The solution of the given equation √x - 3 + 1 = 6 will be x = 64 so option (A) will be correct.
What is the equation?An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For example 8x + 7y = 15.
Given the equation,
√x - 3 + 1 = 6
√x + (-3 + 1) = 6
√x - 2 = 6
√x = 6 + 2 = 8
By squaring
x = 8² = 64.
Hence "The solution of the given equation √x - 3 + 1 = 6 will be x = 64".
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Answer:the correct answer is C.28
Step-by-step explanation:
1. A daycare center charges a $100 sign up fee, plus $50 per week. Write an equation that represents the total cost, f(x), for x weeks.
f(x) = _____x + ______
a. Identify the rate of change and interpret its meaning in the context of the problem.
b. Identify the y-intercept and interpret its meaning in the context of the problem.
c. What does x represent? What does f(x) represent?
d. Find the cost for a baby to attend daycare for 12 weeks. Write your answer using function notation.
e. Calculate f(-3). Explain what this question is asking you to find in the context of the problem, then discuss the reasonanbleness of this question and its answer.
Answer:
f(x)=50x+100
a)rate of change is 50
b)y-intercept is 100
c)x represents the no. of weeks
f(x) represents the the total cost for x weeks.
d)f(12)=700
e)Cost and week cannot be negative
Step-by-step explanation:
Sign up fee at daycare = $100
Cost of 1 week = 50
Cost of x weeks = 50 x
So, Total cost = 100+50x
Thus f(x)=50x+100
a)
General equation : y=mx+c
m = slope = rate of change
On comparison
m = 50
So, rate of change is 50
50 is the cost of daycare per week
b)
y intercept : y intercept is a point where a line 's graph intersects (crosses) the Y-axis i.e. x=0
Substitute x = 0 in equation
f(x)=50(0)+100
f(0)=100
So, y-intercept is 100
$100 is a signup fee
c)
x represents the no. of weeks
f(x) represents the the total cost for x weeks.
d)
Substitute x = 12
So, Cost for a baby to attend daycare for 12 weeks:
f(12)=50(12)+100
f(12)=700
e)
f(-3)=50(-3)+100=-50
Here it is asking about negative 3 weeks which is not possible
Since no. of weeks cannot be negative
On solving we are getting the negative total cost
Cost and week cannot be negative
Plot point F so that △ABC ≅ △FGH. Identify a sequence of rigid motions that maps △ABC onto △FGH and use a theorem to complete the explanation of why the triangles are congruent.
Answer:
Step-by-step explanation:
Point F is plotted at (5, 4)
Translate ΔABC so that point B maps to point G.
B(1, -1) → G(0, 3)
Rule for the translation,
(x, y) → [x - 1, y + 4]
By this rule,
Point C will map the point,
C(-1, -2) → C'[(-1 - 1), (-2 + 4)]
→ C'(-2, 2)
A(-4, 0) → A'[(-4 - 1), (0 + 4)]
→ A'(-5, 4)
Now reflect these points across y-axis.
Rule for the reflection across y-axis,
(x, y) → (-x, y)
Points after reflection will be,
A'(-5, 4) → F(5, 4)
B'(0, 3) → G(0, 3)
C'(-2, 2) → H(2, 2)
Distance formula,
d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
AB = [tex]\sqrt{(1+4)^2+(-1-0)^2}[/tex] = [tex]\sqrt{26}[/tex]
BC = [tex]\sqrt{(-2+1)^2+(-1-1)^2}[/tex] = [tex]\sqrt{5}[/tex]
CA = [tex]\sqrt{(-4+1)^2+(-2-0)^2}[/tex] = [tex]\sqrt{13}[/tex]
FG = [tex]\sqrt{(5-0)^2+(4-3)^2} =\sqrt{26}[/tex]
GH = [tex]\sqrt{(2-0)^2+(2-3)^2}=\sqrt{5}[/tex]
HF = [tex]\sqrt{(4-2)^2+(5-2)^2}=\sqrt{13}[/tex]
AB ≅ FG, BC ≅ GH, CA ≅ HF
By the SSS property Triangle congruence theorem, ΔABC ≅ ΔFGH
Janet's dog weighs 18.2 pounds. Charlie's dog weighs 7.4 pounds. About how much more does Janet's dog weigh than
Charlie's dog?
25 pounds
26 pounds
11 pounds
10 pounds
Answer:
11 Pounds
Step-by-step explanation:
Since it says "about how much" we can round 18.2 to 18 and 7.4 to 7 then we subtract 18-7=11
That means the answer would be 11 pounds.
Hope that helps and have a great day!
Given f(x) = 3x^3 + kx + 1, and x – 1 is a factor of f(x), then
what is the value of k?
Step-by-step explanation:
Hope it helps man ...........
The value of k is -4.
Given that,
The equation is [tex]f(x) = 3x^3 + kx + 1[/tex].And, x - 1 is the factor of f(x).Based on the above information, the calculation is as follows:
[tex]f(x) = 3x^3 + kx + 1\\\\= 3(1)^3 + k(1) + 1\\\\= 3 + k + 1 \\\\k = -4[/tex]
Therefore, we can conclude that the value of k is -4.
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Today I am 6 years less than half my fathers age. In 6 years, I will be 6 years more than 1/3 my father's age. How old was my father when I was born?
The answer fam is........ 30
Belindas blossom boutique is having a one day sell. Any two daisies cost $1.50. How many daisies could you buy for 8.25
Answer:
11
Step-by-step explanation:
Divide 8.25 by 1.50:
8.25/1.50
= 5.5
Since any two daises cost 1.50, multiply this amount by 2:
5.5(2)
= 11
So, you could buy 11 daisies.
Write an equation in the line in slope intercept form
Answer:
Y=2x-1
Step-by-step explanation:
In order to find the slope, its rise over run. So you would move from (0,-1) to the next point it intercepts, (1,1) and find it from there
As for the Y-Intercept, it would just be wherever the line connects with the Y axis, which happens to be (0,-1) or Negative 1.
Help it’s for algebra 1
3) 4 pounds of meat cost $18. How much will 10 pounds of the same meat cost?
Answer:
$45
Step-by-step explanation:
4 lbs = $18
2 lbs = $9
10 lbs = $45
Answer:
If 4 pounds cost $18. you gotta find the cost of 1 pound
divide 18 by 4 = 4.5
and 4.5 times 10 is: 45
Step-by-step explanation:
$45 dollars for 10 pounds!
Hope this helps!
Pls mark brainliest
What are all the values of x for which (x−1)(x+2)<0?
(A) x<1
(B) x<−2
(C) −2≤x≤1
(D) −2 (E) x<0
Answer:
C -2<=x<=1
Step-by-step explanation:
x-1<0 ===> x<1
x+2<0 ===> x<-2
Consider matrix A.
A=[−385−123]
What matrix results from the elementary row operations represented by −3R2+4R1?
Enter your answer by filling in the boxes.
Answer:
[tex]\left[\begin{array}{ccc}-3&8&5\\-9&26&11\end{array}\right][/tex]
Step-by-step explanation:
Given the matrix A
[tex]\left[\begin{array}{ccc}-3&8&5\\-1&2&3\end{array}\right][/tex]
We are to find the matrix that results from the elementary row operations represented by −3R2+4R1
R2 means row 2
R1 means row 1
Applying the elementary row operation will change the second row of the matrices.
For the first column, second row (a₂₁)
If R1 = -3, R2 = -1
a₂₁ = -3R2+4R1
a₂₁ = -3(-1)+4(-3)
a₂₁ = 3-12
a₂₁ = -9
For a₂₂
If R1 = 8, R2 = 2
a₂₂ = -3R2+4R1
a₂₂ = -3(2)+4(8)
a₂₂ = -6+32
a₂₂ = 26
For a₂₃
If R1 = 5, R2 = 3
a₂₃ = -3R2+4R1
a₂₃ = -3(3)+4(5)
a₂₃ = -9+20
a₂₃ = 11
Hence the resulting matrix will be:
[tex]\left[\begin{array}{ccc}-3&8&5\\-9&26&11\end{array}\right][/tex]-3R2+4R1
Answer:
[-3 5 2]
[-36 23 -1]
Step-by-step explanation:
Note abidemiokin did the steps right just has the "given" wrong.
Given the matrix A
[-3 5 2]
[ 8 -1 3]
We are to find the matrix that results from the elementary row operations represented by −3R2+4R1
R2 means row 2
R1 means row 1
Applying the elementary row operation will change the second row of the matrices.
For the first column, second row (a₂₁)
If R1 = -3, R2 = 8
a₂₁ = -3R2+4R1
a₂₁ = -3(8)+4(-3)
a₂₁ = -24-12
a₂₁ = -36
For a₂₂
If R1 = 5, R2 = -1
a₂₂ = -3R2+4R1
a₂₂ = -3(-1)+4(5)
a₂₂ = 3+20
a₂₂ = 23
For a₂₃
If R1 = 2, R2 = 3
a₂₃ = -3R2+4R1
a₂₃ = -3(3)+4(2)
a₂₃ = -9+8
a₂₃ = -1
Hence the resulting matrix will be:
[-3 5 2]
[-36 23 -1] -3R2+4R1
is -45 less than,greater than or equal to -50?
greater than.
mistype
Answer:
It is greater than -50
Step-by-step explanation
Since that -45 is more closer to 0, It will greater than -50.
HELP!!!!
Solve x=9w−3z−15 for w. Do not write w= in your answer.
Answer:
Your answer is: x/9 + z/3 + 5/3
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Hope this helped : )
I want to decorate my room with leaves and turkeys for Thanksgiving. The number of leaves is twenty more than twice the number of turkeys. The number of leaves is ten less than 4 times the number of turkeys. How many of each type of decoration should I use?
Answer:
50 leaves, 15 turkeys
Step-by-step explanation:
set up an equation
l = leaves
t = turkeys
l = 2t+20
l = 4t-10
2t+20=4t-10
30=2t
15=t (so that means that there would be 15 turkey decorations, but we're not done yet)
substitute (either equation):
l = 2(15)+20
l = 30+20
l = 50 (so this means there would be 50 leaves)
hope this helps!
2. What is the difference?
Complete the subtraction sentence.
5-5=
Answer:
0
Step-by-step explanation:
Please help if possible!! Really need help
Answer:
it is a x= 40 degrees
Step-by-step explanation:
What is the solution to (x – 3)^3(x+ 1)(x - 2)<0?
Answer:
i have no answer
Step-by-step explanation:
(((x-3²)•3)•(x+1))•(x-2)<0
(3•(x-9)•(x+1))•(x-2)<0
3•(x-9)•(x+1)•(x-2)<0
3•(x-9)•(x+1)•(x-2)<0
Answer:
B
Step-by-step explanation:
Got it on edge
There are 108 pigeons that need pigeon coops. Each coop can hold up to 7 pigeons. How many coops are needed for all 108 pigeons?
15 coops are needed for 108 pigeons
What is unitary method ?
The unitary method is a technique for solving a problem but first finding the value of a single unit , and then finding the necessary value by multiplying the single unit value
using unitary method
Total pigeon = 108
each coop can hold = 7 pigeons
7 pigeons are held by = 1 coop
108 pigeons will be held by = 108 / 7 = 15.43 =15
15 coops are needed for 108 pigeons
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There are 108 pigeons that need pigeon coops, each coop can hold up to 7 pigeons, coops are required for all 108 pigeons.
What are pigeons?"Pigeons are gentle, plump, small-billed birds with a skin saddle (cere) between the bill and forehead."
What are coops?"Pigeon houses are also sometimes referred to as "coops" although the word seems to have originally applied to the breeding pens inside the housing."
Total number of pigeons that needed coops [tex]=108[/tex]
Number of pigeons each coop can hold [tex]=7[/tex]
Number of coops required
[tex]=\frac{108}{7} \\=15.42\\=16[/tex]
Hence, we need approximately 16 coops for all 108 pigeons.
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I ran 3 1/4 miles in 30 minutes how fast was I going
Before adding the following fractions, you need to find the common ? 2/3 + 1/6 =
Answer:
denominator
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
2/3×2/2 + 1/6
4/6 + 1/6
5/6
34 full. He uses 16 of a full tank’s gas per day driving to and from work.
How many days can Drew drive to work with the gas he has in the tank?
find the slope of the graphed line
Answer:
C
Step-by-step explanation:
It is a negative slope because the y value decreases as the x value increases. It goes down 2 for every three that it goes across, so we can find, using rise over run, that the slope is -2/3
Rectangle A’B’C’D’ is the image of rectangle ABCD after which of the following rotations?
Answer:
You're right!
Step-by-step explanation:
Answer:
Were you right?
Step-by-step explanation:
Solve the following equation
4(3-2x)=15
Answer:x= -3/8
Step-by-step explanation:
Answer:
-3/8
Step-by-step explanation:
4(3-2x)=15
-3/8
4.11. According to a survey conducted by Netpop Research, 65% of new-car buyers use online search engines as part of their car-buying experience. Another study reported that 11% of new-car buyers skip the test drive. Suppose 7% of new-car buyers use online search engines as part of their car-buying experience and skip the test drive. If a new-car buyer is randomly selected a. What is the probability that the buyer used an online search engine as part of the car-buying experience or skipped the test drive
Answer:
Prob (Online search or Skip test drive) = 0.69
Step-by-step explanation:
Prob (Online search) = P(OS) = 65% = 0.65
Prob (Skip test drive) = P (STD) 11% = 0.11
Prob (Online search & Skip test drive) = P (OS ⋂ STD) = 7% = 0.07
Prob (Online search or Skip test drive) = P (OS U STD) :-
P(OS) + P (STD) - P (OS ⋂ STD)
= 0.65 + 0.11 - 0.07
= 0.69
Describe the error in the work shown below.
18 + 30 = 6(3 + 10)
Answer:
18+30 = 48
6(3+10) = 78
so they're not equal
Step-by-step explanation:
to be equal we have to change 6(3+10) to 6(3+5)
18+30 = 48
6(3+5) = 48
now they're equal
1b) Answer the following: *
If arc WX = 40' and arc Y Z = 92, find m23.
Answer:
m<3 = 66°
Step-by-step explanation:
<3 is an angle with its vertex inside the circle shown in the diagram. This, it's an internal angle.
The measure of an internal angle is equal to half the sum of the measure of the arcs intercepted.
Thus, the equation that shows relationship between <3 and arc WX and arc YZ is shown below:
m<3 = ½(40 + 92)
m<3 = ½(132)
m<3 = 66°
The measure of m<3 = 66°
Calculation of the measure:Since arc WX = 40' and arc Y Z = 92
So we know that
The measure of an internal angle should be equivalent to half the sum of the measure of the arcs intercepted.
So based on this
m<3 =0.50 (40 + 92)
m<3 = 0.50(132)
m<3 = 66°
hence, The measure of m<3 = 66°
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Which of the following best describes the solution to the equation below?
3(5x+9)=4(6x+10)
A. exactly one real solution,
B. no real solutions
C. exactly one real solution,
D. infinite real solutions
Answer:
can someone answe my question
Step-by-step explanation:
Answer: I need helppp
Step-by-step explanation:
write the number whose prime factorization is give: 2×2×2×7
Answer:
56
Step-by-step explanation:
Multiply it out 2×2×2×7 = 56
Simplify this expression
(6 x 2) + 8 - (40 - 4 x 5)
8 Simplify this expression:
30
12
Answer:
the first one, if you solved it using the calculator, the answer will be 0
