The Solution:
Let the two number be x and y133-x (
Such that:
[tex]\begin{gathered} x<133-x \\ x=small\text{ number} \\ 133-x=larger\text{ number} \end{gathered}[/tex]So,
[tex]\begin{gathered} 4x=3(133-x) \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=399-3x \\ \text{ Collect the like terms.} \\ 4x+3x=399 \\ 7x=399 \end{gathered}[/tex]Divide both sides by 7.
[tex]x=\frac{399}{7}=57[/tex]Therefore, the correct nswers are:
57 and 76
Drag each figure to show if it is similar to the figure shown or why it is not similar.
It is found that all the figures in the options except the fourth figure are similar to the given figure.
What are geometric shapes called?Geometric forms are figures in mathematics that depict the shape of items we observe in our daily lives. Shapes are the forms of things in geometry that have boundary lines, angles, and surfaces. There are several sorts of 2d and 3d shapes.
The given figure is a rectangle with dimensions 4 feet and 8 feet for length and breadth respectively.
We need to determine similar figure from the given options.
The first figure has a rectangle shape with different dimensions which is similar to given figure.
The second figure is also similar to given figure as it is also a rectangle with different dimensions.
By looking at the third figure, we can see that it has same rectangle shape and dimensions as the given figure which is 4 feet and 8 feet for length and breadth respectively.
The fourth figure is not a rectangle so it is not similar to the given figure.
Also, the last figure is a rectangle with different dimensions so it is similar to given figure.
Thus, we conclude that all the figures in the options except the fourth figure are similar to the given figure.
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Which interval notation represents a function with a domain of all real numbers greater than -3 and less than 6?A.) -2
The domain is the values of x, and if we want x to fit the inequalities they gave us, we have that
[tex]-3\leq x<6[/tex]A student was measuring water in a graduated cylinder. The student read the amount of water at 20 ml. The actual amount of water in the graduated cylinder was 17 ml, What is the approximate percent error?
Recall that percent error is given by the formula:
[tex]|\frac{real\text{ value-measured value}}{\text{real value}}|\cdot100[/tex]Therefore in our case this becomes:
[tex]|\frac{17-20}{17}|\cdot100=|\frac{3}{17}|\cdot100\approx17.65[/tex]Therefore the rounded (to two decimals) answer is : 17.65 %
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. f((x) = (x + 1)(x + 4)(x + 5)^5
Answer:
The graph falls to the left and rises to the right.
Explanation:
Given f(x) defined below:
[tex]f\mleft(x)=(x+1)(x+4)(x+5)^5\mright?[/tex]We are to determine the end behavior of the polynomial using the Leading Coefficient Test.
When using the Leading coefficient test, the following rule applies:
• When the ,degree is odd, and the ,leading coefficient is positive,, the graph falls to the left and rises to the right.
,• When the ,degree is odd, and the ,leading coefficient is negative,, the graph rises to the left and falls to the right.
,• When the ,degree is even, and the ,leading coefficient is positive,, the graph rises to the left and right.
,• When the ,degree is even, and the ,leading coefficient is negative,, the graph falls to the left and right.
Back to our function, f(x):
[tex]\begin{gathered} f(x)=(x+1)(x+4)(x+5)^5 \\ \text{Degree}=7\text{ (Odd)} \\ \text{Leading Coefficient = 1 (Positive)} \end{gathered}[/tex]From the first rule above, we can conclude that the graph falls to the left and rises to the right.
A graph of f(x) is attached which confirms this end behavior.
6. Use common denominators for these fractions. Arrange them from smallest to largest.
Given the fractions:
[tex]\frac{9}{16},\frac{3}{8},\frac{1}{4},\frac{5}{8}[/tex]We will arrange them from the smallest to the greatest using the common denominators
So, the common denominator for the fractions will be = 16
[tex]\begin{gathered} \frac{9}{16}=\frac{9}{16} \\ \\ \frac{3}{8}=\frac{2\cdot3}{2\cdot8}=\frac{6}{16} \\ \\ \frac{1}{4}=\frac{4\cdot1}{4\cdot4}=\frac{4}{16} \\ \\ \frac{5}{8}=\frac{2\cdot5}{2\cdot8}=\frac{10}{16} \end{gathered}[/tex]So, the answer will be the arrange will be:
[tex]\begin{gathered} \frac{4}{16},\frac{6}{16},\frac{9}{16},\frac{10}{16} \\ \\ \frac{1}{4},\frac{3}{8},\frac{9}{16},\frac{5}{8} \end{gathered}[/tex]
What 4x 5 + 2?????? ????
Given:
[tex]4\times5+2[/tex]To find the value:
Using the BODMAS rule,
[tex]\begin{gathered} 4\times5+2=(4\times5)+2 \\ =20+2 \\ =22 \end{gathered}[/tex]Hence, the answer is 22.
Please help me!! This is really hard for me and I need a tutor to explain it to me
SOLUTION
We want to find the solution of the equation
[tex]x^2=64[/tex]This becomes
[tex]\begin{gathered} x^2=64 \\ we\text{ move the square to the other side it becomes square root, we have} \\ x=\sqrt{64}\text{ the square root sign attracts }\pm,\text{ so we have } \\ x=\pm\sqrt{64} \\ x=\pm8 \end{gathered}[/tex]Hence the answer is
[tex]\pm8[/tex]Note that square root of 64 is 8
Two real numbers have coordinates w and t as shown on the number line below. Copy the number line into your Student Answer Booklet W + 2 3 -5 -4 3 2 1 0 1 4 5 a. What are the two real numbers represented by w and t on the number line? b. The coordinate of Point A on the number line is w + t. Plot and label Point A on the number line and explain how you decided upon its location. c. The coordinate of Point B on the number line is w — t. Plot and label Point B on the number line and explain how you decided upon its location, . d. The coordinate of Point C on the number line is wet. Plot and label Point C on the number line and explain how you decided upon its location.
1.
The location of w and t on the number line arenot exact so you will need to approximate .
In the first point w, it is between -4 and - 3 but closer than -4 compared to -3.Additionally, the point w is located at a position greater than -3.5 .It will be okay to approximate point w at -3.6.
w= -3.6
In the second point t, it is located between 0 and 1 but closer to 0 than 1. Additionally, t is less than 0.5 because it is located at a position less than 0.5, hence it is approximately at : t = 0.4
w= -3.6 and t = 0.4 -------approximated actual values
The two real numbers for w and t will be :
w= - 4 and t = 0 ---------approximated real numbers.
NB;
w= -3.7 and t= 0.3 is also a correct approximate because the difference of +/- 0.1 can be allowed for this case.
Mars is about 142 million miles from the sun. The earth is about 93,000,000 miles from the sun. How much farther from the sun is Mars than the earth? Express the answer in scientific notation State the letter of the correct answer. A.) 235x10 B.) 2.35x107 C) 4.9x10 D.) 49x107
D)
1) Let's visualize it to better understand this
2) Let's pick the distance between Mars and the Sun, and subtract it by the distance (Earth-Sun):
[tex]142,000,000-93,000,000=49,000,000=49\cdot10^6\text{ or 4.9 }\cdot10^7[/tex]3) So Mars is 4.9 x 10^7 miles farther from the sun than the Earth.
How many tablespoons of blue paint should Elena mix with 6 cups of white paint and blue paint? How many batches would this make?
According to the given graph, 2 cups of white paint are in the same ratio as 6 tablespoons of blue paint.
So, if she has 6 cups of white paint, we just have to multiply the number of tablespoons by 3.
[tex]6\times3=18[/tex]So, Elena needs 18 tablespoons of blue paint.Additionally, this would make three batches because the given ratio is being multiplied by 3.Find the area of the given geometric figure. If the figure is a circle, give an exact area and then use 22/7 as an approximation for pie to approximate the area. r=2in
the area of a circle is given by:
[tex]\text{Area}=\pi\cdot radius^2[/tex]Step 1
replace
[tex]\begin{gathered} \text{Area}=\frac{22}{7}\cdot(2inches)^2 \\ \text{Area}=\frac{22}{7}\cdot4in^2 \\ \text{Area}=\frac{22\cdot4}{7} \\ \text{Area}=12.57 \end{gathered}[/tex]so, the answer is 12.57 square inches
The point P. = (x,1/3) lies on the unit circle shown below. What is the value of x insimplest form?
When a point (x,y) lies on a unit circle, the following equation holds true:
[tex]x^2+y^2=1[/tex]We are given
[tex]y=\frac{1}{3}[/tex]and need to find x.
Let's put it into the equation and figure out x. Shown below:
[tex]\begin{gathered} x^2+y^2=1 \\ x^2+(\frac{1}{3})^2=1 \\ x^2+\frac{1}{9}=1 \\ x^2=1-\frac{1}{9} \\ x^2=\frac{8}{9} \\ x=\sqrt[]{\frac{8}{9}} \\ x=\frac{\sqrt[]{8}}{\sqrt[]{9}} \\ x=\frac{\sqrt[]{8}}{3} \end{gathered}[/tex]We can simplify the square root of 8 by using the radical property:
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\sqrt[]{b}[/tex]Thus, square root of 8 becomes:
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=\sqrt[]{4}\sqrt[]{2}=2\sqrt[]{2}[/tex]Thus, the simplest form of x is:
[tex]x=\frac{2\sqrt[]{2}}{3}[/tex]Solve for Time Principle $2,000Interest $480Rate 8%
ANSWER:
t = 3
STEP-BY-STEP EXPLANATION:
Given:
Principle (P) = 2000
Interest (I) = 480
Rate (r) = 8% = 0.08
The simple interest formula is the following:
[tex]I=P\cdot r\cdot t[/tex]We substitute each value and solve for t, like this:
[tex]\begin{gathered} 480=2000\cdot 0.08\cdot \:t \\ \\ t=\frac{480}{2000\cdot0.08}=\frac{480}{160} \\ \\ t=3 \end{gathered}[/tex]Therefore, the time would be 3 periods (it depends on the interest rate if it is annual, monthly, etc.)
What is the domain and range of y=-1/2x+3
For the function
[tex]y=-\frac{1}{2}x+3,[/tex]the range is all the values y can have and the domain is all the possible values that x can take.
In our function there seems to be no restriction on what values x and y can take—our function is defined for all real values of x and y — therefore, the domain and the range of our function is all real numbers.
Calculate Jayden's simple interest on a 5-year car loan for $33,486 at 2.38%.
Answer:
$3984.83.
Explanation:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]In this particular case:
• The principal/loan amount = $33,486.
,• Rate = 2.38%.
,• Time = 5 years.
Substituting these into the formula above:
[tex]\begin{gathered} Simple\: Interest=\frac{33,486\times2.38\times5}{100} \\ =\$3984.83 \end{gathered}[/tex]Jayden's simple interest is $3984.83.
In the X Y -plane, a line crosses the Y - axis at the point (0,3) and passes through the point ( 4,5). Which of the following is an equation of the line?A. y = x + 3 2B. y = 2x + 31 C. y = x – 4 2D. y = 2x – 4
Given two points of a line (x1, y1) and (x2, y2), the equation of the line is:
[tex]\begin{equation*} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{equation*}[/tex]We are given the points (0, 3) and (4, 5). Plugging in these values:
[tex]y-3=\frac{5-3}{4-0}(x-0)[/tex]Operating and simplifying:
[tex]\begin{gathered} y-3=\frac{2}{4}x \\ \\ y=\frac{1}{2}x+3 \end{gathered}[/tex]An unusual die has the numbers 2,2,3,3, 7 and 7 on its six faces. Two of these dice are rolled, and the numbers on the top faces are added. How many different sums are possible?
To find the total numbers of sum, we just have to elevate the number of faces by the second power.
[tex]6^2=36[/tex]There are 36 total numbers of sums.
However, there are just 6 different sums.
[tex]\begin{gathered} 2+2=4 \\ 2+3=5 \\ 2+7=9 \\ 3+3=6 \\ 3+7=10 \\ 7+7=14 \end{gathered}[/tex]Therefore, there are 6 different sums.Select all that apply. What value(s) for x make(s) the equation true?-8y - 2 = -8y - 2
According to the given data we have the following equation:
-8y - 2 = -8y - 2
In order to calculate the value(s) for x make(s) the equation true we would have to calculate variable y as follows:
We would substitute the y with the values 0, -15, 37, 343
So, if we substitute for 0
-8(0)-2=-8(0)-2
0-2=0-2
-2=-2
value for x=0 applies.
if we substitute for -15
-8(-15)-2=-8(-15)-2
120-2=120-2
118=118
if we substitute for 37
-8(37)-2 +8(37)+2=0
-296-2 +296+2=0
if we substitute for 343
-8(343) -2 +8(343)-2=0
What are the first and third quartiles of rainfall of this data? Q1 = 5. Q3 = 8 Q1 = 6, Q3 = 8 Q1 = 4, Q3 = 7 Q1 = 5, Q3 = 7.5
Answer:
Q1 = 5, Q3 = 8
Explanation:
There are a total of 19 dots on the chart.
[tex]\begin{gathered} Item\; in\; Q_1=\frac{1}{4}\times19 \\ =4.75th\text{ item} \end{gathered}[/tex]The 5th item on the chart =5, therefore:
• Q1 = 5
Similarly:
[tex]\begin{gathered} Item\; in\; Q_3=\frac{3}{4}\times19 \\ =14.25th\text{ item} \end{gathered}[/tex]The 14th and 15th item on the chart =8, therefore:
• Q3 = 8
Which additional piece of information would you need to prove these two triangles are congruent using the side-side-side or SSS triangle congruence postulate?
By using congruency of triangles, the result obtained is
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
Third option is correct
What is Congruency of triangles?
Two triangles are said to be congruent if the corrosponding sides and corrosponding angles are same.
The different axioms of congruency are SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom
In [tex]\Delta STU[/tex] and [tex]\Delta SHU[/tex]
ST = HU [Given]
SU is common
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
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Complete Question
The diagram has been attached here
Jen Butler has been pricing Speed-Pass train fares for a group trip to New York Three adults and tour children must pay $124. Two adults and three children must pay $88. Find the serice of the addit's ticket and the price of a child's ticketThe price of a child's ticket is $The price of an adult's ticket is $
It is given that two adults and three children pay $88.
Represent it as equation
2x+3y=88
Then three adults and four children pay $124.
It is written is equation form as follows.
3x+4y=124
Here x is adults' price and y is children's price.
Solve the system of equation as follows.
[tex]\begin{gathered} 3x+4y=124 \\ 2x+3y=88 \\ 6x+8y=248 \\ 6x+9y=264 \end{gathered}[/tex]Now subtract each of the last two equations to get -y=-16
Hence y = 16
Substitute in equation 1, we get
[tex]\begin{gathered} 2x+48=88 \\ 2x=40 \\ x=20 \end{gathered}[/tex]Therefore, adult price is $20 and children price is $16
A piece of wire 32 cm long is cut into two pieces, each to be bent to make a square. The length of a side of one square is to be 4 cm longer than the length of a side of the other How should the wire be cut?The length of the shorter piece of wire is :
Let P1 represent the perimeter of the larger square and let P2 represent the perimeter of the smaller square. Since the piece of wire is 32 cm long and both squares are made of this wire, we have the following:
[tex]P_1+P_2=32[/tex]Now let x be the length of the side of the smaller square. Since the larger square has sides 4cm longer than the length of the side of the other square, we have the following:
[tex]\begin{gathered} P_1=4(x+4) \\ P_2=4x \end{gathered}[/tex]using these expressions on the first equation and solving for x, we get:
[tex]\begin{gathered} 4(x+4)+4x=32 \\ \Rightarrow4x+16+4x=32 \\ \Rightarrow8x=32-16=16 \\ \Rightarrow x=\frac{16}{8}=2 \\ x=2 \end{gathered}[/tex]we have that x = 2. Then, the length of the shorter piece of wire will be the perimeter of the smaller square, therefore, the length of the shorter piece of wire is P2 = 4(2) = 8 cm
Use to reflect over the x-axis. Identify the transformed vector.
To reflect the given matrix over the x-axis, you have to multiply both matrices:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}[/tex]Multiply each term of the first row of the first matrix with the corresponding terms of the column of the second matrix and add the results:
Repeat the process for the second row of the first matrix
The resulting matrix is:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}=\begin{bmatrix}{(1\cdot7)+(0\cdot-12)} \\ {\square}(0\cdot7)+(-1\cdot-12)\end{bmatrix}=\begin{bmatrix}{7} \\ {12}\end{bmatrix}[/tex]The correct option is option D.
solve for y in the equation below
2 4y = 9
Answer:9/24
Step-by-step explanation
Graph the line 3x - 5y = 18
Given:
3x - 5y = 18
To graph this line, rewrite the equation in slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Subtract 3x from both sides:
3x - 3x - 5y = -3x + 18
-5y = -3x + 18
Divide all terms by -5:
[tex]\begin{gathered} \frac{-5y}{-5}=\frac{-3x}{-5}+\frac{18}{-5} \\ \\ y=\frac{3}{5}x-\frac{18}{5} \end{gathered}[/tex]Thus, the slope intercept form of the equation is:
[tex]y=\frac{3}{5}x-\frac{18}{5}[/tex]Any line can be graphed using two or more points.
Let's determine two points on the line.
Input 6 for x and solve for y:
[tex]\begin{gathered} y=\frac{3}{5}\ast6-\frac{18}{5} \\ \\ y=\frac{18}{5}-\frac{18}{5} \\ \\ y=0 \end{gathered}[/tex]Also, the y-intercept is:
[tex](0,-\frac{18}{5})[/tex]convert the fraction to decimal:
[tex]-\frac{18}{5}=-3.6[/tex]Thus, we have the points:
[tex]\begin{gathered} (0,-3.6) \\ (6,\text{ 0)} \end{gathered}[/tex]x y
0 -3.6
6 0
Mark the points on a graph and make a straight line that passes through the points.
The graph is attached below:
Lola has 8 bear figurines. These bear figurines make up 40% of her collection of animal figurines. Find the total number
Hence, the total number of bear figurines are 20
Find the area of the shaded region.3112Note: Use either the pi button on your calculator or 3.14 for pi. Round to the nearest tenth.
The area of a sector of a circle can be calculated by using the formula:
[tex]A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ where }\theta\text{ is the angle in degrees and r is the radius}[/tex]The total area of a circle can be calculated as:
[tex]A_{total}=\pi\cdot r^2\text{ where r is the radius}[/tex]To find the area of the shaded region, you need to calculate the total area of the circle and then subtract the area of the non-shaded region, as follows:
[tex]\begin{gathered} A_{total}=\pi\cdot r^2\text{ The given value for r is 3} \\ A_{total}=\pi\cdot3^2\text{ } \\ A_{total}=\pi\cdot9 \\ A_{total}=3.14\cdot9 \\ A_{total}=28.3 \end{gathered}[/tex]Now let's calculate the area of the non-shaded region:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ the given values for }\theta=112\text{ and r=3} \\ A=\frac{112}{360}\cdot\pi\cdot3^2\text{ } \\ A=0.31\cdot3.14\cdot9 \\ A=8.8 \end{gathered}[/tex]The area of the shaded region will be:
[tex]\begin{gathered} A_{SR}=A_{total}-A \\ A_{SR}=28.3_{}-8.8 \\ A_{SR}=19.5 \end{gathered}[/tex]Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for 2005 through 2014 can be approximated by 7.1x-y=-254. The number of network and data analyst jobs for the same years can be approximated by 12.2x-y=-231. For both equations, x is the number of years since 2005 and y is the number of jobs in thousands.Solution to the ordered pairs:(5, 286)Use your result from part (a) to estimate the year in which the number of both jobs is equal.
Given the system of equations:
7.1x - y = -254
12.2x - y = -231
Where x is the number of years since 2005
y is the number of Jobs in thousands.
After solving the system, we have the solution:
(x, y) ==> (5, 286)
Let's determine the year in which the number of both jobs is equal.
The graph of both lines will meet at the solution point.
Given that x represents the number of years since 2005, the year which the number of both jobs is equal will be 5 years after 2005.
Hence, we have:
Year in which number of both jobs are equal = 2005 + 5 = 2010
Therefore, in 2010, the number of both jobs will be equal.
ANSWER:
2010
What is the value of x?
Answer:
The two angles are congruent, so: 2x+2=3x-52
2x-3x=-2-52
-x=-54
x=54
if p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<13 = ?
Answer:
[tex]m\angle13=92^o[/tex]Explanation:
First, we match the angles
9 = 11
10 = 12
16 = 14
15 = 13
Therefore, if we find angle 15, we find an angle 13.
Angle 15 is supplementary to angle 16; therefore,
[tex]\angle16+\angle15=180^o[/tex]Since
[tex]\angle16=88^o[/tex]Therefore,
[tex]88^o+\angle15=180^o[/tex]subtracting 88 from both sides
[tex]\angle15=180^o-88^o[/tex][tex]\angle15=92^o[/tex]which is our answer!