Answer:
You would do 9 x 3 first.
Step-by-step explanation:
PEMDAS. There is subtraction and multiplication, and multiplication is before subtraction.
P- Parenthesis
E- Exponent
M- Multiplication
D- Division
A- Addition
S- Subtraction
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The quadratic function f(x) has roots of −2 and 6, and it passes through the point (1, 15). What is the vertex form of the equation of f(x)?
f(x) = (x − 2)2 + 16
f(x) = (x + 2)2 + 16
f(x) = −(x − 2)2 + 16
f(x) = −(x + 2)2 + 16
Answer:
f(x) = −(x − 2)^2 + 16
Step-by-step explanation:
See attached graph.
Find the equation of a line that passes through (3,-1) and is perpendicular to the equation 3x+y=2
Answer:
y = (1/3)x - 2
Explanation:
First, we need to identify the slope of the equation 3x + y = 2, so we need to solve for x as:
[tex]\begin{gathered} 3x+y=2 \\ y=2-3x \end{gathered}[/tex]Now, the number beside the variable x is the slope, so the slope is -3
Then, two lines are perpendicular if the product of both slopes is equal to -1. It means that the slope m for our equation should be:
[tex]\begin{gathered} -3\cdot m=-1 \\ m=\frac{-1}{-3}=\frac{1}{3} \end{gathered}[/tex]Now, we can find the equation of the line using the following:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and (x1, y1) is a point on the line. So, replacing my 1/3 and (x1, y1) by (3, -1), we get:
[tex]\begin{gathered} y=\frac{1}{3}(x-3)+(-1) \\ y=\frac{1}{3}x-\frac{1}{3}\cdot3-1 \\ y=\frac{1}{3}x-1-1 \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]Therefore, the equation of the line is: y = (1/3)x - 2
24PS-10 Question Help In a certain chemical, the ratio of zinc to copper is 3 to 14. A jar of the chemical contains 294 grams of copper. How many grams of zinc does it contain?
the ratio of zinc to copper is 3 to 14, that menas that for each 3 grams of zinc there are 14 grams of copper, so we can made a rule of three to find
Use inductive reasoning to find a pattern and then make a reasonable conjecture for the next number in the sequence.
We will find the pattern as follows:
105 - 104 = 1
104 - 102 = 2
102 - 99 = 3
99 - 95 = 4
95 - 90 = 5
90 - 84 = 6
So, it is reasonable to assume that the next value will be 77.
I NEED HELP WITH THIS ASAP!!!! The following diagram describes the mixture's volume of blue and red paint. What is the ratio of blue color to real paint in the mixture?
The ratio of blue color to red paint in the mixture is 5 :3.
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of one value compared to the frequency of another value. The sign that is used to measure ratio is :.
In order to determine the ratio, count the number of blue tiles and the number of red tiles.
Number of blue tiles = 10
Number of red tiles = 6
The ratio of blue to red is 10 : 6. When expressed in its simplest form, it is 5 : 3.
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name the rule and list the next three terms in the pattern 2,4,8,16,32...
This is Geometric progression G P
[tex]\begin{gathered} \\ 2^1=2 \\ 2^2=4 \\ 2^3=8 \\ 2^4=16 \\ 2^5=32 \\ 2^6=64 \\ 2^7=128 \\ 2^8=256 \end{gathered}[/tex]The next three terms are;
64,128,256
You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?(1 point)
Responses
20 mph
10 mph
60 mph
50 mph
Write the equation of the line passing through the points (-7.4) and (7.2).
The equation of the line is
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Answer: y = -1/7x + 3
Step-by-step explanation:
Write the equation of the line passing through the points (-7.4) and (7.2).
First, find the slope of the two points by the y2-y1/x2-x1 slope formula.
The slope is -1/7.
Then, use the point slope form y-y1 = m(x-x1).
16 more than s is at most -80 interval notation
The answer in interval notation is given by {96, ∞}.
What is an interval notation?An interval notation can be defined as a set of real numbers which comprises all of the real numbers that are representing a continuous function and lies between two set of numbers.
This ultimately implies that, an interval notation can be used as a technique for writing all of the subsets of the real number line.
Translating the given word problem into an inequality algebraic expression:
16 - s ≤ -80
Adding 80 to both sides of the expression, we have:
80 + 16 - s ≤ -80 + 80
96 - s ≤ 0
Rearranging the expression, we have:
s ≥ 96
Therefore, we have {96, ∞}.
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Complete Question:
Translate and solve: 16 more than s is at most -80.
Give your answer in interval notation.
Jason compares the price of x pizzas which all have a one-time delivery fee. This question has two parts.
18.30x +3.75
19.35x + 5.00
13.25x +3.99
What is the cheapest pizza without a delivery fee?
What is the cheapest delivery fee?
The cheapest pizza without a delivery fee is 13.25 × and the cheapest delivery fee is $3.75.
What is the cheapest delivery fee?Delivery fees are used to defray the cost of transporting food to customers. We'll discuss the various ways that restaurants might approach this revenue channel and how these fees are calculated based on how a restaurant runs its delivery service.A price assessed by the delivery business as compensation for the service.
Taxes: Your order will be subject to the applicable state and local sales taxes. The cost of having food delivered is known as the delivery fee.The cheapest pizza without a delivery fee is 13.25 × and the cheapest delivery fee is $3.75.Therefore, the cheapest pizza without a delivery fee is 13.25 × and the cheapest delivery fee is $3.75.
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the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. if a bank has an interest rate at the 45th percentile, what is the interest rate at this bank?
The interest rate at the bank = 2.324 %
Let X be the random variable representing the interest rate on a five-year certificate of deposit (cd) for banks in South Florida in 2018.
Then X follows the Normal Distribution with,
Mean, μ = 2.28 % and,
Standard Deviation, σ = 0.37 %
We need to find the X at the 45th percentile.
45th percentile implies z-value = 0.45
The z-score at 45th percentile or 0.45 probability = -0.12 [From the z-tables]
We have, z = (x-μ)/σ
⇒ zσ = x-μ
⇒ x = zσ+μ
⇒ x = (0.12 x 0.37) + 2.28
= 2.324
Hence the interest rate at the bank = 2.324 %
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Josie sold 790 tickets to a local car show for a total of $4,390.00. A ticket for a Child costs $4.00 and adult ticket costs $7.00. How many of each ticket did she sell? A) Children’s ticket? B) Adult Ticket?
Let's define the following variables first.
A = number of tickets sold for adults
C = number of tickets sold for children
From the question, we can say that or form the following equations:
1. A + C = 790 tickets
2. $7A + $4C = $4, 390
The first equation can also be written as A = 790 - C. We can use this equation and replace "A" in the second equation.
[tex]7(790-C)+4c=4,390[/tex]From that, we can solve "C" by solving the equation formed above.
[tex]\begin{gathered} \text{Distribute 7 to the terms inside the parenthesis.} \\ 7(790)-7(C)+4C=4,390 \\ 5,530-7C+4C=4,390 \\ \text{Subtract 5,530 on both sides of the equation.} \\ -7C+4C=-1140 \\ -3C=-1140 \\ \text{Divide -3 on both sides.} \\ C=380 \end{gathered}[/tex]Therefore, 380 tickets for children were sold.
Since there are 790 tickets in total that are sold and 380 tickets for children were sold, we can say that 410 tickets for adult was sold.
[tex]\begin{gathered} A=790-C \\ A=790-380 \\ A=410 \end{gathered}[/tex]A rectangular toolbox has a length of 20 inches, The width of the toolbox is 7 inches and it's height is 7.5 inches. How much metal would be needed to make the toolbox?
ok
I'll calculate the surface area to answer your question.
Area of the base and top = 2x20x7 = 280 in^2
Area of the frontal and behind faces = 2 x 7x7.5 = 105 in^2
Area of the left and right faces = 2x20x7.5 = 300 in^2
Total area = 280 + 105 + 300
= 685 in^2
The amount of wood needed is 685 in^2
May someone please help me?
Answer: [tex]x=-\frac{1}{2}, y=\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]5x+7=7x+8\\\\2x=-1\\\\x=-\frac{1}{2}\\\\\implies y=5\left(-\frac{1}{2} \right)+7=\frac{9}{2}[/tex]
Answer:
y = 5x + 7 ---1
y = 7x + 8 ---2
Substitute either one of the equations into the other.
I will substitute 1 into 2.
5x + 7 = 7x + 8
Simplify and solve for x.
2x = -1
x = -1/2
Substitute x into either one of the equations to find y.
I will substitute x into 1.
y = 5(-1/2) + 7
= 9/2
Hence, x = -1/2, y = 9/2
At a simple annual interest rate of 4.5%, how many years will it take Sam to earn $135 interest on an original deposit of $1,000?
A. 3
B. 4
C. 5
D. 6
Answer: A
Step-by-step explanation:
Interest = Principal * Rate * Time
135 = 1000 * 4.5% * T
135 = 1000 * 0.045 * T
135 = 45 * T
T = 135/45
T = 3 (A)
if A=D and C =F which additional statement does not allow you to conclude that ABC=DEF?1. AC=DF2.B=E3.BC=EF4.AB=DE
Given that 2 of the angles are congruent, we can conclude that the others angles are congruent too, because the sum of inner angles of a triangle is equal to 180. So the additional information we need is
[tex]\angle B\cong\angle E[/tex]And having that we could use AAA criteria. Also we could need AC = DF and use ASA criteria.
What is the volume of a triangular pyramid that is 10 in. tall and has a base area of 9 square in?
The volume of a triangular pyramid that is 10 in. tall and has a base area of 9 square inches is 30 cubic inches.
Volume of a triangular pyramidTetrahedrons are polyhedra made up of four triangular faces, six straight edges, and four vertex corners. They are also referred to as triangular pyramids.
The given shape is known as a triangular pyramid and the formula for calculating its volume is expressed as:
V = BH/3
where
B is the base area
H is the height of the prism
Determine the base area
B = 1/2 * base * height
B = 9 square inches
H = 10 inches
Substitute the given parameters into the formula
V = 9*10/3
V = 3*10
V = 30 cubic inches
This given the required volume of the prism
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If 8,x,y ,-4 are in A.p find x and y
Answer:
Step-by-step explanation:
firstly, 8+d=x and y+d= -4 where d is the common difference of the AP.
Also,
x+d=y;
therefore d=y-x;
so,
8+y-x=x (from the first equation)
=>8+y=2x
=>y=2x-8
Now from the second equation,
y+d= -4
(2x-8)+(y-x)= -4
=>x-8+2x-8= -4
=>3x=12
=>x=4
similarly,
y=2(4)-8
=>y=0
In the figure below, AX'Y'Z' is a dilation of AXYZ. Find the scale factor of the dilation, andspirit as an enlargement or a reduction. What is the scale factor?What is the Classify?
The scale factor can be obtained by determining the ratio of the length of the sides of the old and new figures.
In other words, it can be obtained by stating that:
[tex]\text{scale factor=}\frac{lengthofsideoftriangleX^IY^IZ^I}{\text{length of side of triangle XYZ}}\text{ }[/tex]Specifically, we can say that:
[tex]\text{scale factor=}\frac{X^IY^1}{XY}=\frac{X^IZ^I}{XZ}=\frac{Y^IZ^I}{YZ}[/tex]Now, if each block (or cell) on the graph represents 1 units, we have that:
X'Y' = 10 units and XY = 5 units
Therefore:
[tex]undefined[/tex]what is the slope for 5/3 x-4
Answer:
The slope is 5/3
Step-by-step explanation:
y = 5/3x - 4
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 5/3 and the y intercept is -4
Which postulate would prove the triangles congruent?
Answer:
AAS
Step-by-step explanation:
Because of vertical angle theorem, angle rts and vtu are congruent. This means there are 2 congruent angles with a non-included side
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Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
If function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
The function is
f(x) = [tex]x^2[/tex] + 4x -1
The function is the expression that represents the relationship between one variable and another variable. If one variable is dependent variable then the another variable is independent variable.
The value of g(x) = f(x+4)
First we have to find the value of f(x+4)
Substitute the values in the function
f(x) = [tex]x^2[/tex] + 4x -1
f(x+4) = [tex](x+4)^2[/tex] + 4(x+4) - 1
= [tex]x^2[/tex] + 8x +16 + 4x+16 - 1
Rearrange the terms and combine the like terms
= [tex]x^2[/tex] + 8x+4x + 16+16-1
= [tex]x^2[/tex] + 12x +31
Hence, if function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
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Question Progress
Homework Progress
7/21 Marks
Solve the equation
3x-2
4
-
2x-5
3
=
1+x
6
Answer: x= 1.20833
The way it was written was a little confusing but hope this helps, This may be wrong just re write it for me and it should be correct next time.
Step-by-step explanation:
Step 1: Make parentheses
( 3x - 2 ) 4 ( -2x - 5 ) 3 = ( 1 + x ) 6
Step 2: Solve parentheses ( Multiplication and division first )
(4 * 3x = 12x) - (4 * 2 = 8) -> 12x - 8
(-2x * 3 = -6x) - (3 * 5 = 15) -> -6x - 15
(6 * 1 = 6) + (6 * x = 6x) -> 6 + 6x
New and improved equation:
-12x - 8 - 6x - 15 = 6 + 6x
Step 3: add like terms
-12x - 6x = -18x
-8 - 15 = -23 so...
-18x - 23 = 6 + 6x
Step 4: solve it
-18x - 23 = 6 + 6x
+ 23
-18x = 29 + 6x
-6x
-24x = 29
x= 1.20833
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In triangle ABC measure of angle A equals 45°. The altitude divides the side AB into two parts of 20 and 21 units. Find BC.
In triangle ABC, BC = 29 units.
Given,
In Δ ABC, ∠A = 45°.
A perpendicular line segment traced from a triangle's vertex to its opposite side is said to be the triangle's altitude.
Let altitude meet AB on D.
So, AD = 20 units and DB = 21 units and ∠ADC = ∠BDC = 90°
In ΔADC,
tan A = DC/AD
tan 45° = DC/20
1 = DC/20
DC = 20 units
In ΔBDC,
BC² = BD² + DC² (Pythagorean Theorem)
= 21² + 20²
= 441 + 400
= 841
BC = √841
= 29
Hence, BC = 29 units.
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select all the angles that are congruent to <6
The angles that are congruent to angle 6 in the given diagram are:
∠2, ∠3, and ∠5.
What are Congruent Angles?Interior angles that lie opposite to each other along a transversal that cut across the parallel lines they are found on are said to be congruent angles based on the alternate interior angles theorem.
Also, vertical angles have angle measure that are the same, that is, they are congruent as well, so also are corresponding angles.
In the image given, angles 3 and 6 are alternate interior angles. Therefore, they are congruent.
∠5 is congruent to ∠6 because they are vertical angles.
∠2 is congruent to ∠6 because they are corresponding angles.
The angles that are congruent to angle 6 are: angles 3, 5, and 2.
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It took Brian 3 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 23 mph and make the return drive in only 2 hours. Find his average speed on the return drive.The equation from part 2 is 3x=2(x+23)Step 3 of 3: Solve the equation found in part 2 for x. Use this information to answer the given word problem.
Answer:
69 mph
Explanation:
The equation that represents this situation is:
[tex]3x=2(x+23)[/tex]We are required to determine Brian's average speed on the return drive.
To do this, we first find the value of x.
[tex]\begin{gathered} \text{Open the bracket} \\ 3x=2x+46 \\ \text{Subtract 2x from both sides} \\ 3x-2x=46 \\ x=46\; \text{mph} \end{gathered}[/tex]Using the value of x, we find the average speed on the return drive.
[tex]x+23=46+23=69\text{mph}[/tex]Therefore, the average speed on the return drive will be 69 mph.
Carter wants to use the model above to solve 273 ÷ 13. Explain how he would find parts A, B, and C of the model. Unfortunately I can’t show the model because “it hurts their feelings”
Answer: The answer to the division problem is 21
Answer: I know 273 divided by 13 is 21 but without the model I don't know what else you need. sorry!
Step-by-step explanation:
A car's velocity is modeled by v(t) = 0.5t^2 -14t+ 80 for 0 less than or equal to t less than or equal 14, where the velocity is in feet per second and time is in seconds. Where does the car come to a complete stop?
Answer:
8 seconds
Step-by-step explanation:
See attach worksheet.
Find the value of X using your method
Answer:
[tex]x = 30[/tex]
Step-by-step explanation:
In the diagram above, MN is a straight line which equals 180.
RL is vertically opposite to KS
(Vertically opposite angles are equal ⟹RL = KS).
So, MN becomes:
[tex]90 + 2x + 30 = 180[/tex]
Collect like terms
[tex]90 + 30 + 2x = 180→120 + 2x = 180→2x = 180 - 120→2x = 60[/tex]
Divide 2x = 60 by 2
[tex]x = \frac{60}{2} [/tex]
Therefore: [tex]x = 30[/tex]
You will have $ in 15 years if you set aside $100 a year at 6%.
The most appropriate choice for simple interest will be given by -
Amount obtained = $28.5
What is simple interest?
Simple interest is the interest earned on a certain principal at a certain rate over a certain period of time.
If principal is p, rate is r%, time is t years
Simple interest = [tex]\frac{p \times r \times t}{100}[/tex]
On adding principal and simple interest, we get amount.
Amount = Principal + Simple interest.
Principal = $15
Rate = 6%
Time = 15 years
Simple interest = [tex]\frac{15 \times 6 \times 15}{100}[/tex]
= $13.5
Amount obtained = $(15 + 13.5)
= $28.5
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