The amount that was invested in the first fund is $8300.
The amount that was invested in the second fund is 3700.
What are the linear equations that represent the question?0.09a + 0.03b = $858 equation 1
0.1a + 0.01b = $867 equation 2
Where:
a = amount invested in the first fund b = amount invested in the second fund How much was invested in the second fund?Multiply equation 2 by 0.9:
0.09a + 0.009b = 780.30 equation 3
Subtract equation 1 from equation 3
0.021b = 77.70
Divide both sides by 0.021
b = $3700
How much was invested in the first fund?
Substitute for b in equation 1: 0.09a + 0.03(3700) = $858
0.09a + 111 = 858
a = (858 - 111) / 0.09
a = $8300
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In Autobiography by Abraham Lincoln and the Life of Abraham Lincoln by John Hugh Bowers, each author tells the same story about Lincoln's life, but they provide different_________.
A settings
B. dialogue
C. facts
Solve the radical equation.
x + 4 =√x + 10
What is the extraneous solution to the radical equation?
O The solution -1 is an extraneous solution.
O Both -1 and -6 are true solutions.
O The solution -6 is an extraneous solution.
ONeither -1 nor -6 is a true solution to the equation.
The solution -1 is an extraneous solution
Neither -1 nor -6 is a true solution to the equation.
Option D is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the equation x + 4 = √(x + 10), we need to isolate the radical term on one side of the equation and then square both sides to eliminate the radical.
Here are the steps:
x + 4 = √(x + 10)
Subtract 4 from both sides:
x = √(x + 10) - 4
Square both sides:
x² = (√(x + 10) - 4)²
Expand the right side using the formula (a - b)^2 = a^2 - 2ab + b^2:
x² = x + 6 - 8√(x + 10)
Move all terms to the left side:
x² - x - 6 + 8√(x + 10) = 0
To solve this equation, we can use a substitution u = √(x + 10):
u = √(x + 10)
Square both sides:
u² = x + 10
Substitute into the original equation:
(u² - 10) + 4 = u
Simplify:
u² - u - 6 = 0
Factor:
(u - 3)(u + 2) = 0
So u = 3 or u = -2.
But u = -2 leads to a negative value under the square root in the substitution u = √(x + 10), which is not allowed.
Therefore, we only consider u = 3, which gives:
√(x + 10) = 3
Square both sides:
x + 10 = 9
Subtract 10 from both sides:
x = -1
So the solution to the original equation is x = -1.
To check if it is extraneous, we need to substitute it back into the original equation:
x + 4 = √(x + 10)
-1 + 4 = √(-1 + 10)
3 = √9
3 = 3
The equation is true, so x = -1 is a valid solution and not extraneous.
Therefore,
Neither -1 nor -6 is a true solution to the equation.
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convert 29/6 and 16/7 to fraction with denominator 42
answer is given below
29/6 = 203/42
16/7 = 96/42
to make the denominator 42 we use common tables for this just multiplying .
Answer:
the fractions are 203/42 and 96/42
Step-by-step explanation:
[tex]for \: \frac{29}{6} \\ \: multply \: the \: numerator \: and \: denominator \: by \: 7 \\ \frac{29}{6} \times \frac{7}{7} = \frac{203}{42} \\ for \: \frac{16}{7} also \: multiply \: the \: numerator \\ and \: denominatorby \: 6 \\ = \frac{16}{7} \times \frac{6}{6} = \frac{96}{42} [/tex]
Find the distance between the points (3, –8) and (0, –9).
Answer:
B. 3.16
Step-by-step explanation:
1) formula of the required distance is:
[tex]d=\sqrt{(X_A-X_B)^2+(Y_A-Y_B)^2} ;[/tex]
2) if A(3;-8) and B(0;-9), then according to the formula above:
[tex]d=\sqrt{(0-3)^2+(-9+8)^2} =\sqrt{10}.[/tex]
d≈3.16
PLSS HELP ME WITH THIS! 20 POINTSS!
Answer:
c
Step-by-step explanation:
Select the correct location on the table.
Select the expression that is equivalent to . (Refer to the image)
Answer:
left one on 3rd row
Step-by-step explanation:
using the rules of exponents/ radicals
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
given
[tex]12^{-\frac{4}{7} }[/tex]
= [tex]\frac{1}{12^{\frac{4}{7} } }[/tex]
= [tex]\frac{1}{\sqrt[7]{12^{4} } }[/tex]
a=-2(negative 2) b=3 and c=5 what is 3ac-a+2b.With explanation
Step-by-step explanation:
a = -2
b = 3
c = 5
Question:[tex]3ac - a + 2b[/tex]
= Solution,
= 3 ( - 2 ) × 5 - ( - 2 ) + 2 × 3
here ... ( + ) × ( - ) = ( - )
= - 6 × 5 - ( - 2 ) + 2 × 3
here .... ( - ) × ( - ) = ( + )
= - 6 × 5 + 2 + 2 × 3
= - 30 + 2 + 6
= - 30 + 8
here the ( - ) have greater variable so...
= - 22
hence - 22 is the answer . ....
Which statement best describes the function shown in the graph?
A. The function is positive when x > 1.
B. The function is positive for all values in the domain.
C. The function is positive when x > 0.
D. The function is positive when x > -5.
Answer:
B
Step-by-step explanation:
since domain should be in positive i thinks this should be answer B
Find the measure of
Answer:
Angles around a point sum to 360°
⇒ ∠SPT + ∠TPU + 86° + 60° + 154° = 360°
⇒ ∠SPT + ∠TPU = 60°
Therefore:
∠SPQ clockwise = ∠SPT + ∠TPU + 86°
= 60° + 86°
= 146°
∠SPQ anticlockwise = 60° + 154°
= 214°
Answer:
See below ~
Step-by-step explanation:
The total internal measure is 360°.
154° + 60° + 86 + ∠STP + ∠TUP = 360°2∠STP + 300 = 360°2∠STP = 60°∠STP = ∠TUP = 30°Finding ∠SPQ (clockwise):
2∠STP + 86°2(30) + 86146°Finding ∠SPQ (counterclockwise) :
360° - 146°214°anyone understand this?
Find the indicated measure in LMNQ. Explain your reasoning.
Answer:
In Exercises 9 − 16, Ind the indicated measure in a LMNQ. Explain your reasoning. m ∠ L M N Answer m ∠ L M N = 80 ∘ View Answer Discussion You must be signed in to discuss. AS Ahin S. February 11, 2021 Find m?LMN in parallelogram LMNQ AS Ahin S. February 11, 2021 Watch More Solved Questions in Chapter 7 Problem 1 Problem 2 Problem 3 Problem 4
Step-by-step explanation:
Bear weight loss during hibernation is extreme. Male black bears will typically drop between 17 to 29 percent of their body weight. Let x represent the percent of body weight loss for a male black bear. Suppose that clic follows a uniform distribution. Find the probability that the male will lose between 19.41 and 23.74 percent of their body weight.
Using the uniform distribution, it is found that there is a 0.3608 = 36.08% probability that the male will lose between 19.41 and 23.74 percent of their body weight.
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
In this problem, male black bears will typically drop between 17 to 29 percent of their body weight, hence the bounds are a = 17 and b = 29.
The probability that the male will lose between 19.41 and 23.74 percent of their body weight is given by:
[tex]P(19.41 \leq X \leq 23.74) = \frac{23.74 - 19.41}{29 - 17} = 0.3608[/tex]
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If $570 is invested at an interest rate of 4% per year and is compounded continuously, how much will the investment be worth in 10 years? Use the continuous compound interest formula: A = Pert.
$593.26
$655.66
$726.74
$850.34
Continuous compounding is the potentially endless number of periods in which compound interest may be calculated. The worth of the investment after a period of 10 years will be $850.34.
What is Continuous Compound Interest?Continuous compounding is the potentially endless number of periods in which compound interest may be calculated and reinvested into an account's balance.
[tex]\rm A = Pe^{rt}[/tex]
where,
A is the principal amount after t number of years,
r is the rate at which the principal is been compounded, and P is the principal amount.
Given the principal amount of $570 is invested for a period of 10 years, and at a rate of 4% per year, therefore, the worth of the investment after 10 years will be,
[tex]\rm A = \$570 \times e^{(0.04 \times 10)} = \$850.34[/tex]
Hence, the worth of the investment after a period of 10 years will be $850.34.
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Can you help me please
From the figure given above, angel < ABE = 40°
Calculation of unknown angleThe angle of a straight line = 180°
That is angle <ABC = 180°
If <EBC is = 140°
Therefore, <ABE = 180 - 140
= 40°
Therefore, from the figure given above, angel < ABE = 40°
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1/2 x 1350 x 144 = 97200 J where did they get the 144 from?
Speed^2 or velocity^2 because 12x12=144
It's looks like the Kinetic energy equation:
KE = 1/2mv^2
Hope this helps!
Write an equation in standard form of the line
With slope 2/5 and going through (-3,6).
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{\cfrac{2}{5}}(x-\stackrel{x_1}{(-3)})\implies y-6=\cfrac{2}{5}(x+3)[/tex]
[tex]y-6=\cfrac{2}{5}x+\cfrac{6}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y-6)~~ = ~~5\left( \cfrac{2}{5}x+\cfrac{6}{5} \right)}\implies 5y-30~~ = ~~2x+6 \\\\\\ -2x+5y-30=6\implies -2x+5y=36\implies 2x-5y=-36[/tex]
Describe the end behavior of each function.
3) f(x) = -x^4+x^2 -x+1
Answer:
End Behavior is
y -> -inf as x -> -inf
y -> -inf as x -> +inf
Step-by-step explanation:
I am not sure if your teacher has explained how to look at the equation and determine the end behavior of that function without a graph. Here is a picture that explains it.
please help me do this mathematics question..experts .
The partial differential expression is equal to the expression 30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²) and the total differential formula is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).
How to apply partial derivatives and total differentials
In the first part of this question we must apply the concept of partial derivatives to find the form of the entire expression, whose variables are two. Partial differentiation is a generalization of the ordinary differentiation:
[tex]\frac{\partial f}{\partial x} = 6\cdot x^{5}+12\cdot x^{3}\cdot y^{4}+y^{6}[/tex] (1)
[tex]\frac{\partial^{2} f}{\partial x^{2}} = 30\cdot x^{4}+36\cdot x^{2}\cdot y^{4}[/tex] (2)
[tex]\frac{\partial^{2} f}{\partial x \,\partial y} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (3)
[tex]\frac{\partial f}{\partial y} = 12\cdot x^{4}\cdot y^{3} +6\cdot x \cdot y^{5}[/tex] (4)
[tex]\frac{\partial^{2} f}{\partial y^{2}} = 36\cdot x^{4}\cdot y^{2} + 30\cdot x\cdot y^{4}[/tex] (5)
[tex]\frac{\partial f}{\partial y \,\partial x} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (6)
Then, the entire expression is:
30 · x⁴ + 36 · x² · y⁴ + 36 · x⁴ · y² + 30 · x · y⁴
30 · (x⁴ + x · y⁴) + 36 · (x² · y⁴ + x⁴ · y²)
30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²)
In the second part we must determine the total differential of z with respect to two variables:
[tex]\Delta z = \frac{\partial f}{\partial x}\cdot \Delta x + \frac{\partial f}{\partial y}\cdot \Delta y[/tex] (7)
If we know that z = sin (x³ + y³), Δx = 0.3 and Δy = 0.2, then the total differential of the function is:
Δz = 3 · cos (x³ + y³) · x² · (0.3) + 3 · cos (x³ + y³) · y² · (0.2)
Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³)
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What time will it be after these minutes have passed? 10 minutes
Answer:
21 minutes
Step-by-step explanation:
hope it helps you
How many edges does the following shape have?
Answer:
6
Step-by-step explanation:
PLEASE HELP PLEASE HELP PLEASE
Answer:
1:1
Step-by-step explanation:
Can someone answer theese questions do all of them and I will give you brainily
1 .
What does each line on the protractor stand for?
five degrees
one-half of a degree
ten degrees
one degree
2 What part of the protractor do you line up with the vertex?
zero line
degree line
center mark
top of the protractor
3.
What is the first step in constructing an angle?
Make a mark at the number of degrees you want the angle to be.
Connect the endpoint and the mark at the angle measure
Draw a horizontal ray.
Place the center of the protractor on the endpoint of the ray, and line up the ray with the zero line of the protractor.
Answer: i think is b
Step-by-step explanation: because I do read lesson so I guess I think is b that why.
Find cot(theta) if tan(theta)=2 and 180°<(theta)<270°. ( 20 POINTS ) (Trigonometric Identities )
Answer:
Cot theta = 0.2
Step-by-step explanation:
[tex]180^\circ < \theta < 270^\circ[/tex]
So, theta is in the third quadrant
[tex]Cot \ \theta =\dfrac{1}{Tan \ \theta}\\[/tex]
[tex]= \dfrac{1}{2}[/tex]
[tex]\sf Cot \ \theta = 0.5[/tex]
what is the value of 7x-3y-1 for x = -2 and y = 4?
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
what is the value of 7x-3y-1 for x = -2 and y = 4?
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Replace x with -2 and y with 4:-
[tex]\sf{7(-2)-3(4)-1}[/tex]
On simplification,
[tex]\sf{-14-12-1}[/tex]
On further simplification,
[tex]\sf{-27}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Can someone help with this? I've been stuck on this for a while
Step-by-step explanation:
how is that math ?
anyway,
*♡ = O
●* = H
arrow up and filed triangle = E
arrow down and 3/4 circle = R
Use the axiomatic approach for vectors to prove the distributive law of vectors
Step-by-step explanation:
Find the HCF of 9m 80cm 8m 40cm 4m 20cm
need the answer asap
Answer:
The price for ounce is: $0.25 and she bought 16 ounces of straberris
Step-by-step explanation:
If you have 16 ounces and its 4 dollars you do 4/16 to get 0.25
What expression represents the volume of the cylinder, in cubic units?
Answer:
2πx3
Step-by-step explanation:
the perimeter of a rectangle is 84cm if the width of rectanle is 16 cm Find its lenth
Answer:
26 cm
Step-by-step explanation:
Formula for Perimeter
Perimeter = 2(Length + Width)Solving (given Perimeter is 84 cm and width is 16 cm)
84 = 2(Length + 16)42 = Length + 16Length = 42 - 16Length = 26 cmAnswer:
L= 26cm
Step-by-step explanation:
Perimeter= 2(l x w)
Perimeter= 84cm
Width= 16cm
Length=?
84= 2l + 32
2l = 84-32
2l= 52
L= 52/2
L= 26cm
a pentagon with sides 3 4 5 6 and 7 has area 48m. find the perimeter of a similar pentagon whose area is 27m
Answer:
19.8 rounded to 20m
Step-by-step explanation:
reason;
Area=1/2 x perimeter x apothem
27=1/2 x p x 2.726
Divide both sides by 1/2
54= p x 2.726
Now divide both sides by 2.726 to isolate p
Answer p=19.8
