Answer:
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 - (3 - 2) = 10 - 1 = 9
Step-by-step explanation:
h(x) = [tex]x^2 + 1[/tex]
k(x) = x - 2
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 -(3 - 2) = 10 - 1 = 9
1. Slove the system of equations, first by graphing, and then algebraically. (8 points) y=x-2 and y=-2x+7
The solution of the equation is [tex]x=3[/tex] and [tex]y=1[/tex]
Explanation:
The equations are [tex]y=x-2[/tex] and [tex]y=-2 x+7[/tex]
First we shall solve the equation graphically.
The image of the graph is attached below.
This contains the solution to the system of equations.
The equations [tex]y=x-2[/tex] and [tex]y=-2 x+7[/tex] are plotted on the graph.
The intersection of these two equations are the solutions of the system of equations.
Thus, the intersection of the two equations are [tex]x=3[/tex] and [tex]y=1[/tex]
Now, we shall solve the equation algebraically.
Let us solve the equation using substitution method.
Let us substitute [tex]y=x-2[/tex] in [tex]y=-2 x+7[/tex], we get,
[tex]x-2=-2x+7[/tex]
Adding both sides by 2x, we have,
[tex]3x-2=7[/tex]
Adding both sides by 2, we get,
[tex]3x=9[/tex]
Dividing both sides by 3,
[tex]x=3[/tex]
Thus, the value of x is 3.
Substituting [tex]x=3[/tex] in [tex]y=x-2[/tex], we get,
[tex]y=3-2\\y=1[/tex]
Thus, the value of y is 1.
Hence, The solution of the equation is [tex]x=3[/tex] and [tex]y=1[/tex]
Solve the problem.
The formula P = 0.62x2 - 0.043x + 3 models the approximate population P, in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 42,336 fish?
Answer:
The population reaches 42,336 fish in 2258
Step-by-step explanation:
Given:
[tex]P = 0.62x^2 - 0.043x + 3[/tex]
To Find:
Time taken to reach 42,336 = ?
Solution:
According to the question x is the number of years after which the population .
Then
[tex]42336 = 0.62x^2 - 0.043x + 3[/tex]
[tex]0 = 0.62x^2 - 0.043x + 3- 42333[/tex]
[tex]0.62x^2 - 0.043x -42333[/tex] = 0
Solving using quadratic formula
[tex]x =\frac{ -b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
[tex]x =\frac{ -(-0.043)\pm \sqrt{(-0.043) -4(0.62)(42333)}}{2(42333)}[/tex]
[tex]x =\frac{ -(-0.043)\pm \sqrt{(0.001849) -0.10664}}{84666}[/tex]
x=261.337 x=−261.268
Neglecting the negative value we get
x = 261.337
x = 261 approx
261 years after 1997 = 2258
To find the year when the population reaches 42,336 fish, solve the quadratic equation P = 42.336 by factoring, completing the square, or the quadratic formula.
Explanation:To find the year when the population reaches 42,336 fish, we need to solve the equation P = 42.336.
First, rewrite the equation as a quadratic equation: 0.62x^2 - 0.043x + 3 = 42.336.
Then, solve the quadratic equation using factoring, completing the square, or the quadratic formula. The solution will give you the value of x, which represents the number of years since 1997. Add this value to 1997 to find the year when the population will reach 42,336 fish.
Learn more about Solving a quadratic equation here:https://brainly.com/question/33455297
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Aaron invest $50 each month for 9 months in an account that pays 7.5% APR compounded monthly. What is the future value of Aaron's account after 9 months?
Answer: 461.45 APEX
Step-by-step explanation:
Answer:
its is $461.45
Step-by-step explanation:
1. Which of the following shows the correct use of the Distributive Property when solving 1/3( 33
- y) = 135. 2
• (33 - y) = 1/3 * 135.2 (your response)
. (1/3*33) - 1/3y = 1/3* 135.2
. (1/3 * 33) - 1/3y = 135.2
. (1/3 * 33) + 1/3y = 135.2
Please I need this asp
Answer:
The option [tex](\frac{1}{3}\times 33)-\frac{1}{3}y=\frac{1}{3}135.2[/tex] is correct
Step-by-step explanation:
Given equation is [tex]\frac{1}{3}(33-y)=135.2[/tex]
The option shows correct usage of distributive property is
[tex](\frac{1}{3}\times 33)-\frac{1}{3}y=\frac{1}{3}135.2[/tex]
( by distributive property [tex]a(x+y)=ax+ay [/tex] here [tex]a=\frac{1}{3}[/tex], x=33 and y=-y )
Therefore the option [tex](\frac{1}{3}\times 33)-\frac{1}{3}y=\frac{1}{3}135.2[/tex] is correct.
The correct use of the Distributive Property for the equation 1/3(33 - y) = 135.2 is to apply multiplication to each term inside the parentheses by 1/3, resulting in (1/3 * 33) - (1/3)y = 135.2.
The question is asking for the correct use of the Distributive Property when solving the equation 1/3(33 - y) = 135.2.
The correct application of the Distributive Property to solve the equation would involve multiplying both terms inside the parentheses by 1/3. Here's how the property is correctly applied:
(1/3 * 33) - (1/3 * y) = 135.2
(33/3) - (1/3)y = 135.2
11 - (1/3)y = 135.2
Hence, the correct option that uses the Distributive Property properly is:
(1/3 * 33) - (1/3)y = 135.2
If the angular size of a tree at a distance of 0.5 miles is 1/2, how tall is the tree
The tall of the tree is 23.048 ft.
Solution:
Given data:
Angular size of a tree = [tex]\left(\frac{1}{2}\right)^{\circ}[/tex]
Distance = 0.5 miles = 2640 feet
To find the tall of the tree:
Formula to calculate the height of the tree is
[tex]$\text{Physical size}= \text{Angular size}\times\frac{2\pi\times \text{distance}}{360^{\circ}}[/tex]
[tex]$ = \left(\frac{1}{2}\right)^{\circ}\times\frac{2\pi\times 2640}{360^{\circ}}[/tex]
[tex]$ = \left(\frac{1}{2}\right)^{\circ}\times\frac{44\pi}{3^{\circ}}[/tex]
[tex]$ = 23.048[/tex]
Physical size = 23.048 ft
Hence the tall of the tree is 23.048 ft.
Which expressions are equivalent to 2^5•2^4? Check all that apply.
Option A: [tex]2^9[/tex]
Option E: [tex]2^{-2}.2^{11}[/tex]
Option F: [tex](2.2.2.2.2)(2.2.2.2)[/tex]
Solution:
Given expression is [tex]2^5.2^4[/tex].
To find which expression is equivalent to the given expression.
Option A: [tex]2^9[/tex]
Using exponent rule: [tex]a^b.a^c=a^{(b+c)}[/tex]
[tex]2^5.2^4=2^{(5+4)}=2^9[/tex]
Therefore [tex]2^9[/tex] is equivalent to the given expression.
Option B: [tex]2^{20}[/tex]
It is not equivalent to the given expression.
Option C: [tex]2.2^9[/tex]
[tex]2.2^9=2^{(1+9)}=2^{10}[/tex]
Therefore, It is not equivalent to the given expression.
Option D: [tex]2^{10}.2^2[/tex]
[tex]2^{10}.2^2=2^{(10+2)}=2^{12}[/tex]
Therefore, It is not equivalent to the given expression.
Option E: [tex]2^{-2}.2^{11}[/tex]
[tex]2^{-2}.2^{11}=2^{(2-11)}=2^9[/tex]
Therefore, It is equivalent to the given expression.
Option F: [tex](2.2.2.2.2)(2.2.2.2)[/tex]
[tex](2.2.2.2.2)(2.2.2.2)=2^5.2^4[/tex]
Therefore, It is equivalent to the given expression.
Hence option A, Option E and Option E are equivalent to the given expression.
Answer:
AEF
Step-by-step explanation:
I need help with this question
Answer:
You should disagree with the student's claim.
The number of revolutions during a five-mile ride is 323.4
Given the following geometric sequence, find the common ratio: {16, 64, 256, ...}.
Answer:
The common ratio is 4
Step-by-step explanation:
We need to divide a term by the previous term to find the common ratio in a geometric sequence:
64 ÷ 16 = 4
256 ÷ 64 = 4
By doing it twice we can confirm that the common ratio is 4
Given the following geometric sequence, the common ratio would be 4.
A school football team is selling raffle tickets As a fundraiser it cost them $155 to print the tickets and they would like to make at least a $2500 profit how much money do they need to raise to cover the cost of the printing and meet their goals
Answer:
They need $2655 to raise to cover the costs of the printing and meet their goal.
Step-by-step explanation:
Consider the provided information.
As a fundraiser it cost them $155 to print the tickets and they would like to make at least a $2500 profit
Let x (in dollar) represents the fund raised.
The money spent on printing ticket is $155.
The profit they would like to make at least is $2500.
Therefore, the required inequality is:
[tex]x-155\geq 2500[/tex]
Simplify the inequality.
[tex]x\geq 2500+155\\x\geq 2655[/tex]
Therefore, they need $2655 to raise to cover the costs of the printing and meet their goal.
How do you do this question?
Answer:
x={1,2,3}
Step-by-step explanation:
The given inequality is
[tex]1 \leqslant \frac{6x - 1}{3} \: < \: 7[/tex]
We multiply through by the LCM of 3 to get:
[tex]3\leqslant 6x - 1\: < \: 21[/tex]
We add 1 to both sides to get:
[tex]3 + 1\leqslant 6x \: < \: 21 + 1[/tex]
[tex]4\leqslant 6x \: < \: 22[/tex]
Divide through by 6 to get:
[tex] \frac{4}{6} \leqslant x \: < \: \frac{22}{6} [/tex]
This gives us:
[tex]\frac{2}{3} \leqslant x \: < \: \frac{11}{3} [/tex]
[tex]0.67 \leqslant x \: < \:3.67[/tex]
Since x is an integer, the possible values are:
x={1,2,3}
Which best describes the function on the graph?
A. direct variation; k = 3
B. direct variation; k = 1/3
C. inverse variation; k = 3
D. inverse variation; k = 1/3
Answer:A i think
Step-by-step explanation:
Answer:
B. Direct Variation: k = 1/3
Step-by-step explanation:
Your Welcome
If Kayla ran 9/10 mile yesterday today she ran 8/9 the distance she ran yesterday which day did Kayla run more miles? Explain your reasoning
Answer:
Kayla ran longer miles yesterday than today
Step-by-step explanation:
Distance Kayla ran yesterday be x
Then x = [tex]\frac{9}{10}[/tex] mile
That is x = 0.9 miles
The Distance she ran today be y
Then y = [tex]\frac{8}{9}[/tex] of the distance she ran yesterday
So the distance Kayla ran today
= [tex]\frac{8}{9}[/tex] [tex]\times \text { the distance she ran yesterday }[/tex]
On substituting the value
y = [tex]\frac{8}{9} \times\frac{9}{10}[/tex]
y = [tex]\frac{8}{10}[/tex]
y = 0.8 miles
x is greater than y
0.9 > 0.8
What is X plus 11 equals 15
Answer:
X plus 11 equals 15 is 4. X equals 4.
Step-by-step explanation:
X + 11 = 15
4 + 11 = 15
X = 4
to find X you needed to subtract 11 from 15 and what you got would be X
Janelle ate 82% of the pie. What fraction of the pie remained? help meee
Answer:
There is 18% left of the pie.
Step-by-step explanation:
There is only 100% of a pie. If she at 82% then there is 18% left. 100-82=18
Answer:
9/50
Step-by-step explanation:
for a percentage to turn into a fraction all u have to do put the percent over 100 so in this case first subtract total 100-82= 18% so then 18/100 simplified it would be 9/50
-4/4+160%+1/5 as an exact decimal
Answer:
0.8
Step-by-step explanation:
-4/4=-1
160%=1.6
1/5=0.2
--------------
-1+1.6+0.2
0.6+0.2
0.8
What is the approximate area of the circle shown? Use 3.14 to approximate pi. Round your answer to the nearest hundredth.
Answer:
[tex]A=153.86\ cm^2[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ cm[/tex] ----> the radius is half the diameter
substitute
[tex]A=(3.14)(7)^{2}=153.86\ cm^2[/tex]
Answer:
C
Step-by-step explanation
THE ANSWER IS C
janice is asked to solve0=64x^2+16x-3 what is x
Answer:
x=-1/8 or 3/8
Step-by-step explanation:
64x^2+16x-3=0
By Mid term breaking
64x^2-24x+8x-3=0
8x(8x-3)+1(8x-3)=0
(8x+1)(8x-3)=0
Either
8x+1=0 OR 8x-3=0
8x=-1 OR 8x=3
x=-1/8 OR x=3/8
Marco has baked and frosted 4 dozen heart-shaped sugar cookies to bring to his class party. He wants to
put 3 gumdrops on each cookie. He has 4 bags of 40 gumdrops. Does he have enough gumdrops to put 3
on each cookie? Explain.
Answer:
16Step-by-step explanation:
4 x 12=48 48 divided by 3=16
ak = v+w solve for a
Answer:
a = [tex]\frac{v+w}{k}[/tex]
Step-by-step explanation:
Given
ak = v + w ( isolate a by dividing both sides by k )
a = [tex]\frac{v+w}{k}[/tex]
Which choice shows a correct way to find 6 × 3 × 5?
A. 6 × (3 × 5)
B. 6 + 5 × 3
C. 6 × (3 + 5)
D. 6 × (5 – 3)
Answer:
C
Step-by-step explanation:
Maggie has a circular table cloth with a 72-inch diameter that she plans to sew lace around. if the lace comes in 3-foot rolls, how many rolls will she need?
She will need 7 rolls of lace
Step-by-step explanation:
The given is:
Maggie has a circular table cloth with a 72-inch diameterShe plans to sew lace aroundThe lace comes in 3-foot rollsWe need to find how many rolls she will need
∵ The diameter of the table is 72 inches
- Change the inches to feet because the length of the lace in
the rolls by feet
∵ 1 foot = 12 inches
∴ 72 inches = 72 ÷ 12 = 6 feet
∵ She plans to sew lace around the table
∴ The length of the lace is equal to the circumference of the table
∵ The circumference of a circle = π d, where d is its diameter
∴ The length of the lace = π(6)
∴ The length of the lace = 18.84955592 feet
∵ The lace comes in 3-foot rolls
- Divide the length of lace by 3 to find the numbers of the rolls
∴ The number of rolls = 18.84955592 ÷ 3
∴ The number of rolls = 6.283185
∴ She must buy 7 rolls
She will need 7 rolls of lace
Learn more:
You can learn more about the circumference of a circle in brainly.com/question/8929610
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Jolie uses the childcare facilities at her gym. Her monthly dues are $32, and childcare is $9 per visit. This month, she does not
wish to spend more than $122 for both dues and childcare. If x represents the number of times she can use childcare services,
which of the following inequalities symbolizes this situation?
A.
$32x+ $9 > $122
B. $32x + $9 < $122
C. $9x + $32> $122
D. $9x + $32 < $122
Answer:
The answer is D
Step-by-step explanation:
Answer:
D. $9x + $32 < $122
Step-by-step explanation:
given :
x is the number of visits
$9 is the cost per visit
$32 is the monthly dues
the amount she pays each month
= monthly dues + (cost per visit x number of visits)
= 32+ 9x (rearrange)
= 9x + 32
given that she does not wish to spend more than $122, that means she wants to spend LESS than $122, i.e
amount spent < $122
or
9x + 32 < 122 (answer D)
4/6 x - 6 = - 24
Solve for X
Answer:
-27
Step-by-step explanation:
4/6x-6=-24
+6 +6
4/6x=-18
6/4×4/6x=-18×6/4 ->multiply by reciprocal to get rid of x
x=-108/4
x=-27
Laura created a website to create T-shirts. In the first month she put up her website she had only a single T-shirt order. Each month she got more orders. Following this function f(n)=2n-1
How many total orders did she receive over the first year?
Laura received 144 orders over the first year
Solution:
Given function is:
f(n) = 2n - 1
Where, "n" is the month
In the first month she put up her website she had only a single T-shirt order
f(1) = 2(1) - 1 = 2 - 1
f(1) = 1
There are 12 months in a year
For the second month, and third month and so on, substitute n = 2, 3 and so on
f(2) = 2(2) - 1 = 4 - 1 = 3
f(3) = 2(3) - 1 = 6 - 1 = 5
f(4) = 2(4) - 1 = 8 - 1 = 7
f(5) = 2(5) - 1 = 10 - 1 = 9
f(6) = 2(6) - 1 = 12 - 1 = 11
f(7) = 2(7) - 1 = 14 - 1 = 13
f(8) = 2(8) - 1 = 16 - 1 = 15
f(9) = 2(9) - 1 = 18 - 1 = 17
f(10) = 2(10) - 1 = 20 - 1 = 19
f(11) = 2(11) - 1 = 22 - 1 = 21
f(12) = 2(12) - 1 = 24 - 1 = 23
Thus total orders received over first year:
Total orders = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Total orders = 144
Thus she received 144 orders over the first year
The circumference of a circle is about 37.7 cm and the diameter is about 12 cm. What expression best represents the value of π?
6/37.7
37.7/12
37.7/6
12/37.7
Answer:
The best expression represents the value of π is [tex]\frac{37.7}{12}[/tex] ⇒ 2nd answer
Step-by-step explanation:
π is the ratio between the circumference of the circle and the length of its diameter
[tex]\frac{C}{d}=\pi[/tex] , where
C is the circumference of the circled is the diameter of the circle∵ The circumference of the circle is about 37.7 cm
∵ The diameter of the circle is about 12 cm
- Find the ratio between them
∴ [tex]\frac{C}{d}=\frac{37.7}{12}[/tex]
∵ [tex]\frac{C}{d}=\pi[/tex]
- Equate the two right hand sides
∴ [tex]\frac{37.7}{12}=\pi[/tex]
∴ The best expression represents the value of π is [tex]\frac{37.7}{12}[/tex]
Raj and Dev leave the school at 3:30 PM and cycle in opposite direction. If their speeds are 5km/hr and 7km/hr respectively, at what time they will be 18 km apart?
They will be 18 km apart at 5 pm.
Step-by-step explanation:
Speed of Raj is 5km/hr and speed of Dev is 7km/hr
Since they are going in opposite direction,
So, every 1 hours there difference will be (7 + 5) km = 12 km
Now, they will be apart 18 km distance 18/12 hours = 1 hour 30 min
The time will be 3:30 PM + 1 hour 30 min = 5 :00 PM
P divided by 28 = -26
Answer:54 when ever you have a positive and plus you always add
Step-by-step explanation:
How do you change 2/5 to a precent
Answer:
40%
Step-by-step explanation:
Percent is how much out of 100.
We have 2/5, so find equivalent fractions:
2/5 = 4/10 = 40/100
2/5 = 40%
A shop sells one pound bags of peanuts for $2 and three pound bags of peanuts for $5. If 9 bags are purchased for a total of $36, how many three pound bags were purchased?
Answer:7
Step-by-step explanation:
5x7=35
Answer:
Six
Step-by-step explanation:
What do we know?
1 lb pack = $2
3 lbs pack = $5
9 packs are purchased for $36
Solve
The biggest amount of 3-pound bags can be 7. That cannot be because that would be $35, and there are no 1-pound bags.
Go down to 6. 6 bags of 3 pounds would cost $30. You can also get 3 2-pound bags to get to 36. Cost is reached. 6+3 = 9. Number of bags reached.
six 3-pound bags
What is the circumference of a tire with a radius of 22 centimeters
Answer:
Step-by-step explanation:
circumference= 2πr
= 2*[tex]\frac{22}{7}[/tex]*22
= 44*[tex]\frac{22}{7}[/tex]
= 968/7
= 138.28 cm
Answer:
Circumference of the Tire is [tex]138.16cm[/tex]
Step-by-step explanation:
Circumference of any figure is the total length of its boundaries.
Considering the tire as a circle.
Given:
radius of the tire= [tex]22cm[/tex]
circumference of a circle = [tex]2\pi r[/tex]
[tex]=2*\pi *22\\\\=44*\pi\\\\ =44(3.14)\\\\=138.16cm[/tex]
So, the circumference of the Tire is [tex]138.16cm[/tex]