Info given
Bob and dale served a total of 83 orders Monday at the school cafeteria. rita served 9 fewer orders than bob. Dale served 2 times as many orders as bob. how many orders did they each serve
Solution
We can find the number of orders for Rita like this:
[tex]\text{Rita}=83-9=74[/tex]And for Dale we have this:
[tex]\text{Dale}=2\cdot83=166[/tex]The sum of sixteen times a number and twelve is 172. Find the number.
Answer:
Step-by-step explanation:
1. (16 · x) + 12 = 172
2. x= 172-12/16
3. x = 10
4. The number is 10.
Once Farid spends 15 minutes on a single level in his favorite video game, he loses a life. Hehas already spent 10 minutes on the level he's playing now.Let x represent how many more minutes Farid can play on that level without losing a life.Which inequality describes the problem?
If he spends 15 minutes on a single level, he loses his life.
He has already spent 10 minutes on the level he is playing now.
x = the number of minutes he can play without losing a life.
The inequalities that can be use to represent this scenario will be
[tex]10+x<15[/tex]The circle at the right represents a planet. The radius of the planet is about 6600 km. Find the distance to the inizon that a person can seeon a clear day from the following heighth above the planeth 7 km
Interpret Linear Function Coefficients (From Graph)
Remember that the equation of the line in slope-intercept form is equal to
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
In this context
we have
C=mt+b
step 1
Find out the slope
we need two points
looking at the graph
we take (0,100) and (1,150)
so
m=(150-100)/(1-0)
m=50 --------> that means $50 per month (monthly fee to remain a member)
the y-intercept is the value of y when the value of x is zero
in this context, the y-intercept is the cost C when the value of t is zero
b=100 ------> that means a one-time fee to join
substitute
C=50t+100and the slope is $50 per month (monthly fee to remain a member)Select the correct answer.Solve the equation using the method of completing the square.A. B. C. D.
Answer:
C. -4 ± 2√6
Explanation:
The given equation is
3x² + 24x - 24 = 0
First, add 24 to both sides
3x² + 24x - 24 + 24 = 0 + 24
3x² + 24x = 24
And factorize 3 on the left side
3(x² + 8x) = 24
Then, to complete the square, we need to add and substract (b/2)² to the expression in parenthesis. In this case, b = 8, so
(b/2)² = (8/2)² = 4² = 16
Then, add and subtract 16 as follows
3(x² + 8x + 16 - 16) = 24
3(x² + 8x + 16) - 3(16) = 24
3(x² + 8x + 16) - 48 = 24
Finally, we can factorize and solve for x
3(x + 4)² - 48 = 24
3(x + 4)² - 48 + 48 = 24 + 48
3(x + 4)² = 72
3(x + 4)²/3 = 72/3
(x + 4)² = 24
Solving for x, we get
[tex]\begin{gathered} x+4=\pm\sqrt{24} \\ x+4-4=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{4\cdot6} \\ x=-4\pm2\sqrt{6} \end{gathered}[/tex]Therefore, the answer is
C. -4 ± 2√6
2) Coefficient of u^2v^2 in expansion of (2u - 3v)^4
Answer
Step-by-step Explanation
In the expansion of variables in a bracket raised to a particular power, we either use the Binomial theorem or the Pascal's triangle.
The Binomial theorem teaches how to use permutaion and combination to obtain the coefficients of each term while the Pascal's triangle presents the coefficient of each term for different integer powers of the variables in a triangular form where the next line of the triangle can be obtained from the previous line just by starting with a 1 and adding two consecutive terms of that previous line and ending with 1.
Given: AB - BC, ZA ZC and BD bisects ABC. Prove: A ABD ~ ACBD.
Since BD bisects ABC, then angles ADB and BDC are congruent. Now that we have that both triangles ABD and CBD have the same two sides and angle, we have that they are congruent (because the side-angle-side postulate)
2. Write the equation of the graph shown below. 3 1 -2 0 2 1-
The function in the graph is V shaped, this indicates that it corresponds to a function of an absolute value of x:
[tex]f(x)=|x|[/tex]The V opens downwards, which means that the coefficient that multiplies the module (a) is negative:
[tex]f(x)=-|x|[/tex]→ This means rthat when we calculate the value of "a", this value has to be negative
As you can see in the graph, the vertex of the function is (0,3)
Following the vertex form:
[tex]f(x)=a|x-x_v|+y_v[/tex]Where xv represents the x-coordinate of the vertex and yv represents the y-coordinate of the vertex. Replace them in the formula and we get that:
[tex]\begin{gathered} f(x)=a|x-0|+3 \\ f(x)=a|x|+3 \end{gathered}[/tex]Now all we need to do is determine the value of "a", for this we have to use one point of the function and replace it in the formula, this way "a" will be the only unknown.
Lets take for example one of the roots (points where the function crosses the x-axis)
Point (1, 0)→ replace it in the formula
[tex]\begin{gathered} 0=a|1|+3 \\ 0=a+3 \\ a=-3 \end{gathered}[/tex]Now that we know the value of a, we can determine the wquation of the function as
[tex]f(x)=-3|x|+3[/tex]If 8 people share 21 muffins, how many does each person get?
ANSWER
[tex]\frac{21}{8}or\text{ 2}\frac{\frac{5}{}}{8}[/tex]EXPLANATION
The total number of muffins is 21.
To find out how many muffins each person will receive, you have to divide the total number of muffins by the number of people it is to be shared with;
[tex]\begin{gathered} x=\frac{21}{8} \\ =2.625 \end{gathered}[/tex]Each person will receive 2.625 muffins
Use a proportion to find the missing side length, x.
Answer:
The measure of angle ABC is;
[tex]m\measuredangle ABC=72^0[/tex]Explanation:
Given the triangle ABC.
Recall that the sum of angles in a triangle is 180 degrees;
[tex]8x+6x+6x=180[/tex]solving for x, we have;
[tex]\begin{gathered} 8x+6x+6x=180 \\ 20x=180 \\ x=\frac{180}{20} \\ x=9 \end{gathered}[/tex]From the diagram,
[tex]\begin{gathered} \measuredangle ABC=8x \\ \measuredangle ABC=8(9) \\ \measuredangle ABC=72^0 \end{gathered}[/tex]Therefore, the measure of angle ABC is;
[tex]m\measuredangle ABC=72^0[/tex]Simplify (3^z)^6 leave your answer in exponential notation
[tex](3^z)^6[/tex][tex]3^{6z}[/tex]
mean is 95.3standard deviation is 15.4 finf the probability that a randomly selected adult IQ is greater than 119.8
we are asked to determine the probability that a variable x is greater than 119.8. To do that we will assume a normal distribution of probability and use the following relationship:
[tex]P(x>119.8)=1-P(x\le119.8)[/tex]To determine the probability that x is smaller than 119.8 we need first to find the z-score of the data set using the following formula:
[tex]z=\frac{x-\bar{x}}{\sigma}[/tex]Where
[tex]\begin{gathered} \bar{x}\colon\operatorname{mean} \\ \sigma\colon\text{ standard deviation} \end{gathered}[/tex]replacing we get:
[tex]z=\frac{119.8-95.3}{15.4}=1.59[/tex]Now we use this value to look into the chart for probabilities, we get 0.94408. This is the probability that x is smaller than 119.8. Replacing in the initial relationship we get:
[tex]P(x>119.8)=1-0.94408=0.056[/tex]Therefore, the probability is 5.6%.
2. Here is a riddle: “I am thinking of two numbers that add up to 5.678. The difference between them is 9.876. What are the two numbers?”•Name any pair of numbers whose sum is 5.678. •Name any pair of numbers whose difference is 9.876.•The riddle can be represented with two equations. Write the equations.•Solve the riddle. Explain your reasoning.( You do not need to name a variable for each number in the first part)
• You know that the sum of the two numbers must be:
[tex]5.678[/tex]In order to find any pair of numbers whose sum is that number shown above, you can subtract 1 from it:
[tex]5.678-1=4.678[/tex]Now you can set up that:
[tex]1+4.678=5.678[/tex]• To find any pair of numbers whose difference is:
[tex]9.876[/tex]You can add 2 to it:
[tex]9.876+2=11.876[/tex]Then, you can set up that:
[tex]11.876-2=9.876[/tex]• Let be "x" and "y" the numbers that add up to 5.678. and whose difference is 9.876.
Then, you can set up these equations:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• To solve the riddle, you can follow these steps:
- Set up a System of equations using the equations found in the previous part:
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ \end{gathered}[/tex]- Apply the Elimination Method by adding both equations and solving for "x":
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ ------------ \\ 2x=15.554 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{15.554}{2} \\ \\ x=7.777 \end{gathered}[/tex]- Substitute the value of "x" into one of the original equations and solve for "y":
[tex]\begin{gathered} (7.777)+y=5.678 \\ \\ y=5.678-7.777 \\ \\ y=-2.099 \end{gathered}[/tex]Therefore, the answers are:
• Any pair of numbers whose sum is 5.678:
[tex]1\text{ and }4.678[/tex]• Any pair of numbers whose difference is 9.876:
[tex]11.876\text{ and }2[/tex]• Equations that represents the riddle:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• Solution of the riddle:
[tex]\begin{gathered} x=7.777 \\ y=-2.099 \end{gathered}[/tex]
answer choices:454ft square inches, 252ft square inches, 156ft square inches
Tp fint the total area of the figure start by calculating the area of the square and the triangle separately.
Area of the square is calulated by mutiplying the side by the side
[tex]\begin{gathered} A=(14ft)\cdot(14ft) \\ A=196ft^2 \end{gathered}[/tex]Area of the triangle follows the formula:
[tex]A=b\cdot\frac{h}{2}[/tex]The base of the triangle is the same as the length of the square's side.
[tex]\begin{gathered} A=\frac{(14ft)\cdot(8ft)}{2} \\ A=56ft^2 \end{gathered}[/tex]Add both sides to find the total area
[tex]\begin{gathered} A_t=56ft^2+196ft^2 \\ A_t=252ft^2 \end{gathered}[/tex]Find the sales tax in total cost of espresso machine that cost $46.95 the tax rate is 4% rounding your answer to the nearest cent
Given:
The total cost of espresso machine costs $46.95. and the tax rate is 4%.
To find:
Find the sales tax?
Explanation:
[tex]Sale\text{s tax=Sales tax percenatge}\times pre-tax\text{ cost}[/tex][tex]Total\text{ cost=Pre-tax value +Sales tax}[/tex]Solution:
We will start by converting sales tax percentage into a decimal by moving
the point two spaces to the left.
6%=0.06
Now, we need to multiply the pre-max cost of this item by this value
in order to calculate the sales tax cost
[tex]\begin{gathered} Sales\text{ tax=}0.04\times46.95 \\ Sales\text{ tax=1.878} \end{gathered}[/tex]Round to two decimal places
[tex]Sales\text{ tax=\$1.88}[/tex]Last, add this value of the pre-tax value of the item to find the total cost.
[tex]\begin{gathered} Total\text{ cost=Pre tax value + Sales tax} \\ Total\text{ Cost=46.95+1.88} \\ Total\text{ cost=}48.83 \end{gathered}[/tex]Hence, these are the required values.
find the total and the interestprincipal $3200rate 5 1/2 yearscompounded semiannually for 6 years
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$3,200
r=5 1/2 %=5.5%=0.055
t=6 years
n=2
substitute the given values
[tex]A=3,200(1+\frac{0.055}{2})^{2\cdot6}[/tex]A=$4,431.31 ------> the totalFind out the interest
I=A-P
I=4,431.31-3,200
I=$1,231.31 -----> interestI need help I am a teacher and have to explain this to my students
Solve the given inequality as shown below
[tex]\begin{gathered} r+6\ge11 \\ \Rightarrow r+6-6\ge11-6 \\ \Rightarrow r\ge5 \end{gathered}[/tex]Therefore, any number equal to or greater than 5 is a solution to the given inequality.
The correct answers are 5, 6, and, 7.
the sum of 1/3 and 3/8
Answer:
17/24
Explanation:
To add the fractions
[tex]\frac{1}{3}+\frac{3}{8}[/tex]we first find their common denominators.
The common multiple of 3 and 8 is 24 because 3 * 8 = 24; therefore,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{1\cdot8}{3\cdot8}+\frac{3\cdot3}{8\cdot3}[/tex][tex]=\frac{8}{24}+\frac{9}{24}[/tex]Adding the numerators gives
[tex]\frac{8}{24}+\frac{9}{24}=\frac{17}{24}[/tex]Hence,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{17}{24}[/tex]5.) Figure 10.85 shows a method for constructing isosceles triangles. A. use the method of figure 10.85 to drawl two different isosceles triangles B. use the definition of circles to explain why this method will always produce an isosceles triangle.
You first draw two circles when different radii.
When you select two point over the circumference, and you connect a line in between these points and the center of the circle, you will always obtain two sides with the same length. It is because the length of these sides coincides witht the ratio of the circle.
Then, when you connect the points over the circumference between them, you have a side that can have a different length compared with the lengths of the lines connected to the center. Thus, you obtain an isosceles triangle; you have two sides with the same length (remember, it's the same as the radius) and one side with another length.
Can you please help me out with a question
Step 1: Write out the formula
By the intersecting secant theorem (interior),
[tex]z=\frac{x+y}{2}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]x=40^0,y=52^0,z=m<1[/tex]Therefore,
[tex]m<1=\frac{40^0+52^0}{2}=\frac{92^0}{2}=46^0[/tex]Hence, m<1 = 46 degrees
Factor. x2 − x − 72 (x − 8)(x + 9) (x − 6)(x + 12) (x + 8)(x − 9) (x + 6)(x − 12)
The solution of the given equation are; (x + 8)(x − 9)
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We have been given the quadratic equation as;
x² − x − 72
Solving;
x² − (9-8)x − 72
x² − 9x +8x− 72
The factors are;
(x + 8)(x − 9)
Therefore, the solution of the given equation are; (x + 8)(x − 9)
Learn more about quadratic equations;
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need help converting point slope form equation to slope intercept form(y+10)=1/3(x+9)
The slope-intercept form is
→ y = m x + b
→ m is the slope
→ b is the y-intercept
∵ The given equation is
[tex]y+10=\frac{1}{3}(x+9)[/tex]First, multiply the bracket (x + 9) by 1/3
[tex]\begin{gathered} \because y+10=\frac{1}{3}(x)+\frac{1}{3}(9) \\ \therefore y+10=\frac{1}{3}x+3 \end{gathered}[/tex]Subtract 10 from both sides
[tex]\begin{gathered} \because y+10-10=\frac{1}{3}x+3-10 \\ \therefore y+0=\frac{1}{3}x-7 \\ \therefore y=\frac{1}{3}x-7 \end{gathered}[/tex]The equation in the slope-intercept form is y = 1/3 x - 7
When a positive number x is divided by 7, the remainder is 4. What is
the remainder when x is divided by 4?
When a positive number x is divided by 7, the remainder is 4. The remainder when x is divided by 4 is 7.
What is a remainder?
The quantity "leftover" after executing a computation in mathematics is referred to as the remainder. The remainder is the integer that remains after dividing two integers to get an integer quotient in mathematics.
The remainder operator (%) returns the amount of one argument that is left over after dividing it by another operand. For instance, when 41 is divided by 7, the remaining is 6 and the quotient is 5.
Solution Explained:
A/Q
x / 7 = 4
Solving this equation
x = 4 X 7 = 28
Now putting the value of x in the equation
x / 4
= 28 / 4 = 7
Therefore, the remainder when x is divided by 4 is 7.
To learn more about remainder, use the link given
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_+_=10.5 _-3.25=_help me pls
These questions can have multiple answers
for instance,
a)
_+_=10.5
8.5 + 2 = 10.5
5.5 + 5 = 10.5
3.5 +7 = 10.5
5.25 + 5.25 = 10.5
b)
_-3.25 =_
7 - 3.25 = 3.75
7.25 - 3.25 = 4
10. 5 - 3.25 = 7.25
c)
if each _ have the same value
x + x = 10.5
2x= 10.5
x= 5.25
d)
if each _ have the same value
_-3.25 =_
x -3.25= x
x-x = 3.25
0= 3.25
In this case, each x cannot be the same, it would have to be a number that you subtract 3. 25 and it remains the same number. That is not possible.
but if i use x= 5.25
5.25- 3.25= 2
The key concepts used to convert units between different systems of measurement are shown without the final twosteps.1. Identify the units of measure to be converted,2. Write conversion factors,3. Cancel units.4.5.Which two steps will complete the list correctly?4. Divide the original measurement by the conversion factors.5. Check for reasonableness,4. Multiply the original measure by the conversion factors.5. Simplify the answer.4. Multiply the original measure by the conversion factors.5. Check for reasonableness,4. Divide the original measure by the conversion factors.
Here, we want to select from the options, the two best statements that completes the steps
The two steps are;
Multiply the origi
Solve the equation, give the exact solution then approximate the solution to the nearest hundredth
Given the expression:
[tex]10-3x^2=4[/tex]We can find its solution by solving like a linear equation up until the exponent:
[tex]\begin{gathered} 10-3x^2=4 \\ \Rightarrow-3x^2=4-10 \\ \Rightarrow-3x^2=-6 \\ \Rightarrow x^2=\frac{-6}{-3}=2 \\ x^2=2 \end{gathered}[/tex]now, we can apply the square root on both sides to get the following:
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt[]{2} \\ \Rightarrow x=\pm\sqrt[]{2=} \\ x=\pm1.41 \end{gathered}[/tex]therefore, the solutions of the equation are x=1.41 and x=-1.41
Which expression is equivalent to (3x^5+ 8x^3) – (7x^2 - 6x^3)?3x^5 +14x^3 – 7x^23x^5+ 2x^3 – 7x^2- 4x^5+ 14x^3- 4x^3 + 14
so the answer is option #1
how do i solve for d ?3(2d-4) = 6(d-2)
Solution:
Given the equation;
[tex]3(2d-4)=6(d-2)[/tex]SImplify:
[tex]6d-12=6d-12[/tex]Since the two sides of the equation are equal, d has infinitely many solutions.
what is the value of x and y ?2x+3=Y
There can be infinite solutions for x and y, this is because if we look at the equation like a slope intercept equation
[tex]\begin{gathered} 2x+3=y \\ y=2x+3 \end{gathered}[/tex]we can see that this is the equation for a straight line.
if we graph it
All values of x and y that are obtain by the line can be a solution to the equation given.
Which answer choice represents a simplified form of the expression 2.5 + 7 1 - 2.3 - 4?* O (2.5 + 2.3) - 7-4 0 (2.5 - 2.3) - (7-4) O (2.5 - 2.3) + (7 - 4) 4 + 7 + (2.5 - 2.3)