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2 years ago

Which statement proves that quadrilateral HIJK is a kite?

Mathematics

2 answers:

weeeeeb [17]2 years ago

6 0

Answer:

B.) IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK.

Step-by-step explanation:

kolezko [41]2 years ago

4 0

Answer: B

Step-by-step explanation:

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A sample of size 60 from one population of weights had a sample average of 10.4 lb. and a sample standard deviation of 2.7 lb. A

Olegator [25]

Answer:

z= 0.278

Step-by-step explanation:

Given data

n1= 60 ; n2 = 100

mean 1= x1`= 10.4; mean 2= x2`= 9.7

standard deviation 1= s1= 2.7 pounds ; standard deviation 2= s2 = 1.9 lb

We formulate our null and alternate hypothesis as

H0 = x`1- x`2 = 0 and H1 = x`1- x`2 ≠ 0 ( two sided)

We set level of significance α= 0.05

the test statistic to be used under H0 is

z = x1`- x2`/ √ s₁²/n₁ + s₂²/n₂

the critical region is z > ± 1.96

Computations

z= 10.4- 9.7/ √(2.7)²/60+( 1.9)²/ 100

z= 10.4- 9.7/ √ 7.29/60 + 3.61/100

z= 0.7/√ 0.1215+ 0.0361

z=0.7 /√0.1576

z= 0.7 (0.396988)

z= 0.2778= 0.278

Since the calculated value of z does not fall in the critical region so we accept the null hypothesis H0 = x`1- x`2 = 0 at 5 % significance level. In other words we conclude that the difference between mean scores is insignificant or merely due to chance.

3 0

2 years ago

Alvin and Bala has 26 stickers.Alvin had 8 more stickers thab Bala.How many stickers did Bala have?

Brilliant_brown [7]

Bala had 9 stickers

You could set this up as a equation. Because there was a total of 26 you would for sure put =26. Next you are told Alvin has 8 MORE than Bali, therefore you would be adding the unknown value of Bala by 8. This could be represented as x+8=26. Now that you have x added to 8 you need to add another x to the equation to fully represent the problem since Alvin has 8 more stickers than Bala does. The new equation would become 2x+8=26.

You must now isolate x by first subtraction 8 from both sides which will leave you with 2x=18. Then you divide on both sides by 2 and will leave you with x=9

3 0

2 years ago

A sequence has a common ratio of Three-halves and f(5) = 81. Which explicit formula represents the sequence? f(x) = 24(Three-hal

Ede4ka [16]

Answer:

$f(x)=16\, (\frac{3}{2} )^{x-1}$

Step-by-step explanation:

Since we are given the common ratio (3/2), all we need to find to define the geometric sequence, is its multiplicative factor ( $a$ ) that corresponds to the first term of the sequence - remember that all consecutive terms will be generated by multiplying this first value repeatedly by the common ratio (3/2) as shown below:

$f(1)=a\\f(2)=a\,*\,(\frac{3}{2} )\\f(3)=a\,*\,(\frac{3}{2} )^2\\f(4)=a\,*\,(\frac{3}{2} )^3\\f(5)=a\,*\,(\frac{3}{2} )^4$

Since we are given the information that $f(5)=81$ we can use this to find the value of the first term:

$f(5)=\,a\,*\,(\frac{3}{2} )^4\\81=\,a\,*(\frac{81}{16} )\\a\,*\,81=\,81\.*\,16\\a\,=\,16$

Notice as well that the first term doesn't contain the common ratio, the second term contains the common ration (3/2) to the power one, the third one contains the common ratio to the power two, the fourth one contains it to the power three, and so forth. So the exponent at which the common ratio appears is always one unit less than the order (x) of the term in question. This concept helps us finalize the expression for the sequence's formula:

$f(x)=16\,*\,(\frac{3}{2} )^{x-1}$

6 0

2 years ago

Read 2 more answers

N(17+x)=34x−r<br> I need to solve for x

Paraphin [41]

Answer:

The value of x is, $x= \frac{17N+r}{34-N}$

Explanation:

Given: $N(17+x)=34x-r$

Distributive Property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately.

If $a\cdot(b+c) =a\cdot b + a\cdot c$

Now, using distributive property on left hand side of the given expression as:

$N\cdot 17+N\cdot x = 34x-r$ or $17N+Nx = 34x-r$

Addition Property of equality state that we add the same number from both sides of an equation.

Add r to both sides of an equation:

$17N+Nx+r=34x-r+r$

Simplify:

$17N+Nx+r=34x$

Subtraction Property of equality state that we subtract the same number from both sides of an equation.

Subtract Nx from both sides of an equation;

$17N+Nx+r-Nx=34x-Nx$

Simplify:

$17N+r=34x-Nx$

$17N+r=x(34-N)$

Division Property of equality states that we divide the same number from both sides of an equation.

Divide by (34-N) to both sides of an equation;

$\frac{17N+r}{34-N}= \frac{x(34-N)}{34-N}$

On Simplify:

$x= \frac{17N+r}{34-N}$

4 0

2 years ago

Read 2 more answers

To test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindrical

denis23 [38]

Answer:

A)196J

B)-208J

C)3467J

Step-by-step explanation:

We are given that a 20 kg cylindrical mass is dropped onto the mat from a height of 1 m above the mat. During the impact, the cylinder’s vertical velocity reaches zero at the instant the mat has compressed to only 4 cm thick.

So, The Mat gets compressed by : 10cm - 4 cm = 6 cm=0.06 m

Using Conservations of energy

Potential energy at the top = Kinetic energy at the point before touching the surface

Kinetic energy = mgh= $20 \times 9.8 \times 1 = 196 J$

Work done by the mat do to stop the fall of the cylinder = $-mg(h+0.06)=-20 \times 9.8(1+0.06)=-208 J$

Work done= $\text{Average force} \times \text{ Compression of mat}$

$208=F \times 0.06$

F=3467J

8 0

2 years ago