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irga5000 [103]
2 years ago
5

Not including tax, a total of 19 pens and markers cost $11.50. The pens cost $0.25 each, and the markers cost $0.75 each. Which

system of equations could be used to solve for the number of pens (p) and the number of markers (m) bought?
Mathematics
1 answer:
trapecia [35]2 years ago
7 0

Answer:

The system of equations would be:

p + m = 19

0.25p + 0.75m = 11.50

Step-by-step explanation:

To set up a system of equations, use the total number purchased as the first equation.

p + m = 19

Now use the cost and the total spent for the second equation.

0.25p + 0.75m = 11.50

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If AD and BD are bisectors of CAB and CBA respectively. Find the sum of angles x and y.
olchik [2.2K]
The picture in the attached figure

step 1
we know that
It is given that AD and BD are bisectors of ∠CAB and ∠CBA respectively.
Therefore,
x = ∠CAB/2 -----> equation 1
y = ∠CBA/2 -----> equation 2

step 2
In triangle ABC,
∠CAB + ∠CBA + ∠ACB = 180° ----> [The sum of all three angles of a triangle is 180°]
∠CAB + ∠CBA + 110° = 180°
∠CAB + ∠CBA = 180° - 110°
∠CAB + ∠CBA = 70° ------> divide by 2 both sides
∠CAB/2 + ∠CBA/2 = 70/2 -------> equation 3
substitute equation 1 and equation 2 in equation 3
x+y=35

hence

the answer is
x+y =35°
⇒ x + y = 35° ...[From equation (1) and (2)]

5 0
2 years ago
Michael is shipping his mother's birthday gift to her in a rectangular box. If the gift's dimensions are 2 inches long by 5 inch
stepan [7]

Answer:

112

Step-by-step explanation:

4 0
2 years ago
Solve for x in the equation ? 2x^2 +3 x-7 =x^2 +5x +39
otez555 [7]

Answer:

1 ± √47

Step-by-step explanation:

Combine like terms in 2x^2 +3 x-7 =x^2 +5x +39:

2x^2 - x^2 = x^2 (first term);

3x - 5x = -2x (second term);

-7 - 39 = -46 (third term)

Then we have, all on the left side, x^2 - 2x - 46, which is a quadratic equation.  Here the coefficients are a = 1, b = -2 and c = -46.

Then the discriminant, b^2 - 4ac, is:

(-2)^2 - 4(1)(-46) = 4 + 184.

The roots are:

     -(-2) ±√188         2 ± √4√47

    ------------------- = -------------------

              2                         2

                             = 1 ± √47 (last of the answer choices)

=

x = ------------------

3 0
2 years ago
Set up a double integral for calculating the flux of the vector field F⃗ (x,y,z)=xi⃗ +yj⃗ through the open-ended circular cylind
katrin [286]

Parameterize the cylinder (call it S) by

\vec s(\theta,z)=\sqrt8\cos\theta\,\vec\imath+\sqrt8\sin\theta\,\vec\jmath+z\,\vec k

with 0\le\theta\le2\pi and 0\le z\le9. Then

\vec F(x(\theta,z),y(\theta,z),z(\theta,z))=\sqrt8\cos\theta\,\vec\imath+\sqrt8\sin\theta\,\vec\jmath

Take the normal vector to S to be

\vec s_\theta\times\vec s_z=\sqrt8\cos\theta\,\vec\imath+\sqrt8\sin\theta\,\vec\jmath

Then the flux of \vec F across S is

\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(\theta,z),y(\theta,z),z(\theta,z))\cdot(\vec s_\theta\times\vec s_z)\,\mathrm dz\,\mathrm d\theta

=\displaystyle\int_0^{2\pi}\int_0^98(\cos^2\theta+\sin^2\theta)\,\mathrm dz\,\mathrm d\theta=\boxed{144\pi}

7 0
2 years ago
Jada is making lasagna and pizzas for a party recipe calls for 1 1/4 cups and she uses 1/2 she doubled her recipe and made 5 piz
grigory [225]

This question is not correctly written

Complete Question

Jada is making lasagna and pizzas for a large party. Her lasagna recipe calls for 1 1/4 cups of tomato paste, and her pizza recipe uses 1/2 cup of tomato paste per pizza. She will double her lasagna recipe and make 5 pizzas. Write and evaluate an expression for how many 3/4- cup cans of tomato paste she will need in all.

Answer:

The evaluate and for how many 3/4-cup cans of tomato she need in all is 20/3

Step-by-step explanation:

Step 1

From the question, we are told that:

1 single lasgna recipe uses: 1 1/4 cups of tomato paste = 5/4 cups

If she doubles her recipe, the number of cups of tomato paste =

2 × 5/4 cups of tomato paste

= 10/ 4 = 5/2 cups of tomato pastes

Step 2

From the question, we are told that:

1 Pizza recipe = 1/2 cup of tomato pastes

5 Pizza =

5 × 1/2 cup of tomato paste

= 5/2 cups of tomato paste

Steps 3

The total number of cups of tomato paste Jada will use in making double lasagna and 5 pizzas is calculated as

= 5/2 + 5/2

= (5 + 5)/ 2

= 10/2

= 5 cups.

Step 4

We are asked to evaluate how many 3/4 -cup cans of tomato she need in all.

This means we should find how many 3/4 - cup cans can be found in the total number of cups of tomato paste that Jada used.

Total number of cups that Jada used = 5 cups of tomato paste

The number of 3/4-cup cans in 5 cups is calculated as:

5 ÷ (3/4)

= 5 × 4/3

= 20/3

Therefore, the evaluate and for how many 3/4-cup cans of tomato she need in all is 20/3

8 0
2 years ago
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