Answer:
C. 12x + 6y = 30
Step-by-step explanation:
A. x 3 4 5
y 3 6 9
We need to make and equation
slope = (y2-y1)/(x2-x1)
= (9-3)/(5-3)
6/2
3
The slope is 3
Using point slope form
y-y1 = m(x-x1)
y-3 = 3(x-3)
Distribute
y-3 = 3x-9
Add 3 to each side
y = 3x-9+3
y = 3x-6
Let x=0
y = 0-6
y = -6
B. y = 4x – 7
Let x = 0
y = 0-7
y = -7
C. 12x + 6y = 30
Let x = 0
12(0) + 6 y = 30
6y = 30
Divide by 6
6y/6 = 30/6
y =5
D. A linear function that goes through point 1, negative 1 and point 0, 4
The point ((0,4) says when x=0 y=4
y =4
y=5 is the max so the answer is C
Use the diagram to find the measurement of each of the angles
Answer:
1. ∠LOQ = 80°
2. ∠LRQ = 40°
3. ∠LBQ = 40°
Step-by-step explanation:
The measure of a central angle (angle that goes to the center of the circle) is EQUAL to the ARC from which it is intercepted. The measure of the angle that is on opposite side, on the circumference, of the circle is HALF of the ARC from which it is intercepted.It is given that ARC QL has a measure of 80.
Central angle from ARC QL (with same measure) are angle LOQ only.Opposite angles (half of measure of ARC QL) from ARC QL (on opposite side on circumference) are angles LRQ and LBQ.1.
m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.
∠LOQ = 80°
2.
m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.
∠LRQ = [tex]\frac{1}{2}(80)=40[/tex]
∠LRQ = 40°
3.
m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.
∠LBQ = [tex]\frac{1}{2}(80)=40[/tex]
∠LBQ = 40°
Find the area of 9.5 and 4.1
Answer:
38.94
Step-by-step explanation:
To find the area, multiply the length times the width. In this case 9.5 times 4.1.
Calculate the partial sum S for the sequence 243,81,27,....
Answer:363
Step-by-step explanation:
We have to find partial sum for the sequence 243 , 81 , 27 ..... up to 5 terms(S5 given)
The sequence actually is 3^5,3^4.,3^3.....
Therefore first 5 terms are 1) 3^5 I.e. 243
2) 3^4 I.e. 81
3) 3^3 I.e. 27
4)) 3^2 I.e. 9
5) 3^1 I.e. 3
Adding all those no. we get partial sum of first 5 no. of the sequence
So, 243 + 81 + 27 + 9 + 3
= 363
Hope it helps!!!
Answer:
D. 363 is the one
A colony of bacterial doubled every week. If the colony began with 40 bacteria, how many bacteria are present after 4 weeks?
Answer:
640 bacteria.
Step-by-step explanation:
Make a chart.
Bacteria Weeks
40 0
80 1
160 2
320 3
640 4
It starts off with 40 bacteria, which means no weeks have passed so far. That is why 40 pairs with 0 rather than 1.
A ball rolling down an inclined plane travels, in successive seconds, k feet, 2.5k feet, 4k feet, etc… . Find the distance traveled by the ball
Final answer:
To calculate the total distance traveled by the ball in the first four seconds, we sum the distances for each second, yielding 13k feet.
Explanation:
The student has provided a sequence of distances that a ball rolls down an inclined plane, with distances increasing each second. The distances in successive seconds are given by k feet, 2.5k feet, 4k feet, and so on. To calculate the total distance traveled by the ball in the first four seconds, we use the arithmetic sequence formula.
Let's calculate the distance for each second:
1st second: k feet
2nd second: 2.5k feet
3rd second: 4k feet
4th second: By the same pattern it follows that the 4th second should cover 5.5k feet.
To find the total distance, we sum these values:
Total distance = k + 2.5k + 4k + 5.5k = 13k feet.
This is the total distance traveled by the ball in the first four seconds.
Lina invested $7,800 in a mutual fund at a simple interest rate of 4.35%. She earned $1,696.50 in interest. How long (in years) was the money invested?
Answer:
5 years.
Step-by-step explanation:
She earns $339.3 per year on interest rate. So I divided 1,696.50 by 339.3 to get the amount of ears.
Lina invested for 5 years.
What is simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.The formula to calculate simple interest is Prt, where P is the principle amount, r is the rate and t is the time in years.How to know how long (in years) was the money invested?According to the problem,
Lina invested $7,800 in a mutual fund at a simple interest rate of 4.35%.She earned $1,696.50 in interest.So, we can say $ 1,696.50 is the interest
∴ Prt = 1696.50
⇒ (7800)(4.35/100)t = 1696.50
⇒ t = 5
∴ Line invested for 5 years.
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What is the x-intercept of the line with the equation 1/3x+y=-15
The x-intercept is for y = 0.
substitute y = 0 to the equation of the function:
[tex]\dfrac{1}{3}x+y=-15\\\\\dfrac{1}{3}x+0=-15\\\\\dfrac{1}{3}x=-15\qquad\text{multiply both sides by 3}\\\\\boxed{x=-45}[/tex]
Answer: x-intercept = -45 → (-45, 0).Answer:
(-45,0)
Step-by-step explanation:
I took the test
A parabola with vertex (h, k) and a vertical axis of symmetry is modeled by the equation y - k = a(x - h)2. Determine the vertex for a parabola modeled by y = (x − 5)2 + 8
The vertex of the parabola y = (x – 5)² + 8 with a vertical axis of symmetry is the point (5, 8).
Explanation:The question is asking for the vertex of the parabola y = (x − 5)² + 8 which has a vertical axis of symmetry. In the general equation for a parabola, y - k = a(x - h)², the vertex is denoted by the (h, k). So, comparing this with the given parabola equation, we can determine that the h value corresponds to the value inside the brackets in the (x – h)² part of the equation, and the k value corresponds to the term added or subtracted outside the squared term.
For the given equation, y = (x – 5)² + 8, we can see that h = 5 and k = 8. Therefore, the vertex of the parabola is at the point (5, 8).
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QUESTION WORTH 30 POINTS!
Answer:
changing by one
Step-by-step explanation:
The quantity (t + 4) exceeds 31
Answer:
t > - 27
Step-by-step explanation:
t + 4 > 31. Next, solve for t: t > -27
Answer:
t+4 > 31
t > 27
Step-by-step explanation:
(t + 4) exceeds 31
t+4 > 31
Subtract 4 from each side
t+4-4 > 31-4
t > 27
Sally scores 381 points in a game ty scores 262 points how many more points dose sally score than ty
Answer:
119
Step-by-step explanation:
381-262
Miss teng, a school teacher, usually walks at a speed of 0.5 m/s for y km to reach her school on time. On one cloudy day, she decided to walk the y km at a faster speed of w m/s in case it rained. If she reached her school 5 minutes earlier than usual, calculate y.
Answer:
[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]
Step-by-step explanation:
We are given
Miss Teng normal walk:
speed =0.5 m/s
distance traveled =y km =y*1000
now, we can find time
we know
time = distance / speed
[tex]t_1=\frac{1000y}{0.5}[/tex]
[tex]t_1=2000y[/tex]
Miss Teng walk on cloudy day:
speed =w m/s
distance traveled =y km =y*1000
now, we can find time
we know
time = distance / speed
[tex]t_2=\frac{1000y}{w}[/tex]
If she reached her school 5 minutes earlier than usual
so,
[tex]t_1-t_2=5\times 60 sec[/tex]
[tex]t_1-t_2=300[/tex]
now, we can plug values
[tex]2000y-\frac{1000y}{w}=300[/tex]
now, we can solve for y
we can multiply both sides by w
[tex]2000yw-\frac{1000y}{w}w=300w[/tex]
[tex]2000wy-1000y=300w[/tex]
[tex]1000y\left(2w-1\right)=300w[/tex]
[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]
Your friend factors the expression 48x-16. Is your friend correct? Explain your reasoning.
Answer:
16(3x - 1)
Step-by-step explanation:
the greatest common factor of 48 and 16 is 16, hence
48x - 16 = 16(3x - 1)
Final answer:
After factoring out the greatest common factor of 16 from the expression 48x-16, the correct factored form is 16(3x - 1). The friend's factorization is correct if this result was obtained, demonstrating the universal application of mathematical rules.
Explanation:
To evaluate if your friend factored the expression 48x-16 correctly, we look for the greatest common factor that both terms in the expression share. Both 48x and 16 are divisible by 16. Factoring out the greatest common factor of 16, we get:
16(3x - 1)
This is the factored form of the expression 48x-16, which shows that your friend is correct if they arrived at this result. This method is an application of the distributive property, which states that a(b + c) = ab + ac. In this case, we take out a '16' from both terms, which is the inverse process - factoring.
Moreover, the principles that apply to factoring expressions are the same regardless of location or time, demonstrating the universality of mathematical rules. Whether we are factoring polynomials or checking arithmetic, using the correct rule and applying it properly is essential.
The slope of the line passing through the points (7, 5) and (21, 15) is ???
Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point ???
Answer:
(21,5)
Step-by-step explanation:
To find the slope that passes through the points (7,5) and (21,15) , we use the formula
m = (y2-y1)/ (x2-x1)
= (15-5)/(21-7)
= 10/14
=5/7
We want a slope that is 1/3 this slope so we will multiply by 1/3
5/7 * 1/3= 5/21
We know the slope and one point (0,0) we can use the same formula to figure out x and y
m = (y2-y1)/ (x2-x1)
5/21 = (y2-0)/ (x2-0)
Let the tops be equal and the bottoms be equal
5 = y2-0
5 =y2
and the bottoms
21 = x2-0
21= x2
We have the point
(21,5)
Answer:
here you go
View the picture for your answer!
have a wonderful day :))
Calvin goes shopping over the weekend and buys a new pair of shoes,a T-Shirt, a pair of sunglasses, and a hat that costs $9. The shoes are twice as much as the shirt, and the sunglasses are half as much as the shirt. The total cost of his purchase is $65. How much does each cost?
Let the costs of shoes, t-shirt, and glasses be represented by s, t, g, respectively. The problem statement tells us these relationships:
... s = 2t
... g = t/2
... s +t +g +9 = 65 . . . . . the $9 cost of the hat is added into the total
_____
Solution
Substituting for s and g, we have ...
... 2t +t +t/2 +9 = 65
... (3 1/2)t = 56 . . . . . collect terms
... t = 56/3.5 = 16 . . . . divide by the coefficient of t
The shoes are 2t, so $32.
The t-shirt is t, so $16.
The sunglasses are t/2, so $8.
The hat is $9.
What is the nth term of the geometric sequence 4, 8, 16, 32, ... ?
Answer:
tn = a*2^(n - 1)
Step-by-step explanation:
a = 4
r = 2
tn= a*2^(n-1)
Try it
t3 = 4*2^(3 -1) Combine the power
t3 = 4 * 2^2 Find 2^2
t3 = 4 * 4 Multiply
t3 = 16 Answer for t3
Answer:
2^(n+1)
Step-by-step explanation:
You don't even need to use algebraic methods or the formula for this; it's just common sense. 4=2^2, 8=2^3, 16=2^4.
4 is the term 1
8 is term 2
2=term # (1) + 1 for 4
3 = term # (2) + 1 for 8
And so on
So it is 2 to the power of (term # + 1)
solve for h
A=1/2 bh
Answer:
2A /b = h
Step-by-step explanation:
A=1/2 bh
We want to isolate h
First we multiply by 2
2A = 2 * 1/2 bh
2A = bh
Then we divide by b to isolate h
2A /b = bh/b
2A /b = h
PQR has medians QM and PM that intersect at Z. If ZM = 4, find QZ and QM.
Answer:
value of QZ = 8 units and QM = 12 units.
Step-by-step explanation:
Given: In triangle PQR has medians QM and PN that intersect at Z.
If ZM = 4 units.
In the figure given below; second median divided the two triangles formed by the first median in the ratio 2:1.
We have to find the value of QZ and QM;
QZ:ZM = 2: 1
⇒ [tex]\frac{QZ}{ZM} = \frac{2}{1}[/tex]
Substitute the value of ZM =4 units and solve for QZ;
[tex]\frac{QZ}{4} = \frac{2}{1}[/tex]
Multiply both sides by 4 we get;
[tex]QZ = 2 \times 4 = 8 units[/tex]
Now, calculate QM;
QM = QZ+ZM = 8 + 4 = 12 units.
Therefore, the value of QZ and QM are; 8 units and 12 units
Which subtraction expression has the difference 1 + 4i? (–2 + 6i) – (1 – 2i) (–2 + 6i) – (–1 – 2i) (3 + 5i) – (2 – i) (3 + 5i) – (2 + i)
Answer:
(3 + 5i) – (2 + i)
Step-by-step explanation:
(–2 + 6i) – (1 – 2i)
The real parts -2-1 = -3
The imaginary parts 6i--2i = 6i+2i = 8i
(–2 + 6i) – (–1 – 2i)
The real parts -2 +1 = -1
The imaginary parts 6i --2i = 6i+2i =8i
(3 + 5i) – (2 – i)
The real parts 3-2 =1
The imaginary parts = 5i --i = 5i+i = 6i
(3 + 5i) – (2 + i)
The real parts 3-2 =1
The imaginary parts 5i -i = 4i
Answer:
d.(3 + 5i) – (2 + i)
Step-by-step explanation:
which of the following is true for the graph of the quadratic function f(x)=3(x+2)(×-2)
Answer:
A
Step-by-step explanation:
given y = 3(x + 2)(x - 2) = 3(x² - 4) = 3x² - 12
for the y- intercept let x = 0
f(0) = - 12 → y-intercept is the point (0, - 12) → True
for x-intercepts let y = 0
3(x + 2)(x - 2) = 0
x + 2 = 0 ⇒ x = - 2
x - 2 = 0 ⇒ x = 2
x- intercepts are (- 2, 0) and (2, 0) → not (0, - 12)
since f(x) = 3x² - 12 is symmetric about the y-axis
the vertex is at (0, - 12 ) → not (- 2, 2)
If a muffin calls for 1 and 3/4 cups of sugar, how many cups of sugar will be needed if only 1/4 of the recipe is being made?
Answer: 7/16 or .4375
Step-by-step explanation: 1/4 of 1 is 1/4. 1/4 of 3/4 is .1875 which also equals 3/16. Add 1/4 and 3/16 to get 7/16 cups of sugar or 0.4375. Hope this helps!
The sum of two consecutive whole numbers is 57. What is the value of the greater of the two numbers
[tex]n,\ n+1-\text{ two consecutive whole numbers}\\57-\text{the sum}\\\\n+n+1=57\qquad\text{subtract 1 from both sides}\\2n=56\qquad\text{divide both sides by 2}\\n=28\\\\n+1=28+1=29\\\\Answer:\ \boxed{\text{The greater of the two numbers is 29}}[/tex]
The two consecutive whole numbers that sum to 57 are 28 and 29. The solution was achieved by setting up an equation and solving for x which represents the smaller number. The greater number is 29.
Explanation:The sum of two consecutive whole numbers is 57 pertains to a simple arithmetic problem. If two consecutive numbers sum to 57, we can set up an equation to solve for the numbers. Let's call the smaller number 'x'. This means the next number would be 'x + 1' since it's consecutive, or next in line. The equation for your problem would then be x + (x + 1) = 57. Simplifying the equation gives us 2x + 1 = 57, and then subtracts 1 from both sides to get 2x = 56.
The last step is to divide both sides by 2, which gives us: x = 28. So, the smaller number is 28 and the greater number is 29.
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how much will the interest be for a $500 loan at 6% interest for one year
Answer:
300 dollars of interest
Step-by-step explanation:
5000 (0.06)
300
Answer:
$30
Step-by-step explanation:
You are being asked to figure out simple interest, I think.
Givens
i = ?P = 500r = 6%t = 1 yearFormula
i = P*r*t
Solution
i = 500*6%*16% = 6/100 = 0.06i = 500 * 0.06 * 1i = 30Edit
You want this to be done using a % proportion. Is that correct from what I read in the comments after the question (which I didn't see -- sorry).
6/100 = x/500 That's the proportion. Cross multiply6 * 500 = 100*x Multiply the numbers on the left3000 = 100 x Divide both sides by 1003000/100 = 100x/100 Do the division30 = xSo it comes to the same thing.
you have one penny 1 nickel 1 dime and 1 quarter you select two coins at random. what is the probability that you will have exactly $0.15?
Answer:
the probability of getting the exact coins that make $0.15 is 33.3% (1/3)
Step-by-step explanation:
in a sale, normal prices reduced by 10% nathalie bought a pair of shoes in the sale for 54£ what was the original price of shoe
Answer:
60 pounds
-hope this helps
Answer:
£60
Step-by-step explanation:
100% represents the original price of the shoes
then (100 - 10) = 90% of the original price
Divide the cost by 90% to find 1% then multiply by 100 for the original price
original price = [tex]\frac{54}{90}[/tex] × 100 = £60
Please explain how I solve this thanks
Answer:
C
Step-by-step explanation:
$4.50 x 4 = $18.00 $6.00 x 2 = $12.00 $18 + $12 = $30
$4.50 + $6.00 = $10.50
Evaluate the expression a/b for a=24 and b=4
Answer:
a/b =6
Step-by-step explanation:
We want to evaluate a/b
a=24, b=4
Substitute these values into the expression
a/b =24/4
= 6
Final answer:
When evaluating the expression a/b with a=24 and b=4, the result is 6, as you simply divide 24 by 4.
Explanation:
The expression to evaluate is a/b, where a=24 and b=4.
To calculate this, simply divide the value of a by the value of b:
Step-by-step calculation:
Insert the known values into the expression: a/b = 24/4.
Divide 24 by 4 to get the result.
24 divided by 4 equals 6.
Therefore, if a=24 and b=4, the value of a/b is 6.
Help me!! <ABC = ____?
Triangles NPM and ABC are similar by SAS, establishing that angle ABC corresponds to angle NPM. Thus, <ABC = <MNP.
In triangles NPM and ABC, the given information suggests that these triangles are similar by the Side-Angle-Side (SAS) criterion. Specifically, MP = AC, AB = NM, and BC = PN, along with the corresponding equal angles A = M, B = N, and C = P.
The Angle-Angle Similarity Postulate asserts that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Therefore, triangles NPM and ABC are similar.
The corresponding angles in similar triangles are equal. Hence, angle ABC is equal to angle NPM. Therefore, the correct answer is:
<MNP
This is because angle ABC in triangle ABC corresponds to angle NPM in triangle NPM.
Determine the domain and range. Please help!!
The domain is the set of all numbers. The range is also the set of all real numbers.
Why is this the case? Because the line extends forever in both directions along the x and y axis. We can plug in any x value and solve for y, or vice versa, and we don't have any restrictions for the input or output.
-----------------------
To write "the set of all real numbers" in interval notation, you would write [tex](-\infty, \infty)[/tex]
This is the interval from negative infinity to positive infinity, spanning the entire real number line.
In geometry the four sides of a square are all the same length. One side measures (3x+4) and the perimeter of the square is 76. Find the value of X. Hint: First set up an equation to help you solve for X
Answer:
Step-by-step explanation:
We can set up an equation:
4(3x+4)=76
We can distribute the left side and get:
12x+16=76
Subtract 16 from both sides:
12x=60
Divide 12 from both sides:
x=5
Check:
4(3*5+4)
4(15+4)
4(18)
76
So x=5