Please help me with these questions (It’s due tomorrow)

ira [324]

This would simplify to 6.60 meters/second.

8 0

2 years ago

A baker charges $30 for each batch of cupcakes she makes. She adds $0.09 for each frosting flower. Write an expression to repres

Lisa [10]

Answer:

$30+0.09x$

Here, $x$ denotes number of frosting flowers

Step-by-step explanation:

Let $x$ denotes number of frosting flowers.

Amount charged by baker for each batch of cupcakes = $30

Amount charged for each frosting flower = $0.09

So,

Amount charged for $x$ frosting flowers = $\$0.09x$

Therefore,

Total cost of a batch of cupcakes with frosting flowers = $30+0.09x$

8 0

2 years ago

Calculus: Help ASAP

wariber [46]

$\bf \displaystyle \int~\cfrac{sec^2(x)}{\sqrt{1+tan(x)}}\cdot dx\\\\
-------------------------------\\\\
u=1+tan(x)\implies \cfrac{du}{dx}=sec^2(x)\implies \cfrac{du}{sec^2(x)}=dx\\\\
-------------------------------\\\\
\displaystyle \int~\cfrac{\underline{sec^2(x)}}{\sqrt{u}}\cdot\cfrac{du}{\underline{sec^2(x)}}\implies \int~\cfrac{1}{\sqrt{u}}\cdot du\implies \int~u^{-\frac{1}{2}}\cdot du
\\\\\\
2u^{\frac{1}{2}}\implies 2\sqrt{1+tan(x)}+C$

6 0

2 years ago

Read 2 more answers

Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral

Stella [2.4K]

Answer:

a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus

b. The equation of the diagonal line AC is y = 5 - x

The equation of the diagonal line BD is y = 5 - x

c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other

Step-by-step explanation:

The vertices of the given quadrilateral are;

A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)

a. The length, l, of the sides of the given quadrilateral are given as follows;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

The length of side AB, with A = (1, 4) and B = (6, 6) gives;

$l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}$

The length of side BC, with B = (6, 6) and C = (4, 1) gives;

$l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}$

The length of side CD, with C = (4, 1) and D = (-1, -1) gives;

$l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}$

The length of side DA, with D = (-1, -1) and A = (1,4) gives;

$l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}$

Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus

b. The diagonals are AC and BD

The slope, m, of AC is given by the formula for the slope of a straight line as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Therefore;

$Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1$

The equation of the diagonal AC in point and slope form is given as follows;

y - 4 = -1×(x - 1)

y = -x + 1 + 4

The equation of the diagonal AC is y = 5 - x

$Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1$

The equation of the diagonal BD in point and slope form is given as follows;

y - 6 = 1×(x - 6)

y = x - 6 + 6 = x

The equation of the diagonal BD is y = x

c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;

The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs

The point of intersection of the two diagonals is given as follows;

5 - x = x

∴ x = 5/2 = 2.5

y = x = 2.5

The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.

5 0

3 years ago

Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? 1 m = 100 cm.

mart [117]

Answer:

Diego

Step-by-step explanation:

Diego is because 1m = 100 and Diego is 165 and that is alote bigger from 1.7.

8 0

3 years ago