Answer: 17 and 31
Step-by-step explanation:
first number = x
second number = y
x+y=48
-(x-y=14)
---------------
2y=34
y=17
x=31
Answer:
17 and 31
Step-by-step explanation:
17 + 31 = 48, I basically just plugged in random numbers until I got the answer.
A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 30% copper and (blank) kilograms of the metal alloy that is 55% copper. (show your work)
Answer:
20kg
Step-by-step explanation:
Write a polynomial equation of degree 4 that has the following roots : -1 repeated three times and 4
Answer:
x^4 -x^3 -9x^2 -11x -4
Step-by-step explanation:
We can use the zero product property
(x-a) (x-b) (x-c) (x-d) where a b c d are the roots
(x- -1)(x- -1)(x- -1) ( x-4) since the root -1 is repeated 3 times and 4 is a root
(x+1)(x+1)(x+1) ( x-4)
Foil the first two terms and the last two terms
(x^2 + 2x+1)( x^2 -3x-4)
Foil again
x^4 -3x^3 -4x^2 +2x^3 -6x^2 -8x +x^2 -3x-4
Combine like terms
x^4 -x^3 -9x^2 -11x -4
Answer:
Step-by-step explanation:
roots = -1, -1, -1, 4
(x + 1)(x + 1)(x + 1)(x - 4) = 0
(x^2 + 2x + 2)(x^2 - 3x - 4) = 0
x^2(x^2 - 3x - 4) + 2x(x^2 - 3x - 4) + 2(x^2 - 3x - 4) = 0
x^4 - 3x^3 - 4x^2 + 2x^3 - 6x^2 - 8x + 2x^2 - 6x - 8 = 0
x^4 - x^3 - 8x^2 - 14x - 8 = 0
Mr. Johnson's lunch bill is $29.90, which includes a 15% típ
What is the price before tip, b, of Mr. Johnson's lunch?
Answer:
price before tip (b) = $26
Step-by-step explanation:
29.90 is INCLUDING tip, so the real bill, b, would be less.
Now, since 29.90 is including 15% tip, and we let the original bill be "b", we can say:
b INCREASED by 15% gives us 29.90
We need to come up with an equation and solve for b.
15% means 15/100 = 0.15
Now, we can write:
b + 15% of b = 29.90
or
b + 0.15b = 29.90
then
1.15b = 29.90
b = 29.90/1.15
b = 26
So, price before tip (b) = $26
Answer:
the answer is 26
Step-by-step explanation:
The range of which function is (2, infinity)? y = 2x y = 2(5x) y = 5x +2 y = 5x + 2
Answer:
I think your functions are [tex]y=2^{x}[/tex] ,[tex]y=2*5^{x}[/tex] and [tex]y=2+5^{x}[/tex]
If yes then then the third function which is [tex]y=2+5^{x}[/tex].
Step-by-step explanation:
The function [tex]c^{x}[/tex] where c is a constant has
Domain : [tex]c\geq 0[/tex]
Range : ( 0 , ∞ )
The above range is irrespective of the value of c.
I have attached the graph of each of the function, you can look at it for visualization.
[tex]y=2^{x}[/tex] ⇒ This function is same as [tex]c^{x}[/tex] so its range is ( 0 , ∞ ).[tex]y=2*5^{x}[/tex] ⇒ If we double each value of the function [tex]y=5^{x}[/tex], which has range ( 0 , ∞ ), but still the value of extremes won't change as 0*2=0 and ∞*2=∞. Therefore the range remains as ( 0 , ∞ ).[tex]y=2+5^{x}[/tex] ⇒ If we add 2 to each value of the function [tex]y=5^{x}[/tex], which has range ( 0 , ∞ ), the lower limit will change as 0+2=2 but the upper limit will be same as ∞. Therefore the range will become as ( 2 , ∞ ).Answer:
y = 5∧× + 2
Step-by-step explanation:
Nancy is going to glaze 6-ounce servings of pretzels and put them into gift boxes. If pretzels
are sold in -pound bags, how many bags will Nancy need for 100 gift boxes?
A. 16
B. 17
C. 22
D. 27
Please show how you got this answer
Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval.
I NEED HELP ASAP
Answer:
Increasing : [tex]-5<x<-1[/tex] or [tex]-1<x<1[/tex]
Decreasing : [tex]-8<x<-5[/tex] or [tex]4<x<7[/tex]
Neither : [tex]1<x<4[/tex]
Step-by-step explanation:
Increasing function : In this function, the y-value increases as the x-value increases.
From the given graph it is clear that the function is increasing on
[tex]-5<x<-1[/tex]
[tex]-1<x<1[/tex]
Decreasing function : In this function, the y-value decreases as the x-value increases.
From the given graph it is clear that the function is decreasing on
[tex]-8<x<-5[/tex]
[tex]4<x<7[/tex]
Neither increasing nor decreasing function : In this function, the y-value remains constant as the x-value increases.
From the given graph it is clear that the function is neither increasing nor decreasing on
[tex]1<x<4[/tex]
To determine if a function is increasing, decreasing, or neither over intervals on a graph, analyze the direction of the graph. If the graph goes up, the function is increasing. If it goes down, the function is decreasing. If it remains flat, the function is neither increasing nor decreasing.
Explanation:The question asks to determine if the function is increasing, decreasing, or neither over each interval on the given graph. To do this, we need to analyze the direction of the graph. If the graph goes up as we move from left to right, the function is increasing. If the graph goes down, the function is decreasing. If the graph remains flat, the function is neither increasing nor decreasing. Drag the intervals to the appropriate box based on these observations.
Jaquez completed 1/8 of his test in 3/5 hour. If Jaquez's rate stayed the same, how much of his test was finished in one hour. Show Work!
(A) 3/40
(B) 1/24
(C) 1/12
(D) 5/24
Answer:[tex]\dfrac{5}{24}[/tex]
Step-by-step explanation:
Let [tex]r[/tex] be the rate at which Jaquez completes his test.
Let [tex]x[/tex] part of test be completed by Jaquez in [tex]t[/tex] hours.
Then,
[tex]x=rt[/tex]
Given that Jaquez completed 1/8 of his test in 3/5 hour.
So,[tex]\frac{1}{8}=r\times \frac{3}{5}[/tex]
[tex]r=\frac{5}{24}[/tex]
To know how much he completes in one hour,substitute [tex]1[/tex] in the above equation.
So,[tex]x=r\times 1=\frac{5}{24}[/tex]
Jaquez completes [tex]\frac{5}{24}[/tex] of his test in [tex]1[/tex] hour
Answer:
Option (d)
5/24
Explanation:
Hour taken to complete 1/8 of his test=3/5 hour
Suppose r is the rate at which Jackuez completes his test
For completing the test in t hours
The equation is
y= r t
where y is the part of test which will be completed in t hour
with the information given
substituting the values
[tex]\frac{1}{8}=r \frac{3}{5}[/tex]
[tex]r=\frac{5}{24}[/tex]
now when t=1 hour
substituting the value
[tex]\mathrm{x}=\frac{5}{24} \times 1[/tex]
[tex]\mathrm{x}=\frac{5}{24}[/tex]
hence at 1 hour his test was completed [tex]\frac{5}{24}[/tex]
please help me.
A mixture of gasoline and oil is supposed to contain K ounces of oil for every gallon of gasoline.
Which coordinate is represented on the graph?
Answer:
(1,K) hope i could help
Step-by-step explanation:
Answer:
[tex](1,K)[/tex]
Step-by-step explanation:
According to the problem, the mixture must contain K ounces of oil for every gallon of gasoline. That is, each gallon of gasoline equals K ounces, this can be expressed as
[tex](1,K)[/tex]
Where [tex]x=1[/tex] expresses each gallon of gasoline and [tex]y=K[/tex] represents ounces of oil.
Therefore, the coordinate on the graph must represent [tex](1,K)[/tex], that is, K ounces of oil per gallon of gasoline.
Could these triangles be congruent?
Answer:
no, because the hypotenuses must have different lengths.
Step-by-step explanation:
Which of the following is the correct factorization of the polynomial below?
x3 -12
O A. (x+3)(x-4)
O B. (x-3)(x + 4)
O C. (x+3)(x2 - 4x + 4)
O D. The polynomial is irreducible.
Answer: The polynomial is irreducible
Step-by-step explanation:
There is nothing we can subtract between x3-12
For example: you are trying to find the polynomial of x4-6
Options:
A. (x+4)(x-6)
B. (x+1+3)(x-6)
C. None the polynomial is irreducible.
You would chose C because there is no subtraction sign in between the parentheses. If you would choose a right answer, you would rewrite it as:
(x+4)-(6)
Marsha serves the Volleyball to Rhonda with an upward velocity of 14.5 ft./s. The bar is 4 feet above the ground when she strikes it. How long does Rhonda have to react, before the Volleyball hits the ground? Round your answer to two decimal places.
Answer:
The taken by Rhonda to react before volleyball hits ground is 2.39 seconds
Step-by-step explanation:
Given as :
The upward velocity of the volleyball = 14.5 ft/s
The height of the ball above ground = 4 feet
Consider value of acceleration due to gravity = 9.8 m/s
Let the time for Rhonda to react before ball hits ground = t sec
Now,
S = u t + [tex]\frac{1}{2}[/tex] a t²
where s = height
u = initial velocity , a = acceleration due to gravity , t = time in sec
So, 4 = 14.5× t + [tex]\frac{1}{2}[/tex] × 9.8 × t²
or, 4 = 14.5 t + 4.9 t²
or, 4.9 t² + 14 .5 t - 4 = 0
Now, solve for t
t = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
or, t = [tex]\frac{-14.5\pm \sqrt{14.5^{2}-4\times 4.9\times (4)}}{2\times 4.9}[/tex]
Or, t = [tex]\frac{-14.5\pm \sqrt{80.5025}}{9.8}[/tex]
Or, t = - 2.39 , - 2.76
Hence The taken by Rhonda to react before volleyball hits ground is 2.39 seconds . Answer
How do you calculate constant rate of change from a proportional graph given the coordinates (x, y)?
Question 1 options:
x/y
y + x
xy
y/x
Answer:
y/x
Step-by-step explanation:
If y is directly proportional to x, then:
y = kx
k is the coefficient of proportionality, or the constant rate of change. Solving for k:
k = y/x
Latoya's cow gives 1 1/2gallons milk each day. How much is this in quarts?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
6 quarts
Step-by-step explanation:
1 gallon = 4 quarts
1 1/2 gallon * (4 quarts / 1 gallon) = (1 + 1/2) * 4 = 1*4 + 1/2*4 = 4 +2 = 6 quarts
Rome was able to gain its empire in large part by extending some form of citizenship to many of the people it conquered. Military expansion drove economic development, bringing enslaved people and loot back to Rome, which in turn transformed the city of Rome and Roman culture.
Answer:
is this a question or a passage
Answer:
very confused, are you trying to inform us?
Step-by-step explanation:
the area of a circular plot is 9856 metre square.calculate the cost of fencingthe plot at Rs.32.50 per metre.
Answer:
Rs 11440Step-by-step explanation:
Area of a circular plot is [tex]9856\text{ }m^{2}[/tex].
The area of a circle with radius [tex]r[/tex] is given by [tex]\pi r^{2}[/tex]
[tex]\pi r^{2}=9856\\r^{2}=9856\times\frac{7}{22}=3136\\r=56\text{ }m[/tex]
So, the radius of the circular plot is [tex]56\text{ }m[/tex].
Cost of fencing the plot is [tex]32.50\frac{Rs}{m}[/tex].
Total circumference of the circular plot is given by [tex]2\pi r[/tex]
Circumference = [tex]2\times\frac{22}{7}\times56=352\text{ }m[/tex]
Cost of fencing = [tex]352\text{ }m\times 32.50\frac{Rs}{m}=11440\text{ }Rs[/tex]
∴ Cost of fencing = Rs 11440
-1 2/3 + (-2 1/6)
A. Use the real number of properties to write an equivalent expression for this sum.
B. Find the sum. Express your answer as a mixed number in lowest terms.
MUST SHOW PART A AND PART B!!
Answer:
-3 5/6 (-3.83333)
Step-by-step explanation:
(-1x3+2)/3+-(2x6+1)/6
-5/3+-13/6
-5x2/6+-13x1/6
-10/6+-13/6
(-10+-13)/6
-23/6
-(3x6+5)/6
=-3 5/6 or (-3.83333)
Which two operations are needed to write the expression that represents "eight more than the product of a number and twa
multiplication and subtraction
division and subtraction
multiplication and addition
division and addition
Answer:
multip[laction and addition
Step-by-step explanation:
One day, the Jerry Bakery produced 800 pieces of bread and sold a total of 750 pieces.
Find the percentage of bread left.
A. 63%
B.6%
C.93%
D. 93%
The right answer is Option B.
Step-by-step explanation:
Pieces of bread produced = 800
Pieces of bread sold = 750
Pieces left = Pieces produced - Pieces sold
Pieces left = 800 - 750 = 50
Percentage of bread left = [tex]\frac{Pieces\ left}{Pieces\ of\ bread\ produced}*100[/tex]
[tex]Percentage\ of\ pieces\ left=\frac{50}{800}*100\\Percentage\ of\ pieces\ left=\frac{5000}{800}\\Percentage\ of\ pieces\ left= 6.25\%\\[/tex]
Rounding off to nearest whole percent;
Percentage of pieces left= 6%
The right answer is Option B.
Keywords: percentage, subtraction
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A quadrilateral has vertices A(4,9), B(2,5), C(8,2), and D(10,6). Which statement about the quadrilateral is true?
Answer:
it is letter B
The given quadrilateral is not a parallelogram, is convex, and is not a square.
The question asks for the statement that is true about the given quadrilateral with vertices A(4,9), B(2,5), C(8,2), and D(10,6). To determine the truth of statements, we need to consider the properties of the given quadrilateral.
One statement that is true is that it is not a parallelogram. This can be proven by showing that opposite sides are not parallel, as the slopes are not equal.
Another statement that is true is that it is a convex quadrilateral. A convex quadrilateral is one where all interior angles are less than 180 degrees. To prove this, we can calculate the angles and show that they are all less than 180 degrees.
Lastly, a true statement is that it is not a square. A square is a special type of parallelogram with 4 equal sides and 4 right angles. We can determine this by calculating the lengths of the sides and showing that they are not all equal.
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Which equation has infinitely many solutions?
A. 12 + 4x = 6x + 10 – 2x
B. 5x + 14 – 4x = 23 + x – 9
C. x + 9 – 0.8x = 5.2x + 17 – 8
D. 4x – 2x = 20
An equation has infinitely many solutions if it can be manipulated all the way to an identity (i.e. an equality where the right and left hand side are the same). We have:
A) [tex]12+4x=6x+10-2x \iff 12+4x=10+4x \iff 12=10[/tex]
which is impossible
B) [tex]5x+14-4x=23+x-9 \iff x+14 = x+14[/tex]
which is an equality
C) [tex]x+9-0.8x=5.2x+17-8\iff 0.2x+9=5.2x+9 \iff 0.2x=5.2x\iff x=0[/tex]
which has a unique solution
D) [tex]4x-2x=20 \iff 2x=20 \iff x=10[/tex]
which has a unique solution
The slope of line éb is zac
What is the equation of D. simplified?
B(2a, 2b)
y-yı = m(x - xı)
y-0=(220)(x-c)
y=[0]x-(22b)
y=(220 fer-(2 bezed
y=(22]x- (226)
O y=(,20 ]- (250)
Ela, b)
A(0, 0)
Dac, 0)
C(2c, 0)
Answer:
[tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]
Step-by-step explanation:
The straight line BD passes through points B(2a,2b) and D(c,0).
Therefore, the equation of the straight line BD will be given by
[tex]\frac{y - 2b}{2b - 0} = \frac{x - 2a}{2a - c}[/tex]
⇒ [tex]y - 2b = \frac{2b}{2a - c}x - \frac{4ab}{2a - c}[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x - \frac{4ab}{2a - c} + 2b[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x + \frac{-4ab + 4ab - 2bc}{2a - c}[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]
Therefore, third option is correct. (Answer)
We know that the equation of a straight line passing through the points ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by
[tex]\frac{y - y_{1} }{y_{1} - y_{2}} = \frac{x - x_{1} }{x_{1} - x_{2}}[/tex]
Joe bought 5.8 pounds of
grapes to have as a snack with
his 10 friends. If he shares his
grapes evenly, how many
pounds of grapes will each of
his friends get?
Answer:6.8
Step-by-step explanation:
Answer:
0.58 pounds per friend
Step-by-step explanation:
divide 5.8 into the 10 friends.
What is the next number in this pattern? 1,7,8,15,23,38,61
Answer:
72
Step-by-step explanation:
1 then 7+1=8 8+7=15 15+8=23 23+15=38 38+23=61
Ta Da I have taught you the pattern now you can show your work just in case you have one of those teachers hope this helped
The next number in the pattern 1,7,8,15,23,38,61 is 99. The pattern can be understood by calculating the differences between consecutive numbers, and observing a pattern in these differences.
Explanation:Let's take a look at the pattern 1,7,8,15,23,38,61 closely. At every step, we're adding an increasing number to get to the next term in the sequence. From 1 to 7, we add 6. From 7 to 8, we add 1. From 8 to 15, we add 7, from 15 to 23, we add 8, from 23 to 38, we add 15 and from 38 to 61, we add 23.
The difference between these numbers (6, 1, 7, 8, 15, 23) reads as follows: 5, 6, 1, 7 and 8. So, the next difference could be 15 (continuing the pattern in the differences). So, the next term would be obtained by adding 15 to previous term's difference (23) and then adding that result to 61.
Finally, we calculate 61 + (23 + 15) = 61 + 38 = 99. So, the next number in this pattern should be 99.
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What is the value of x in the equation 3x - 1 y = 18, when y = 27?
o 5
ООО
Answer:
X would equal 15
Step-by-step explanation:
-1 × 27 = -27
-27 + 27 =0
18 + 27 = 45
3x ÷ 3 = x
45 ÷ 3 = 15
x = 15
Factors of 42
I need to know what factors make 42
Those are the factors of 42 c:
(1, 42), (2, 21), (3, 14) and (6, 7).
HELPPPPPPPPPPPPPPP RATE 5 STARSS
Answer:
13. c,
14. a.
Step-by-step explanation:
13. The length of a side PQ with coordinates of
P as (x,y) and Q as (w,z)
is: [tex]\sqrt{(x-w)^{2} +(y-z)^{2} }[/tex]
so, the length of the side AB =[tex]\sqrt{(5-5)^{2}+(-2+7)^{2} } =\sqrt{0^{2}+5^{2} } =5[/tex]
the length of side BC =[tex]\sqrt{(5-1)^{2}+(-7+2)^{2} } =\sqrt{(4)^{2}+(-5)^{2} } =\sqrt{4^{2}+5^{2} }[/tex]
the length of side AC=[tex]\sqrt{(5-1)^{2} +(-2+2)^{2} } =\sqrt{4^{2} } =4[/tex]
now, the easiest one will be when the vertices are on the coordinate axes.
so, option c will be the most appropriate one.14. If u see the figure clearly, the lines l and FH are parallel.
the parallel postulate, i.e, the alternate interior angles will always be congruent.
here, the alternate interior angles are angle1 and angle4.therefore to prove this step, he used parallel postulate as a reason.so, the correct option is "a"Which situation has a unit rate of $7?
A
Trevor spent $49 on 2 theater tickets.
B
Sally bought a pack of 5 t-shirts for $35.
C
Brandon bought 7 gallons of gas for $14.
D
Gina bought nail polish for $5 and a pack of gum for $2.
The right answer is Option B.
Step-by-step explanation:
A unit rate describes how many units of one type of quantity corresponds to one unit of other type of quantity.
A. Trevor spent $49 on 2 theater tickets.
2 theater tickets = $49
1 theater ticket = [tex]\frac{49}{2} = \$24.5[/tex]
B. Sally bought a pack of 5 shirts for $35.
5 shirts = $35
1 shirt = [tex]\frac{35}{5} = \$7\\[/tex]
C. Brandon bought 7 gallons of gas for $14.
7 gallons = $14
1 gallon = [tex]\frac{14}{7}=\$2[/tex]
D . Gina bought nail polish for $5 and a pack of gum for $2.
1 nail polish = $5
1 pack of gum =$2
The pack of 5 shirts for $35 has a unit rate of $7.
The right answer is Option B.
Keywords: unit rate, division
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Factor −13 out of −13x−8.
−13x−8=
Answer:
- 13(x + [tex]\frac{8}{13}[/tex])
Step-by-step explanation:
Given
- 13x - 8 ← factor out - 13 from each term
= - 13(x + [tex]\frac{8}{13}[/tex])
The question asked to factor out -13 from the expression -13x - 8. The steps include dividing each term by -13. Therefore, the expression factored out by -13 is -13(x + 8/13).
Explanation:In this mathematical problem, we are asked to factor out -13 from the expression -13x - 8. Factoring out in algebra means to divide each term in the expression by that common factor, which in this case is -13. So, we proceed as follows:
Divide -13x by -13 to get x.Divide -8 by -13 to get 8/13.Therefore, the expression -13x - 8 factored out by -13 is -13(x + 8/13).
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11 X +11 Y equals -5
Answer:
Step-by-step explanation:
11x+11y=-5
eanyone know??? get it correct u get 50 points
Answer:
J would be the answer, my friend.
log2 (24/3) = log5 (x)
log(8)/log(2) = log(x)/log(5)
log(x) = [log(5)][3]
log(x) = log(5^3)
x = 5^3 = 125
Step-by-step explanation:
Answer:
x = 125
Step-by-step explanation:
[tex] \log_2 24 - \log_2 3 = \log_5 x [/tex]
Use the rule of subtracting logs:
[tex] \log_b x - \log_b y = \log_b \dfrac{x}{y} [/tex]
[tex] \log_2 \dfrac{24}{3} = \log_5 x [/tex]
[tex] \log_2 8 = \log_5 x [/tex]
[tex] 3 = \log_5 x [/tex]
Use the definition of log:
[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]
[tex] x = 5^3 [/tex]
[tex] x = 125 [/tex]