question is down below thanks

In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

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The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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Answer:

centre = (5, - 6 ) , radius = 7

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )

x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )

x² - 10x + y² + 12y = - 12

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36

(x - 5)² + (y + 6)² = 49 = 7² ← in standard form

with centre (5, - 6 ) and radius = 7

Answer:

Center = (5, -6)

Radius = 7

Step-by-step explanation:

To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.

To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:

\(x^2-10x+y^2+12y=-12\)

Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:

\(x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2\)

Simplify:

\(x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2\)

       \(x^2-10x+25+y^2+12y+36=-12+25+36\)

       \(x^2-10x+25+y^2+12y+36=49\)

Factor the perfect square trinomials on the left side:

\((x-5)^2+(y+6)^2=49\)

The standard equation of a circle is:

\(\boxed{(x-h)^2+(y-k)^2=r^2}\)

where:

Comparing this with the rewritten given equation, we get

Therefore, the center of the circle is (5, -6) and its radius is r = 7.

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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If the electric potential is -2000 v at x = 8 m and is +400 v at x = 2 m, the magnitude of the electric field is 400 V/m.

The electric field is related to the electric potential by the formula:

E = -dV/dx

where E is the electric field, V is the electric potential, and x is the distance along the direction of the electric field.

Using the given values, we can find the change in electric potential over the distance from x = 8 m to x = 2 m:

ΔV = V₁ - V₀= 400 V - (-2000 V) = 2400 V

where , V₁  is final electric potential and V₀ is initial electric potential

We can also find the corresponding change in distance:

Δx = x₁  - x₀ = 2 m - 8 m = -6 m

Note that the negative sign indicates that the electric field points in the opposite direction to the direction of decreasing potential.

Then, we can use the formula for the electric field:

E = -dV/dx = ΔV/Δx = -2400 V / (-6 m) = 400 V/m

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Answer:

Goals of Union:maintain unity,maintain state sovereignty,defend home ground from enemy boost

Goals of Confederacy in Civil War: protect the institution of slavery,abolish slavery,international trade

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

:)

Answer:

30

Step-by-step explanation:

3 ten thousands/1 thousand=30

Answer:

Sure, here are the answers to your questions:

**A) The value of $f(-5)$ is $-2$.**

To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:

$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$

**B) The vertex of the parabola is $(2,6)$.**

To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:

$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$

Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:

$$f(x)=-2(x+2)^2-20$$

The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.

[Image of a parabola with vertex at (-2, -20)]

**C) The $y$-intercept is the point $(0,14)$.**

The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:

$$f(0)=-2(0)^2-8(0)+14=14$$

Therefore, the $y$-intercept is the point $(0,14)$.

**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**

To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:

$$-2x^2-8x+14=0$$

We can factor the left-hand side of the equation as follows:

$$-2(x-2)(x-3)=0$$

This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:

$$x=2\text{ or }x=3$$

However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:

$$x=2.5\text{ and }x=-3.5$$

Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.

Answer:

B

Step-by-step explanation:

y+4x=0

-y-2x=-2

2x=-2

x=-1

y+4(-1)=0

y-4=0

y=4

Answer:

Step-by-step explanation:

By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).

We can use the formula for compound interest to solve this problem. The formula is:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = the total amount in the account

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know the values for A, r, n, and t, so we can solve for P:

\(A = P(1 + r/n)^{(nt)\)

\(22,099.87 = P(1 + 0.022/2)^{(2*13)\)

\(22,099.87 = P(1.011)^{26\)

22,099.87 = 1.329P

P = 22,099.87 / 1.329

P = 16,637.55

Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

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Answer:

1/2d+c^2-b = 21

Step-by-st ep explanation:

= 1/2(10) + 5^2 -9

= 5 + 25 - 9

= 30 - 9

= 21

Answer:

8

Step-by-step explanation:

Because its a 2,2

A formula that gives the amount is

The half life of the element is calculated from the formula

N(t) = N'(1/2)^(t/t')

where

N(t) = quantity of the substance remaining

N' = initial quantity of the substance

t = time elapsed

t' = half life of the substance

Plugging the values from the problem

N(t) = ?

N' = 70 grams

t = t

t' = 2.6 years

N(t) = 70 (0.5)^t/2.6

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The value of "a" will be 30 for the given Algebraic expression.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, a algebraic expression 6a -4a +5a = 210

Simplifying the equation in terms of a

6a -4a +5a = 210

adding or subtracting the terms with the same variables

7a = 210

divide by 7 on both sides

a = 30

Therefore, the value of "a" will be 30 for the given Algebraic expression.

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a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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In both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

What is  Obtuse triangle?

Triangle B = Obtuse triangle

Triangle C = Obtuse triangle

in both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

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Answer:

96 in^2

Step-by-step explanation:

This is because u have to multiply the two bases and the lateral sides to get your area

Answer:

96

Step-by-step explanation:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces.

Area = l x w

4 x 4 = 16

16 x 6 = 96

The selling price of the item at 10% marlkup is $55

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Selling price = Cost To Store * (1 + Markup)

substitute the known values in the above equation, so, we have the following representation

Selling price = 50 * (1 + 10%)

Evaluate

Selling price = 55

Hence the selling price of the item is $55

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Answer:

4 = 1x

Step-by-step explanation:

(3x)9 = (4x)5

9 = (1x) 5

4 = 1x

Answer:

a=20

Step-by-step explanation:

7+13=20

20-7=13

Answer:

67.25

Step-by-step explanation:

Since they can each get 1/2 the jelly beans but need to eat it over 4 days they will be eating 1/2*1/4 jelly beans per day. This is equal to 1/8x where x is the total jelly beans. We know the total so we can plug 538 in for x and divide 538 by 8 to get 67.25

The range of a function f(a) = |a| - 3 is  {-3, -2, 0, 2} if the domain of a function is {–3, –1, 0, 5}.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(a) = |a| - 3

The domain =  {–3, –1, 0, 5}

Plug a = -3

f(-3) = |-3| - 3

f(-3) = 3 - 3 = 0

f(-1) = |-1| - 3 = -2

f(0) = 0 - 3 = -3

f(5) = |-5| - 3 = 5-3 = 2

The range = {-3, -2, 0, 2}

Thus, the range of a function f(a) = |a| - 3 is  {-3, -2, 0, 2} if the domain of a function is {–3, –1, 0, 5}.

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Answer:

use phythagoras formula of calculating right angles

a^2=b^2+c^2

42^2=b^2+78^2 (substitution + transposement)

b^2=72^2-42^2

b^2=3420 (introduce a square root both sides)

what you do on the left .you also do it on the right

b is the unknown side of the triangle

b=58.48 inched

The lengths of the legs of the right angle triangle is 30 inches and 72 inches.

A triangle is a closed plane figure formed by joining three noncolinear points.

We know Pythagoras's theorem which states the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given one leg of a right-angle triangle is 42 inches longer than the other leg.

Assuming the smallest leg to be x inches.

∴ The other leg is (x + 42) inches also given hypotenuse is 78 inches.

∴ (x + 42)² + x² = 78².

x² + 84x + 1764 + x² = 6084.

2x² + 84x - 4320 = 0.

x² + 42x - 2160 = 0.

As length can not be negative value of x = 30 inches.

∴ The smaller leg is 30 inches and the larger leg is (30 + 42) = 72 inches.

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hola i can help... all you have to do is grab a calculator and add 100 to each number, them sbract them by 302