Solve for t: 35t + 70 (7-t) = 385

Answer:

ΔABP is congruent to ΔBAQ

ΔABP ≡ ΔBAQ

Explanation:

We are given two triangles; ΔABP and ΔABQ

In these two triangles, we have:

AB as a common side

∠ABP = ∠BAQ

AQ = BP

We can conclude that these two triangles are congruent by SAS (side-angle-side) postulate which states that:

"When two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle, then the two triangles are congruent"

Note that when writing congruency statements, the order of the letters is critical as each angle/side in the first triangle must be congruent to its corresponding angle/side in the second triangle.

Based on the above, the congruency statement would be:

ΔABP is congruent to ΔBAQ

Hope this helps :)

Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.

The polar coordinate of any point can be written as:

(r, θ) = (r, θ + 2nπ)                                           --> when positive

 (r, θ) = [ - r, θ + (2n + 1)π ]                           --> when negative

 where n is any integer.

The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).

When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)

where n is any integer.

When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.

Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].

The polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

The coordinates of point p are given as:

p = (5, [tex]\pi[/tex]/3)

A point represented as (r, θ) has the following polar coordinates

(r, θ + 2n[tex]\pi[/tex]) for positive r, and (- r, θ + [2n + 1][tex]\pi[/tex]) for negative r

By comparing (r, θ) and (5, [tex]\pi[/tex]/3), we have:

r = 5

[tex]\theta = \pi/3[/tex]

So, we have:

(r,[tex]\theta[/tex]) = (r, [tex]\theta[/tex] + 2n[tex]\pi[/tex])

The equation becomes

(5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

Also, we have:

(-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

Hence, the polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])

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The measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.

Complementary angles are a pair of angles whose sum is always equal to 90°.

If A and B are complementary angles, then A + B = 90°.

In the question, we are asked to find the measure of each angle, given that the angles (5x)° and (4x - 18)° are complementary angles.

As we know that these angles are complementary, we can write the equation to solve for x as,

5x + (4x - 18) = 90

or, 5x + 4x - 18 = 90

or, 9x = 90 + 18 = 108

or, x = 108/9 = 12.

Therefore, the value of these angles are:

Therefore, the measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.

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Next step to isolate the variable is to divide by -3 .

Given,

-3x-9=-27

Firstly,

Add 9 to both side of the equation,

-3x-9+9=-27+9

-3x=-18

Now,

Divide -3 to each side

-3x/-3=-18/-3

x=6

Now,

Check:

-3x-9=-27

Substitute x with 6

-3(6)-9=-27

-18-9=-2

Thus, the next step to isolate the variable is to divide -3 to both side of equation.

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Answer:

The record ski jump for women is 360.89 feet.

Step-by-step explanation:

The record ski jump for women is 110 meters.

Record ski jump = 110 m

We need to find what is this length in feet.

We have the conversion 1 m = 3.28084 ft

Using the above conversion

We will get

             1 m = 3.28084 ft  

             110 m = 110 x 3.28084 = 360.89 ft

The record ski jump for women is 360.89 feet.

Answer:

Step-by-step explanation:

In order to solve this we just have to create a system of equations, because we have to unknown values, for the base salary we are going to use X and for the comission we will use Y, now we know that when she sold $400 in merchandise she earned $388 and and when she sold $100 se got paid $520 both equations would look like this:

[tex]x+400y=388\\x+1000y=520][/tex]

Now we can solve them by elimination, multiplying one function by -1.

[tex](-1)(x+400y=388)= -x-400y=-388\\x+1000y=388\\1000y-400y=132\\600y=388\\y=\frac{132}{600} \\y=0.22=22%[/tex]

Now we know that the percentage that she earns is 22% of the merchandise she sells.

Now to know how much does she makes on her base pay we just put the value into one of the functions:

[tex]x+1000y=520\\x+1000(.22)=520\\x+220=520\\x=300[/tex]

So her base pay is $300.

To calculate how much she will earn when she sells $3,300 in merchandise we just put that value into the formula:

[tex]x+3300y=\\300+3300(.22)\\300+726=1026[/tex]

So when she sells 3300 she will make 1026 total.

Answer: 2.5 inches.

Step-by-step explanation:

The given statement : Larry's dining room table measures five feet in diameter.

i.e. We are given that the diameter of Larry's dining room table = 5 feet

The scale used by him 1 inch =2 feet

i.e. [tex]\text{1 feet =}\dfrac{1}{2}\text{ inch}[/tex]

Now, [tex]\text{5 feet =}5\times\dfrac{1}{2}\text{ inches}=2.5\text{ inches}[/tex]

Therefore, the scale diameter he will use = 2.5 inches.

Final answer:

The center of the circumscribed circle about triangle EFG with given vertices is found by calculating the perpendicular bisectors of the triangle's sides and locating their intersection point, which is the center (8,3).

Explanation:

To find the center of the circumscribed circle about triangle EFG with vertices E(6,4), F(6,2), and G(10,2), we need to determine the perpendicular bisectors of at least two sides of the triangle and then find their intersection point, which will be the center of the circumscribed circle.

The Excel function you should use to find the lowest score in a series of test scores is the MIN function. It determines the smallest number in a set of values.

The Excel function that should be used to find the lowest score on a series of student test scores is the MIN function. This function allows you to determine the smallest number in a set of values. For instance, if you have the scores in cells A1 to A10, you would write the formula as =MIN(A1:A10).

It's important to note that the other options provided, such as median, sum, and dmin, would not accurately find the lowest score. The median would find the middle score, sum would add all the scores together, and dmin is a database function that extracts the smallest number from a selected database column based on the specified conditions.

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X=k/y

X=2, y=48

2=k/48

K=2*48 = 96

X= 96/24

X=4

Answer:

0.75

Step-by-step explanation:

Final answer:

The probability of drawing a red or blue marble from a bag containing 25 marbles (10 black, 13 red, 2 blue) is 3/5. This is calculated by dividing the total number of red and blue marbles (15) by the total number of marbles (25).

Explanation:

The question involves calculating the probability of drawing a red or a blue marble from a bag containing 25 marbles: 10 black, 13 red, and 2 blue. To find the probability of an event happening, we divide the number of ways that event can happen by the total number of outcomes. Here, the total number of marbles is 25.

The total ways to get a red or a blue marble is the sum of red and blue marbles, which is 13 (red) + 2 (blue) = 15. Therefore, the probability of drawing a red or blue marble is 15/25. Simplifying that fraction gives us 3/5.

The correct answer is 3/5. This calculation shows how to approach problems involving the probability of one event or another happening, especially when dealing with specific quantities.

linear increase would be something added to an equation.

 she started with 40,

she spent 10 on flip flops and also spent 15 of sunglasses those are decreases

she added 20 for allowance which is an increase and we can assume she gets the same amount of allowance every week

 so that would be the linear increase

Bentley had $40 in birthday money in her piggy bank. Bentley got $20 for her allowance which is represented by a linear increasing interval.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Bentley had $40 in birthday money in her piggy bank.

She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week.

Finally, she spent $15 on new sunglasses.

linear increase would be something added to an equation.

she started with $40 in her piggy bank.

She spent 10 on flip-flops and also spent 15 on sunglasses. This show decreases.

she added 20 for the allowance which is an increase and we can assume she gets the same amount of allowance every week.

So, that would be the linear increase.

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