Danielle has taken five math tests so far this year. The tests are out of twenty points, and she has gotten the following scores.

17, 19, 20, 14, 16

What must Danielle score on her sixth test in order to have a mean of 17.5?

17
18
20
19

Answer:

the answer is c for Friday and 6 3/12 hours for them both combined

Step-by-step explanation:

because 3 5/12 is closest to 3 1/2=3 6/12

for fir day and Saturday day combined it would be 6 3/12

because 5/6 is 10/12 and 5/12 + 10/12 is 15/12 which is also 1 3/12

so add 3 +2=5 and then add the fraction 1 3/12 which would be 6 3/12 hours

The four rectangles can be painted with 7 different paints in 840 ways.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}, there are no other ways to arrange the elements of set A.

The formula for permutattion is;

\(P_r_n = \frac{n!}{(n-r)!} \\\)

where r = 4

n = 7

Substituting the values for n and r

\(P = \frac{7!}{(7-4)!}\)

\(P = \frac{7!}{3!}\)

P = 840 ways.

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The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

Step-by-step explanation:

The x value comes first. The y value second. (alphabetical order).

A (-1,4)

B (2,3)

C (3,0)

The side length x round to the nearest tenth is 3.8 units

The figure in the image is a right-triangle.

Angle θ = 40°

Adjacent to angle θ = x

Hypotensue = 5

To find the measure of x, we use the trigonometric ratio.

cosine = adjacent / hypotensue

Plug in the values

cosθ = x / 5

cos( 40 ) = x / 5

Solve for x

x = cos( 40 ) × 5

x = 3.8

Therefore, the value of x is 3.8.

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Answer:

Ninafanya hivi kwa kujifurahisha

Step-by-step explanation:

The surface area of the sphere is 1810 cm²

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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Answer:

y=0.13x^2+13.68x+750

this the function rule

Step-by-step explanation:

brainliest

Answer:

im the other

make sure u give it to tfue_the_god

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3+2+7=12

Hope this helps! Please give brainliest!

Answer:

- x + y - 4

Step-by-step explanation:

Given polynomial:

\( \rm \: x+2y+1-(2x+y+5)\)

Solution:

Removing parentheses,we obtain

Collecting and combining like terms,we obtain

Done!

Answer:

1/5 or .20 or 20% (same answer in different formats!)

Step-by-step explanation:

Subtract 1/2 from 7/10

make the denominators the same, so 7/10 - 5/10. You get 2/10 or 1/5.

Answer:3 /8

Step-by-step explanation:

The vector for the line through the origin and the point (3,7,-7) is given as follows:

r(t) = (3 + t, 7 + t, -7 + t).

The origin has the coordinates given as follows:

(0, 0, 0).

Considering the point (3,7, -7) at a time of t = 1, the normal vector is given as follows:

(3 - 0, 7 - 0, - 7 - 0) = (3,7,-7).

Considering t = 0 at the origin, the equation of the line is given as follows:

r(t) = (3 + t, 7 + t, -7 + t).

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Answer:

D is approximately (-2, -1)

Step-by-step explanation:

\({ \tt{slope \:AB = slope \: CD }} \\ \\ { \tt{ \frac{(4 - 3)}{( - 1 - 2)} = \frac{(y - ( - 2))}{(x - ( - 2))} }} \\ \\ { \tt{ \frac{1}{ - 3} = \frac{y + 2}{x + 2} }} \\ \\ { \tt{x + 2 = - 3y - 6}} \\ { \underline{ \tt{ \green{ \: \: 3y + x = - 8 \: \: }}}}\)

\({ \tt{slope \: AD= slope \: BC}} \\ \\ { \tt{ \frac{y - 3}{x - 2} = \frac{ - 2 - 4}{ - 2 - 1} }} \\ \\ { \tt{ \frac{y - 3}{x - 2} = \frac{6}{3} }} \\ \\ { \tt{ \frac{y - 3}{x - 2} = 2}} \\ \\ { \tt{y - 3 = 2(x - 2)}} \\ { \tt{y - 3 = 2x - 4}} \\ { \underline{ \tt{ \blue{ \: \: y - 2x = - 1 \: \: }}}}\)

Solve the green equation and blue equation simultaneously:

\({ \boxed{ \tt{ \red{ \: y \approx - 2 \: \: }}and \: \: { \red{x \approx - 1}}}}\)

Let the co-ordinates of D be (a,b)

\(\\ \tt\hookrightarrow \dfrac{4-3}{-1-2}=\dfrac{b+2}{a+2}\)

\(\\ \tt\hookrightarrow \dfrac{-1}{2}=\dfrac{b+2}{a+2}\)

\(\\ \tt\hookrightarrow -a-2=2b+4\)

\(\\ \tt\hookrightarrow a+2b+6=0\dots(1)\)

\(\\ \tt\hookrightarrow \dfrac{b-3}{a-2}=\dfrac{-2-4}{-2+1}\)

\(\\ \tt\hookrightarrow \dfrac{b-3}{a-2}=6\)

\(\\ \tt\hookrightarrow 6a-12=b-3\)

\(\\ \tt\hookrightarrow 6a-b-9=0\dots(2)\)

Multiplying 2 with eq(2)

\(\\ \tt\hookrightarrow 12a-2b-18=0\dots(3)\)

\(\\ \tt\hookrightarrow 13a-12=0\)

\(\\ \tt\hookrightarrow a=12/13=0.9\to 1\)

\(\\ \tt\hookrightarrow 12/13+2b+6=0\)

\(\\ \tt\hookrightarrow 90/13=-2b\)

\(\\ \tt\hookrightarrow b=-90/26=-3 4\to 3\)

Answer:

Step-by-step explanation

Okay so lets solve step by step/

15% can be written as a  fraction: 15/100

The of in the equation means multiplying.

15/100= 3/20

3/20*9= 270/20

27/2 is answer

Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.

Answer:

\(CD = 3\)

Step-by-step explanation:

Given

\(CD = x\)

\(BC = 5x - 5\)

\(BD = 2x + 7\)

Required

Determine CD

Since, C is a point on BD, the relationship between the given parameters is;

\(BD = BC + CD\)

Substitute the values of BD, BC and CD

\(2x + 7 = 5x - 5 + x\)

Collect Like Terms

\(2x - 5x - x = -5 - 7\)

\(-4x = -12\)

Divide both sides by -4

\(\frac{-4x}{-4} = \frac{-12}{-4}\)

\(x = 3\)

To determine the length of CD;

Substitute 3 for x in \(CD = x\)

Hence;

\(CD = 3\)

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answerj,   C v v .

Step-by-step explanation:

Answer:

Angle DCA = Angle CAB. (Alternate Interior Angle)

Angle DCA = 68°

Angles(DCA + ACB + BCE) = 180°. (Linear Pair)

Angle ACB + 68° + 33° = 180°

Angle ACB = 79°

Therefore,

Angle ABC = 33°. (Alternate Interior Angle)

EXPLANATION :

From the problem, we have the inequality :

The first is to locate y = -3

That's below the x-axis.

And all y values must be less than or equal to -3

So the region is from that line up to the negative infinity.

The only option that satisfies this condition is the blue graph.

Answer:

just do it urself

Step-by-step explanation:

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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a) The angle swept out  since kelsey started skiing: 1.1498 radians

b) The distance Kelsey skied:  3.334 km

In this question, we have been given Kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail.

Consider the following figure for reference.

We need to find the angle θ and the distance kelsey skied (i.e., the arc length)

Here, the horizontal distance x = 1.185 km and the vertical distance y = 2.647 km

a. the tangent of angle θ would be,

tan(θ) = y/x

tan(θ) = 2.647/1.185

tan(θ) = 2.2337

θ = arctan(2.2337)

θ = 65.88°

θ = 1.1498 radians

b. The length of the arc is:

s = rθ

s = 2.9 * 1.1498

s = 3.334 km

Therefore, a) the angle swept out : 1.1498 radians

b) the distance Kelsey skied:  3.334 km

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Answer:

The rocket will hit the ground after 113.28 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}\)

\(\Delta = b^{2} - 4ac\)

The height of a rocket, after t seconds, is given by:

\(h(x) = -16x^2 + 1812x + 59\)

Using this equation, find the time that the rocket will hit the ground.

This is x for which \(h(x) = 0\). So

\(-16x^2 + 1812x + 59 = 0\)

Then \(a = -16, b = 1812, c = 59\)

\(\Delta = (1812)^2 - 4(-16)(59) = 3287120\)

\(x_{1} = \frac{-1812 + \sqrt{3287120}}{2*(-16)} = -0.03\)

\(x_{2} = \frac{-1812 - \sqrt{3287120}}{2*(-16)} = 113.28\)

The rocket will hit the ground after 113.28 seconds.

Answer:

7x - 7

Step-by-step explanation:

Product of x and 7 = 7x

7 minus 7x

7x - 7

Hence the expression is :

7x - 7