The expression given is,
[tex]x^2-x-20[/tex]Factorize the expression above
[tex]\begin{gathered} Break\text{ the expressions into two groups} \\ \left(x^2+4x\right)+\left(-5x-20\right) \\ Factorize\text{ out the common terms} \\ =x\left(x+4\right)-5\left(x+4\right) \\ \mathrm{Factor\:out\:common\:term\:}x+4 \\ =\left(x+4\right)\left(x-5\right) \end{gathered}[/tex]Hence, the answer is
[tex]\left(x+4\right)\left(x-5\right)[/tex]Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?
We can find the factor of dilation by finding the ratio between two correspondent sides of the quadrilaterals.
Consider Q'R' and QR.
[tex]\begin{gathered} QR=6 \\ Q^{\prime}R^{\prime}=2 \\ \Rightarrow\frac{Q^{\prime}R^{\prime}}{QR}=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Therefore, the scale factor for the dilation is equal to 1/3
Answer: 1/3
Step-by-step explanation: just did it on edge
Which of the following Platonic solids is made from squares? Check all thatapply.A. icosahedronB. cubec. tetrahedronD. octahedronE, hexahedronF. dodecahedron
From the information on platonic solids, we can say that cube is the only platonic solid that is made from squares. Thus, option B is correct.
Platonic solids, also referred to as regular solids or regular polyhedrons, are the types of solids that have identical faces composed of congruent regular convex polygons.
A platonic solid can be defined as a 3D shape where each face is similar to a regular polygon and consists of same number of faces that meet at each vertex of the polygon.
There are 5 different types of platonic solids that are -
Tetrahedron - A tetrahedron is referred to as a triangular pyramid in geometry. The tetrahedron comprises of 4 triangular faces, 6 straight edges, and 4 vertex corners.Cube - A cube can be defined as 3D solid object with 6 square faces and consists of the sides that are of the same length. The cube is also called as a regular hexahedron which is a box-shaped solid with 6 equivalent square faces.Octahedron - An octahedron is in fact, a polyhedron consisting of 8 faces, 12 edges, and 6 vertices and at each of the vertices, the 4 edges coincide. The faces of an octahedron are shaped in the form of an equilateral triangle.Dodecahedron - A dodecahedron is referred to as a platonic solid comprising of 12 sides and 12 pentagonal faces. Icosahedron - An icosahedron is a platonic solid with 20 faces, 30 edges, and 12 vertices. The shape of an icosahedron consists of equilateral triangle faces.Thus, from the above information on platonic solids, we can say that cube is the only platonic solid that is made from squares. Thus, option B is correct.
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A third box is designed so that it is also a cube that has sides that are half of solid 1's. find the volume of solid 3. then find the ratio of the volume of solid 1 to the volume of solid 3. explain why the ratio is not 2 to 1
Given :
Solid 1:
The side of the cube is, a = 8 cm.
Solid 3:
The side of the cube is, b = 4 cm.
The volume of the third cube can be calculate as,
[tex]V=b^3=(4cm)^3=64cm^3[/tex]The volume of first cube is,
[tex]V^{\prime}=a^3=(8cm)^3=512cm^3[/tex]Thus, the ratio can be calculated as,
[tex]\frac{V^{\prime}}{V}=\frac{512}{64}=\frac{8}{1}[/tex]Thus the required ratio is 8:1.
Since the volume is proprtional to the cube of the side, the ratio will also be in the range of cube of the fractional difference between the sides.
what is 8 7/8+1/2 and what is 45.35 + 40 7/10
8 7/8+1/2
1) We need to turn that Mixed number into an improper fraction, by keeping the denominator and multiplying it by the whole number, and then adding to the numerator of that Mixed Number:
[tex]8\frac{7}{8}=\frac{8\cdot8+7}{8}=\frac{71}{8}[/tex]2) Adding then:
[tex]\frac{71}{8}+\frac{1}{2}=\frac{8\colon8\times71+8\colon2\times1}{8}=\frac{71+4}{8}=\frac{75}{8}[/tex]Turning back to Mixed Number:
Dividing 75 by 8 and placing the quotient as the whole number, the divisor as the denominator, and the remainder as the numerator we have the mixed number back.
2)45.35 + 40 7/10
Rewriting 45.35 as a fraction:
[tex]\begin{gathered} 45.35\text{ =}\frac{4535}{100} \\ 40\frac{7}{10}+\frac{4535}{100} \\ \frac{407}{10}+\frac{4535}{100} \\ \frac{4070+4535}{100} \\ \frac{8605}{100} \\ \frac{1721}{20} \end{gathered}[/tex]Note that we've rewritten as fractions, and then turned them into improper ones, added them, and then simplified.
3) Hence, the answer is
[tex]\begin{gathered} a)9\frac{3}{8}\text{ or }\frac{75}{8} \\ b)\text{ }\frac{1721}{20} \end{gathered}[/tex]Which equation represents a line which is parallel to the y-axis?a) x=4yb) x=1/4yc) x=3d) y=-6
The graph of x = 3 is a line parallel to the y-axis, which passes through the point (3, 0). This means that x = 3 for every value of y.
To get the 10% discount, a shopper must spend no less than $400.Use d to represent the spending (in dollars) of a shopper who gets the discount.
d represents the amount spent by a shopper who gets the discount.
The expression for d would be
[tex]d\text{ }\ge400[/tex]d is greater than or equal to 400I’m done answering. Do you understand my explanation?
ху Evaluate when x = 6 and y = 13. x + y
EXPLANATION
When x=6 and y=13 x+y = 6 + 13 = 19
x + y = 19
Max has 15-foot long piece of plastic pipe. He wants to cut it into four equivalent pieces to make corner flag poles for the soccer field. What should be the length of each flagpole that will be cut?
Answer:
3.75 feet
Explanation:
To know the length of each flagpole, we need to divide 15 (the total length of the piece of plastic pipe) by 4 because he wants 4 pieces. Then:
15 ÷ 4 = 3.75 feet
Then, each flagpole should have a length of 3.75 feet.
Which rule describes the X – coordinates in this translation
Translation of function is :
[tex]x\rightarrow x-6[/tex]At any point for x is translat for B is x=2 then :
[tex]\begin{gathered} x^{\prime}=x-6 \\ x^{\prime}=2-6 \\ x^{\prime}=-4 \end{gathered}[/tex]For point x=4
[tex]\begin{gathered} x^{\prime}=x-6 \\ x^{\prime}=4-6 \\ x^{\prime}=-2 \end{gathered}[/tex]So x - coordinates in the translation:
[tex]=x-6[/tex]
Divide.
-10/25 8/10
What is the quotient?
Enter your answer as a simplified fraction in the box.
Answer:
-10/25÷8/10
-10/25×10/8
-100/25(8)
-100/200
-1/2
Hope this is right!!
Answer:
-1/2
Step-by-step explanation:
change the sign from divide to multiply: -10/25 X 8/10
flip the second fraction: -10/25 X 10/8
simplify the expression: -10 divide 5/ 25 divide 5 x 10 divide 2/ 8 divide 2
cancel out greatest factor: -2/5 x 5/4
simplify: - 2 /4
answer: - 1/2
A factory makes candles. Each candle is in the shape of a triangular prism, as shown below. If the factory used 14,700 cm^3 of wax,how many candles did the factory make?
Answer:
Explanation:
Step 1
First, we find the volume of one the triangular prism shaped candles.
The volume of a prism is calculated using the formula:
[tex]V=\text{ Cross-Sectional Area}\times\text{ Length}[/tex]The cross section of the prism is a triangle with:
• Base = 10cm
,• Height = 7cm
Length of the Prism = 6cm
Therefore:
[tex]\begin{gathered} V=\frac{1}{2}bh\times L \\ =\frac{1}{2}\times10\times7\times6 \\ =210\;cm^3 \end{gathered}[/tex]The volume of one of the candles is 210 cubic cm.
Step 2
Next, divide the volume of wax used by the factory by the volume of one candle.
[tex]\text{Number of candles made}=\frac{14700}{210}=70[/tex]How do I solve this I think I did it incorrectly
Given:
The diameter of the circle = d = 14 cm
The radius of the circle = r = d/2 = 7 cm
The circumference is given by the formula: 2πr
so, the exact value = 2π * 7 = 14π cm
The approximated value to the nearest hundredth = 43.98 cm
The area of the circle is given by the formula: πr²
The exact value of the area = π * 7² = 49π cm²
The approximated value to the nearest hundredth = 153.94 cm²
I am trying to find the slope-intercept form of the following equation:Find the equation of a line through (7, -3) that is perpendicular to the line y = -x/3 - 8
Given:
The equation of line is,
[tex]y=-\frac{x}{3}-8[/tex]As given that the required line is perpendicular to the above line.
It means the slope of required line will be negative reciprocal of above line.
[tex]\begin{gathered} y=-\frac{x}{3}-8 \\ \text{Compare it with y=mx+b} \\ \Rightarrow m=-\frac{1}{3} \end{gathered}[/tex]The slope of the required line will be,
[tex]m_1=-\frac{1}{m}=-\frac{1}{-\frac{1}{3}}=3[/tex]Now, given that the required line passing through point (7,-3) .
[tex]\begin{gathered} y=m_1x+b \\ (x,y)=(7,-3) \\ -3=3(7)+b \\ b=-24 \end{gathered}[/tex]The slope-intercept form is,
[tex]\begin{gathered} y=m_1x+b \\ y=3x-24 \end{gathered}[/tex]find the perimeter of the following folded then be sorted and the crew correct units in your answer
Solution
Given a triangle of the followingdimensions
[tex]19in,17in,14in[/tex]To find the perimeter, P, of a triangle, the formula is
[tex]\begin{gathered} P=a+b+c \\ \text{Where a, b and c are the side lengths} \end{gathered}[/tex]Then,
[tex]\begin{gathered} a=19in \\ b=17in \\ c=14in \end{gathered}[/tex]Substitute the values to find P.
[tex]\begin{gathered} P=a+b+c \\ P=19+17+14=50in_{} \\ P=50in \end{gathered}[/tex]Hence, the perimeter, P, is 50 inches
What is the intensity of an earthquake in Hawaii
which measured 3.92 on the richter scale?
Use the formula M = log(i/s)
S= 1 micron
- 7,943 microns
- 6904 microns
- 8318 microns
- 2818 microns
8318 microns is the intensity of an earthquake in Hawaii.
What is Richter scale?The Richter scale was originally developed to measure the magnitude of moderate earthquakes (magnitude 3 to magnitude 7) by assigning numbers so that the magnitude of one earthquake can be compared to another. This scale was developed for the Southern California earthquake recorded by the Wood He Anderson seismograph whose epicenter was less than 600 km (373 mi) from the seismometer location. However, today's seismometers can be calibrated to calculate the Richter magnitude, and modern methods of measuring earthquake magnitude are designed to give results consistent with those measured using the Richter scale. Developed.
The magnitude of an earthquake is determined using the logarithm of the amplitude (height) of the largest seismic wave, calibrated to scale by the seismograph.
Using the formula,
[tex]M = log \frac{i}{s}\\ 3.92 = log\frac{i}{1 micron} \\10^3.92 = \frac{i}{s} \\i = 8318[/tex]
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11) The table below represents a linear equation. If the y-intercept is at point (0, b), what is the value of b?X-125Y-1817
step 1
Find the slope of the linear equation
we take the points
(-1,-1) and (2,8)
so
m=(8+1)/(2+1)
m=9/3
m=3
step 2
Find the equation of the line in sloe intercept form
y=mx+b
we have
m=3
point (2,8)
substitute
8=3(2)+b
solve for b
8=6+b
b=2
the equation is
y=3x+2
and the value of b is 2
which of the following expression has a coefficient of 10 and a constant of 5 10+5x. 10+5. 10 - 5. 10x+5
the coefficient is the number that accompanies the variable, in this case it would be the number that accompanies the x
and a constant is a number without company
so, the expression is
[tex]10x+5[/tex]the last option
help me on this math question! please
Answer:
X: -2, -1, 0, 1, 2
Y: -3, -1, 1, 3, 5
Step-by-step explanation:
A problem solver site says the table will look like this
What is the constant of proportionality in the table below? Hours worked 3 6 9 12 Money Earned $45.75 $91.50 $137.25 $183.00 $ I per hour
If the "hours worked" and the "Money earned" are proportional, this means that both variables increase and decrease at the same rate. You could say that the more hours you work, the more money you make, and vice-versa.
The constant of proportionality indicates the rate of change of one of the variables with respect to the other.
Let "y" represent the money earned and "x" represent the hours worked, you can express the proportional relationship between both variables as follows:
[tex]y=kx[/tex]Where "k" represents the constant of proportionality and can be calculated by dividing the value of y by the value of x:
[tex]k=\frac{y}{x}[/tex]To determine the said value you have to choose any ordered pair of the table and do as follows:
Using the pair
Hours worked x=3
Money earned y=$45.75
[tex]\begin{gathered} k=\frac{y}{x} \\ k=\frac{45.75}{3} \\ k=15.25 \end{gathered}[/tex]The constant of proportionality is $15.25 per hour.
Rewrite the expression with a positive rational exponent. Simplify, if possible.100-1/2
We need that the 100 has a 2 in the denominator. To do this, we can multiply on top and bottom by 2:
[tex]100\cdot\frac{2}{2}=\frac{200}{2}[/tex]Now, we can make the subtraction:
[tex]\frac{200}{2}-\frac{1}{2}=\frac{199}{2}[/tex]The answer is 199/2
What is the average rate of change of the function f(x) = x^2 – 2x + 4 over the interval –2 ≤ x ≤ 3?
The rate of change of a function is the increase or decrease that a function experiences as the independent variable changes from one value to another.
The corresponding equation of the average rate of change is:
[tex]TVM(x_1,x_2)=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case, x1 is 3 and x2 is 3
Remember that according to the notation of the limits, they take the values of 2 and 3.
Now, we solve f(3) and f(2)
[tex]\begin{gathered} f(3)=3^2-2\cdot(3)+4 \\ f(3)=9-6+4 \\ f(3)=7 \end{gathered}[/tex][tex]\begin{gathered} f(2)=2^2+2\cdot(2)+4 \\ f(2)=4-4+4 \\ f(2)=4 \end{gathered}[/tex]This way now we can replace the values in the TVM equation and I will solve this.
[tex]\begin{gathered} TVM(3,2)=\frac{7-4}{3-1_{}} \\ TVM(3,2)=\frac{3}{1}=3 \end{gathered}[/tex]In conclusion, the average rate of change of the function
two gongs strike at intervals of 90 and 60 minutes respectively.At what time will they strike together again if they start simultaneously at 12 noon
Both the gongs will strike together at 3 pm.
Given,
Two gongs strike at intervals 90 and 60 minutes respectively.
Use LCM to find at what time they will strike together
Using prime factorization:
LCM of (60,90)=[tex]2^2*3^2*5=4*9*5=180[/tex]
They will strike together after 180 minutes i.e. 3 hours
Hence, if they start simultaneously at 12 noon then they will strike together again at 3 pm
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the U.S senate has 100 members. there are 6 more democrats than republicans, with no other parties represented. how many memebr of each party were there in the senate
The number of republicans and democrats will be 47 and 53 respectively.
Define equation.Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It shows that the expressions printed on the left and right sides have an equal relationship. In any mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity.
Given data -
Total number of members in U.S senate = 100
Let the number of republicans in U.S senate be x members
As republicans outnumber democrats by six,
Therefore, number of democrats = (x+6) members
According to the given data,
x + (x+6) = 100
2x + 6 = 100
2x = 94
x = 47
Number of members as a republicans will be 47.
Number of members as a democrats will be (100-47) = 53
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Which of the following lines is NOT parallel toy = 3x + 4?
We are to look for lines that are not parallel to y=3x + 4
Comparing the above equation with y=mx + b, the slope(m) = 3
Equations of lines are said to be parallel, if they have the same slope
So, we need to re-write each equation in the slope-intercept form to see which is NOT parallel to the given equation
OPTION A
3y - 9x - 6 = 0
[tex]y=\frac{9x}{3}+\frac{6}{3}[/tex][tex]y=3x+2[/tex]slope = 3 which implies. it is parallel to the given equation
OPTION B
-2y + 6x + 4 = 0
[tex]2y=6x+4[/tex]Divide through by 2
[tex]y=3x\text{ + 2}[/tex]slope = 3 which implies the line is parallel to the given line
OPTION C
2y - 6x - 4 = 0
[tex]2y=6x\text{ + 4}[/tex]Divide through the equation by 2
[tex]y=3x\text{ + 2}[/tex]slope = 3 which implies the line is parallel to the given line
OPTION D
2y - 4x - 8 = 0
[tex]2y=4x\text{ + 8}[/tex]Divide through the equation by 2
[tex]y=2x\text{ + 4}[/tex]slope = 2, which means tthe line is NOT parallel to the given line.
Therefore, the line which is NOT parallel to y=3x+ 4 is D. 2y - 4x - 8 = 0
rogers father vompares the text plan from two different companies dail up charges $5.00 for 100 text messages and ring ring charges $8 for 200 text messages
Rogers father compares the text plan from two different companies dial up charges $5.00 for 100 text messages and ring ring charges $8 for 200 text messages
Step 1
find the unit price
Company 1
price= $ 5
number of text messages=100
[tex]\begin{gathered} \text{unit price=}\frac{\text{price}}{\text{number of text messages}} \\ \text{unit price=}\frac{5}{100} \\ \text{unit price=0.05} \end{gathered}[/tex]Company 2
price= $ 8
number of text messages=200
[tex]\begin{gathered} \text{unit price=}\frac{8}{200} \\ \text{unit price=}0.04 \end{gathered}[/tex]Step 2
compare the text plan
[tex]\begin{gathered} \text{price 1 }then, the text message is cheaper in the company 2rick is preparing a roast beef for his family.the roast beef weighs 2 3/4 pounds. if he wants to make each serving to be 1/2 pounds of meat how many servings can he make
To find the number of roast beef servings that Rick can make, we proceed as follows:
Step 1: Divide the total weight of the roast beef by the amount of weight of meat per serving, as follows:
[tex]\begin{gathered} \text{Total weight of roast beef =}2\frac{3}{4}\text{ pounds=}\frac{11}{4}\text{ pounds} \\ \text{amount of weight of meat per serving = }\frac{1}{2}\text{ pounds} \\ \text{Therefore:} \\ \text{Number }of\text{ servings =}\frac{T\text{otal weight of roast beef}}{A\text{mount of weight of meat per serving}} \\ \Rightarrow\text{ Number }of\text{ servings =}\frac{\frac{11}{4}}{\frac{1}{2}} \\ \Rightarrow\text{Number }of\text{ servings =}\frac{11}{4}\times\frac{2}{1}=\frac{22}{4}=\frac{11}{2}=5.5\text{ } \end{gathered}[/tex]Therefore, the number of roast beef servings that Rick can make is 5.5
How is this equation true?4/4 * x/1 + 1/4 = 4x/4 + 1/4 = 4x+1/4
Given
[tex]\frac{4}{4}*\frac{x}{1}+\frac{1}{4}[/tex]Simplify as shown below,
[tex]\begin{gathered} \frac{4}{4}*\frac{x}{1}+\frac{1}{4}=\frac{4*x}{4*1}+\frac{1}{4} \\ =\frac{4x}{4}+\frac{1}{4} \\ =\frac{4}{4}*x+\frac{1}{4} \\ =1*x+\frac{1}{4} \\ =x+\frac{1}{4} \end{gathered}[/tex]If the initial equation is correct, the last equality in the question tab is incorrect. The simplification is x+1/4, not 4x+1/4.
How much would $700 be worth after 8 years, if it were invested at 5%interest compounded continuously? (Use the formula below and round youranswer to the nearest cent.)
ANSWER :
D. $1044.28
EXPLANATION :
From the problem, the present value is P = $700, the interest rate is r = 5% or 0.05, and the time is t = 8 years
Using the given formula :
[tex]A(t)=Pe^{rt}[/tex]Then :
[tex]\begin{gathered} A(t)=700e^{0.05(8)} \\ A(t)=1044.28 \end{gathered}[/tex]7.) A jug of egg nog sells for $5.12One jug holds(128 punces. What is the unit priceper ounce?
Answer:
The unit price per ounce is;
[tex]\text{\$0.04 per ounce}[/tex]Explanation:
Given that A jug of egg nog sells for $5.12 and One jug holds 128 ounces.
We can derive the unit price per ounce by dividing the price by the number of ounces;
[tex]\begin{gathered} r=\frac{\text{ \$5.12}}{128\text{ ounces}} \\ r=\text{ \$0.04 per ounce} \end{gathered}[/tex]Therefore, the unit price per ounce is;
[tex]\text{\$0.04 per ounce}[/tex]In 2009, Mariana paid $5,160 in federal income tax. In 2010, she paid 70% more than in 2009. How much did Mariana pay in 2010?
finishing. What is the percent of decrease in the number of finishers?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 5160}}{\left( \cfrac{70}{100} \right)5160}\implies 3612~\hfill \underset{for~2010}{\stackrel{5160~~ + ~~3612}{\text{\LARGE 8772}}}[/tex]
Answer:
3,612
Step-by-step explanation:
70% of 5,160
0.70•5,160= 3612