Can the sides of a triangle have lengths 13, 5, and 16?
Answer:
Yes
Step-by-step explanation:
13 + 5 > 16
16 - 3 < 5
Yes :D
Which graph shows a function where f(2)= 4?
From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.
Equation of quadratic graphA quadratic graph is in form of a parabola opened upward or downward.
According to the question, we are to select a graph that has a coordinate (2, 4) on its curve.
To determine thus, we will locate the value of 2 on the x-axis and value of 4 on the y-intercept and trace whether the intersecting point is on the curve.
From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.
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Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x squared over 10 equals 1 y squared over 10 minus x squared over 15 equals 1 x squared over 10 minus y squared over 40 equals 1 x squared over 10 minus y squared over 15 equals 1
The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
How to determine the equation of the hyperbola?The given parameters are:
Directrices at x = ±2 Foci at (5, 0) and (−5, 0)The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
[tex]\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1[/tex]
Evaluate
[tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
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Three teams, A, B and C, play in a competition.
games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 10 games.
In total, how many games have the three teams won?
Answer:
47.5 games
Step-by-step explanation:
Finding A :
⇒ Games by A : Games by B = 3 : 1
⇒ Games by A : 10 = 3 : 1
⇒ Games by A = 30
==============================================================
Finding C :
⇒ Games by B / Games by C × Games by A / Games by B = 3 × 4/3
⇒ Games by A / Games by C = 4
⇒ Games by C = 30/4
⇒ Games by C = 7.5
==============================================================
Total games won :
⇒ Games by A + Games by B + Games by C
⇒ 30 + 10 + 7.5
⇒ 47.5 games
If you invest $18000 at an interest rate of 6.7%, compound quarterly, find the time needed for your investments to be worth $23,000
It will take approximately 5.5 years for the investment to be worth $23,000
Compound interestFrom the question, we are to determine when the investments will worth $23,000
Using the compound interest formula,
[tex]A = P (1+\frac{r}{n})^{nt}[/tex]
Where A is the amount
P is the principal
r is rate
n is the number of times it is compounded
and t is the time in years
From the given information,
A = $23000
P =$18000
r = 6.7%
n = 4
t = ?
Putting the parameters into the formula, we get
[tex]23000 = 18000(1+\frac{6.7}{100 \times 4})^{4t}[/tex]
[tex]\frac{23000}{18000} = (1.01675)^{4t}[/tex]
[tex]1.4375= (1.01675)^{4t}[/tex]
[tex]1.4375 = (1.0687)^{t}[/tex]
t = 5.46
t ≅ 5.5 years
Hence, it will take approximately 5.5 years for the investment to be worth $23,000
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If 8^y = 16^y+w, what is the value of Y?
Quincy's retirement party will cost $30 if he invites 10 guests. If there are 16 guests, how much will Quincy's retirement party cost? Solve using unit rates.
Answer:
$48
30/10 is equal to 3/1, 16 x 3 equals to 48.
Answer:$48
Step-by-step explanation:
$30/10p = $3 per person
3x6=18
18+30=48
Tony is interested in the favorite activities of the students in his school. He surveys all the members of the school's chess club. Did Tony survey a random sample of all the students in the school? Explain.
Suppose that y varies directly with x and inversely with z, and y = 4 when x = 8 and z = 14. find z when x = 36 and y = 6. first, what is the equation of variation? y =
The value of z if x = 36 and y = 6 is 42
Direct and inverse variationSuppose that y varies directly with x and inversely with z, hence the required expression will be:
y = kx/z
If y = 4 when x = 8 and z = 14 then;
4 = k(8)/14
8k = 56
k = 7
To find z when x = 36 and y = 6, we will have:
6 = 7(36)/z
1 = 7(6)/z
z = 42
Hence the value of z if x = 36 and y = 6 is 42
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Answer:
Keep it simple. Answer:
y=kx/z
k=7
z=42
Step-by-step explanation:
can someone help me find the answer for this?
Answer for number 1: d and w, or C.
Step-by-step explanation:
because the corner of d and w both are corners of an angle, obtuse. obtuse angles look like this = \_ or _/. the d and w are in those corners
HURRY I NEED IT FAST
15 POINTS
Solve: 3(4-2x)= -x+1 A.x=11/5 B.x=13/5 C.x=-11/7 D. x = 11
Answer:
A) x = [tex]\frac{11}{5}[/tex]
Step-by-step explanation:
3(4 - 2x) = -x + 1
Distribute on the left:
12 - 6x = -x + 1
+ x + x
12 - 5x = 1
- 12 - 12
-5x = -11
Divide both sides by -5 to get x on its own:
x = [tex]\frac{-11}{-5}[/tex]
OR
x = [tex]\frac{11}{5}[/tex]
Have a nice day!
The area of a circle is 18.31cm2.
find the length of the radius rounded to 2 dp.
Answer:
Step-by-step explanation:
The median of the data shown on the graph is
Answer:
Median 39,000
Step-by-step explanation:
If im lookng at this right the numbers are:
20,000, 25,000, 35,000, 39,000, 41,000, 48,000, 53,000
The middle number is:
20,000, 25,000, 35,000, 39,000, 41,000, 48,000, 53,000
Tell me if im wrong
A monument in the shape of a square pyramid was built in a park.
The four lateral faces of the pyramid will be painted. The cost and coverage information for regular paint and metallic paint are shown in the table. Both paint types will be used on the monument.
PAINT TYPE COST(dollars per gallon) GALLONS(sq ft per gallon)
regular $35 200
metallic $100 80
The regular paint will require 2 coats, and the metallic paint will require 1 coat. Both paint types are sold only by the gallon. Based on the table, what is the least amount of money that should be budgeted to paint the monument?
The least amount of money that should be budgeted to paint the monument is $1692.
Least amount of money that should be budgetedFirst step
Using Pythagorean theorem to find the surface area
Since POR is a right triangle
Hence:
PO=20
BR=12
OR=12
PR=√20²+12²
PR=400+144
PR=544
Area of PBC=1/2×24×√544
Area of PBC=12√544
Lateral surface area=4×12√544
Lateral surface area=48√544
Lateral surface area=1119.54²ft
Second step
Since regular paint is 2 coats 200 sq. ft per gallon
Hence:
Number of gallons=1119.54×2/200
Number of gallons= 11.2 gallons
11.2×35= 392
1119.54/80=13 gallons
13×100 =1300
Last step
Least amount=392+1300
Least amount= $1692
Therefore the least amount of money that should be budgeted to paint the monument is $1692.
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Which expression is equivalent to 3(8 + 7)?
Answer:
3 • 15
Step-by-step explanation:
Add 8 and 7 to factor out the equation, creating an equivalent expression.
Your friend Dave has an obsession with hats! The only problem - it's an expensive habit but Dave doesn't seem to think so. You want to help show him exactly how much he is spending on hats. Each hat Dave buys costs \ (\$281). Write an expression to represent the total amount Dave spends on hats (\(h\)).
Answer:
281x
Step-by-step explanation:
each hat (x) cost 281. x times cost is total
Suppose a bag contains 5 blocks. 3 red, 1 yellow and 1 green. what is the probability of selecting a red block?
answer is 3/5
since there are 3 red, there is a 3 blocks out of 5 blocks chance that a red block will chosen
Are the equations 18=3x-6+x and 18=4x-6 equivalent?
Answer:
Yes, they are equivalent
Step-by-step explanation:
18 = 3x - 6 + x
+6 +6
24 = 3x + x
24 = 4x
24/4 = 4x/4
6 = x
18 = 4x - 6
+6 +6
24 = 4x
24/4 = 4x/4
6 = x
Both equations are equal to x = 6, therefore they are equivalent
Answer:
Yes
Step-by-step explanation:
18 = 3x - 6 + x
x = 1x
Combine like terms
3x + 1x = 4x
18 = 4x - 6 and 18 = 4x - 6
They are equivalent.
(4-x)/(x^2-5x+4)+(2)/(x-1)=1
show all steps please!!
Answer:
[tex]x = 2, 4[/tex]
Step-by-step explanation:
Given :
[tex]\frac{4-x}{x^{2} -5x+4} + \frac{2}{x-1} =1[/tex]
=============================================================
Factorize the denominator of the first term :
⇒ x² - 5x + 4
⇒ x² - x - 4x + 4
⇒ x(x - 1) - 4(x - 1)
⇒ (x - 4)(x - 1)
============================================================
Hence, the equation now is :
[tex]\frac{4-x}{(x-1)(x-4)} + \frac{2}{x-1} =1[/tex]
============================================================
Multiply the second term by (x - 4) in the numerator and denominator :
[tex]\frac{4-x}{(x-1)(x-4)} + \frac{2(x-4)}{x-1(x-4)} =1[/tex]
============================================================
Combine the numerator of both terms and bring the denominator to the other side :
[tex]\frac{4-x+2(x-4)}{(x-1)(x-4)} = 1[/tex]
[tex]4 - x+2x-8 = x^{2} - 5x + 4[/tex]
[tex]x - 4 = x^{2} - 5x + 4[/tex]
[tex]x^{2} -5x-x+4+4=0[/tex]
[tex]x^{2} -6x+8=0[/tex]
[tex](x-4)(x-2)=0[/tex]
[tex]x = 2, 4[/tex]
what are the ways to determine if a relation is a function? select EACH correct answer
Answer:
the two selected are correct.
Step-by-step explanation:
A relation is a function only if it relates each element in its domain to only one element in the range. When you graph a function, a vertical line will intersect it at only one point. You can determine whether each element of the domain is paired with exactly one element of the range. For example, if given a graph, you could use the vertical line test; if a vertical line intersects the graph more than once, then the relation that the graph represents is not a function. The best way to find out whether an equation represents a function or not is by graphing the equation and then applying the vertical line test. Graph the two-variable equation on graph paper. For a straight line this means graphing two or more points on the line and connecting the dots.
Find the value of y in 4y + 2x = 8 and 2x + 5y = 14.
Answer:
y = 6
Step-by-step explanation:
4y + 2x = 8 → (1)
5y + 2x = 14 → (2)
subtracting (1) from (2) term by term will eliminate x
y + 0 = 6
y = 6
Make x the subject of the formula. y=(x-4)2+6 p.s the two is square
[tex]~~~~~~~~y = (x-4)^2 +6\\\\\implies (x-4)^2 = y-6 \\\\\implies x -4 = \pm\sqrt{y-6}\\\\\implies x = \pm\sqrt{y-6} +4[/tex]
Exponential form of 5670
Answer:
The exponent form of 5670 is 5.67 × 103.
Step-by-step explanation:
you can also use this
it's pretty easy
https://calculator.name/decimal-to-scientific-notation/5670
What are the x-intercepts of the following graph?
1
2 3 4
+
3
G
3
&
a. (0, 2) and (0, -2)
b. (0,4)
c. (2,0) and (-2, 0)
d. (1, 0) and (3, 0)
Answer:
c (2,0) and (-2,0) I hope ot helps
Select the best answer to the problem.
Which of the following has the numbers in the right order?
A. 2, 5, 9, 7
B. 3, 5, 9, 12
C. 5, 8, 6, 10
D. 6, 9, 14, 12
Over what interval is the function in this graph constant?
W
OA. -3≤x≤2
OB. -4sxs-2
OC. -2≤x≤3
OD. -5≤x≤5
The function in this graph is constant in the range of -4 ≤x≤-2 , Option B is the correct answer.
What is a function ?A function is a mathematical statement which identifies relation between independent and dependent variable.
A graph is given
The graph will be considered constant when the y value is constant for any value of x
The value of y is constant in the range of
-4 ≤x≤-2
Therefore Option B is the correct answer.
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A fish tank is three-fourths full.
One-third of the water leaks out.
How full is the fish tank now?
Answer: [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
We will subtract the amount of water that leaked out from the amount of water originally in the fish tank.
[tex]\displaystyle \frac{3}{4} - \frac{1}{3} =\frac{3*3}{4*3} -\frac{1*4}{3*4} =\frac{9}{12} -\frac{4}{12}=\frac{5}{12}[/tex]
The fish tank is [tex]\frac{5}{12}[/tex] of the way full.
Translate the shape A four squares right and two squares up.
What are the coordinates of the vertices of the image?
will award brainliest to correct answer
Answer:
(5, 6)
Step-by-step explanation:
The original coordinate is (1, 1) (3, 1) (1, 4)
Translate four squares : (5, 1) (7, 1) (5, 4)
Translate two squares up: (5, 3) (7, 3) (5, 6)
The vertices of the image is (5, 6)
If the sales price is 55.50, and the discount is 75%, what is the original price
Answer:
£74
Step-by-step explanation:
£55.50 = 75%
Find 1% of discounted price by dividing both sides by 75 :
£0.74 = 1%
Using 1%, multiply by 100% to find original price :
£74 = 100%
Check our answer :
£74 × 0.75 (75%) = £55.50 ✅
Hope this helped and brainliest please
Answer:
the original price is 416.25. because you take the 55.50 and times ... percent of discount is 75%, sale price is 55.50
Step-by-step explanation:
5. janelle got invited to a shopping spree with a friend and is supposed
to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,
she has noticed that it takes about two hours for her to travel to the mall.
she has also noticed that it takes her 30 minutes
to get ready before leaving her apartment. she concludes that she
needs to start getting ready at 0:30 p.m. this is an example of what?
inductive reasoning or deductive reasoning?
The given example is inductive reasoning.
What is inductive reasoning?The method of arriving at a conclusion based on a series of observations is known as inductive reasoning. It is not a valid method of proof in and of itself.
We have the information that. Janelle got invited to a shopping spree with a friend and is supposed to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,
she has noticed that it takes about two hours for her to travel to the mall. she has also noticed that it takes her 30 minutes to get ready before leaving her apartment. she concludes that she needs to start getting ready at 0:30 p.m.
The given information is giving us the series of the data like we are having a sequence of the timing at what time what she did so we have a series of observations here.
Therefore the given example is inductive reasoning.
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