Answer:
18
Step-by-step explanation:
For this problem, you have to look at the ratios of the corresponding sides.
Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18
Find the common ratio: 64, -16, 4, -1, ...
The common ratio of the given sequence is -1/4. In a geometric sequence, the common ratio is the value that is in between each number in the sequence.
What is the common ratio?The ratio of the value of a term in the sequence to the value of the previous term in the sequence is said to be the common ratio. I.e.,
C.R = (nth term)/(n - 1)th term
Calculation:The given sequence is 64, -16, 4, -1, ...
Taking the ratio of the second term to the first term, we get
-16/64 = -1/4
Similarly, the ratio of the third term to the second term,
4/16 = -1/4
Since the ratios are equal, then the common ratio of the sequence is -1/4.
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NO LINKS! Help me with this problem
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Equation of directrix is : y = 1, so we can say that it's a parabola of form : -
[tex]\qquad \sf \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]
h = x - coordinate of focus = -4k = y - coordinate of focus = 5a = half the perpendicular distance between directrix and focus = 1/2(5 - 1) = 1/2(4) = 2and since the focus is above the directrix, it's a parabola with upward opening.
[tex]\qquad \sf \dashrightarrow \: (x - ( - 4)) {}^{2} = 4(2)(y - 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: (x + 4) {}^{2} = 8(y - 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 8x + 16 = 8y - 40[/tex]
[tex]\qquad \sf \dashrightarrow \: 8y = {x}^{2} + 8x + 56[/tex]
[tex]\qquad \sf \dashrightarrow \: y = \cfrac{1}{8} {x}^{2} + x + 7[/tex]
Directrix
y=1Focus
(h,k)=(-4,5)Focus lies in Q3 and above y=1
Parabola is opening upwardsThen
Perpendicular distance
(5-1)=4Find a for the equation
a=4/2=2Now the equation is
[tex]\\ \rm\dashrightarrow 4a(y-k)=(x-h)^2[/tex]
[tex]\\ \rm\dashrightarrow 4(2)(y-5)=(x+4)^2[/tex]
[tex]\\ \rm\dashrightarrow 8(y-5)=x^2+8x+16[/tex]
[tex]\\ \rm\dashrightarrow 8y-40=x^2+8x+16[/tex]
[tex]\\ \rm\dashrightarrow 8y=x^2+8x+16+40[/tex]
[tex]\\ \rm\dashrightarrow 8y=x^2+8x+56[/tex]
[tex]\\ \rm\dashrightarrow y=\dfrac{x^2}{8}+x+7[/tex]
Please help solve this equation?
[tex]{ \red{ \bold{cos \: y \: }}}[/tex]
Step-by-step explanation:
[tex]{ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)[/tex]
But, as you know that
[tex]{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}} [/tex]
Then the equation (1) becomes
[tex]{ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \: [/tex]
Multiply Numerator and Denominator by [tex] \frac{cos \: y}{cos \: y} [/tex]
then,
[tex]{ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}} [/tex]
[tex] = { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}[/tex]
take cos y as common, then
[tex]{ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}[/tex]
Here, (1+cos y/cos y + 1) gets cancelled.
Then the remaining answer is cos y.
what is the greatest number that can divide 13,17 and 21 and have one as a remainder
Answer:
4
Step-by-step explanation:
this is the same question as what number can divide
13-1 = 12, 17-1 = 16 and 21-1 = 20 and has 0 remainder ?
the greatest number that can do that is 4.
we can easily see that, but formally, let's do prime factorization :
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 2 no
3 ÷ 3 = 1 finished
12 = 2×2×3
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1 finished
16 = 2×2×2×2
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 2 no
5 ÷ 3 no
5 ÷ 5 = 1 finished
20 = 2×2×5
so, the largest common factor is the combination of the longest streaks per factor they have in common.
they only have 2s in common.
and the longest common streak is 2×2 = 4.
hence the answer
Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measure.
m∠1=(50x−50)∘, m∠2=(20x+70)∘
Alt. Ext. ∠s Thm.
m∠1 = 130°, m∠2 = 130°
Same-Side Int. ∠s Thm.
m∠1 = 130°, m∠2 = 130°
Alt. Int. ∠s Thm.
m∠1 = 150°, m∠2 = 150°
Corr. ∠s Post.
m∠1 = 150°, m∠2 = 150°
The theorem used and the angle measures are:
D. corresponding angles postulate
m∠1 = 150°, m∠2 = 150°
What is the Corresponding Angles Postulate?According to the corresponding angles postulate, if two angles lie on same relative corner along a transversal that cuts two parallel lines (corresponding angles), then their measures are equal.
Thus, ∠1 and ∠2 are corresponding angles, therefore:
m∠1 = m∠2 [corresponding angles postulate]
Given the following:
m∠1 = (50x − 50)∘,
m∠2 = (20x + 70)∘
Therefore, we would have:
50x − 50 = 20x + 70
Subtract 20x from both sides
50x − 50 - 20x = 20x + 70 - 20x
30x − 50 = 70
Add 50 to both sides of the equation
30x − 50 + 50 = 70 + 50
30x = 120
Divide both sides by 30
30x/30 = 120/30
x = 4
Plug in the value of x
m∠1 = (50x − 50) = 50(4) − 50 = 150°
m∠2 = (20x + 70)∘ = 20(4) + 70 = 150°
Thus, the answer is: D. corresponding angles postulate
m∠1 = 150°, m∠2 = 150°
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What form is 950,000 in
Answer:
standard form
hope this helps! <3
A drink bottle is 3/8 full. It contains 240 millilitres of water. How much water does the bottle contain when it is half-full?
Answer: 320 mL
Step-by-step explanation:
Given information
The bottle is currently 3/8 full
Current Volume = 240 mL
Concept:
Imagine the water in the bottle being separated into 8 parts
Currently, 3 parts are being occupied
Determine the volume for 1 part
3 parts = 240 mL
1 part = 240 / 3 = 80 mL
Determine the volume for half-full (4 parts)
1 part = 80 mL
4 parts = 80 × 4 = [tex]\Large\boxed{320~mL}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The sum of three numbers is 100. The second number is 2 times the third. The third number is 8 less than the first. What are the numbers?
Answer:
Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)
Therefore,y=2z
z=x-8
y=2x-16
substituting the values of x,y and z into the question,we have
x+(2x-16)+(x-8)=100
Simplifying,we have
4x-24=100
adding 24 to both sides of the equation,
4x=100+24
4x=124
dividing both sides of the equation by the co-efficient of x,we have
4x/4=124/4
4.31=124
therefore,x=31.
Suppose you are in charge of setting up tables and ordering
appetizers and cookies for an awards dinner. The principal
expects 168 seventh-graders and 112 eighth-graders to attend
the dinner. Each grade will have dinner in a separate room.
1. Decide how many tables and how many chairs per table you will need, based on
the following criteria:
• No more than 15 tables in each room, and no more than 15
chairs per table.
• All tables in both rooms must have the same number of chairs.
Only 280 chairs can be ordered.
●
Answer: 10 tables in each room 14 kids at each table
A metallurgist has one alloy containing 26% copper and another containing 69% copper. How many pounds of each alloy must he use to make 53 pounds of a third alloy containing 50% copper?
The pounds of alloy that contains 26% copper that would be used is 23.42 pounds.
The pounds of alloy that contains 69% copper that would be used is 29.58 pounds.
What are the linear equations that represent the question0.26a + 0.69b = (53 x 0.5)
0.26a + 0.69b = 26.50 equation 1
a + b = 53 equation 2
Where:
a =pounds of alloy that contains 26% copperb = pounds of alloy that contains 69% copperHow many pounds of each alloy should be in the third alloy?Multiply equation 2 by 0.26
0.26a + 0.26b = 13.78 equation 3
Subtract equation 3 from equation 2
12.72 = 0.43b
b = 12.72 / 0.43
b = 29.58 pounds
a = 53 - 29.58 = 23.42 pounds
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19. At a boardroom meeting, the sales manager is happy to announce that sales have risen from $850,000 to $1,750,000 at a
rate of 4.931998% per year. How many years did it take for the sales to reach $1,750,000?
The number of years it would take sales to reach $1,750,000 is 14.65 years.
What is the number of years?The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:
Number of years : In (FV / PV) / r
Where:
FV = future level of sales - $1,750,000PV = present level of sales = 850,000r = rate of growth - 4.931998%Number of years : In ($1,750,000 / 850,000) / 0.04931998
Number of years : In (2.06) / 0.04931998
Number of years : 14.65 years
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Find the difference. Enter your answer in lowest terms in the box below as a
fraction, using the slash mark (/) for the fraction bar. 8/11 - 4/15
Answer:
76/165
Step-by-step explanation:
The difference of fractions can be found using the formula ...
a/b -c/d = (ad -bc)/(bd)
DifferenceUsing the given values in the formula, we have ...
[tex]\dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}[/tex]
Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.
The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.
Answer:
Step-by-step explanation:
76/165 is the answer
Can u guys please give me the correct answe
Answer:
35
Step-by-step explanation:
Since the two sides are equal in a parallelogram angle B = y ,so we have angle to be equal to 145°
We sum both angles and divide from
360° - [145° +145°]
360° - 290° = 70
Since the left sides( X And Z) are equal then we divide what we got into 2
70 ÷ 2 = 35
therefore angle X equals 35
An older person is 9 years older than four times the age of a younger person the sum of their ages is 24 find their ages
Step-by-step explanation:
let the younger person be x and older be y
4x + 9 = 24
4x = 15
x = 3.75
y = 24 - 3.75
y = 20.25
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
The factored form of the given quadratic expressions are
1. (x -1)(x +7)
2. (x -2)(x -3)
3. (x +1)(x -7)
4. (x -1)(x +6)
5. (x -3)(x +4)
6. (x +2)(x -4)
7. (x +1)(x -5)
8. (x -1)(x +3)
9. (x +4)(x -4)
10. (x +3)(x -4)
11. (x -3)(x -6)
12. (x +2)(x -7)
13. (x -2)(x -5)
14. (x -3)(x -8)
15. (x +5)(x -6)
Factoring quadratic expressionsFrom the question we are to factor the given quadratic expressions
1. x² + 6x - 7
x² +7x -x - 7
x(x +7) -1(x +7)
(x -1)(x +7)
2. x² -5x +6
x² -3x -2x +6
x(x -3) -2(x -3)
(x -2)(x -3)
3. x² -6x -7
x² -7x +x -7
x(x -7) +1(x -7)
(x +1)(x -7)
4. x² +5x -6
x² -x +6x -6
x(x -1) +6(x -1)
(x -1)(x +6)
5. x² + x - 12
x² +4x -3x -12
x(x +4) -3(x +4)
(x -3)(x +4)
6. x² -2x -8
x² -4x +2x -8
x(x -4) +2(x -4)
(x +2)(x -4)
7. x² -4x -5
x² -5x +x -5
x(x -5) +1(x -5)
(x +1)(x -5)
8. x² + 2x - 3
x² +3x -x -3
x(x +3) -1(x +3)
(x -1)(x +3)
9. x² - 16
(x +4)(x -4)
10. x² -x -12
x² -4x +3x -12
x(x -4) +3(x -4)
(x +3)(x -4)
11. x² -9x +18
x² -6x -3x +18
x(x -6) -3(x -6)
(x -3)(x -6)
12. x² -5x -14
x² -7x +2x -14
x(x -7) +2(x -7)
(x +2)(x -7)
13. x² -7x +10
x² -5x -2x +18
x(x -5) -2(x -9)
(x -2)(x -5)
14. x² -11x +24
x² -8x -3x +24
x(x -8) -3(x -8)
(x -3)(x -8)
12. x² -x -30
x² -6x +5x -30
x(x -6) +5(x -6)
(x +5)(x -6)
Hence, the factored form of the given quadratic expressions are
(x -1)(x +7)
(x -2)(x -3)
(x +1)(x -7)
(x -1)(x +6)
(x -3)(x +4)
(x +2)(x -4)
(x +1)(x -5)
(x -1)(x +3)
(x +4)(x -4)
(x +3)(x -4)
(x -3)(x -6)
(x +2)(x -7)
(x -2)(x -5)
(x -3)(x -8)
(x +5)(x -6)
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phoebe needs to use 3/4 cups of sugar to make one batch of cookies. how many batches can she make with 12 cups of sugar?
Answer:
16 batches
Step-by-step explanation:
we can divide 12 by 3/4 or 0.75: 12/0.75 = 16
Derive Integral equation for dy/dv
By the fundamental theorem of calculus,
[tex]\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}[/tex]
In general,
[tex]\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}[/tex]
what is 4,928 will rounded to the nearest hundred
Answer:
The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).
---
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How many milliliters are contained in 3 liters of fluid?
Answer:
3000Step-by-step explanation:
1 liter = 1000 milliliters
so
3 liters = 3000 milliliters
------------------------
1 : 1000 = 3 : x
x = 3 * 1000 : 1
x = 3000
Answer: 3000 mL
Step-by-step explanation:
1 L = 1000 mL
3x1000 = 3000
Bluff is at a hardware store trying to decide what brand of wood glue to buy for his carpentry project 11. Ounces of Orangutan wood glue cost $5.99
Answer:
yes
Step-by-step explanation:
yes
A glass inform of frustrum of cone
The volume of the cone illustrated will be 117.2 unit³.
How to illustrate the information?From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.
It should be noted that the volume of a cone is calculated as:
= 1/3 πr²h.
where,
π = 3.142
r = radius = 4cm
h = height = 7cm
In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:
= 1/3πr²h
= 1/3 × 3.14 × 4² × 7
= 117.2 unit³
Therefore, the volume of the shape is 117.2 unit³.
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Complete question:
A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.
Find all of the zeros for f(x).
f(x) = 6x³ + 25x² + 2x − 8
Arrange your answers from smallest to largest.
(-4, 0)
(-0.667, 0)
(0.5, 0)
Please help!
Express the area of the region bounded by the x-axis, y = 1/2x - 2 and y equals the cubed root of x, using definite integrals.
The integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2
How to integrate between two curves?
We are given the functions as;
y = ¹/₂x - 2
y = ∛x
Now, from the graph the coordinate of the point where both curves intersect is at; (8, 2)
Thus, the x-coordinate here is x = 8
∛x - (¹/₂x - 2)
∛x - ¹/₂x + 2
Similarly, another point of intersection of both curves is at the coordinate (0, -2). Thus, the x-coordinate here is; x = 0
Thus, the integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2
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|x - 1| > 4 is equivalent to which of the following?
a. -3 < x < 5
b. x > 5
c. x > 5 or x < −3
d. x < 5
*show your work*
Answer:
C. x > 5 or x < - 3
Step-by-step explanation:
|x - 1| > 4Step 1:
x - 1 > 4
x > 4 + 1
x > 5
Step 2:
x - 1 < -4
x < -4 + 1
x < -3
HP: {x > 5 or x < -3} (c)
given the quadriatic equation
x² + 6x + 9 = 4kx
find the set values for which k has real roots
Answer:
⇒ The given quadratic equation is x2−kx+9=0, comparing it with ax2+bx+c=0
∴ We get, a=1b=−k,c=9
⇒ It is given that roots are real and distinct.
∴ b2−4ac>0
⇒ (−k)2−4(1)(9)>0
⇒ k2−36>0
⇒ k2>36
⇒ k>6 or k<−6
∴ We can see values of k given in question are correct.
f(x)=x3 −4x even odd or neither
Answer:
The function would be odd
The answer is neither.
Let's take an odd number and substitute.
f(3) = 3³ - 4(3)f(3) = 27 - 12f(3) = 15 (odd)Now, let's take an even number.
f(4) = 4³ - 4(4)f(4) = 64 - 16f(4) = 48 (even)Since both even and odd numbers are possible, it is neither.
Enter the letter for the function graphed
below.
1
a) y = √x - 5
b) y = √x-5
c)y = 5-√√x
d) y = √x + 5
e) y = √x + 5
The letter for the graphed function is y = √(x) - 5
How to determine the letter for the graphed function?The parent function is given as:
y = √x
From the graph, we can see that the function is shifted downwards by 5 unts
This is represented as:
y = √(x) - h
Where h = 5
Substitute the known values in the above equation
y = √(x) - 5
This means that the letter for the graphed function is y = √(x) - 5
Hence, the letter for the graphed function is y = √(x) - 5
So, the complete functions are
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Give that m/_ y=39, find the measures of angles a and b
Answer:
∠a = 39°
∠b = 129°
Step-by-step explanation:
Vertical angles are congruent. An exterior angle of a triangle is equal to the sum of the remote interior angles.
ApplicationAngle y and angle 'a' are vertical angles, so congruent.
∠a = ∠y = 39°
The angle marked 'b' is an exterior angle to the triangle. Its remote interior angles are 'a' and the one marked 90°.
∠b = ∠a +90° = 39° +90°
∠b = 129°
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\longrightarrow\bold{m<a= \: 39}[/tex] ✓[tex]\longrightarrow\bold{m<b= \: 141}[/tex]In the given figure, angles a and y are vertically opposite angles. The measure of vertical angles is equal, therefore :-
[tex]\small\longrightarrow\sf{m<a = m<y}[/tex]
[tex]\small\longrightarrow\sf{m<a= \: 39^\circ}[/tex]
Next, angles a and 90° are the opposite interior angles to the exterior angle b. By the triangle theorem below :-
[tex]\small\longrightarrow\sf{m<b=m<a+90^\circ}[/tex]
[tex]\small\longrightarrow\sf{39^\circ+90^\circ}[/tex]
• [tex]\small\longrightarrow\sf{m<b= 129^\circ}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
m<a= [tex]\large\sf{\boxed{\sf 39^\circ}}[/tex]
m<b = [tex]\large\sf{\boxed{\sf 129^\circ}}[/tex]
f(x)=2x-6 Match each transformation of f(x) with its description
The transformation of the function is illustrated below
How to match the transformation?Parent function is: f(x) = 2x - 6
Transformations are:
shifts f(x) 4 units down
f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10
stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24
shifts f(x) 4 units right
f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14
compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6
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Captain's Autos sells 22 used cars on
Monday, and 18 cars on Tuesday. This was
25% of the number of sales for the week.
How many cars did they sell altogether that
week?
Answer:
160
Step-by-step explanation:
22+18=40, and this was 25% of the cars.
So, 40(4)=160 cars were sold that week.
The number of cars Captain's Autos sold in total that week is 160.
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Number of used car on monday= 22
Number of cars on tuesday= 18
Now,
Let's call the total number of cars sold during the week "x".
We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:
22 + 18 = 0.25x
Simplifying, we get:
40 = 0.25x
Dividing both sides by 0.25, we get:
x = 160
Therefore, by the unitary method the answer will be 160.
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