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katen-ka-za [31]

3 years ago

10

The base of a triangle exceeds the height by 7 centimeters. If the area is 400 square centimeters, find the length of the base a

nd the height of the triangle.

1 answer:

zvonat [6]3 years ago

8 0

Answer:

Base = 32 cm

Height = 25 cm

Step-by-step explanation:

Area of a triangle can be calculated as:

$Area = \frac{1}{2}\times Base \times Height$

We are given that the base of triangle exceeds the height by 7 cm. This can be expressed in an equation form as:

Base = Height + 7

Lets use B to represent base and H to represent height

B = H + 7

The equation of area can be stated as:

$Area=\frac{1}{2}bh\\\\ Area=\frac{1}{2}(h+7)(h)\\\\ 400=\frac{1}{2}h(h+7)\\\\ 800=h^{2}+7h\\\\ h^{2}+7h-800=0$

This is a quadratic equation which can be solved using a quadratic equation as shown below:

$h=\frac{-7+-\sqrt{49-4(1)(-800)} }{2(1)} \\\\ h=\frac{-7+-57}{2}\\\\h=-32,25$

Since the height cannot be negative, we'll consider the positive value only i.e height is equal to 25 cm.

Therefore, the length of base will be 25 + 7 = 32 cm.

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Which of the following is an extraneous solution of the square root of -3x-2=x+2

yarga [219]

Answer:

x=-6 is an extraneous solution

Step-by-step explanation:

we have

$\sqrt{-3x-2} =x+2$

squared both sides

$-3x-2=(x+2)^2$

$-3x-2=x^2+4x+4$

$x^2+7x+6=0$

solve the quadratic equation by graphing

The solution is x=-6 and x=-1

see the attached figure

<u><em>Verify each solution</em></u>

substitute the value of x in the original expression

For x=-6

$\sqrt{-3(-6)-2} =-6+2$

$\sqrt{16} =-4$

$4=-4$ ----> is not true

so

Is an extraneous solution

For x=-1

$\sqrt{-3(-1)-2} =-1+2$

$\sqrt{1} =1$

$1=1$ ----> is true

so

Is the solution

4 0

3 years ago

Does anyone know <br> 2x=8y=7<br> 4x-2y=9

Fantom [35]

Assuming you mean 2x-8y=7, we can start by multiplying the first equation by -2 and adding it to the second (to cross out the x), resulting in -18y=-5. After that, we can divide both sides by -18, resulting in y=5/18. Next, plugging that into 4x-2y=9, we have 4x-10/18=9. Adding 10/18 to both sides, we get 4x=9+10/18. After that, we can divide both sides by 4, resulting in x=(9+10/18)/4=

5 0

3 years ago

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

Luden [163]

Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

6 0

2 years ago

Answer please........

Likurg_2 [28]

you have to show the graph

4 0

3 years ago

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kiruha [24]

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6 0

3 years ago

Read 2 more answers