Option C
Points: A, B, C, D
Line segments: AB, AD, AC, DC, BC
find the slope and y intercept, then write out the linear equation (y=mx+b) below
Answer:
y = 2x + 3
Step-by-step explanation:
You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.
Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.
The slope is 2. Fill in 2 in place of m in
y = mx + b
y = 2x + b
Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.
y = 2x + 3
Which recipe makes more cookies per cup of chocolate chips?
We are given the recipes of Grandma and Betty Potter box.
We are asked to find out which of them makes more cookies per cup of chocolate chips.
Let us find the unit rate for both of them and compare which is greater.
Grandma:
She uses 1 1/2 cups of chocolate chips to make 24 cookies.
The unit rate is
[tex]\frac{24}{1\frac{1}{2}}=\frac{24}{\frac{3}{2}}=24\times\frac{2}{3}=16[/tex]So the unit rate is 16 cookies per chocolate chip.
Betty Potter box:
60 cookies are made using 3 chocolate chips.
80 cookies are made using 4 chocolate chips.
200 cookies are made using 10 chocolate chips.
The unit rate is
[tex]\begin{gathered} \frac{60}{3}=20 \\ \frac{80}{4}=20 \\ \frac{200}{10}=20 \end{gathered}[/tex]So the unit rate is 20 cookies per chocolate chip.
As you can see, the recipe of Better Potter box makes more cookies per cup of chocolate chip.
A cone has a height of 17 centimeters and a radius of 7 centimeters. What is its volume? Use = 3.14 and round your answer to the nearest hundredth. cubic centimeters
To find the volume of the cone, we will use the formula below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height
From the question,
π = 3.14
r =7
h=17
substitute the values into the formula
[tex]V=\frac{1}{3}\times3.14\times7^2\times17[/tex][tex]V\approx871.87\text{ cubic centimeters}[/tex]
The heights, in feet, of 12 trees in a park are shown below.8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47Use the drop-down menus to explain the interquartile range of the data.
Given:
The heights, in feet, of 12 trees in a park are:
8,11,14,16,17,21,21,24,27,31,43,47.
Required:
To find the interquartile range of the given data.
Explanation:
We have given the heights of 12 trees in feet.
Therefore, the total number of quantitties (elements) in given data is even.
Thus, the median (M) of the data is,
[tex]\begin{gathered} M=\frac{21+21}{2} \\ \Rightarrow M=\frac{42}{2} \\ \Rightarrow M=21 \end{gathered}[/tex]The median (Q) of the first half of the data 8,11,14,16,17 is given by,
[tex]Q=14[/tex]since the number of quantities are odd.
The median (Q') of the second half of the data 24,27,31,43,47 is given by,
[tex]Q^{\prime}=31[/tex]since the number of quantities are odd.
Hence, the interqurtile range (R) is,
[tex]\begin{gathered} R=Q^{\prime}-Q \\ \Rightarrow R=31-14 \\ \Rightarrow R=17 \end{gathered}[/tex]Final Answer:
The interquartile range is,
[tex]R=17[/tex]The first option is spread.
The second option is range.
The third option is 17.
The fourth option is middle 50%.
Write an exponential expression: Let 10 be the base and an even number between 1 and 10 be the exponent.
Then write the exponential expression in expanded form and standard form.
The exponential expression as required to be chosen is; 10⁴.
The expanded form of the expression is; 10 × 10 × 10 × 10.
The standard form of the expression is; 10,000.
Exponential expressions in expanded form and Standard form.It follows from the task content that the exponential expression is to be written in expanded and standard form.
Since the exponential expression must have 10 as the base and an even number between 1 and 10 as the exponent.
An example of such exponential expression is therefore;
10⁴.
Hence, to write the expression in expanded form; it is written as a product of factors as follows;
10 × 10 × 10 × 10
Also, the expression can be written in standard form as the result of the multiplication above;
= 10,000.
Read more on exponential expressions in expanded and standard form;
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Solye for x.7(x - 3) + 3(4 - x) = -8
Explanation
Step 1
apply the distributive property to eliminate the parenthesis
[tex]\begin{gathered} 7(x-3)+3(4-x)=-8 \\ 7x-21+12-3x=-8 \end{gathered}[/tex]Step 2
add similar terms
[tex]\begin{gathered} 7x-21+12-3x=-8 \\ 4x-9=-8 \end{gathered}[/tex]Step 3
add 9 in both sides
[tex]\begin{gathered} 4x-9=-8 \\ 4x-9+9=-8+9 \\ 4x=1 \end{gathered}[/tex]Step 4
divide each side by 4
[tex]\begin{gathered} 4x=1 \\ \frac{4x}{4}=\frac{1}{4} \\ x=\frac{1}{4} \end{gathered}[/tex]How to put 7^3/4 in radical form
Given:
[tex]7^{\frac{3}{4}}[/tex]Resolving it to its radical form can be gotten based on the general laws of indices.
We have:
[tex]A^{\frac{x}{y}}=\sqrt[y]{A^x}[/tex]I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.
Thus:
[tex]\begin{gathered} 7^{\frac{3}{4}}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{\frac{1}{4}}=343^{(\frac{1}{2}\times\frac{1}{2})} \\ =343^{(\frac{1}{2}\times\frac{1}{2})}=\sqrt[]{343^{\frac{1}{2}}} \end{gathered}[/tex]Now, we have our value in the square root form as:
[tex]\sqrt[]{343^{\frac{1}{2}}}=\sqrt[]{7^{\frac{3}{2}}}[/tex]Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
I inserted a picture of the questionPlease state whether it’s A B C or DCheck all that apply
Given the initial function,
[tex]f(x)=2^x[/tex]In general, a vertical stretch/compression is expressed by
[tex]f(x)\to k\cdot f(x)[/tex]If k>1, the function gets a vertical stretch; on the other hand, if 0Therefore, in our case,
[tex]g_1(x)=\frac{1}{3}f(x)\to\text{vertical compression by a factor of 1/3}[/tex]A vertical shift is given by the following formula
[tex]\begin{gathered} f(x)+k \\ k>0\to\text{shifted up} \\ k<0\to\text{shifted down} \end{gathered}[/tex]In our case,
[tex]g(x)=g_1(x)-7\to\text{vertical shift down by 7 units.}[/tex]Therefore, the answers are B and D.
Kareem ordered some books online and spent a total of . Each book cost and he paid a total of for shipping. How many books did he buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers , , and . Let represent the number of books.
(b) Solve the equation in part (a) to find the number of books.
Answer:
A
Step-by-step explanation:
Carla has a music box that has a base area of 9 1/2 in² and a height of 3 1/5 inches.What is the volume of the music box?
Given in the question:
a.) Base area of music box = 9 1/2 in²
b.) Height of music box = 3 1/5 in.
Let's recall the formula for getting the volume of a rectangular prism:
[tex]\text{ Volume = Length x Width x Height or Base Area x Height}[/tex]Before we plug in the values, let's first transform the mixed numbers into improper fractions.
[tex]\text{ 9 }\frac{1}{2}\text{ = }\frac{1\text{ + (2 x 9)}}{2}\text{ = }\frac{1\text{ + 18}}{2}\text{ = }\frac{19}{2}[/tex][tex]\text{ 3 }\frac{1}{5}\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}\text{ = }\frac{16}{5}[/tex]Let's now plug in the values to get the volume of the music box.
[tex]\text{ Volume = Base Area x Height}[/tex][tex]=\text{ 9 }\frac{1}{2}\text{ x 3 }\frac{1}{5}\text{ = }\frac{19}{2}\text{ x }\frac{16}{5}\text{ = }\frac{304}{10}\text{ }[/tex][tex]\frac{304}{10}\text{ = }\frac{\frac{304}{2}}{\frac{10}{2}}=\frac{152}{5}\text{ or 30 }\frac{2}{5\text{ }}in.^3[/tex]Therefore, the volume of the music box is 30 2/5 in.^3.
what is the conjugate of the denominator of the expression 9i/-2+7i
The answer is D.
An air plane can cruise at 640mph. How far can it fly in 3/2 Ths of an hour?
Answer: 960 miles
3/2 of an hour would be 1 hour and 30 min or an hour and a half
640mph (mph = miles per hour)
1/2 of an hour is 30 minutes so its 640 miles in half so 320
now all you gotta do is add it
so 640 + 320 = 960
use accounting principles to find the number of outcomes: How many ways can Mark create a 4-digitcode for his garage door opener?
To creat a 4 - digit code, we need to consider that for each digit we have 10 options:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -----> 10 options for each digit.
Next, we multiply the number of options we have for each digit. In this case, since we need the code to have 4 digits:
[tex]10\times10\times10\times10[/tex]We multiply 4 times 10.
And the result is:
[tex]10\times10\times10\times10=10,000[/tex]He has 10,000 ways to create a 4-digit code.
In the diagram below, if < ACD = 54 °, find the measure of < ABD
Opposite angles in a quadrilateral inscribed in a circle add up to 180, therefore:
[tex]\begin{gathered} m\angle ACD+m\angle ABD=180 \\ 54+m\angle ABD=180 \\ m\angle ABD=180-54 \\ m\angle ABD=126^{\circ} \end{gathered}[/tex]Answer:
b. 126
61 less than twice vidy's score
We are given the following word problem
"61 less than twice Vidy's score"
Let us translate the word problem into an algebraic expression
Let v represents Vidy's score
twice Vidy's score means 2 times v
61 less than means to subtract 61 from 2 times v
So, the algebraic expression becomes
[tex]2v-61[/tex]What is the product of V3 and 7V30 in simplest radical form?
Determine the product of two expressions.
[tex]\begin{gathered} \sqrt[]{3}\times7\sqrt[]{30}=7\sqrt[]{30\cdot3} \\ =7\sqrt[]{3\cdot3\cdot10} \\ =7\cdot3\sqrt[]{10} \\ =21\sqrt[]{10} \end{gathered}[/tex]So answer is,
[tex]21\sqrt[]{10}[/tex]What is an equation of the line that passes through the points (-3,-5) and (-5, -3)? Put your answer in fully reduced form.
Express the general equation of a line passing through two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,
[tex]\begin{gathered} y+5=\frac{-3+5}{-5+3}(x+3) \\ y+5=\frac{2}{-2}(x+3) \\ y+5=-x-3 \end{gathered}[/tex]Further simplifying gives,
[tex]y=-x-8[/tex]Therefore, the equation of the line is y=-x-8.
In a school, 10% of the students have green eyes. Findthe experimental probability that in a group of 4students, at least one of them has green eyes.The problem has been simulated by generating randomnumbers. The digits 0-9 were used. Let the number "9"represent the 10% of students with green eyes. A sampleof 20 random numbers is shown.
Given that in a group of 4 students at least one has green eyes.
Also, the number 9 represents the 10% of the students with green eyes.
From the 20 random experimental numbers given, the number 9 appeared in only nine of them.
The experimental probability in percentage will be:
[tex]\frac{9}{20}\ast100\text{ = }45\text{ percent}[/tex]ANSWER;
45%
Carlos is adding insulation to a room he just finished framing in his home. The room is 16ft. by 12ft., and the ceilings are 9ft. tall. There are two windows in the room measuring 5ft. by 6ft. each. How many square feet of insulation does Carlos need?
Solution
Now
[tex]A=2(16\times12)+2(16\times9)+2(9\times12)-2(5\times6)[/tex][tex]828ft^2[/tex]square feet of insulation Carlos need is
[tex]828ft^2[/tex]A high school counselor wants to look at the relationship between GPA and the numberof absences for students in the senior class this year. That data shows a linear patternwith the summary statistics shown below.I answered som of it I just can’t do part D, part E, part F
D.
The slope of a line means the increase in y for each unitary increase in x:
[tex]b=\frac{\Delta y}{\Delta x}[/tex]If the slope is equal to -0.1625, that means if x increases 1 unit, y will decrease by 0.1625 units.
E.
Using x = 3 in the regression equation, we have:
[tex]\begin{gathered} y=a+bx \\ y=3.71-0.16x \\ y=3.71-0.16\cdot3 \\ y=3.71-0.48 \\ y=3.23 \end{gathered}[/tex]So the estimated GPA is 3.23.
F.
If r is the value of the standard deviation, therefore r² is the variance:
[tex]\begin{gathered} r=-0.65 \\ r^2=0.4225 \end{gathered}[/tex]The variance is the average of the squared difference from each point to the mean, and it measures the average of how much each point differs from the mean.
write your answer in exponential form. 3^9 * 3^-3
Step 1
Given;
[tex]3^9\times3^{-3}[/tex]Required; To write the answer in exponential form
Step 2
[tex]\begin{gathered} Using\text{ the index law below;} \\ a^b\times a^c=a^{bc} \\ Hence,\text{ 3}^9\times3^{-3}=3^{9-3}=3^6 \end{gathered}[/tex]Answer;
[tex]3^6[/tex]find the value of the 30th percentile of the following set of data
The given data is:
[tex]18,9,7,5,11,7,17,20,19,2,17,12,5,1,13,12,11,15,16,20[/tex]Rearrange the data in ascending order:
[tex]1,2,5,5,7,7,9,11,11,12,12,13,15,16,17,17,18,19,20,20[/tex]in the graph below line k,y=-x makes a 45 degree angle with the x and y axescomplete the following
step 1
The equation of line k is y=-x
The rule of the reflection across the line y=-x is equal to
(x,y) -------> (-y,-x)
so
we have the point (2,5)
Apply the rule
(2,5) -----> (-5,-2)
step 2
Reflection across the x axis
The rule of the reflection across the x axis is
(x,y) ------> (x,-y)
so
Apply the rule to the point (-5,-2)
(-5,-2) ------> (-5,2)
therefore
the answer is
(-5,2)? QuestionWhat is the equation of the quadratic function represented by this table?х5678910f(x)-4585-4-19HolaType the correct answer in each box. Use numerals instead of words.f(x) =(x -12 +
To determine the equation of the quadratic equation, which is a parabola, we substitute the coordinates of the vertex of the parabola (h,k) into the general equation.
[tex]y=a(x-h)^2+k[/tex]From the given, notice that the only value of f(x) that does not repeat is 8. This means that the vertex is at (7,8).
[tex](h,k)=(7,8)[/tex]Thus, we only need to obtain the value of a.
Substitute the coordinate of a point (x,y) into the equation and the vertex as well. In this case, let us use the first given point, (5,-4).
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ (5,-4)\rightarrow-4=a(5-7)^2+8 \end{gathered}[/tex]Simplify the obtained equation.
[tex]\begin{gathered} (5,-4) \\ -4=a\mleft(5-7\mright)^2+8 \\ -4=a\mleft(-2\mright)^2+8 \\ -4=a(4)+8 \\ -4-8=4a \\ -12=4a \\ a=\frac{-12}{4} \\ a=-3 \end{gathered}[/tex]Now that we have the value of a, substitute the coordinates of the obtained vertex and the value of a into the equation of the quadratic equation.
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=-3(x-7)^2+8 \end{gathered}[/tex]To check, the graph of the given function is as follows:
Therefore, the equation of the quadratic equation is y=-3(x-7)²+8.
do an addition in binary (inverse code) on following numbers:
00011101
+ 111111101
please, help asap thank u
The first complement of the binary addition is 00011111.
The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system. The binary system consists of only two digits, 1 and 0.
Given that, the addition of the given number
00011101 + 11111101
In the binary addition,
0+1 = 1
1+0 = 1
1+1 = 0
00011101 + 11111101 = 11100000
Then inverse code means first complement of the answer.
In the first complement, 0 is the inverse of 1 and 1 is inverse of 0.
11100000 = 00011111
Hence, The first complement of the binary addition is 00011111.
To learn more about binary addition from the given link:
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converting to slope intercept formmatch each equation to an equivalent equation written in slope intercept form.
Statement Problem: Match each equation to an equivalent equation written in slope-intercept form.
Solution:
A slope intercept form equation is written as;
[tex]y=mx+b[/tex](a)
[tex]2y-6=x[/tex]Add 6 to both sides of the equation;
[tex]\begin{gathered} 2y-6+6=x+6 \\ 2y=x+6 \end{gathered}[/tex]Divide each term by 2;
[tex]\begin{gathered} \frac{2y}{2}=\frac{x}{2}+\frac{6}{2} \\ y=(\frac{1}{2})x+3 \end{gathered}[/tex](b)
[tex]undefined[/tex]You have to multiple the whole number and the fraction if you don’t know how to do it
We need to find how much spare represents the given space for vegetables.
The total are is 24 square feet and she will use 3/4 of the space for vegetables.
Then, you need to multuply the result by 3 and then, we need to divide 24 by 4.
Therefore:
24*(3/4) =72/4 = 18
Hence, she will use 18 square feet for vegetables.
I’m struggling on this math question and could use some help on it
Let's determine the values of f(-4) and g(6).
For f(-4),
[tex]\text{ f\lparen x\rparen= -2x}^3\text{ - 5}[/tex][tex]\text{ f\lparen-4\rparen= -2\lparen-4\rparen}^3-5\text{ = -2\lparen-64\rparen- 5}[/tex][tex]\text{ f\lparen-4\rparen = 128 - 5}[/tex][tex]\text{ f\lparen-4\rparen = 123}[/tex]Therefore, f(-4) = 123
For g(6),
[tex]\text{ g\lparen x\rparen = -3x - 3}[/tex][tex]\text{ g\lparen6\rparen = -3\lparen6\rparen - 3 = -18 - 3}[/tex][tex]\text{ g\lparen6\rparen = -21}[/tex]Therefore, g(6) = -21
what is the answer to this? 3√5+15√5
what is the answer to this? 3√5+15√5
we have
3√5+15√5=18√5
answer is 18√5