Answer:
k=8
The problem:
The function y=2x+2 and y=-x+k intersect at the point (2,6).
Find the value of k.
Step-by-step explanation:
(2,6) is a point contained by both y=2x+2 and y=-x+k.
Let's see if it actually on y=2x+2.
x=2,y=6
y=2x+2
6=2(2)+2
6=4+2
6=6 is true so it (2,6) is on y=2x+2.
Now we want k such that (2,6) is on y=-x+k.
6=-2+k
Add 2 on both sides:
8=k
So k=8.
Answer:
k = 8
Step-by-step explanation:
y = 2x + 2
y = -x + k
2x + 2 = - x +k
3x = k - 2
x= 2 : k-2= 6
k = 8
Solve 23(3x+9)=−2(2x+6).
11 help cause I'm stuck
:3
11
let's say each restaurant has a container of soup which is the same size, let's say there is a total of "s" amount of soup in the container of each restaurant, so 5/4 of that much will just be (5/4)s and 7/4 of "s" is just (7/4)s.
well, one restaurant makes 20 servings from 5/4 of it and the other makes 25 from 7/4 of it,
[tex]\bf \cfrac{5}{4}s\div 20\implies \cfrac{5}{4}s\div \cfrac{20}{1}\implies \cfrac{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{4}s\cdot \cfrac{1}{\underset{4}{~~\begin{matrix} 20 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \boxed{\cfrac{1}{16}}s \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{4}s\div 25\implies \cfrac{7}{4}s\div \cfrac{25}{1}\implies \cfrac{7}{4}s\cdot \cfrac{1}{25}\implies \boxed{\cfrac{7}{100}}s[/tex]
now, which one is larger? well, we can simply put both fractions with the same denominator by multiplying one by the other's denominator,
[tex]\bf \cfrac{1}{16}\cdot \cfrac{100}{100}\implies \boxed{\cfrac{100}{1600}}\qquad \qquad \qquad \stackrel{\textit{\Large larger}}{\cfrac{7}{100}\cdot \cfrac{16}{16}\implies \boxed{\cfrac{112}{1600}}}[/tex]
You pay $1,261.95 for a table and chair set. The sales tax in your city is 5.25%. What was the original
price of the dining set?
$999
$1,099
$1,199
$1,256
Answer:$1,199
Step-by-step explanation:
$1,199 X 5.25%=$1,261.95
y = f(x) = -5X
Find f(x) when x = 0.
The value of the function f(x) = -5x when x = 0 is 0. This point also represents the y-intercept of a declining straight line graph.
To find the value of the function f(x) when x equals 0, we simply substitute 0 for x in the given function. The function provided is f(x) = -5x, which implies a linear relationship between y and x. Therefore:
f(0) = -5(0) = 0
The value of f(x) at x = 0 is 0, which also represents the y-intercept of the graph. Since the coefficient of x is negative, we know the graph is a declining straight line. However, at the point where x = 0, the graph will intersect the y-axis.
in this diagram below, the 2 line segments are congruent. Find the value of x
Answer:
Step-by-step explanation:
because the two line segments are the same length-->
12+10-x=18
x=22-18=4
The question aims to determine the value of x for two congruent line segments, typically involving algebraic and geometric methods; however, no specific solution can be provided without the diagram.
Explanation:The question involves finding the value of x when given two congruent line segments in a diagram. This typically requires the use of algebraic methods or the application of geometric theorems to establish relationships between the lengths represented in the diagram and solve for x.
Without the specific diagram, we cannot provide the direct steps to solve for x.
However, the context suggests the use of equations to calculate lengths. Common strategies include setting equations equal to each other when line segments are congruent and simplifying to find x.
The mention of bisectors and lines intersecting at right angles can also imply the use of properties related to parallel and perpendicular lines or the Pythagorean theorem.
Remember, when equations have two solutions for x, it's necessary to consider which solution is consistent with the geometric context of the problem.
u=3a-1
Solve the equation for the indicated variable: a
7x = 2y solve for y in terms of x
Y=?
Answer:
7x/2
Step-by-step explanation:
7x=2y
1) Divide both sides by 2:
y=7x/2
d÷2+3=21 can someone please answer this
Answer:
frist add 3 plus 2 then multiply it by 21 and then you will get 105 and 105 will represent d
A waitress sold 10 ribeye steak dinners and 45 grilled salmon dinners, totaling $591.99 on a particular day. Another day she sold 24 ribeye steak dinners and 15 grilled salmon dinners, totaling $583.39. How much did each type of dinner cost?
Answer:
The cost of a ribeye steak dinner is $18.68 and the cost of a grilled salmon dinner is $9.00
Step-by-step explanation:
Let
x ----> the cost of a ribeye steak dinner
y ----> the cost of a grilled salmon dinner
we know that
10x+45y=591.99 -----> equation A
24x+15y=583.39 ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (18.68,9.00)
see the attached figure
therefore
The cost of a ribeye steak dinner is $18.68 and the cost of a grilled salmon dinner is $9.00
Use the drop-down menus to complete the statements.
42 is
32 +3²
Therefore, AJKL is
52 is
32 +42
Applying the same method, AABC is
J
3
Answer:
Less than, acute, equal to, and right
Step-by-step explanation:
correct on edge.
Use the drop-down menus to complete the statements.
42 is less than 3^2 + 362.
Therefore, △JKL is acute.
5^2 is equal to 3^2 + 4^2.
Applying the same method, △ABC is right.
Your question is incomplete. Please read below to find the content.
Less than, acute, equal to, and right are the correct drop-down menus.
What is the acute angle?An angle that is measuring much less than ninety degrees is called an acute angle. This perspective is smaller than the proper angle (that is equal to 90 stages). For an instance, ∠30°, ∠forty-five°, ∠60°
What is called right angle?Any shape that could be a rectangular or a rectangle, will have its corners equal to ninety tiers or right angle. A proper attitude is therefore referred to as a ninety-diploma perspective. In geometry, the figure formed through two rays, referred to as the perimeters of the angle, sharing a common endpoint, known as the vertex of the angle is referred to as an attitude.
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Sheila, Lydia and Leila are sisters. One of them is allergic to dairy products.
At the school bazaar, Lydia ordered a chocolate milk, Leila ordered a coffee
milk shake, and Sheila ordered a ginger ale. Which sister has the allergy to
dairy products?
Answer:Sheila
Step-by-step explanation:
Yanni threw his paper airplane 15 1/2 feet. Adrian threw his paper airplane 3/4 of yanni's distance. What is the distance Adrian paper airplane? Explain how you found your answer
Answer:
19.125
Step-by-step explanation:
multiply 15.5 by 3 and then divide the answer by 4
Final answer:
To find the distance Adrian's paper airplane traveled, convert Yanni's distance to an improper fraction, calculate 3/4 of that, and then convert back to a mixed number. Adrian's paper airplane flew 11 5/8 feet.
Explanation:
The question asks us to calculate the distance Adrian's paper airplane traveled, given that it is 3/4 of the distance Yanni's airplane traveled, which was 15 1/2 feet. First, we need to convert Yanni's distance to an improper fraction. This gives us 31/2 feet. To find 3/4 of this distance, we multiply 31/2 feet by 3/4:
(31/2) × (3/4) = (31 × 3) / (2 × 4) = 93/8 feet.
Now, we convert the improper fraction back to a mixed number to find the distance. This gives us 11 5/8 feet (since 93 divided by 8 is 11 with a remainder of 5).
Therefore, Adrian's paper airplane traveled a distance of 11 5/8 feet.
Rewrite the function f of x equals 4 times one third to the 2 times x power using properties of exponents. f of x equals 4 times one ninth to the x power f of x equals 4 times two sixths to the x power f of x equals 16 times one third to the x power f of x equals 16 times one ninth to the x power
Answer:
A
Step-by-step explanation:
Answer:
Option 1
Step-by-step explanation:
Given : Function f of x equals 4 times one third to the 2 times x power.
To find : Rewrite the function using properties of exponents ?
Solution :
Writing the function in numeric terms,
f of x equals 4 times one third to the 2 times x power
i.e. [tex]f(x)=4\times (\frac{1}{3})^{2x}[/tex]
Solve the expression,
[tex]f(x)=4\times (\frac{1}{3}^2)^{x}[/tex]
[tex]f(x)=4\times (\frac{1}{9})^{x}[/tex]
i.e. f of x equals 4 times one ninth to the x power.
Therefore, Option 1 is correct.
5) A survey of 9,000 men in 2005 shows that 55% of them want to try a male birth control pill. How many of men
DO NOT want to try it? (2 points)
Please help
Answer:
@misterking_59 i 2,000 no prb
Step-by-step explanation:
∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?
Vertical angles are the same,
Set the two equations to equal each other to solve for x:
5x-7 = 8x-55
Subtract 5x from both sides:
-7 = 3x -55
Add 55 to both sides:
3x = 48
Divide both sides by 3:
x = 48 /3
x = 16
Now you have a value for x, solve angle D:
8x -55 = 8(16) - 55 = 128 - 55 = 73 degrees.
Answer:
The answer is m∠D is 73.
Step-by-step explanation:
In order to determine the answer, we have to know about vertical angles.
Vertical Angles are the angles opposite each other when two lines cross. These angles share the same vertex. I have attached an image that shows vertical angles.
So, according to the definition:
m∠C=m∠D
m∠C=5x-7
m∠D=8x-55
[tex]5x-7=8x-55\\5x-8x=-55+7\\-3x=-48\\x=\frac{-48}{-3}\\ \\x=16[/tex]
m∠D=8*16-55=73
Finally, the angle m∠D is 73.
Pd).
cot x/sec x
show that -=cos ecx -sin x
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• cot x = [tex]\frac{cosx}{sinx}[/tex]
• sec x = [tex]\frac{1}{cosx}[/tex] and cosec x = [tex]\frac{1}{sinx}[/tex]
Consider the left side
[tex]\frac{cotx}{secx}[/tex]
= [tex]\frac{cosx}{sinx}[/tex] × cosx
= [tex]\frac{cos^2x}{sinx}[/tex]
= [tex]\frac{1-sin^2x}{sinx}[/tex]
= [tex]\frac{1}{sinx}[/tex] - [tex]\frac{sin^2x}{sinx}[/tex]
= cosec x - sin x
= right side ⇒ verified
Keith has $500 in a savings account at the beginning of the summer. He withdraws $25 per week for food,clothing, and movie tickets. How many weeks can Keith withdraw money from his account?
Answer:
20 weeks.
Step-by-step explanation:
So, he has $500 in savings and he's taking out $25 each week. That would be $25 x ?. Which is the same as 500 divided by 25 which equals 20. I hope this helps!
Keith can withdraw $25 each week from his $500 savings account for 20 weeks.
Keith starts with $500 in his savings account and withdraws $25 every week. To determine how many weeks he can continue these withdrawals, we need to divide his initial amount by the weekly withdrawal amount.
Let's perform the calculation step by step:
Initial amount in the savings account: $500Weekly withdrawal amount: $25Number of weeks Keith can withdraw money = $500 / $25Perform the division: $500 ÷ $25 = 20 weeksSo, Keith can withdraw money from his account for 20 weeks.
What is the polynomial function of least degree whose only zeros are -3, ,-2, and 4 ?
The polynomial function of least degree with zeros -3, -2, and 4 is f(x) = (x+3)×(x+2)×(x-4), which is a cubic polynomial.
The polynomial function of least degree with given zeros of -3, -2, and 4 is derived from the fact that if a polynomial has zeros at x=a, x=b, and x=c, then it can be represented as f(x) = k×(x-a)×(x-b)×(x-c), where k is any non-zero constant. Given the zeros -3, -2, and 4, the polynomial function is:
f(x) = k×(x+3)×(x+2)×(x-4)
Because the question does not specify a leading coefficient, we can assume k=1 for the least degree polynomial. Thus, the final form of the polynomial would be:
f(x) = (x+3)×(x+2)×(x-4)
Expanding this would give us a cubic polynomial, which is the polynomial of least degree that satisfies the condition of having exactly these three zeros.
Triangle PQR is transformed to similar triangle P'Q'R'.
What is the scale factor of dilation?
1 over 2
1 over 3
1 over 4
1 over 5
Please explain your work, it'd really help if I understood why that's the answer then just accepting an answer. I'm really confused so please, if you can, explain your work!
Answer:
The answer is 1/2
Step-by-step explanation:
If you look at the distance between P and R and the dilation between P' and R' you would get 4 and 2. This the scale dilation is 1/2. Multiply 1/2 by 4 and you would get 2.
Answer:
1/2
Step-by-step explanation:
10
TIME REMAINING
53:10
The functions f(x) and g(x) are graphed.
Which represents where f(x) = g(x)?
O f(2) = g(2) and f(0) = g(0)
O f(2) = g(0) and f(0) = g(4)
O f(2) = g(0) and f(4) = g(2)
O f(2) = g(4) and f(1) = g(1)
Answer:
first one. Since its X crosses or passes (2,0)
Step-by-step explanation:
The value of function represents with same domain f(x)= g(x) is f(2) = g(2) and f(0) = g(0).
We know that two functions f and g are said to be equal if:
(i) f and g have same domain D
(ii) for all x ∈ D, f(x) = g(x)
Thus, we must select the response that best captures the situation where f(x) = g. (x)
Considering the fact that f(x) and g(x) are defined on the same domain
If they are equivalent for all values of x in the domain, then f(x) = g(x).
Thus, f(2) = g(2) and f(0) = g(0)
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What digit is in the tens place in the number 35,176?
Answer:7
Step-by-step explanation:
Ten Thousands Thousands Tens
3 5 7
Answer:
7
Step-by-step explanation:
The ones place always starts on the left then it works it way up.
ones, Tens, hundreds, thousands, ten thousands and it goes on in the same ones tens hundreds pattern
A house on the market was valued at $262,000. After several years, the value increased by 9%. By how much did the house's value increase in dollars? What is the current value of the house?
Answer:
The house increases by $23,580 and he current value of the house is $285,580
Step-by-step explanation:
A house on the market was valued at $262,000. After several years, the value increased by 9%.
The first part of the question is to find by how much the house's value increase in dollars, to calculate this, we will simply find;
9% of $262,000
= [tex]\frac{9}{100}[/tex] × $262 000
= [tex]\frac{2358000}{100}[/tex]
=$23580
Therefore, the house's value increase by $23580
The second part of the question is to fin the current value of the house. Hence;
Current value of the house = $262,000 + $23580=$285,589
Therefore the current value of the house is $285,589
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Divide the following polynomial and then place the answer in the proper location on the grid.
8y 7 ÷ 4y 5
Answer:
2y^2. 8/4 = 2 and y^7/y^5 is y^2 i don't know if this is what you completely asked for but here is the answer
Step-by-step explanation:
Division of the given polynomial [tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]is equal to [tex]2y^{2}[/tex].
What is division?" Division is defined as the distribution of a given quantity into equal parts as per the given condition."
Formula used
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] [tex]= a^{m-n} , m > n[/tex]
According to the question,
Given polynomial,
[tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]
Division of given polynomial also use the formula we get,
[tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]
[tex]= 2 y^{7-5} \\\\= 2y^{2}[/tex]
Hence, division of the given polynomial [tex]8y^{7}[/tex] ÷ [tex]4y^{5}[/tex]is equal to [tex]2y^{2}[/tex].
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the perimeter of a rectangle if the width is 3 centimeters and the length is 6 centimeters longer than the width.
Answer:
24
Step-by-step explanation:
Length 9 (3+6)
Width 3
Perimeter = 2 times length + 2 times width
18 + 6 = 24
you are designing a room for a house and are drawing a floor plan. The room is actually 18 feet wide. On your floor plan, you draw the room as 6 inches wide. what is the scale factor for the floor plan
Answer:
1:3
Step-by-step explanation:
18 / 6 = 3
Answer:
3 feet per inch
Step-by-step explanation:
trust me bro
George has a mass of 65kg. What would George weigh on the Moon? (The gravitational field strength on the Moon is 1.6N/kg.)
George would weigh
65 kg × 1.6N /kg = 104 Newtons
That's compared to around 650 Newtons on earth.
Answer: Weight of George on Moon =104 N
Step-by-step explanation:
Given : George has a mass of 65 kg.
The gravitational field strength on the Moon is 1.6N/kg.
Then, the weight of George on Moon = George's Mass x Gravitational field strength
=[tex]65\times1.6=104\text{ Newtons}[/tex]
Hence, the weight of George on Moon =104 N
I need help on 21 can you please show your work
is -8 a solution to the equation 3x=16-5x
Answer: YEP
Step-by-step explanation: -8 makes it -24=16-40, which is -24
I HOPE THIS HELPS. HAVE THE MOST AMAZING WEEKEND EVER CHILD
༼ つ ◕_◕ ༽つ
Can someone please help me
Answer:
C
Step-by-step explanation:
Given
2r + (t + r) ← distribute parenthesis by 1
= 2r + t + r ← collect like terms
= 3r + t
Which is not represented by the given options → C
Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4% interest on the total investment. How much money did he put in each account?
Answer:
Mathew invested $600 and $2400 in each account.
Solution:
From question, the total amount invested by Mathew is $3000. Let p = $3000.
Mathew has invested the total amount $3000 in two accounts. Let us consider the amount invested in first account as ‘P’
So, the amount invested in second account = 3000 – P
Step 1:
Given that Mathew has paid 3% interest in first account .Let us calculate the simple interest [tex](I_1)[/tex] earned in first account for one year,
[tex]\text {simple interest}=\frac{\text {pnr}}{100}[/tex]
Where
p = amount invested in first account
n = number of years
r = rate of interest
hence, by using above equation we get [tex](I_1)[/tex] as,
[tex]I_{1}=\frac{P \times 1 \times 3}{100}[/tex] ----- eqn 1
Step 2:
Mathew has paid 8% interest in second account. Let us calculate the simple interest [tex](I_2)[/tex] earned in second account,
[tex]I_{2} = \frac{(3000-P) \times 1 \times 8}{100} \text { ------ eqn } 2[/tex]
Step 3:
Mathew has earned 4% interest on total investment of $3000. Let us calculate the total simple interest (I)
[tex]I = \frac{3000 \times 1 \times 4}{100} ----- eqn 3[/tex]
Step 4:
Total simple interest = simple interest on first account + simple interest on second account.
Hence we get,
[tex]I = I_1+ I_2 ---- eqn 4[/tex]
By substituting eqn 1 , 2, 3 in eqn 4
[tex]\frac{3000 \times 1 \times 4}{100} = \frac{P \times 1 \times 3}{100} + \frac{(3000-P) \times 1 \times 8}{100}[/tex]
[tex]\frac{12000}{100} = \frac{3 P}{100} + \frac{(24000-8 P)}{100}[/tex]
12000=3P + 24000 - 8P
5P = 12000
P = 2400
Thus, the value of the variable ‘P’ is 2400
Hence, the amount invested in first account = p = 2400
The amount invested in second account = 3000 – p = 3000 – 2400 = 600
Hence, Mathew invested $600 and $2400 in each account.