Step 1
Given:
[tex]35+3x-11=23[/tex]Required: To find the value of x
Step 2
Find the value of x
[tex]\begin{gathered} \text{Bring like terms together} \\ 3x=23+11-35 \end{gathered}[/tex][tex]undefined[/tex]What is negative 279 divided by negative 45?
Answer:
6.2
Step-by-step explanation:
Roaring Zoo has 68 different species of birds. Because of cold weather, only 24 species stayed at the zoo, while the others were transported to the barn until warmer weather returned.
Which equation shows how many species of birds were transported?
Based on the total number of species of birds, and the number that stayed at the zoo, the equation that shows the species of birds that were transported is b + 24 = 68.
How to find the equation?The total number of birds in Roaring Zoo adds up to 68 different species which means that the number of birds that stayed and the number that were trasnported will add up to 68.
Assuming the number of birds transported was b, the equation to find this number of birds is:
Number of transported birds + Number of birds that stayed at zoo = Total number of birds
b + 24 = 68
Options for this question are:
b + 24 = 68
b − 24 = 68
b + 68 = 24
b − 68 = 24
Find out more on birds in zoo at https://brainly.com/question/19754455
#SPJ1
The figure below is made from squares given the area of the figure find its perimeter to the nearest tenth. A=90ft squared
As the figure is made for 6 squares, the total area of the figure divided into 6 is the area of one square:
[tex]\begin{gathered} A_F=90ft^2 \\ \\ A_S=\frac{90ft^2}{6}=15ft^2 \end{gathered}[/tex]The area of one square is 15 square feet.
The area of a square is equal to the square lenght
[tex]A=l^2[/tex]Then, as the given squares have area of 15 square feet the measure of the lenght of one square is:
[tex]\begin{gathered} 15ft^2=l^2 \\ \sqrt[]{15}ft=l \end{gathered}[/tex]Then, as each side of each square is square root of 15 feet you have the next:
The perimeter of the figure is the sum of all the sides: The figure has 12 sides: 2 sides have a measure of 2square root of 15 feet and the other 10 sides have a measure of square root of 15 feet:
[tex]\begin{gathered} P=2(2\sqrt[]{15})ft+10(\sqrt[]{15})ft \\ \\ P=4\sqrt[]{15}ft+10\sqrt[]{15}ft \\ \\ P=14\sqrt[\square]{15}ft \\ \\ P=14.491ft\approx14.5ft \end{gathered}[/tex]Then, the perimeter of the figure is 14.5 feet
(a) Write a linear equation to represent all the combinations of numbers of
hi-res (x) and lo-res (y) photos Rohan can store on his memory card.
(b)
14
What is the slope of the line, and what does it mean in this context?
frate
(a) The general equation of a straight line is y = mx + c, where m is the slope and c is the y-intercept of the line. The given question can be represented in terms of straight line as y = -2x + 7000.
(b) The slope of the line is -2 and it represents the rate of decrease of hi-res pictures with respect to low-res pictures.
What is the equation of a Straight Line between any two points?The equation of a Straight Line between points (x₁,y₁) and (x₂,y₂) can be given as y = (x-x₁)(y₂-y₁)/(x₂-x₁)+y₁ where (y₂-y₁)/(x₂-x₁) is the slope of the line.
In the given question, Suppose number of hi-res pictures be x.
And, number of low-res pictures be y.
Then, value of x at y = 0 is 3500 and value of y at x = 0 is 7000.
There are two points (3500,0) and (0,7000).
Slope of the line is given as (7000-0)/(0-3500) = -2.
The y-intercept is 7000.
Therefore, the equation of line is given by y = -2x + 7000 and the slope of this line represents the rate of decrease of hi-res pictures with respect to low-res pictures.
Hence, the equation of line is given by y = -2x + 7000 and its slope = -2 represents rate of decrease of hi-res pictures with respect to low-res pictures.
To know more about Straight lines click on the following link,
https://brainly.com/question/28951575
#SPJ1
The equation [tex]f(x)=7a^{2+x}-b[/tex] has an x-intercept equivalent to
A) [tex]x=\frac{logb-log7}{loga}-2[/tex]
B) [tex]x=7a^{2}-b[/tex]
C) [tex]x=\frac{y+b}{7a^{2}}[/tex]
D) [tex]x=0[/tex]
I have the answer key so I know the answer. I just don't know how they got to the answer so please show your work.
Answer:
[tex]\textsf{A)} \quad x=\dfrac{\log b - \log 7}{ \log a}-2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=7a^{2+x}-b[/tex]
The x-intercepts occur when the function equals zero.
[tex]\implies 7a^{2+x}-b=0[/tex]
Add b to both sides:
[tex]\implies 7a^{2+x}=b[/tex]
Divide both sides by 7:
[tex]\implies a^{2+x}=\dfrac{b}{7}[/tex]
Take logs of both sides of the equation:
[tex]\implies \log \left(a^{2+x}\right)= \log \left(\dfrac{b}{7}\right)[/tex]
[tex]\textsf{Apply the Power log law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies (2+x)\log a= \log \left(\dfrac{b}{7}\right)[/tex]
[tex]\textsf{Apply the Quotient log law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]
[tex]\implies (2+x)\log a= \log b-\log 7[/tex]
Divide both sides by log a:
[tex]\implies 2+x=\dfrac{\log b - \log 7}{ \log a}[/tex]
Subtract 2 from both sides:
[tex]\implies x=\dfrac{\log b - \log 7}{ \log a}-2[/tex]
17.) The base of a triangle is 1 meter more than three times the height.Set up and solve an equation to find the base and the height if the1area is 40 square meters. Use: z(base)(height) = Area(12 pts)
SOLUTION
Step 1: List out the given parameters.
[tex]\begin{gathered} \text{Let the height be x} \\ \text{Base}=3x+1 \\ A=40m^2 \end{gathered}[/tex]Step 2: Write the formula for the area of the triangle and solve.
[tex]\begin{gathered} A=\frac{1}{2}\times\text{base x height} \\ \end{gathered}[/tex]Substitute the parameters in step 1 into the formula in step 2
[tex]\begin{gathered} 40=\frac{1}{2}\times(3x+1)\times x \\ 80=3x^2+x \\ 3x^2+x-80=0 \end{gathered}[/tex]Solving the above quadratic equation by quadratic formula method, we will get:
[tex]x=5\text{ and x=}\frac{-16}{3}[/tex]Since the value for a side of a triangle cannot be negative, x=5 is the only value of x we can use.
Therefore:
[tex]\begin{gathered} \text{height}=x=5m \\ \text{Base}=(3x+1)=(3(5)+1)=(15+1)=16m \end{gathered}[/tex]So we can conclude that:
The base is 16 meters and the height is 5 meters.
How many matches are in the 50th diagram of the pattern?
=======================================================
Explanation:
n = diagram number
m = number of matches for diagram n
The given figures show that we have this info so far
[tex]\begin{array}{|c|c|} \cline{1-2}n & m\\\cline{1-2}1 & 3\\\cline{1-2}2 & 5\\\cline{1-2}3 & 7\\\cline{1-2}\end{array}[/tex]
In other words, we have this sequence of values to represent the number of matches: 3, 5, 7
Each time we generate a new figure, we add 2 matches to the far right side. One match being horizontal and the other vertical.
This shows the common difference of this arithmetic sequence is d = 2.
The starting term is [tex]a_1 = 3[/tex].
Let's find the nth term.
[tex]a_n = a_1 + d(n-1)\\\\a_n = 3 + 2(n-1)\\\\a_n = 3 + 2n-2\\\\a_n = 2n+1\\\\[/tex]
Then we can determine the 50th term.
[tex]a_n = 2n+1\\\\a_{50} = 2(50)+1\\\\a_{50} = 100+1\\\\a_{50} = 101\\\\[/tex]
There are 101 matches in the 50th diagram of the pattern.
Express the difference in the amount of $1227.23 and $286.13 in the form of percentage? what is the formula to figure out the answer to this problem?it is the retail price of something and then the sale price of something I need to know how much percentage it is off
Answer:
76.68%
Explanation:
To know how much percentage it is off, we will use the following equation:
[tex]\frac{\text{ Initial value - Final Value}}{\text{ Initial Value}}\times100[/tex]So, if the prices are $1227.23 and $283.13, we can replace the values as
[tex]\frac{\text{ \$1227.23 - \$286.13 }}{\text{ \$1227.23}}\times100=\frac{941.1}{1227.23}\times100=76.68\text{ \%}[/tex]Therefore, the percentage of discount is 76.68%
The area of the
polygon is 224cm².
What is its perimeter?
The perimeter of the given polygon is 60 cm.
What do you mean by a polygon?A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both. A polygonal circuit's segments are referred to as its edges or sides.A two-dimensional geometric shape with a finite number of sides is called a polygon.A polygon's sides are constructed from segments of straight lines joined end to end.So, according to the attached image, the polygon is a square.
Area of square: A = s²Now, calculate for sides:
224 = s²s = √224s = 14.96Rounding off: 15cm
Now, we know that each side of the square is 15 cm.Then perimeter:
P = 4sP = 4(15)P = 60 cmTherefore, the perimeter of the given polygon is 60 cm.
Learn more about polygons here:
brainly.com/question/24464711
#SPJ1
This graph represents the function /(4) = }cos(t)What is the amplitude of the function?
Given:
[tex]f(x)=\frac{1}{2}cos(x)[/tex]Required:
We need to find the amplitude of the equation.
Explanation:
The given equation is of rhe form
[tex]f(x)=Acos(Bx)+D[/tex]Where A =1/2, B=1, and D=0.
We know that A is the amplitude.
[tex]Amplitude\text{ =}\frac{1}{2}[/tex]Final answer:
[tex]Amplitude\text{ =}\frac{1}{2}[/tex]QuestionMultiply: (6√22a²) (4√2a6).
Answer:
48√11a^8
Step-by-step explanation:
4x + 8y = 32( Write In slope intercept form)
Here, we want to write the given equation in the slope-intercept form
Mathematically, we have the general form of the slope-intercept form as follows;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and b represents the y-intercept
So in clearer terms, all we need do is to isolate y which is same as making y the subject of the formula
We have this as;
[tex]\begin{gathered} 8y\text{ = -4x+32} \\ \text{divide through by 8} \\ \frac{8y}{8}\text{ = -}\frac{4x}{8}+\text{ }\frac{32}{8} \\ \\ y\text{ = -}\frac{1}{2}x\text{ + 4} \end{gathered}[/tex]Help with number one a-f is all part of number one
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
carnival game:
spinner: 1 to 8
Step 02:
simple probability:
p = favorable outcomes / total outcomes
1. probability of an event:
a. p (odds):
p (odds) = 4 / 8 = 1 / 2
b. p (evens):
p (evens) = 4 / 8 = 1 / 2
c. p (3):
p (3) = 1 / 8
d. p (4 or 6):
p (4 or 6) = 2 / 8 = 1 / 4
e. p (7'):
p (7') = 7 / 8
f. p (1):
p (1) = 1 / 8
That is the full solution.
Convert 4 3/4 to a decimal
Given
[tex]4\frac{3}{4}[/tex]One fourth as a decimal value is
[tex]\frac{1}{4}=0.25[/tex]To determine how much 3/4 is equivalent to, multiply 0.25 by 3
[tex]3\cdot0.25=0.75[/tex]add the decimal value to 4
[tex]4\frac{3}{4}=4+0.75=4.75[/tex]Summarizing and visual cues fill in the blanks to complete the rule
According to the given statements, the answers are as follows:
1. number of sides (n) = number of interior angles = number of exterior angles
2. All interior angles are congruent.
3. All exterior angles are congruent.
4. sum of interior angles = (n-2)180°.
5. sum of exterior angles = 360°.
6. measure of each interior angle = (n-2)180°/n.
7. measure of each exterior angle = 360°/n.
23The steps to convert to a decimal are shown below:45.714 23.00- 2030Step 1Step 2Step 3-264-4Step 40In what step is the first error?step 1step 2step 3step 4
Answer:
step 3
Step-by-step explanation:
You want to know the step where the first error occurred in the long division calculation shown.
Long divisionThe value subtracted in step 3 should be the product of 4 and 7. That value is 28 (not 26). The error is in using -26 instead of -28 for Step 3.
<95141404393>
find the coordinates of the image given the coordinates of the preimage and the translation
The transformation is a translation of 7 units in the x-axis and (-1) in the y-axis.
We can write this transformation for a point P=(x,y) as:
[tex]P=(x,y)\longrightarrow P^{\prime}=(x+7,y-1)[/tex]Then, if we apply the transformation to J, F and N we will get:
[tex]J=(-3,1)\longrightarrow J^{\prime}=(-3+7,1-1)=(4,0)[/tex][tex]F(-2,3)\longrightarrow F^{\prime}=(-2+7,3-1)=(5,2)[/tex][tex]N=(-2,0)\longrightarrow N^{\prime}=(-2+7,0-1)=(5,-1)[/tex]The transformed points are J'=(4,0), F'=(5,2) and N'=(5,-1).
I need to know the answer to this question please
the mathematical property demonstrated is associative property (3rd option)
Explanation:Given:
[tex](24\times8)\times2\text{ = 24}\times(8\times2)[/tex]To find:
the mathematical property
[tex]\begin{gathered} cummutative\text{ property of multiplication is given as:} \\ a\times b\text{ = b}\times a \\ \\ Associative\text{ property of multiplication:} \\ a\times(b\times c)\text{ = \lparen a}\times b)\times c \\ \\ Distributive\text{ property:} \\ a(b\text{ + c\rparen = ac + bc} \end{gathered}[/tex]The property with the same arrangement as the given expression is associative property as it has to do with grouping.
Hence, the mathematical property demonstarted is associative property (3rd option)
A teaspoon of salt has a mass of 6 grams. What is its mass in milligrams?0) 600 milligrams60 milligrams0) 6.000 milligrams60.000 milligrams Ten points if you get this pls
1 milligram = 0.001 gram
x milligrams = 6 grams
By crossmultiplying, it becomes
0.001 * x = 6 * 1
0.001x = 6
x = 6/0.001
x = 6000
The mass in milligrams is 6000 milligrams
a rectangular solid has dimensions (a+2) by (a+4) by (3a). find it's volume
Volume of a rectangular solid = Length x breadth x height
=(a+2) x (a+4) x (3a)
=(a+2)(a+4)(3a)
[tex]\begin{gathered} V=(a^2+4a+2a+8)(3a) \\ V=3a(a^2+6a+8) \\ V=(3a^3+18a^2+24)\text{ cubic unit} \end{gathered}[/tex]For a confidence level of 99% with a sample size of 11, find the critical t value.
Solution
Given that
sample size n = 11
The degree of freedom df = n - 1 = 11 - 1 = 10
At 99% confidence level,
[tex]\begin{gathered} \alpha=1-99\%=1-0.99=0.01 \\ \\ \frac{\alpha}{2}=0.005 \end{gathered}[/tex][tex]t_{\frac{\alpha}{2},df}=t_{0.005,10}=3.1693[/tex]Checking the table,
Therefore, the Critical value t value = 3.169
Which of the following is a point-slope equation for a line with the point(-2, 4) and a slope of 3?O A. y+2=3(x-4)O B. y-4=3(x+2)O C. y-2=3(x-4)O D. y - 4= 3(x-2)
Given that
The point is (-2, 4) and the slope is 3.
And we have to find the point-slope equation for this data.
Explanation -
First, we will write the formula to find the point-slope equation and then we will substitute the values to find the required equation.
The general point-slope equation is given as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope and the point is \lparen x}_1,y_1) \end{gathered}[/tex]We have slope, m = 3 and point (x1, y1) = (-2, 4)
Hence the required equation is
[tex]\begin{gathered} y-4=3(x-(-2)) \\ y-4=3(x+2) \end{gathered}[/tex]So the correct option is B.
Final answer -
Hence the final answer is y-4 = 3(x + 2)A triangle has a base of 3^2 units and a height of 2^3 units. Write two equivalent expressions for the triangles area using exponents
36 or 4 × 3² is equivalent expressions for the triangles area using exponents.
What is a triangle answer?
A triangle is a polygon with three sides. It has three sides as well as three vertices that make up its three angles. Any triangle with vertices and is represented below as A B C: varieties of triangles Triangle of Scalene: The lengths of the sides are not equal.Having three sides, a triangle is a form. The various triangle varieties go under various names. The size of the angles and side lengths determine what kind of triangle it is (corners). According on how long their sides are, triangles can be classified as equilateral, isosceles, or scalene.Area of a triangle = (1/2) × b × h
Area = (1/2) × 3² × 2³
Therefore, by indices Area = 2² × 3².
or Area = 4 × 3²
= 4 * 9 = 36
Learn more about triangle
brainly.com/question/2773823
#SPJ1
You want a college fund for your newborn which will be worth 300,000 in 18 years. You purchase a CD with an 18 year maturity at 7%, compounded quarterly. How much did you pay for the CD if it will be worth what you want it to?
Given:
[tex]\text{Amount}=300,000;\text{ r=}7\text{ \% ; }n=4\text{ ; t=18}[/tex][tex]\text{Amount(A)}=P(1+\frac{r}{n})^{nt}[/tex][tex]300000=P(1+\frac{0.07}{4})^{4\times18}[/tex][tex]300000=P(\frac{4.07}{4})^{4\times18}[/tex][tex]300000=P(1.0175)^{72}[/tex][tex]P=\frac{300000}{(1.0175)^{72}}[/tex][tex]P=86028.6615[/tex]Therefore , I have to pay 86028.66 .
Make x the subject of h = 4(x + 3y) + 2
To make x the subject means to solve the equation for x (or basically to get x to stand by itself.)
First, we expand the bracket :
h = 4x + 12y + 2
Minus both sides by 12y + 2 :
h - 12y - 2 = 4x
Divide both side by 4 :
(1/4)h - 3y - 1/2 = x
Therefore, x = (1/4)h - 3y - 1/2.
If data for the topics below were collected and displayed in a frequency table, which topic would most likely need to be shown in intervals?heights of treeseye colorfavorite foodfoot length of newborn babies
Given
frequency table
Find
which topic would most likely need to be shown in intervals?
Explanation
as trees varies a lot , so it must be in interval.
and all other options does not vary that much.
so , the height of trees most likely need to be shown in intervals.
Final Answer
Therefore, the correct option is Height of Trees
the table below provides the amount of savings y generated after saving money for x weeks use the table below to answer the following questions A) Below is a copy of a students work finding the liner equation that models the given data describe the error in the students work of finding the liner equation B) correctly find the liner equation in slope intercept form that models the given data
A)
Consider that the slope 'm' of the line, representing the relationship between 'y' and 'x', is given by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]As observed, the student applied the formula between the points (3,350) and (5,450) but the student made a mistake in the denominator.
Mistake: The student took (3-5) in the denominator which is wrong as per the numerator. He/she should take (5-3) in the denominator.
And the correct slope will be calculated as,
[tex]\begin{gathered} m=\frac{450-350}{5-3} \\ m=\frac{100}{2} \\ m=50 \end{gathered}[/tex]B)
Let the linear model representing the relation between 'y' and 'x' be,
[tex]y=mx+b[/tex]Substitute the value of the slope,
[tex]y=50x+b[/tex]Pick any of the given pair of values (x,y) from the table.
Since the equation of line is the model for all the given data, coordinates of each point must satisfy the linear equation. This logic can be used to obtain the value of unknown variable 'b'.
Let us take the point (7,550) to obtain the value of 'b' as follows,
[tex]\begin{gathered} 550=50(7)+b \\ 550=350+b \\ b=550-350 \\ b=200 \end{gathered}[/tex]Substitute the value back in the linear equation,
[tex]y=50x+200[/tex]Thus, the required linear equation is obtained as,
[tex]y=50x+200[/tex]Ernesto and his family have finished dinner at a restaurant in a region where themeal taxis 5% of the price of the meal. Ernesto leaves a 17% tip. With tax and tip, the total cost is$58.56. Create an equation, where p is the price of the meal. Determine what the cost ofthe meal was.
Answer:
58.56 = 1.22p (the equation)
Explanation:
Given:
meal tax = 5% of the price f the meal
The tip = 17% of the price of the meal
Total cost including meal tax and tip = $58.56
To find:
a) An equation where p is the price of the meal
b) The cost of the meal
a) let p = price of the meal
meal tax = 5% (p) = 0.05(p)
meal tax = 0.05p
tip = 17% (p) = 0.17(p)
tip = 0.17p
Total cost including meal tax and tip = price of the meal + meal tax + tip
58.56 = p + 0.05p + 0.17p
58.56 = 1.22p (the equation)
b) To determine the cost of the meal, we will solve for p:
[tex]\begin{gathered} \frac{58.56}{1.22}\text{ = }\frac{1.22p}{1.22} \\ p\text{ = 48} \end{gathered}[/tex]The price of the meal is $48
How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 3 years? The account pays 5.9% interest compounded semiannually[Round your final answer to two decimal places
We are asked to determine the present value of an annuity that is paid at the end of each period. Therefore, we need to use the formula for present value ordinary, which is:
[tex]PV_{ord}=C(\frac{1-(1+i)^{-kn}}{\frac{i}{k}})[/tex]Where:
[tex]\begin{gathered} C=\text{ payments each period} \\ i=\text{ interest rate} \\ n=\text{ number of periods} \\ k=\text{ number of times the interest is compounded} \end{gathered}[/tex]Since the interest is compounded semi-annually this means that it is compounded 2 times a year, therefore, k = 2. Now we need to convert the interest rate into decimal form. To do that we will divide the interest rate by 100:
[tex]\frac{5.9}{100}=0.059[/tex]Now we substitute the values:
[tex]PV_{ord}=4000(\frac{1-(1+0.059)^{-2(3)}}{\frac{0.059}{2}})[/tex]Now we solve the operations, we get:
[tex]PV_{\text{ord}}=39462.50[/tex]Therefore, the present value must be $39462.50
Roberta is thinking about joining the food co-op store. If she pays $10.00 to join, she will get 10% off on all the grocerie must she buy before her savings equal her membership fee?
Answer:
cat
Step-by-step explanation: