Answer:
We get x = -5/3 and x = -3
Step-by-step explanation:
[tex](5x+15) (6x-10)[/tex]
Multiplying this and equating to zero, to find x.
[tex]30x^{2} -50x+90x-150=0[/tex]
[tex]30x^{2} +40x-150=0[/tex]
Factoring out 10.
[tex]3x^{2} +4x-15=0[/tex]
[tex]3x^{2} +9x-5x-15=0[/tex]
3x(x+3)-5(x+3)=0[tex]
[tex](3x-5)(x+3)=0[/tex][/tex]
We get x = -5/3 and x = -3
Chaz rides 1/3 mile every 1/6 hour. How far does he ride in 1 hour?
(01.02 MC)Maya is showing her work in simplifying (5.2 − 4.5) − 5.5 + 4.8. Identify any error in her work or reasoning. Step 1: (5.2 − 4.5) − 5.5 + 4.8 Step 2: 5.2 + (− 4.5 − 5.5) + 4.8 (identity property) Step 3: 5.2 − 10 + 4.8 Step 4: 5.2 + 4.8 − 10 (commutative property) Step 5: 10 − 10 = 0
She wrote identity instead of commutative in Step 2.
She wrote commutative instead of distributive in Step 4.
She wrote identity instead of associative in Step 2.
She wrote commutative instead of associative in Step 4.
In her work, Maya misidentified the associative property as the identity property in step 2 and the commutative property in step 4.
Explanation:The question pertains to the simplification of the given expression: (5.2 − 4.5) − 5.5 + 4.8. The error lies in Maya's interpretation of the mathematical properties used in the simplification process. In Step 2, she has referred to the rearrangement of minus signs as the result of the 'identity property'. However, this should be the 'associative property' which allows the grouping of numbers to be changed. In Step 4, she refers to her re-ordering of the addition and subtraction as the 'commutative property'. However, it should be 'associative property' as it allows changing of grouping but the order within groups must be maintained.
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On the football team, two out of every seven players are seniors. If the team has 84 players, how many of the players are not seniors?
Answer: 60
Step-by-step explanation:
Given : The fraction of football players are senior = [tex]\dfrac{2}{7}[/tex]
If the team has 84 players, then by using the MULTIPLICATION OPERATION, we have
The number of players are senior = [tex]\dfrac{2}{7}\times84=24[/tex]
Then by using Subtraction operation , the number of players are not seniors =84-24=60
how do you know if two line segments are parallel
What is the quotient of 6,559 and 21 ?
How many 1/2 miles are in 12 miles corresponding division expression
Which expression shows the result of completely factoring and simplifying 3x+9x ? (A) 12x
(B) 3x(3x+9x)
(C) −6x
(D) 9(x+1)
19.18,23,23,31,32,16 all of the questions use these numbers except for the last one
in which stem does most of the data fall?
A 1
B 2
C 3 or
D 4
next question
steams leaves
.
1 | 1 1 2 3 4 5
. 2 | 2 3 4 4 7
. 3 | 2 5 7 9
what is the median?
A 24
B 28
C 22
D 23
A tractor tire makes one complete rotation every 14.3 seconds. How long does it take the tire to complete 4.25 rotations? Enter your answer in the box.
Answer:
60.775 seconds
Step-by-step explanation:
Hello, you can solve this using a simple rule of three
Step 1
let
A tractor tire makes one complete rotation every 14.3 seconds,it is
1 rotation ⇒ 14.3 seconds
How long does it take the tire to complete 4.25 rotations?,it is
4.25 rotations ⇒ x seconds
Step 2
if
1 rotation ⇒ 14.3 seconds
4.25 rotations ⇒ x seconds
the relation is
[tex]\frac{1}{14.3}=\frac{4.25}{x}\\ isolate \ x \\\frac{x}{14.3}=4.25\\x=4.25*14.3\\x=60.775\ seconds[/tex]
Have a great day
Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weigh of the carrots she buys is 28 kg. How many kilograms of carrots will Jennifer get ?
Answer:
7 kilograms of carrots.
Step-by-step explanation:
Jennifer's grandmother buys carrots at the farm stand.
The total weight of the carrots she buys = 28 kilograms
She and her 3 grandchildren equally shares the carrots.
The number of persons among carrots were distributed = 4 persons
To calculate how many kg of carrot each person will get = [tex]\frac{\text{total weight of carrots}}{\text{total number of persons}}[/tex]
They each will get = [tex]\frac{28}{4}[/tex]
= 7 kilograms.
Jennifer will get 7 kilograms of carrots.
Which expression is equivalent? (35 pts)
−3(5x + 8) − 7(5x + 3)
A) 50x + 45
B) 50x − 45
C) −50x + 45
D) −50x − 45
Answer:
-50x-45
Step-by-step explanation:
The solution of the given expression is -50x - 45. The correct option is D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is −3(5x + 8) − 7(5x + 3). The given expression will be solved as below,
E = −3(5x + 8) − 7(5x + 3)
E = -15x - 24 - 35x -21
E = -50x - 45
Therefore, the solution of the given expression is -50x - 45. The correct option is D.
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Fifty students were eating lunch in the school cafeteria. The ratio of boys to girls was 25:25. Mrs. White asked Kym to explain what that ratio meant. Kym said it meant that 25% of the students in the cafeteria were boys. Explain why Kym is incorrect.
Answer:
Sample Response: The ratio of boys to total students was 25:50. Written as a fraction, this is 25/50. Rewrite the fraction with a denominator of 100 to 50/100. So 50% of the students were boys.
Step-by-step explanation:
Simplify the expression: 5+12 divided by 2x2
Steven earns extra money babysitting. He charges $23.25 for 3 hours and $54.25 for 7 hours. Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he changes.
A sales representative earns a 2.5% commission on sales. Find the commission earned when the total sales are $80,700.
To find the commission earned by a sales representative, multiply the total sales by the commission rate of 2.5%. For total sales of $80,700, the commission earned would be $2,017.50.
Explanation:To find the commission earned by a sales representative, we need to multiply the total sales by the commission rate.
In this case, the total sales are $80,700 and the commission rate is 2.5%.
So, the commission earned can be calculated as:
$80,700 x 0.025 = $2,017.50
Therefore, the sales representative will earn a commission of $2,017.50.
An 8-ounce can of tomatoes costs $1.14.A 12-ounce can costs $1.75.Which can of tomatoes cost the least per ounce
Answer:
8-ounce can tomatoes costs the least per ounce.
Step-by-step explanation:
Cost of an 8-ounce can of tomatoes = $1.14
cost per ounce of tomatoes = [tex]\frac{1.14}{8}[/tex]
= $0.1425 ≈ $0.14 per ounce
Cost of an 12-ounce can of tomatoes = $1.75
cost per ounce of tomatoes = [tex]\frac{1.75}{12}[/tex]
= $0.1458 ≈ $0.15 per ounce
Therefore, 8-ounce can of tomatoes cost the least per ounce.
What is the greatest common of 48 and 14
You make 3 batches of cookies to make bags for a sale. You put 5 cookies in each bag. Given 14(5)+2=3(24). What do the terms represent? Please help!!
find the slope of a line parallel to 3x+5y=15
Answer:
A. [tex]-\frac{3}{5}[/tex].
Step-by-step explanation:
We have been given equation of a line [tex]3x+5y=15[/tex]. We are asked to find the slope of a parallel line to our given line.
We know that slopes of parallel lines are equal, so slope of the parallel line will be equal to slope of our given line.
To find the slope of our given line, we will convert our given equation in slope-intercept form of equation [tex]y=mx+b[/tex], where m represents slope of line.
First of all, we will subtract 3x from both sides of our given equation as:
[tex]3x-3x+5y=15-3x[/tex]
[tex]5y=-3x+15[/tex]
Now, we will divide both sides by 5.
[tex]\frac{5y}{5}=\frac{-3x+15}{5}[/tex]
[tex]y=\frac{-3x}{5}+\frac{15}{5}[/tex]
[tex]y=-\frac{3x}{5}+3[/tex]
Upon comparing our equation with slope-intercept form, we can see that [tex]m=-\frac{3}{5}[/tex] and option A is the correct choice.
isaiah wrote this problem in his notebook. Using the Vocabulary boxes,label the parts of the division problem. then, using the vocabulary, explain how isaiah can check whether his quotient is correct. quotient, divisor, dividend
Answer:
9 is divisor, 648 is dividend and 72 is the quotient.
Isaiah can check his work by multiplying divisor(9) and quotient (648). If quotient is correct the product will be equal to dividend.
Step-by-step explanation:
Consider the provided information.
A number by which another number is to be divided is called divisor.
A number which is divided by another number is called dividend.
A result obtained by dividing one number by another is called quotient.
Here 9 is the number which divide 648.
Therefore, 9 is divisor.
648 is the number which is divided by 9.
Therefore, 648 is dividend.
The result obtained by dividing 648 by 9 is 72.
Therefore, 72 is the quotient.
Isaiah can check his work by multiplying divisor(9) and quotient (648). If quotient is correct the product will be equal to dividend.
the lifetime of a smartphone battery while playing video is described by a normal model. if 95% of batteries last between 8.5 and 11.5 hours, what are the mean and standard deviation of the distribution of battery lifetime while playing videos?
Which souvenirs cost less than $2.25 per item?
Check all that apply.
tote bags: 25 for $49.00
picture frames: 15 for $32.25
water bottles: 12 for $27.60
mugs: 8 for $15.92
T-shirts: 10 for $25.00
Answer:
tote bags, picture frames, and mugs
Step-by-step explanation:
Can someone help me on this
You earn $7.80 an hour working as a dog sitter. You work 12.5 hours during the weekend. How much money do you make?
Heather was asked to graph 3x - y = -4 by using slope and y-intercept. Her graph is shown.
Which choice supports the graph that she has drawn?
A) The slope is positive 3 and the y-intercept is (0,4).
B) The slope is negative 3 and the y-intercept is (0,4).
C) The slope is positive 3 and the y-intercept is (0,-4).
D) The slope is negative 3 and the y-intercept is (0,-4).
The correct choice that supports the graph that Heather has drawn is:
The slope is positive 3 and the y-intercept is (0, 4).
Option A is the correct answer.
We have,
To determine which choice supports the graph that Heather has drawn for the equation 3x - y = -4, we need to consider the slope and y-intercept.
The equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Comparing the given equation to the standard form, we can rearrange it as y = 3x + 4.
From this, we can determine that the slope is positive 3 and the y-intercept is (0, 4).
Therefore,
The correct choice that supports the graph that Heather has drawn is:
The slope is positive 3 and the y-intercept is (0, 4).
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need help on #15 please
Use the distributive property to expand the expression. −(3x2 + 4y) + (8z2 − 2) A) −3x2 + 4y + 8z2 − 2 B) −3x2 − 4y − 8z2 + 2 C) −3x2 − 4y + 8z2 − 2 D) −3x2 − 4y − 8z2 − 2
HELP ME PLEASE!!!!!!
Tracy needs to find the length and width of the equipment storage room where she works. The room is 3 meters longer than it is wide. Its perimeter is 18 meters. Find the width in meters
Which graph represents the solution set of the system of inequalities?
{ y < -3x - 2
{ y ≤ x - 2
The common shaded region of the given inequality is given by figure 3 with yellow color.
What is an inequality and how to graph it ?An inequality is a statement that compares two expressions we can solve an inequality by adding same number to both sides or by subtracting same number from both side.
To graph the inequality
Replace the sign of the inequality with equal to sign.Graph the equation made with equal to line.If the point (x, y) satisfies the inequality then check whether the inequality is satisfied on that point or not.Shade the region on that side of line where any point satisfies the equation if not shade the opposite side of region.if the sign of inequality is < ,> with equal to gin then make the line dotted for respective equality otherwise a solid line.Given inequalities are :
y < -3x -2
y ≤ x-2
For y < -3x-2 consider the equality y = -3x -2
Put x =0 ⇒ y = -2 , ( 0, -2)
Put y = 0 , x = -2/3, ( -2/3 , 0)
∴ y = -3x -2 is the line passing through the points ( 0, -2) and ( -2/3 , 0)
⇒ Put (0,0) in y<-3x-2 ⇒ 0 < -3(0) -2 ⇒0 < -2 which is false
Therefore , the inequality y<-3x-2 is the shaded region shown in figure 1
Similarly for inequality y ≤ x - 2 , Consider y = x - 2
Put x = 0 ⇒ y =-2, (0,-2)
Put y=0 ⇒ x =2 , (2,0), thus y = x - 2 is the line passing through (2,0) and (0,-2)
Put (0,0) in y ≤ x - 2⇒ 0 ≤ -2 , which is false
therefore the region of this inequality is as shown in figure 2.
The common shaded area is given by yellow color figure 3 .
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4/5(2x+5)−4=1
x = 1 1/4
x = 1 2/5
x = 5/8
x = 3 1/5