Answer:
Factor and set each factor equal to zero. Y=x2+5x−8
Step-by-step explanation:
←
How many solutions does this linear system have
y =
x+2
6x - 4y = -10
Answer:
This linear system has one solution.
Step-by-step explanation:
First equation: y = x + 2
Second equation: 6x - 4y = -10
Let's change the second equation in slope-intercept form y = mx + b.
Slope-intercept form
y = mx + b
m ... slope
b ... y-intercept
[tex]6x - 4y = -10[/tex]
[tex]6x + 10 = 4y[/tex]
[tex]\frac{6}{4}x + \frac{10}{4} = y[/tex]
[tex]\frac{3}{2}x + \frac{5}{2} = y[/tex]
If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.
If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.
If two lines have different slopes then they intersect in one point - system has one solution.
We see that lines have different slopes. First line has slope 1 and the other line has slope [tex]\frac{3}{2}[/tex]. So the system has one solution.
You can also check this by solving the system.
Substitute y in second equation with y from first.
6x - 4y = -10
6x - 4(x + 2) = -10
Solve for x.
6x - 4x - 8 = -10
2x = -2
x = -1
y = x + 2
y = -1 + 2
y = 1
The lines intersect in point (-1, 1). <-- one solution
Which system has no solutions? x < 3 x < 1 x > 3 x > 1 x < 3 x > 1 x > 3 x < 1
The system of inequalities with no solution is x > 3 x < 1
How to determine the system with no solutions?The systems of inequalities are given as:
x < 3 x < 1
x > 3 x > 1
x < 3 x > 1
x > 3 x < 1
As a general rule, it is impossible for a variable to be greater than a higher number and less than a smaller number.
This means that if x is greater than 3, then it must be greater than 1
Hence, the system of inequalities with no solution is x > 3 x < 1
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Solve the following system of equation using inverse matrix method.
5x + 2y=4
7x + 3y=5
[tex]5x+2y = 4~~~~~~~~~~...(i)\\\\7x +3y = 5~~~~~~~~~~...(ii)\\\\\text{Write in AX = B form.}\\\\~~~~~~\begin{bmatrix}5&2\\7&3 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\begin{bmatrix}5&2\\7&3 \end{bmatrix}^{-1}\\\\\\[/tex]
[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-7\\-2&5\end{bmatrix}^{T}}{\begin{vmatrix}5&2\\ 7&3 \end{vmatrix}}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}}{5(3) -2(7)}\\\\\\[/tex]
[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}12-10\\-28+25 \end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}2\\-3\end{bmatrix}\\\\\\\text{Hence,}~ (x,y) = (2,-3)[/tex]
Solve for h
-8 = - 2 (h - 6)
H=
The first step that we need to take before solving is to understand what the question is asking us to do and what is given to us to do that. Looking at this problem, we are given the goal of this problem which is to solve for h and we are given an expression to do so.
The next step that we need to take is to distribute the -2 to the contents inside of the parenthesis.
Distribute
[tex]-8 = - 2 (h - 6)[/tex][tex]-8 = (- 2 * h) + (-2 * - 6)[/tex][tex]-8 = (- 2h) + (12)[/tex]After we have distributed the -2 to the contents inside of the parenthesis we can move onto the next step to isolate h which is to subtract 12 from both sides which would just leave us with -2h.
Subtract 12 from both sides
[tex]-8 = - 2h + 12[/tex][tex]-8 - 12 = - 2h + 12 - 12[/tex][tex]-20 = - 2h[/tex]The next step that we will take to finish the problem is to divide both sides by -2 which will isolate h. Then we will simplify the expression and that will give us our final answer.
Divide both sides by -2
[tex]-20 = - 2h[/tex][tex]\frac{-20}{-2} = \frac{- 2h}{-2}[/tex][tex]\frac{-20}{-2} = h[/tex]Simplify the expression
[tex]\frac{-20/-2}{-2/-2} = h[/tex][tex]\frac{10}{1} = h[/tex][tex]10= h[/tex]We have now completed solving for h for the expression that was provided in the problem statement and we were able to determine that h is equal to 10.
What are the exact values of x and y?
x =
y =
Answer:
[tex]x = 2\\y = 2\sqrt{3}[/tex]
Step-by-step explanation:
**Look at the picture
184 is 130% more than what number?
Answer:
80
Step-by-step explanation:
The wording "130% more" suggests that we have the result of adding 130% of the original number to the original number.* This can be expressed as an equation to be solved for the original number.
__
Let x represent the original number. The given relation is ...
184 = x + 130% × x
184 = 2.30x . . . . . . . . . collect terms (130% = 1.3)
80 = x . . . . . . . divide by 2.3
184 is 130% more than 80.
_____
* One needs to be a little careful here. You will often see the wording ...
"<some number> times more".
Usually the intention there is that the result is <some number> times the original amount. That is, percentages are often treated differently from other number expressions in problems like this.
A certain 300-term geometric sequence has first term 1337 and common ratio $-\frac12$. How many terms of this sequence are greater than 1
There are 6 terms in the sequence greater than 1.
What is a geometric series ?A geometric series is sum of infinite numbers which has a common ratio between its successive terms.
The missing common ratio value is -1/2
It is given in the question that
the number of terms in the sequence = 300
Sum = a₁ (1-rⁿ)/(1-r)
nth term is given by
aₙ = a₁r⁽ⁿ⁻ ¹⁾
1337(1/2)^(n - 1) = 1
(1/2)^(n - 1) = 1/1337
Applying log on both sides
log (1/2)^(n - 1) = log (1/1337)
(n - 1) log(1/2) = log(1/1337)
n = log (1/1337)/ log (1/2) + 1 ≈ 11.384
the 11th term is 1337(-1/2)^(10) ≈ 1.305
and
And the 12th term is 1337(-1/2)^11 = -.653
As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.
Therefore there are 6 terms in the sequence greater than 1.
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A philanthropist pledges to donate 10% of a fund each year. If the fund initially has $450,000 how much will
the fund have after 7 years?
Fund Balance = $
After 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent. [tex]\rm y = a^x[/tex]
where a is a constant and a>1
We have:
A philanthropist pledges to donate 10% of a fund each year.
We can find the amount left after 7 years as follows:
A = 450000(1 - 0.1)⁷
10% of a fund each year.
Rate r = 10% = 0.1
A = 450000(0.9)⁷
A = $2152336.05
Thus, after 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
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Which are the solutions of x2 = –7x – 8?
StartFraction 7 Over 2 EndFraction minus StartFraction StartRoot 17 EndRoot Over 4 EndFraction comma StartFraction 7 Over 2 EndFraction + StartFraction StartRoot 17 EndRoot Over 4 EndFraction
StartFraction negative 7 Over 2 EndFraction minus StartFraction StartRoot 17 EndRoot Over 4 EndFraction comma StartFraction negative 7 Over 2 EndFraction + StartFraction StartRoot 17 EndRoot Over 4 EndFraction
StartFraction 7 minus StartRoot 17 EndRoot Over 2 EndFraction comma StartFraction 7 + StartRoot 17 EndRoot Over 2 EndFraction
StartFraction negative 7 minus StartRoot 17 EndRoot Over 2 EndFraction comma StartFraction negative 7 + StartRoot 17 EndRoot Over 2 EndFraction
The solution to the system of equation is x = -7+√17/2 and -7-√17/2
Equations and expressionsEquations are expressions separated by an equal sign
Given the equation
x^2 = –7x – 8
Equate to zero
x^2+7x+8 = 0
Factorize
x = -7±√49-4(8)/2
x = -7±√17/2
x = -7+√17/2 and -7-√17/2
Hence the solution to the system of equation is x = -7+√17/2 and -7-√17/2
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Answer:
Option 4
Step-by-step explanation:
The answer above is correct.
if 6 men. 8 women and 16 boys together can do a piece of work in 288 days by working 6 hours each day in how many days can 12 men, 18 women and 28 boys complete the same & work by working 8 hours each day? The work efficiency of men, women and boys proportion 3:2:1 respectively?
Answer:
144 days
Step-by-step explanation:
Let's put the efficiency in terms of b
m = 3b w = 2b b=b
starting with 6 m = 18 b
8w = 16 b
16b = 16 b total 50 b
then increase 12m = 36b
18w = 36b
28b = 28 b total = 100 b
You doubled 'b' workers so work time will be halved to 144 days
Anyone know the answer
Step-by-step explanation:
-2g(1+g)
-2g - 2g²
(-2)g - (2)g²
Subtract − 3 x 2 + 4 x + 10 −3x 2 +4x+10 from 2 x 2 − 2 x 2x 2 −2x.
Answer:
10+12x
Step-by-step explanation:
1. simplify both sides using PEMDAS.
(2 x 2) − ((2 x 2x) 2) −2x
4-8x-2x
4-10x
− (3 x 2) + 4x + 10 −(3x 2) +4x+10
-6+4x-6x+4x+20
2x+14
2. (2x+14)-(4-10x)= 10+12x
sorry if its rong it was kinda confusing finfing if it was an x or multiplecation.
Triangle JKL is transformed to create triangle J'K'L'. The angles in both triangles are shown.
AngleJ = 90° AngleJ' = 90°
AngleK = 65° AngleK' = 65°
AngleL = 25° AngleL' = 25°
Which statement is true about this transformation?
The correct statement is AngleL = 25° AngleL' = 25°.
We have given that,
Triangle JKL is transformed to create triangle J'K'L'.
We have to choose the correct option.
What is the information about the transformed triangle?
The following information should be considered:
In a rigid transformation, the image & pre-image are congruent.
Reflection, translation, and rotation are rigid transformations.
In a non-rigid transformation, the image and pre-image are similar.
Dilation is a non rigid transformation.
In a rigid or nonrigid transformation, the corresponding angles are the same.
If the corresponding sides are the same, then it is a rigid transformation.
If the corresponding sides are proportional, then it is a nonrigid transformation.
It can be a rigid or a nonrigid transformation based on whether the corresponding side lengths have the same measures.
Therefore option 3 is correct.
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What is the equivalent to 1 tablespoon?
Answer:
3 teaspoons
Step-by-step explanation:
Three teaspoons are equivalent to one tablespoon
. Which volume-to-surface-area ratio would be better for an ice cube— the lowest possible or the highest possible? Use the table to help you try different shapes and sizes to make your selection (You can show your work on a separate piece of paper.):
The volume-to-surface-area ratio would be better for an ice cube is the highest possible one.
How to explain the volume?When you put ice into your drink, the goal is to have the ice chill your drink. This takes time. Therefore, you would want the ice to slowly melt and cool the drink for as long as you can.
You would want to have the highest possible volume to surface area ratio in an ice cube. If your ice cube is mostly surface area with less volume, it will melt quickly and water down your drink. If your ice cube has a higher ratio of volume to the surface area, it will stay solid longer and chill your drink longer.
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Evaluate this function at the given value using the remainder theorem.
F(x)=x^4+5x^3-18x+1 at x=-4
Please show work , I give brainliest. :)
Answer:
9
Step-by-step explanation:
[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]
What is the (LCD) of 3/5 and 5/6
Answer: 30
Step-by-step explanation:
A LCD, or least common denominator, is the lowest common multiple of both denominators.
Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...
Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, ...
We can see the LCD of 3/5 and 5/6 is:
30
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The first step that we should take before attempting to solve any problem is to understand what the problem statement is asking for us to do and what is given to us to help us achieve that goal. In this case, the problem is asking us to determine the LCD or least common denominator of two numbers. We are provided with two fractions that we will use to help determine our solution. However, before solving for the LCD let us first define what LCD means.
Least Common Denominator ⇒ LCD is a term that is used to help describe a number that can be used in the bottom of the fraction (also known as a denominator) that is common between two numbers. For example, the LCD between 2 and 5 is 10 because that is a time where both of them can be equal to.Looking at our problem we can see that the denominators that are given to us is 5 and 6 so let us determine the multiples of them until we have a duplicate.
Multiples of 5 ⇒ 5, 10, 15, 20, 25, 30Multiples of 6 ⇒ 6, 12, 18, 24, 30Now that we have determine the multiples of 5 and 6 we were able to see that the lowest duplicate that we have is at 30 which means that 30 is our LCD.
50. a skateboard shop stocks 10 types of board decks, 3 types of trucks, and 4 types of wheels. how many different skateboards can be constructed?
Please help me, I really appreciate it! Thanks!
Answer: See the attached images below.
The steps and explanations are on those screenshots, so there's not much for me to mention right here on this main page. The decimal results are approximate to 6 decimal places. Make sure your calculator is in degree mode.
i need help with these two questions ASAP and preferably shown work.. Thank you!
Answer:
1: sin B, cos B, and tan B = 36.87°
2: x = 11.7
Step-by-step explanation:
Question 1: As toy can see they all have the same angle answer just different methods of finding it
Question 2:
adjacent is the closest side to the angle
opposite is the side across from the angle
hypotenuse is always the longest side
x = 11.7025
Hope it helps :)
If you have any questions or anymore help lmk, happy to help with any school work!!
Have a nice day, you’ll make it thru <3
DONT BE AFRAID TO ASK IF YOU CANT READ MY HANDWRITTING
If Randy sells 8 times as many vacuum cleaners as Janice, and Janice sells 690 vacuum cleaners per year, on average, how many does Randy sell each month
Randy sells, in average, 460 vacuum cleaners per month.
How many vacuum cleaners does Randy sell each month?.
First, we know that Janice sells 690 units per year.
There are 12 months in a year, so the amount that she sells, in average, per month is:
J = 690/12 = 57.5
This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:
R = 8*57.5 = 460
This means that Randy sells 460 units per month.
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(05.05 mc)
~
a a food truck did a daily survey of customers to find their food preferences. the data is partially entered in the frequency table. complete the table to analyze the data and answer the to
questions:
likes hamburgers does not like hamburgers total
likes burritos
29
41
does not like burritos
54
135
total
110
205
part a: what percentage of the survey respondents do not like both hamburgers and burritos? (2 points)
part b: what is the marginal relative frequency of all customers that like hamburgers? (3 points)
part c: use the conditional relative frequencies to determine which data point has strongest association of its two factors. use complete sentences to explain your answer. (5 points)
The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos
How to find the percentage?A) The percentage of respondents who do not like both hamburgers and burritos is; 33/250 * 100% = 16.09%
B) Marginal relative frequency of all customers that like hamburgers will be the ratio of the sum of the customers that like hamburgers to the total number of respondents. Thus;
MRF = 134/205 = 0.65
C) Let us first find the ratio of all the four data with the total;
Ratio of those who like Hamburgers and burritos = 39/134 = 0.29
Ratio of those who like Hamburgers but not burritos = 95/134 = 0.71
Ratio of those who like burritos but not Hamburgers = 38/71 = 0.53
Ratio of those who do not like burritos or Hamburgers = 33/71 = 0.47
Thus, The data point that has the strongest association of its two factors is Ratio of those who like Hamburgers but not burritos
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Help me please this is due today :((
Show all work for it pleaseee
Answer:
Length C, B= 90 mi
Step-by-step explanation:
The small square in the corner in any shape always represent 90°
Hope it helps!!
Which number in the monomial 125x18y3z25 needs to be changed to make it a perfect cube? 3 18 25 125
Answer: 25
Reason:
The exponent 25 is not a multiple of 3. If it was something like 24, then we would have a perfect cube as shown below
[tex]w = 125x^{18}y^3z^{24}\\\\w = 5^{1*3}x^{6*3}y^{1*3}z^{8*3}\\\\w=(5^1x^6y^1z^8)^3\\\\w = (5x^{6}yz^{8})^3\\\\[/tex]
When going from step 2 to step 3, I used the rule that [tex](abcd)^e = a^eb^ec^ed^e[/tex]. Basically the exponent e gets applied to each factor inside.
Answer:
25
Step-by-step explanation:
geometry i need help!!
Answer: 130 degrees
Step-by-step explanation:
If we are assuming this is an isosceles trapezoid, then this means angles B and C are congruent.
What is a factor of X2–9 X +14
The factors of the expression x^2 - 9x + 14 are (x - 7) and (x - 2)
How to factor the expression?The expression is given as:
x^2 - 9x + 14
Expand
x^2 - 2x - 7x + 14
Factorize the expression
x(x - 2) - 7(x - 2)
Factor out x - 2 from the expression
(x - 7)(x - 2)'
Hence, the factorized expression of x^2 - 9x + 14 is (x - 7)(x - 2)'
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x^k=1/x^-1
Someone help me please
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^k~~ = ~~\cfrac{1}{x^{-1}}\implies x^k~~ = ~~x^1\implies k=1[/tex]
Find the quotient. Simplify your answer.
s + 1/
s²1
÷
s^2/
6s²
Enter the correct answer.
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{5s^2}{s}[/tex]
[tex]\\ \rm\Rrightarrow 5s[/tex]
What are the solutions to the following system of equations? x + y = 3 y = x2 − 9 (3, 0) and (1, 2) (−3, 0) and (1, 2) (3, 0) and (−4, 7) (−3, 0) and (−4, 7)\
The solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
Simultaneous linear and quadratic equationsFrom the question, we are to determine the solutions to the given system of equations
The given system of equations are
x + y = 3 ----------- (1)
y = x² - 9 ----------- (2)
From equation (1)
x + y = 3
We can write that
y = 3 - x -------- (3)
Substitute this into equation (2)
y = x² - 9
3 - x = x² - 9
x² +x -3 - 9 = 0
x² +x -12 = 0
Solve quadratically
x² +x -12 = 0
x² +4x -3x -12 = 0
x(x +4) -3(x +4) = 0
(x -3)(x +4) = 0
∴ x -3 = 0 OR x +4 = 0
x = 3 OR x = -4
Now, using equation (3)
When x = 3
y = 3 - x
y = 3 - 3
y = 0
When x = -4
y = 3 - -4
y = 3+4
y = 7
∴ When x = 3, y = 0; and when x = -4, y = 7
Hence, the solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
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Jane had a salad In her refrigerator she ate 2/8 of it for lunch and 3/8 of it dinner and what fraction of the salad is left
Answer:
3/8
Step-by-step explanation:
2 + 3=5, (8/8)-( 5/8) =3/8
Answer:
3/8
Step-by-step explanation: