Using the given function, it is found that the projectile hits the ground after 20 seconds.
When does the projectile hits the ground?It hits the ground when it's height, given by h(t), is equals to zero.
In this problem, the function that models it's height is given by:
h(t) = -4.9t^2 + 98t.
Then:
h(t) = 0
-4.9t^2 + 98t = 0.
-4.9t(t - 20) = 0
t - 20 = 0 -> t = 20.
The projectile hits the ground after 20 seconds.
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The ratio of the number of dolls Jacky had to the number of dolls Peter had was 5:2 but, after Jacky gave 15 dolls to Peter, they have an equal number of dolls. How many dolls did they have altogether?
Answer:
70 dolls
Step-by-step explanation:
Hello!
The ratio is 5:2, which are division of a whole. They can be represented as 5x and 2x.
Jacky has 5x dolls, and Peter has 2x dolls. They were equal after subtracting 15 dolls from 5x and adding them to 2x.
Equation:
5x - 15 = 2x + 15Solve:
5x - 15 = 2x + 155x - 30 = 2x5x = 2x + 303x = 30x = 10So Jacky has 5(10) dolls, or 50 dolls, and Peter has 2(10) or 20 dolls.
The total sum is 70 dolls.
PLEASE HELP!! Need by 3/29/22!
Find the area of these shapes
Answer:
Step-by-step explanation:
area of A=15*18=270 cm^2
area of B=15*18=270 cm^2
area of C=1/2 ×x×18=9x cm²
area of D=1/2×15×18=135 cm²
What is the value of w in the equation 2(2w − 16) = 0?
Answer:
[tex]w=8[/tex]
Step-by-step explanation:
[tex]2(2w-16)=0\\4w-32=0\\4w=32\\w=8[/tex]
Answer:
w = 8
Step-by-step explanation:
2(2w − 16) = 0
Divide each side by 2
2w-16 = 0
Add 16 to each side
2w-16 +16 =0 +16
2w = 16
Divide each side by 2
2w/2 = 16/2
w = 8
Solve for area and perimeter in each of the following problems.
Answer:
1. perimeter =2(l+w)
=2(17+10)
= 54 yards
Are of the perimeter=l times b
=17 x 10
=170 yd square
Just follow this concept for all of them. It the same thing. Good Luck!!
Step-by-step explanation:
Please help! will give brainlest! locks in 30 min!
Answer:
[tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
Simplify the expression:
sin [tex]\frac{3pi}{4}[/tex]
Rewrite the angle as a sum or difference with its reference angle:
sin (pi - [tex]\frac{pi}{4}[/tex])
Simplify the expression
(sin [tex]\frac{pi}{4}[/tex])
Evaluate the expression:
[tex]\frac{\sqrt{2} }{2}[/tex]
hope this helps and is right!! p.s. i really need brainliest :)
What information is included in this loan agreement that would NOT be included if Ron had gotten a loan from a bank or credit union?
gi i need help with this question if you can help me asap that whould be great
Use the following compound interest formula to complete the problem. a = p (1 startfraction r over n endfraction) superscript n superscript t victor has a credit card with an apr of 13.66%, compounded monthly. he currently owes a balance of $1,349.34. assuming that victor makes no purchases or payments, how much will he owe after one year, to the nearest cent? a. $1,349.34 b. $1,533.66 c. $1,545.65 d. $1,364.70
The final amount that Victor will owe after one year, to the nearest cent is given by: Option C: $545.65
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
For this case, we're provided that:
The interest rate is r = 13.66% = 13.66/100 = 0.1366 (converted percent to decimal)
It is compounding monthly, thus, 12 times a year, or n = 12
The initial amount that the credit card of Victor has = p = $1349.34
Time for which interest was compounded = a year = 1 = t
Thus, the final amount that Victor will owe after one year to the nearest cent is calculated as;
[tex]a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 1349.34(1 + \dfrac{0.1366}{12})^{12\times 1}\\\\a = 1349.34(1.01138)^{12} \approx 1245.65 \: \rm (in \: dollars)[/tex]
Thus, the final amount that Victor will owe after one year, to the nearest cent is given by: Option C: $545.65
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Answer:
C
Step-by-step explanation:
I took the test and passed with 100
On May 1, Anna purchased a new condo. She pays a monthly maintenance fee of $230. Her monthly property taxes equal 13.5% of the monthly fee. How much will Anna pay in property taxes for this calendar year?
Answer:
$31.05
Step-by-step explanation:
You can get this answer by changing percent (13.5%) to just 13.5, or in other words, a decimal. you also change 230. to a decimal by by moving the decimal point two times to the left to get 2.30. You can then get your answer by multiplying the values together (2.30 x 13.5)
What is the approximate measure of angle B?
Answer: D
Step-by-step explanation:
What is the tangent ratio of angle KJL?
Answer: (1)
Step-by-step explanation:
Using the properties of a 30 60 90 triangle, we get that ML=24sqrt3 and JM=24.
This means that the tangent is 24sqrt3 / 24.
A square rug has an area of 256 square feet. What is the perimeter of the rug?
Answer:
64
Step-by-step explanation:
[tex]\sqrt{256}[/tex] = 16 (length of each side)
A square (rug) has 4 sides.
Add to find perimeter:
16 + 16 + 16 + 16
= 64
Answer: 8ft
Step-by-step explanation:
4A= 256
4A/4 = 256/4
A = 64
A = a²
64 = 4²
a² = 64
a = ±√64
a = ±8
∴a = ±8
Hence, the length of a side of each rug is 8ft.
Bobby has 58 of a pepperoni pizza in his refrigerator. He eats 14 of this for his lunch. Of the following, which is the best estimate of the fraction of the original pizza left after Bob's lunch?
Answer:
5/32
Step-by-step explanation:
A. where will vertex A be located after a rotation of -90°
B. where will vertex B be located after a rotation of 90°
C. where will vertex C be located after a -180° rotation
D. where will vertex D be located after a 270° rotation?
Answer:
this image should help a lot:
vertex b: (-5,3)
vertex a: (0,-1)
vertex c: (-6,-7)
vertex d: (-4,-1)
Step-by-step explanation:
Triangle ABC is congruent to B triangle A"B"C".
Which sequence of transformations could have been used to transform triangle abc to produce triangle A'' B'' C''? transform triangle ABC triangle A"B"C"?
A. Triangle ABC was translated 7 units down and then 9 units right.
B. Triangle ABC was translated 10 units to the right and then reflected across the x Axis.
C. Triangle ABC was reflected across the x Axis and then translated 9 units right.
D. triangle ABC was reflected across the y Axis and then translated 7 units down.
Answer: D
Step-by-step explanation:
HELP PLEASE!! <3
i honestly don't understand what they want me to do here
Answer:
(a)
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 20 ← is in this form , then
centre = (0, 0 ) and r = [tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]
Please help and explain WILL MARK BRAINLIEST!!!!
Answer:
x is 19.5 degress
Step-by-step explanation:
hmmm so here oh i see now okay:
since a line is 180 degress lets write
2x + 82.5 + 3x = 180
now we umm add the ones with the same variable and power
5x + 82.5 = 180
5x = 180 - 82.5
5x = 97.5
x = 19.5
This is an angle on a straight line and It is equal to 180°
2x° + 3x° + 82.5° = 180°
5x° = 180° - 82.5°
5x = 97.5°
x = 19.5°
To indicate the angle
2x => 2(19.5°) => 39°
3x => 3(19.5°) => 58.5°
The angle are (39°, 82.5°, 58.5°
Charmaine got a prepaid debit card with $15 on it. for her first purchase with the card, she bought some bulk ribbon at a craft store. the price of the ribbon was 21 cents per yard. if after that purchase there was $12.27 left on the card, how many yards of ribbon did charmaine buy?
Answer:
15- 12.27 = 2.73
2.73 is how much she spent on the ribbon.
2.73/ 0.21 = 13
She purchased 13 yards.
Photo attached with instructions
Step-by-step explanation:
using cosine rule,
BC²= AC² + BC² - 2*AC*BC*COSc
= 13² + 6² - 2*13*6*-cos(180-91)
= 169 + 36 - (-2.72)
= 202.28
√BC² = √202.28
BC = 14.22
BC = 14.20cm to nearest tenth
In the image below, why must triangle A'B'C be similar to ABC?
(Don't mind the chosen answer)
Answer: Option (3)
Step-by-step explanation:
You can get 2 pairs of corresponding angles from the parallel segments, meaning that they are similar by angle-angle.
Kindly solve this question
Answer:
x=-1/7
Step-by-step explanation:
[tex]\frac{3x-1}{3} -\frac{2x}{x-1} =x[/tex]
[tex]\frac{(3x-1)(x-1)}{3x-3} -\frac{2x(3)}{3x-3} =x[/tex]
[tex]\frac{3x^2-4x+1}{3x-3} -\frac{6x}{3x-3} =x[/tex]
[tex]\frac{3x^2-10x+1}{3x-3} =x[/tex]
[tex]\frac{3x^2-10x+1}{3x-3} =\frac{x(3x-3)}{3x-3}[/tex]
[tex]\frac{3x^2-10x+1}{3x-3} =\frac{3x^2-3x}{3x-3}[/tex]
[tex]3x^2-10x+1=3x^2-3x[/tex]
[tex]-10x+1=-3x[/tex]
[tex]-7x=1[/tex]
[tex]x=-1/7[/tex]
Simplify: 14-30/ 2 (- 4)
Thanks! :)
Answer:
The answer is 2
-16/-8=2
A farmer plans to build the small silo shown to store chicken feed. What is the circumference of the base of the silo if it can hold a maximum of 132 cubic feet of feed?
The circumference of the base of the silo that can hold a maximum of 132 cubic feet of feed is approximately 28.796 feet.
How to determine the circumference of the base of a silo
The circumference is the measure of the contour of a circle. In this question we have to determine the radio of the base of the cone from the volume formula and later the circumference is found by this finding:
Volume
V = (π/3) · R² · h (1)
Circumference
s = 2π · R (2)
Where:
R - Radius of the base, in feeth - Height of the silo, in feetIf we know that V = 132 ft³, h = 6 ft, then the circumference that can hold the given capacity is:
[tex]R = \sqrt{\frac{3\cdot V}{\pi \cdot h} }[/tex]
[tex]R = \sqrt{\frac{3\cdot (132\,ft^{3})}{\pi\cdot (6\,ft)} }[/tex]
R ≈ 4.583 ft
s = 2π · (4.583 ft)
s ≈ 28.796 ft
The circumference of the base of the silo that can hold a maximum of 132 cubic feet of feed is approximately 28.796 feet. [tex]\blacksquare[/tex]
RemarkThe statement is complete, complete form is introduced below:
A farmer plans to buid the small silo to store chicken feed. The silo is a cone with a height of 6 feet. What is the circumference of the base of the silo if it can hold a maximum of 132 cubic feet of feed?
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which is the answers
Answer:
1. any number from 42 to 68
e.g 52
2. any number less than 42 or greater than 68
e.g 76
Jin's family took a road trip to Niagara Falls. Jin slept for the last 24 miles of the trip. If the total length of the trip was 400 miles, what percentage of the total trip had they travelled when Jin fell asleep?
Answer:
94%
Step-by-step explanation:
400-24=376
Find 376 out of 400 as a decimal:
376/400 = 0.94
0.94x100 = 94%
If 5^2x = 1, what is the value of 'x' ?
Answer:
x = 0
Step-by-step explanation:
5^0 is 1, meaning that x must equal to 0 for the answer to be 5^0.
on a coordinate plane, the endpoints of line segment JL are
J(-6,-4) and L(6,8). Point K lies on line segment JL and divides it into two
line segments such that the ratio of JK to KL is 5:1. What are the
coordinates of point K?*
Answer: (4,6)
Step-by-step explanation:
We are splitting the line segment into 6 parts, so we can start by finding the displacement in the x and y coordinates.
The change in x is 12, and the change in y is 12.
This means that for each of the 6 parts we are splitting the segment into, the value of x will change by 2, and so will y.
This means that to find K, we can subtract one of these displacements from point L.
This means that K has coordinates (6-2, 8-2)=(4,6)
log2^2-log2^16 what is the answer
Answer:
-4.1-4.1212
Step-by-step explanation:
Log2^2-log 2^16
log2^2/2^16
log2^2-16
log2^-14
-14log2
-14×0.3010
-4.1-4.1214
Demarcus has to wrap a gift for his friend's birthday party. The gift is in a rectangular box with the dimensions shown below. He's trying to figure out how much gift wrap he needs to cover the entire box. Should he calculate the total surface area or the lateral surface area? Pick the right measurement and then calculate it for him.
In your answer, specify whether he should use total surface area or lateral surface area. Calculate the one you choose, give that measurement of the box, and then explain how you calculated it.
The surface area of the box is 1048 square inches
How to calculate the total surface area of the boxThe formula for calculating the surface area of the prism is expressed as:
Surface area = 2(lw + wh +lh)
Given the following
l = 20in
w = 8in
h = 13in
Substitute the given parameters'
Surface area = 2(lw + wh +lh)
Surface area = 2(20(8) + 8(13) +20(13))
Surface area = 2(160+104+260)
Surface area = 1048 square inches
Hence surface area of the box is 1048 square inches
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You have a cup of lemonade. Each ice cube has a length of 2 cm, a width of 1 1/4 cm and a height of 3 cm. What is the volume of one of the ice cubes? Show your steps and Explain how you used math to come to your decision.
volume : 7.5 cm²
volume of cube : length * width * height[tex]\hookrightarrow \sf Length \ * Width \ * \ Height[/tex]
[tex]\hookrightarrow \sf 2 \ * 1\dfrac{1}{4} \ * \ 3[/tex]
[tex]\hookrightarrow \sf 2 \ * \dfrac{5}{4} \ * \ 3[/tex]
[tex]\hookrightarrow \sf \dfrac{15}{2}[/tex]
[tex]\hookrightarrow \sf 7.5 \ cm^2[/tex]
Answer:
[tex]\sf volume=7 \frac12 \ cm^3[/tex]
Step-by-step explanation:
Formula
volume of cuboid = length × width × height
Given dimensions of the ice cube:
length = 2 cmwidth = 1 1/4 cmheight = 3cmSubstituting the given values into the formula:
[tex]\sf \implies volume=2\times 1 \frac14 \times 3[/tex]
Converting to improper fractions:
[tex]\sf \implies volume=\dfrac21\times \dfrac54 \times \dfrac31[/tex]
[tex]\sf =\dfrac{ 2\times 5 \times 3}{1 \times 4 \times 1}[/tex]
[tex]\sf =\dfrac{30}{4}[/tex]
Dividing the numerator and denominator by the highest common factor:
[tex]\sf \implies volume=\dfrac{30 \div 2}{4 \div 2}[/tex]
[tex]\sf =\dfrac{15}{2}[/tex]
Converting the improper fraction into a mixed number:
[tex]\sf \implies volume=7 \frac12 \ cm^3[/tex]