Answer:
r ≤ 29, r-5, The sale price can be compared with the regular price, r-5 ≤ 24
Step-by-step explanation:
Amount to spend = $24Regular price = rSale = $5Sale Price = r-5The regular price will be at most $5 more than the amount Roopesh has to spend.
The sale price will be $24 or less than that for Roopesh to afford.
Inequality for regular price :
r-5 ≤ 24
r ≤ 29
Therefore, the product Roopesh can afford is $29 or less than that.
What is the unknown? r ≤ 29Which expression can represent the sale price? Sale price = r-5 (mentioned above)Which comparison could be used? The sale price can be compared with the regular priceWhich inequality represents the situation? r-5 ≤ 24!!
80 increased by 25%, then decreased by 25% is
Answer:
See below.
Step-by-step explanation:
Increases by 25% :- it is 80 * 1.25 = 100.
100 decreased by 25% = 100 * 0.75
= 75.
Answer:
75
Step-by-step explanation:
We are given that 80 is increased by 25% and then decreased by 25% so we are to find the final value.
Increase of 25% in 80 = 25% of 80
= 25/100 × 80
= 20
So our new value after 25% increase = 80 + 20 = 100
Now this new value is decreased by 25% = (100 - 25)% of 100
= 75/100 × 100
= 75
The numbers if nickels and quarters in a bank are in the ratio 23:25. If the coins are worth $7, how mnay of each type are there?
Answer:
25 nickels and 23 quarters
Step-by-step explanation:
The smallest possible integer solution is 23 nickels and 25 quarters.
23×0.05 + 25×0.25 = 1.15 + 6.25 = $7.40.
That's already over $7.00.
We can't solve the problem as stated unless we use fractional numbers of coins, and that's impossible.
Assume the correct ratio is 25/23
Let n = number of nickels
and q = number of quarters. Then we have two conditions.
(1) n/q = 25/23
(2) 0.05n + 0.25q = 7
(3) n = (25/23)q Multiplied (1) by q
(4) 0.05(25/23)q + 0.25q = 7 Substituted (3) into (1)
0.05435q + 0.25q = 7 Simplified
0.3043q = 7 Combined like terms
(5) q = 23 Divided each side by 0.3043
n/23 = 25/23 Substituted (5) into (1)
n = 25 Divided each side by 23
There are 25 nickels and 23 quarters.
Check:
(1) 25/23 = 25/23 (2) 0.05×25 + 0.25×23 = 7
1.25 + 5.75 = 7
7 = 7
OK.
A new candle is 12 inches tall. It burn at a rate of 0.75 inches an hour. How tall will it be after 4.6 hours?
Answer:
8.55 inches
Step-by-step explanation:
We can use the slope intercept form to write this equation
y = mx+b where m is the lope and b is the y intercept
The y intercept, b, is how tall the candle is when we start, 12 inches
The slope is the rate at which it is burning or -.75 (the negative is because it is burning or getting smaller)
y = -.75x+12
or rewriting
t = 12-.75h where h is the hours and t is how tall
We are burning for 4.6 hours
t = 12-.75(4.6)
t = 12 -3.45
t= 8.55
The vertices of the triangle are A (3,5), B (6, 1), and C(5,9) is dilated using a scale factor 2. Find the coordinates of the
dilated triangle.
Answer:
2nd choice
Step-by-step explanation:
How you have to is multiply the coordinates by 2 since the scale factor you want to dilate image at is at 2.
That is the pre-image is (x,y) and the image is (2x,2y) per each point.
A(3,5) becomes A'(3*2,5*2)=A'(6,10)
B(6,1) becomes B'(6*2,1*2)=B'(12,2)
C(5,9) becomes C'(5*2,9*2)=C'(10,18)
So 2nd choice.
The coordinates of the dilated triangle are (6,10) , (12,2) and (10,18)
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures
How to find the coordinates of a dilated triangle?To find the final coordinates we need to multiply the initial coordinates by the scale factor which is 2.So for the coordinate A(3, 5), the coordinate of the dilated triangleA' = (3 x 2, 5 x 2) = (6, 10)
For the coordinate B (6, 1), the coordinate of the dilated triangleB' = (6 x 2, 1x 2) = (12,2)
Similarly C' will be (10 , 18)
So the coordinates of the dilated triangle are (6,10) , (12,2) and (10,18)
So option B is correct.
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a salesman earns 40% commission on all the merchandise that he sells. Last month he sold $700 worth of merchandise. How much in commission (in dollars) did he earn last month?
The salesman earned $280 in commission last month, which was calculated by taking 40% of the $700 worth of merchandise he sold.
Explanation:This question is about calculating commission which falls under the topic of percentage calculations in math. The salesman earns a 40% commission on the merchandise he sells. So, to find out how much he earned in commission last month, we need to calculate 40% of the total value of merchandise he sold, which is $700.
To do this, multiply $700 by 40% (or 0.4 in decimal form). That would give you $280. So, the salesman earned $280 in commission last month.
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To find out how much commission the salesman earned, we need to calculate 40% of the $700 worth of merchandise that he sold. The commission rate is expressed as a percentage, which we can also write as a decimal for the purpose of calculation.
First, let's convert the commission rate from a percentage to a decimal. To do this, we divide the percentage by 100:
40% / 100 = 0.40
Now that we have the commission rate as a decimal, we can calculate the commission by multiplying the sales amount by the commission rate.
The calculation is as follows:
Commission = Sales Amount × Commission Rate
Commission = $700 × 0.40
Calculating this gives us:
Commission = $280
Therefore, the salesman earned $280 in commission last month.
1.5% of h is 12. what is h?
h = 800
Step-by-step explanation:In this question, we're trying to find the value of h.
Lets set up an equation:
[tex]1.5/100 * h = 12[/tex]
With the equation above, we can solve it to find the answer.
[tex]1.5/100h = 12\\\\\text{We would first divide 1.5 by 100}\\\\0.015h=12\\\\\text{Now, we would simply divide}\\\\h=800[/tex]
When you're done solving, you should get 800.
This means that h = 800
We can check to see if it's correct:To check if it's correct, we could multiply 800 by 0.015 (1.5%) to see if it gives us 12.
[tex]800*0.015=12[/tex]
Now, we can confirm that the answer is h = 800
I hope this helps you out.Good luck on your academics.Have a fantastic day!Gloria has 11 markers in a backpack. One of them is purple and one is gray. Find the probability Gloria will reach into the backpack without looking and grab the purple marker and then reach in a second time and grab the gray marker. Express your answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
She has 1 in 11 chances of getting the purple one
One of her choices is gone after she takes out the purple one. She has a 1 in 10 chance of taking out the gray one.
1/11 * 1/10 = 1/110
The probability that Gloria will draw the purple marker first and then the gray marker from her backpack on consecutive tries without replacement is 1/110.
The question asks to find the probability that Gloria will pull the purple marker and then the gray marker out of the backpack on consecutive tries without replacement. To calculate the combined probability of two independent events happening in succession, you multiply the probability of each event occurring separately.
On the first draw, the probability of selecting the purple marker is 1 out of 11 markers, or 1/11. After drawing the purple marker, it is not replaced, so there are now only 10 markers left, one of which is gray. The probability of drawing the gray marker on the second draw is then 1 out of the remaining 10 markers, or 1/10.
To find the overall probability of both events happening, multiply the two probabilities: (1/11) x (1/10) = 1/110.
The probability that Gloria will draw the purple marker first and then the gray marker is 1/110.
Many credit card companies charge a compound interest rate of 1.8% per month on a credit card balance. Nelson owes $950 on a credit card. If he makes no purchases or payments, he will go deeper and deeper into debt.
Which of the following sequences describes his increasing monthly balance
Answer:
the answer is A
Step-by-step explanation:
always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to
start with the 950 * .018 = 171.00
950 + 171.00 = 1121.00
then you follow this process
1121.00 * .018 = 201.78
1121.00 + 201.78 = 1322.78
The answer is A
What sequences describe his increasing monthly balance?Always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to
Start with the 950 *.018 = 171.00
950 + 171.00 = 1121.00
Then you follow this process
1121.00 * .018 = 201.78
1121.00 + 201.78 = 1322.78
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
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Allen needs to compare a compound for the patient to pick up tomorrow. He needs to mix 2/3 of drug A, with 5/3 of drug B and 9/3 of drug C. What is the total amount of the drugs mixed together
Step-by-step explanation:
A + B + C
2/3 + 5/3 + 9/3
16/3
Or as a proper fraction, 5⅓.
The slope intercept forth of the equation of a line that passes through point (-2, -13) is y = 5x - 3. What is the point slope
form of the equation for this line?
Answer:
y + 13 = 5(x + 2)Step-by-step explanation:
The point-slope form of an equation:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line:
[tex]y=5x-3[/tex]
therefore the slope m = 5.
Put the value of the slope and the coordinates of the given point (-2, -13) to the equation of a line:
[tex]y-(-13)=5(x-(-2))\\\\y+13=5(x+2)[/tex]
Select the correct answer.
Which table represents a nonlinear function?
Answer:
C.
Step-by-step explanation:
If equal changes in x result in equal changes in y, then the function is linear.
A. Are the changes from (2, 4) to (4, 1) and from (4, 1) to (6, 11) equal?
The change from (2, 4) to (4, 1):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from -9 to 1; the change is 1 - (-9) = 10
The change from (4, 1) to (6, 11):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from 1 to 11; the change is 11 - 1 = 10
For a change in x of 2, the change in y is 10 in both cases. This function is linear.
B. Are the changes from (2, -14) to (4, -16) and from (4, -16) to (6, -18) equal?
The change from (2, -14) to (4, -16):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from -14 to -16; the change is -16 - (-14) = -2
The change from (4, -16) to (6, -18):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from -16 to -18; the change is -18 - (-16) = -2
For a change in x of 2, the change in y is -2 in both cases. This function is linear.
C. Are the changes from (2, 0) to (4, 6) and from (4, 6) to (6, 16) equal?
The change from (2, 0) to (4, 6):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from 0 to 6; the change is 6 - 0 = 6
The change from (4, 6) to (6, 16):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from 6 to 16; the change is 16 - 6 = 10
For a change in x of 2, the change in y is 6 in one case and 10 in the other case. This function is not linear.
D. Are the changes from (2, -9) to (4, -6) and from (4, -6) to (6, -3) equal?
The change from (2, -9) to (4, -6):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from -9 to -6; the change is - 9 - (-6) = -3
The change from (4, -6) to (6, -3):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from -6 to -3; the change is -6 - (-3) = -3
For a change in x of 2, the change in y is -3 in both cases. This function is linear.
Which best describes the incenter of a triangle helpppppp plzzzz
Answer: A . The point where the three angle bisector intersect.
Step-by-step explanation:
The incenter of a triangle is a point constructing the origin of a circle inscribed inside it. The incenter of a triangle is created by taking the intersection of the angle bisectors of the three vertices of the triangle such that it is equidistant from all the vertices of the triangle.
Therefore, the statement which best describes the incenter of a triangle is " the point where the three angle bisector intersect"
Answer:
The point where the three angle bisector intersect.
Step-by-step explanation:
A town planner is interested in getting some demographic data about the households in the city. The city has four wards with the following numbers of households: ward A has 2,107, ward B has 903, ward C has 1,505, and ward D has 1,499. The budget for the project allows the planner to survey 100 households. She plans to use a stratified sampling method. How many households should be chosen from ward B? Enter a whole number.
Answer:
15
Step-by-step explanation:
Population size= 2107+903+1505+1499
= 6014
Calculating the sample of ward B by using the stratified random sampling formula:
Stratified Random Sample, np= ( Np / N ) * n
where
np= pth stratum sample size
Np= pth stratum population size
N = population size
n = sample size
Stratified Sample (ward B) = 100 / 6014 * 903 = 15 !
about how far apart do aesha and Josh live
Answer:
D. about 8.5 mi
Step-by-step explanation:
To go from Aesha to Josh, you go 6 units right and 6 units up.
Each unit is a mile, so you go 6 miles right and 6 miles up.
Think of each 6 mile distance as a leg of a right triangle, and the direct distance from one place to the other as the hypotenuse of the right triangle. Use the Pythagorean theorem to find the length of the hypotenuse.
a^2 + b^2 = c^2
The 6-mile legs are a and b. c is the hypotenuse.
(6 mi)^2 + (6 mi)^2 = c^2
c^2 = 36 mi^2 + 36 mi^2
c^2 = 72 mi^2
c = sqrt(72) mi
c = sqrt(36 * 2) mi
c = 6sqrt(2) mi
c = 6(1.4142) mi
c = 8.5 mi
Wich graph of the equation y-1=2/3(x-3)?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y-1=\frac{2}{3}(x-3)[/tex]
This is the equation of the line into point slope form
The slope is m=2/3
The point is (3.1)
To easily identify the graph look for the intercepts of the line
The y-intercept is the value of y when the value of x is equal to zero
For x=0
[tex]y-1=\frac{2}{3}(0-3)[/tex]
[tex]y=-2+1=-1[/tex]
The y-intercept is the point (0,-1)
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0-1=\frac{2}{3}(x-3)[/tex]
[tex]-3=2x-6[/tex]
[tex]2x=3[/tex]
[tex]x=1.5[/tex]
The x-intercept is the point (1.5,0)
Plot the intercepts and join the points to identify the graph
using a graphing tool
The graph in the attached figure
Need help please, solve the system of equations. Check photo
Answer:
The solution is
[tex]x=\frac{9}{11}[/tex]
[tex]y=\frac{17}{11}[/tex]
Step-by-step explanation:
We have the system:
-4x+6y=6
-7x+5y=2
I would like to solve this by elimination because I don't feel like rearranging both equations and they both have the same form which is crucial in elimination. The only thing is I will need opposites in a column (where the variable are).
So I'm going to focus on the x's. I want the x part to be opposites.
I know if I multiply the first equation by 7 I will get -28x plus... and if I multiply the last equation by -4 I will get 28x plus... .
28x and -28 are opposites and we all know what happens to opposites when you add them. They zero out; cancel out. That is -28x+28x=0.
So let's multiply first equation by 7 and
multiply bottom equation by -4:
-28x+42y=42
28x-20y=-8
----------------------We are ready to add the equations:
0+22y=34
22y=34
Divide both sides by 22:
y=34/22
Reduce the fraction:
y=17/11 (I divided top and bottom by 2.)
Now if y=17/11 and -4x+6y=6, we can find x by inserting 17/11 for y in the second equation I wrote in this sentence.
[tex]-4x+6\cdot \frac{17}{11}=6[/tex]
Perform the simplification/multiplication of 6 and 17/11:
[tex]-4x+\frac{102}{11}=6[/tex]
Subtact 102/11 on both sides:
[tex]-4x=6-\frac{102}{11}[/tex]
Find a common denominator:
[tex]-4x=\frac{66}{11}-\frac{102}{11}[/tex]
[tex]-4x=\frac{-102+66}{11}[/tex]
[tex]-4x=\frac{-36}{11}[/tex]
Divide both sides by -4:
[tex]x=\frac{-36}{-4(11)}[/tex]
Reduce 36/4 to 9:
[tex]x=\frac{9}{11}[/tex]
[tex]x=\frac{9}{11}[/tex]
The solution is
[tex]x=\frac{9}{11}[/tex]
[tex]y=\frac{17}{11}[/tex]
Consider the following sets.
U = {all real number points on a number line}
A = {solutions to the inequality 3x+4>13}
B = {solutions to the inequality 1/2x+3<4}
For which values of x is A U B =ø
The values of x for which A U B = ø (empty set) are x > 3 AND x < 2, but no number can satisfy both inequalities simultaneously.
Explanation:To find the values of x for which A U B = ø (empty set), we need to find the values that make both inequalities false. Let's solve each inequality separately:
Inequality 1: 3x + 4 > 13
Subtracting 4 from both sides, we get 3x > 9. Dividing both sides by 3, we have x > 3.
Inequality 2: 1/2x + 3 < 4
Subtracting 3 from both sides, we get 1/2x < 1. Multiplying both sides by 2, we have x < 2.
Therefore, the values of x that satisfy both inequalities are x > 3 AND x < 2.
However, no number can be greater than 3 and less than 2 at the same time, so the solution for A U B = ø (empty set).
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What is the greatest common factor of the numbers 12 and 54?
Answer:
6
Step-by-step explanation:
54=2x3x3x3
12=2x2x3
common factors are 2 and 3 so 2x3=6
The equation tan(55°)= 15/b
can be used to find the length of AC
What is the length of Ac? Round to the nearest tenth.
Answer:
10.5
Step-by-step explanation:
tan(55°)=15/b
b=15/tan(55°)
=10.5
Answer:
AC ≈ 10.5
Step-by-step explanation:
tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{15}{b}[/tex]
Multiply both sides by b
b × tan55° = 15 ( divide both sides by tan55° )
b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5
Hence b = AC ≈ 10.5 ( to the nearest tenth )
Solve x2 - 8x = 3 by completing the square. Which is the solution set
[4 - 19,4 + /19}
{4 - V11, 4 + /11)
{4 - V8, 4 + }
[4 - V3, 4 + (3)
Answer:
4\pm\sqrt{19}
Step-by-step explanation:
Move everything to left side
[tex]x^{2} -8x -3 =0[/tex]
Now to solve this square equation we need to find Descriminant
[tex]D=b^{2} -4ac=64+12=76[/tex]
As Descriminant D is greater than 0 then we have 2 solutions which we can calculate by this formula
[tex]x_{1,2}=\frac{-b\pm\sqrt{D}}{2a} =\frac{8\pm2\sqrt{19}}{2}=4\pm\sqrt{19}[/tex]
Completing the square in mathematics is a technique used to solve quadratic equations by transforming them into a perfect square trinomial form. It helps in finding the roots of the equation more efficiently.
Completing the square involves transforming a quadratic equation into a perfect square trinomial form to solve it. In the case of x^2 - 8x = 3, the steps would include halving the coefficient of x, squaring that value, and adding/subtracting it to both sides of the equation to complete the square.
The solution set for the equation x^2 - 8x = 3 would be {4 + √19, 4 - √19}, as completing the square helps in finding the roots of the quadratic equation.
Completing the square is a helpful technique in mathematics for solving quadratic equations more easily and efficiently.
Find the product of 3x^2 and 2x+1 .
[tex]3x^2(2x+1)=6x^3+3x^2[/tex]
Round 56.0649702307 to 4 decimal places.
Answer:
56.0650
Step-by-step explanation:
here is your answer
i hope this is what u want
In this question the number that is in the 4th decimal place is...
56.0649702307
Nine is the 4th decimal, so this is the number that you will determine if it gets rounded or not.
This question wants you to have four decimal places left after you finish rounding
To determine if you round up or stay the same you must look at the number after the asked decimal place. In this case the number after the 4th decimal is 7. A number will round up if this number (7) is 5 or greater. If it is smaller then 5 then the decimal will not round up.
In this case 7 is bigger then 5. This means that the 4th decimal place (9) will round up
56.0650
^^^Since the fourth decimal is 9 when you round up the next number is ten. This means that the rounding will be bumped to the number in front of the 9 and the 9 will simply become zero.
Let me know if this makes sense!
~Just a girl in love with Shawn Mendes
A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer than the side along the building. the third side is 7 feet longer than the side along the building. find the length of all three sides of the reflecting pool
Answer:
Leg side along the wall = x ft = 8 ft
The other leg side = 7+x ft = 7+8=15 ft
The Hypotenuse =9+x ft = 9+8 = 17 ft
Step-by-step explanation:
In the question, the shape of the pool is right triangle.
Let the leg side along the wall to be the x ft
Let the other leg side to be 7+x ft
Let the longest side/hypotenuse to be x+9 ft
Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse
This means;
[tex]x^2 +(x+7)^2=(x+9)^2\\\\[/tex]
Expand the terms in brackets
[tex]x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81[/tex]
collect like terms
[tex]x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0[/tex]
solve for x in the quadratic equation by factorization
[tex]x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8[/tex]
Taking the positive value of x;
x=8ft
Finding the lengths
Leg side along the wall = x ft = 8 ft
The other leg side = 7+x ft = 7+8=15 ft
The Hypotenuse =9+x ft = 9+8 = 17 ft
CD is the perpendicular bisector AB. G is the midpoint of AB. points E and F lie on CD. which pair of line segments must be congruent?
Answer:
AE and BE
Step-by-step explanation:
Please refer to the image attached with this.
Here in we have made a diagram a per the conditions given in the question. If we observe ΔABE, We see
AG=GE ( CD is perpendicular bisector of AB , Hence G is mid point)
∠AGE = ∠BGE = 90°
GE = GE
Hence
ΔAGE ≅ ΔBGE
Therefore the theorem of congruent triangles ,
AE ≅ BE
To answer the question, let's break down what we know from the given information:
1. CD is the perpendicular bisector of AB: This means that CD intersects AB at a 90-degree angle (perpendicular) and divides AB into two equal parts (bisector).
2. G is the midpoint of AB: This means that point G is exactly in the middle of AB, which implies that AG is equal in length to GB.
3. Points E and F lie on CD: Without additional information, we cannot determine any specific relationships between E and F and the other points. However, since E and F are on CD, they are somewhere along the line that includes the perpendicular bisector.
The question asks which pair of line segments must be congruent.
Since G is the midpoint of AB and CD is the perpendicular bisector of AB, by definition of the perpendicular bisector, AG must be congruent to GB. This is because a perpendicular bisector not only intersects a segment at a right angle but also cuts the segment into two congruent parts.
Therefore, the pair of line segments that must be congruent are AG and GB.
The sum of two integers is 45. If one of them is (-200). Find the other.
Step-by-step explanation:
Let the number be x
ATQ,
-200+x =45
x=45+200
x=245
The other integer is equal to 245.
Explanation:We know that [tex]x+y=45[/tex]. We also know that [tex]x=-200[/tex].
Substitute the value into the equation. [tex]-200+y=45[/tex]
Add 200 to both sides of the equation. [tex]y=45+200=245[/tex]
Now, you have the answer. [tex]y=245[/tex]
which expression is equivalent to ^5 square root 13^3
Answer:
[tex]\sqrt[5]{13^3} = 13^{\frac{3}{5}}[/tex]
Step-by-step explanation:
Answer:
D on EDGE
Step-by-step explanation:
what is the simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)?
Answer:
Step-by-step explanation:
distribute the first part of each term
(21/5x+12)+(-3+5/2x)
combine the xs and the numbers
9+6.7x
For this case we must simplify the following expression:
[tex]3(\frac{7}{5}x+4)-2(\frac{3}{2}-\frac{5}{4}x)=\\\frac{3*7}{5}x+ 3*4-\frac{2*3}{2} +\frac{2*5}{4}x=\\\frac{21}{5}x +12-\frac{6}{2} +\frac{10}{4}x=\\\frac{21}{5}x +12-3+ \frac{10}{4}x=[/tex]
We add similar terms:
[tex]\frac{21}{5}x+ \frac{10}{4}x+ 9=\\(\frac{21}{5} +\frac{10}{4})x +9=\\\frac{67}{10}x +9[/tex]
ANswer:
[tex]\frac{67}{10}x+9[/tex]
What is the area of a triangle that has a base of 4 feet and a height of 4 feet? 2ft sq 4ft sq 8ft sq 16ft sq
Answer:
8ft sq is your area.
Step-by-step explanation:
Solve the area of a triangle by using the following equation:
Area (of a triangle) = 1/2(base * height)
Note:
Height = 4 feet
Base = 4 feet
Plug in the corresponding numbers to the corresponding variables.
Area = 1/2(base * height)
Area = 1/2(4 * 4)
Solve. Follow PEMDAS. First, solve the parenthesis, then divide:
Area = 1/2(4 * 4)
Area = 1/2(16)
Area = 16/2
Area = 8
8ft sq is your area.
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Answer:
Third option: [tex]8\ ft^2[/tex]
Step-by-step explanation:
The area of a triangle can be calculated with the following formula:
[tex]A=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height of the triangle.
In this case you know that this triangle has a base of 4 feet and a height of 4 feet, then:
[tex]b=4\ ft\\h=4\ ft[/tex]
Therefore, you can substitute these values into the formula, getting that the area of this triangle is:
[tex]A=\frac{(4\ ft)(4\ ft)}{2}\\\\A=8\ ft^2[/tex]
A delivery truck is transporting boxes of two size: the combined weight of a large box and a small box is 65 pounds. The truck is transporting 60 large boxes and 55 small boxes if the truck is carrying a total of 3775 pounds in boxes, how much does each type of box weigh?
pretty much about the same as before.
a = weight of a large box
b = weight of a small box.
we know their combined weight is 65 lbs, thus a + b = 65.
we also know that the truck has 60 large ones, and 55 small ones, thus 60*a is the total weight for the large ones and 55*b is the total weight for the small ones, and we know that is a total of 3775, 60a + 55b = 3775.
[tex]\bf \begin{cases} a+b=65\\ \boxed{b}=65-a\\ \cline{1-1} 60a+55b=3775 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{60a+55\left( \boxed{65-a} \right)=3775} \\\\\\ 60a+3575-55a=3775\implies 5a+3575=3775\implies 5a=200 \\\\\\ a=\cfrac{200}{5}\implies \blacktriangleright a = 40 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=65-a\implies }b=65-40\implies \blacktriangleright b=25\blacktriangleleft[/tex]
Match each sequence to its appropriate recursively defined function
Answer:
f(1) = -24; f(n) = 4·f(n-1)f(1) = 13; f(n) = f(n-1) + 26f(1) = 28; f(n) = -4·f(n-1)Step-by-step explanation:
Identify the first term of the sequence. First terms are -24, 13, 28. Find the matching f(1). There are two choices for each first term.
Then determine the relation of each term to the previous term. In two of the sequences, a factor of 4 is involved. For the sequence starting with -24, the adjacent terms have the same sign, so the factor is +4. For the sequence starting with 28, adjacent terms have alternating signs, so the factor is -4.
For the sequence starting with 13, the second term is 3 times the first, but it is also 26 added to the first. You have to look at the next term to see if the sequence is geometric with a ratio of 3, or arithmetic with a difference of 26. The latter is the case, so the recursive definition will involve addition, not multiplication.
The recursively defined functions are shown above in the order of the given sequences.
Answer: just took the test
Step-by-step explanation:
#plato