Using a system of equations, the total number of marbles that they have is given by:
A. 27.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Eve's marbles.Variable y: Solene's marbles.Variable z: Steve's marbles.Eve has two more marbles than Solene, hence:
x = y + 2.
Solene has twice as many marbles as Steve, hence:
y = 2z -> z = y/2.x = 2z + 2.Steve has 7 less marbles than eve, hence:
z = x - 7.
Hence:
[tex]\frac{y}{2} = x - 7[/tex]
y = 2(x - 7)
y = 2(y + 2 - 7)
y = 2y - 10
y = 10.
Then:
x = y + 2 = 10 + 2 = 12.z = x - 7 = 12 - 7 = 5.Hence the total is given by:
T = 12 + 10 + 5 = 27.
Which means that option A is correct.
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which terms could have the greatest common factor of 5m2n2? select two:
m5n5
5m4n3
10m4n
15m2n2
24m3n4
Answer:
5m4n3 and 15m2n2
Step-by-step explanation:
you just have to find the 2 that each are divisible by 5m2n2, which are 5m4n3 and 15m2n2.
Z varies directly as x^3 and inversely as y^3. If z=167 when x = 3 and y=10, find z if X=4 and y=6
Answer is 1832.7
step by step
z=kx^3 / y^3
167=27k/1000
k=16700/27
k=6185.2, then
z=6185.2×4^3/6^3
z=6185.2×64/216
z=1832.7
Which number produces a rational number when added to 1/2?
Answer:
Another rational number.
Step-by-step explanation:
For example, [tex]\pi[/tex] is incorrect because It is a irrational number
you must add another rational number to 1/2 to make the sum rational.
Rational number are numbers that can be converted into a fraction.
all natural numbers, whole numbers, integers, are rational.
and all rational and irrational numbers are real numbers
What is 1+1? 10 point if u get it right.
Answer:
11
Step-by-step explanation:
duh add 1 and 1 merge it together to get 11
that's a hard question imma go with 2 though
Step-by-step explanation:
for this problem let's let x=1 and y also =1 so x+y=2 hope this helps
(a) Solve the following formula for b.
1
A = ab
(b) Evaluate b when A= 18 and a =
6/5
1
(a) The formula A = ab solved for b is b = 3X
6
(b) Evaluate b when A= 18 and a = 5
b = (Type an integer or a simplified fraction.)
Answer:
a. b = 2A/a
b. 30
Step-by-step explanation:
a. to solve for b:
[tex]A = 1/2 ab[/tex]
multiply both sides by 2
[tex]2A = ab[/tex]
divide both sides by a
[tex]2A/a=b[/tex]
so b = 2A/a
b. using the equation b = 2A/a
[tex]b = 2*18/(6/5)\\= 36/(6/5)\\= 30[/tex]
Find the solution for x in the equation below.
x² + 72x = 8
[tex]x^2+72x=8\\x^2+72x+1296=1304\\(x+36)^2=1304\\x+36=\sqrt{1304} \vee x+36=-\sqrt{1304} \\x=-36+2\sqrt{326} \vee x=-36-2\sqrt{326}[/tex]
Evaluate: y(x+x)+3, where x=1 and y=3 A. 3 B. 10 C. 9 D. 5
Answer:
C. 9
Step-by-step explanation:
y(x+x) +3
{x= 1 , y= 3}
Putting values..
3 (1+1) +3
= 3 (2) +3
= 6 + 3
= 9
So, the option C. 9 is the correct answer.
Find x and Y pls help
Answer:
Step-by-step explanation:
Comment
The angle supplementary to x and 3x are equal.
Supplementary angles = 180
Solution
x + 3x = 180
4x = 180 Divide by 4
4x/4 = 180/4
x = 45
The angle supplementary to x is 3x
3x = 3*45
3x = 135
This angle is vertically opposite y. Vertically opposite angles are equal. So y = 135
Answer
x = 45
y = 135
Select the correct answer. Which number best represents the slope of the graphed line? A linear function on a coordinate plane passes through (minus 6, minus 7), and (4, minus 2) also intercepts the x-axis at 8 units and the y-axis at minus 4 units. A. B. C. D.
The number best represents the slope of the graphed line is 1/2.
We have given the two points,
(-6,-7) and (4,-2) and slope-intercept is 8 units
What is the slope-intercept form of a line?
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
y = y coordinate of the second point
[tex]y_1[/tex] = y coordinate of point one
m = slope
x = x coordinate of the second point
[tex]x_{1}[/tex]= x coordinate of point one
Therefore the
[tex]slope=\frac{y_2-y_1}{x_2-x_!}[/tex]
[tex]=\frac{-2-(-7)}{4-(-6)} \\=\frac{5}{10}\\ =\frac{1}{2}[/tex]
Therefore the correct option is 1/2.
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Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is t ≥ 0
The greatest concentration of the medication is 5mg/L
Given that:
C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is: t ≥ 0
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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ABC is an isosceles triangle, with AB = AC. find X
Answer:
67.13°
Step-by-step explanation:
First separate triangles then you use Pythagoras theorem to get the third side and then apply the sine rule
From Kansas City to Denver is twice as far as from Kansas City to St. Louis the two distance together total 900 miles what are the two distance?
Answer:
KC to StL = 300
KC to Den = 600
Step-by-step explanation:
KC to StL was the base distance, so we'll call that x.
KC to Denver is twice as long, so we'll call that 2x.
If we add the together is is 900 miles total.
x + 2x = 900 Combine like terms
3x = 900 Divide by 3
x = 300
If x is 300, then 2x is 600.
Which is the graph of f,(x) = 0.5(4)*
I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.
Steve is ordering burgers and individual pizzas for $1000. He plans to buy not more than 80 items. The costs of each burger and each pizza are $7 and $4. Select the inequality that describes this situation. Use the given numbers and the following variables. x = the number of burgers. y = the number of pizzas.
[tex]x+y\leq 80[/tex]
[tex]7x+4y=1000[/tex]
The number of burgers = [tex]x[/tex]
the number of pizzas = [tex]y[/tex]
the cost of each burger = $[tex]7[/tex]
the cost of each pizza = $[tex]4[/tex]
not more than 80 items: [tex]x+y\leq 80[/tex]
total price =[tex]7x+4y=1000[/tex]
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Classify each of the following variables as quantitative or qualitative. For those which are quantitative, classify them further as continuous or discrete.
a) Weight of adult females
b) Street addresses in Addis Ababa
c) Years of professional experience of employees
d) Number of courses offered to students in AAU in this semester.
Answer:
a) quantitative - continuous
b) qualitative
c) quantitative - discrete
d) quantitative - discrete
Explanation:
A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.
A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.
Compute the length of sides AB, AC.
use the point-slope formula to write an equation of the line that passes through (6,- 3) and (3,1).
Write the answer in slope-intercept form (if possible).
The slope of the line is
[tex]\frac{-3-1}{6-3}=\frac{-4}{3}[/tex]
Substituting into point-slope form using the point (3,1),
[tex]\boxed{y-1=-\frac{4}{3}(x-3)}\\\\y-1=-\frac{4}{3}x+4\\\\\boxed{y=-\frac{4}{3}x+5}[/tex]
Answer: The equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex] +5.
Step-by-step explanation:
Point-slope formula : (y - y1) = m(x - x1)
y = y coordinate of second point
y1 = y coordinate of first point
m = slope
x = x coordinate of second point
x1 = x coordinate of first point
slope (m) = [tex]\frac{1-(-3)}{3-6}[/tex]
m = [tex]\frac{4}{-3}[/tex] or [tex]\frac{-4}{3}[/tex]
now put values in point-slope formula : (y - 1) = [tex]\frac{-4}{3}[/tex](x - 3)
y - 1 = [tex]\frac{-4x}{3\\}[/tex] + 4
y = [tex]\frac{-4x}{3}[/tex] +5
So the equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex]+5.
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Which absolute value function, when graphed, will be wider than the graph of the parent function, f(x) = |x|?
f(x) = |x| + 3
f(x) = |x − 6|
f(x) = |x|
f(x) = 9|x|
The absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
How to determine the function?The parent function is given as:
f(x) =|x|
A wider function would have the following equation
f(x) = k|x|
Where:
k > 0
From the list of options, we have:
f(x) = 9|x|
Hence, the absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
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Answer:
getting to the point , D.
Step-by-step explanation:
trust
if the ratio of three angles of a triangle is 2:3:4 find the size of the largest angle
Which statement is true about the end behavior of the graphed function?
Step-by-step explanation:
both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.
Which of these could be the graph of F(x) = log₂ x?
A
A. Graph A
B. Graph B
C. Graph C
D. Graph D
The graph of the function is shown in the attached image.
Complete the statements below with the process used to achieve steps 1-4.
Select the correct answer from each drop-down menu.
Consider the equation below.
-2(5x+8)=14+6x
The equation was solved using the following steps.
The statements can be completed by using the following :
1) -2 is multiplied with (5x+8)
2) transposing of numeral values and variable values
3) The numerical values are taken one side and added to each other
4) 30 is divided by -16
5) The numerator and denominator are cancelled to the lowest possible value
x= -15/8
Given: -2(5x+8)=14+6x
and steps for solving them have also been given
In the first step, -2 is multiplied with (5x+8) and we get
-10x -16 = 14 +6x
In step 2, transposing of numeral values and variable values is done and we get -16x - 16 = 14
In step 3,
The numerical values are taken one side and added to each other and we get -16x=30
In step 4, 30 is divided by -16
In step 5, they are cancelled to the lowest possible value and we get
x= -15/8
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Pleas hurry!!!!! Which line is perpendicular to a line that has a slope of -5/6
line JK
line LM
line NO
line PQ
Answer:
LM
Step-by-step explanation:
Perpendicular slope would be - 1 / m = - 1/(-5/6) = 6/5
slope m = rise / run line LM rises 6 for a run of 5
Find the value of JN in the figure.
Answer:
JN = 32
Step-by-step explanation:
Δ JMN and Δ JKL are similar ( AA postulate )
then the ratios of corresponding sides are in proportion, that is
[tex]\frac{JM}{JK}[/tex] = [tex]\frac{JN}{JL}[/tex] ( substitute values )
[tex]\frac{24}{33}[/tex] = [tex]\frac{JN}{JN+12}[/tex]
[tex]\frac{8}{11}[/tex] = [tex]\frac{JN}{JN+12}[/tex] ( cross- multiply )
11 JN = 8(JN + 12)
11 JN = 8 JN + 96 ( subtract 8 JN from both sides )
3 JN = 96 ( divide both sides by 3 )
JN = 32
(07.01) A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours?
Answer: By 8 hours, there will be 65536 bacteria in the culture.
Step-by-step explanation:
The numerical expression used for this problem is [tex]4^{8}[/tex].
You can find the value of this on a calculator. I hope this helps!! :)
If that is not the answer, then try 32 because 4*8=32.
evaluate 7/8+1/4÷6/7
Step-by-step explanation:
[tex] = \frac{7}{8} + \frac{1}{4} \div \frac{6}{7} [/tex]
[tex] = \frac{7}{8} + \frac{1}{4} \times \frac{7}{6} [/tex]
[tex] = \frac{7}{8} + \frac{7}{24} [/tex]
[tex] = \frac{7 \times 3}{8 \times 3} + \frac{7}{24} [/tex]
[tex] = \frac{21}{24} + \frac{7}{24} [/tex]
[tex] = \frac{28}{24} [/tex]
[tex] = \frac{7}{6} [/tex]
7/8+(1/4÷6/7)
1/4 ÷ 6/7 = 7/24
7/8 + 7/24 = 7/6 = 1 1/6
What complex number is represented by the polar coordinates (4, -pi/4)
Answer:
[tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
Step-by-step explanation:
A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as |z|).
Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.
Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.
[tex]\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}[/tex]
Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.
[tex]\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
Hence, the complex number that has polar coordinate of (4,-45°) is [tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
pls help!!!
What is the range of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
Answer:
All real numbers greater than or equal to 2.
Step-by-step explanation:
To find the range, we look at the y values. Since all the y values never dip under 2 and also keep increasing to infinity, the range is [tex]y\geq 2[/tex].
Answer:
all real numbers greater than or equal to 2
Step-by-step explanation:
Edge
Which best describes the range of the function #(x) = 2(3)x? O y>0 O y≥0 O y = 2 O y≥2
Answer:
The range of the function f(x) : is y > 0.
The correct option is (A)
Step-by-step explanation:
The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Given function is :
If we draw the graph for this, then we can see that the horizontal asymptote is 0.
So, the range is real numbers higher than 0.
Hence, the range should be y > 0.
A 7 x 8 array is 7 rows of ____
Answer:
8
Step-by-step explanation:
It's 7 rows of 8 items
