Mrs garcia is is 1 year less than 3 times as old as her daughter. seven years from now, she will be 4 years more than twice as old as her daughter will be then

Answer:

A

Step-by-step explanation:

hope it helps!!!!!!!

Answer:

A on edge 2020

Step-by-step explanation:

The given linear equation will have only one possible solution

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to find the total number of solutions for the linear equation -

10(x + 6) 2 - 9 = (15x + 1) 3 - 8

A linear equation is a equation of degree one. The number of solutions of a equation are equal to its degree. So, the given linear equation will have only one solution.

Therefore, the given linear equation will have only one possible solution.

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Answer:

y =7x , follows the direct variation.

Step-by-step explanation:

Direct variation states that a relationship between two variables in which one is a constant multiple of the other. In other words,  when one variable changes the other changes in proportion to the first.

If y is directly proportional to x i.e, [tex]y \propto x[/tex] or

y = kx              .....[1]  where k is the constant variation

Given : y = 7x

On comparing this with equation [1] we get;

k(constant of variation) = 7

therefore,

it follows the direct variation as [tex]y \propto x[/tex]  or

y = 7x where k =7 is the constant of variation.

Therefore, y =7x follows the direct variation.

The volume of the solid is found by integrating the area of circular cross-sections of the cylinder across its height affected by the plane z = y + 8. The integration from y = 0 to y = 8 and then doubling the result gives a volume of 12288π cubic units.

To find the volume of the solid bounded above by the plane z = y + 8, below by the xy-plane, and on the sides by the circular cylinder x2 + y2 = 64, we can use the method of cross-sectional areas.

The equation x2 + y2 = 64 represents a circle with radius 8 in the xy-plane. The cross-sectional area of the cylinder at any height y is a circle's area, which is πr2. Since the radius r is 8, the area A is 64π.

The solid is bounded above by the plane, which means the height of this solid at any point (x, y) on the xy-plane is z = y + 8. To find the volume, we integrate the area over the range of y values within the cylinder, which are from -8 to 8. Keeping the symmetry in mind, we can double the integral from 0 to 8 to account for the full height.

So, the volume V is calculated as:

V = 2 × ∫0864π(y+8) dy

When you integrate, you get:

V = 2 × 64π[½ y2 + 8y]08

V = 2 × 64π[32 + 64]

Finally, simplifying the expression:

V = 2 × 64π(96)

V = 12288π cubic units.

This is the volume of the solid.

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Answer:

The museum is 1 block west and 3 blocks north from the hotel.

Step-by-step explanation:

First of all, Ruby goes Northeast to a coffe shop, walking 4 blocks to the east and 2 blocks to the north. Then, she goes 5 blocks to the west, and 1 block to the north.

Therefore, she walks:

-3 blocks north

-4 blocks east

-5 blocks west

As east and west are contrary, we have to substract the lower number to the higher one in order to know the difference between both directions (5 W - 4 E = 1 W). As a result, Ruby finally moved west by 1 block.

Finally, we know that the museum is 1 block west and 3 blocks north from the hotel.

Answer:

Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).

Counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).

Step-by-step explanation:

Given  : rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4)

To find :  transformed according to the rule 90º , what is the location of q?

Solution : we have given that

vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4).

By the rule of 90º rotation clock wise rule : (x ,y ) →→ ( y , -x )

90º rotation counter clock wise rule : (x ,y ) →→ ( -y , x ).

Then   Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).

counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).

Therefore, Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).

counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).

The Pythagorean theorem is applied to a right triangle with the longer leg being one inch longer than the shorter leg and the hypotenuse being nine inches longer than the shorter leg. The side lengths of the triangle are found to be 5 inches, 6 inches, and 14 inches.

The subject of this question is mathematics, specifically the part of geometry that deals with right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c), is equal to the sum of the squares of the other two sides (a and b), i.e., a² + b² = c².

In this problem, the longer leg (a) is represented as b = a + 1 and the hypotenuse (c) as c = a + 9. If you substitute these two equations into the Pythagorean theorem, you get (a + 1)² + a² = (a + 9)². Solving this equation gives a = 5 inches.

Substituting a = 5 inches into the expressions for b and c, we get b = 6 inches and c = 14 inches. Therefore, the sides of the triangle are 5 inches, 6 inches, and 14 inches.

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The statement that is always true is: D. adjacent linear pairs of angles are supplementary.

Linear pairs of angles are angles that lie on the straight line. The sum of a linear pair is always 180 degrees, thus, they are regarded as supplementary angles.

Therefore, the statement that is always true is: D. adjacent linear pairs of angles are supplementary.

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B. 2-x = 4x+3

x 2-x 4x+3

-3 5 -9
-2 4 -5
-1 3 -1
0 2 3
1 1 7
2 0 11
3 -1 15

The table shows that none of the integers from [-3,3] work because in no case does
2-x = 4x+3

To find the solution we need to rearrange the equation to the form x=n
2-x = 4x+3
2 -x + x = 4x + x +3
2 = 5x + 3
2-3 = 5x +3-3
5x = -1
x = -1/5

The only point that satisfies both equations is where x = -1/5
Find y: y = 2-x = 2 - (-1/5) = 2 + 1/5 = 10/5 + 1/5 = 11/5
Verify we get the same in the other equation
y = 4x + 3 = 4(-1/5) + 3 = -4/5 + 15/5 = 11/5

Thus the only actual solution, being the point where the lines cross, is the point (-1/5, 11/5)

C. To solve graphically 2-x=4x+3
we would graph both lines... y = 2-x and y = 4x+3
The point on the graph where the lines cross is the solution to the system of equations ...
[It should be, as shown above, the point (-1/5, 11/5)]

To graph y = 2-x make a table....
We have already done this in part B

x 2-x x 4x+3
_ __
-1 3 -1 -1
0 2 0 3
1 1 1 7

Just graph the points on a Cartesian coordinate system and draw the two lines. The solution is, as stated, the point where the two lines cross on the graph.

I hope I helped! 

I will still trying to see if I can solve them another way that might be clearer.

x^2 - 2x -4 =0

Using the quadratic formula -b +/- √b^2 - 4(ac) / 2a

Replace the letters with the values from the equation:

2 +/- √-2^2 -4*(1*-4) / 2*1

X = 2 +/- 2√5 / 2

x = 1 +/-√5

The answer is:  x^2 - 2x -4 =0

Answer:

16 feet

Step-by-step explanation:

The relationships between displacement (position), velocity and acceleration are:

[tex]\boxed{\boxed{\begin{array}{c}\textbf{DISPLACEMENT (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]

To find the distance a particle travels in its first 4 seconds of travel, we first need to determine if the particle changes direction at any point during this time.

The instant(s) when the particle changes direction is when its velocity is zero. Therefore, set the velocity function v(t) to zero and solve for t:

[tex]\begin{aligned}v(t)&=0\\-t^2+4&=0\\-t^2&=-4\\t^2&=4\\t&=\pm 2 \end{aligned}[/tex]

So, the particle changes direction at t = 2 seconds in its first 4 seconds of travel. This means that to find the distance the particle travels in its first 4 seconds of travel, we need to integrate the velocity function over the two intervals [0, 2] and [2, 4] seconds to find the particle's displacement over these intervals.

The displacement of the particle in its first 2 seconds of travel is:

[tex]\begin{aligned}\displaystyle \int^2_0 (-t^2+4)\; \text{d}t&=\left[\dfrac{-t^{2+1}}{2+1}+4t\right]^2_0\\\\&=\left[-\dfrac{t^{3}}{3}+4t\right]^2_0\\\\&=\left(-\dfrac{(2)^{3}}{3}+4(2)\right)-\left(-\dfrac{(0)^{3}}{3}+4(0)\right)\\\\&=-\dfrac{8}{3}+8+0-0\\\\&=\dfrac{16}{3}\end{aligned}[/tex]

The displacement of the particle in its next 2 seconds of travel is:

[tex]\begin{aligned}\displaystyle \int^4_2 (-t^2+4)\; \text{d}t&=\left[\dfrac{-t^{2+1}}{2+1}+4t\right]^4_2\\\\&=\left[-\dfrac{t^{3}}{3}+4t\right]^4_2\\\\&=\left(-\dfrac{(4)^{3}}{3}+4(4)\right)-\left(-\dfrac{(2)^{3}}{3}+4(2)\right)\\\\&=-\dfrac{64}{3}+16+\dfrac{8}{3}-8\\\\&=-\dfrac{32}{3}\end{aligned}[/tex]

The negative value means that the particle is travelling in the opposite direction.

So, the particle travels 16/3 feet in its first 2 seconds of travel, changes direction at t = 2 seconds, and travels 32/3 feet in the opposite direction in the next 2 seconds of travel.

Therefore, the total distance the particle travelled is the sum of the absolute values of the two displacements:

[tex]\textsf{Distance}=\dfrac{16}{3}+\dfrac{32}{3}=\dfrac{48}{3}=16\;\sf feet[/tex]

So, the particle travels 16 feet in its first 4 seconds of travel.

The distance a particle travels in the first 4 seconds, moving according to the velocity equation v(t)= -t² + 4, is found by integrating the velocity function over that interval, which yields 5.33 feet.

To find the distance a particle travels given its velocity equation v(t)= -t² + 4 (in feet/sec), we need to integrate the velocity function over the desired time interval.

Since velocity is the rate of change of position with respect to time, the integral of the velocity function from 0 to 4 seconds will give us the displacement of the particle in that time interval.

The integral of v(t) from 0 to 4 seconds can be computed as follows:

However, the absolute value of -5.33 feet is needed, because distance must be positive. Hence, the particle travels 5.33 feet in the first 4 seconds.

Answer:

C

Step-by-step explanation:

Cause i'm a genius

The lines through points P and Q and points R and S are not perpendicular.

To determine if the line through points P(-8, -10) and Q(-5, -12) is perpendicular to the line through points R(9, -6) and S(17, -5), we need to calculate the slopes of both lines and check if they are negative reciprocals of each other. The slope of a line (m) through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1).

For line PQ:

mPQ = (-12 + 10) / (-5 + 8) = -2 / 3

For line RS:

mRS = (-5 + 6) / (17 - 9) = 1 / 8

Now, the product of the slopes of two perpendicular lines is -1. Let's check if the product of mPQ and mRS is -1:

mPQ * mRS = (-2 / 3) * (1 / 8) = -2 / 24 = -1 / 12

Since -1 / 12 is not equal to -1, the lines are not perpendicular. Therefore, the line through points P and Q is not perpendicular to the line through points R and S.

Kalahira is correct but the letters at the end might confuse you.

Correct answer:

the correct answer is =

The slope of the line is 3.5

This means that every pound

of dried fruit cost $3.50

   Slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.

   From the graph attached,

Points shown on the graph are (4, 14) and (8, 28).

Since, slope of a line passing two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (4, 14) and (8, 28) will be,

Slope = [tex]\frac{28-14}{8-4}[/tex]

          = [tex]\frac{14}{4}[/tex]

          = 3.5

This means that every of dried fruit costs $3.5 per lb.

       Therefore, slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.

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Answer:

The value of x is [tex]\frac{7}{4}[/tex].

Step-by-step explanation:

It is given that the inverse variation equation is

[tex]xy=k[/tex]                  ..... (1)

The value of y is 4 and the value of k is 7.

Substitute y=4 and k=7 in equation (1).

[tex]x\times 4=7[/tex]

Divide both sides by 4.

[tex]\frac{x\times 4}{4}=\frac{7}{4}[/tex]

[tex]x=\frac{7}{4}[/tex]

Therefore the value of x is [tex]\frac{7}{4}[/tex].