Answer:
A. [tex]g(x)=-2x+1[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=-2x+7[/tex]
The function [tex]f(x)[/tex] is shifted 6 units below which forms the function [tex]g(x)[/tex]
To find the function [tex]g(x)[/tex], we apply the following translation rules:
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units up.
If [tex]c<0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units down.
Since the function [tex]f(x)[/tex] is shifting 6 units below, thus value of [tex]c<0[/tex] which is taken as -6.
The translation occurring here is given by:
[tex]f(x)\rightarrow f(x)-6[/tex]
Thus,
[tex]g(x)=f(x)-6[/tex]
Substituting [tex]f(x)=-2x+7[/tex]
[tex]g(x)=-2x+7-6[/tex]
∴ [tex]g(x)=-2x+1[/tex]
I HAVE MY MOCKS TOMORROW AND I WILL DO THE SAME TEST THAT I HAVE KNOW HEEEEELP
Answer:
[tex]p=\frac{4\sqrt{10}}{5}[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
Remember that AB is a tangent to the circle at point B
so
AB is perpendicular to OA
The radius of the circle is equal to the segment OA
In the right triangle OAB
[tex]sin(30\°)=\frac{OA}{OB}[/tex]
[tex]OA=(OB)sin(30\°)[/tex]
substitute the values
[tex]OA=(16)0.5=8\ units[/tex]
step 2
Find the value of p
In the right triangle OPQ
see the attached figure to better understand the problem
Applying the Pythagoras Theorem
[tex]OP^2=OQ^2+PQ^2[/tex]
substitute the values
Remember that OP is the radius
[tex]8^2=p^2+(3p)^2[/tex]
[tex]64=p^2+9p^2[/tex]
[tex]64=10p^2[/tex]
[tex]p^2=\frac{64}{10}[/tex]
[tex]p=\frac{8}{\sqrt{10}}[/tex]
simplify
[tex]p=\frac{4\sqrt{10}}{5}[/tex]
Complete the table with values for x or y that make this equation true: 3x+y=15
For the equation 3x + y = 15, when x is 2, y is 9; when x is 6, y is -3; when x is 0, y is 15; and when x is 3, y is 6.
To complete the table for the equation 3x + y = 15, substitute the given values of x into the equation to find the corresponding values of y:
1. For x = 2:
[tex]\[ 3(2) + y = 15 \implies 6 + y = 15 \implies y = 9 \][/tex]
2. For x = 6:
[tex]\[ 3(6) + y = 15 \implies 18 + y = 15 \implies y = -3 \][/tex]
3. For x = 0:
[tex]\[ 3(0) + y = 15 \implies 0 + y = 15 \implies y = 15 \][/tex]
4. For x = 3:
[tex]\[ 3(3) + y = 15 \implies 9 + y = 15 \implies y = 6 \][/tex]
So, the completed table is:
x 2 9 6 0 3
y 9 3 -3 15 6
The missing values for y when x = 2 and x = 3 are 9 and 6, respectively.
The complete question is:
Complete the table with values for x or y that make this equation true: 3x+y=15
x 2 ___ 6 0 3 ___ ___
y ___ 3 ___ ___ ___ 0 8
Brainlist
Please help me
Answer:
Yes she made an error. Explanation is below.
Step-by-step explanation:
Let the sample space for a six sided number cube be S
[tex]n(S) = \{1,2,3,4,5,6\}\\n(S) = 6[/tex]
Let the event of a number getting greater than two be B
[tex]n(B) = \{3,4,5,6\}\\n(B) = 4[/tex]
To find:
the probability of complement of B that is
p(~B) = ?
Solution"
First we need to solve probability for number getting greater than two
[tex]p(B) = \frac{n(B)}{n(S)}[/tex]
Now substituting the values we get
[tex]p(B) = \frac{4}{6}[/tex]
[tex]p(B) = \frac{2}{3}[/tex]
but we need complement of B so
[tex]p(\textrm{complement of B)} = 1 - p(B)\\p(\~B) = 1 - p(B)\\p(\~B) = 1 - \frac{2}{3}\\ =\frac{1}{3} \\[/tex]
P(complement of rolling a number greater than two) = [tex]\frac{1}{3}[/tex]
Find the inequality represented by the graph
Answer:
[tex]y<\frac{1}{4}x+3[/tex]
Step-by-step explanation:
we know that
The solution of the inequality in the graph is the shaded area below the dashed line
The slope of the dashed line is positive
The y-intercept of the dashed line is (0,3)
The dashed line pass through the points (0,3) and (4,4)
The slope of the dashed line is
[tex]m=(4-3)/(4-0)=1/4[/tex]
The equation of the dashed line in slope intercept form is
[tex]y=\frac{1}{4}x+3[/tex]
therefore
The inequality represented by the graph is
[tex]y<\frac{1}{4}x+3[/tex]
Need help with this math problem
x = 17
m∠JKL = 87°
m∠KJL = 58°
m∠KLJ = 35°
m∠KLM = 145°
Step-by-step explanation:
The exterior angle theorem says that the sum of two interior angles is equal to the exterior angle
In the given triangle, the interior angles are:
m∠K = (7x-32)°
m∠J = (5x-27)°
The interior angle is:
m∠L = (9x-8)°
So writing mathematically
m∠J+m∠K = m∠L
[tex]7x-32+5x-27 = 9x-8\\12x -59 = 9x - 8\\12x-9x = 59-8\\3x = 51[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3} =\frac{51}{3}\\x = 17[/tex]
Now m∠JKL
= [tex]7x-32\\=7(17) - 32\\=119-32\\=87[/tex]
m∠KJL
[tex]= 5x-27\\=5(17)-27\\=85-27\\=58[/tex]
m∠KLJ
[tex]=188-9x\\=188-153\\=35[/tex]
m∠KLM
[tex]=9x-8\\=9(17) -8\\=153-8\\=145[/tex]
Hence,
x = 17
m∠JKL = 87°
m∠KJL = 58°
m∠KLJ = 35°
m∠KLM = 145°
Keywords: Angles, Triangle
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Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.
What is the range of this relation?
A.
0 ≤ y ≤ 5
B.
y ≤ 5
C.
y ≥ 0
D.
3 ≤ y ≤ 5
Answer:
3 ≤ y ≤ 5
Step-by-step explanation:
Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.
Therefore, the speed (y) of Rosalie ranges from 5 mph to 3 mph including the values.
So, the range of this relation is 3 ≤ y ≤ 5. (Answer)
We can see here that the range of this relation is: D. 3 ≤ y ≤ 5
How we arrived at the solution?To determine the range of this relation, let's first calculate the distances Rosalie covers during each phase of her training:
Jogging phase:
Time = 30 minutes = 0.5 hours
Speed = 5 miles per hour
Distance = Speed × Time = 5 × 0.5 = 2.5 miles
Walking phase:
Time = 60 minutes = 1 hour
Speed = 3 miles per hour
Distance = Speed × Time = 3 × 1 = 3 miles
Now, let's consider the range of distances Rosalie covered during her training:
The minimum distance she covered is 2.5 miles (jogging phase), and the maximum distance is 2.5 + 3 = 5.5 miles (jogging + walking phases).
The given options are:
A. 0 ≤ y ≤ 5
B. y ≤ 5
C. y ≥ 0
D. 3 ≤ y ≤ 5
Since the minimum distance covered is 2.5 miles and the maximum distance covered is 5.5 miles, the correct option that represents the range of this relation is:
D. 3 ≤ y ≤ 5
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helphelphelphelphelp
Answer:
15/8 pounds of soil or 1 7/8 pounds of soil
Step-by-step explanation:
5 pots * 3/8 pound per pot = 15/8 pounds of soil
Suppose yoko borrows $3500 at an interest rate of 4% compounded each year Find the amount owed at the end of 1 year
Amount owed at the end of 1 year is 3640
Solution:Given that yoko borrows $3500.
Rate of interest charged is 4% compounded each year
Need to determine amount owed at the end of 1 year.
In our case :
Borrowed Amount that is principal P = $3500
Rate of interest r = 4%
Duration = 1 year and as it is compounded yearly, number of times interest calculated in 1 year n = 1
Formula for Amount of compounded yearly is as follows:
[tex]A=p\left(1+\frac{r}{100}\right)^{n}[/tex]
Where "p" is the principal
"r" is the rate of interest
"n" is the number of years
Substituting the values in above formula we get
[tex]\mathrm{A}=3500\left(1+\frac{4}{100}\right)^{1}[/tex]
[tex]\begin{array}{l}{A=\frac{3500 \times 104}{100}} \\\\ {A=35 \times 104} \\\\ {A=3640}\end{array}[/tex]
Hence amount owed at the end of 1 year is 3640
Factor by grouping.
72x^3 - 56x^2 + 45x - 35
Answer:
[tex](8x^{2} +5)(9x-7)[/tex]
Step-by-step explanation:
[tex]72x^{3}-56x^2+45x-35[/tex]
Out of 72x^3 and 56x^2 you can factor 8x^2
Out of 45x and -35 you can factor 5
So if you put those together you get 8x^2+5
8x^2*9x=72x^3 and 8x^2*-7= -56x^2
5*9x=45x and 5*-7= -35
what is -2.6c - 2.8c equal??
Answer:
-5.4c
Step-by-step explanation:
We're combining two "like" terms here.
It may make the problem easier to visualize if we write one of these terms over the other, as follows:
-2.6c
- 2.8c
----------
Adding, we get:
-2.6c
- 2.8c
----------
- 5.4c (answer)
Alberto has four rectangular tiles. The dimensions of the tiles, in inches, are 2 x 3, 3 x 5, 1 x 4, and 4 x 6. He puts all four tiles together, without gaps or overlaps, to form a single square. What is the side length of the square?
Answer:
The side length of the square is 7 inches².
Step-by-step explanation:
Given:
The dimensions of the tiles are 2 x 3, 3 x 5, 1 x 4, and 4 x 6 to form a single square.
Now, to get the length of the square formed by the tiles. We need to get the area of the square.
Area of the square formed by the four tiles = [tex]2\times 3+3\times 5+1\times 4+4\times 6[/tex]
= [tex]6+15+4+24[/tex]
= [tex]49[/tex]
So, the area of the square is 49 inches².
Putting the formula of square for getting the side length:
Area of the square = side²
[tex]49=side^{2}[/tex]
using square root on both sides:
[tex]7=side[/tex]
Therefore, the side length of the square is 7 inches².
Jasmine has 84 flowers available to make bouquets for the farmer's market. To make the bouquets more appealing to the
she would like to have an odd number of flowers in each. She wants to use all of the available flowers. To meet lasmines
requirements, how many flowers could she put in each bouquet?
HELP PLZZ
Answer:
Jasmine could have 84 bouquets with 1 flower in each,28 bouquets with 3 flower in each,12 bouquets with 7 flower in each or 4 bouquets with 21 flower in each.Step-by-step explanation:
The total number of flowers that jasmine has to make bouquets is 84.
We need to note that she want to use all the flowers.
Now let us write down all factors of 84.
84= 1 * 84 ....(1)
= 2 * 42 ....(2)
= 3 * 28 ....(3)
= 4 * 21 ....(4)
= 6 * 14 .....(5)
= 7 * 12 ....(6)
Now all we need is odd number of flowers in each bouquet,i.e,
All the numbers written in the right hand side of the above 1 to 6
numbered equations are factors of 84.
Since Jasmine wanted no flowers to be wasted so we can assume that number of flowers in each bouquet must be an odd factor of 84.
Therefore, odd factors of 84 are 1,3,7,21.
So Jasmine could have 84 bouquets with 1 flower in each,28 bouquets with 3 flower in each,12 bouquets with 7 flower in each or 4 bouquets with 21 flower in each.
Answer:
the answer is 7
Step-by-step explanation:
Amelia sells exquisite, hand-crafted jewelry. She makes a total of 12%
commission off of her sales. How much commission will Amelia make if
she sells $22,540 worth of jewelry?
Answer:
$2704.80
Step-by-step explanation:
If she makes 12% commission off of it, she makes [tex]\frac{22540}{1} *\frac{12}{100}=$2704.80\\[/tex]
Final answer:
To calculate Amelia's commission, convert the 12% commission rate to a decimal (0.12) and multiply it by her sales of $22,540. Amelia will earn a commission of $2,704.80.
Explanation:
The question asks us to calculate how much commission Amelia makes on her sales of hand-crafted jewelry, given a commission rate of 12% and sales amounting to $22,540. To find the commission, we need to multiply the total sales by the commission rate expressed as a decimal.
Steps to Calculate Commission
Convert the commission rate from a percentage to a decimal by dividing by 100: 12% / 100 = 0.12.
Multiply the sales amount by the decimal commission rate: $22,540 × 0.12 = $2,704.80.
Amelia's commission for selling $22,540 worth of jewelry is $2,704.80.
Which expression is equal to (2x − 2)(3x – 3)?
6x2 - 12x +6
5x2 - 6x-5
6x2 – 123 - 5
6x2 + 12x - 6
Answer:
6x^2-12x+6
Step-by-step explanation:
(2x-2)(3x-3)
6x^2-6x-6x+6
6x^2-12x+6
The product of (2x - 2) and (3x - 3) using the FOIL method is 6x^2 - 12x + 6.
Explanation:The expression (2x − 2)(3x – 3) can be considered as a product of two binomials and can be solved by applying the distributive property or the FOIL method - First, Outer, Inner, Last. We first distribute the 2x from the first binomial to each term in the second binomial (6x2 - 6x) and do the same with -2 (-6x + 6). Adding these together leads to 6x2 - 12x + 6, which is none of the options provided.
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Arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown.
162m3n4 + 45n
= 9n(_______ + 5)
Answer:
the answer is 18m3n3
Step-by-step explanation:
Answer:
the answer is 18m3n3
Step-by-step explanation: :)) good luck!!
Given: x + y = 15.
Which of the following are ordered pairs of this equation?
{(-3, 14),(0, 15),(3, 16)}
{(16, -3),(15, 0),(14, 3)}
{(-3, 16),(0, 15),(3, 14)}
Answer:
{(-3, 16),(0, 15),(3, 14)}
Step-by-step explanation:
It shows on a graph.
Damian has a spinner. He spun the arrow 60 times and it landed on green 12 times.
Based on the data, how many times would the arrow land on green if Damian only spun it 10 times?
Answer:
it would be 2
Step-by-step explanation:
what you do to find the probability is to divide so you divide 60 from 12 which automatically = 5 so then you divide 10 from 5 which gives you 2
The Correct Answer is 2 times
On spinning 60 times domain landed arrow 12 times.
On 1 time spinning, he will land an arrow [tex]\frac{60}{12}[/tex]=5
∴ number of times arrow landed on green = [tex]\frac{10}{5}[/tex]=2
How do you calculate probability?Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring. In the case of rolling a 3 on a die, the number of events is 1 (there's only a single 3 on each die), and the number of outcomes is 6.
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Spotlight Dance increased the number of dancers on its competition team. Last
season, there were 10 dancers this season, there were 18. What was the perecent
of increase?
Answer:
80%
Step-by-step explanation:
To find percentage increase, we use the following formula:
Percentage Increase = [tex]\frac{New-Old}{Old}*100[/tex]
Here
New means the latest value (which is 18 dancers)
Old means the previous value (which is 10 dancers)
The Multiplication by 100 is to convert the decimal answer to percentage.
So, we have:
New = 18
Old = 10
Now we substitute and find:
[tex]\frac{New-Old}{Old}*100\\\frac{18-10}{10}*100\\\frac{8}{10}*100\\80[/tex]
So, there was an increase of 80%
The stem and leaf plot shows high temperatures
recorded each day at the beginning of the month.
Which temperature occurs the most frequently?
degrees
During how many days was the high in the 70s?
days
Answer: 54 Degrees, 2days
Step-by-step explanation:
Answer:
54 Degrees, 2days
Step-by-step explanation:
Marcus solved this problem and found that 190% of 20 is 380. Is he correct? Explain why or why not.
Answer:
no
Step-by-step explanation:
because, 190% as a decimal is 1.9. So 1.9 times 20 is 38. Not 380.
Please mark me brainliest
Number 41, 42, 43,44, and 45 please. Or whichever one you can help with ñ. Tysm
Answer:
41) 7 packages
42) not sure
43) 11. 8.69/.79
44) 5. 14.50/2.90
45) 13.72. subtract
Answer:
41)7 packages
42)$10.00
43)$8.69
44)5 packages
Step-by-step explanation:
41) 14 packages =$40
÷2 ÷2
___ ___
7 20
42) 28 kuna :$5.00
28x2=56 $5.00x2=10.00
43) 1p= $0.79
$8.69/.79=11
11p=$8.69
44) So, 44 is basically the same thing as 43, but different #s. if 1s=2.90, 14.50/2.90=5
I will give brainliest
7.which pair of numbers is relatively prime?
14/35
14/38 *
14/81
14/91
8. what value of b solves the equation?
b-^3=1/27
9
3
27 *
81
9.
what is 10^-5 written in standard form?
10,000
1000
0.0001
0.00001
10.
what is 100,000,000,000 written as a power of ten?
9
8 *
10
11
CHECK ANSWERS
Answer:
7. The numbers 14/81 are relatively prime
8. b=3
9. 0.00001
19. 11
Step-by-step explanation:
7. Relatively prime numbers have no common factors. We only have to factor each number and compare
14=2*7
35=5*7
38=2*19
81=9*9
91=7*13
The first two numbers have 7 in common
The second have 2 in common
The third set have no common factors
The fourth set have 7 in common
The numbers 14/81 are relatively prime
8. [tex]b^{-3}=\frac{1}{27} => b^3=27 => b=\sqrt[3]{27} =3[/tex]
9. [tex]10^{-5}=\frac{1}{100000}=0.00001[/tex]
10. 100,000,000,000=10*10*...10 as many times as zeroes there are, so
[tex]100,000,000,000=10^{11}[/tex]
Use 4 fours to make 2
Answer:
4/2=2
Step-by-step explanation:
Step-by-step explanation:
4/4 + 4/4
1 + 1
2
A pattern has 6 blue triangles to every 42 yellow triangles what is the ratio of yellow triangles to blue triangles
How long is a guy wire reaching from the top of a 6ft. Pole to a point on the ground 4ft. From the pole
Answer:
the guy wire is 7.211 ft long
Step-by-step explanation:
Notice that we are in the presence of a right angle triangle formed by: the height (the standing 6 ft pole), the base (the distance from the pole to the anchoring point on the ground), and the actual guy wire. See attached image for reference.
Notice that since pole and ground are perpendicular to each other (at 90 degrees) , the guy wire forms what is called the "hypotenuse" (longest side) of the right angle triangle. We can therefore use the Pythagorean Theorem to solve this problem with the formula for the hypotenuse:
[tex]Hypotenuse=\sqrt{side1^2 +side2^2} \\Hypotenuse= \sqrt{6^2+4^2}\\Hypotenuse=\sqrt{36+16} \\Hypotenuse=\sqrt{52} \\Hypotenuse=7.2111\, ft[/tex]
An automobile travels 1266 miles on 150 gal of gasoline. What is the average mileage per gallon of gasoline?
Answer:8.44 miles per gallon
Step-by-step explanation:
1266/150=
8.44 miles per gallon
combine like terms 5x+3+2x
Answer:
7x+3
Step-by-step explanation:
The only like terms are 5x and 2x
5+2=7
Answer:
7x + 3
Step-by-step explanation:
Like terms are numbers with the same variables.
In 5x+3+2x, there are two terms that have the variable x.
You can combine 5x and 2x to be 7x.
5x + 3 + 2x
= 7x + 3
3 cannot be combined with them because it has no variable.
Length 10 cm and width 7 cm
Answer:
70 cm^2
Step-by-step explanation:
A=LW=10*7=70
Tamara has 1 1/4 cups of flour.It takes 5/16 of a cup to make one of her jumbo muffins.With the flour she has,how many jumbo muffins can Tamara make?
5/16 cups___1 muffin
5/4 cups___X=4 muffins
(5/4) / (5/16) = 4
MATH PEOPLE 25 POINTS TO ANSWER THIS HELP MEEEEEEE
Answer:
Step-by-step explanation:
1d
2c
3a
4c
6 4=110(alt exter) 3=70(Suppl of 4) 1=70(vertical with 3)
7 x=3
8x+8=32
8x=24
x=3
8
42=8x-14
56=8x
x=7
42=56-14