When multiplying or dividing integers, if the signs are the same, you keep the sign for the answer

False

True

Answer:

D. 127.5 square units

Step-by-step explanation:

AC=17

BD=15

AB=11.5

Diagonal (1&2) are given, base of the rhombus is also given.

Height is not given

Area of a rhombus given the diagonals

=1/2×d1×d2

Where,

d1=AC=17

d2=BD=15

Area of a rhombus=1/2×d1×d2

=1/2×17*15

=1/2×255

=127.5

D. 127.5 square units

Answer:

D for sure

Step-by-step explanation:

Answer:

slope m=1/7

Step-by-step explanation:

x-7y=-6

-7y=-x-6

y=-x/-7 -6/-7

y=1/7 x+6/7

Answer:

a) 60 degrees

Step-by-step explanation:

b) The triangle shown is an equilateral triangle as all the sides are the same. This means that all the angles are the same as well.

Angles in a triangle add up to 180 degrees. There are 3 angles. Each angle is 60 degrees.

Angle x is an exterior corresponding angle and hence, that is why x = 60 degrees.

Answer:

All of the measures of the interior angles of an equilateral triangle are 60°. Because x and 60° are alternate interior angles of parallel lines, this means that they are equal, therefore x = 60°.

Answer:

PEMDAS DAT

Step-by-step explanation:

Answer:

x = 19.

Step-by-step explanation:

By the tangent - secant theorem:

BD^2 = AB * EB

so:

8^2 = (x - 7 + 4) * 4

4(x - 3) = 64

4x - 12 = 64

4x = 64 + 12 = 76

x = 76/4

= 19.

Answer: 28

Step-by-step explanation:

The shape is grouped into 4 identical parallelograms.  

Thus, as the combined area of the figure is 308, you can divide 308/4 to get 77.  Thus, each parallelogram has an area of 77.

Then, divide 14/2 to get that the height of each parallelogram is 7.  

The area of a parallelogram is l*w.  Thus, because l = 7, each parallelogram has a width of 11 because 77/7 = 11.  

Then, simply add 11+11+6 to get y.

Hope this helps <3

Answer:

Step-by-step explanation:

Confidence interval for population proportion is expressed as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

From the information given,

Sample proportion, p = 65/100 = 0.65

q = 1 - 0.65 = 0.35

n = 200

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96

Margin of error = 1.96√(0.65)(0.35)/200

Margin of error = 0.066 = 6.6%

The maximum boundary of the interval is

0.65 + 0.066 = 0.716

Answer:

7.5 mL

Step-by-step explanation:

If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.

Answer:

12 meters

Step-by-step explanation:

Draw a picture of the two pathways 30° apart.  Add a circle representing the illumination of the light on one of the pathways.  Draw a line from the center of the circle to the last point where it intersects the pathway without lights.

This forms a triangle.  One leg is x, the length of the pathway without lights.  Another leg is 5n, where n is an integer.  This represents how far the light is from where the pathways meet.  The third and final leg is 6, the radius of the illumination.

Use law of cosine to solve:

6² = x² + (5n)² − 2x(5n) cos 30°

36 = x² + 25n² − 5√3 xn

0 = x² − 5√3 xn + 25n² − 36

In order to have a solution, the discriminant must be greater than or equal to 0.

b² − 4ac ≥ 0

(-5√3 n)² − 4(1)(25n² − 36) ≥ 0

75n² − 100n² + 144 ≥ 0

144 − 25n² ≥ 0

144 ≥ 25n²

144/25 ≥ n²

12/5 ≥ n

So n must be an integer less than 12/5, or 2.4.  Therefore, the largest value of n is 2.  Substituting:

0 = x² − 5√3 x(2) + 25(2)² − 36

0 = x² − 10√3 x + 64

Solve with quadratic formula:

x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)

x = (10√3 ± √44) / 2

x = 5√3 ± √11

x ≈ 5.34 or 11.98

We want the larger value of x.  So approximately 12 meters of the pathway without lights is illuminated.

Answer:

4 AND 2

Step-by-step explanation:

Answer:

Hello!

______________________

This question is very easy.

2 + 2 = 4

1 + 1 = 2

Step-by-step explanation: Add.

Hope this helped you!

Answer:

Option D is correct.

The equation with roots 3 plus or minus square root 2 is x² - 6x + 7

Step-by-step explanation:

The roots of the unknown equation are

3 ± √2, that is, (3 + √2) and (3 - √2)

The equation can then be reconstructed by writing these roots as the solutions of the quadratic equation

x = (3 + √2) or x = (3 - √2)

The equation is this

[x - (3 + √2)] × [x - (3 - √2)]

(x - 3 - √2) × (x - 3 + √2)

x(x - 3 + √2) - 3(x - 3 + √2) - √2(x - 3 + √2)

= x² - 3x + x√2 - 3x + 9 - 3√2 - x√2 + 3√2 - 2

Collecting like terms

= x² - 3x - 3x + x√2 - x√2 - 3√2 + 3√2 + 9 - 2

= x² - 6x + 7

Hope this Helps!!!

Answer:

a= 5    and   b=1

Step-by-step explanation:

To solve, we will follow the steps below:

2x + 3y = 7

(a-b)x + (a+b)y = 3a + b - 2​

We should note that since it has infinitely many solutions then,

[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]

Hence

2/a-b  =  3/a+b   =     7/3a +b-2

2/a-b  =  3/a+b

cross-multiply

3(a-b) = 2( a+b)

open the bracket

3a - 3b = 2a + 2b

collect like term

3a - 2a = 2b + 3b

a = 5b  -------------------------------------------(1)

Similarly

3/a+b   =     7/3a +b-2

cross-multiply

7(a+b)  = 3(3a+b -2)

7a + 7b = 9a + 3b -6

take all the variables to the left-hand side of the equation

7a - 9a+ 7b-3b =   -6

-2a + 4b = -6 ---------------------------------(2)

but a = 5b

substitute a= 5b in equation (2)   and solve for b

-2(5) + 4b = -6

-10  +  4b  = -6

add 10 to both-side of the equation

-10  + 10+ 4b  = -6+10

4b = 4

divide both-side of the equation by 4

b = 1

substitute b= 1 in equation (1)

a = 5b

a =5(1)

a=5

Therefore,   a= 5    and   b=1

Answer:

Area = 147.03 cm²

Step-by-step explanation:

Area of parallelogram = [tex]Base*Heigth[/tex]

Where base = 16.9 cm, Height = 8.7 cm

Area = 16.9*8.7

Area = 147.03 cm²

Answer:

147.03 square cm

Step-by-step explanation:

[tex]area \: of \: parallelogram \\ = base \times height \\ = 16.9 \times 8.7 \\ = 147.03 \: {cm}^{2} \\ [/tex]

Answer:

5/18

Step-by-step explanation:

Let's say the original packaging was 1 lb of packaging for $1.

The cost was $1/lb.

Then the weight went down by 10% and the price went up by 15%.

Now 0.9 lb of packaging cost $1.15.

The new unit cost is $1.15/(0.9 lb)

The difference is

$1.15/(0.9 lb) - $1/lb =

= $1.15/(0.9 lb) - $0.9/(0.9 lb)

= $0.25/(0.9 lb)

=$25/(90 lb) = $5/(18 lb)

The price went up by 5/18.

Answer:

Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.

Step-by-step explanation:

Sea x el precio de los perros calientes y y el precio de las hamburguesas.

Escribiendo los datos de la primera familia en forma de ecuación tenemos:

[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)

Escribiendo los datos de la segunda familia:

[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)

Vamos a resolver este sistema de ecuaciones por el método de suma y resta:

[tex]4x+3y=43,000\\5x+y= 34,500[/tex]

Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:

[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]

Por lo tanto, un perro caliente cuesta 5,500 pesos.

Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:

[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]

Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una

Answer:

x = 4

x = -10

Step-by-step explanation:

(x + 3)² = 49

Take the square root of both sides.

x + 3 = ±7

The equation is x + 3 = 7 or x + 3 = -7.

x + 3 = 7

Subtract 3 on both sides.

x = 4

x + 3 = -7

Subtract 3 on both sides.

x = -10

Answer:

x₁ = -10

x₂ = 4

Step-by-step explanation:

(x + 3)² = 49

x + 3 = ± 7

x + 3 = -7 → x = -10

x + 3 = 7 → x = 4

Hope this helps! :)

Answer:

5/9

Step-by-step explanation:

There are 9 total combinations and 3 of them include a burger, 2 of them that have salad but not a burger. If you add them together it equals 5/9

The probability of selecting a combination that includes a burger or a salad is 5/9

Since the total of 6 outcomes include fries or fruit as the side dish.

There is a total of 9 possible meal combinations. A person must choose an Entree and a side dish.

The Entrees consist of burgers, tacos, and pizzas.

The side dishes consist of salad, fries, and fruit.

To find the number of combinations consisting of fries or fruit, we calculate the individual combinations.

With fries as side dish, which can choose a burger, a pizza or a taco as your Entree.

There are 3 combinations each, there are a total of 6 combinations with fruit or fries as the side dish.

There are 9 total combinations and 3 include a burger, rest 2 that have salad but not a burger.

then probability = 5/9

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ2

Answer:

Angle B is the answer

(V.O.A) means vertically opposite angle.

Answer:

Around 10/3 or 3.33 times farther.

Step-by-step explanation:

We simply divide the larger distance by the smaller distance to find our ratio:

2(10⁸)/6(10⁷)

10/3

*Remember when you divide exponents, you subtract them

Answer:

4 lb

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

The ratio of 1:3 mean that one part is 1 to the other part being 3.

That means the total is 1 + 3 = 4.

1 part to 3 parts is the same as 1 part to a whole of 4 and 3 parts to a whole of 4.

Answer: 3rd option

Answer:

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

Step-by-step explanation:

I like to call the numbers in the ratio 1 : 3 "ratio units".

That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).

_____

Coment on the answer wording

I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".

In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."

Answer:

115/5 23 so 20% =23 23x4 =92

Answer:

x = -12

Step-by-step explanation:

-10x+1+7x=37

Combine like terms

-3x+1 = 37

Subtract 1 from each side

-3x+1-1 = 37-1

-3x = 36

Divide by -3

-3x/-3 = 36/-3

x = -12

Answer:

√3 + 1

Step-by-step explanation:

Step below are self-explanatory

Answer:

x=-20 or x=68

Step-by-step explanation:

you can either make it so 47 remains the largest number and so take 67 from 47 (=-20) or you can leave 1 as the smallest number and add 67 to 1 (=68)

I know you don't need this anymore but for the ones who do this is the answer.........Look at the graph and trust it. Yes, I know it says to substitute and you can following the last page on part a) Doing what they do in the tables and it will get you the same answer as if you'd just look at the graph.

The answer for the y- value at x=p IS 8. and the answer for the y-value at x=p+k IS 5. So go ahead and write that down if you haven't already!

For step2 Find the difference between the endpoints of the interval on the y-axis. The answer to your question, Is and always will be 3! The difference is 3 because you subtract 3 from 8 and you get 5.

If you didn't read clearer, I'll write it for you again, The length interval is K, it is the length between p and p+k.

For the following questions, does your answer to step 2 depend on p, well I suppose. This is why....The answer does depend on p because we are dealing with a slope. if you move up or down the slope it will not be the same.

For the question..... Is the difference between the y-values the same regardless of where the interval starts? The answer is yes!!! And No!!! But WRITE YES! Why? Because if the interval moves as a whole the difference between the y-values is the same! Try it for yourself. Move K back two x-values and the difference for the y-values will be the same, IT WILL STILL BE THREE.

Hope you understood!

And for part one the answer on part c (-2). It depends on K.

Answer:

e.29 d.1

Step-by-step explanation:

we will replace with the values we have :