Answer:
Solving the equation using quadratic formula we get [tex]\mathbf{x=0.119\:or\:x=-2.785}[/tex]
Step-by-step explanation:
We need to use the quadratic formula to find the solutions for
[tex]y = 3x^2 + 8x - 1[/tex]
(Note: quadratic formula is used when x^2 is in the equation. So considering 3x^2 instead of 3x^3)
The quadratic formula is: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
From the given equation [tex]y = 3x^3 + 8x - 1[/tex] we have a =3, b=8 and c =-1
Putting values in the formula and finding solutions:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-8\pm\sqrt{(8)^2-4(3)(-1)}}{2(3)}\\x=\frac{-8\pm\sqrt{64+12}}{6}\\x=\frac{-8\pm\sqrt{76}}{6}\\x=\frac{-8\pm8.71}{6}\\x=\frac{-8+8.71}{6}\:or\:x=\frac{-8-8.71}{6}\\x=0.119\:or\:x=-2.785[/tex]
So, Solving the equation using quadratic formula we get [tex]\mathbf{x=0.119\:or\:x=-2.785}[/tex]
350 kilometers in 5 hours i dont get it
Answer:
I cant see the question
Step-by-step explanation:
Penny reads 13 pages in 1/4 hour. What is the unit rate for pages per hour? For hours per page?
Answer:
52 pages per 1 hour
Step-by-step explanation:
If Penny reads 13 pages in 1/4 of an hour you need to multiply 13 by 4 to see how many pages she will read in 1 hour.
The unit rate:
52 pages per hour.
0.02 hours per page.
What is division?One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.
To find the unit rate of pages per hour, we need to convert 1/4 hour to hours first.
1/4 hour = 0.25 hour
Then, we can use the formula:
Unit rate = Pages ÷ Time
Unit rate = 13 pages ÷ 0.25 hour
Unit rate = 52 pages per hour
To find the unit rate of hours per page, we can use the reciprocal of the previous unit rate:
Unit rate = Time ÷ Pages
Unit rate = 0.25 hour ÷ 13 pages
Unit rate = 0.0192 hours per page
Rounded to the nearest hundredth, the unit rate is 0.02 hours per page.
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6. The length of a football field is 30 yards more than its width.
Express the length of the field in terms of its width. If the perimeter
of the field is 340 yards. find the width of the field. I
Answer:
the width be 70 yards
Step-by-step explanation:
The computation of the width of the field is as follows:
As we know that
The Perimeter of the rectangle is
= 2 × (length + width)
Where
Perimeter is 340 yards
Let us assume the width be x
So, the length would be x + 30
Now put these values to the above formula
340 = 2 × (x + x + 30)
340 = 2 × (2x + 30)
340 = 4x + 60
4x = 280
x = 70
The length would be
= 70 + 30
= 100
Hence, the width be 70 yards
5. Murphy obtains a 15/5 balloon mortgage to finance $113,500 at 4.95%. How much principal and interest will he have already pald when his balloon payment is due? (2 points)
$85,433.10
O $70,863.13
O $52,781.40
O $53,676.00
Answer:
$278.15×60= $16688.969
Step-by-step explanation:
Murphy has a 15/5 balloon mortgage plan therefore he would make constant payments monthly for five years and then pay the balance of the loan/balloon payment for the 10 years left in bulk
To calculate principal+interest on loan before balloon payment is due, we simply calculate Murphy's constant/monthly payments for the 15 year loan amortization and multiply by number of payments before balloon payment is due:
Formula for monthly payments
A= P×r×r(1+r)^n/(1+r)^n-1
Where A= monthly payments
P= mortgage loan value
r= interest rate on loan
n= number of payments = 15×12= 180 monthly payments
Substitute :
A= $113500×0.0495×0.0495(1+0.0495)^180/(1+0.0495)^180-1
A= $113500×0.0495×296.104/5980.90
A= $113500×0.0495×0.049508
A= $278.15
To calculate our principal and interest before balloon payment, we multiply by number of payments(5×12=60 payments) before due balloon payment
60×$278.15= $16688.969
You wash dishes for a chemistry laboratory to make extra money for laundry. You earn 12 dollars/hour, and each shift lasts 75 minutes. Your laundry requires 12 quarters/load.Part AHow many shifts must you work if you wish to wash 10 loads of laundry
Answer:
2 shifts
Step-by-step explanation:
Amount earned washes dishes = 12 dollars / hour
Shift duration = 75 minutes
Cost of laundry = 12 quarters per load
Cost of 10 loads of laundry = (10 * 12 quarters) = 120 quarters
1 quarter = 25 cents
120 quarters = (25 * 120) = 3000 cents
100 cents = $1
3000 cents = 3000/ 100 = $30
Hence, to make $30 from washing dishes :
$12 = 1 hour
$30 = x
x = 30 / 12
x = 2.5 hours
1 shift lasts 75 minutes
2.5 hours = (2.5 * 60) = 150 minutes
150 / 75 = 2 shifts
A biologist studied the frequency of croaks for frogs from two different regions. From a random sample of 32 frogs located in the northern region, the mean number of croaks per hour was 21.3, and from a random sample of 38 frogs located in the southern region, the mean number of croaks per hour was 28.9. To estimate the difference in the mean number of croaks (southern minus northern), a 95 percent confidence interval was constructed from the samples. The interval was reported as (7.1, 8.1). Which of the following claims is supported by the interval?
A. All southern frogs croak more times per hour than do all northern frogs.
B. The northern frogs are likely to have a greater mean number of croaks per hour than the southern frogs.
C. The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
D. All frogs in the study have about the same number of croaks per hour.
E. The northern and southern frogs have the same mean number of croaks per hour.
Answer:
C
Step-by-step explanation:
Since at the 95% confidence, the difference between the number of croaks per hour between southern and northern region frog is lying in the rage 7.1 to 8.1, this shows that the southern region's frogs' croak frequency is highly likely to be greater than that of northern region's frogs' croaks' frequency.
The claim supported by the interval is
Option C. The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
What does the interval tell obtained in the hypothesis testing?The interval we obtain at certain confidence tells that the value of the test statistics will lie in that interval with that confidence.
How to identify what is the obtained interval indicating?Since the test statistics was measuring the croak frequency difference
with southern - northern, and since at 95% confidence, the difference will lie in interval (7.1, 8.1), which is positive, thus the frequency of crocks for southern frogs is greater than the frequency of crocks for northern frogs.
Thus,
The claim supported by the interval is
Option C. The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
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Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly correctly without making mistakes
Answer:
648 cups, 3 fluid ounces
Step-by-step explanation:
You need to know that 1 cup = 8 fluid ounces (fl. oz).
convert to fl. oz:
1296 cups = 10368 fl.oz.
total fl.oz. = 10368+6 = 10374
10374 / 2 = 5187 fl.oz.
= 648 cups and 3 fluid ounces
Ally made 60 donuts on Friday. She made 3x donuts on Wednesday and 2x donuts on Thursday. How much donuts did she make in all?
Answer:
Step-by-step explanation: 60 x 3= 380
2 x 60= 270
270 + 380= 810
ASAP need help with system of equations... I'm too small brain to do it.
Answer:
(x=0, y=11)
(x=2, y=9)
Step-by-step explanation:
first equation substitution for x first.
y=11-x
plug into 2nd equation
(x+2)^2+(11-x-7)^2=20
this should lead you into a quadratics equation.
you get x=0, x=2.
do the same for y value this time, subbing in the x value
(11-y+2)^2+(y-7)^2=20
this also leads into a quad equation
solve and you get y=11, and y=9
Find the slope of the line through each pair of points.
1. (4,-16), (7,18)
2. (2,1), (-9, -3)
3. (-11,2), (15,5)
4. (5,6), (10, -12)
Answer:
1. 11 1/3
2. 4/11
3. 3/26
4. -18/5
Step-by-step explanation:
someone plssss help (15 points) ty
Answer:
x = 67
Step-by-step explanation:
2x - 17 + 63 = 180 {Linear pair}
2x + 46 = 180
2x = 180 - 46
2x = 134
x = 134/2
x = 67
[tex]\color{plum}\bold{x \tt \: = 67}[/tex]
Steps to derive the correct solution :∠63° and ∠(2x-17)° are a linear pair, so their sum will be equal to 180°.
Which means :
[tex] = 63 + 2x - 17 = 180[/tex]
[tex] = 63 + 2x = 180 + 17[/tex]
[tex] = 63 + 2x = 197[/tex]
[tex] = 2x = 197 - 63[/tex]
[tex] = 2x = 134[/tex]
[tex] = x = 67[/tex]
Let us place 67 in the place of x and see if the substitution is equivalent to 180° :
[tex] = 63 + 2 \times 67 - 17 = 180[/tex]
[tex] = 63 + 134 - 17 = 180[/tex]
[tex] = 63 + 117 = 180[/tex]
[tex] = 180 = 180[/tex]
Thus, the value of x we found out is correct.
Therefore, x = 67
Please help photo attached
Answer:
12/20
Step-by-step explanation:
Cosine is a trigonometric identity. It is a ratio of the adjacent side and hypotenuse of a right triangle.
The adjacent side to angle Θ is 12. The hypotenuse of this triangle is 20.
cosΘ in this case would be 12/20.
There are 40 mg of bacteria in the sample. The next day there are 50 mg of bacteria, and the following day there are 62.5 mg of bacteria. The bacteria sample continues to grow exponentially. What function can be used to model this situation?
Answers
A A(t)=40(1.25)^t
B A(t)=40(.75)^t
C A(t)=50(.25)^2
D A(t)=50(1.25)^t
A recreational court is twice as long as it is wide. if the perimeter is 210 feet, find the width and length .
Answer:
The court has a length of 70 feet, and a width of 35 feet.
Step-by-step explanation:
We know two things:
the the length is twice the width
l = 2w
We also know that the perimeter is 210 feet. Noting that the perimeter of a rectangle is equal to twice its length plus twice its width, we can say:
210 = 2w + 2l
Now we can substitute the first definition of l into the second equation:
210 = 2w + 2(2w)
And now we can solve for w:
210 = 2w + 2(2w)
210 = 2w = 4w
210 = 6w
w = 210 / 6
w = 35
Now that we have w, we can plug that into our first little equation to find l:
l = 2w
l = 2 × 35
l = 70
So the width of the court is 35 feet, and it's length is 70.
What expression can be used to find the nth term in the sequence 5,7,9, 11,...?
2n - 3
n + 2
n - 3
2n + 3
Answer:
The required expression which can be used to find the nth term in the sequence is:
[tex]a_n=2n+3[/tex]
Hence, the fourth option i.e. 2n+3 is the correct option.
Step-by-step explanation:
Given the sequence
5, 7, 9, 11,...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]7-5=2,\:\quad \:9-7=2,\:\quad \:11-9=2[/tex]
The difference between all the adjacent terms is the same and equal to
d = 2
So
a₁ = 5d = 2Thus, the nth term of the sequence is
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substitute a₁ = 5 and d = 2 in the sequence
[tex]a_n=2\left(n-1\right)+5[/tex]
[tex]a_n=2n+3[/tex]
Therefore, the required expression which can be used to find the nth term in the sequence is:
[tex]a_n=2n+3[/tex]
Hence, the fourth option i.e. 2n+3 is the correct option.
Polygon ABCD has the following vertices:
A(−4, 2), B(3, 2), C(3, −5), and D(−4, −2)
Calculate the area of the polygon.
28 units squared
38.5 units squared
40.5 units squared
49 units squared
get it right because i can check and i'll not give you brainlyest
:)
To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.
The base is formed by the segment connecting point A and point B.
While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.
The formula for area of trapezoid is given as:
A = b (h1 + h2) / 2
Where,
b = base of the trapezoid = 3 – (-4) = 7
h1 = shorter height = 2 – (-2) = 4
h2 = longer height = 2 – (-5) = 7
Therefore the area is:
A = 7 (4 + 7) / 2
A = 77 / 2
A = 38.5
Triangle TUV has sides that measure 12, 8, and 6. Triangle XYZ has sides that measure
8,6,and 3. Can triangles TUV and XYZ be similar polygons?
A. Yes. Regardless of the lengths of the sides, you can always join them by angles that
form similar triangles.
B. Yes. The ratio of 12:6 is the same as the ratio of 6:3.
C. No. The ratio 12:6 is the same as the ratio of 6:3.
D. No. The ratio of the longest sides is 12:8 and the shortest sides is 6:3.
Alyssa's cat weighs 12 pounds, which is 3/8 of the weight of her dog. Use the equation 3/8d=12 to find the weight of Alyssa's dog.
Answer:
0.5 pounds!
Step-by-step explanation:
help please :(( please please please
9514 1404 393
Answer:
A, B, D
Step-by-step explanation:
A. Multiplication is the same as repeated addition.
B. Multiplying a fraction by an integer effectively multiplies only the numerator. The denominator remains unchanged.
C. (false -- see B)
D. A product is unchanged if a factor is removed from the multiplicand and is applied to the multiplier. (The associative property of multiplication tells you this.)
4 × 1/6
= (2 × 2) × 1/6 = 2 × (2 × 1/6)
= 2 × 1/3
Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 16 inches long. What is the side length of each piece?
To do this problem you would need to have at least one side length AND the hypotenuse to figure out the other side length.
how do you explain 15 video games to 18 video games in ratios and rates?
15 vg
18 vg
Just put a line in-between them to make a fraction.
Which questions are True or False?
1.) Supplementary angles always add up to 90°.
2.) Complementary angles always add up to 180°.
3.) Vertical angles always have the same measure.
4.) ∠x is complementary to the 34°angle.
5.) ∠z is vertical to the 112°angle.
6.) ∠y is a linear pair with the 146°angle.
Answer:
1) false
2) false
3) true
4)false
5) true
6) true
Help me pls. Due Today, I will MARK AS BRAINLIEST
Answer:
CDA and BDA are the same
Step-by-step explanation:
use a common denominator
What does 1/9 equal?
Answer:
2/18
Step-by-step explanation:
because i multiplied 1/9 by 2
Find the perimeter of the following shape:
Answer:
37.5in
Step-by-step explanation:
you add all the outer lengths up. the altitude doesn't count.
12+11.5+14= 27.5. Hope this helps.
the temperature at 6:00 am was -12°f. temperature increased by 1/2 °F each hour for 6 hours.what was the temperature in degrees Fahrenheit at noon?
Answer:
600
Step-by-step explanation:
Answer:-9
Step-by-step explanation:
❤
How many different committees can be formed from 7 teachers and 30 students if the committee consists of three teachers and four students
Answer:
959175
Step-by-step explanation:
a) Teachers' committee:
[tex]C^3_7=\frac{7!}{3!4!}=35;[/tex]
b) Students' committee:
[tex]C^4_{30}=\frac{30!}{4!(30-4)!}=\frac{27*28*29*30}{2*3*4}=35*27*29=27405;[/tex]
c) Teachers & Students:
[tex]C^3_7*C^4_{30}=35*27405=959175.[/tex]
How is Solve this equation
M + A = 68 and M = A + 24
Hi there! :)
[tex]\large\boxed{A = 22 \text{ , } M = 46 }[/tex]
We can solve by setting both equations equal to the same variable.
We are given that M + A = 68 and M = A + 24. The easiest variable to set both equal to would be M.
Rearrange the first equation by subtracting A from both sides:
M = -A + 68
Now that both equations equal to M, we can set the two equal to each other:
-A + 68 = A + 24
Add A to both sides:
68 = 2A + 24
Subtract 24 from both sides:
44 = 2A
Divide both sides by 2:
A = 22.
Plug this back into an equation to solve for M:
M + 22 = 68
M = 68 - 22
M = 46.
is 1/3 bigger than 33.3%
33.33 percentage
Step-by-step explanation:
Just multiply a fraction by 100%
to convert it to percentage form.
1/3= 100%=33.33%
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A series of maths books consists of four volumes. The first has x pages and the second has 54 more. The third and fourth volumes have 32 more pages than the second volume. The number of pages of all volumes is 866. Calculate the number of pages in each volume.
Answer:
1st volume = 160
2nd volume = 160 + 54 = 214
3rd volume = 160 + 54 + 32 = 246
4th volume = x + 54 + 32 = 246
Step-by-step explanation:
Given that:
Number of volumes = 4
1st volume = x pages
2nd volume = 54 more = x + 54
3rd volume = 32 more = x + 54 + 32
4th volume = 32 more = x + 54 + 32
Total number of pages = 866
Hence,
1st + 2nd + 3rd + 4th = 866
x + x + 54 + x + 54 + 32 + x + 54 + 32 = 866
4x + 226 = 866
4x = 640
x = 160
1st volume = 160
2nd volume = 160 + 54 = 214
3rd volume = 160 + 54 + 32 = 246
4th volume = x + 54 + 32 = 246