Answer:
6 (2 x + 1)
Step-by-step explanation:
Simplify the following:
4 (3 x + 2) - 2
Hint: | Distribute 4 over 3 x + 2.
4 (3 x + 2) = 12 x + 8:
12 x + 8 - 2
Hint: | Group like terms in 8 + 12 x - 2.
Grouping like terms, 8 + 12 x - 2 = 12 x + (8 - 2):
12 x + (8 - 2)
Hint: | Subtract 2 from 8.
8 - 2 = 6:
12 x + 6
Hint: | Factor out the greatest common divisor of the coefficients of 12 x + 6.
Factor 6 out of 12 x + 6:
Answer: 6 (2 x + 1)
What is the scale factor in the dilation?
Answer Choices
2/5
1/2
2
2 1/2
Answer:
either 2 or 2 1/2
Step-by-step explanation:
Since the pre-image gets bigger, the scale factor is larger than 1.
Type the correct answer in the box. Use numerals instead of words.
Find the sum of the finite geometric series.
Mr. Jamison deposited $100 into a new savings account on January 1. On the first day of each month thereafter, he deposited three times the amount he deposited in the previous month. On June 15 of the same year, the total amount Mr. Jamison has deposited is $
Answer:
$36,400
Step-by-step explanation:
Mr Jamison deposited $100 in January
February=3*100=$300
March=3{3(100)=3^2(100)=9*100=$900
April=3^3(100)=27*100=$2,700
May=3^4(100)=81*100=$8,100
June=3^5(100)=243*100=$24,300
Total amount=$100 + $300 + $900 + $2700 + $8100 + $24300
=$36,400
The total amount deposited by Mr Jamison on June 15 is $36,400
Help please, I would really appreciate it. :)
Answer:
9, 13, 17, 21
Step-by-step explanation:
If x=2,
y=1+4(2)
y=9
This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.
The base of a right triangle is increasing at a rate of 2 meters per hour and the height is decreasing at a rate of 3 meters per hour. When the base is 9 meters and the height is 22 meters, then how fast is the HYPOTENUSE changing
Answer:
dL/dt = - 2,019 m/h
Step-by-step explanation:
L² = x² + y² (1) Where x, and y are the legs of the right triangle and L the hypotenuse
If the base of the triangle, let´s call x is increasing at the rate of 2 m/h
then dx/dt = 2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h
If we take differentials on both sides of the equation (1)
2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt
L*dL/dt = x*dx/dt + y*dy/dt (2)
When the base is 9 and the height is 22 according to equation (1) the hypotenuse is:
L = √ (9)² + (22)² ⇒ L = √565 ⇒ L = 23,77
Therefore we got all the information to get dL/dt .
L*dL/dt = x*dx/dt + y*dy/dt
23,77 * dL/dt = 9*2 + 22* ( - 3)
dL/dt = ( 18 - 66 ) / 23,77
dL/dt = - 2,019 m/h
Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.
The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:
[tex]h^2 = x^2 + y^2[/tex]
In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:
[tex]h^2 = 9^2 + 22^2[/tex]
[tex]h = \sqrt{9^2 + 22^2}[/tex]
[tex]h = 23.77[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Simplifying by 2:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].
We want to find [tex]\frac{dh}{dt}[/tex], hence:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]
[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]
[tex]\frac{dh}{dt} = -2.02[/tex]
The hypotenuse is changing at a rate of -2.02 meters per hour.
A similar problem is given at https://brainly.com/question/19954153
If 2/3 inch on a map corresponds to an actual distance of 9 miles, what distance on the map will represent 21 miles?
Answer:
14/9 inches, or an inch and 5/9 of an inch.
Step-by-step explanation:
If 2/3 inch is the same as 9 miles, then x inches represents 21 miles. We can then set up a proportion.
[tex]\frac{\frac{2}{3} }{9} =\frac{x}{21}[/tex]
9 * x = (2/3) * 21
9x = 2 * 7
9x = 14
x = 14/9 inches.
Hope this helps!
Answer:
1 5/9 ich represent 21 miles
Step-by-step explanation:
Proportions:
2/3 inch ⇔ 9 miles
M inch ⇔ 21 miles
M = 21*(2/3) / 9
M = 14/9
14/9 = 9/9 + 5/9 = 1 + 5/9 = 1 5/9 inch
Donald has a bunch of nickels and dimes in his piggy bank. There are 100 coins in the bank that make a total of $6.60 in change. If n is the number of nickels and d is the number of dimes, how many of each type of coin does Donald have?
Answer:
78 nickels and 22 dimes
Step-by-step explanation:
Nickels = n, Dimes = d
Number of coins = 100
n + d = 100Total sum in the piggy bank = $6.60
5n + 10d = 660Consider the first equation in the second:
5(100 -d) + 10d = 660500 - 5d + 10d = 6605d = 110d = 110/5d = 22n = 100 - 22n = 78Answer: nickels 78 and dimes 22
Answer:
78 nikes and dimes 22
solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11
Step-by-step explanation:
One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After
what was the temperature?
hours
O 24 degrees
O 16 degrees
40 degrees
O 32 degrees
Es Review
Answer:
Hey there!
The temperature started at -8 degrees.
The total rise of the temperature was 6(4) or 24 degrees.
-8+24=16
The temperature after 6 hours was 16 degrees.
Let me know if this helps :)
The temperature after 6 hour is 16°. Therefore, option B is the correct answer.
What is temperature?Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.
Given that, One January day, the low temperature in Fargo, ND was -8 degrees.
Over a period of six hours, the temperature rose 4 degrees per hour.
So, total temperature rose in 6 hours is 24 degrees
Temperature after 6 hour is -8+24
= 16°
The temperature after 6 hour is 16°. Therefore, option B is the correct answer.
Learn more about the temperature here:
https://brainly.com/question/11464844.
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[tex]2x {}^{2} + 10x - 72[/tex]
What is the factor
Answer:
2(x-4) (x+9)
Step-by-step explanation:
5. Find the product of p(x) and q(x) if p(x) = 2x+7 and q(x) = 4x-9
a. Is p(x) a polynomial? If not, give an explanation.
b. Is q(x) a polynomiala If not, give an explanation.
c. Is the product a polynomials If not, give an explanation,
d. If the product is a polynomial, identify type and degree.
Answer:
p(x), q(x), and their product are all polynomials.
p(x) · q(x) = 6x² + 10x - 63
Step-by-step explanation:
First of all P(x) and q(x) are polynomials because polynomials refer to any sum, difference, or product of a collection of algebraic terms. The word polynomials is general. P(x) and q(x) are polynomials but more specifically they are binomials since they only have two terms. Their product is a polynomial as well, but more specifically its a trinomial because it has three terms.
process of multiplying
Using the distributive property (or foil method) when multiplying p(x) and q(x) you would first get the expression 6x² - 18x + 28x - 63. From here you would combine "like terms". This would give you your final answer of
6x² + 10x - 63. Sorry, I couldn't help you with the D question but I hope this helps ;)
–14=–(-2x+2)8)51=7(-1+2v)+2
Answer:
x = -6; v = 4.
Step-by-step explanation:
–14 = –(-2x + 2)
-14 = 2x - 2
2x - 2 = -14
2x = -12
x = -6.
51 = 7(-1 + 2v) + 2
51 = -7 + 14v + 2
51 = 14v - 5
14v = 56
v = 4.
Hope this helps!
88 feet/second = 60 miles/hour. How many feet per second is 1 mile? (Hint: divide both side of the equation by the same amount.)
Answer:
1 mile/hour is equivalent to 1.47 feet/seconds
Step-by-step explanation:
Given
[tex]88 ft/s= 60 miles/hr[/tex]
Required
Determine the equivalent of 1 mile/hour
[tex]88\ ft/s= 60\ miles/hr[/tex]
Express 60 as 60 * 1
[tex]88\ ft/s= 60 * 1\ mile/hr[/tex]
Divide both sides by 60
[tex]\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}[/tex]
[tex]\frac{88\ ft/s}{60}= 1\ mile/hr[/tex]
Reorder
[tex]1\ mile/hr = \frac{88\ ft/s}{60}[/tex]
Divide 88 by 60
[tex]1\ mile/hr = 1.46666666667\ ft/s[/tex]
Approximate to 3 significant figures
[tex]1\ mile/hr = 1.47\ ft/s[/tex]
Hence;
1 mile/hour is equivalent to 1.47 feet/seconds
Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number. Start with 10, build a sequence of 5 numbers.
Answer:
10,26,74,218,650
Explanation:
Each number is 4 less then 3 times than previous number.
The list of number is bounded by a set of rules that guide the creation of the set of numbers. The first 5 terms are: 10, 26, 74, 218, 650
Represent the number of terms with n.
So, the nth term is: [tex]T_n[/tex]
The start of the build is 10 means:
[tex]T_1 = 10[/tex]
The rule to generate the next terms is:
[tex]T_{n+1} = 3 \times T_n - 4[/tex] ---- i.e. 4 less than 3 times the previous term
So, the next terms till the 5th are:
[tex]T_{2} = 3 \times 10 - 4 = 26[/tex]
[tex]T_{3} = 3 \times 26- 4 = 74[/tex]
[tex]T_{4} = 3 \times 74- 4 = 218[/tex]
[tex]T_{5} = 3 \times 218- 4 = 650[/tex]
So, the first 5 terms are: 10, 26, 74, 218, 650
Read more about patterns at:
https://brainly.com/question/13382968
construct a right-angled triangle ABC where angle A =90 degree , BC= 4.5cm and AC= 7cm. please ans fast........ Very urgent. Pls don't give wrong answers
Answer and Step-by-step explanation: The described right triangle is in the attachment.
As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:
AC² = AB² + BC²
[tex]AB^{2} = AC^{2}-BC^{2}[/tex]
[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]
[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]
[tex]AB =\sqrt{28.75}[/tex]
AB = 5.4
Then, right triangle ABC measures:
AB = 5.4cm
BC = 4.5cm
AC = 7cm
I dont really understand how to solve this
Answer:
2040 miles
Step-by-step explanation
Gas costs 1.35 per gallon and Jose had 81 dollars for gasoline
with this info we can find out how many gallons of gas Jose can buy.
81 divided by 1.35 is 60 gallons of gas
we also know that he can travel 34 miles for each gallon of gas
with this we can find out how far jose can travel
34 multiplied by 60 is 2040 miles
so, with $81, Jose can travel 2040 miles if gas prices are $1.35
The lines on a 2-cup liquid measuring cup divide each cup into eighths. If you measure 1 3/4 cups of water, between which two quantities can you be certain that your exact measurement will be?
Answer:
1 3/4 cups is between the 13th and 15th lines from the bottom.
Step-by-step explanation:
The bottom of the cup has no line and corresponds to 0 eights.
1st line up: 1/8 cup
2nd line up: 2/8 cup this is also called 1/4 cup
3rd line up: 3/8 cup
4th line up: 4/8 cup this is also called 1/2 cup
5th line up: 5/8 cup
6th line up: 6/8 cup this is also called 3/4 cup
7th line up: 7/8 cup
8th line up: 8/8 cup this is also called 1 cup
9th line up: 9/8 cup
10th line up: 10/8 cup this is also called 1 1/4 cup
11th line up: 1 3/8 cup
12th line up: 1 4/8 cup this is also called 1 1/2 cup
13th line up: 1 5/8 cup
14th line up: 1 6/8 cup this is also called 1 3/4 cup
15th line up: 1 7/8 cup
16th line up: 1 8/8 cup this is also called 2 cups
1 3/4 cups is between the 13th and 15th lines from the bottom.
I need a lot of help
To add fractions with different denominators you must find the highest common factor (the highest number they both go into).
For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8
now, whatever you do to the bottom, you must do to the top.
So:
3 x 2 = 6 and 5 x 4 = 20
Therefore, your answer would be 6/8 + 20/8
You do that for the rest of them as well, do you get it?
Answer:
3/4 + 5/2 = 3/4 + 10/4 = (3+10)/4 = 13/43. 4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15
5. 2/3 + 7/10 = 20/30 + 21/30 = (20+21)/30 = 41/30
In the figure below, if the angle is right what is the value of x?
Answer:
x = 50
Step-by-step explanation:
Since the angle is right = 90°, then
40 + x = 90 ( subtract 40 from both sides )
x = 50
Answer:
[tex]\boxed{\sf x = 50\ degrees}[/tex]
Step-by-step explanation:
x = 90 - 40 [Complementary angles add up to 90 degrees]
x = 50 degrees
Evaluate 0.6721 x 0.0261 and express your answer in standard form
Answer:
Step-by-step explanation:
0.6821 multiplied by 0.0261 is .01754181
putting that into standard from would be 1.754181 x 10^-2
30 POINTS!! Quadratic function F(x) =2x^2- 4x- 6 is shown below. Which describes the domain of this function.
A. All real numbers greater than or equal to -8
B. All real number less than or equal to -8
C. All real number greater than 10
D. All real numbers
Answer:
D. All real numbers
Step-by-step explanation:
The domain is the set of values that can be used for x. There is no restriction on x, so the domain is all real numbers.
Answer:
all real numbers
Step-by-step explanation:
The domain is the possible input values
Since x can be any value, the domain is all real numbers
A piece of aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. What is its density of the aluminum rounded to the nearest hundredth? Only enter numerical values, which can include a decimal point.
Answer:
6.87 g/mL
Step-by-step explanation:
The density of an object can be found by dividing the mass by the volume.
[tex]density=\frac{mass}{volume}\\\\ d=\frac{m}{ v}[/tex]
We know that the aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. Therefore, the mass is 87.3 g and the volume is 12.7 mL.
[tex]m= 87.3 g\\\\v=12.7 mL[/tex]
Substitute the values into the formula.
[tex]d= \frac{87.3 g}{12.7 mL}[/tex]
Divide 87.3 g by 12.7 mL
[tex]d=6.87401575 g/mL[/tex]
Round to the nearest hundredth. The 4 in the thousandth place tells us to leave the 7 in the hundredth place.
[tex]d= 6.87 g/mL[/tex]
The density of the aluminum is about 6.87 grams per milliliter.
how to do this question plz answer me step by step plzz plz plz plz plz I really struggling
Answer: 48
There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.
========================================================
1 min = 60 sec
30 min = 1800 sec (multiply both sides by 30)
1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")
The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.
There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.
--------------------
Extra info:
If you're curious about finding the more accurate value, then you could follow these steps
1 prize = 2014 seconds
x prizes = 86400 seconds (number of seconds in a full day)
1/x = 2014/86400
1*86400 = x*2014
86400 = 2014x
2014x = 86400
x = 86400/2014
x = 42.8997020854021
Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.
determine if the equation is a linear equation -x + 3y^2=18
Answer:
No
Step-by-step explanation:
Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.
A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.
-x + 3y² = 18
We know here that this is not a linear function. But we can try to write it in slope-intercept form:
3y² = x + 18
y² = x/3 + 6
y = √(x/3 + 6)
We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).
Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:
In a chocolate chip cookie recipe flour,brown sugar, and chocolate chips are mixed in the ratio 5:3:4 if the total volume of the three ingredients is 720 ML how many mL of Chocolate chips are in the mix
Answer:
240 mL.
Step-by-step explanation:
The following data were obtained from the question:
Ratio of Flour = 5
Ratio of brown sugar = 3
Ratio of chocolate = 4
Total volume = 720 mL
Next, we shall determine the total ratio. This can be obtained as follow:
Total ratio = ratio of flour + ratio of brown sugar + ratio of chocolate
Total ratio = 5 + 3 + 4
Total ratio = 12
Finally, we shall determine the volume of the chocolate chips in the mixture as shown below:
Volume of chocolate chips = ratio of chocolate /total ratio x total volume
Ratio of chocolate = 4
Total ratio = 12
Total volume = 720 mL
Volume of chocolate chips =..?
Volume of chocolate chips = ratio of chocolate /total ratio x total volume
Volume of chocolate chip = 4/12 x 720
Volume of chocolate chip = 240 mL
Therefore, the volume of the chocolate chips in the mixture is 240 mL.
A student says that the function f (x) = –x² – 9 has the x-intercepts (-3,0) and (3,0). Is the student correct? If not, expl.
why.
Answer:
No
Step-by-step explanation:
The student is wrong because the function has no solutions.
You cannot factor it because the x² is negative.
If it was x² - 9 instead, you could factor it into (x-3)(x+3) which would get you the x-intercepts (-3,0) and (3,0).
But instead, -x² - 9 cannot be factored at all and has no x-intercepts/solutions.
There is a point $A$ with positive coordinates such that the sum of the coordinates of $A$ is $14$. If the $x$-coordinate of $A$ is $a$, then point $P$ is at $(3a, a^2+13a-11)$. If the slope of a line passing through $A$ and $P$ is $7$, find $a$.
Answer:
5
Step-by-step explanation:
Given:
A = (a, 14-a)
P = (3a, a^2 +13a -11)
the slope of AP is 7
a > 0
Find:
a
Solution:
The slope of AP is ...
m = (Py -Ay)/(Px -Ax)
7 = (a^2 +13a -11 -(14 -a))/(3a -a)
14a = a^2 +14a -25
25 = a^2
a = √25 = 5 . . . . . the positive solution
The value of 'a' is 5.
_____
Check
The point A is (a, 14-a) = (5, 9).
The point P is (3a, a^2 +13a -11) = (15, 79)
The slope of AP is (79 -9)/(15 -5) = 70/10 = 7.
Please help ASAP. The question is down below.
Answer:
2.7 hours
Step-by-step explanation:
We can use the formula
1/a + 1/b = 1/c
where a and b are the times working alone and c is the time working together
1/8 + 1/b = 1/2
Multiply each side by 8b to get rid of the fractions
8b( 1/8 + 1/b = 1/2)
b + 8 = 4b
Subtract b from each side
b+8-b = 4b-b
8 = 3b
Divide each side by 3
8/3 = 3b/3
2.666666repeating = b
Round to 1 decimal place
2.7 = b
Answer:
2.7 hr
Step-by-step explanation:
2/8 +2/x = 1
2x+16 =8
16/8
x=8/3 =2.7
What is the justification for step 3 in the solution process?
0.8a - 0.1 a= a - 2.5
Step 1: 0.7a= a - 2.5
Step 2: -0.3a = -2.5
Step 3:
a= 8.3
OA.
the division property of equality
OB
B. combining like terms
O c. the subtraction property of equality
OD. the addition property of equality
Answer:
c. the subtraction property if equality
Step-by-step explanation:
i just did this and got it right
The justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equation is:
0.8a - 0.1 a = a - 2.5
The above equation represents the linear equation in one variable.
Step 1: 0.7a = a - 2.5 (adding like terms)
Step 2: -0.3a = -2.5 ( subtraction property of equality)
Step 3: a = 8.3 (the division property of equality)
Thus, the justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.
Learn more about the linear equation here:
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divide this decimals 5.2 divided 4
Answer:
1.3
Step-by-step explanation:
5.2/4 = 1.3
To check, 1.3 multiplied by four is 5.2.
Answer:
It’s 1.3
Step-by-step explanation:
Make meeee brainliest
Which table shows a function that is decreasing over the interval (−2, 0)? A 2-column table with 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 0, negative 5, 0, 5. A 2-column table with 4 rows. The first column is labeled x with entries negative 2, 0, 2, 4. The second column is labeled f of x with entries negative 15, negative 5, negative 20, negative 30 A 2-column table with 4 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24.
Answer:
A 2-column table with 4 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24.
Step-by-step explanation:
The table shown in the attachment has the function that is decreasing in the interval of interest.
"Decreasing" means that for increasing x-values, each f(x) value is less than the one before.
Answer:
The answer is C
Step-by-step explanation:
I just took the test and got it right.
Hopefully this helps you :)
pls mark brainlest ;)
Solve |2x+3/4 |=5 1/2 Please help!!!!
Answer:
=2x+3/4=5.50
x=19/8 or 2 3/8
hope this helps
Step-by-step explanation:
