Answer: Jake is 9 and his dad is 33.
Step-by-step explanation: 9x3=27+6=33 9+33=42
Answer:
Jake is 9 and Jake's dad is 33
Step-by-step explanation:
To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake
J+D=42
3J+6=D
Solve by substitution
A website developer wished to analyze the clicks per day on their newly updated website. Let the mean number of clicks per day be μ. If the website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average, what are the null and alternative hypotheses?
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Step-by-step explanation:
We are given that a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
Let [tex]\mu[/tex] = mean number of clicks per day.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.
On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.
Hence, this is the correct null and alternative hypotheses.
Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Step-by-step explanation:
Let [tex]\mu[/tex] be the mean number of clicks per day.
Given, a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]
Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.
So, Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Hence, the required null and alternative hypotheses.
Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
An apple orchard has an average yield of 32 bushels of apple per acre. For each unit increase in tree density, yield decreases by 2 bushels per tree. How many trees per acre should be planted to maximize yield
An apple orchard has an average yield of 32 bushels of apples per tree if tree density is 26 trees per acre. For each unit increase in tree density, the yield decreases by 2 bushels per tree. How many trees per acre should be planted to maximize the yield?
Answer:
Step-by-step explanation:
From the given information:
Let assume that 26+x trees per acre are planted
then the yield per acre will be (26+x)(32-2x)
However;
As x = 0 (i.e. planting 26 per acre), we have;
= (26+0) (32 - 2 (0))
= 26 × 32
= 832
As x = 1 (i.e planting 19 per acre), we have:
= (26+1) (32-2(1)
= 27 × 30
= 810
As x = 2 (i.e. planting 20 per acre), we have:
= (26 +2 ) ( 32 - 2(2)
= 28 × 28
= 784
The series continues in a downward direction for the yield per acre.
Thus, for maximum plant 19 per acre, it can achieved by method of calculus given that the differentiation of the maximum point of x = 1
Finally, due to integer solution, it is not advisable to use calculus as such other methods should be applied.
The length of a rectangle is twice its width.
If the area of the rectangle is 200 yd?, find its perimeter.
Answer:
The answer is 60cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
Area of rectangle = l × w
where
l is the length
w is the width
From the question
The length is twice its width is written as
l = 2w
Substitute this into the formula for finding the area of the rectangle
Area = 200 yd²
200 = 2w²
Divide both sides by 2
w² = 100
Find the square root of both sides
width = 10cm
Substitute this value into l = 2w
That's
l = 2(10)
length = 20cm
Perimeter of the rectangle is
2(20) + 2(10)
= 40 + 20
= 60cmHope this helps you
What is the value of this expression when x = -6 and y = — 1/2? 4(x^2+3) -2y A. -131 B. -35 C. 57 1/2 D. 157
Answer:
D
Step-by-step explanation:
[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]
The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
4(x² + 3) - 2y
Substitute x = -6 and y = -1/2 to find the value of expression,
= 4 ((-6)² + 3) - 2(-1/2)
= 4 (36 + 3) + 1
= 4 x 39 + 1
= 156 + 1
= 157
The required value of the expression is 157.
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Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester.
University A University B
Sample Size 50 40
Average Purchase $260 $250
Standard Deviation (s) $20 $23
We want to determine if, on the average, students at University A spent more on textbooks then the students at University B.
a. Compute the test statistic.
b. Compute the p-value.
c. What is your conclusion? Let α = 0.05.
Answer:
The calculated Z= 10/4.61 = 2.169
The P value is 0.975 .
Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.
Step-by-step explanation:
We set up our hypotheses as
H0 : x 1= x2 and Ha: x1 ≠ x2
We specify significance level ∝= 0.05
The test statistic if H0: x1= x2 is true is
Z = [tex]\frac{x_1-x_2}\sqrt\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2}[/tex]
Z = 260-250/ √400/50 + 529/40
Z= 10 / √8+ 13.225
Z= 10/4.61 = 2.169
The critical value for two tailed test at alpha=0.05 is ± 1.96
The P value is 0.975 .
It is calculated by dividing alpha by 2 for a two sided test and subtracting from 1. When we subtract 0.025 ( 0.05/2)from 1 we get 0.975
Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.
Last question of the day!!
Answer:
Correct options are 2, 5 and 7.
Step-by-step explanation:
Consider the given vertices of triangle are A(-3,-3), B(-3,2) and C(1,2).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{(-3-(-3))^2+(2-(-3))^2}[/tex]
[tex]AB=\sqrt{(0)^2+(5)^2}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5[/tex]
Similarly,
[tex]BC=\sqrt{(1-(-3))^2+(2-2)^2}=4[/tex]
[tex]AC=\sqrt{(1-(-3))^2+(2-(-3))^2}=\sqrt{16+25}=\sqrt{41}[/tex]
From the above calculation it is clear that AC>AB and AC>BC.
According to Pythagoras theorem, in a right angle triangle, the square of largest side is equal to the sum of squares of two small sides.
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex]AC^2=(\sqrt{41})^2=41[/tex]
[tex]AB^2+BC^2=(5)^2+4^2=24+16=41=AC^2[/tex]
So, given triangle is a right angle triangle and AC is its hypotenuse.
Therefore, the correct options are 2, 5 and 7.
The graph below shows the quadratic function f, and the table below shows the quadratic function g.
x -1 0 1 2 3 4 5
g(x) 13 8 5 4 5 8 13
Which statement is true?
A.
The functions f and g have the same axis of symmetry and the same y-intercept.
B.
The functions f and g have different axes of symmetry and different y-intercepts.
C.
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
D.
The functions f and g have the same axis of symmetry, and the y-intercept of f is less than the y-intercept of g.
Answer:
D
Step-by-step explanation:
The true statement is:
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
As, per the graph and table is:
From the graph of f(x):
Axis of symmetry will be at x = 2
The maximum value of f(x) = 10
From the table of g(x):
Axis of symmetry will be at x = 2
The minimum value of g(x) = 4
thus, The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
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The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (; for example, enter x2 as x^2.
This is equivalent to x^2+8x+13
======================================================
Explanation:
The vertex of f is at (0,0). The vertex of g is at (-4, -3). The vertex has moved 4 units to the left and 3 units down.
To shift to the left, we replace x with x+4. So we have f(x) = x^2 turn into f(x+4) = (x+4)^2 so far.
Then we subtract off 3 to move everything 3 units down. We have
g(x) = (x+4)^2-3
---------------------
Optionally we can expand things out like so
g(x) = (x+4)^2-3
g(x) = (x+4)(x+4)-3
g(x) = x(x+4)+4(x+4)-3
g(x) = x^2+4x+4x+16-3
g(x) = x^2+8x+13
Showing that (x+4)^2-3 is equivalent to x^2+8x+13
Fill in the blanks and explain the pattern
0,1,1,2,3,5,__,__,21,34,55
Answer:
8,13
Step-by-step explanation:
Look at the pattern :
0,1,1,2,3,5,...,...,21,34,55.
As you see the number in the pattern was made by the sum of 2 numbers behind it. Then, the blanks must be filled by :
3 + 5 = 88 + 5 = 13So, the blanks must be filled by 8 and 13
Answer:
In the two blanks would be 8, 13.
The pattern is practically the Fibonacci Code.
Step-by-step explanation:
The Fibonacci Code is a mathematical sequencing in which you start with two numbers and add them together to make the third number, then you add the third number and the second number together. Practically you keep adding each new sum and the number before it in the sequence to find the next new sum.
After 55 in this pattern, the pattern would go 89, 144, 233, 377, 610, 987,...
Please answer this correctly without making mistakes
Answer:
3 1/4
Step-by-step explanation:
Hey there!
Well if Cedarburg to Westford is 8 3/4 miles and Oxford to Westford is 5 1/2 miles, we can make the following,
CO = CW - OW
CO = 8 3/4 - 5 1/2
Make the denominators the same,
5 1/2
improper
11/2
*2
22/4
Proper
5 2/4
8 3/4 - 5 2/4
3 1/4 miles
Hope this helps :)
1001112 = [ ? ]10
?
what number belongs where the question mark is
I suppose you're supposed to convert 100111 from base 2 to base 10. We have
[tex]100111_2=2^5+2^2+2^1+2^0=32+4+2+1=39_{10}[/tex]
so the missing number is 39.
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $ 63,042 . The variable costs will be $ 11.25 per book. The publisher will sell the finished product to bookstores at a price of $ 25.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer:
4424 books
Step-by-step explanation:
After the revenue from each book pays for its own cost, it can contribute to the payment of the fixed costs. That "contribution margin" is ...
$25.50 -11.25 = $14.25
If each book sold contributes that much to the recovery of fixed costs, then the total number of books that must be sold to break even is ...
$63,042/($14.25/book) = 4424 books
4424 books must be produced and sold so production costs equal sales.
Which statement about class ll is true
A?
B?
C?
D?
Answer:
D
Step-by-step explanation:
Let's first find the mean and median of each class.
Class 1:
The mean is simply all the numbers added up and then divided by the number of elements. There are 9 students in Class 1. Thus, we add all the ages up and then divide by 9. Thus:
[tex]\text{Class 1 Mean }= \frac{14+15+15+16+16+16+17+17+18}{9} \\=144/9=16[/tex]
The median is simply the middle number when the data sets are placed in order. The median of Class 1 is 16, the number in the middle.
Class 2:
Again, Class 2 has 9 students. Add up all the ages and then divide:
[tex]\text{Class 2 Mean }= \frac{13+14+15+16+16+17+18+18+19}{9}\\ =146/9\approx16.2222[/tex]
The median is the middle number of the data set. The median of Class 2 is 16.
Therefore, the mean of Class 2 is larger than the mean of Class 1. The medians of the two classes are equivalent.
Of the answer choices given, only D is correct.
Answer:
The mean of class II is larger and the median is the same
Step-by-step explanation:
Class I
14,15,15,16,16,16,17,17,18
The mean is
(14+15+15+16+16+16+17+17+18)/9
144/9 = 16
The median is the middle number
14,15,15,16, 16, 16,17,17,18
median = 16
Class II
13,14,15,16,16,17,18,18,19
The mean is
(13+14+15+16+16+17+18+18+19)/9
146/9 = 16.2repeating
The median is the middle number
13,14,15,16 ,16, 17,18,18,19
median = 16
Each student in a school was asked, "What is your favorite color?" The circle graph below shows how they answered
Which color was chosen by approximately one fourth of the students?
Approximately what percentage of the students chose purple or green?
Answer:
a). BLUE color
b). 20%
Step-by-step explanation:
a). "Which color was chosen by approximately one fourth of the students?"
Since one fourth of the students will be represented by one fourth area of the circle given.
That means color of choice represented by the quarter of the circle will be the color liked by one fourth students.
In the figure attached, BLUE color is the choice of one fourth students in the class.
b). Area represented by purple, green and other colors is a quarter of the circle.
If we divide this quarter into five equal sections, then the total of purple and green will be [tex]4\times \frac{1}{5}[/tex] of the the quarter of the circle.
Measure of the angle defined by purple or green sections = [tex]\frac{4}{5}\times 90[/tex]
= 72°
Percentage of the students who preferred purple or green = [tex]\frac{72}{360}\times 100[/tex]
= 20%
Answer:
blue
20%
Step-by-step explanation:
2. An economist reports that 576 out of a sample of 1,200 middle-income American households participate in the stock market. A confidence interval of [0.468, 0.492] was calculated. What confidence level was used in this calculation
Answer:
Confidence level = 59.46%
Step-by-step explanation:
Given that:
An economist reports that 576 out of a sample of 1,200 middle-income American households participate in the stock market.
sample mean = 576
sample size = 1200
The sample proportion [tex]\hat p[/tex] = x/n
The sample proportion [tex]\hat p[/tex] = 576/1200 = 0.48
A confidence interval of [0.468, 0.492] was calculated. What confidence level was used in this calculation?
The confidence interval level can be determined by using the formula:
[tex]M.E =Z_{critical} \times \sqrt{\dfrac{\hat p (1- \hat p)}{n}}[/tex]
If the calculated confidence interval was [0.468, 0.492]
Then,
[tex]\hat p[/tex] - M.E = 0.468
0.48 -M.E = 0.468
0.48 - 0.468 = M.E
0.012 = M.E
M.E = 0.012
NOW;
[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.48 (1- 0.48)}{1200}}[/tex]
[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.48 (0.52)}{1200}}[/tex]
[tex]0. 012 =Z_{critical} \times \sqrt{\dfrac{0.2496}{1200}}[/tex]
[tex]0. 012 =Z_{critical} \times \sqrt{2.08\times10^{-4}}[/tex]
[tex]0. 012 =Z_{critical} \times 0.01442[/tex]
[tex]\dfrac{0. 012}{0.01442} =Z_{critical}[/tex]
[tex]Z_{critical} =0.8322[/tex]
From the standard normal tables,
the p - value at [tex]Z_{critical} =0.8322[/tex] = 0.7973
Since the test is two tailed
[tex]1 - \alpha/2= 0.7973[/tex]
[tex]\alpha/2= 1-0.7973[/tex]
[tex]\alpha/2= 0.2027[/tex]
[tex]\alpha= 0.2027 \times 2[/tex]
[tex]\alpha= 0.4054[/tex]
the level of significance = 0.4054
Confidence level = 1 - level of significance
Confidence level = 1 - 0.4054
Confidence level = 0.5946
Confidence level = 59.46%
prove:
[tex] \frac{1}{secθ + \tanθ} - \frac{1}{cosθ} = \frac{1}{cosθ} - \frac{1}{secθ - tanθ} [/tex]
Answer:
I hope you are searching for this......
If a square has an area of x, then, in terms of x, what is the circumference of the largest circle that can be inscribed in the square? Answer: pi square root x AKA π√ x This is an SAT Math question no CALCULATOR. Show all the work
Answer:
C = pi sqrt(x)
Step-by-step explanation:
The area of a square is x
A = s^2 where s is the side length
x = s^2
Take the square root of each side
sqrt(x) = s
This would be the diameter of the inscribed circle
The circumference of a circle is given by
C = pi d
C = pi sqrt(x)
Answer:
See below.
Step-by-step explanation:
Assign the variable n to be the sides of the square.
Since a square has four equal sides, the area of the square is n^2 or x.
Therefore:
[tex]n=\sqrt{x}[/tex]
The largest circle that can be inscribed in the square will have the largest possible diameter. The largest possible diameter will be straight across the center of the circle. So, the largest possible diameter will be the side length, n.
Therefore, the radius will be n/2.
The circumference of a circle is:
[tex]C=2\pi r[/tex]
Plug in n/2 for the radius:
[tex]C=2\pi (\frac{n}{2})\\ C=n\pi[/tex]
Now, substitute n for the square root of x:
[tex]C=\pi\sqrt{x}[/tex]
Which equation is represented by the graph shown in the image? A. y + 2= x B. y + 1= x C. y - 1= x D. y - 2= x Please show ALL work! <3
Answer:
A. y + 2= x
Step-by-step explanation:
Which equation is represented by the graph shown in the image?
A. y + 2= x
B. y + 1= x
C. y - 1= x
D. y - 2= x
Please show ALL work! <3
The graph shown has a slope of +1 and a y intercept of -2.
All given answer choices have a slope of +1, so that's not the problem.
We need one that has a y-intercept of -2, or the equation should be
y = x-2, or equivalently y+2 = x
which corresponds to answer choice A.
Use the drawing tools to form the correct answers on the grid.
Mark the vertex and graph the axis of symmetry of the function.
fix) = (x - 2)2 - 25
Answer:
Step-by-step explanation:
Hello, this is pretty straight forward. Let me remind you the following.
The standard equation of a parabola is
[tex]y=ax^2+bx+c[/tex]
But the equation for a parabola can also be written in "vertex form":
[tex]y=a(x-h)^2+k[/tex]
In this equation, the vertex of the parabola is the point (h,k) .
So, here the vertex is the point (2, -25) and the axis of symmetry is x = 2
Thank you
Answer:
if anyone still needs the answer I added a pic
Step-by-step explanation:
(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet
Answer:
d. 27 cubic feet
Step-by-step explanation:
volume of cube = s^3 = B * s
volume of pyramid = (1/3) * B * h
The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.
volume of pyramid = 9 cu ft
volume of cube = 3 * 9 cu ft = 27 cu ft
Answer: d. 27 cubic feet
Answer:
27 ft^3 (Answer d)
Step-by-step explanation:
Here the volume of the pyramid is (1/3) the volume of the cube:
Letting s represent the length of one side of the base,
(1/3)(s)^2(s) = 9 ft^3, equivalent to s^3 = 27.
Solving for s, we get s = 3 ft.
Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)
How to evaluate this help me out so lost?
Answer:
5443
Step-by-step explanation:
Order of Operations: BPEMDAS
Always left to right.
Step 1: Add 68 and 5042
68 + 5042 = 5110
Step 2: Add 5110 and 333
5110 + 333 = 5443
And we have our answer!
Tom is afraid of heights above 9 feet. He is asked to repair a side of a high deck. The bottom of the ladder must be placed 6 feet from a deck. The ladder is 10 feet long. How far above the ground does the ladder touch the deck? Is Tom afraid of the height?
Answer:
8 ftnoStep-by-step explanation:
The height on the side of the deck (h) can be found using the Pythagorean theorem. It tells you ...
6^2 + h^2 = 10^2
h = √(10^2 -6^2) = √64 = 8
The ladder touches the deck 8 feet above the ground. Tom is not afraid of that height.
A poker hand consisting of 7 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 3 face cards. Leave your answer as a reduced fraction.
Answer:
The probability is 2,010,580/13,378,456
Step-by-step explanation:
Here is a combination problem.
We want to 7 cards from a total of 52.
The number of ways to do this is 52C7 ways.
Also, we know there are 12 face cards in a standard deck of cards.
So we are selecting 3 face cards from this total of 12.
So also the number of cards which are not face cards are 52-12 = 40 cards
Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4
Thus, the required probability will be;
(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560
= 20,105,800/133,784,560 = 2,010,580/13,378,456
Factor.
x2 - 7x + 10
(x - 10)(x + 1)
(x + 1)(x - 10)
(x - 5)(x - 2)
(x + 5)(x + 2)
Answer:
The answer is option C
Step-by-step explanation:
x² - 7x + 10
To factor the expression rewrite - 7x as a difference
That's
x² - 5x - 2x + 10
Factor out x from the expression
x( x - 5) - 2x + 10
Factor - 2 from the expression
x(x - 5) - 2( x - 5)
Factor out x - 5 from the expression
The final answer is
( x - 2)(x - 5)Hope this helps you
Find the area of the shape shown below.
3.5
2
2
Answer:
26.75 units²
Step-by-step explanation:
Cube Area: A = l²
Triangle Area: A = 1/2bh
Step 1: Find area of biggest triangle
A = 1/2(3.5)(2 + 2 + 5)
A = 1.75(9)
A = 15.75
Step 2: Find area of 2nd biggest triangle
A = 1/2(5)(2)
A = 1/2(10)
A = 5
Step 3: Find area of smallest triangle
A = 1/2(2)(2)
A = 1/2(4)
A = 2
Step 4: Find area of cube
A = 2²
A = 4
Step 5: Add all the values together
A = 15.75 + 5 + 2 + 4
A = 20.75 + 2 + 4
A = 22.75 + 4
A = 26.75
Which of the following expressions are equivalent to (x+y) - (-z)? A. (x+y) - z B. x+ (y+z) C. None of the above
=========================================
Explanation:
Subtracting a negative is the same as adding. Example: 2-(-3) = 2+3 = 5.
So (x+y)-(-z) is the same as x+y+z. We can group up terms inside parenthesis and it won't change the result. Meaning that x+y+z is the same as any of the following below
(x+y)+zx+(y+z)We could also swap the order of either x, y or z, and still have the same result.
what is the domain of f(x)=(1/4)^x
Answer:
B All real numbers
hope you wil understand
Answer:
[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]
Step-by-step explanation:
The domain is all possible values for x.
[tex]f(x)=(\frac{1}{4} )^x[/tex]
There are no restrictions on the value of x.
The domain is all real numbers.
5 STARS IF CORRECT! In general, Can you translate a phrase or sentence into symbols? Explain the answer.
Answer:
Step-by-step explanation:
I answered this already a few minutes ago.
Answer:
yes you can
Step-by-step explanation:
you can write algebraic expressions and use variables for the unknown
A right triangle has the following vertices Find the area of the triangle
(7,-3) (4,-3) (4,9)
20 pnts
Answer:
Area = 18 square units
Step-by-step explanation:
To find the area of the triangle, let's go through the following steps:
(i) Let the vertices be;
A = (7, -3)
B = (4, -3)
C = (4, 9)
(ii) The sides of the triangle are therefore,
AB, BC and CA
(iii) Using the distance formula, calculate the lengths of AB, BC and CA
[tex]AB = \sqrt{(7-4)^2 + ( -3 - (-3))^2}[/tex]
[tex]AB = \sqrt{3^2 + (0)^2}\\[/tex]
[tex]AB = \sqrt{9}[/tex]
[tex]AB = 3[/tex]
[tex]BC = \sqrt{(4-4)^2 + ( -3 - 9)^2}[/tex]
[tex]BC = \sqrt{0^2 + (-12)^2}[/tex]
[tex]BC = \sqrt{144}[/tex]
[tex]BC = 12[/tex]
[tex]CA = \sqrt{(4-7)^2 + ( 9 - (-3))^2}[/tex]
[tex]CA = \sqrt{(-3)^2 + (12)^2}[/tex]
[tex]CA = \sqrt{9 + 144}[/tex]
[tex]CA = \sqrt{153}[/tex]
[tex]CA = 12.4[/tex]
(iv) Now that we have all the sides, let's calculate the area of the triangle using the Heron's formula.
Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where;
p = [tex]\frac{a + b + c}{2}[/tex]
a, b and c are the sides of the triangle.
In our case,
let
a = AB = 3
b = BC = 12
c = CA = 12.4
∴ p = [tex]\frac{3 + 12 + 12.4}{2}[/tex]
p = 13.7
Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]
Area = [tex]\sqrt{13.7(13.7-3)(13.7-12)(13.7-12.4)}[/tex]
Area = [tex]\sqrt{13.7(10.7)(1.7)(1.3)}[/tex]
Area = [tex]\sqrt{323.9639}[/tex]
Area = 17.999
Area = 18 square units
OR
To get the area of the triangle, we can use a much simpler approach.
Since the triangle is a right triangle,
(i) the hypotenuse, which is the longest side is CA = 12.4
(ii) the other two sides are AB and BC. These two sides will form the right angle.
Therefore, we can use the relation:
Area = [tex]\frac{1}{2}[/tex] x base x height
Where;
the base or height can either be AB or BC
Area = [tex]\frac{1}{2}[/tex] x 3 x 12
Area = 18 square units
PS: In a right triangle, the other two sides apart from the hypotenuse form the right angle.
At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?
Answer:
£32 in total for the top and two trousers
Step-by-step explanation:
The price for a top In the "cloth for you" shop= £10
The price for a bermuda trouser In the "cloth for you" shop= £12
There is a 20% discount on tops
The price If I bought one top and would trouser will be
(10-(0.2*10)) for the top
2(12) for the trouser
Total= (10-(0.2*10))+ 2(12)
Total = 10-2+24
Total = £32
So I spent £32 in total for the top and two trousers
