10 POINTS!!

Draw a tree diagram to show the sample space for each event.

dessert choices: a cake or a shake, each available in vanilla or strawberry flavors

Answer:

A

Step-by-step explanation:

In the figure shown, ABC is a right triangle with side lengths a, b, and c, and CD is an altitude to side AB. This altitude divides the triangle into two right triangles ADC and BDC. In these triangles,

So,

[tex]\triangle ABC\sim \triangle CBD\sim \triangle ACD[/tex]

1. From the similarity [tex]\triangle ABC\sim \triangle CBD,[/tex] you have

[tex]\dfrac{AB}{BC}=\dfrac{BC}{BD}\\ \\\dfrac{c}{a}=\dfrac{a}{s}[/tex]

2. From the similarity [tex]\triangle ABC\sim \triangle ACD,[/tex] you have

[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}\\ \\\dfrac{c}{b}=\dfrac{b}{r}[/tex]

Hence, option A is true

Final answer:

The correct proportions for the right triangle ABC with altitude CD are c/a = b/r and c/b = a/s, derived from the similarity of the triangles ACD and CBD with triangle ABC.(Option c)

Explanation:

In the given right triangle ABC with altitude CD, we can apply similarity properties to find the true proportions related to the side lengths labeled a, b, and c, and the segments of the altitude, labeled h, r, and s. To solve the problem, we can consider the two right triangles ACD and CBD created by drawing altitude CD. Since these triangles are similar to ABC, their corresponding side ratios will be equal.

Applying the similarity of triangles (Theorem 22), two sets of proportions become evident:

These proportions come from setting the sides of the smaller triangles against the hypotenuse c of the larger triangle ABC and using corresponding sides of similar triangles. Thus, the correct answer is that the true proportions are c/a = b/r and c/b = a/s, which match option C) in the question.

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

we have

[tex]\frac{2}{5}(x-4)=2x[/tex]

Solve for x

Multiply by 5 both sides

[tex]2(x-4)=10x[/tex]

Divide by 2 both sides

[tex]x-4=5x[/tex]

Subtract x both sides

[tex]x-4-x=5x-x[/tex]

[tex]-4=4x[/tex]

Divide by 4 both sides

[tex]x=-1[/tex]

Answer:

see explanation

Step-by-step explanation:

(10)

To evaluate f(- 4) substitute x = - 4 into f(x)

f(x) = 7x - 4x + 3 = 3x + 3

f(- 4) = 3(- 4) + 3 = - 12 + 3 = - 9

(11)

To evaluate f(- 2) substitute x = - 2 into f(x)

f(- 2) = 2(- 2)² - 8 = 2(4) - 8 = 8 - 8 = 0

(12)

To evaluate g(- 3) substitute x = - 3 into g(x)

g(- 3) = - 2(- 3)² + 3(- 3) = - 2(9) - 9 = - 18 - 9 = - 27

Answer:

18

Step-by-step explanation:

(5+1)3=5*3+1*3=15+3=18

The measure of the hypotenuse is 25.0 units

Step-by-step explanation:

Let us revise how to find the length of the hypotenuse in a right Δ

∵ The legs of a right triangle measure 7 units and 24 units

∴ x = 7 units and y = 24 units

∵ [tex]z=\sqrt{x^{2}+y^{2}}[/tex]

- Substitute the values of x and y in the rule to find z

∵ [tex]z=\sqrt{(7)^{2}+(24)^{2}}[/tex]

∴ [tex]z=\sqrt{49+576}[/tex]

∴ [tex]z=\sqrt{625}[/tex]

∴ z = 25 units

∵ z is the hypotenuse

∴ The measure of the hypotenuse = 25 units

The measure of the hypotenuse is 25.0 units

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Answer:

70s-10       s=7

Step-by-step explanation:

first you want to multiply 7 * 10 which will give you 70 s -10 then you want to divide the 70 by 10 and you will get seven as your answer

Answer:

Step-by-step explanation:

7(10s-10)

= 70s - 70

Answer:

Rolling a 2 seven times = [tex]3.57\times 10^{-6}[/tex]

Step-by-step explanation:

Given:

A die is rolled seven times.

Number of possible outcomes in a die = {1, 2, 3, 4, 5, 6}

So, n(S) = 6

Now, rolling a '2' is given as:

[tex]P(2)=\frac{\textrm{Favourable outcome}}{\textrm{Total possible outcomes}}=\frac{1}{6}[/tex]

Now, rolling a die seven times resulting in a '2' is given as the product of the probability at each time.

Therefore, the experimental  probability of rolling a 2 seven times is given as:

[tex]=[P(2)]^7\\\\=(\frac{1}{6})^7\\\\=3.57\times 10^{-6}[/tex]

Use the formula (b/2)² in order to create a new term in order to find the perfect square trinomial.

a² - 2ab + b²

Answer:

The answer is never

Step-by-step explanation:

I hope this helps

Answer:

A

Step-by-step explanation:

Note that (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 6x² - 4 - (2x + 2) ← distribute parenthesis by - 1

= 6x² - 4 - 2x - 2 ← collect like terms

= 6x² - 2x - 6 → A

Answer:

A.  6x^2 - 2x - 6.

Step-by-step explanation:

( f - g)(x)

= 6x^2 - 4 - (2x + 2)

= 6x^2 - 4 - 2x - 2

= 6x^2 - 2x - 6.

A. Part 1- The scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.

B. Part 2- The length of side EF is 221/182

C. Part 3- The exact area of EFGH is 7213127/33124​  square inches.

Let's solve each part step by step:

A. Part 1:

To find the scale factor from BC to FG, we need to find the ratio of the lengths of the corresponding sides of the similar quadrilaterals.

Given:

Diagonal AC (in quadrilateral ABCD) has length 7.

Diagonal EG (in quadrilateral EFGH) has length 13.

Using the fact that the diagonals of similar quadrilaterals are proportional, we have:

BC/ FG​ = AC/ EG

Substituting the given values:

BC/ FG​ = 7/13

So, the scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.

B. Part 2:

Given side AB has a length of 17/26 . To find the length of side EF, we use the scale factor found in Part 1.

If the scale factor from BC to FG is 7/13 , then the length of side EF can be found using the proportion:

EF/ AB​ = FG/ BC

Substituting the given values:

EF=7/13×17/ 26

Solving for EF:

EF= 13/ 7​ × 17/ 26 = 221/ 182

So, the length of side EF is 221/182

​C. Part 3:

If the area of quadrilateral ABCD is 147 square inches, and the scale factor is 7/13 , the area of quadrilateral EFGH can be found using the scale factor squared.

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

So,

( EF/AB )^2 =( 7/13 )^2

( 221/ 182)^2 =( 7/13 )^2

Solving for ( 221/ 182 )^2 :

( 221/182 )^2 = 48841/ 33124

Now, if the area of ABCD is 147 square inches, then the area of EFGH would be:

147× 48841/ 33124 = 7213127 /33124

So, the exact area of EFGH is 7213127/33124​  square inches.

Answer:

55 minutes :)

Step-by-step explanation:

Rate of drop of temperature = Change in temperature/Rate

=> (165 - 135)/15

=> 30/15

=> 2 ⁰F/min

Now, The time at which the temperature of will be 70⁰F = 70/Rate

=> 70/2

=> 35 min

Time for 110⁰ F

=> 110/2

=> 55 min

Answer:

34 minutes

Step-by-step explanation: I just took the test

Answer:

11 minutes.

Step-by-step explanation:

To print 500 pages the first printer takes 20 minutes.

Then in one minute it can print [tex]\frac{500}{20} = 25[/tex] pages.

Again, to print 500 pages the first printer takes 25 minutes.

Then in one minute it can print [tex]\frac{500}{25} = 20[/tex] pages.

So, working together both the printer will print (20 + 25) = 45 pages in 1 minute.

Therefore, they will print 500 pages in [tex]\frac{500}{45} = 11.11[/tex] minutes ≈ 11 minutes. (Answer)

Answer:

The Value of tan x is the option E.

[tex]\tan x=\dfrac{4}{3}[/tex]

Step-by-step explanation:

Given:

[tex]\textrm{Opposite side to angle x}= 8[/tex]

[tex]\textrm{Adjacent side to angle x}= 6[/tex]

To Find:

[tex]\\tan x=?[/tex]

Solution:

In a Right Triangle Tangent Identity is

[tex]\tan x= \dfrac{\textrm{side opposite to angle x}}{\textrm{side adjacent to angle x}}[/tex]

Substituting the values we get

[tex]\tan x= \dfrac{8}{6}=\dfrac{4}{3}[/tex]

The Value of tan x is the option E.

[tex]\tan x=\dfrac{4}{3}[/tex]

Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis. The coordinates of a given point represent how far along each axis the point is located.

Step-by-step explanation:

The location of solutions in the coordinate plane is described using a Cartesian coordinate system, involving movements either vertically (upward or downward) or horizontally (to the right or left) from the origin, represented by coordinates (x, y).

The location of the solutions in the coordinate plane can be described using a Cartesian coordinate system. This system is based on two perpendicular lines, the x-axis (horizontal) and the y-axis (vertical), intersecting at the origin (0,0). When we are looking at solutions on this grid, we can describe their positions in relation to the origin.

If a solution moves vertically upward from the origin, its y-coordinate increases while the x-coordinate remains the same.

Moving vertically downward means the y-coordinate decreases.

Horizontally to the right, the x-coordinate increases from the origin.

Horizontally to the left, the x-coordinate decreases.

The point at which the solution lies can be described by a pair of numbers, or coordinates, such as (x, y), where x is the position along the horizontal axis and y is the position along the vertical axis.

Answer:

12x-183

Step-by-step explanation:

2(4x+3)+3(x-63)+x

8x+6+3x-189+x

12x+6-189

12x-183

Answer:

b $80

Step-by-step explanation:

Interest = Principal x Interest Rate x Time

$40 = P x 0.1 x 5

$40 = 0.5 P

Dividing the equation by 0.5 we get;

P = $40 / 0.5

P = $80

Answer:

C

Step-by-step explanation:

note that (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 10x + 7 - (x² - 7x) ← distribute parenthesis by - 1

= 10x + 7 - x² + 7x ← collect like terms

= - x² + 17x + 7 → C

Final answer:

To find (f - g)(x), you need to subtract the function g(x) from the function f(x). The answer is -x^2 + 17x + 7.

Explanation:

To find (f - g)(x), we need to subtract the function g(x) from the function f(x).

Given f(x) = 10x + 7 and g(x) = x^2 - 7x, we substitute these values into (f - g)(x):

(f - g)(x) = f(x) - g(x) = (10x + 7) - (x^2 - 7x)

Expanding and simplifying, we get (f - g)(x) = -x^2 + 17x + 7.

Answer:

6

Step-by-step explanation:

Answer:

[tex]5280 \: feet \: = 1 \: mile \\ \\ = > 1 \: mile \: = 5280 \: feet \\ \\ = > 3.5 \: miles \: = \: 3.5 \times 5280 \: feet \\ \\ = > 3.5 \: miles \: = \: 18480 \: feet[/tex]

Answer:

The area of the region inside the circumcircle of the triangle but outside the triangle is

[tex]A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the area of triangle

we have an equilateral triangle

Applying the law of sines

[tex]A_t=\frac{1}{2}(b^2)sin(60^o)[/tex]

where b is the length side of the equilateral triangle

we have

[tex]b=9\ units[/tex]

[tex]A_t=\frac{1}{2}(81)sin(60^o)[/tex]

[tex]A_t=\frac{1}{2}(81)\frac{\sqrt{3}}{2}[/tex]

[tex]A_t=81\frac{\sqrt{3}}{4}\ units^2[/tex]

step 2

Find the area of circle

The area of the circle is equal to

[tex]A_c=\pi r^{2}[/tex]

The formula to calculate the radius of the circumcircle of the triangle equilateral is equal to

[tex]r=b\frac{\sqrt{3}}{6}[/tex]

where b is the length side of the equilateral triangle

we have

[tex]b=9\ units[/tex]

substitute

[tex]r=(9)\frac{\sqrt{3}}{6}[/tex]

[tex]r=3\frac{\sqrt{3}}{2}\ units[/tex]

Find the area

[tex]A_c=\pi (3\frac{\sqrt{3}}{2})^{2}[/tex]

[tex]A_c=\frac{27}{4} \pi\ units^2[/tex]

step 3

Find the area of the shaded region

we know that

The area of the region inside the circumcircle of the triangle but outside the triangle is equal to the area pf the circle minus the area of triangle

so

[tex]A=(\frac{27}{4} \pi-81\frac{\sqrt{3}}{4})\ units^2[/tex]

Simplify

[tex]A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2[/tex]

Final answer:

The equation of a line perpendicular to y=2/3x-6 has a slope of -3/2. The general form of the equation is y = -3/2x + b, where b is the y-intercept.

Explanation:

The student has asked for an equation of a line that is perpendicular to the line given by y=2/3x-6. For two lines to be perpendicular, the product of their slopes must be -1. Since the slope (m₁) of the given line is 2/3, the slope of the line perpendicular to it (m₂) must satisfy the equation m₁×m₂ = -1. Therefore, m₂ must be -3/2 (since (2/3)×(-3/2) = -1).

An equation of a straight line can be represented by y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line perpendicular to y=2/3x-6, we can use the slope m₂ = -3/2. The general form of the equation of the line we are seeking would then be y = -3/2x + b, where b is the y-intercept that can be determined based on a specific point the line passes through.

Answer:1 2/3

Step-by-step explanation:

2/3+1/3+2/3=5/3=1 2/3

Answer:

a. 1200          f. 900

b. 600           g. 5700

c. 900           h. 4800

d. 300           i. 8300

e. 800           j. 8500

Step-by-step explanation:

First of all, you need to compute the sums. I find a calculator handy for this.

To round to hundreds, you can examine the digit in the next place to the right of the hundreds place. That digit in the tens place needs to be compared to 5. If it is 5 or greater, add 1 to the digit in the hundreds place. After you have done that, set the digits to the right of the hundreds place to zero.

__

Alternatively, you can add 1/2 of 100 to the sum, then set the digits to the right of the 100s place to zero. (Adding 50 will only change the 100's place digit if the 10's place digit is 5 or more.) This method doesn't require you do any thinking about the size of the digit; it is purely mechanical.

The sums and their rounded values are ...

a. 1221 ⇒ 1200

b. 568 ⇒ 600

c. 931 ⇒ 900

d. 347 ⇒ 300

e. 798 ⇒ 800

f. 911 ⇒ 900

g. 5681 ⇒ 5700

h. 4766 ⇒ 4800

i. 8328 ⇒ 8300

j. 8507 ⇒ 8500

For this case we must find the solution set of the following inequalities:

[tex]x> -5[/tex]

The solution is given by all values of x greater than -5.

[tex]x <5[/tex]

The solution is given by all values of x greater than -5.

Then, the solution set is given by all real numbers.

Answer:

The solution is given by all real numbers.

Option C

The solution set for the given conditions corresponds to all real numbers between and inclusive of -5 and 5.

The given sets are {x | x > -5} U {x | x < 5}, which represents the union of numbers greater than -5 and numbers less than 5. Considering both conditions, the solution set encompasses all real numbers in between these two values, inclusive of -5 and 5. Therefore, the correct solution is All real numbers.

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Answer:

The Proof is given below.

Step-by-step explanation:

Given:

M is the Mid Point of HS and GT

To Prove:

Δ GMH ≅ Δ TMS

Proof:

In  Δ GMH and Δ TMS

M is the Mid Point of HS and GT ........{Given}  

     GM ≅ MT               ....……….{ M is the Mid Point of GT }

     HM ≅ SM               …………..{ M is the Mid Point of HS }

∠ GMH ≅ ∠ TMS         ....……….{ Vertical opposite angles are equal}

Δ GMH ≅ Δ TMS         ..........….{ By Side-Angle-Side test}  ...Proved

Answer:

7

Step-by-step explanation:

The point is reflected over the x-axis so we just need to look at the y-value.

The distance between the two points will be twice the y-value.

|3.5 * 2| = 7

Answer:

The System of equation are [tex]\left \{ {{3x+4y=44.50} \atop {4x+8y=84.00}} \right.[/tex]

Step-by-step explanation:

Let the Cost of bags of popcorn be 'x'.

Let the Cost of drinks be 'y'.

Given:

Kevin spends a total of $44.50 on 3 bags of popcorn and 4 drinks.

Now Total Money Spend by Kevin is equal to sum of Number of bags of popcorn multiplied by Cost of bags of popcorn and number of drinks multiplied by Cost of drinks.

framing in equation form with given details we get;

[tex]3x+4y=44.50[/tex]

Also Given:

Levi spends a total of $84.00 on 4 bags of popcorn and 8 drinks.

Now Total Money Spend by Levi is equal to sum of Number of bags of popcorn multiplied by Cost of bags of popcorn and number of drinks multiplied by Cost of drinks.

framing in equation form with given details we get;

[tex]4x+8y=84.00[/tex]

Hence The System of equation are [tex]\left \{ {{3x+4y=44.50} \atop {4x+8y=84.00}} \right.[/tex]

Answer:

angle b is 135 degrees

Step-by-step explanation:

lets work backwards to solve this

if angle c is 45, c is vertical to angle a, and we know vertical angles equal each other, we can reduce that angle a equals 45

if angle a is supplementary to angle b, and we know angle a is 45 degrees, we can make the equation 45+b=180. subtracting 45 from 180, we get 135 degrees for angle B

Answer:

b, d, and e

Step-by-step explanation:

The analysis, the following statements are true:

The line goes through the origin.

The line is sloping upward.

The x-intercept is 0.

The equation of the line using the point-slope form of a linear equation:

Point-slope form: y - y₁ = m(x - x₁),

where (x₁, y₁) is a point on the line, and m is the slope.

Given:

Point (x₁, y₁) = (-4, -3)

Slope (m) = 3/4

Substitute these values into the point-slope form:

y - (-3) = (3/4)(x - (-4))

y + 3 = (3/4)(x + 4)

Now, let's simplify this equation:

y + 3 = (3/4)x + 3

y = (3/4)x

This is the equation of the line.

Now, let's evaluate the statements:

The line is horizontal. (False)

The slope of the line is 3/4, which means it has a positive slope and is sloping upward.

The line goes through the origin. (True)

The line does not pass through the origin (0, 0) because its y-intercept is 3.

The point (3, 4) lies on the line. (False)

Let's substitute the coordinates (3, 4) into the equation:

y = (3/4)x

4 = (3/4)(3)

4 = 9/4

Since 4 ≠ 9/4, the point (3, 4) does not lie on the line.

The line is sloping upward. (True)

The slope is positive (3/4), so the line is indeed sloping upward.

The x-intercept is 0. (False)

To find the x-intercept, set y = 0 and solve for x:

0 = (3/4)x

x = 0

This shows that the x-intercept is 0.

Based on the analysis, the following statements are true:

The line is sloping upward.

The x-intercept is 0.

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Answer:

(0-4)/(1-k)= -2

-4/(1-k)= -2

-2(1-k)= -4

-2 +2k = -4

2k = -2

k = -1

(-1, 4)

y - 4 = -2( x + 1)

y - 4 = -2x - 2

y = -2x + 2

No, Sam is not correct. Cosine and sine are not always equal for congruent angles.

No, Sam is not correct. Congruent angles have the same measure, but cosine and sine are not always equal for congruent angles. Cosine measures the ratio of the adjacent side to the hypotenuse in a right triangle, while sine measures the ratio of the opposite side to the hypotenuse. These ratios are not the same in most cases, so cos X will not equal sin Y for congruent angles.