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HACTEHA [7]
3 years ago
9

The difference of the square of a number and 28 is equal to 3 times that number find the positive solution

Mathematics
1 answer:
lutik1710 [3]3 years ago
8 0
<h2>The required positive number is 7.</h2>

Step-by-step explanation:

Let the number = x

To find, the positive number = ?

According to question,

x^{2}-28=3x

⇒ x^{2} - 3x - 28 = 0

By Factorisation method,

⇒ x^{2} - 7x + 4x - 28 = 0

⇒ x(x - 7) + 4(x - 7) = 0

⇒ (x - 7)(x + 4) = 0

⇒ x - 7 = 0 or, x + 4 = 0

⇒ x  = 7 or, x = - 4 [ - 4 is a negative number)

⇒ x  = 7

Thus, the required positive number is 7.

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The pair of triangles that are congruent by the ASA criterion is . The pair of triangles that are congruent by the SAS criterion
anzhelika [568]

Answer:

The pair of triangles that are congruent by the ASA criterion isΔ ABC and Δ XYZ.

The pair of triangles that are congruent by the SAS criterion is Δ BAC and ΔRQP.


Step-by-step explanation:

Two triangles are congruent by ASA property if any two angles and their included side are equal in both triangles .In triangles Δ ABC and Δ XYZ the equal side 5 is between the two equal angles. So these triangles are congruent by ASA criterion.

Two triangles are congruent by SAS if  two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle .In triangles  Δ BAC and ΔRQP. the included angles A and Q are equal and hence the triangles are congruent by SAS criterion.

5 0
3 years ago
Read 2 more answers
The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with me
iragen [17]

Answer:

a) 229 and 305 days

b) 229 days or less

c) 305 days or more

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 267

Standard deviation = 19

(a) Between what values do the lengths of the middle 95% of all pregnancies fall?_____________and___________days

By the Empirical rule, 95% of all pregnancies fall within 2 standard deviations of the mean.

So

267 - 2*19 = 229 days

to

267 + 2*19 = 305 days

(b) How short are the shortest 2.5% of all pregnancies?______days or less

95% of all pregnancies fall within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. Since the distribution is symmetric, 2.5% is more than 2 standard deviations below the mean(shortest 2.5%) and 2.5% is more than 2 standard deviations above the mean(longest 2.5%). So

267 - 2*19 = 229 days

c) How long do the longest 2.5% of pregnancies last?________days or more

Explanation in b)

267 + 2*19 = 305 days

7 0
3 years ago
How do you solve the three forms: Slope Y-intercept form Standard Form Point slope form
Nostrana [21]

Answer:An equation in the slope-intercept form is written as

y=mx+b

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

Example

Find the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23

We can find the b-value, the y-intercept, by looking at the graph

picture28

b = 1

We've got a value for m and a value for b. This gives us the linear function

y=−23x+1

In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

m=−23

This gives us the equation

y=−23x+b

From this we can solve the equation for b

b=y+23x

And if we put in the values from our first point (-3, 3) we get

b=3+23⋅(−3)=3+(−2)=1

If we put in this value for b in the equation we get

y=−23x+1

which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.

Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their respective position.

4 0
3 years ago
What is the value of y in the equation 5x + 2y = 20, when x = 0.3?
garik1379 [7]
Y=9.25 because 5x0.3=1.5 you move constents to the right hand side and it becomes -1.5 then you do the rest and the answers is 9.25
8 0
3 years ago
Read 2 more answers
Ella bought some key chains and spent a total of $32. Each key chain cost the same whole-dollar amount. She bought between 6 and
MrRa [10]
Ella bought 8 keychains. She spent 4 dollars on each KeyChain. Hope this helps
5 0
3 years ago
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