Factor the polynomial by grouping : x^3+5x^2-6x-30
The idea is to pair up the terms, factor each sub-group, and then pull out the overall GCF to fully factor.
x^3+5x^2-6x-30
(x^3+5x^2)+(-6x-30)
x^2(x+5)+(-6x-30)
x^2(x+5)-6(x+5)
(x^2-6)(x+5)
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Answer: (x^2-6)(x+5)
8640 divided by40 long division
Sam drives his car at a constant speed. He travels a distance (d) of 15 miles with 1/2 of a gallon of gas (g).
Write an equation in the form of d=rg that represents the relationship between distance (d) and the number of gallons of gas (g), where r is the constant of proportionality.
Answer:
[tex]d =30g[/tex]
Step-by-step explanation:
Sam drives his car at a constant speed. He travels a distance (d) of 15 miles with 1/2 of a gallon of gas (g)
Distance d= 15
Gallons of gas (g)= 1/2
Equation is d= rg
Now plug in the values
15 = r* 1/2
Now we divide by 1/2 on both sides
[tex]r=\frac{15}{\frac{1}{2}}=15 * \frac{2}{1}= 30[/tex]
r=30
Now we replace the value of 'r' in the equation d=rg
[tex]d = 30g[/tex]
Using the given scale factor and center dilate the following figures and state the new coordinates
See the attachment
Step-by-step explanation:Each of the points moves to 3 times the distance from A that it is currently.
For example, point B is 1 unit left and 2 units up from A. It moves to 3 units left and 6 units up from A.
What is the best estimate of 28 × 4,417?
Answer:
132600
Step-by-step explanation:
I was always taught like this, and this should be the best estimate:
28 x 4417 --> 30 * 4420 --> 132600
Some other possible estimates with simpler values:
30 * 4400 --> 132000
30 * 4500 --> 135000
30 * 4000 --> 120000
can yall help me????
Hi There!
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Remember to follow PEMDAS.
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Problem #1:
= (25 - 6.25) + (5 · 3)²
= (18.75) + (15)²
= 18.75 + 225
= 243.75
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Problem #2:
= (8 + 3)² + 10 · (-4)
= (11²) + 10 · (-4)
= 121 + 10 · (-4)
= 121 + (-40)
= 81
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Hope This Helps :)
The recipe for mint chocolate ice cream requires 2 1/4 cups of cream for 5 people. You need ice cream for 15 people. How much cream will you need?
Answer:
Step-by-step explanation:
i know it'
convert 2 1/4 into improper fraction or do it as same as it is
So, this is ratio and proportion. so, multiply 2 1/4 or 2.25 to 8 and divide it to 5. so, the answer is 3.6 or 3 3/5.
A chef bought 5 1/5 liters of oil for $26. What was the cost per liter of oil
Answer:5
Step-by-step explanation:
Answer:
$ 5.25 per liter
Step-by-step explanation:
Answer for some points
Since you already know that two of the sides equal 10.8 mi which concludes to an isosceles triangle you'll add them which comes to 21.6 and lastly you just subtract 31 from 21.6 which is 9.4
the variables y and x have a proportinal relationship and y=12 when x=5 . what is the value of y when x=8?
Answer:
y = [tex]\frac{96}{5}[/tex]
Step-by-step explanation:
given that y and x are proportional then the equation relating them is
y = kx ← k is the constant of proportionality
to find k use the given condition y = 12 when x = 5
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{5}[/tex]
y = [tex]\frac{12}{5}[/tex] x ← equation of proportionality
when x = 8, then
y = [tex]\frac{12}{5}[/tex] × 8 = [tex]\frac{96}{5}[/tex]
f(x) = -3x^2 + 6x. Find f(2).
Answer:
f(2) = 0
Step-by-step explanation:
Evaluate the function at x = 2.
f(x) = -3x^2 + 6x
f(2) = -3(2^2) + 6 * 2
f(2) = -3(4) + 12
f(2) = 0
Passes through (-1, 10) slope = -6
Point slope form?
Y- 10 = -6 ( X + 1 )
During Reconstruction, the Black Codes
A) protected the Constitutional rights and liberties of freed slaves.
B) forced Congress to do the bidding of former Confederate politicians.
C) were enacted by the Radical Republicans to prevent racial discrimination in the South.
Eliminate
D) were laws passed by mainly Southern states to keep African Americans in a system of virtual slavery.
Answer:
D) were laws passed by mainly Southern states to keep African Americans in a system of virtual slavery.
Step-by-step explanation:
The Black Codes were created by the Southern States and were extremely similar to slavery, in which the African Americans were not allowed many of their newly gotten rights, such as a right to education, voting, etc, and the African Americans had to endure a lot of codes that were created to make them feel inferior.
~
Answer: D) were laws passed by mainly Southern states to keep African Americans in a system of virtual slavery.
given ef intersects gh at point D and ef is perpendicular to gh, what is the measure of hdf
Below is an image of what you have described. Since EF intersects GH perpendicularly - all resulting angles will be 90° by the definition of intersection of perpendicular lines.
This is to say that, Angle GDE, GDF, HDF, and HDE are all 90° angles.
Please help with this question
Answer:
The answer is y=1.4x
Step-by-step explanation:
You have to find the change of y over the change of x. So you have to find how much each value is changing by.
Y-side
5.6-2.8= 2.8
8.4-5.6=2.8
11.2-8.4=2.8
X-side
4-2=2
6-4=2
8-6=2
If you divide 2.8 by 2 you get 1.4
So the slope is 1.4
I need help with 4 plz
Check out the attached image below. I've marked two red points on the line such that the points have whole number coordinates. This way I could compute the slope of this line to be -2/5
We move down 2 units (rise of -2) as shown by the blue arrows. Afterward, we move 5 units to the right as shown by the green arrows (which is the run). This gets us from the left red point to the right red point.
rise = -2, run = 5
slope = rise/run = -2/5
the original line shown has a slope of -2/5
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Next we do two things to get the perpendicular slope.
Flip the fraction: -2/5 becomes -5/2
Flip the sign: -5/2 becomes +5/2 or simply 5/2
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Final Answer: 5/2
A friend is having trouble finding the sum of -84 and 28. A) What is the solution to this problem and B) what explanation would you give your friend to help them solve this problem?
Question: A) What is the solution to -84 + 28 =
B) What explanation would you give your friend to help them solve this problem?
Answer:
A) -56
Step-by-step explanation:
B) First, you have to ignore the plus sign, and recognize that the second negative number means you are subtracting that number.
If this is correct, please like the comment so others can know, too!
What is the equation of a line with a slope of 3 and a point (3, 1) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
Enter your answer in the box.
Answer:
The equation of the line would be y = 3x - 8
Step-by-step explanation:
To find any equation when you have the slope and a point, start with point-slope form and then solve for y.
y - y1 = m(x - x1)
y - 1 = 3(x - 3)
y - 1 = 3x - 9
y = 3x - 8
in year 4 the store sold 112% of the total number of scooters sold during the previous three years combined determine the number of scooter sold in year 4
Answer:
2, 240
Step-by-step explanation:
In the table, the values should be
Year 1 725
Year 2 579
Year 3 696
Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.
[tex]\frac{112}{100} =\frac{x}{2000}[/tex]
We solve through cross multiplication of numerator and denominator of the opposite fraction.
[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]
Which is the equation of a line that has a slope of -2/3 and passes through point (-3,-1)?
Answer:
Step-by-step explanation:
You have to use Point Slope Form:
y - Y1 = m (x - X1)m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineAbout Problem:
Since -2/3 is the slope, it represents m in y - Y1 = m (x - X1) form.-3 represents X1 in y - Y1 = m (x - X1) form-1 represents Y1 in y - Y1 = m (x - X1) formy - Y1 = m (x - X1)
y - -1 = -2/3 (x - -3) ---- This is in Point Slope Form
If you want to solve it, & put it in Slope Intercept form, it would look like this:
y = mx + b
y = -2/3 - 2 --- This is in Slope intercept Form.... I might've solved it wrong... I'm not sure...
Really really sorry if I'm incorrect...
Answer: The required equation of the line is [tex]2x+3y+9=0.[/tex]
Step-by-step explanation: We are given to find the equation of a line that has a slope of [tex]-\dfrac{2}{3}[/tex] and passes through point (-3,-1).
SLOPE-INTERCEPT FORM :
The equation of a line having slope m and passing through the point (a, b) is given by
[tex]y-b=m(x-a).[/tex]
For the given line, we have
[tex]m=-\dfrac{2}{3},\\\\\\(a,b)=(-3,-1).[/tex]
Therefore, the equation of the line is given by
[tex]y-b=m(x-a)\\\\\Rightarrow y-(-1)=-\dfrac{2}{3}(x-(-3))\\\\\\\Rightarrow y+1=-\dfrac{2}{3}(x+3)\\\\\Rightarrow 3y+3=-2x-6\\\\\Rightarrow 2x+3y+9=0.[/tex]
Thus, the required equation of the line is [tex]2x+3y+9=0.[/tex]
Which of the following segments is a radius a circle A
Bc
Ac
Cm
Rs
Answer:
the segment that states the radius is AC.
Step-by-step explanation:
Mr.Jimerson earns $24 per hour working. He qualifies for a 15% raise in salary. What is his salary after his raise?
Final answer:
Mr. Jimerson will earn $27.60 per hour after receiving a 15% raise on his original $24 per hour salary, resulting in a $3.60 increase per hour.
Explanation:
Mr. Jimerson earns $24 per hour working and qualifies for a 15% raise in salary. To calculate his new hourly salary after the raise, first determine the amount of the raise by finding 15% of his current hourly wage. Since 15% can be written as 0.15, we multiply his current wage by 0.15 to find the raise amount.
0.15 × $24 = $3.60
Next, add this raise amount to his original hourly wage to find his new salary:
$24 + $3.60 = $27.60 per hour
Therefore, Mr. Jimerson's salary after the raise will be $27.60 per hour.
If the sum of two or more mixed numbers is a whole number, then the sum of their fraction parts is a whole number. True or false? Please help
Identify the value of the 7 in 7.724 (the one before the point)
Evaluate the following expression.
6 -3
The simplification of the given expression is obtained as 1/216.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given expression is 6⁻³.
It can be simplified as below,
Rewrite the given expression as,
6⁻³ = ((6)⁻¹)³
Now, (6)⁻¹ = 1/6
⇒ 6⁻³ = (1/6)³
⇒ 1/6 × 1/6 × 1/6 = 1/216
Hence, the given expression can be simplified as 1/216.
To know more about exponents click on,
https://brainly.com/question/5497425
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The list below shows all of the possible outcomes for flipping four coins. HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT What is the probability of getting the same number of heads and tails?
Answer:
3/8
Step-by-step explanation:
there are 6 outcomes with two heads and two tails, and 16 total outcomes. 6/16=3/8
The probability of getting the same number of heads and tails is 3/8
The sample space (S) is given as:
S = {HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT}
The outcomes (E) that the number of heads and tail are the same is
E = {HHTT HTHT HTTH THHT THTH TTHH}
The probability of getting the same number of heads and tails is then calculated as:
[tex]Pr = \frac{n(E)}{n(S)}[/tex]
So, we have:
[tex]Pr = \frac{6}{16}\\[/tex]
Simplify
[tex]Pr = \frac{3}{8}[/tex]
Hence, the probability of getting the same number of heads and tails is 3/8
Read more about probabilities at:
https://brainly.com/question/8652467
translate this sentence into an equation. the product of janelles saving and 3 is 54 . use the variable j to represent janelles saving.
Ellie is going to an amusement park. The price of admission into the park is $35, and once she is inside the park, she will have to pay $3 for every ride she rides on. How much money would Ellie have to pay in total if she goes on 14 rides? How much would she have to pay if she goes on (r) rides?
Answer:
she would have to pay 42 dollars for 14 rides
so $3 for each ride 3* 14 is 42 or just add 3, 14 times
Is 3pi/2pi a rational number or an irrational number? Explain your reasoning
Answer:
It is rational
Step-by-step explanation:
The pi terms cancel out when you divide. This is due to the rule x/x = 1 where x is any number you want except x cannot be zero. So replace x with pi and we have pi/pi = 1
Therefore,
(3pi)/(2pi) = (3/2)*(pi/pi)
(3pi)/(2pi) = (3/2)*1 .... use the rule mentioned above
(3pi)/(2pi) = 3/2
we get a fraction or a ratio of two whole numbers, so this proves that the given expression is rational.
the temperature fell from o degrees to 6 3/5 degrees below 0 in 2 1/5 hours. what was the temperature change per hour?
Answer:
The temperature change per hour was -3 degrees per hour.
Step-by-step explanation:
We know that the temperature fell from [tex]0[/tex] degrees to [tex]-6\frac{3}{5}[/tex] degrees in a time period of [tex]2\frac{1}{5}[/tex] hours.
So to find the rate of change of the temperature, we will divide the change in temperature by the number of hours.
For that, we will change the mixed number into improper fractions and then solve:
[tex]-6\frac{3}{5}=-\frac{33}{5}degrees[/tex]
[tex]2\frac{1}{5}=\frac{11}{5} hours[/tex]
Temperature change per hour = [tex]\frac{-\frac{33}{5}}{\frac{11}{5}} = \frac{33}{5}*-\frac{5}{11}=-3[/tex]
Therefore, the temperature change per hour was -3 degrees per hour.