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2 years ago

Find the values of X and Y in the parallelogram.

Mathematics

1 answer:

galben [10]2 years ago

6 0

Answer: x=-5, y=20

Step-by-step explanation:

Opposite sides of a parallelogram are congruent, so AB=CD.

$x^{2}-15=-2x\\x^{2}+2x-15=0\\(x+5)(x-3)=0\\x=-5, 3$

But as distance must be positive, as CD=-2x, x must be negative, so x=-5.

Opposite angles of a parallelogram are congruent, so $m\angle D=m\angle B$ .

$4y+26=106\\4y=80\\y=20$

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The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than

svlad2 [7]

The shop sold 36 sundaes and 28 banana spilts

Solution:

Let "a" be the number of sundaes sold

Let "b" be the number of banana spilts sold

Cost of 1 sundaes = $ 2

Cost of 1 banana spilt = $ 3

On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156

Therefore,

Number of sundaes sold = 8 + number of banana spilts sold

a = 8 + b ------- eqn 1

Also, given that they made $ 156

Therefore, we frame a equation as:

Number of sundaes sold x Cost of 1 sundaes + number of banana spilts sold x Cost of 1 banana spilt = 156

$a \times 2+b \times 3 = 156$

2a + 3b = 156 ---------- eqn 2

Substitute eqn 1 into eqn 2

2(8 + b) + 3b = 156

16 + 2b + 3b = 156

16 + 5b = 156

5b = 156 - 16

5b = 140

Substitute b = 28 in eqn 1

a = 8 + 28

Thus the shop sold 36 sundaes and 28 banana spilts

4 0

4 years ago

Order the following values from least to greatest. 25 -14 _-4 21

Vikki [24]

-14
-4
21
25
Least to greatest.

7 0

3 years ago

Read 2 more answers

Sammy wants to deposit into a 7% annual simple interest account she will also deposit twice as much in a certificate of deposit

antiseptic1488 [7]

Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.

Step-by-step explanation:

Let x represent the amount that he would deposit in the simple interest account.

Let y represent the amount that he would deposit in the certificate of deposit.

she will deposit twice as much in the certificate of deposit. It means that

y = 2x

Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x

Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.

The total interest from both accounts would be $390. It means that

0.07x + 0.05y = 390- - - - - - - - - - 1

Substituting y = 2x into equation 1, it becomes

0.07x + 0.05 × 2x = 390

0.07x + 0.1x = 390

0.17x = 390

x = 390/0.17 = $2294

y = 2x = 2 × 2294

y = 4588

4 0

3 years ago

What is the value of the exponential expression below?

7nadin3 [17]

The square root of 64 is 8 but put 8 to the 1/2 power
The answer is 4

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3 years ago

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I have these factoring questions I need help with.

snow_lady [41]

$f(x)=4x^2+4x-3$

1. Determine y-intercept.

The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.

2. Determine the zeros.

Factor the polynomials first. $(2x-1)(2x+3)$ This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2

3. Determine the Axis of Symmetry

We can solve this by using the formula of $x=-\frac{b}{2a}$ However, I'll be solving the Axis of Symmetry with Calculus instead.

$f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4$

Then let f'(x) = 0 to find the Axis of Symmetry.

$8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}$

Therefore, the Axis of Symmetry is -1/2

4. Determine the vertex.

Substitute the value of Axis of Symmetry in f(x).

$f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4$

Therefore the vertex is at (-1/2, -4)

5. Does the vertex representing max-pont or min-point?

The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE.

7. Graph f(x)

Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).

--------------------------- End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

$y=ax^2+bx+c$

The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is.

For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.

3. Write in Factored Form

$y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)$

These are factored forms with different types of operators.

The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)

4. Write in Vertex Form.

$y=a(x-h)^2+k$

The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.

The vertex is at (h,k) and the axis of symmetry is at x = h.

For example, $y=(x-2)^2+3$

The vertex would be at (2,3) and the axis of symmetry is x = 2.

3 0

3 years ago