Question 1
[tex]\text{Evaluate x}^2\text{ + 5x - 8 for x = 2}[/tex]Substitute x in the expression
[tex]\begin{gathered} =2^2\text{ + 5 }\times\text{ 2 - 8} \\ =4\text{ + 10 - 8} \\ =14\text{ - 8} \\ =6 \end{gathered}[/tex]Examples: Find the area of the following figures.1.6cm10cm7cm4cm
The figure below is a Trapezium.
Let's write out the formula for the area of a trapezium,
[tex]\text{Area of a trapezium=}\frac{1}{2}(a+b)h[/tex]1) Let us write out the data given in the first figure,
[tex]\begin{gathered} a=7\operatorname{cm} \\ b=10\operatorname{cm} \\ h=4\operatorname{cm} \end{gathered}[/tex]Let us solve for the area of the figure,
[tex]\begin{gathered} \text{Area of the trapezium=}\frac{\text{1}}{2}(7+10)\times4 \\ =\frac{1}{2}(17)\times4 \\ =34cm^2 \end{gathered}[/tex]The area of the trapezium is 34cm².
Part EWhat is a possible explanation for why the y-intercept is negative for all three functions?
In this problem
x -----> number of meals sold
y ----> profit
Remember that
the y-intercept is the value of y, when the value of x is zero
In this context
the y-intercept is the value of the profit when the restaurant begin or start to sell meals
In this case, the y-intercept is negative, which means when the restaurant started, there have a negative profit (loss) {the cost is greater than the revenue) because the number of meals sold is zero.
Answer:
The restaurants incur costs to prepare meals, such as labor and supplies, before any meals are sold. So, the restaurants will lose money until they sell a number of meals equal to the first x-intercept.
Step-by-step explanation:
Edmentum
can you please give me some more information about this
We can see that the segment is defined by the points (-5, 5) & (-3, -4).
Now, we calculate the mid-point by using the following expression:
[tex]mp=(\frac{x_2-x_1}{2},\frac{y_2-y_2}{2})[/tex]So, now we replace:
[tex]mp=(\frac{-5-(-3)}{2},\frac{-4-5}{2})\Rightarrow mp=(-1,\frac{1}{2})[/tex]So, the mid point is (-1, 1/2).
The shore, a rope, and a dock that is 8 meters long enclose a rectangular swimming area along thelakeshore. The length of swimming area is 6 meters more than its width and the swimming area must bemore than 180 square meters. If the rope is 34 meters long, then what are the dimensions of theswimming area?
So we have two conditions, the first one is that the length (L) of the swimming area is 6 meters more than the width (W) so:
[tex]L=6W[/tex]and the other condition is that the area is 180 square meters so we can writte it like:
[tex]180=L\cdot W[/tex]Now we have 2 equations and 2 ingognitas so we can replace the first equation into the second equation like this:
[tex]180=(6W)\cdot W[/tex]and we solve for W so
[tex]\begin{gathered} 180=6W^2^{} \\ W^2=\frac{180}{6}=30 \\ W=\sqrt[]{30}=5.5 \end{gathered}[/tex]Now with the value of W we can replace it in the first equation so:
[tex]L=6(5.5)[/tex]so:
[tex]L=33[/tex]The dimensions are:
[tex]\begin{gathered} \text{length}=33m \\ \text{width}=5.5m \end{gathered}[/tex]indentify the coordinates of the reflected figure across the y-axis?
to write coordinates you need see x firts and y late and write
the A point is
[tex](2,5)[/tex]because is 2 on x and 5 on y
The B point
[tex](7,5)[/tex]The C point
[tex](7,2)[/tex]The D point
[tex](2,2)[/tex]to reflect across Y you need to change the sign of x or the first term on the coordinate
so
A'
[tex](-2,5)[/tex]B'
[tex](-7,5)[/tex]C'
[tex](-7,2)[/tex]D'
[tex](-2,2)[/tex]what are all the possible causes of x that satisfy x/4+8>24?
Answer : x > 64
Given that
x / 4 + 8 > 24
[tex]\begin{gathered} \frac{x}{4}\text{ + 8 > 24} \\ \text{Firstly, we n}eed\text{ to find the common denominator} \\ \frac{x\text{ + 32}}{4}\text{ > 24} \\ \text{Cross multiply} \\ \text{x + 32 > 24 }\cdot\text{ 4} \\ \text{x + 32 > 96} \\ \text{Isolate x} \\ x\text{ > 96 - 32} \\ x\text{ > 64} \end{gathered}[/tex]The quotient of 18 and anumber x Answer
Answer:
Step-by-step explanation:
is 1/8 greater than 18%
Consider than 18% in decimal is 0.18.
Next, take into that 1/8 = 0.125
0.18 is great
The half life of iodine-131 is 7.2 days. If you start with 80 milligrams of iodine-131, how much of the substance will remain after 36 days?
Given
The half-life of iodine-131 is 7.2 days. If you start with 80 milligrams of iodine-131, how much of the substance will remain after 36 days?
Solution
[tex]\begin{gathered} 0.5=e^{-7.2k} \\ \ln 0.5=-7.2k \\ \text{divide both sides by -7.2} \\ \\ \frac{\ln 0.5}{-7.2}=-\frac{7.2k}{-7.2} \\ \\ k=0.09627044174 \\ \end{gathered}[/tex][tex]\begin{gathered} A=80e^{-kt} \\ A=80e^{-0.09627044174(36)} \\ A=2.5\text{miligrams} \end{gathered}[/tex]2.5 milligrams will remain after 36 days
this figure us a square, with side lengths as shown
The profit y in dollars) for a business from selling x gloves is represented by y = 21x. Graph the equation.
The equation is:
[tex]y=21x[/tex]To graph that equation, as it is a equation for a line, you need to find the coordinates (x,y) for two points on the line.
To find a point on the line you give for one of the variables a value and calculate the value of the other variable with the equation.
If x= 5
[tex]\begin{gathered} y=21(5) \\ y=105 \end{gathered}[/tex]Then, when x=5 y=105. The first point have coordinates (5, 105)
If y= 0
[tex]\begin{gathered} 0=21x \\ \frac{0}{21}=x \\ x=0 \end{gathered}[/tex]Then, when y=0 x=0. The second point have coordinates (0, 0)
You put that points in the plane:
Draw a line that passes through taht points:
[tex]6 \sqrt{72} [/tex]Simplify in simplest form:
we have:
[tex]\frac{6}{\sqrt[]{72}}[/tex]first, we can multiply and divide by sqrt{72} (to get the sqrt of the denominator)
[tex]\frac{6}{\sqrt[]{72}}\cdot\frac{\sqrt[]{72}}{\sqrt[]{72}}=\frac{6\sqrt[]{72}}{(\sqrt[]{72)^2^{}}}=\frac{6\cdot\sqrt[]{72}}{72}[/tex]now we can simplify sqrt{72} writing 72 as 2*36
[tex]\frac{6\cdot\sqrt[]{36\cdot2}}{72}=\frac{6\cdot\sqrt[]{36}\cdot\sqrt[]{2}}{72}=\frac{6\cdot6\cdot\sqrt[]{2}}{72}=\frac{\sqrt[]{2}}{2}[/tex]So the answer is:
[tex]\frac{\sqrt[]{2}}{2}[/tex]A drone that costs $129.50 is discounted 40%. the next month,the sale price is discounted and additional 60%. is the drone now free .if the drone is free please explain.if the drone is not free what is the sales price?
We have an original price of $129.50.
Then, the price is discounted 40%. After that, the price is discounted 60%.
We can think of this discount in steps:
1) the first discount of 40% means that the new price is 100%-40% = 60% of the original price:
[tex]P^{\prime}=(\frac{100-40}{100})\cdot P=0.6\cdot P[/tex]2) The second discount of 60% means that the new price is 100%-60% = 40% of the already discounted price:
[tex]P^{\prime\prime}=(\frac{100-60}{100})P^{\prime}=0.4\cdot P^{\prime}=0.4\cdot(0.6P)=0.24\cdot P[/tex]Then, the final price after the two discounts is 24% of the original price:
[tex]P^{\prime\prime}=0.24\cdot P=0.24\cdot129.50=31.08[/tex]Answer: The drone is not free. The final price of the drone is $31.08.
Iron and Steel carries a $564,800 inventory. The company estimates the annual cost of carrying the inventory at 27 percent of the value of the inventory. What is the approximate annual cost of carrying the inventory?
The 27% of $564800 is $152496 therefore, the approximate annual cost of carrying the inventory is $152496.
What is the percentage?The percentage is also called the indicating hundredths.
The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
As per the given,
Value of the inventory = $564800
The annual cost of carrying the inventory = 27% of 564800
It is known that x% of y is given by (x/100)y
Therefore,27% of 564800 will be,
⇒ (27/100) × 564800
⇒ $152496
Hence "The 27% of $564800 is $152496 therefore, the approximate annual cost of carrying the inventory is $152496".
For more about the percentage,
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plot the solution of the equation on the number line
Answer:
Explanation:
Given the equation:
[tex]7x+7=-14[/tex]First, subtract 7 from both sides:
[tex]\begin{gathered} 7x+7-7=-14-7 \\ 7x=-21 \end{gathered}[/tex]Next, divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}=-\frac{21}{7} \\ x=-3 \end{gathered}[/tex]The solution of the equation on the number line is shown below:
Suppose that the functions and g are defined for all real numbers x as follows f(x) = 3x + 5; g(x) = x + 4 Write the expressions for (f + g)(x) and (fg)(x) and evaluate (f - g)(1) .
Answer:
(f + g)(x) = 4x + 9
(fg)(x) = 3x² + 17x + 20
(f - g)(x) = 2x + 1
Explanation:
We know that
f(x) = 3x + 5
g(x) = x + 4
Then, we can find (f + g)(x) as follows
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (3x + 5) + (x + 4)
(f + g)(x) = 3x + 5 + x + 4
(f + g)(x) = 4x + 9
In the same way, we can calculate (fg)(x) and (f - g)(x) as follows
(fg)(x) = f(x)g(x)
(fg)(x) = (3x + 5)(x + 4)
(fg)(x) = 3x(x) + 3x(4) + 5(x) + 5(4)
(fg)(x) = 3x² + 12x + 5x + 20
(fg)(x) = 3x² + 17x + 20
(f - g)(x) = f(x) - g(x)
(f - g)(x) = (3x + 5) - (x + 4)
(f - g)(x) = 3x + 5 - x - 4
(f - g)(x) = 2x + 1
Therefore, the answers are
(f + g)(x) = 4x + 9
(fg)(x) = 3x² + 17x + 20
(f - g)(x) = 2x + 1
Divide 180 into two parts such that the first part is 12 less thantwice the second part.a 100, 80b 90,90c 116, 64d 99. 81
You can find a math expression dividing the statment as follow:
Divide 180 into two parts such that: x and y
the first part: X
is 12 less than: X= -12
twice the 2(
second part: Y
the first (X) part is 12 less than twice the second part (Y):
X=2Y-12
what is the equation of the line that passes through the point[tex]( - 3 - 11)[/tex]y=2x-4
Answer
To check if a line passes through a point replace x in the equation
For example:
y= 2x-4
replacing
y = 2*( -3) -4
y= -6-4
y = -10
So then y= 2x-4 passes through the point (-3, -10)
tell whether each point is on the graph of y=3x squared minus 5
From the above explanation, the value of y gotten from the function when x = -3 does not match with the value given
Prior to making deposits of $75 and $50 Marian had a balance of $102in her checking account. How much must she deposit so that her balance winbe at least $300 and she can avoid a service fee
Marian had a balance of $102
Then she made two deposits, one of $75 and the other for $50
We can calculate the balance of her checking account after the deposits were done
New balance = $102 + $75 + $50 = $227
The account needs to have at least $300 to avoid a service fee, so we calculate how much is needed to complete that amount
New deposit = $300 - $227 = $73
So, if Marian deposits at least $73, the account balance will be $300 or more
Answer: She must deposit at least $73
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:1.7 * 10^5 m
Step-by-step explanation:
move the numbers to the blanket to order them from least to greatest value.
The given numbers from least to greatest are
• 1 - 21 = -20
,• -0.89
,• 0.4
,• 0.5
,• 9/8 = 1.125
To order the number from least to greatest, we just have to know the value of each one. For example, 1 - 21 equals -20, this will be the least number because it has the greatest absolute value as a negative number. Then, we have -0.89, which is greater than -20. And so on.
Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 11? (b) What is the probability that the sum of the numbers on your dice is an even number or a number less than 6? (c) What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
Rolling a pair of six-sided dice, we have the following sample space:
(a) The probability that the sum of the numbers on your dice is 9 or 11 is
P(X = 9) + P(X = 11)
= 4/36 + 2/36
= 6/36
= 1/6
(b) The probability that the sum of the numbers on your dice is an even number or a number less than 6 is:
P(X = even) + P(X < 6)
= 21/36 + 10/36
= 31/36
(c) The probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
P(X = prime) + P(X > 5)
= 14/36 +
Question 8 of 10 Evaluate the expression and enter your answer in the box below. [(5 + 11) + 4] + 9*(6-4)
Explanation
[tex]\begin{gathered} \mleft[\mleft(5+11\mright)+4\mright]+9\cdot(6-4) \\ \end{gathered}[/tex]
Determine the endpoints of the midsegment connecting side YX and side YZ.Question options:A) (4, 3) and (8, 0)B) (4, 3) and (5, –1)C) (1, 2) and (7, 4)D) (9, –4) and (7, 4)
Answer:
B ; (4,3) and (5,-1)
Explanation:
Here, we want to get the coordinates of the endpoints of the midsegments
Let us firstly give a representation of what we are to calculate:
Now, from the above, what we are to calculate are the coordiantes of the points A and B
If we notice, the point A is the midpoint of the line XY
the point B is the midpoint of YZ
By simply finding the midpoint coordiantes of these lines, we will able to get what we are looking for
We start as follows:
[tex](x,y)\text{ = (}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]The above will give us the coordiantes of the midpoints
Let us get the coordinates of the individual vertex points
X is (7,4)
Y is (1,2)
Z is (9,-4)
So, for point A that lies between X and Y, we have its coordiante as:
[tex](x,y)\text{ = (}\frac{7+1_{}}{2},\frac{4+2}{2})\text{ = (4,3)}[/tex]Lastly for point B that lies between Y and Z , we have:
[tex](x,y)\text{ = (}\frac{1+9}{2},\frac{2-4}{2})\text{ = (5,-1)}[/tex]rosco needs to paint the wall in his living room. The rooms dimensions are 20 feet long by 15 feet wide with 8 foot tall ceilings. if 1 gallon of paint covers 350 square feet, how many gallons of paint is needed for 2 coats of paint?
Answer:
3.2 gallons
Explanation:
The dimension of the room
• Length= 20 feet
,• Wide = 15 feet
,• Height = 8 feet
First, we determine the Surface Area of the wall in the room.
[tex]TS.A.=2(LH+WH)[/tex]Substituting the given values, we have:
[tex]\begin{gathered} TSA=2(20\times8+15\times8) \\ =2(160+120) \\ =2(280) \\ =560\text{ square f}eet \end{gathered}[/tex]Since the room needs 2 coats of paint, the total surface area to be covered will be:
[tex]\begin{gathered} =2\times560 \\ =1120\text{ square f}eet \end{gathered}[/tex]Since 1 gallon of paint covers 350 square feet, the number of gallons needed will be:
[tex]\begin{gathered} =\frac{1120}{350}\text{ gallons} \\ =3.2\text{ gallons} \end{gathered}[/tex]find the excluded value(s) of x in the rational expression f(x)= x^2+7x/ x^+14x+49so how am I supposed to combine like terms and get to the answer
Given
[tex]f(x)=\frac{x^2+7x}{x^2+14x+49}[/tex]
Procedure
Factoring
[tex]\begin{gathered} f(x)=\frac{x(x+7)}{(x+7)(x+7)} \\ f(x)=\frac{x}{x+7} \end{gathered}[/tex]Answer:
x ≠ – 7
I need help with this math problem I have a picture that I can show you of what it is
The 18 % off of the listed price x can be denoted as,
[tex]\frac{100-18}{100}x=0.82x[/tex]18% more than the amount x can be denoted as,
[tex]\frac{100+18}{100}x=1.18x[/tex]3/10 of the origianl voulme x drained out is denoted as,
[tex]x-\frac{3}{10}x=\frac{10x-3x}{10}=\frac{7x}{10}[/tex]3/10 stock is added,
[tex]x+\frac{3}{10}x=\frac{10x+3x}{10}=\frac{13x}{10}[/tex]A figure has vertices A = (0,0), B = (1, 3), C = (0,4), and D = (-1, 1).Which of the following is the most precise classification for figure ABCD?
Let's draw the figure ABCD!
Now you can conclude what is the right choice!
can u help me with the boxplot of Area 1?
In order to create a boxplot of the Area 1 dataset, first let's put the dataset in crescent order:
[tex]12,24,30,32,35,44,45,56,57,59,61,65,68,92,100.[/tex]Since the set has 15 elements, the median is the 8th element, so the median is 56.
The median will divide the set into two smaller sets with 7 elements each. The first interquartile (IQ1) is the median of the first subset (so it will be the 4th element), and the third interquartile (IQ3) is the median of the second subset (so it will be the 12th element).
So the first interquartile is 32 and the third interquartile is 65.
Now we need the lower and upper limit of the set.
The lower limit is 12 and the upper limit is 100.
Now, creating the boxplot, we have: