[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 8.5\%\to \frac{8.5}{100}\dotfill &0.085\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}[/tex]
[tex]A=10000\left(1+\frac{0.085}{12}\right)^{12\cdot 15}\implies A=10000\left( \frac{2417}{2400} \right)^{180}\implies A\approx 35626.53[/tex]
Find the area of the figure below.
16 in
19 in
30 in
19.4 in
Answer:
392 square inches
Step-by-step explanation:
To solve this we need to look at this quadrilateral as two shapes that share a side - a triangle and a rectangle.
You can see in the attatchment how I have drawn a dotted line indicating where they share a side.
From here we find the area of each shape seperately and add those areas together!
Rectangle:
Looking at the rectangle portion we can see that the width is 16 in and the length is 19 inches. Don't be fooled by the long 30 inch side. Remember, we are only looking at the portion that makes up the rectangle.
A = l*w = 16*19 = 304 inches squared
Triangle:
To find the area of the triangle, we use the formula A = (b*h)/2 where b = the length of the base and h = the height.
We can see in this attatched drawing that the height of the triangle is the same length as the width of the rectangle which is 16 inches.
To find the base, you can do one of two things.
1) use the pythagorian theorem (A^2 + B^2 = C^2) to solve for the missing side of the right triangle, where A is 16 inches, B is unknown and C is 19.4 inches.
2) *easier* using the information given, we can see that the longest side of this shape is 30 inches and is made up of the length of the rectangle (19 inches) and the base of the triangle (which is unkown - we can call it x)
Given that we know the total length and the length of the portion that belongs to the rectangle, we can say x = 30-19 = 11. Therefore the base of the rectangle is 11 inches.
From here we use b*h/2
11*16/2 = 88 = area of the triangle in square inches.
Now for the easy part - add up the areas for the total!
Area (rectangle) + Area (triangle) = Area (total)
304 + 88 = 392 square inches
In a basketball game, you made 4 baskets out of 12 attempts. Your teammate made 3 baskets out of 8 attemps
Answer:
4/12 and 3/8
Step-by-step explanation:
Mr. Jones has a cylindrical water storage
tank. The tank has a diameter of 6 feet and
a height of 12 feet. Mr. Jones wants to
paint the tank but since the tank rests on a
concrete slab, he will not need to paint the
bottom of the tank. How much paint will
he need to paint the water storage tank?
Answer:
254.47sqft (square feet) of paint
Step-by-step explanation:
The surface area of the cylinder (282.74) minus the area of the one circle that doesn't need to be painted (28.27) is 254.47sqft which is the amount of paint he will need Mr. Jones.
The number of students taking algebra increased 20% in one year. If
60 students are taking algebra this year, how many took algebra last
year?
Answer: 50 students
Step-by-step explanation:
You know that the number of students last year plus 20% of that number equals the number of students this year, which can be written as: x + 0.2x = 60 →
1.2x = 60 → x = 50 students :)
Answer: 50 students
Step-by-step explanation:
x + .2x = 60
1.2x = 60
x = 60/1.2
x = 50
This one is hard! try your best please.
A box contains 9 identical glass spheres that are used to make snow globes. The spheres are tightly packed, as shown below.
Answer:
1. 301.6 [tex]in^{3}[/tex]
2. 576 [tex]in^{3}[/tex]
3. 274.41 [tex]in^{3}[/tex]
Step-by-step explanation:
We know that the diameter of one of the spheres must be 4 in, because the length of the box is 12 in and there are 3 spheres along each side, and [tex]\frac{12}{3} =4[/tex]. That means that the radius of a sphere is 2 in. Put 2 into the formula for the volume of a sphere, and then multiply your solution by 9, to get the total volume.
Then, you can find the volume of the box, because you know its dimentions are 12x12x4.
Subtract your answer for part 1 from your answer for part 2, and you have the solution to part 3. Hope this helps!! :-)
6 , 9 , 12 , . . . 6,9,12,... Find the 34th term. Find the 34th term.
Answer:
105
Step-by-step explanation:
nth term=a+(n-1)d (a=first term,d=difference)
a=6,d=9-6=3
34th term=6+(34-1)3
=6+(33×3)
=6+99=105
look figure and give exact answer.
Answer:
Those two lines are equal
Can someone please help me with this? I need to turn it in tomorrow and I don't understand what to do.
Answer:
Step-by-step explanation:
Slope intercept form
y + 7 = 3(x + 4) Change all the double minuses to pluses.
y + 7 = 3x + 12 Remove the brackets.
y + 7 - 7 = 3x + 12-7 Subtract 7 from both sides
y = 3x + 5
Slope
Whatever number is in front of the x is the slope Answer: 3
y intercept
Whatever comes after the plus sign (or minus sign) is the y intercept. It is a single number. Answer: 5
x intercept.
This occurs when y = 0
0 = 3x + 5 Subtract 5 from both sides
-5 = 3x + 5 -5
-5 = 3x Divide by 3
-5/3 = 3x / 3
-5/3 = x
Answer: x_intercept = -5/3
Finish the steps below to write a quadratic function for the parabola shown. use the vertex form, f(x) = a(x – h)2 k, and substitute in the values for h and k. f(x) = a(x – 5)2 3 use another point and substitute in values for x and f(x). solve for a. 5 = a(6 – 5)2 3 write the function, using the values for h, k, and a. the function is f(x) = (x – )2 .
The vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]
What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
Substitute the values for h and k in the above vertex form.
[tex]f(x) = a(x -5)^2+ 3[/tex]
Use another point and substitute in values for x and f(x). Solve for a.
[tex]5 = a(6 - 5)^2 +3\\5-3=a(1)\\a=2[/tex]
Rewrite the function, using the values for h, k, and a. The function is
[tex]f(x) = 2(x -5)^2+ 3[/tex]
Hence, the vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]
Learn more about the vertex form of the parabola here;
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Answer: 1st slot: 2 | 2nd slot: 5 | 3rd slot: 3 | correct on edge 2023!
Given f(x)=x^3+9x+k, and x-1 is a factor of f(x), then what is the value of k?
Answer:
r:
The function is
The remainder when f(x) is divided by x−2 is 23.
To find:The value of k.
Solution:
According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).
It is given that, the remainder when f(x) is divided by x−2 is 23. By using remainder theorem, we get
Put x=2, to find the value of f(2).Therefore, the value of k is 8.
Step-by-step explanation:
Write two different expressions that
represent the quantity x decreased
by 30%.
Answer:
Step-by-step explanation:
x - 30 = 14 - 3x
4x = 44
x = 11
Let's call the unknown number x
Now let's decrease it by 30, that is x-30
Now let's write out "14 decreased by three times the number", that is 14 - 3x
The problem says these are the same, that is x - 30 = 14 - 3x
We now want to isolate, or solve for, x
Move the x to one side of the equation by adding 3x to both sides
3x + x -30 = 14 - 3x + 3x
4x -30 = 14
Now move the 30 to the right hand side by adding 30 to both sides
4x - 30 + 30 = 14 + 30
4x = 44
Now all we have to do to get x is divide both sides by 4
4x/4 = 44/4
x = 11
Help me on this question please!
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
═════════════════════
[tex]x+5[/tex]
[tex]x^{1-1} [/tex]
[tex]x^{0} [/tex]
[tex] = 1 [/tex]
─────────────────────┈
[tex](2x + 3)[/tex]
[tex]2x^{1-1} [/tex]
[tex]2x^{0} [/tex]
[tex]2\times 1 [/tex]
[tex] = 2[/tex]
══════════════════════
Step-by-step explanation:
#Carry on learning
What is the answer to this question????
Answer:
Yes, its a linear function
Step-by-step explanation:
See, all the results here are one-one which means for a distinct input there will be a distinct output.
That's why its a linear function
Anita is 42 1/2 feet below jared. Steph is 67 3/7 feet above anita. What is stephs position compared to jared. Explain
Check the picture below.
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{42\frac{1}{2}}\implies \cfrac{42\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{85}{2}} ~\hfill \stackrel{mixed}{67\frac{3}{7}}\implies \cfrac{67\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{472}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{472}{7}~~ - ~~\cfrac{85}{2}\implies \cfrac{(2)472~~ - ~~(7)85}{\underset{\textit{using this LCD}}{14}}\implies \cfrac{944~~ - ~~595}{14}\implies \cfrac{349}{14}\implies 24\frac{13}{14}[/tex]
Given f(x) = 3x2 + kx – 7, and the remainder when f (x) is divided by x – 4 is
81, then what is the value of k?
Answer:
-243
Step-by-step explanation:
{3׳ykx-7 incluye
In each diagram shown below, solve for the length of side CD using the information given. Show the trig ratio you use and your algebra to find your final answer. Round all answers to the nearest tenth
Applying the trigonometry ratios, we have:
a. CD = 63.6
b. CD = 33.8
c. CD = 16.1
d. CD = 15.9
What are the Trigonometry Ratios?The trigonometry ratios are used to find a length or angle in any right triangle. They are:
SOH, which is sin ∅ = opp/hypCAH, which is cos ∅ = adj/hypTOA, which is tan ∅ = opp/adja. ∅ = 32°
hyp = 75
adj = CD
Apply CAH:
cos 32 = CD/75
CD = cos 32 × 75
CD = 63.6
b. ∅ = 56°
opp = 28
hyp = CD
Apply SOH:
sin 56 = 28/CD
CD = 28/sin 56
CD = 33.8
c. ∅ = 43°
opp = 15
adj = CD
Apply TOA:
tan 43 = 15/CD
CD = 15/tan 43
CD = 16.1
d. ∅ = 27°
hyp = 35
opp = CD
Apply SOH:
sin 27 = CD/35
CD = sin 27 × 35
CD = 15.9
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Angel had $21 to spend on two notebooks. After buying them he had $13 left. How much did each note book cost?
Answer:
each notebook would cost $4
Step-by-step explanation:
21-13=8. 8/2=4
Will choose Brainliest.
Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.
How many more cookies will Jessica have than Martha?
If x represents the number of cookies Jessica started with, complete the statements below.
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0
Jessica has at least
_ cookies more than Martha.
Answer:
Part A: [tex]x^2-30x+224\geq 0[/tex]
Part B: Jessica has at least 2 cookies more than Martha
Step-by-step explanation:
Since there are 2 question-
Let,
How many more cookies will Jessica have than Martha?If x represents the number of cookies Jessica started with, complete the statements below. Be Part A:
Let,
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0 Jessica has at least _ cookies more than Martha.
Be Part B:
Hint:
J=Jessica
30-J=Martha
(J-6)*((30-J)-6)<=80
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve:
Starting with Part A: Find the inequality that describes the relationship between the number of cookies each one of them has
Let,
"x" be the number of cookies when Jessica started
"30-x" be the number of cookies when Martha started
Given us that:
Each of them ate 6 cookies from their bag
Therefore,
Cookie left in each bag are:
(x-6) which is - Jessica
30 - x - 6 = (24 - x) - Martha
Solution - (x-6)(24-x)
The product of the number of cookies left in each bag is not more than 80.
Thus,
[tex](x-6)(24-x\leq 80[/tex]
[tex]24x-x^2-144+6x\leq 80[/tex]
[tex]-x^2+30x-144-80\leq 0[/tex]
[tex]-x^2+30x-244\leq 0[/tex]
[tex]\mathrm{Multiply\;by\;-1\;both\;sides}[/tex]
[tex]x^2-30x+224\leq 0[/tex]
Hence, Answer = [tex]x^2-30x+224\leq 0[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve:
Part B: Solve the quadratic equation:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:14\le \:x\le \:16\:\\ \:\mathrm{Interval\:Notation:}&\:\left[14,\:16\right]\end{bmatrix}[/tex]
[tex]\left(x-14\right)\left(x-16\right)\le \:0[/tex]
[tex]14\le \:x\le \:16[/tex]
The solution is x=16 cookies
Thus, (30-x)=30-16=14 cookies
Now we know that;
The number of cookies when Jessica started was 16 cookies
The number of cookies when Martha started was 14 cookies
So,
The number of cookies left in each bag is equal to
Jessica:
16-6=10 cookies
Martha:
14-6=8 cookies
10 > 8
As a result, Jessica has at least 2 cookies more than Martha.
Fill in blank for:
The inequality that describes the relationship between the number of cookies each one of them has is x^2 - __30__ x +224 >= 0.
Jessica has at least __2__ cookies more than Martha.
~Lenvy~
Which expressions are equivalent to Tan(< g
Answer:
Can u post a picture so I can see what your talking about!?
Zoe considers the lunch choices as she looks at the menu. What is the probability that she will choose cheese pizza, apple, milk?
Meal: Cheese Pizza, Cheeseburger, Hotdog, Salad
Side: Banana, Apple, Yogurt
Beverage: Milk, Water, Juice
Multiple choices:
1/10
1/21
1/12
1/36
Answer:
1/10
Step-by-step explanation:
There are ten options and Salad is one of them; therefore, the answer would be 1/10.
An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that apply.
Answer:
71° and 71°.⠀
Step-by-step explanation:
The triangle having two sides equal along with one different side is called an isosceles triangle.
⠀
So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.⠀
We know that,
The sum of all angles of a triangle is 180°⠀
So, According to the question :
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]
⠀
Therefore,
The measure of the two other angles of the isosceles triangle are 71° and 71°.for each pair of lines, determine whether they are parallel, perpendicular, or neither
x - 3y = 4
2x - 5y = 8
solve by substitution
Answer:
y = 0
x = 4
Explanation:
x - 3y = 42x - 5y = 8make x the subject,
x - 3y = 4
x = 4 + 3y __ equation 1
2x - 5y = 8
x = (8+5y)/2 __ equation 2
using substitution method:
(8+5y)/2 = 4 + 3y
8 + 5y = 8 + 6y
6y - 5y = 8 - 8
y = 0
Find x,
x = 4 + 3y
x = 4 + 3(0)
x = 4
Answer:
x = 4
y = 0
Step-by-step explanation:
Step 1. Pick one equation and rewrite in the form of x= OR y=x - 3y = 4 (original)
x = 4 + 3y (rewritten)
Step 2. Substitute for x in the other equation2x -5y = 8 (second equation)
2(4 + 3y) - 5y = 8 (substitute 4 + 3y for x)
Step 3. Solve for the unknown variable, y2(4 + 3y) - 5y = 8 (distribute)
8 + 6y - 5y = 8 (combine like terms)
y = 0 (first variable)
Step 4. Find x by plugging y into an equationx - 3y = 4 (original)
x - 3(0) = 4 (substitute 0 for y)
x = 4 (second variable)
FINAL SOLUTION: x = 4, y = 0You can double check this by plugging these numbers back into each equation; x = 4 and y = 0 is true for both.
I hope this helps!
Solve the equation and enter the value of x below.
-3x-9=-27
x=
Answer:
6
Step-by-step explanation:
-3x=-27+9
-3x=-18
x=-18/-3
x=6
Answer:
[tex]\displaystyle 6 = x[/tex]
Step-by-step explanation:
[tex]\displaystyle -3x - 9 = -27 \hookrightarrow \frac{-3x}{-3} = \frac{-18}{-3} \\ \\ x = 6[/tex]
I am joyous to assist you at any time.
Solve the equation 4 ( c - 3 ) = 8
Answer:
c=5
Step-by-step explanation:
4(c-3)=8 Distribute
4c-12=8 Add 12 to both sides
4c=20 Divide by 4 on both sides
c=5
Answer:
c = 5Step-by-step explanation:
METHOD 1:
4(c - 3) = 8 |divide both sides by 4
4(c - 3)/4 = 8/4
c - 3 = 2 |add 3 to both sides
c - 3 + 3 = 2 + 3
c = 5
METHOD 2:
4(c - 3) = 8 |use the distributive property: a(b - c) = ab - ac
4 · c - 4 · 3 = 8
4c - 12 = 8 |add 12 to both sides
4c - 12 + 12 = 8 + 12
4c = 20 |divide both sides by 4
4c/4 = 20/4
c = 5
Number 5? Pre Cal- A small airplane is cruising at an airspeed of 235 kph heading in a direction of 45° (measured from the positive z-axis). The wind is blowing at 60kph in a direction of 120°. Find the resulting direction and groundspeed of the airplane to the nearest whole number.
Answer:
c
Step-by-step explanation:
c
How do solve this
h(x)=1/2x-14; h(4)
Answer:
-12
Step-by-step explanation:
h(x) = ½x - 14 where x = 4:
h(4) = ½(4) - 14
= 2 - 14
= -12
These cones are similar. find the surface
area of the smaller cone. round to the
nearest tenth.
2 cm
3 cm
surface area = [? ] cm2
surface area = 75 cm?
Answer:
33.3 is your answer
Step-by-step explanation:
The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Two cones A₁ and A₂ are similar.
The radius of A₁ = 2 cm
radius of A₂ = 3 cm
The surface area of A₁ = ? cm²
surface area of A₂ = 75 cm²
Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.
Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,
(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)
We can use this relationship to solve for the surface area of A₁:
(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)
Substituting the given values, we get:
(surface area of A₁) = (2/3)² × 75
(surface area of A₁) = 4/9 × 75
(surface area of A₁) ≈ 33.3 cm²
Therefore, (surface area of A₁) ≈ 33.3 cm²
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#SPJ7
24. generalize what are the attributes of fractions
that are equivalent to 100%
Answer:
when a fraction equals 100% it means it has the same numbers for its numerator and denominator such as 4/4 or 18/18
Step-by-step explanation:
When it has the same numbers for its numerator and denominator it will be 100%
how do I multiply 6ab (xa+ya^6 +8)
Answer:
6xba^2 + 6yba^7 + 48ab
Step-by-step explanation:
To do this, you have to multiply 6ab by each of the inside terms,
So you can write it out like this
6ab (xa + ya^6 + 8)
6ab(xa) + 6ab(ya^6) + 6ab(8)
Then you can simplify:
6xba^2 + 6yba^7 + 48ab
(When you multiply the same variable by itself, you turn it into an exponent)
For example x * x = x^2
Or x^4 * x^3 = x^7