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3 years ago

Which of the following are solutions to the question below? Check all that apply.

Mathematics

1 answer:

AveGali [126]3 years ago

7 0

Answer:

Step-by-step explanation:

Given

6x² - 2x + 36 = 5x² + 10x ( subtract 5x² + 10x from both sides )

x² - 12x + 36 = 0 ← in standard form

(x - 6)² = 0 ← in factored form, thus

x - 6 = 0 ⇒ x = 6 → D

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Find an equation of the line that is perpendicular to the graph of 2x+5y=5 and contains the point of intersection of the graphs

gavmur [86]

Answer:

5(x+1) -2(y-3) = 0

Step-by-step explanation:

For a given line ax+by=c and point (h, k), a perpendicular line through the point can be written as ...

b(x-h) -a(y-k) = 0

A graphing calculator shows the point of intersection of the graphs of the two lines to be (x, y) = (-1, 3), so the line perpendicular to 2x+5y=5 through that point can be written ...

5(x+1) -2(y-3) = 0

_____

In the attached graph, the requested line is shown in black.

3 0

3 years ago

Brady made a scale drawing of a rectangular swimming pool on a coordinate grid. The points (-20, 25), (30, 25), (30, -10) and (-

djverab [1.8K]

Answer:

Length = 50 units

width = 35 units

Step-by-step explanation:

Let A, B, C and D be the corner of the pools.

Given:

The points of the corners are.

$A(x_{1}, y_{1}})=(-20, 25)$

$B(x_{2}, y_{2}})=(30, 25)$

$C(x_{3}, y_{3}})=(30, -10)$

$D(x_{4}, y_{4}})=(-20, -10)$

We need to find the dimension of the pools.

Solution:

Using distance formula of the two points.

$d(A,B)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ ----------(1)

For point AB

Substitute points A(30, 25) and B(30, 25) in above equation.

$AB=\sqrt{(30-(-20))^{2}+(25-25)^{2}}$

$AB=\sqrt{(30+20)^{2}}$

$AB=\sqrt{(50)^{2}$

AB = 50 units

Similarly for point BC

Substitute points B(-20, 25) and C(30, -10) in equation 1.

$d(B,C)=\sqrt{(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}$

$BC=\sqrt{(30-30)^{2}+((-10)-25)^{2}}$

$BC=\sqrt{(-35)^{2}}$

BC = 35 units

Similarly for point DC

Substitute points D(-20, -10) and C(30, -10) in equation 1.

$d(D,C)=\sqrt{(x_{3}-x_{4})^{2}+(y_{3}-y_{4})^{2}}$

$DC=\sqrt{(30-(-20))^{2}+(-10-(-10))^{2}}$

$DC=\sqrt{(30+20)^{2}}$

$DC=\sqrt{(50)^{2}}$

DC = 50 units

Similarly for segment AD

Substitute points A(-20, 25) and D(-20, -10) in equation 1.

$d(A,D)=\sqrt{(x_{4}-x_{1})^{2}+(y_{4}-y_{1})^{2}}$

$AD=\sqrt{(-20-(-20))^{2}+(-10-25)^{2}}$

$AD=\sqrt{(-20+20)^{2}+(-35)^{2}}$

$AD=\sqrt{(-35)^{2}}$

AD = 35 units

Therefore, the dimension of the rectangular swimming pool are.

Length = 50 units

width = 35 units

7 0

3 years ago

Cting Polynomials: Practice

Colt1911 [192]

The option that's true regarding the sum and difference of the polynomial p(x) and b is B. The sum and difference of p(x) and b are polynomials.

<h3>How to illustrate the information?</h3>

From the information given, it was stated that p(x) is a polynomial and is given as p(=) = a₁ + a₁ + a₂=² + ... + an.

In this case, it should be noted that the sum and difference of p(x) and b are polynomials.

They can't be integers as the function given is represented as a polynomial.

In conclusion, the correct option is B.

Learn more about polynomial on:

brainly.com/question/16340513

#SPJ1

7 0

1 year ago

A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a day waiting period to purchase

il63 [147K]

Answer:

The 90% confidence interval for the difference between proportions is (-0.260, -0.165).

Step-by-step explanation:

The question is incomplete. The complete question is:

"A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a 15 day waiting period to purchase a gun?” Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said ‘‘yes”. Use this information to find a 90% confidence interval for the difference in the two proportions, pm - pw. Subscript pm is the proportion of men who support the proposed law and pw is the proportion of women who support the proposed law. (Round answers to 3 decimal places.)"

We want to calculate the bounds of a 90% confidence interval.

For a 90% CI, the critical value for z is z=1.645.

The sample of men, of size nm=-0.26 has a proportion of pm=0.612.

$p_m=X_m/n_m=318/520=0.612$

The sample 2, of size nw= has a proportion of pw=0.824.

$p_w=X_w/n_w=379/460=0.824$

The difference between proportions is (pm-pw)=-0.212.

$p_d=p_m-p_w=0.612-0.824=-0.212$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_m+X_w}{n_m+n_w}=\dfrac{318+379}{520+460}=\dfrac{697}{980}=0.711$

The estimated standard error of the difference between means is computed using the formula:

$s_{pm-pw}=\sqrt{\dfrac{p(1-p)}{n_m}+\dfrac{p(1-p)}{n_w}}=\sqrt{\dfrac{0.711*0.289}{520}+\dfrac{0.711*0.289}{460}}\\\\\\s_{pm-pw}=\sqrt{0.00039+0.00045}=\sqrt{0.001}=0.029$

Then, the margin of error is:

$MOE=z \cdot s_{pm-pw}=1.645\cdot 0.029=0.0477$

Then, the lower and upper bounds of the confidence interval are:

$LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.212-0.0477=-0.260\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.212+0.0477=-0.165$

The 90% confidence interval for the difference between proportions is (-0.260, -0.165).

6 0

3 years ago

In Δ,∠=70°,∠=50° ∠ . ℎ ∠.

AveGali [126]

Answer:

100°

Step-by-step explanation:

A triangle is a polygon shape with three sides. Triangles are of different types such as obtuse, scalene, equilateral, isosceles etc.

In triangle ABC:

70° + 50° + ∠C = 180° (sum of angles in a triangle)

120 + ∠C = 180

∠C = 180 - 120

∠C = 60°

Since ∠C is bisected into ∠ACD and ∠BCD, hence:

∠ACD = ∠BCD = ∠C / 2

∠ACD = ∠BCD = 60 / 2

∠ACD = ∠BCD = 30°

In triangle ACD:

∠A + ∠ACD + ∠ADC = 180° (sum of angles in a triangle)

50 + 30 + ∠ADC = 180

∠ADC + 80 = 180

∠ADC = 100°

6 0

3 years ago