Answer:
Radius is half the diameter of a circle
Step-by-step explanation:
If the diameter was 6, then the radius is 3
Due to unexpected circumstances, you take out a loan for $5,000 to pay for a lawyer. You agree to pay it back over the next 5 years at a rate of 22.5% (because your credit score is really really low). At the end of the 5 years, how much did this "unexpected circumstance" end up costing you in all?
9 A book publishing company selected 30 out of 50 books submitted for publishing.
What decimal is equivalent to the fraction of books selected for publishing?
Answer:
Step-by-step explanation:
30/50= 3/5= 0.6
A computer technician charges $190 for a 3-hour appointment and $370 for a 7-hour appointment. Which of these represents a linear function that models the charge for hiring the technician for x hours?
A y = 55x + 190
B y = 55x + 45
C y = 45x + 190
D y = 45x + 55
Answer:
D. y = 45x + 55
Step-by-step explanation:
If a computer technician charges $190 for a 3-hour appointment and $370 for a 7-hour appointment, we can say that;
when c1 = $190, t1 = 3
when c2 = $370, t2 = 7
c is the amount charged
t is the time taken
First thug is to get the slope;
slope = c2-c1/t2-t1
slope = 370-190/7-3
slope = 180/4
slope = 45
Next is to get the intercept by substituting m = 45 and (190, 3) into the standard form of the equation y = mx+c as shown;
190 = 45(3)+c
190 = 135+c
c = 190-135
c = 55
Substitute into the standard form of the equation;
y = mx+c
y = 45x + 55
Hence option D is correct
Use the given information to write the equation of the parabola.
Vertex: [tex](0,0)[/tex]
Focus: [tex](0,-\dfrac{1}{2})[/tex]
Answer:
x² = -2y
Step-by-step explanation:
The focus is p away from the vertex, and so is the directrix.
To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.
Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)Vertical parabola [Standard form]: (x – h)² = 4p(y – k)If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).
Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).
For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).
You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).
If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.
Now we can just plug in our known information to derive the equation!
h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →
(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →
x² = -2y.
Also p = 1/4a, if you are wondering.
So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.
Answer:
[tex]\boxed {\boxed {\sf x^2=-2y}}[/tex]
Step-by-step explanation:
First, plot the two points. We can see the focus is below the vertex. The result will be a vertical parabola. Since the parabola must contain the focus, it will have to open downward.
From this information, we know that the following equation must be used:
[tex](x-h)^2=-4p(y-k)[/tex]
where (h,k) is the vertex and p is the distance from the focus to the vertex.
Next, find p, the distance between the focus and vertex. We can use the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The vertex is (0,0) and the focus is (0, -1/2). Therefore:
[tex]x_1=0\\y_1=0\\x_2=0\\y_2= -1/2[/tex]
[tex]d=\sqrt{(0-0)^2+(0--1/2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(0+1/2)^2}[/tex]
[tex]d=\sqrt{0+(1/2)^2}[/tex]
[tex]d=\sqrt{0+1/4}[/tex]
[tex]d=\sqrt{1/4}[/tex]
[tex]d=1/2[/tex]
Now we know the distance and vertex. We can plug the values into the equation.
d=1/2 and (h,k)= (0,0)
[tex](x-0)^2=-4(1/2)(y-0)[/tex]
[tex](x)^2=-2(y)[/tex]
[tex]x^2=-2y[/tex]
The equation of the parabola is x²= -2y
A and B are postive integers such that 1/a + 1/b +1/ab = 1. Find ab
Answer: ab =6
have:
[tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\<=>\frac{a+b+1}{ab}=1[/tex]
=> a + b + 1 = ab
⇔ a + b + 1 - ab = 0
⇔ b - 1 - a(b - 1) + 2 = 0
⇔ (b - 1)(1 - a) = -2
because a and b are postive integers => (b - 1) and (1 - a) also are integers
=> (b - 1) ∈ {-1; 1; 2; -2;}
(1 -a) ∈ {-1; 1; 2; -2;}
because (b -1).(1-a) = -2 => we have the table:
b - 1 -1 1 2 -2
1 - a 2 -2 -1 1
a -1 3 2 0
b 0 2 3 -1
a.b 0 6 6 0
because a and b are postive integers
=> (a;b) = (3;2) or (a;b) = (2;3)
=> ab = 6
Step-by-step explanation:
If Tina rode her bike at a constant rate for the first three hours, what was Tina's average calories burned, in calories per hour, between hour 0 and hour 3?
Answer: 400 calories per hour
Step-by-step explanation:
Q: Tina recorded the number of calories she burned during a bike ride. The graph shows Tina’s calories burned, y, after x hours. If Tina rode her bike at a constant rate for the first three hours, what was Tina’s average calories burned, in calories per hour, between hour 0 and hour 3?
Expalanation: It is seen from the graph that her rate of burning calories increased to 1200 in the first three hours of riding and then remained constant for the rest of the period (2 extra hours).
Her rate of calorie use therefore would be given as: (total calorie used up) / (total hours spent riding for the period of usage)
This is given as: 1200 calories / 3 hours = 400 calories per hour.
HELP ASAP! Relations and Functions!!! Giving brainliest!!!
Answer:
Step-by-step explanation:
Neither are a function because they do not pass the vertical line test.
What is the quotient of -3/8 And -1/3?
Answer:
Actually, I didn't get your question, is it -3/8÷ -1/3 or -1/3÷ -3/8?
If it is -3/8÷ -1/3, the answer will be 9/8
But if is -1/3÷ -3/8, the answer will be 8/9
Step-by-step explanation:
-3/8÷ -1/3
= -3/8× 3/-1
= -9/-8
= 9/8
If your question is -1/3÷ -3/8, the answer is 8/9 in the same way.
Solve for x: x+ 1/6 = 5/12
Answer:
x=3/12 or 1/4
Step-by-step explanation:
x + 1/6 = 5/12
x + 2/12 = 5/12
x = 3/12
converts to 1/4
Answer:
x= 1/4
Step-by-step explanation:
5/12- 1/6 = 1/4
4x-3=2x+7 solve the equation
Answer:
First collect like terms
4x-2x=7+3
6x=10
x=10/6
x=1.66666666667
x=1.67
Step-by-step explanation:
Please give me brainliest
When asked to write the domain for the equation y= |x - 6| + 3, Mary wrote the Domain is y < 3. What mistake(s) did Mary make? Write the correct domain for Mary using inequality notation. Explain to Mary how you found your answer.
Answer:
Ok, the domain is the set of values that we can input in a function.
In this case, we have:
y = Ix - 6I + 3.
Notice that there is no restriction here, x can actually take any value, then the domain will be the set of all real numbers.
The correct domain is x, x ∈ R
Now, if we had (for example) something like:
y = Ix - 6I < 3
Now we have a restriction in the domain because we can not have y equal or larger than 3.
To find the domain, we can break the absolute value:
Ix - 6I < 3
is equivalent to:
-3 < x - 6 < 3
now let's add 6 in each side.
-3 + 6 < x - 6 + 6 < 3 + 6
3 < x < 9
That will be the domain in that case.
The population of a city increases by 5% every year. If its population today is 300,000, what will its population be
in 2 years?
Answer:
330,750 people
Step-by-step explanation:
If the population increases by 5% every year, in 2 years the population of the city will be 330,750 people. D is also the correct answer as shown in the file.
Population after 2 year is 330,750
Growth rate problem:Given that;
Growth rate = 5% = 0.05
Current population = 300,000
Find:
Population after 2 year
Computation:
Population after 2 year = 300,000(1 + 0.05)²
Population after 2 year = 300,000(1.05)²
Population after 2 year = 330,750
Find out more information about 'Growth rate'.
https://brainly.com/question/13870574?referrer=searchResults
Maliah goes to an electronics store. Let y represent the price of a laptop and let z represent the price of a television. The equation
y=32 + 12 relates the prices.
Answer:
hi
Step-by-step explanation:
Molly is getting an early start on holiday shopping! She has $55.00 to spend on gifts. She first buys her mom a sweater for 17.50. She then found matching bracelets for her friends that cost $7.50 each. How many bracelets did she buy?
a) Write a let statement below to define your variable(s): *
b) Set up an equation using the variable you defined in (a): *
c) Solve your equation & Check. How many bracelets did Molly buy? JUST TYPE THE NUMBER. EXAMPLE: IF she bough 17 bracelets JUST TYPE "17" *
d) Upload a picture of your SOLUTION & CHECK. *
Plz help me anyone oi need help
Answer:
5
Step-by-step explanation:
55$-17.50=37.5
37.5/7.5=5
Please Help And Hurry!! (WORTH 20 POINTS)
Solve
5h – 15 + 7h = 40
(Sorry if this is easy I'm bad at math)
Step-by-step explanation:
h= 55/12 if thats what u askin for
5h – 15 + 7h = 40
To find?value of h
Explanation:[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]
[tex] :\implies \bold{5h + 7h = 40 + 15}[/tex]
[tex] :\implies \bold{12h= 55}[/tex]
[tex]:\implies \bold{h = \dfrac{55}{12} }[/tex]
[tex]:\implies\underline{\boxed{ \bold{h = 4.583}}}[/tex]
Verification:[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]
[tex]:\implies \bold{(5 \times 4.583) – 15 +( 7 \times 4.583)= 40}[/tex]
[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]
[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]
[tex]:\implies\underline{\boxed{ \bold{ 40= 40}}}[/tex]
Please HELP me!!!! I will mark as brainlist!!!
Answer:
4. CDB+DBE= CBE (55+35=90)
5. Definition of a right angle (90 degrees)
6. Linear pair postulate ( i think)
7. ABC and CBE are both 90 degrees
Step-by-step explanation:
1) Which of the following is NOT a property of reflection?
A)distance between points is preserved (stays the same)
B)angle measure is preserved (stays the same)
C)pre-image and image are congruent
D)orientation is preserved (stays the same)
Answer:
orientation is preserved (stays the same)
Step-by-step explanation:
9 3/4 as a percent step by step
Answer:
9 3/4 in a percent is 975%.
If you change 9 3/4 into a decimal, it will be 9.75, and 9.75 converted into a percent is 975%
How many solutions can be found for the equation 4x + 5 = 10? (4 points)
a. Zero
b. One
c. Two
d. Infinitely Many
Luis le dice a su amiga: "Yo tengo ahora el triple de edad que tú tenías, cuando yo tenía la edad que tú tienes ahora". Si entre los dos suman 50 años, ¿cuántos tiene cada uno?
Answer:
Luis tiene 30 años de edad y su amiga tiene 20 años edad.
Step-by-step explanation:
Cuando Luis tenia 20 años de edad (hace 10 años), su amiga tenia solamente 10 años de edad. Si multiplicamos 10 x 3 nos da como resultado 30, que es la edad actual de Luis.
L + A = 50
3(A - x) = L
L = 50 - A
3A - 3x = 50 - A
4A = 50 + 3x
en este punto podemos probar diferentes alternativas para x:
x = 5, entonces 4A = 50 + 15
A = 16.25 no es factible porque estamos buscando numeros enteros
x = 6, entonces 4A = 50 + 18
A = 17
al reemplazar, nos da una edad de 3(17 - 5) = 36 para Luis, pero 36 + 17 = 53
x = 8, entonces 4A = 50 + 24
A = 18.5 no es factible porque estamos buscando numeros enteros
x = 10, entocnes 4A = 50 + 30
A = 20
al reemplazar, nos da una edad de 3(20 - 10) = 30 para Luis, y 30 + 20 = 50
Simplify this fraction (multi choice)
What is the slope of a line that is perpendicular to the graph of y = 4/5x+9?
Answer:
m = -5/4
General Formulas and Concepts:
Algebra I
The slope of the perpendicular line is the negative reciprocal of the original slope.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope-Intercept Form (Original): y = 4/5x + 9
Step 2: Break Original Function
Slope m = 4/5
y-intercept b = 9
Step 3: Find slope of perpendicular line
Take the negative reciprocal.
Perpendicular Slope m = -5/4
Please help asap
25m^2+30m-30m-36
Answer:
(5m+6) (5m-6)
Step-by-step explanation:
That's how you factor it since +30 and -30 cancel out
What is the solution to this system of linear equations?
y − x = 6
y + x = −10
A. (−2, −8)
B. (−8, −2)
C. (6, −10)
D. (−10, 6)
Thank you if you can help me!
What does the graph of the function represent
PLEASE HELP ILL GIVE BRAINLIEST!!!!
Answer:
The first one is x=45
The second one is w=14
The third one is x=6
Step-by-step explanation:
Function 1: Alan starts with $30 this week. He spends $5.30 per week. Let y be the amount remaining as a function of the number of weeks, X. 0 30 1 24.70 2 19.40 3 14.1
Answer:
y = 30 - 5.30x
Step-by-step explanation:
y-intercept: 30
slope: 5.30x
Just plug in the amount of weeks on x, and then subtract from 30.
Use the substitution method to solve the system of equations. Choose th correct ordered pair. y = 8x - 4 x = 4 A. (2. 12) OB. (4, 28) C. (4, 4) D. (2.4)
9514 1404 393
Answer:
B. (4, 28)
Step-by-step explanation:
Substitute the value of x into the first equation. This gives you the value of y.
y = 8x -4x = 4After substitution, we have ...
y = 8(4) -4
y = 28
Then the point is (x, y) = (4, 28).
The figure is cut into 6 equal pieces. shade 2/3 of the figure
Answer:
you need to shade 4/6
Step-by-step explanation:
White any four rational numbers having the denominator 2 or power of
2. then express them in decimals. Are the decimals always terminating?
While the remarks of your investigation.
9514 1404 393
Answer:
1/2 = 0.53/16 = 0.18755/64 = 0.0781257/2048 = 0.00341796875yesStep-by-step explanation:
A terminating decimal has an equivalent denominator that is a power of 10. That is, it is the product of a power of 2 and a power of 5.
Any fraction that has a denominator that is a power of 2 can be expressed as an equivalent fraction with a power of 10 as the denominator.
Example:
[tex]\dfrac{7}{2048}=\dfrac{7}{2^{11}}=\dfrac{7\cdot5^{11}}{2^{11}\cdot5^{11}}=\dfrac{7\cdot5^{11}}{10^{11}}=0.00341796875[/tex]
hope this helps.enjoy!!!!!!