Answer:
h(x) = 3^(x + 1)
Step-by-step explanation:
The exponential function is;
g(x) = 3^(x)
Now, in transformation of exponential functions of say f(x) = b^(x), when the new function g(x) is created by stretching by a factor of say c along the y-axis, we have;
g(x) = c•b^(x)
In this question, we are told it is stretched by a factor of 3 along the y-axis.
Thus, new function h is;
h(x) = 3 × 3^(x)
Using law of indices, we have;
h(x) = 3^(x + 1)
Can someone help me with this math homework please!
Answer:i dont know
Step-by-step explanation:
Which of the following square root of the following number below? Check all that apply. 361
Answer:
strangely worded question....
[tex]361^{1/2} = \sqrt{361}[/tex]
Step-by-step explanation:
=========================================================
Explanation:
Notice how (19)^2 = 19*19 = 361
This shows that 19 is a square root of 361. We can say [tex]\sqrt{361} = \sqrt{19^2} = 19[/tex]
Similarly, (-19)^2 = (-19)*(-19) = 361. The two negatives cancel each other out. So that's why there are two solutions to [tex]x^2 = 361[/tex] which are x = 19 and x = -19.
So far that accounts for answer choices B and D.
-------------------------------------------
The other two answers are [tex]-361^{1/2}[/tex] and [tex]361^{1/2}[/tex] (choices C and F) because anything to the 1/2 power represents a square root.
[tex]x^{1/2} = \sqrt{x}[/tex]
anything to the 1/3 power is a cube root
[tex]x^{1/3} = \sqrt[3]{x}[/tex]
anything to the 1/4 power is a fourth root
[tex]x^{1/4} = \sqrt[4]{x}[/tex]
and so on.
-------------------------------------------
Side note: For choice C, the exponent is done first before we apply the negative. So technically we could say [tex]-1*(361)^{1/2}[/tex] for choice C to mean the same exact thing. If your teacher said [tex](-361)^{1/2}[/tex] then this would not be an answer because this results in a non-real number.
Can some help with this problem
Answer:
x+115=180 x=65
90+65+y=180 y=25
Step-by-step explanation:
Which of the four graphs has the greatest standard deviation? please help me
Answer:
Standard deviation is how far away the values are from the mean.All of your graphs have normal distribution, meaning the mean is in the center.The more spread out your graph is, the greater the standard deviation.
So the option with the most spread out graph, which I think is A, can't see very clear.
Really struggling with these problems please help!
Solve.
[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]
Answer:
[tex]y_1 = -2[/tex] and [tex]y_2 = 4[/tex]
Step-by-step explanation:
[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]
Move the constant to the right-hand side and change their sign.
[tex] \sqrt{10y + 24} = y + 1 + 3 [/tex]
combine like terms
[tex] \sqrt{10y + 24} - 3 = y + 4[/tex]
Square both side to remove square brackets.
10y + 24 - 3 = y²+ 8y + 16
Move the expression to the left-hand side and change its sign.
10y + 24 - y² - 8y - 16 = 0
Combine like terms
10y - 8y + 24 - 16 - y² = 0
2y + 8 - y² = 0
Use commutative property to reorder the terms.
-y² + 2y + 8 = 0
Change the sign of expression.
y² -2y -8 = 0
split -2y
y² + 2y - 4y - 8 = 0
Factor out y from the first pair and -4 from the second equation.
y ( y + 2 ) - 4 ( y + 2 ) = 0
Factor out y+2 from the expression.
( y + 2 ) ( y - 4)
When the products and factors equals 0, at least one factor is 0.
y + 2 = 0
y - 4 = 0
Solve for y
y = -2
y = 4
When we plug the both solution as y we found that both is true solution of this equation.
This equation has two solutions which are -2 and 4.
Answer:
Solution given:
[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]
keep the constant term in one side
[tex] \sqrt{10y + 24} =y+1+3[/tex]
solve possible one
[tex]\sqrt{10y+24}=y+4[/tex]
now
squaring both side
[tex](\sqrt{10y+24})²=(y+4)²[/tex]
10y+24=y²+8y+16
taking all term on one side
10y+24-y²-8y-16=0
solve like terms
8+2y-y²=0
doing middle term factorisation
8+4y-2y-y²=0
4(2+y)-y(2+y)=0
(2+y)(4-y)=0
either
y=-2
or
y=4
y=-2,4
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+g)(x).
O A. (f+g)(x) = -34 - 2x - 14
B. (f+ g)(x) = 3x - 2x + 14
O C. (f+ g)(x) = 5x + 6
D. (f+ g)(x) = 3x + 2x + 6
Help! I’m getting really confused which one it is
Answer:
O D
Step-by-step explanation:
f+g(x)
3x+10+2x-4
3x +2x+6
© Find the quotient of 3/8 and ,4/9
Give your answer as a fraction in its simplest form.
[tex] \frac{3}{8} \div \frac{4}{9} \\ = \frac{3}{8} \times \frac{9}{4} \\ = \frac{27}{32} [/tex]
Hope it helps!!!
Thanks!!!
The angle of elevation of a tree at a distance of 10m from the foot of the tree is 43°. Find the height of the tree
Answer:
9.32m is the height of. the tree from the ground.
I need help plz help
answer is C. 252 ft^2
split the figure into two pieces and first figure out the rectangle (shown in turquoise).
If you multiply the width and length (18*6) you should get 108.
Then figure out the trapezoid (in magenta). the formula is (a+b)/2*h where a and b are the bases and h is the height. the bases are given, 6 and 18. to find the height, subtract the entire figure's height by 6, which is 18-6 and gives us 12. so the formula converted to this problem is (6+18)/2*12. simplify parenthesis and get 24/2*12. 24/2=12, so multiply 12*12. The area of the trapezoid is 144. Add the areas of both figures together and get 252.
what is the slope of the graph?
Answer:
The slope is 1.5
Step-by-step explanation:
To get the slope of the graph, we proceed to select any two points lying on the given line, and applying the slope formula
The two selected points are as follows;
(x1,y1) = (-4,0)
(x2,y2) = (-2,3)
m = (y2-y1)/(x2-x1)
m = (3-0)/(-2-(-4)
m = 3/2 = 1.5
100 people study one language at a college. Some people study French, some study Spanish. The rest of the people study German. 54 of the people in Year 10 and the rest in Year 11. 20 of 29 people who study Spanish in Year 11. 31 people study German, 15 year 11 students study French. Work out the number of Year 10's who study German.
Hello,
[tex]Data:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&-&-&-&54\\Y11&15&20&-&-\\----&----&----&----&---\\&-&29&31&100\\\end{array}\\\\Calculus:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&25&9&20&54\\Y11&15&20&11&46\\----&----&----&----&---\\&40&29&31&100\\\end{array}\\\\[/tex]
20 Year10's students learn German.
========================================================
Explanation:
Make a table that has "Year 10", "Year 11", and "Total" as the three rows.
Then you'll have the columns "French", "Spanish", "German", "Total".
In the bottom right corner is the value 100. This is the grand total of everyone surveyed.
We're told that 54 people are in Year 10, which leaves 100-54 = 46 people in Year 11.
Along the "total" column on the far right side, we'll have 54, 46, and 100 in that order from top to bottom.
--------------------------
The info that "20 of the 29 people who study Spanish in Year 11" tells we have 20 people in year 11 who study Spanish, out of 29 people who study Spanish. That leaves 29-20 = 9 people in Year 10 who study Spanish. In the "Spanish" column, we have the values 9,20,29 in that exact order from top to bottom.
Next, we'll write 31 at the bottom of the "German" column to indicate 31 people study German.
The last bit of info is that "15 Year 11 students study French". So we'll write 15 in the "year 11" row and "french" column.
--------------------------
After all that info is sorted out and entered into the table, you should end up with what is shown in figure 1 (see attached image below). Ignore figure 2 for now as we'll work our way to getting there eventually.
The variables a,b,c,d are placeholders for positive whole numbers.
There are probably a few approaches to take, but possibly the quickest is to notice that in the second row, we can say
15+20+c = 46
c+35 = 46
c = 46-35
c = 11
We have 11 students who study German in Year 11.
Once you determine c, it helps us find b. Focus on the German column to see that
b+11 = 31
b = 31-11
b = 20
There are 20 students in Year 10 who study German. You could stop here if you want.
--------------------------
Just two more variables to go.
Along the top row, we see that
a+9+20 = 54
a+29 = 54
a = 54-29
a = 25
and along the bottom row we see that
d+29+31 = 100
d+60 = 100
d = 100-60
d = 40
Or you could note along this first column to say
a+15 = d
d = a+15
d = 25+15
d = 40
So there are a few alternative paths to take.
--------------------------
All of the sections mentioned so far only involve filling out the table that is shown below in figure 2.
To answer the question your teacher wants to ask, which is how many Year 10 students study German, well that's simply 20 students. Refer to the conclusion of the previous two sections earlier.
By this point, we just simply copy the value from the completed table. This value being of course in the "Year 10" row and "German" column.
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
Answer:
1866.10604
Step-by-step explanation:
V=3.14(r sqaured)1/3h
write the equation of the line that passes through the points (1,6) and (9,-8). put your answer in fully reduced slope form, unless it is a vertical or horizontal line.
Answer:
Y = - 7/4 X + 31/4
Step-by-step explanation:
M = 14/-8 = - 7/4
6 = - 7/4 + B
24 = -7 + 4B
31 = 4B
B = 31/4
find f(-2)for f(x)=5*3^x
f ( - 2 ) = 5 × 3^( - 2 )
f ( - 2 ) = 5 × 1/9
f ( - 2 ) = 5/9
If and are the zeroes of the polynomial 2x^2+3x+5 then the value of 1/alpha + 1/beta
Pls answer fast..I’ll mark the brainlest
Answer:
-4/15
Step-by-step explanation:
Mathematically, we know that;
alpha= -b/a and beta = c/a
a refers to the coefficient of the x^2 which is 2
b is the coefficient of x which is 3
c is the last number which is 5
alpha = -b/a = -3/2
beta = c/a = 5/2
1/alpha = -2/3
1/beta = 2/5
so we have the sum as;
-2/3 + 2/5
= -5(2) + 3(2)/15 = (-10 + 6)/15 = -4/15
8 Find the value of x a (22²)x is exponent of (22²) = 64
Given:
Consider the given equation is:
[tex](2\cdot 2^2)^x=64[/tex]
To find:
The value of x.
Solution:
We have,
[tex](2\cdot 2^2)^x=64[/tex]
It can be written as:
[tex](2\cdot 4)^x=8\times 8[/tex]
[tex]8^x=8^2[/tex]
On comparing the exponents of both sides, we get
[tex]x=2[/tex]
Therefore, the value of x is 2.
Two
1 1 sides of trapezium are bound 60 cm & 77cm
outer sides are 25cm. & 26cm Find the
area of trapezium
Answer:
area ABEC[tex]s =\frac{25 + 26 + 17}{2} = 34[/tex]
area ∆ BEC[tex] = \sqrt{34 \times 9 \times 8 \times 17} [/tex]
[tex]17 \times 3 \times 2 \times 2 = 204cm ^{2} [/tex]
area ∆ BEC
[tex] = \frac{1}{2} \times 17 \times h = 204[/tex]
[tex]h = \: \frac{204 \times 2}{17} = 24[/tex]
[tex]area \: trap \: \: abcd \\ = \frac{1}{2}(60 + 77) \times 24 \\ = 137 \times 12 = 1644cm ^{2} [/tex]
Step-by-step explanation:
❣️Jess bragoli❣️#keep learning!!
Find the area of the triangle whose vertices are (2, 3); (-1, 0); (2, -4)...
[Also show the steps of the solution]
Please answer correctly, it's really urgent!
Answer:
Area = 14.5
Step-by-step explanation:
Let's label the given coordinates A, B, C;
Thus;
A = (2, 3)
B = (-1, 0)
C = (2, -4)
From the coordinate geometry formula, the formula for area of a triangle with 3 vertices is;
Area = [Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2
Area = [2(0 - (-4)) + (-1)(-4 - 3) + 2(3 - (-4))]/2
Area = 29/2
Area = 14.5
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High frequency EM is thought to be a cause of cancer; the lower frequencies associated with household current are generally assumed to be harmless. The following table summarizes the probability distribution for cancer sufferers and their wiring configuration in the Denver area.
Leukemia Lymphoma Other Cancers
High Frequency wiring 0.242 0.047 0.079
Low frequency wiring 0.391 0.098 ???
(a) What is the missing probability (labelled ???) in the above table?
(b) What is the probability of having high frequency wiring among cancer suffers in the Denver area?
(c) Is the event "Having Leukemia" independent of the event "Having high frequency frequency wiring"? Explain.
Answer:
[tex]x = 0.143[/tex]
[tex]P(High\ |\ Cancer) = 0.215[/tex]
Not independent
Step-by-step explanation:
Given
See attachment for proper table
Solving (a): The missing probability
First, we add up the given probabilities
[tex]Sum = 0.242+0.047+0.079+0.391+0.098[/tex]
[tex]Sum = 0.857[/tex]
The total probability must add up to 1.
If the missing probability is x, then:
[tex]x + 0.857 = 1[/tex]
Collect like terms
[tex]x = -0.857 + 1[/tex]
[tex]x = 0.143[/tex]
Solving (b): P(High | Cancer)
This is calculated as:
[tex]P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}[/tex]
So, we have:
[tex]P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}[/tex]
[tex]P(High\ |\ Cancer) = \frac{0.079}{0.368}[/tex]
[tex]P(High\ |\ Cancer) = 0.215[/tex]
Solving (c): P(Leukemia) independent of P(High Wiring)
From the attached table
[tex]P(Leukemia\ n\ High\ Wiring) = 0.242[/tex]
[tex]P(Leukemia) = 0.242 + 0.391 =0.633[/tex]
[tex]P(High\ Wiring) = 0.242+0.047+0.079=0.368[/tex]
If both events are independent, then:
[tex]P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)[/tex]
[tex]0.242 = 0.633 * 0.368[/tex]
[tex]0.242 \ne 0.232[/tex]
Since the above is an inequality, then the events are not independent
is Catholic Schools bad?
Answer:
Not really。。
Step-by-step explanation:
this school had remained excellent。students grduating from these school have higher ACT scores
Which correlation is most likely a causation?
the positive correlation between the sales of apples and sales of oranges at a farmer’s market
the positive correlation between the number of crimes in a city and the number of cars in the city
the positive correlation between the height of a person and the number of times a person bumps their head on a low ceiling
the positive correlation between the number of socks and number of shoes in a home
Answer:
The positive correlation between the number of socks and the number of shoes in home
Step-by-step explanation:
Nah i just get an example so that i can get clue,if my answer is wrong sorry in advanced
Determine if the ordered pair (-1,-5) is a solution to the inequality y<_ -3/4x-1.
A.) No,because (-1,-5) is above the line
B.) Yes, because (-1,-5) is below the line
C.) No, because (-1,-5) is on the line
D.) Yes, because (-1,-5) is on the line
Answer:
the answer is B, comment if you need explanation
Step-by-step explanation:
what is the quotient of 3/4 ÷ 5/12
Answer:
1 4/5
Step-by-step explanation:
3/4 ÷ 5 /12
Copy dot flip
3/4 * 12/5
Rewriting
3/5 * 12/4
3/5 * 3
9/5
1 4/5
a. 1.3
b. 9.6
c. 13
d. 1
Answer: I believe the answer would be 1.3
HOWEVER, if you do have to round to the nearest tenth then the answer would be 1
Step-by-step explanation:
2x+7 = 12x - 6
(subtract 2x from both sides)
7 = 10x - 6
(add 6 to both sides)
13 = 10x
(divide 13/10)
1.3 = x
Question 18 (5 points)
Determine the sum of the measures of the interior angles of a dodecagon (12-sided
polygon).
540°
1,800°
360°
2,160°
Answer:
its 540 bro
Step-by-step explanation:
Round your answer to one decimal places where necessary. Please give steps.
4/3 x 3.14 x 2.25 = ?
Answer:
4/3 x 3.14 x 2.25=9.42
Hope This Helps!!!
Answer:
9.4
Step-by-step explanation:
[tex] \sf \frac{ \bold{4 }}{ 3 } × 3.14 × \underline{2.25}[/tex]
Step 1 :- Multiply decimal by the number. So, that the results equals whole number.
[tex] \sf \frac{ \underline{ 4 }}{ 3 } \\ [/tex] × 2.25 × 3.14 .
[tex] \sf \frac{9}{ 3 } \\ [/tex] × 3.14
Step 2 :- Divide the fraction.
= 3 × 3.14.Step 3 :- Multiply both .
= 9.42.Round to one decimal place :- 9.4
Solve The inequality
Answer:
D is the correct answer.
Please thank me
Step-by-step explanation:
Solve simultaneously
4X + 3y= 19
2X +5y= 20
answer
4
2
Step-by-step explanation:
4x+3y=19
4x=19-3y
4x=16
x=16/4
x=4
2x+5y=20
5y=20/2x
5y= 10
y=10/5
y=2
Which point is a solution to the inequality shown in this graph
Answer: C. (0, -3)
Step-by-step explanation:
You don't even need to find the function, just mentally graph every point in the options on the graph.
If it land in the white area, it's not a solution.If it land in the blue area or on the line, it's a solution.The line is not dotted, showing that the inequality is probably either ≥ or ≤, so points on the line do count as solution.
The owner of a new pet store wishes to display tropical fish in display tanks. The above table shows the species that cannot live together. What is the minimum number of different tanks needed to safely house all the fish?
Answer:
The minimum number of different tanks needed to safely house all the fish is:
3 tanks.Step-by-step explanation:
To identify the minimum number of different tanks, we're gonna concentrate in a fish species, in this case can be the A: as you see in the table, the A species can live with all the fish excepting the F and G, by their side, the F and G can't live together , by this reason, this three species must live in a different tank, in the next form:
Tank 1: A Tank 2: F Tank 3: GNow the B species, it can live with A, F and G, but for this example we can put in the tank 1 (the tank of the A species). The C especies can live with A, F and G, but how we have A and B together, we're gonna put the C especies in the tank 3 (the tank of the G especies). The D species can live with A and G, we're gonna put in the tank 1 because can live with B species too. The E species can live with A and F, we're gonna put in the tank 2 (the tank of the F species) because the E species can't live with D that is in the in the tank 1. Al last, the H species just can live with A, E, F, and H species, by this reason, the only tank that can be put is the tank 2. In this form, the order is the next:
Tank 1: A, B, D. Tank 2: F, E, H. Tank 3: G, C.And the owner of the pet store must buy three different tanks to display these tropical fish.