Answer:
x = -3 or x = 1Step-by-step explanation:
[tex]x^2+5x-4=3x-1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\x^2+5x-3x-4=3x-3x-1\\\\x^2+2x-4=-1\qquad\text{add 1 to both sides}\\\\x^2+2x-4+1=-1+1\\\\x^2+2x-3=0\\\\x^2+3x-x-3=0\\\\x(x+3)-1(x+3)=0\\\\(x+3)(x-1)=0\iff x+3=0\ \vee\ x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x+3-3=0-3\\\boxed{x=-3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x-1+1=0+1\\\boxed{x=1}[/tex]
Find y if y = -7x -6 and x=5
Answer: -41
Step-by-step explanation:
-7 × 5 = -35
-35 - 6 = -41
Answer:
-41
Step-by-step explanation:
A square table has an area of "2116" square inches. A tablecloth hang 3 inches over each end of the table, What is the area of the part of the tablecloth that hangs over the table?
The area of the part of the tablecloth that hangs over the table is 285 square inches
Step-by-step explanation:
In order to find the area of table cloth that hangs over the table, we have to find the area of table and the total area of table cloth.
Given
Area of table = [tex]A_t = 2116\ in^2[/tex]
To find the side of the square
[tex]A_t = s^2\\s^2 = 2116[/tex]
Taking Square root on both sides
[tex]\sqrt{s^2} = \sqrt{2116}\\s = 46\ inches[/tex]
When the table cloth is hanged, 3 inches are left to hang over this means that the side will now be: 46+3 = 49 inches
The area of table cloth = [tex]A_c = 49*49 = 2401\ in^2[/tex]
The area of table cloth that will be hung over the table is:
[tex]A_c-A_t\\= 2401-2116\\= 285\ in^2[/tex]
Hence,
The area of the part of the tablecloth that hangs over the table is 285 square inches
Keywords: Square, side
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any help would be great
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y
=
−
2
x
2
+
113
x
−
497
y=−2x
2
+113x−497
The company should sell each widget for $28.25, to the nearest cent.
To maximize profit, we need to find the vertex of the parabola represented by the profit equation y = -2x^2 + 113x - 497. Since the coefficient of x^2 is negative, the parabola opens downwards, and the vertex represents the maximum point. The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula -b/2a.
For the equation y = -2x^2 + 113x - 497, a = -2 and b = 113. Plugging these values into the formula gives us: x = -113 / (2 × -2) = -113 / -4 = 28.25. Therefore, to maximize profit, the company should sell each widget for $28.25, to the nearest cent.
How many edges does this figure have?
Answer:
please show the figure
Step-by-step explanation:
Which figure lol looool
Meredith lives 24 blocks from her friends house if she travels on block every minute how many minutes will it take her to reach her friends house show how you calculate each answer
Meredinth takes 24 minutes to reach her friend house
Solution:
Given that, Meredith lives 24 blocks from her friends house
She travels one block every minute
To find: time taken by Meredith to reach friend house
From given,
Number of blocks between Meredith house and her friedn house = 24
She travels one block every minute
Thus she takes 1 minute for 1 block
One block = 1 minute
So, for 24 blocks, we have to multiply by 24
[tex]24\ block = 1 \times 24\ minute\\\\24\ block = 24\ minute[/tex]
Thus Meredinth takes 24 minutes to reach her friend house
Given: WZ is perpendicular to VY, WZ bisects VY, VZ = 2x+2, and ZY = 3x-4
What is VY?
18
28
14
6
Answer:
28
Step-by-step explanation:
VZ = ZY
2x +2 = 3x -4
6 = x . . . . . . . . add 4-2x to both sides
VZ = 2x +2 = 2(6) +2 = 14
Now we can find VY.
VY = VZ + ZY = 14 + 14 . . . . . . VY is the total of the two halves
VY = 28
if a=(-2 -4) and b=(-8 4) what is the length of AB
Use the distance formula Sqrt ( (x2-x1)^2 +(y2-y1)^2)
Distance = sqrt ( (-8 - -2)^2 +(4- -4)^2)
Distance = sqrt(-6^2 + 8^2)
Distance = sqrt ( 36 + 64)
Distance = sqrt(100)
Distance = 10
The length is 10
Answer: 10 units
Step-by-step explanation: took test hope this helps
which quadratic equation equivalent to (x+2)^2+5(x+2)-6=0
Answer:
[tex]\large\boxed{u^2+5u-6=0,\ where\ u=(x+2)}[/tex]
Step-by-step explanation:
[tex](x+2)^2+5(x+2)-6=0\\\\\text{Substitute}\ (x+2)=u:\\\\\underbrace{(x+2)}_{u}^{}^2+5\underbrace{(x+2)}_{u}-6=0\\\\u^2+5u-6=0[/tex]
Answer:
The answer is C
Step-by-step explanation:
How do you do inverse operation on a fraction ( y/3 ) = -6
[tex]\frac{-1}{18}[/tex]
Solution:
Given expression is [tex]\frac{y}{3}=-6[/tex]
To find the inverse of y.
⇒ [tex]\frac{y}{3}=-6[/tex]
Do cross multiplication.
⇒ y = –6 × 3
⇒ y = –18
Inverse of y means reverse the function.
We know that inverse of y is [tex]\frac{1}{y}[/tex].
⇒ [tex]\frac{1}{y}= \frac{-1}{18}[/tex]
Hence, inverse of y is [tex]\frac{-1}{18}.[/tex]
What is the they answer for
5+4(n+9)=-3
Answer:x=-11
Step-by-step explanation:
The jones family is taking a trip from seattle to san diego CA over the course of 3 days. They plan on traveling 200 miles more on the second day than they will on the first day. They will travel 75 miles less on the third day than they will on the first day. The total distance of the trip is 1058 miles. How many miles will they travel each day?
Jones family will travel for 311 miles on day 1 , 511 miles on day 2 and 236 miles on day 3.
It is given that on day 2 , Jones family travel for 200 miles more than day 1 and on day 3 for 75 miles less than day 1.
We have to find out distance travelled on each day of trip if total distance of trip is 1058 miles.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
As per the questions ;
Jones family has a trip of 3 days.
Let's assume they travel distance of x miles on first day.
Distance they will travel on second day = x + 200 miles
Distance they will travel on third day = x - 75 miles
Total distance of trip = 1058 miles
i.e.,
x + (x + 200) + (x - 75) = 1058 miles
3x + 125 = 1058
3x = 1058 - 125
3x = 933
x = 311 miles
So , they travel for a distance of 311 miles on day 1.
&
On day 2 ;
= 311 + 200
= 511 miles
&
on day 3 ;
= 311 - 75
= 236 miles
Thus , Jones family will travel for 311 miles on day 1 , 511 miles on day 2 and 236 miles on day 3.
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What is the sale price if there is a 60% discount and the original price is $750?
Answer:
17
Step-by-step explanation:
50
The ratio of the number of flowers in basket A to the number of fliers in basket B is 5:2. If there are 40 flowers in basket B
Answer:
there would be 100 flowers in basket a
Step-by-step explanation:
for the second part of the ratio to be 40 you have to multiply the 2 by 20. to find out how many would be in basket a you do the same thing to the other side of the ratio and multiply 5 by 20 which gives you 100
which of the statements is true for the two equations below?
Equation A: 6+3x=3x-3
Equation B: 2(4x-1)=8x-2
A.Equation A has no solution and Equation B has an infinite number of solutions.
B.Equation A has an infinite number of solutions and Equation B has no solution.
C.Equation A and Equation B have an infinite number of solutions.
D. Equation A and Equation B have no solution.
Equation A:
6 + 3x = 3x - 3
This equation has no solution, no matter what number you plug into the equation, it will never = each other
[if you tried simplifying more]
9 + 3x = 3x (added 3 on both sides, then subtracted 3x on both sides)
9 = 0
Equation B:
2(4x - 1) = 8x - 2 Distribute/multiply 2 into (4x - 1)
(2)4x - (2)1 = 8x - 2
8x - 2 = 8x - 2
This will have an infinite number of solutions because whatever number you plugged in, they would always = each other since they are the same on both sides of the equation
[simplified]
8x = 8x (add 2 on both sides, then divide 8 on both sides)
x = x
Your answer is A
Equation A has no solution and Equation B has an infinite number of solutions.
Explanation:The correct answer is D. Equation A and Equation B have no solution. Let's analyze each equation:
For Equation A, we can combine like terms and simplify it to:
6 + 3x = 3x - 3
6 = -3
Since 6 is not equal to -3, Equation A has no solution.
For Equation B, we distribute 2 to the terms inside the parentheses:
2(4x - 1) = 8x - 2
8x - 2 = 8x - 2
Both sides of the equation have the same expression, so Equation B is an identity. It means that for any value of x, both sides will always be equal. Therefore, Equation B has an infinite number of solutions.
Hence, the correct answer is D. Equation A and Equation B have no solution.
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I need help with this question
If 24 people have the flu out of 360 people, how many would have the flu out of
900?
If 24 people have the flue out of 360 people then out of 900, 60 people would have flue if solved through percentage.
What is a percentage?It is a ratio expressed as a fraction of 100. it's expressed using the sign %.
How to calculate percentage?The percentage of individuals gets affected from flue out of 360 is 24*100/360
=2400/360
=6.67%
Then per 6.67% out of 900 approx 60 (900*6.67%) people would be affected from flue.
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There are 6 students that like milk. There is one student who likes water. How many fewer students like water than milk?
Answer:
5
Step-by-step explanation:
Help please time limit...Amanda is choosing between two exercise routines.
In Routine #1, she does only running, 15.5 burning calories per minute.
In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 12.75 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
Use t for the number of minutes spent running, and solve your inequality for ..
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Step-by-step explanation:
Routine # 1;
Calories burned in running = 15.5 per minute
Let,
t be the minutes spent running.
T = total calories burned
T = 15.5t
Routine # 2;
Calories burned while walking = 22 calories
Calories burned while running = 12.75 per minute
T = 12.75t + 22
For burning more calories in Routine 1;
Routine 1 > Routine 2
[tex]15.5t>12.75t+22\\15.5t-12.75t>22\\2.75t>22\\[/tex]
Dividing both sides by 2.75
[tex]\frac{2.75t}{2.75}>\frac{22}{2.75}\\t>8[/tex]
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Keywords: linear inequality, division
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Select 3 expressions that have a sum or difference of 3 /4 .
A . 1/2 + 2/4
B . 11/12 − 1/6
C. 3/5 + 3/20
D . 7/8 − 1/2
E . 2/3 + 1/12
Answer:
The Three expressions that have a sum or difference of 3 /4 .
B . 11/12 − 1/6
C. 3/5 + 3/20
E . 2/3 + 1/12
Step-by-step explanation:
The Three expressions that have a sum or difference of 3 /4 .
are
B . 11/12 − 1/6
[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{1\times 2}{6\times 2}\\\\\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{2}{12}=\dfrac{11-2}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{3}{4}[/tex]
C. 3/5 + 3/20
[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3\times 4}{5\times 4}+\dfrac{3}{20}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{12}{20}+\dfrac{3}{20}=\dfrac{15}{20}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3}{4}[/tex]
E . 2/3 + 1/12
[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{2\times 4}{3\times 4}+\dfrac{1}{12}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{8+1}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{3}{4}[/tex]
Expressions B (11/12 − 1/6), C (3/5 + 3/20), and E (2/3 + 1/12) each simplify to a sum or difference of 3/4 after finding a common denominator and simplifying the fractions.
Explanation:To find 3 expressions that have a sum or difference of 3/4, let's evaluate each option given:
A. 1/2 + 2/4 simplifies to 1/2 + 1/2, which equals 2/2 or 1. This does not equal 3/4.B. 11/12 − 1/6 can be calculated by finding a common denominator, which would be 12. So, 1/6 is equivalent to 2/12. Thus, 11/12 − 2/12 equals 9/12, which simplifies to 3/4.C. 3/5 + 3/20 requires us to find a common denominator, which would be 20. So, 3/5 is equivalent to 12/20. Thus, 12/20 + 3/20 equals 15/20, which simplifies to 3/4.D. 7/8 − 1/2 requires a common denominator, which would be 8. So, 1/2 is equivalent to 4/8. Thus, 7/8 − 4/8 equals 3/8. This does not equal 3/4.E. 2/3 + 1/12 requires a common denominator, which would be 12. So, 2/3 is equivalent to 8/12. Thus, 8/12 + 1/12 equals 9/12, which simplifies to 3/4.Therefore, the three expressions that have a sum or difference of 3/4 are B, C, and E.
If the arc length shown in blue is 21.3 inches, then 0 to the nearest hundredth of a
radian is
Answer: [tex]\theta\approx1.78\ rad[/tex]
Step-by-step explanation:
By definition, the Arc lenght can be calculated with the following formula:
[tex]s=r\theta[/tex]
Where "s" is the Arc lenght, "r" is the radius and [tex]\theta[/tex] is the central angle measured in radians.
From that equation you can solve for [tex]\theta[/tex] dividing both sides of the equation by the radius "r", then:
[tex]\frac{s}{r}=\frac{r\theta}{r}\\\\\theta=\frac{s}{r}[/tex]
According to the information given in the exercise:
[tex]s=21.3\ in[/tex]
And you can identify in the figure that the radius of the circle is:
[tex]r=12\ in[/tex]
Therefore, you can substitute values into the equation:
[tex]\theta=\frac{21.3\ in}{12\ in}[/tex]
Finally, evaluating, you get the following result:
[tex]\theta=1.775\ rad[/tex]
Rounded to the nearest hundredth of a radian:
[tex]\theta\approx1.78\ rad[/tex]
Solve for x in the equation x squared + 14 x + 17 = negative 96. x = negative 7 plus-or-minus 4 StartRoot 6 EndRoot i x = –7 ± 8i x = 7 plus-or-minus 4 StartRoot 6 EndRoot i x = 7 ± 8i
Answer:
[tex]x=-7\pm8i[/tex]
Step-by-step explanation:
we have
[tex]x^{2} +14x+17=-96[/tex]
Equate to zero
[tex]x^{2} +14x+17+96=0[/tex]
[tex]x^{2} +14x+113=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +14x+113=0[/tex]
so
[tex]a=1\\b=14\\c=113[/tex]
substitute in the formula
[tex]x=\frac{-14\pm\sqrt{14^{2}-4(1)(113)}} {2(1)}[/tex]
[tex]x=\frac{-14\pm\sqrt{-256}} {2}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{-14\pm16i} {2}[/tex]
[tex]x=-7\pm8i[/tex]
Answer:
its b on edge
Step-by-step explanation:
19. A county government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
a. Write and solve an absolute value inequality to represent this situation
b. A life guard measures the chlorine level in the pool and finds it is 1.0ppm. Should he add more chlorine? Explain.
To ensure safe chlorine levels in the pool, the inequality |Cl - 3.25| ≤ 1.75 must be met, representing levels between 1.50 ppm and 5.00 ppm. The lifeguard found the level at 1.0 ppm, which is below the safe range, so more chlorine needs to be added.
Explanation:Absolute Value Inequality for Chlorine Levels:
The county government specifies that a safe level of chlorine is within 1.75 ppm of 3.25 ppm. We can express this using an absolute value inequality to represent the acceptable range for the chlorine levels: |Cl - 3.25| ≤ 1.75. This represents that the chlorine level (Cl) can be at most 1.75 ppm above or below 3.25 ppm.
To solve this inequality, we consider both the upper and lower bounds:
Therefore, the chlorine level must be between 1.50 ppm and 5.00 ppm.
Analysis of the Chlorine Level Measurement:
As the lifeguard measures the chlorine level in the pool at 1.0 ppm, it falls below the acceptable range established by the inequality. Consequently, the lifeguard should add more chlorine to bring the concentration up to within the safe range, specifically, at least to the minimum safe level of 1.50 ppm.
What is the scale factor?
Answer:
the scale factor is by what multiplier has a shape been increased by in size
A pickup truck carrying 1000 identical bricks weighs 6,755 pounds. If the empty truck weighs 6,240 pounds, what is the weight of each brick?
Answer:
0.515
Step-by-step explanation:
10 to the 3rd power is 10^3 = 1000 bricks.
The weight of the full truck minus the weight of the empty truck is the weight of the bricks:
6755-6240 = 515 pounds of bricks
Pounds per brick:
515 / 1000 = .515 pounds per brick.
The sum of two numbers is 15. The first number is half of the second number. What are the two numbers?
Answer:
10 5
Step-by-step explanation:
10 ÷ 2 = 5 and 5 + 10 = 15
Answer:
5 and 10
Step-by-step explanation:
X×Y=15
X=15-Y
X=Y/2
Y/2=15-Y
Add Y to both sides
3Y/2=15
3Y=30
Y=10
X=5
How to solve c/-9+6=14
Answer:
c/9+6=14
9c=14-6
9c=8
c=8:9
c=1.125
Step-by-step explanation:
After solving this c/(-9+6) = 14 equation we get c = -42. To solve the equation c/(-9+6) = 14, we first simplify the expression inside the parentheses. (-9 + 6) equals -3.
Therefore, the equation becomes c/(-3) = 14. To isolate the variable c, we multiply both sides of the equation by -3. This gives us c = 14 * (-3), which simplifies to c = -42.
Hence, the solution to the equation is c = -42. Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions and be cautious when dealing with negative signs in equations.
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Compute the perimeter of the figure given below. All angles are right angles.
Answer:
44
Step-by-step explanation:
10 + 12 + 4 + 4 + 6 + 8 = 44
The perimeter of the figure is 26 inches.
The perimeter of the figure is the total length of all the sides. To calculate the perimeter, we simply add up the lengths of all the sides:
Perimeter = 6in + 4in + 4in + 12in
Perimeter = 26in
Therefore, the perimeter of the figure is 26 inches.
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a principal that will amout to 150000 for 8 years at 9/1/2 %
The principal amount is 85227.27 and the interest is 64772.73.
Solution:
Given:
Amount (A)= 150000
Number of years (n)= 8
Rate of interest (r)= [tex]9\frac{1}{2}\%=\frac{19}{2}\%[/tex]
To find: The principal (P)
We know that the principal is the sum of amount and interest. That is, [tex]\bold{P+I=A}[/tex]
This can be written as [tex]\bold{I=A-P \rightarrow(1)}[/tex]
The formula of simple interest is [tex]\bold{I=\frac{Pnr}{100} \rightarrow(2)}[/tex]
On equating (1) and (2) we get,
[tex]\Rightarrow\bold{A-P=\frac{Pnr}{100}}[/tex]
On substituting the values we get,
[tex]\Rightarrow\bold{150000-P=\frac{P\times8\times19}{100\times2}}[/tex]
On solving we get,
[tex]\bold{\Rightarrow 150000-P=0.76P}[/tex]
On grouping the like terms together we get,
[tex]\bold{\Rightarrow 150000=0.76P+P}[/tex]
[tex]\bold{\Rightarrow 150000=1.76P}[/tex]
[tex]\bold{\Rightarrow P=\frac{150000}{1.76}}[/tex]
[tex]\bold{\Rightarrow P=85227.2727\approx85227.27}[/tex]
If principal is 85227.27, then the interest will be [tex]\bold{I=150000-85227.27\rightarrow64772.73}[/tex]
If the base angles of an isosceles triangle each measure 37° then the vertex angle measures 106°
Answer:
the given statement is true.
Step-by-step explanation:
i) It is given that the base angles of an isosceles triangle each measure 37°.
ii) Adding the values of the base angles is = 37° + 37° = 74°
iii) from the property of triangles we know that the sum of all the angles in a triangle is equal to 180°
iv) let the vertex angle be = y°
v) Therefore we can say from ii), iii) and iv) above that
74° + y° = 180°
vi) therefore the vertex angle y = 180° - 74° = 106°
Hence the given statement is true.