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Ivenika [448]
2 years ago
8

Are the following two binomials

Mathematics
1 answer:
Rainbow [258]2 years ago
7 0

Answer: x = 2/3

Step-by-step explanation:

You might be interested in
Points H and F lie on circle c What is the length of line segment GH?
Nina [5.8K]

Answer:

6 units

Step-by-step explanation:

Given: Points H and F lie on  circle with center C. EG = 12, EC = 9 and ∠GEC = 90°.

To find: Length of GH.

Sol: EC = CH = 9 (Radius of the same circle are equal)

Now, GC = GH + CH

GC = GH + 9

Now In ΔEGC, using pythagoras theorem,

(Hypotenuse)^{2} = (Base)^{2} +(Altitude)^{2} ......(ΔEGC is a right triangle)

(GC)^{2} = (GE)^{2} +(EC)^{2}

(GH + 9)^{2} = (9)^{2} +(12)^{2}

(GH )^{2} + (9)^{2} + 18GH = 81 + 144

(GH )^{2} + 81 + 18GH = 81 + 144

(GH )^{2} + 18GH = 144

Now, Let GH = <em>x</em>

x^{2} +18x = 144

On rearranging,

x^{2} +18 x - 144 = 0

x^{2} - 6x +24x + 144 = 0

x (x-6) + 24 (x - 6) =0

(x - 6) (x + 24) = 0

So x = 6  and x = - 24

∵ x cannot be - 24 as it will not satisfy the property of right triangle.

Therefore, the length of line segment GH = 6 units. so, Option (D) is the correct answer.

3 0
2 years ago
Read 2 more answers
In the past, the population proportion of consumers preferring orange juice with no pulp was equation. To test if this populatio
geniusboy [140]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

P = 0.45

For the alternative hypothesis,

P ≠ 0.45

b) For the decision rule, we would reject H0 if 0.1 > p value and accepth H0 if 0.1 < p value

Considering the population proportion, probability of success, p = 0.45

q = probability of failure = 1 - p

q = 1 - 0.45 = 0.55

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 52

n = number of samples = 120

p = 52/120 = 0.43

c) We would determine the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.43 - 0.45)/√(0.45 × 0.55)/120 = - 0.44

Recall, population proportion, P = 0.45

The difference between sample proportion and population proportion(P - p) is 0.45 - 0.43 = 0.02

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.45 - 0.02 = 0.43

the p for the right tail is 0.45 + 0.02 = 0.47

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.3336

We would double this area to include the area in the right tail of z = 0.44 Thus

p = 0.3336 × 2 = 0.67

d) Since alpha, 0.1 < than the p value, 0.67, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the​ null hypothesis

4 0
2 years ago
Which best describes the relationship between the line that
LUCKY_DIMON [66]
Same line so the correct answer is b
5 0
3 years ago
2) Fill in an angle measure greater than 100 degrees for the missing angle in yellow below. You will fill
timama [110]

Answer:

m∠a = 110°

m∠b = 110°

m∠c = 70°

m∠d = 70°

m∠i = 110°

m∠h = 110°

m∠j = 70°

m∠g = 110°

m∠f = 70°

m∠e = 70°

m∠k = 57°

m∠m = 70°

m∠l = 167°

Step-by-step explanation:

Let the measure of the yellow angle = 110°

Therefore;

m∠a = 110°  by vertically opposite angles

m∠b = m∠a = 110° by opposite interior angles of a parallelogram

m∠c = 180° - 110° = 70° by same side interior angles

m∠d = m∠c = 70° by opposite interior angles of a parallelogram

m∠i and m∠c are supplementary angles, therefore, m∠i = 110°

m∠h = m∠i = 110° by vertically opposite angles

m∠j = m∠c = 70° by vertically opposite angles

m∠g and m∠d are supplementary angles, therefore, m∠g = 110°

m∠f = m∠d = 70° by alternate interior angles

m∠f = m∠e = 70° by vertically opposite angles

m∠k = 180° - (m∠h + 13°) = 180° - (110° + 13°) = 57°

m∠b and m∠m are supplementary angles, therefore, m∠m = 70°

m∠l and 13° are supplementary angles, therefore, m∠l = 167°

4 0
3 years ago
If f(x) = 4x-9, evaluate f(3) <br>I need HELP ASAP!!!!!!!!!!!​
seropon [69]

Answer:

substitute 3 as in x:

4(3)-9

= 12-9

= 3

Hope this helped - have a nice day & be safe

8 0
2 years ago
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