Given:
7c - a
a=-5 and c = 2
Substitute the values into the expression
7(2) - (-5)
=14 + 5
= 19
An eighth-grade student estimated that she needs $8,800 for tuition and fees for each year of college. She already has $5,000 in a savings account. The table shows the projected future value of the account in five years based on different monthly deposits.future value of a savings account. initial balance, dollars, $5000, $5000, $5000, $5000. Monthly deposit, dollars. $100, $200, $300, $400. Account value in five years, dollars. $12,273; $18,737; $25,202; $31,667.The student wants to have enough money saved in five years to pay the tuition and fees for her first two years of college. Based on the table, what is the minimum amount she should deposit in the savings account every month?AnswerF$200G$300H$100J$400
Since each year cost $8,800 for two years tuition he will need $17,600 then if he want to save at least this much in five years according to the table he needs to save $200 monthly
Two electrical lines are parallel to each other. One of the lines is represented by theequation - 4x + y = 8. What is the slope of the other electrical line?
What percentage is 1 m longer than 1 yard? Round to one tenth percent. 1 yard = 91.4 cm
In a textbook, 900 digits are used for the page numbers. How many pagesare in the textbook, starting with page 1? (Hint: First find how many digitsare used for pages 1-9 and 10-99.)
Given:
900 digits are used for the page numbers. How many pages are in the textbook, starting with page 1
We will find the number of the pages of the book as follows
The number of digits from 1 to 9 = 9
The number of digits from 10 to 99:
There are 90 numbers, each number has 2 digits
So, the number of digits from 10 to 99 = 90 x 2 = 180
The number of digits from 100 to 999:
There are 900 numbers, and each number has 3 digits
so, the number of digits from 100 to 999 = 900 x 3 = 2700
The overall digits are given = 900
So, number of digits from 1 to 99 = 9 + 180 = 189
Subtract 189 from 900 = 900 - 189 = 711
Divide 711 by 3 = 237
So, the number of pages that have 3 digits = 237
So, the number of pages of the book = 237 + 99 = 336
So, the answer will be 336 pages
[tex]4a ^{2} - 12a - 16[/tex]I need help factoring
4(a-4)(a+1)
1) Factorizing 4a²-12a -16
4a²-12a -16 Note that the GCD (4,12,16) is 4, Rewrite them
4a²- 4*3a - 4* 4
2) 4(a² -3a -4) Rewrite a² -3a -4 answering the question, What are the numbers whose sum is 3 and product is 4?
Answer:
1 -4 = -3
1 x -4 = -4
3) Hence, the answer is:
4a²-12a -16= 4(a-4)(a+1)
i need help asap with this (Its ACD and not AGD just incase that confuses you)
4)
In the case of a square, its diagonals are equal and bisect each other, meeting at 90°.
In our case, using a diagram,
Therefore,
[tex]\begin{gathered} a+2b=90 \\ and \\ 2a-b=90 \end{gathered}[/tex]Solving the system of equations for a and b,
[tex]\begin{gathered} \Rightarrow a=90-2b \\ \Rightarrow2(90-2b)-b=90 \\ \Rightarrow5b=90 \\ \Rightarrow b=18 \end{gathered}[/tex]Finding a,
[tex]\begin{gathered} b=18 \\ \Rightarrow a=90-2*18=90-36=54 \end{gathered}[/tex]The answers are a=54, b=18Use any method to add or subtract (1 point)
5/7 - (3/14 + 3/14)
Answer:
5/7 - (3/14 + 3/14) = 2/7See the steps of solution:
5/7 - (3/14 + 3/14) = Solve parenthesis first5/7 - (3 + 3)/14 = Add fractions with same denominator5/7 - 6/14 = Simplify5/7 - 3/7 = Subtract fractions with same denominator(5 - 3)/7 = Simplify2/7 AnswerAnswer:
2/7 (or) 0.285
Step-by-step explanation:
Given problem,
→ 5/7 - (3/14 + 3/14)
Let's solve the given problem,
→ 5/7 - (3/14 + 3/14)
→ (5/7) - (6/14)
→ ((5 × 2)/(7 × 2)) - (6/14)
→ (10/14) - (6/14)
→ (10 - 6)/14
→ 4/14 = 2/7
Hence, required answer is 2/7.
Which sequence of rigid motions will definitely work to take triangle RPQ onto triangle CAB?
RPQ to CAB transform
Rotation needed = RPQ using C as center ,an angle ACP
Translations= Line RC
Reflections= None
Then answer is
Option D)
Translate RPQ by the direct line segment RC
Use the factor theorem to determine whether x-2 is a factor
Factor theorem is usually used to factor and find the roots of polynomials. A root or zero is where the polynomial is equal to zero. Therefore, the theorem simply states that when f(k) = 0, then (x – k) is a factor of f(x).
In this case here, let's find out if 2 is a root of the polynomial given.
As we can see in the box below, 2 is not a root of the polynomial, therefore (x-2) isn't a factor.
[tex]\begin{gathered} P(x)=-2x^3+4x^2-4x-7 \\ P(2)=-2\cdot2^3+4\cdot2^2-4\cdot2-7 \\ P(2)=-16+16-8-7 \\ P(2)=-15 \end{gathered}[/tex]it says (6^2)^2 then it says select one Add, Subtract, Multiply
Multiply
Here, we want to select the arithmetic operation that could be used to evaluate the given indices expression
The key to solving this is to use an important indices relationship
That is;
[tex](a^x)^y=a^{xy}[/tex]Hence, we have to multiply the powers
So the correct option here is multiply
Solve the system by substitution.y =10xY=4x+22
Given the system:
[tex]\begin{cases}y=10x \\ y=4x+22\end{cases}[/tex]Let's clear x from equation 1:
[tex]\begin{gathered} y=10x\rightarrow\frac{y}{10}=x \\ \rightarrow x=\frac{y}{10}\text{ (A)} \end{gathered}[/tex]And substitute (A) in equation 2:
[tex]\begin{gathered} y=4x+22 \\ \rightarrow y=4(\frac{y}{10})+22 \\ \rightarrow y=\frac{4}{10}y+22 \end{gathered}[/tex]Solving for y:
[tex]\begin{gathered} y=\frac{4}{10}y+22 \\ \rightarrow y-\frac{4}{10}y=22 \\ \rightarrow\frac{3}{5}y=22\rightarrow3y=110\rightarrow y=\frac{110}{3} \end{gathered}[/tex]Now, let's use (A) to calculate x:
[tex]\begin{gathered} x=\frac{y}{10} \\ \rightarrow x=\frac{\frac{110}{3}}{\frac{10}{1}}\rightarrow x=\frac{110}{30}\rightarrow x=\frac{11}{3} \end{gathered}[/tex]This way,
[tex]\begin{gathered} x=\frac{11}{3} \\ \\ y=\frac{110}{3} \end{gathered}[/tex]Find the z-value so that the area to the left of z (shaded in the picture) is 0.9131.
area shaded to the left = 0.9131
by using the Z cumulative table , we can see that the value that corresponds with Z= 0.913 is 0.838
The functions f(x) and g(x) are shown on the graph.F(x)=x^2What is g(x)?A. g(x)= -x^2+3B. g(x)=(-x)^2-3C. g(x)=(-x)^2+3D.g(x)= -x^2-3
On observation of the graphs of the two functions, we can see that f(x) has undergone some transformation to give g(x).
The original function is given as
[tex]f(x)=x^2[/tex]The function is reflected over the x-axis.
The rule for the reflection over the x-axis is given as
[tex]f(x)\to-f(x)[/tex]Applying this to the function, we have the new function to be
[tex]-x^2[/tex]The graph is also shifted downwards by 3 units.
This shift can be represented as
[tex]f(x)\to f(x)-3[/tex]Applying this to our function, we have the new function, g(x), to be
[tex]g(x)=-x^2-3[/tex]The correct option is OPTION D.
Which is the degree measure of an angle whose tangent is 1.19? Round the answer to the nearest whole number.
We know that:
[tex]\tan\theta=1.19[/tex]where theta is the angle we are trying to find; to get the angle we take the inverse tangent at both sides of the equation. Then:
[tex]\begin{gathered} \tan^{-1}(\tan\theta)=\tan^{-1}1.19 \\ \theta=50 \end{gathered}[/tex]Therefore, the angle we are looking for is 50°
#3) Ulices was charged $140 plus a pick up charge of $20 to ship 4 identical boxesbys Fast Ship. The pick up charge applies regardless of how many boxes are pickedup. What would have been the change to Ulices' account if he had shipped just 1box?
To determine the Ulices's account if he shipped just 1 box, calculate the charge for one box. To calculate the charge, compute the quotient between the charge for 4 boxes between 4 boxes, just as folow:
charge per one box = 140/4 = 35
Hence, for 1 box the charge is $35
Due to it is necessary to pay $20 idependenty of the number of boxex, you sum $20 to the cost for one box:
New Ulices's account = $35 + $20 = $55
Hence, Ulices's account would have been of $55
Use the Angle Bisector Theorem to set up an equation and solve for X.
1. AB is the Angle Bisector of 4CAD.
33° B (4x + 1)º A D
Step-by-step explanation:
what happens, if I cut something in half ?
not just into 2 pieces, but outright in half ?
a pizza or a cake ?
well, I get 2 identical pieces.
a bisector (bi = 2 or double, sector = part) splits an angle into 2 equal parts.
that means
33 = 4x + 1
from there we get
32 = 4x
x = 32/4 = 8
Consider the polynomial
1/2a^4 + 3a³ + a.
1) What is the coefficient of the third term?
2) What is the constant term?
1) The coefficient of the third term is one.
2) The constant term is zero.
We are given a polynomial. A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive integer powers of variables. The polynomial is (1/2)a^4 + 3a³ + a. The polynomial has the variable "a". The polynomial has three terms. So, it is a trinomial. The third term of the polynomial is "a". The coefficient of the third term is 1. There is no constant term in the polynomial. So, we can say that the constant term is 0.
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Solve equations x-27=56
Answer:
x = 83
Step-by-step explanation:
Add 27 to both sides
x - 27 +27 = 56 + 27
x = 83
If the product is 900, and the two of its three factors are 3 and 50, what is the third factor?
We have the multiplication of 3 factors, one of them unknown, that give 900 as a result.
We can write this as:
[tex]\begin{gathered} 3\cdot50\cdot x=900 \\ 150x=900 \\ x=\frac{900}{150} \\ x=6 \end{gathered}[/tex]The third factor is 6.
3. When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.Let f(x) refer to the amount of drug left in the body after I hours.(a) Write down an exponential function to model this situation. Write your answer using functionnotation(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number
When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.
Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.
Let f(x) refer to the amount of drug left in the body after I hours.
(a) Write down an exponential function to model this situation. Write your answer using function
notation
(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.
(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number
Part a)
Let
t -----> number of hours
f(x)=a(1+r)^t
where
a=549 mg
r=12%=0.12
substitute
f(x)=549(1+0.12)^t
f(x)=549(1.12)^tPart b)
For t=12 hours
substitute in the function
f(12)=549(1.12)^12
f(12)=2,139 mgPart c)
For t=180 minutes
Remember that
1 h=60 minutes
so
180 minutes=180/60=3 hours
For t=3 hours
substitute
f(3)=549(1.12)^3
f(3)=771 mgPlease help solve the following questions using the exponential equation
SOLUTION
We want to solve
[tex]7^{2x+4}=2^{x-5}[/tex]Taking logarithm of both sides, we have
[tex]\begin{gathered} \log 7^{2x+4}=\log 2^{x-5} \\ (2x+4)\log 7=(x-5)\log 2 \\ \text{expanding we have } \\ (2x)\log 7+(4)\log 7=(x)\log 2-(5)\log 2 \end{gathered}[/tex]Collecting like terms we have
[tex]\begin{gathered} (2x)\log 7-(x)\log 2=-(4)\log 7-(5)\log 2 \\ x(2\log 7-\log 2)=-4\log 7-5\log 2 \\ \text{dividing both sides by }(2\log 7-\log 2),\text{ we have } \\ x=\frac{-4\log 7-5\log 2}{2\log 7-\log 2} \end{gathered}[/tex]Hence the solution set expressed in terms of logarithm is
[tex]x=\frac{-4\log7-5\log2}{2\log7-\log2}[/tex]Using a calculator to obtain a decimal approximation, we have
[tex]\begin{gathered} x=\frac{-4\log7-5\log2}{2\log7-\log2} \\ x=\frac{-3.3804-1.5051}{1.6902-0.3010} \\ x=\frac{-4.8855}{1.3892} \\ x=-3.51677 \\ x=-3.52 \end{gathered}[/tex]Hence the answer is -3.52 to 2 decimal places
S-7>3Help please !Don’t really understand
The given inequality is
[tex]s-7>3[/tex]To solve it, we need to isolate s on one side and the numerical terms on the other side
To do that we need to move 7 from the left side to the right side with 3, so
Add 7 to both sides
[tex]\begin{gathered} s-7+7>3+7 \\ s+0>10 \\ s>10 \end{gathered}[/tex]The solution of the inequality is s > 10
We can represent it on the number line
If h(x) = 3(x2 + 1) - 6, what is the value of h(10)?
Yea I think and if it’s ok we
Explanation: To solve a derivate we can use a simple technique presented below
- First, we take the exponent and multiply it by the function. Second, we subtract a unit of the exponent. Let's visualize it better on the drawing below
Step 1: Now we can use the same concept to calculate all the derivates we need as follows
Final answer: So the final answers are
[tex]\begin{gathered} letter_{\text{ }}a=5x^4 \\ letter_{\text{ }}b=20x^3 \\ letter_{\text{ }}c=60x^2 \\ letter_{\text{ }}d=120x \end{gathered}[/tex].
1 금35Lolo19.Which type of variation is modeled in the table?jointdirectcombinedInverse
The answer to your question is inverse varaiation.
Explanation: Inverse variation is a reciprocal term. Or say a variable is increasing while the other is decreasing.
So it is observed that as when y increases, then x decreases.
And also when y decreases, then x increases.
Thus, It is an inverse variation.
Translate thefollowing phaseinto an inequality-3 times r is at least 33A) inequality B) Solve the equality for r.C) express the solution in interval notation.
Given the phrase:
-3 times r is at least 33
Let's translate the given phrase into an inequality.
• Part A.
Let's figure out the inequality in steps.
-3 times r is written as:
-3r
-3 times s is at least 33 means that -3r is greater than or equal to 33.
Hence, we have the inequality:
[tex]-3r\ge33[/tex]• Part B.
Let's solve the inequality for r.
To solve for r, divide both sides of the inequality by -3:
[tex]\begin{gathered} \frac{-3r}{-3}\ge\frac{33}{-3} \\ \\ r\le-11 \end{gathered}[/tex]• Part C.
Let's express the solution in interval notation.
Here, the solution is:
[tex]r\le-11[/tex]It means s must be less than or equal to 11.
Therefore, the solution in interval notation is:
[tex](-\infty,-11\rbrack[/tex]ANSWER:
• A) -3r ≥ 33
• B) r ≤ -11
• C) (-∞, -11]
hi please help me tysmYour mother places 6 flowers in a vase. How many vases does your mother need for 30 flowers?A. 9B. 7C. 5D. 3
SOLUTION:
Step 1:
In this question, we are given the following:
Your mother placed 6 flowers in a vase.
How many vases does your mother need for 30 flowers?
Step 2:
The details of the solutions are as follows:
[tex]\begin{gathered} 6\text{ flowers = 1 vase} \\ \text{Then, we have that:} \\ 30\text{ flowers = }\frac{(30\text{ x 1)}}{6}=\frac{30}{6}=\text{ 5 vases ( OPTION C)} \end{gathered}[/tex]
based on the side lengths given (a, b, and c), which triangles are right triangles????A. a=4, b=6, c=8B. a=6, b=8, c=10C. a=5, b=6, c=(square root of) 61D. a=6, b=9, c=12 PLEASE HELP!!
Explanation
From the question, a right-angle triangle must obey Pythagoras theorem. Therefore, we can see that
[tex]6^2+8^2=10^2\text{ also, }5^2+6^2=(\sqrt{61})^2[/tex]The rest of the values do not obey Pythagoras theorem. Therefore;
Answer: Option B and Option C
The figure below is a net for a right rectangular prism. Its surface area is 384 cm2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.Yes
Solution
For this case we know the total surface area given by:
384 cm^2
And we have the following: 108+48 +108+48 = 312 cm^2
the ramianing area is:
384 -312= 72 cm^2
And we can do the following:
2*9*? = 72
Solving for ? we got:
? = 72/18 = 4 cm
the final answer is:
The area of each missing face is: 36 cm^2
The lenght of each missing edge is: 4 cm
Abrha lives in an apartment and pays the following expenses each month: electric bill, $44.90; TV streaming service, $24.99; and rent, $625.85 Estimate his total expenses for the month by first rounding each value to the nearest tens place.
Answer: $700
Abrha will be spending $701 monthly, just by arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Abrha lives in an apartment,
electric bill, $44.90 = $50
TV streaming service, $24.99 = $25
Rent, $625.85 = $626
So the Total expenses will be (50+25+626) = $701 just by arithmetic operation
Hence Abrha will be spending $701 monthly.
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