Which pair of triangles is congruent by asa?

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)

Nitella [24]

The equation of a hyperbola is:

(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1

So what we have to do is to look for the values of the variables:

For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9

c = 7 (distance from center to vertices; given from the foci)
c^2 = 49

By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2

b^2 = 49 – 9

b^2 = 40

Therefore the equation of the hyperbola is:

(x^2 / 9) – (y^2 / 40) = 1

5 0

3 years ago

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Su has 3 times as many dolls as Bertha. When Su gives Bertha 4 dolls, they now have the same amount. How many dolls did they EAC

Usimov [2.4K]

Answer: i believe its 8

Step-by-step explanation:

i say 8 because 3x4 is 12 and so if bertha orignally had 4 and was given 4 she would have 8 and if su had 12 and gave away four she would also have 8

5 0

3 years ago

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4. This is a

bixtya [17]

Answer:

Step-by-step explanation:

4). This is an exponential function.

5). Let the equation of this function is,

f(x) = a(b)ˣ

Since, two points (-1, 4) and (0, 6) are lying on the graph of the function,

For (-1, 4),

4 = a(b)⁻¹

4 = $\frac{a}{b}$ --------(1)

For (0, 6),

6 = a(b)⁰

a = 6

From equation (1),

4 = $\frac{6}{b}$

b = $\frac{6}{4}$ = 1.5

Therefore, equation of the function will be,

f(x) = 6(1.5)ˣ

6). Now the value of f(-4) will be,

f(-4) = 6(1.5)⁻⁴

= 1.185

3 0

3 years ago

I need help with this calculators allowed tysm for your time

bagirrra123 [75]

Answer- 7.65 cm
explanation- the perimeter is just all the the sides lengths added together. since we know a square has four equal sides, we know that each side has to be the same length. so you divide 30.6 by 4 to get 7.65 cm.

4 0

3 years ago

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assig

Keith_Richards [23]

Answer:

1. Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part 1

The hypothesis for this case are:

Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have $p$ groups and on each group from $j=1,\dots,p$ we have $n_j$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

We need to find the mean for each group first and the grand mean.

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

If we apply the before formula we can find the mean for each group

$\bar X_A = 27$ , $\bar X_B = 24$ , $\bar X_C = 30$ . And the grand mean $\bar X = 27$

Now we can find the sum of squares between:

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

Each group have a sample size of 4 so then $n_j =4$

$SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72$

The degrees of freedom for the variation Between is given by $df_{between}=k-1=3-1=2$ , Where k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

$MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36$

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

$SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306$

And the degrees of freedom are given by:

$df_{within}=N-k =3*4 -3 = 12-3=9$ . N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

$MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34$

C. 34

Part 4

The test statistic F is given by this formula:

$F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059$

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is $F_{crit}=8.02$

B. 8.02

5 0

3 years ago

Which pair of triangles is congruent by asa?​

Which pair of triangles is congruent by asa?