f(a) = 5(1) + 4a-3. Simplifying further, we get f(a) = 5 + 4/a3.

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The postulate that proves that △JHG and △EFG are congruent is;

Option B; ​ ASA Congruence Postulate ​

From the given image, we can see two triangles namely;

△JHG and △EFG

Now, we can see that;

FG = GH

That is given because we see that G has divided FH into 2 equal parts.

Also, we see the right angle sign at ∠F and ∠H of both triangles.

Thus, since they are both right angles, then we can say that;

∠EFG = ∠JHG

Also, at point G, we have two vertically opposite angles which are;

∠EGF and ∠JGH

Now, from vertically opposite angle theorem, vertically opposite angles are always equal;

Thus; ∠EGF = ∠JGH

So far, we have;

FG = GH

∠EFG = ∠JHG

∠EGF = ∠JGH

This is 2 corresponding equal angles and 1 corresponding equal side. The side is included between the two angles and as such the proof that  △JHG and △EFG are congruent is the ASA Congruence Postulate.

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A) 17000*(1+(0.05*3) = 19550

19550-1700 = $2,550 total interest

B)  $19,550 total amount

C) multiply 5 by 3  = 15 than multiply by 17 = 17 * 15 = 255 , then make it a thousands amount by adding a zero at the end

Answer:

A)

p = 17000

r = 5% or 0.05

t = 3

Simple interest formula = p x r x t

Interest paid in 3 years = [tex]17000\times0.05\times3=2550[/tex] dollars

B)

Total amount to be paid = [tex]17000+2550=19550[/tex] dollars

C)

You can first multiply the years and rate that is 5 and 3 to make 15. Then you can multiply by 17. Then put proper decimals as per the values.

465 / 3 = 155

so -153 + -155 + -157 = -465

Answer:

introducing customer retention strategies

Step-by-step explanation:

Answer:

Hence, the length of board is:

6.5 feet

Step-by-step explanation:

Merry and pippin were working on a project in carpentry class.

They needed to cut 4 lengths of 1 5/8 feet from a board.

That means each of the  piece  is of length 1 5/8 feet which could be written in fraction as:

[tex]1\frac{5}{8}=\dfrac{13}{8} feet[/tex]

Hence, the otal length of the board is addition of length of each board.

i.e.

[tex]\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}=4\times \dfrac{13}{8}=\dfrac{13}{2}feet=6.5feet[/tex]

Hence, the length of board is:

6.5 feet

Answer: [tex]\dfrac{3}{10}[/tex]

Step-by-step explanation:

Given : Each of ten tickets is marked with a different number from 1 to 10 and put in a box.

i.e. The total number of outcomes : 10

Favorable outcomes : 2, 8, or 4

i.e. Number of favorable outcomes = 3

Now, the probability that you will draw 2, 8, or 4 is given by :-

[tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}\dfrac{3}{10}[/tex]

-8,-6,-4

-10,-6,0

these are the possible test points for your three intervals

The given inequality is, x² + 12 x+35≥0

→ x²+7 x +5 x+5×7≥0

→ x (x+7) +5(x+7)≥0

→ (x+5)(x+7)≥0

→ x+5=0  ∧ x+7=0 gives x= -7 ∧ x= -5

Now drawing the number line and marking point ,-5 and -7 on it.

Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).

The solution set of inequality (x+5)(x+7)≥0 is  (-∞ , -7] and [-5,∞).

The set of possible test points for

⇒ (-∞ , -7] → -8,  -10

⇒ [-7,-5] → -6

⇒ [-5,∞) → -4, 0

Option (1) -8,-6,-4 and Option (2) -10,-6,0 satisfies the given condition.

Notice that the above sequence is arithmetic because the common difference: d is constant.

d = second term - first term.

= 15 - 9

= 6

The general term of an arithmetic sequence is,

a_{n} =a_{1} +(n-1)d

Where , nth term = [tex] a_{n} [/tex]

[tex] a_{1} [/tex] = First term

and d = common difference.

The given sequence is: 9, 15, 21, ...

Here a_{1} = 9,

d = 6

We need to find the 31st term. So, n = 31.

Next step is to plug in these values in the above formula. Therefore,

[tex] a_{31} =9 +(31-1)*6 [/tex]

= 9 + 30* 6

= 9 + 180

= 189

So, 31st term of this sequence is 189.

Hope this helps you.

Answer:

189

Step-by-step explanation: