Answer:
Infinitely many solutionsStep-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-3y=15\\3x-9y=45\end{array}\right\\\\\text{Divide both sides of the second equation by 3}\\\\\dfrac{3x}{3}-\dfrac{9y}{3}=\dfrac{45}{3}\\\\x-3y=15\\\\\text{We received the same equation as the first.}\\\\\bold{CONCLUSION}\\\\\text{The system of equations has infinitely many solutions.}[/tex]
[tex]\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2x=c_2\end{array}\right\\\\\text{If}\ a_1=a_2,\ b_2=b_2,\ c_1=c_2,\ \text{then the system of equations}\\\text{ has infinitely many solutions}\\\\\text{If}\ a_1=a_2,\ b_1=b_2,\ c_1\neq c_2,\ \text{then the system of equations}\\\text{has no solutions}\\\\\text{Other the system of equations has one solution.}[/tex]
A population of bacteria doubles every 15 hours. initially, the population of bacteria is 40. What is the population of bacteria after 40 hours? Enter your answer, rounded to the nearest whole number, in the box.
The population of bacteria after 40 hours is 254
Step-by-step explanation:
Initial population of bacteria = 40
Growth rate: Doubles every 15 hours
The population function is given as:
[tex]P_t = P_0 * r^t[/tex]
Here
P0 is the initial population
r is the growth rate
and t is the time in hours
The growth rate will be: [tex]2^{\frac{t}{15}}[/tex]
Putting the values in the function
[tex]P_t = 40 * 2^{\frac{40}{15}}\\P_t = 40 * 2^{2.67}\\P_t = 40 * 6.34960...\\P_t = 253.98416...[/tex]
Rounding off to nearest whole number we get
P_t ≅254
Keywords: Population growth,, bacteria
Learn more about population growth at:
brainly.com/question/96882brainly.com/question/96535#LearnwithBrainly
From the information, the population of the bacteria will be 254.
Based on the information given, the population function will be:
= P × 2r
where, P = initial population of the bacteria
= 40 × 6.349
= 253.98
= 254
Therefore, it can be deduced that the population of the bacteria after 4 hours will be 254.
Learn more about equations on:
https://brainly.com/question/13763238
Solve the literal equation for y.
6x + 7zy = 15
Answer:
Step-by-step explanation:
6x + 7zy = 15
7zy = 15-6x
y = (15-6x)/7z
How many 3/4 are in 2
What fraction is located at point A on the number line?
The location of point A of the number line will be at 2 ¹/₃.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The section between the numbers 2 and 3 will be 3.
The location of point A is given as,
⇒ 2 + 1/3
Convert the expression into a mixed fraction number. Then we have
⇒ 2 + 1/3
⇒ 2 ¹/₃
The location of point A of the number line will be at 2 ¹/₃.
More about the number line link is given below.
https://brainly.com/question/13189025
#SPJ2
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{1}{4}[/tex] and c = - 1, thus
y = [tex]\frac{1}{4}[/tex] x - 1 → C
A sphere has a diameter of 10 in. What is the volume of the sphere?
V = StartFraction 125 Over 3 EndFraction inches cubed
V = StartFraction 500 Over 3 EndFraction inches cubed
V = StartFraction 500 Over 3 EndFraction pi inches cubed
V = StartFraction 4,000 Over 3 EndFraction pi inches cubed
The volume of sphere is [tex]\frac{500}{3}\pi[/tex] inches cubed.
Step-by-step explanation:
Given,
Diameter of sphere = 10 inches
Radius of sphere = [tex]\frac{Diameter}{2}=\frac{10}{2}[/tex]
Radius of sphere = 5 inches
Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex]
V = [tex]\frac{4}{3}\pi (5)^3[/tex]
[tex]V = \frac{4}{3}\pi * 125\\\\V = \frac{500}{3}\pi[/tex]
The volume of sphere is [tex]\frac{500}{3}\pi[/tex] inches cubed.
Keywords: volume, division
Learn more about division at:
brainly.com/question/11306893brainly.com/question/11334714#LearnwithBrainly
Answer:
500/3 pi
Step-by-step explanation:
i took le quiz :)
Anna rode her bike 7 miles to the lake. She rode 3/4 of the distance to the lake before lunch. How many miles did she ride before lunch?
Answer:
3/4 *7= 3/4 * 7/1=21/4=5 1/4
Step-by-step explanation:
I need help with this Geometry question.
Answer:
Given that AC ≅ BC, the sides are of equal measures.
CD is a side in both ΔACD and ΔBCD, so the side is equal in both triangles.
Given that CD if the bisector of ∠ACB, the two angles produced are equal: ∠ACD ≅ ∠BCD.
∠ACB is contained between AC and CD in ΔACD. ∠ACB is contained between BC and CD in ΔBCD.
Therefore by the SAS postulate, ΔACD ≅ ΔBCD.
Step-by-step explanation:
The SAS postulate says that if two triangles have a contained angle between two sides that are known to be equal in the other triangle, then the triangles are congruent.
Prove that two sides are equal, then prove that an angle that is between those two sides is also equal.
The graph of which of the following functions has a vertex at (4, -3)?
f(x) = x2² + 8x + 19
f(x) = x² - 8x + 19
f(x) = x² + 8x + 13
f(x) = x² - 8x + 13
Answer:
Therefore the answer is the fourth option y = f(x) = [tex]x^{2}[/tex] - 8x + 13
Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.
Step-by-step explanation:
i) f(x) = [tex]x^{2}[/tex] + 8x + 19 = [tex](x + 4)^{2}[/tex] + 3. SO the vertex is at (-4, 3)
Therefore the answer is the fourth option y = f(x) = [tex]x^{2}[/tex] - 8x + 13
= ([tex]x^{2}[/tex] - 8x + 16) + 3 = [tex](x-4)^{2}[/tex] - 3
Therefore when x = 4 then y = -3 from the equation of parabola and this is the required vertex.
Final answer:
The function with a vertex at the point (4, -3) is f(x) = x² - 8x + 13. This is concluded by using the vertex formula for a quadratic equation and checking the resulting coordinates against the given options.
Explanation:
The question is asking which of the given functions has a vertex at the point (4, -3). To find the vertex of a quadratic function of the form f(x) = ax² + bx + c, we can use the vertex formula, which is h = -b/(2a) for the x-coordinate, and then plug that back into the equation to find the y-coordinate. In this case, the function with the vertex (4, -3) must have the x-coordinate of the vertex at x = 4. Plugging this into the vertex formula, we get 4 = -b/(2a). We then look for a function where -b/(2a) = 4. The function f(x) = x² - 8x + 13 is the correct one because when we apply the formula -(-8)/(2*1) = 8/2 = 4. To confirm, we substitute x = 4 into the function: (4)² - 8(4) + 13 = 16 - 32 + 13 = -3, which gives us the y-coordinate of the vertex, -3.
A caterer prepares twice as many pizzas as she usually prepares for a large party. The caterer usually prepares 4 pizzas. The caterer also estimates that each party guest will eat 1 2 of a pizza. Drag and drop each expression into the correct boxes to complete the explanation. The expression that represents how many guests the pizzas can serve is . How many party guests will the pizzas serve? Drag and drop the number of guests into the box. The pizzas can serve guests.
Answer:
8 pizzas can serve 16 guests.
Step-by-step explanation:
So the caterer usually prepares 4 pizzas, but now she prepared twice as many, which means that now there are 4 • 2 = 8 pizzas.
Also, there is an estimation that each guest will eat 1/2 of a pizza.
In order to answer how many guests will 8 pizzas serve, we need to write an equation (pizzas per guest multiplied with number of guests equals the number of pizzas). Let's mark the unknown number of guests with x:
1/2 • x = 8
x = 8 / 1/2
x = 16
So, if each guest eats 1/2 of a pizza, then 8 pizzas will be enough to serve 16 guests.
What is 4 3/4 as a improper fraction
Answer: 19/4
Explanation: To write a mixed number as an improper fraction, first multiply the denominator times the whole number and then add the numerator.
So here, we multiply the denominator which is 2 times the whole number, 3, and then we add the numerator. So we have (4 x 4) + 3 which simplifies to 19.
Finally, we put our new number over our old denominator and we have our answer which is 19/4.
So 4 and 3/4 can be rewritten as the improper fraction 19/4.
Explanation of converting [tex]4\frac{3}{4}[/tex] to an improper fraction as 19/4.
To convert the mixed number [tex]4\frac{3}{4}[/tex] to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator:
4 x 4 + 3 = 19
So, [tex]4\frac{3}{4}[/tex] as an improper fraction is 19/4.
A diagonal of a parellelogram measures 37 inches. The sides measure 35 inches and 1 foot. Is the parellelogram a rectangle? Explain yoir reasoning m
Answer:
Yes, it is a rectangle
Step-by-step explanation:
12 ^2 +35^2 =37^2
Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
shift 4 units left, reflect over the x-axis, shift 2 units down
shift 4 units left, reflect over the y-axis, shift 2 units down
shift 4 units right, reflect over the x-axis, shift 2 units down
shift 4 units right, reflect over the y-axis, shift 2 units down
Answer: First option.
Step-by-step explanation:
Below are some transformations for a function [tex]f(x)[/tex]:
1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.
2 If [tex]f(x)-k[/tex], the function is shifted "k" units down.
3. If [tex]f(x-k)[/tex], the function is shifted "k" units right.
4. If [tex]f(x+k)[/tex], the function is shifted "k" units left.
5. If [tex]-f(x)[/tex], the function is reflected over the x-axis.
6. If [tex]f(-x)[/tex], the function is reflected over the y-axis.
Then, given the parent function [tex]f(x)[/tex]:
[tex]f(x)=2^x[/tex]
And knowing that the the other function is:
[tex]g(x)=-2^{(x+4)}-2[/tex]
You can identify that the function [tex]g(x)[/tex] is obtained by:
- Shifting the function [tex]f(x)[/tex] 4 units left.
- Reflecting the function [tex]f(x)[/tex] 4 over the x-axis.
- Shifting the function [tex]f(x)[/tex] 2 units down.
Answer:
A is correct
Step-by-step explanation:
Shift 4 units left, reflect over the x-axis, shift 2 units downMajorie evaluated the expression 3x+2 for x=5 as shown: 3x+2=35+2=37 What was Majorie's mistake? What is the correct value of 3x+2 for x=5?
Answer:
17
Step-by-step explanation:
Given:
The given expression is.
[tex]3x+2[/tex]
We need to solve the given expression for [tex]x = 5[/tex].
Solution:
Rewrite the expression as.
[tex]f(x)=3x+2[/tex]
Substitute x = 5 in above expression.
[tex]f(5)=3(5)+2[/tex]
[tex]f(5)=3\times 5 + 2[/tex]
Now we multiply 5 with 3.
[tex]f(5)=15+2[/tex]
Now we add right side terms.
[tex]f(5)=17[/tex]
Therefore, The correct value of given expression is [tex]3x+2=17[/tex] for [tex]x=5[/tex].
Adding fractions
1/4 + 2/3=
Answer:
The addition of given fractions is [tex]\frac{11}{12}[/tex]
Therefore [tex]\frac{1}{4}+\frac{2}{3}=\frac{11}{12}[/tex]
Step-by-step explanation:
Given fractional expression is [tex]\frac{1}{4}+\frac{2}{3}[/tex]
To find the addition of given fractions :
Adding the given fractions we get
[tex]\frac{1}{4}+\frac{2}{3}[/tex]
[tex]=\frac{1(3)+2(4)}{12}[/tex] ( here taking 12 as LCM )
[tex]=\frac{3+8}{12}[/tex]
[tex]=\frac{11}{12}[/tex]
Therefore [tex]\frac{1}{4}+\frac{2}{3}=\frac{11}{12}[/tex]
The addition of given fractions is [tex]\frac{11}{12}[/tex]
Jeff saves $25 a week How much can he save in one year ( 1 year =52 weeks
Answer:1300
Step-by-step explanation:
in a week =25$
a year has 52wks
so...52×25=1300$in a year
Answer:
$1300
Step-by-step explanation:
$25 / week
52 weeks per year
52($25) = $1300
Hope this helps :)
The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y plus 7 equals negative StartFraction 2 over 5 EndFraction left-parenthesis x minus 10 right-parenthesis.. What is the standard form of the equation for this line?
Answer:
2x + 5y = - 15
Step-by-step explanation:
The line that passes through (–5, –1) and (10, –7) points and the point-slope form of the equation is [tex]y + 7 = - \frac{2}{5}(x - 10)[/tex].
Now, we have to arrange this in the standard form.
So, [tex]y + 7 = - \frac{2}{5}(x - 10)[/tex]
⇒ 5(y + 7) = - 2(x - 10)
⇒ 5y + 35 = - 2x + 20
⇒ 2x + 5y = - 15 (Answer)
1) Which is the best buy?
6 shirts for $25.50
4 shirts for $18.00
5 shirts for $21
Answer:
5 shirts for $21
Step-by-step explanation:
25.50÷6= 4.25
18.00÷4= 4.50
21.00÷5= 4.20
Which expression can be modeled by this diagram!!!please help fast
Answer: i think 4x4/8
Step-by-step explanation:
Answer:first one
Step-by-step explanation:4 2/8
Just watched like 3 vids on multiplying unit fractions by whole numbers
(Pls help) A bicycle trail in the shape of a circle has a diameter of 3 miles. Michelle biked around the trail 4 times. About how far did Michelle bike.
39 miles ------------------------------------------------
A math teacher has budgeted $400 for the purchase of new calculators for the school. The calculators are $70 each. What are the possible numbers of calculators the math teacher can buy?
Answer:
Step-by-step explanation:
Amount the teacher as $400
A calculator cost $70
The no. Of calculator he teacher can get is = 400/70 = 5.71
The teacher can get 5 calculator
D=3 in this problem plz help
Answer:
73
Step-by-step explanation:
Answer:
To do this you want to plug 3 in for d, so your equation will look like this
7(3)^2+10
In the order of PEMDAS you want to do exponents first, because there is no parentheses.
7*9+10 (3^2=9), next you want to multiply
63+10, lastly you want to add
63+10=73
73
Hope this helps ;)
B(-5,1) is one end point of the segment and M(-3,3) is the midpoint of a segment what are cordnates of point A
Answer:
(-1,5)
Step-by-step explanation:
Let the coordinates of point A be (a,b).
We have that B is at (-5,1)
Assuming M(-3,3) is the midpoint of the segment AB, then
[tex](-3, 3 )= ( \frac{a + - 5}{2}, \frac{b + 1}{2} )[/tex]
This means that:
[tex]- 3 = \frac{a + - 5}{2}[/tex]
and
[tex]3 =\frac{b + 1}{2}[/tex]
This implies that 2*-3=a-5 and 3*2=b+1
-6=a-5 and 6=b+1.
a=5-6 and b=6-1
a=-1 and b=5.
Therefore the coordinates of A are:
(-1,5)
The total cost of gasoline varies directly with the number of gallons purchased. Kathy pays $23.36 for 16 gallons of gasoline. Which equation
shows the relationship between the total cost of gasoline, c, and the number of gallons purchased, n?
•
A.C= 1.46n
.
B. n = 1.46c
.
•
C.C = 23.361
D. n = 23.36c
The correct equation that represents the direct variation between the total cost of gasoline and the number of gallons purchased is C = 1.46n.
Explanation:The question involves finding the equation that represents the direct variation between the total cost of gasoline c, and the number of gallons purchased n. Kathy pays $23.36 for 16 gallons of gasoline. To find the unit price, we divide the total cost by the number of gallons:
$23.36 ÷ 16 gallons = $1.46 per gallon
Since the total cost varies directly with the number of gallons, we can express this as c = $1.46 × n. Thus, option A, C = 1.46n, shows the correct relationship between the total cost of gasoline, c, and the number of gallons purchased, n.
3.
"a varies directly with b". If a = 4 when b = 21, find a when b-7.
Step-by-step explanation:
A(promotional sign)b
A=kb
4=21k
K=0. 1904
A=0. 2b
A=0. 2×7
A=1. 4
:
Step-by-step explanation:
a varies directly with b
a ∞ b
a = Kb
K is the constant of proportionality
If a = 4 when b = 21
4 = 21×k
4 = 21k
k = 4/21
: - a = 4b/21
find a when b= 7.
a = 4(7)/21
a = 4/3
a = 1 1/3
How good is pizza and what is 8/2
Answer:
I dont know what they tought you in your school...but pizza is 100% good, and 8/2 is 8divided by2 so the answer is 4.
PLESASE MART BRAINLIEST. IT'S OK IF NOT BUT STILL THX.
Answer:
pizza is very good and 8/2 is 4.
Step-by-step explanation:
pls mark brainliest thx! :)
Boxes of cereal usually cost $4 but they are on sale for $1 off a gallon of milk costs $3 the expression 4b -1b +3 can be used to find the cost in dollars of buying b boxes of cereal and a gallon of milk write the expression in simpler form
Answer:4b +1b + 3 =5b + 3
Step-by-step explanation:add 1b to 4b will give you 5b plus the 3
Answer:
4b+1b+3=5b+3
Step-by-step explanation:
Sue talked on her cell phone for
2 1/2 hours on Monday. She talked
for 4 2/3 hours on Tuesday. How
many more hours does Sue need to
talk to get 8 hours?
A.7 1/6
B.6 3/5
C.1 1/6
D.5/6
Evaluate the expression for b = 5.
7.4b
Answer:
37
Step-by-step explanation:
Plug 5 in for b .
7.4 * 5 = 37
Ashley read 12 books in 16 months. What was her rate of reading in books per month?
Answer:
3/4 book per month
Step-by-step explanation:
12/16=3/4
Ashley's reading rate is calculated by dividing the total number of books she read (12 books) by the number of months it took her to read them (16 months), which gives 0.75 book per month.
Explanation:The question is about determining Ashley's rate of reading in terms of books per month. The rate is determined by dividing the total number of books she has read by the total number of months. In this case, Ashley has read 12 books in 16 months.
To find Ashley's reading rate, you would divide the total number of books she has read (12 books) by the number of months it took her to read them (16 months), that is 12 books ÷ 16 months = 0.75 book per month.
So Ashley's reading rate is 0.75 book per month.
Learn more about Rate Calculation here:https://brainly.com/question/16549128
#SPJ3