HELP ME! In a complete sentence, describe the relationship between the three angles in the diagram below. Write and solve an equation to find the value of b and the measures of ∠QPS, ∠SPT, and ∠TPR.

Step-by-step explanation:

When using the equation of a line, one calculates the value of

y

in terms of

x

, say

y

=

m

x

+

c

, then

m

is the slope of the line and

c

is its intercept on

y

-axis.

As

3

x

−

9

y

=

15

can be written as

3

x

−

15

=

9

y

or

y

=

3

9

x

−

15

9

or

y

=

1

3

x

−

5

3

Hence slope of

3

x

−

9

y

=

15

is

1

3

Product of slopes of two perpendicular lines is

−

1

Hence, the slope of the line that is perpendicular to the line

3

x

−

9

y

=

15

is

−

1

1

3

=

−

1

×

3

1

=

−

3

graph{(3x-9y-15)(3x+y+5)=0 [-10, 10, -7.04, 2.96]}

Answer:

Please use " ^ " for exponentiation: x^2 + 2x + 8 ≤ 0.

Let's solve this by completing the square:

x^2 + 2x + 8 ≤ 0 => x^2 + 2x + 1^2 - 1^2 + 8 ≤ 0. Continuing this rewrite:

(x + 1)^2 + 7 ≤ 0

Taking the sqrt of both sides: (x + 1)^2 = i*sqrt(7)

Then the solutions are x = -1 + i√7 and x = -1 - i√7

There's something really wrong here. I've graphed your function, x^2 + 2x + 8, and can see from the graph that there are no real roots, but only complex roots. Please double-check to ensure that you've copied down this problem correctly.

Answer:

B. The Empty Set

Step-by-step explanation:

Hope this helps!!! Have a great day!!!!   : )

Answer:

Solution : Graph 4

Step-by-step explanation:

Let's break down this function,

{ y = 5 if x ≤ - 2, y = 0 if x = 3, y = - 1 if x > 3 }

As you can see, graph 4 is the only one that represents this.

• When y = 5, x  ≤ - 2. This is represented by a ray with a colored hole, indicating that x = - 2. At the same time this ray extends infinitely in the negative direction, indicating that x < - 2.

• When y = 0, x = 3. This is represented as the point ( 3, 0 ).

• And when y = - 1, x > 3. At y = - 1 another respective ray, that has a non - filled hole, indicates that x ≠ 3. The ray extends infinitely in the positive direction, meeting the criteria that x > 3.

Answer:

La última página que Sandra deberá leer es la página 380.

Step-by-step explanation:

Sandra y Roberto tienen un libro de 760 páginas y se lo dividen, la pregunta es ¿Cuál es la última página que debería leer Sandra de tal manera que ella y Roberto pasen la misma cantidad de tiempo leyendo la novela?

Para que ambos pasen la misma cantidad de tiempo leyendo la novela, tendrían que dividirse el libro a la mitad, por lo que cada uno debería leer 760 ÷ 2 = 380 páginas.

Por lo que Sandra deberá leer de la página 1 a la 380 y Roberto leerá de la 381 a la 760.

Por lo tanto, la última página que Sandra deberá leer es la página 380.

Answer:

4

Step-by-step explanation:

Well first we need to plug in 10 for g and h for 5.

4 - .25(10) + .5(5)

4 - 2.5. + 2.5

1.5 + 2.5

= 4

Thus,

the answer is 4

Hope this helps :)

Answer:

4

Step-by-step explanation:

We are given the expression:

4 - 0.25g + 0.5h

We know that g= 10 and h=5. Therefore, we can substitute 10 and 5 into the expression.

4-0.25(10)+0.5(5)

Now, solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

First, multiply 0.25 and 10

4-2.5+0.5(5)

Next, multiply 0.5 and 5

4-2.5+2.5

Next, subtract 2.5 from 4

1.5+2.5

Finally, add 1.5 and 2.5

4

4 - 0.25g + 0.5h when g=10 and h=5 is 4.

Answer:

β = 22.5°

Step-by-step explanation:

In a triangle, the sum of interior angles must add up to 180°.

Since the angle marked with corners is equal to 90°, we can write an equation to solve for β.

3β + β + 90° = 180°

4β = 180° - 90°

4β = 90°

β = 90° / 4

β = 22.5°

Answer:

T is equal to R

Hope this helps.....

Answer:

x = 3

y = -2

Step-by-step explanation:

x + 2y + 1 = 0

2x - 3y - 12 = 0

Multiply first equation by -2.

-2x + -4y + -2 = 0

2x - 3y - 12 = 0

Add equations.

0x + -7y - 14 = 0

Solve for y.

-7y = 14

y =-2

Put y as -2 in the first equation and solve for x.

x+2(-2)+1=0

x + -4 + 1 = 0

x = 0 + 4 - 1

x = 3

Answer:

[tex]\boxed{x = 3, y = -2}[/tex]

Step-by-step explanation:

[tex]x+2y +1 = 0[/tex]

=> [tex]x+2y = -1[/tex] -------------------(1)

[tex]2x-3y-12 = 0[/tex]

=> [tex]2x-3y = 12[/tex] -------------------(2)

Multiplying (1) by 2

=> [tex]2(x+2y) = 2(-1)[/tex]

=> [tex]2x+4y = -2[/tex] ------------------(3)

Subtracting (3) from (2)

=> [tex]2x-3y+2x-4y = 12+2[/tex]

=> -3y-4y = 14

=> -7y = 14

Dividing both sides by -7

=> y = -2

Now, Put y = -2 in Eq (1)

=> x+2(-2)+1 = 0

=> x -4+1 = 0

=> x - 3= 0

Adding 1 to both sides

=> x = 3

Answer:

(5, 0) and (-3, 0)

Step-by-step explanation:

To find the x-intercepts, let's set y = 0.

0 = x² - 2x - 15

0 = (x - 5)(x + 3) -- To factor x² - 2x - 15, we need to find 2 numbers with a sum of -2 and product of -15; these numbers are -5 and 3.

x - 5 = 0 or x + 3 = 0 -- Use ZPP (Zero Product Property)

x = 5, x = -3

Answer:

x = -3 and x = 5.

Step-by-step explanation:

y = x^2 - 2x - 15

y = (x - 5)(x + 3)

The x-intercepts occur when y = 0. In this case, it's when either (x - 5) = 0, or (x + 3) = 0.

x - 5 = 0

x = 5

x + 3 = 0

x = -3

Hope this helps!

Answer:

8677

Notice that all the numbers in the sequence are divisible by 3 except 8677.

The sum of the digits must be divisible by 3.

8+6+7+7= 2+8 =10

10 isn't divisible by 3.

Answer:

3/2

Step-by-step explanation:

● (-3/8) ÷(-1/4)

Flip the second fraction by putting 1 instead 4 and vice versa.

● (-3/8)* (-4/1)

-4 over 1 is -4 since dividing by 1 gives the same number.

● (-3/8)*(-4)

Eliminate the - signs in both fractions since multiplying two negative numbers by each other gives a positive number.

●( 3/8)*4

● (3*4/8)

8 is 2 times 4

● (3*4)/(4*2)

Simplify by eliminating 4 in the fraction.

● 3/2

The result is 3/2

Answer:

           The distance is:   [tex]\sqrt3\ cm\approx1,73\,cm[/tex]

Step-by-step explanation:

The distance of point E to the PQR plane it is the hight (vertical) of piramid PRQE

If point P is located in the middle of line EH, point Q is in the middle of line EF, and point R is in the middle of line AE than:

EP = EQ = ER = 0.5EF = 3 cm  and  m∠REQ = m∠QEP = m∠REP = 90° so triangles RQE, QPE and PRE are congruent.

RQ = QP = PR so triangle PQR is equilateral and from Pythagorean theorem (for ΔRQE):

[tex]RQ^2=ER^2+EQ^2=3^2+3^2=2\cdot3^2\ \ \implies\ \ RQ=3\sqrt2[/tex]

Then: [tex]RN=\dfrac{RQ\,\sqrt3}2[/tex]

and:  [tex]RK=\dfrac23RN=\dfrac{RQ\,\sqrt3}3=\dfrac{3\sqrt2\cdot\,\sqrt3}3=\sqrt6[/tex]

Therefore from Pythagorean theorem (for ΔERK):

[tex]EK^2+RK^2=ER^2\\\\EK^2=ER^2-RK^2\\\\EK^2=3^2-(\sqrt6)^2\\\\EK^2=9-6=3\\\\EK=\sqrt3\ cm\approx1,73\,cm[/tex]

Answer:

no

Step-by-step explanation:

It is an equal lateral triangle, a right triangle has a side that is longer then the others

Answer:

Option D

Step-by-step explanation:

H(x) = 3^(2x)

G(x) = reflecting H(x) across the y-axis and shifting 2 units down

=>G(x) = 3^(-2x) - 2

3^(2x) and 3^(-2x) - 2 are valid with all values of x.

=> There is no change in the domain of H(x) and G(x), in which all values of x satisfy H(x) and G(x).

3^(-2x) > 0

=> G(x) =  3^(-2x) - 2 > -2

=> Range of G(x) is from -2 to inifinity

Answer:

D.

Step-by-step explanation:

Well lets graph it first,

Look at the image below↓

So the red line is the new line which has been reflected and shifted down 2.

Meaning the domain turns into positive numbers but still remains infinite.

And the range changes

So we can cross out A and B.

Before the range was lower than 1 and now its (-2,∞)

Thus,

answer choice D is correct.

Hope this helps :)

Answer:

f(x) = -7x² - x + 2

Step-by-step explanation:

Quadratic functions are set up in the form ax² + bx + c. f(x) = 0x² + 3x -3 is also set up in this format but 0x² would simplify to 0 which means the equation is actually f(x) = 3x-3 and does not fit in the quadratic function format. The other equations are also not set up in ax² + bx + c.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

A polynomial with degree 2 is called a quadratic equation.

The quadratic equation is in the form of ax² + bx + c.

The equation that represents a quadratic equation is

f(x) = -7x² - x + 2.

It is in the form of ax² + bx + c

Where a = -7, b = -1, and c = 2

Option B is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

A polynomial with degree 2 is called a quadratic equation.

The quadratic equation is in the form of ax² + bx + c.

Now,

f(x) = 2x³ + 2x² - 4

This is not a quadratic equation since it has a degree of 3.

f(x) = -7x² - x + 2

This is a quadratic equation since its degree is 2.

It is in the form of ax² + bx + c

Where a = -7, b = -1 and c = 2

f(x) = -3x + 2

This is not a quadratic equation.

Its degree is 1.

f(x) = 0x² + 3x - 3

f(x) = 3x - 3

This is not a quadratic equation.

Thus,

The equation that represents a quadratic equation is

f(x) = -7x² - x + 2.

It is in the form of ax² + bx + c

Where a = -7, b = -1, and c = 2

Option B is the correct answer.

Learn more about polynomials here:

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Answer:

D

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, thus

DE = BE , substitute values

4y - 8 = y + 10 ( subtract y from both sides )

3y - 8 = 10 ( add 8 to both sides )

3y = 18 ( divide both sides by 3 )

y = 6

Thus

BD = y + 10 + 4y - 8 = 5y + 2 = 5(6) + 2 = 30 + 2 = 32 → D

Answer:

[tex] \boxed{\sf b. \ 8(2a + 9)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies 16a + 72 \\ \\ \sf Factor \: 8 \: out \: of \: 16a + 72: \\ \sf \implies 8 \times 2a + 8 \times 9 \\ \\ \sf \implies 8(2a + 9)[/tex]

Answer:

See explanations and diagram attached.

Step-by-step explanation:

1. angle 4 = angle 3, and angle 5 = angle 2  alternate interior angles with red line parallel to side opposite angle 1

3. angle 1 + angle 4 + angle 5 = 180   because these angles lie on a straight line.

Answer:  D) CPCTC

Step-by-step explanation:

step 6 proves the triangles are congruent.

step 7 states that if the triangles are congruent, then parts of the triangle are congruent.

Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Answer:

Variance =10900.00

Standard deviation=104.50

Step by step Explanation:

Admissions Probability for 1100= 0.2

Admissions Probability for 1400=0.3

Admissions Probability for 1300 =0.5

To find the expected value, we will multiply each possibility by its probability and then add.

mean = 1100*0.2 + 1400*0.3 + 1300*0.5 = 1290

To find the variance, we will start by squaring each possibility and then multiplying it by its probability. We will then add these and subtract the mean squared.

E(X^2)=( 1100²*0.2)+ (1400²*0.3 )+ (1300²*0.5) = 1675000

Variance(X)=E(X²)- [E(X)]²

= 1675000 - (1290)²

=10900

Hence, the Variance(X)=10900

Then to calculate the standard variation , we will use the formular below,

standard variation (X)=√ var(X)= √10900

=104.5

Hence the standard variation=104.5

Answer:

0.7

Step-by-step explanation:

multiply 2.5 by 2 first

5-4.3=0.7

Answer:

Step-by-step explanation:

a) Each place in our decimal place-value number system has a name. In the number 356,039, the left-most digit 3 is in the hundred-thousands place, so it is read (by itself) as "three hundred thousand." Together, the digits 356 of that number signify three hundred fifty-six thousand. They are said to be in the "thousands period." Each period of three digits will be grouped like that to specify the number of hundreds, tens, and ones in the period.

__

b) The given expanded form adds up to give ...

  963,104

Based on the above discussion, the name of this number is ...

  "nine hundred sixty-three thousand one hundred four"

Using digits to help write this, it would be 963 thousand 104.

Answer:

Step-by-step explanation:

[tex]A = (-2, -4) \\ B = (-8, 4) \\ d = (\sqrt{( {x_2 - x_1})^{2} + ({y_2 - y_1})^{2} } [/tex]

[tex]x_1 = - 2 \\ y_1 = - 4 \\ x_2 = - 8 \\ y_2 = 4[/tex]

[tex]d = \sqrt{ {( - 8 - ( - 2)}^{2} + {(4 - ( - 4))}^{2} } \\ d= \sqrt{ {( - 6)}^{2} + {8}^{2} } \\ d = \sqrt{36 + 64} \\ [/tex]

[tex]d = \sqrt{100} \\ d = 10[/tex]

Answer:

10

Step-by-step explanation:

Answer:

8cm

Step-by-step explanation:

the ratio of cm to km is 1 cm on the map equals 40 km. or 1/40 so you have to find what is x/320 using the ratio of 1/40 you gt that x equals 8

I also got the answer 64/49.

:D

The fraction  [tex](\frac{7}{8})^{-2}[/tex] without an exponent can be written as  [tex]\frac{64}{49}[/tex].

To rewrite the fraction [tex](\frac{7}{8})^{-2}[/tex] without an exponent, we can apply the rule of reciprocals.

Reciprocal of a fraction a/b is given by b/a.

So, taking the reciprocal of  [tex](\frac{7}{8})^{-2}[/tex] , we get:

[tex](\frac{7}{8})^{-2}[/tex]  =[tex](\frac{8}{7})^{2}[/tex]

Now let us simplify the numerator and denominator:

[tex]=\frac{8\times 8}{7 \times 7}[/tex]

[tex]=\frac{64}{49}[/tex]

Therefore,  [tex](\frac{7}{8})^{-2}[/tex] can be rewritten as [tex]\frac{64}{49}[/tex].

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Answer:

a)19²=361

b)14²=196

c)3²=9

d)60²=3600

e)105²=11025

Step-by-step explanation:

I I don't know if this is correct sorry.

Answer:

yes you're right it is 14 + 28p = 315

Answer:

C

Step-by-step explanation:

I had this question edge 2021

Answer:

  (x +1)^2 + (y +2)^2 = 25

Step-by-step explanation:

A diagram of the given triangle shows you it has side lengths of 3 and 4, so the square of the hypotenuse is ...

  (AC)^2 = (AB)^2 +(BC)^2 = 3^2 +4^2

  (AC)^2 = 25

The center of the circle is at A(-1, -2), so the equation is ...

  (x -h)^2 +(y -k)^2 = r^2

for the circle centered at (h, k) with radius r.

We know that the square of the radius (r^2) is 25, so we can write the equation as ...

  (x +1)^2 +(y +2)^2 = 25

Answer:

(x + 1)2 + (y + 2)2 = 25

Step-by-step explanation:

Hope this helps :)

Answer:

95.45%

Step-by-step explanation:

To go about this, what we do is to calculate the z-scores of the values in the range given.

Mathematically;

z-scores = (x-mean)/SD

Here in this case , mean is 3 and standard deviation is 0.25

So for 2.5 minutes, we have ;

z-score = (2.5-3)/0.25 = -0.5/0.25 = -2

For 3.5 minutes, we have;

z-score = (3.5-3)/0.25 = 0.5/0.25 = 2

The required probability we want to calculate according to the range is thus;

P(-2<z<2)

We can calculate this value by the use of the standard normal table

Mathematically, we can have the above as;

P(-2<z<2) = P(z<2) - P(z<-2)

We proceed using the table and we have the values as follows;

P(-2<z<2) = 0.97725 - 0.02275 = 0.9545

Now the value 0.9545 in percentage would be 95.45%

Answer:

OPtion B)

Step-by-step explanation:

Answer: Choice C)

y < (-1/5)x + 1

The boundary line is y = (-1/5)x+1 as it goes through the points shown. The boundary line is dashed or dotted, meaning that points on this boundary line are not in the solution set. So we will not have an "or equal to" as part of the inequality sign. More specifically, the inequality sign is "less than" because we shade below the boundary line. So that's how we end up with y < (-1/5)x+1.

Answer:

587.18 in²

Step-by-step explanation:

In the above question, we are given the following values

Diameter = 11 inches

Radius = Diameter/2 = 11 inches/2 = 5.5 inches

Slant height = 28.5 inches.

We were asked to find how many square inches of paper will she need to cover the ENTIRE cone.

To solve for this, we would use formula for Total Surface Area of a Cone

Total Surface Area of a Cone = πrl + πr²

= πr(r + l)

Using 3.14 for π

Total Surface Area of a Cone

= 3.14 × 5.5( 5.5 + 28.5)

= 3.14 × 5.5 × (34)

= 587.18 in²

Therefore, Anita will need 587.18 square inches of paper to cover the entire cone.

Answer:

B

Step-by-step explanation: Just trust me bro