Write the sentences below as a mathematical expression.

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 15 feet by 15 feet by 3 inches for a patio if

DerKrebs [107]

The answer is C. $95.83. To get the answer, you need to convert all units into yard first. Then, multiply all the given numbers having a result of 2.0827 cubic yards. Lastly, multiply the result to the concrete cost of $46. So the cost to pour a slab for a patio is $95.83.

8 0

3 years ago

A group of 19 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planeta

Paladinen [302]

The answer is all of the students are members of the frequent visitor program.

Let x be the number of students that are members of the frequent visitor program.
Let y be the number of students that are not members of the frequent visitor program.
There are in total 19 students: x + y = 19

x students will pay $11, y students will pay $13 for the ticket. Totally, it will be $209: 11x + 13y = 209

Now, we have the system of two equations:
x + y = 19
11x + 13y = 209
____________
Use the method of substitution:
x + y = 19
⇒ x = 19 - y
____________
11(19-y) + 13y = 209
11·19 - 11·y + 13y = 209
209 - 11y + 13y = 209
____________
Rearange:
13y - 11y = 209 - 209
2y = 0
⇒ y = 0

Since y = 0, x = 19:
x + y = 19
x + 0 = 19
x = 19
This means that all of the students in the group are members of the frequent visitor program.

3 0

3 years ago

In an orienteering competition, Jada walks 70 degrees north of west for 200 meters. She then walks due east for 90 meters. How f

soldi70 [24.7K]

The distance Jada is from starting point will be found using the cosine formula:
c²=a²+b²-2abCos C
a=200, b=90, C=70°
thus plugging in our values we get:
c²=200²+90²-2×200×90×cos70
c²=40000+8100-36000(0.3420)
c²=35788
hence
c=189.1772 m'
therefore the distance Jada is from the starting point is 189.1772 m

4 0

4 years ago

Read 2 more answers

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.

Allushta [10]

Answer:

The y-intercept of AB is y=4/3, the x-coordinate of the poit C is 4, the equation of the line that goes through BC is $6x-11=y$

Step-by-step explanation:

To find the y-intercept of AB we first have to find the equation of the line that goes through this segment.

We firt compute the slope of the segement which is given by

$m_1 = \dfrac{y_B - y_A}{x_B - x_A}= \dfrac{1-(-1)}{2-14} =\dfrac{-1}{6}$

Using this we can compute the equation of the line through AB using the point B=(2,1) and the formula

$\dfrac{-1}{6}=\dfrac{1-y}{2-x}$

we solve the last equation for $y$ and so we get

$y=\dfrac{-x}{6}+\dfrac{4}{3}$

The y-intercept of AB is the point in the line with x-coordinate equals to 0. Hence, the y-intercept is

$y(0) = \frac{-0}{6}+\frac{4}{3}=\frac{4}{3}$

Now, since the segments AB and BC are perpendicular, the slope of the line that goes through the segment BC is

$m_2 = -\dfrac{1}{m_1}=-\dfrac{1}{-\frac{1}{6}}=6$

Usinge the slope $m_2$ and knowing that the line goes through the point B=(2,1), to find the equation of the line through the segmen AC we use the following formula

$6=\dfrac{y-1}{x-2}$

we solve the equation for y and we get the equation

$y=6x-11$

Finally, to compute the x-coordinate of the point C we use the last equation and the fact that the y-coordinate is 13, it holds that

$13 = 6 x - 11 \quad \Rightarrow \quad x = \dfrac{13 + 11}{6}=\dfrac{24}{6}=4$

7 0

3 years ago

Read 2 more answers

Mrs. Amos's students understand fractions, and she is now working with them on the addition and subtraction of fractions. She mo

Mariulka [41]

Answer: ( d.)She is giving the students time to practice to promote their metacognition.

Step-by-step explanation:

Metacognition can be explained as one’s ability to use previous knowledge to plan a method for approaching a learning challenge, take adequate steps to solve the problem, look back on and evaluate gotten results, and modify one’s approach to the next challenge. It helps learners to be able to select the right cognitive tool for each task and plays a vital role in successful learning.

The teacher in the above question is only trying to improve her student's awareness of their own knowledge.

She is also building the students ability to think in order to solve future challenges they would face in mathematics.

5 0

4 years ago