which would it be? …….
Answer:
A
Step-by-step explanation:
for the relationship to be a function, then each value from the input must map to exactly one unique value in the output.
This is the case here si represents a function.
What is the inverse equation for h(x) = 2log(x-3) ?
Given the function:
[tex]h(x)=2log\left(x-3\right)[/tex]To find its inverse:
[tex]\begin{gathered} y=2log\left(x-3\right) \\ x=2log\left(y-3\right) \end{gathered}[/tex]solving for y:
[tex]\frac{x}{2}=log(y-3)[/tex][tex]\begin{gathered} 10^{\frac{x}{2}}=y-3 \\ \\ 10^{\frac{x}{2}}+3=y \end{gathered}[/tex]ANSWER
[tex]h^^{-1}(x)=10^{\frac{x}{2}}+3[/tex]A metallurgist has One alloy containing 49% copper and another containing 62% copper. How many pounds of each alloy must he used to make 51 pounds of a third alloy containing 56% copper?
Explanation
Step 1
a)
Let
x represents the pounds of the 49 % copper alloy
y represents the pounds of the 62 % copper alloy
then,
if we want to make a 51 pounds of a new alloy,
[tex]x+y=51\rightarrow equation(1)[/tex]b)this new allo contains 56% of copper , so
total of cooper = pounds of alloy * percentage
[tex]\begin{gathered} 0.49x+0.62y=51\cdot0.56 \\ 0.49x+0.62y=28.56\rightarrow equation\text{ (2)} \end{gathered}[/tex]Step 2
Solve the equations
a) isolate x in equation (1) and replace in equation(2)
[tex]\begin{gathered} x+y=51\rightarrow equation(1) \\ \text{subtract y on both sides} \\ x+y-y=51-y \\ x=51-y\rightarrow equation(3) \end{gathered}[/tex]Now, replace in equation (2)
[tex]\begin{gathered} 0.49x+0.62y=28.56\rightarrow equation\text{ (2)} \\ 0.49(51-y)+0.62y=28.56 \\ 24.99-0.49y+0.62y=28.56 \\ \text{add like terms } \\ 24.99+0.13y=28.56 \\ \text{subtract 24.99 on both sides} \\ 24.99+0.13y-24.99=28.56-24.99 \\ 0.13y=3.57 \\ \text{divide both sides by 0.13} \\ \frac{0.13y}{0.13}=\frac{3.57}{0.13} \\ y=27.46 \\ \end{gathered}[/tex]now, replace the y value into equation (3) to get x
[tex]\begin{gathered} x=51-y\rightarrow equation(3) \\ x=51-y \\ x=51-27.46 \\ x=23.54 \\ \end{gathered}[/tex]therefore, the answer is
23.54 lb of the 49% copper alloy
27.46 lb of the 62% copper alloy
If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a 7 or 5? (Your answer must be in the form of a reduced fraction.)
In a deckk of 52 cards there are four 5 and four 7, so the probability to select randomly a 5 or a 7 is:
[tex]\begin{gathered} \text{prob}=\frac{success\text{ cases}}{total\text{ cases}} \\ \text{prob}=\frac{8}{52}=\frac{2}{13} \end{gathered}[/tex]The probability is 2/13
f (x) = 2x -1find f (-4)
f(x)=2x-1
we repleace the x with the number -4
f(-4)=2(-4)-1=-8-1=-9
f(-4)=-9
Factor using the GCF: 7x-19y
Answer:
1(7x-19y)
Step-by-step explanation:
these are both prime numbers so the gcf is 1
hopes this helps please mark brainliest
Answer: no solution
Step-by-step explanation: 1. Find the gcf for both numbers. The prime factorization for 7x is just 7 * x. The prime factorization for 19y is 19 * y.
2. 7x and 19y have nothing in common, so therefore it's not factorable
1 Decide whether the graph shown below is a function or not.
According to the vertical line test, a curve represents a function only if the vertical line drawn at any point intersects the curve atmost once.
Observe that the given curve fails to satisfy this condition.
This concludes that the given curve does not represent a function.
Determine the equation of the line thatpasses through (0, 2) and (4, 5). Put inslope-intercept form.
Given:
Point ( 0, 2) and (4, 5)
The coordinates are:
x₁=0 y₁=2 x₂=4 y₂=5
First, we need to find the slope(m) using the formula below:
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values and evaluate.
[tex]\text{slope(m)}=\frac{5-2}{4-0}=\frac{3}{4}[/tex]Next, is to find the intercept(b) by substituting m=3/4 x=0 and y=2 into y=mx+b and then solve for b.
2 = 3/4 (0) + b
b=2
We can now proceed to form the equation by substituting the values of m and b into y=mx + b.
Hence, the equation of the line is:
[tex]y=\frac{3}{4}x\text{ + 2}[/tex]Find the circumference of this circleusing 3 for T.C ~ [?]88C = id
We have that d = 8, using the formula:
[tex]C=\pi d[/tex]Where π = 3, then
[tex]\begin{gathered} C=\pi d \\ \\ C=3\cdot8 \\ \\ C=24 \end{gathered}[/tex]Then the circumference is 24
[tex]C=24[/tex]How do I graph y = -4x + 6 thanks!
We have that the equation represents a line in slope-intercept form:
[tex]y=mx+b\Rightarrow y=-4x+6[/tex]We have that m is the slope, in this case, m = -4, and 6 is the y-intercept (0, 6). The y-intercept is the point where the line passes through the y-axis - at this point x = 0.
Therefore, we still need another point to do the graph of the line. This point can be the x-intercept: the point where the line passes through the x-axis, and, at this point, y = 0. Then, to find it, we can proceed as follows:
y = 0
[tex]y=0\Rightarrow0=-4x+6[/tex]Subtracting 6 from both sides of the equation, we have:
[tex]-6=-4x+6-6\Rightarrow-6=-4x[/tex]Now, we can divide both sides of the equation by -4:
[tex]-\frac{6}{-4}=-\frac{4}{-4}x\Rightarrow x=\frac{6}{4}\Rightarrow x=\frac{3}{2}=1.5[/tex]Now, we have the y-intercept (0, 6) and the x-intercept (1.5, 0), and with these two points, we can graph the line. We need to remember that a line can be defined by two points.
Two more than the cube root of a number
two more means add 2 , +2
cube root of a number
A number is x
cube root of x :
∛x
Answer:
∛x + 2
Santa has 3/4 of a bag of grain left. His hens eat 1/6 of a bag of grain every day. How many days will he be able to feed his hens?
To find how many days he is able to feed his hens, divide 3/4 by 1/6.
[tex]\frac{\frac{3}{4}bag}{\frac{1}{6}\frac{day}{day}}[/tex]To solve it multiply the first fraction by the inverse of the second fraction.
[tex]\begin{gathered} \frac{3}{4}bag*\frac{6}{1}\frac{day}{bag} \\ \frac{6*3}{4}days \\ \frac{18}{4}days \\ 4.5days \end{gathered}[/tex]That means he will be able to feed his hens for 4 days.
Answer: 4 days.
2.“Lucy”, a 12 year old 16 kg beagle needs a dose of the antibiotic cefazolin IV to treat her infected bite wound. The dose is 22 mg/kg IV. The concentration is 100 mg/ml. How many mgs of cefazolin will you give to “Lucy”? How many mls will you give to “Lucy”?
To determine the many mls will you give to “Lucy”:
Using a weight measurement by volume conversion
[tex]\text{Volume(ml)}=\frac{\text{mass(kg) x dose(mg/ml)}}{density\text{ (mg/ml)}}[/tex]Mass = 16kg
dose = 22mg/kg
density = 100mg/ml
How many mgs of cefazolin will you give to “Lucy
[tex]\begin{gathered} \text{mass (mg) = 22 mg / kg x 16kg} \\ \text{mass (mg) = 352 mgs} \end{gathered}[/tex]Hence the mass (mgs) of cefazolin given to lucy = 352 mgs
[tex]\begin{gathered} \text{Volume (ml) = }\frac{\text{22 x 16 mg }}{100\text{ mg/ml}} \\ \text{Volume (ml) = }\frac{88}{25}ml \\ \text{Volume = 3.52 ml} \end{gathered}[/tex]Hence the volume (mls) given to lucy = 3.52 ml
I need help to find an surface area! I will include a full photo.
ANSWER:
99.9 square meters
STEP-BY-STEP EXPLANATION:
We have that the area of a cone is given by the following equation
[tex]A_T=A_L+A_B[/tex]Where the lateral area and the base area are calculated as follows:
[tex]\begin{gathered} A_L=\pi\cdot r\cdot g_{} \\ A_B=\pi\cdot r^2 \end{gathered}[/tex]Replacing in each case, g = 7.6 m and r = 3 m:
[tex]\begin{gathered} A_L=3.14\cdot3\cdot7.6_{}=71.6 \\ A_B=3.14\cdot3^2=28.3 \end{gathered}[/tex]Therefore the surface area would be:
[tex]\begin{gathered} A_T=71.6+28.3 \\ A_T=99.9 \end{gathered}[/tex]Find the measure of each angle in the proplem RE contains point P
In the given figure, line LP is lie on the line RE, thus from the linear property
Angle LPR + Angle LPE = 180°
It is given that Angle LPR = 3z, angle LPE = 2z
Angle LPR + Angle LPE = 180°
3z° + 2z° = 180°
5z° = 180°
z = 180/5
z=36
Substitute the value of z = 36 in the angle LPR;
Angle LPR = 3z
= 3(36)
=108°
Angle LPE = 2z
= 2(36)
= 72°
Answer : B) 108 and 72
9+7x = -5Which is the following above Addition property of equality Subtraction property of equality Simplify Division property of equality Symmetric property of equality Distributive property
Given:
[tex]9+7x=-5[/tex]To find:
The properties.
Explanation:
Using the subtraction property of equality,
[tex]\begin{gathered} 9+7x-9=-5-9 \\ 7x=-14 \end{gathered}[/tex]Using the division property of equality,
[tex]\begin{gathered} \frac{7x}{7}=-\frac{14}{7} \\ x=-2 \end{gathered}[/tex]Final answer:
The properties used are,
• The subtraction property of equality
,• The division property of equality
find an equation for the line that passes through the points (-1,5) and (-5,1)
Answer:
x-y=-6
Explanation:
Given the points (-1,5) and (-5,1):
To find the equation of the line, we use the two-point formula:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(-1,5) \\ \mleft(x_2,y_2\mright)=\mleft(-5,1\mright?) \end{gathered}[/tex]Substitute these points into the formula:
[tex]\frac{y-5}{x-(-1)}=\frac{1-5}{-5_{}-(-1)}[/tex]Then simplify:
[tex]\begin{gathered} \frac{y-5}{x+1}=\frac{1-5}{-5_{}+1} \\ \frac{y-5}{x+1}=\frac{-4}{-4} \\ \frac{y-5}{x+1}=1 \\ y-5=x+1 \\ -5-1=x-y \\ x-y=-6 \end{gathered}[/tex]The equation of the line is:
[tex]x-y=-6[/tex]describe the transformation of the graph of the parent quadratic function then identify the vertex
The vertex of a quadratic function can be found by the following expression:
[tex]x=\frac{-b}{2a}[/tex]When we add a number to the argument of the function, "x", we shift the function left or right. If the number is positive the shift happens to the left, if is negative the shift happens to the right.
When we add a number to the whole function we shift the function up or down. If the number is positive the shift is on the upwards direction and if it is negative the shift is on the downwards direction.
When we multiply a function we are stretching or compressing it. If the number is greater than 1, we are compressing the function and if its smaller than 1 we are stretching i.
With this in mind we can find which transformations happened in each option. The original function is:
[tex]f(x)=x^2[/tex]27.
[tex]f(x)=3(x+2)^2+1[/tex]There is a number 3 multiplying the function, so it got compressed by a factor of three. There is a number 2 adding to the variable, so it got shifted left by 2. There is a number 1 adding the whole function, so it got moved upwards by 1.
The vertex of the original function is at (0,0). The function moved upwards by 1 this happens on the y-axis and left by 2 this happens on the x-axis, so the new vertex is (-2,1).
28.
[tex]f(x)=-4(x+1)^2-5[/tex]There is a negaive number, "-4", multiplying the function, so it got compressed by a factor of four and it also got inverted, because the number is negative. There is a number "1" adding the variable, so it got moved one unit to the left. There is a number "-5" adding the whole function, so it got moved five units down.
Since the function moved one unit to the left, changing the x-coordinate for the vertex by "-1" and it also moved five units down, changing the y-coordinate for the vertex by "-5", the new vertex is (-1, -5).
29.
[tex]f(x)=-2x^2+5[/tex]There is a negative number multiplying the function, so it got compressed by a factor of 2 and inverted. There is also a constant adding to the function, so it got moved up by 5 units.
Since the function didn't moved in the x-axis, but got up 5 units on the y-axis the new vertex is (0,5).
30.
[tex]f(x)=\frac{1}{2}(x-1)^2[/tex]There is a number "1/2" multiplying the function, since it is lower than 1, the function got stretched by a factor of 2. There is a constant adding "-1" to the variable, therefore the function got moved to the right by one unit.
Since the function moved 1 unit to the right the new vertex is (1,0).
QUESTION IS IN IMAGE!! DONT SHOW WORK JUST THE ANSWER UNLESS YOU NEED TO
Given:
m∠SPQ = 113 degrees
Let's find the measure of angle RQS, m∠RQS.
By applying the angle-arc relationship, we have:
m∠SPQ = measure of arc SQ = 113 degrees.
Since RQ is the diameter, measure of arc RQ = 180 degrees.
Now, let's find the measure of arc RS:
measure of arc RS = 360 - arc SQ - arc RQ
measure of arc RS = 360 - 113 - 180 = 67 degrees.
To find the m∠RQS, apply angle-arc relationship:
[tex]\begin{gathered} m∠RQS=\frac{1}{2}arcRS \\ \\ m∠RQS=\frac{1}{2}*67 \\ \\ m∠RQS=33.5^o \end{gathered}[/tex]Therefore, the measure of angle RQS is 33.5 degrees.
ANSWER:
m∠RQS = 33.5°
Sally test grades in English and 75 and 80 what grade must she get on her next test so the average is in 85?
Explanation
We are told that Sally scored 75 and 80 on two English tests
We are then asked to determine the next grade she must have so that the average becomes 85
Thus
let the third grade be x
Hence
The total grades of the three tests will be
[tex]75+80+x[/tex]The average of the three tests will be
[tex]\frac{75+80+x}{3}[/tex]Since the average is 85, then we will have
[tex]\frac{75+80+x}{3}=85[/tex]We can now solve for x
[tex]\begin{gathered} 75+80+x=3\times85 \\ 155+x=255 \\ x=255-155 \\ x=100 \end{gathered}[/tex]Thus, she must score 100 on her third test
Write the equation of a line parallel to the given line and passes through points (4, 6), and (-2, -6). Hints find the slope by using the slope formula and then write your equation in slope-intercept form show your work in order to get credit!
Answer:
y = 2x - 2
Step-by-step explanation:
Equation of a line:
In slope-intercept formula, it is:
y = mx + b
In which m is the slope and b is the y-intercept, which is the value of y when x = 0.
Passes through points (4, 6), and (-2, -6).
We find the equation using these two points.
First we find the slope, which is the change in y divided by the change in x.
Change in y: 6 - (-6) = 6 + 6 = 12.
Change in x: 4 - (-2) = 4 + 2 = 6
Slope: m = 12/6 = 2
So:
y = 2x + b
We select one of these points, two find b.
I will select the point (4,6), which means that when x = 4, y = 6. So
y = 2x + b
6 = 2*4 + b
8 + b = 6
b = 6 - 8
b = -2
So the equation of the line is:
y = 2x - 2
The drink booth at the school fair had these 4 types of drinks:root beer, ice tea, orange juice, and apple cider.The 16 students from Mr. Smith's class were asked which drink they ordered. Here are the results:root beer, root beer, apple cider, root beer, root beer, ice tea, orange juice, ice tea, apple cider, apple cider, apple cider, apple cider, apple cider, orangejuice, apple cider, ice teaDraw the bar graph for these data.Frequencyх?S716+5+3-2-0000root beerapple ciderice teaorange juiceType of drink
Hello there. To solve this question, we'll have to construct a bar graph using the data about the drinks ordered by the students.
From 16 students, we know that:
- 4 ordered root beer
- 6 ordered apple cider
- 3 ordered ice tea
- 3 ordered orange juice
The frequency is given by the number of times an option was ordered, therefore we build the following graph:
A line passes through the points (-21, -22) and (-14, -16). Find this line's equation in point-slope form. Using the point (-21, -22), this line's point-slope form equation is: Using the point (-14, -16), this line's point-slope form equation is:the point slope form has to be simplified
Answer:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4
Explanation:
The point-slope form of a line's equation is:
[tex]y-y_1=m(x-x_1)[/tex]Where (x₁, y₁) is a point in the line and m is the slope.
The slope of a line can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x₁, y₁) and (x₂, y₂) are two points in the line. So, replacing (x₁, y₁) by (-21, -22) and (x₂, y₂) by (-14, -16), we get that the slope of the line is:
[tex]m=\frac{-16-(-22)}{-14-(-21)}=\frac{-16+22}{-14+21}=\frac{6}{7}[/tex]Now, using the point (-21, -22), we get that the equation of the line is:
[tex]\begin{gathered} y-(-22)=\frac{6}{7}(x-(-21)) \\ y+22=\frac{6}{7}(x+21) \end{gathered}[/tex]Then, we can simplify the equation as:
[tex]\begin{gathered} y+22=\frac{6}{7}(x)+\frac{6}{7}(21) \\ y+22=\frac{6}{7}x+18 \\ y+22-22=\frac{6}{7}x+18-22 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]On the other hand, using the point (-14, -16), the equation of the line is:
[tex]\begin{gathered} y-(-16)=\frac{6}{7}(x-(-14)) \\ y+16=\frac{6}{7}(x+14) \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} y+16=\frac{6}{7}x+\frac{6}{7}(14) \\ y+16=\frac{6}{7}x+12 \\ y+16-16=\frac{6}{7}x+12-16 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]So, the answers are:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4
What value for x makes the following statement true?
Answer:
2
Step-by-step explanation:
we can isolate the variable by subtracting 3x from both sides
3x + 12 = 5x + 8
-3x -3x
12 = 2x + 8
and then subtracting 8 from both sides
12 = 2x + 8
-8 -8
4 = 2x
then we divide by 2 on both sides
4 = 2x
÷2 ÷2
2 = x
flip the equation to get:
x=2
checking the solution by plugging in 2 in place of x:
(3 * 2) + 12 = (5 * 2) + 8
6 + 12 = 10 + 8
18 = 18
since the equation is true,
the solution x = 2 is correct.
In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=62°, and IJ = 86 feet. Find the length of HI to the nearest tenth of a foot.
To get the angle at H:
The total angle in a triangle = 180
< H = 180 - (90+ 62)
To get the length HI, the hypotenuse
[tex]\cos \text{ 62 = }\frac{86}{x}[/tex][tex]\begin{gathered} x\text{ = }\frac{86}{\cos \text{ 62}} \\ \\ x\text{ = }\frac{86}{0.4695} \\ x\text{ = 183.185 f}eet \end{gathered}[/tex]The length HI = x = 183. 2 Feet to the nearest tenth
Which of the functions below could possibly have created this graph?O A. F(x)=x²+x+3O B. F(x)=1.9x +15x² -6O C. F(x)=-x³ + 2x²-3xO D. F(x) = − 3x²¹ +7x² +15x
Solution
Now
Looking at the given graph, It has four values for x
And Option D has four has exponentswhich implies it has four values for x
The final answer
Option DOpa
Jessica states -79 will make the inequality true.-80 > ? _> -89O FactO Fib
-80>-79>-89
To answer this we have to set a number line.
As we can see in the number line , if we move from left to right, -79 is higher than -80 (-79>-80)
So, the statement is false
60 inches =___ feet please and thank you for your help
We know that:
[tex]1ft=12in\text{.}[/tex]Then:
[tex]1in=\frac{1}{12}ft\text{.}[/tex]Therefore:
[tex]60in=60\cdot(\frac{1}{12}ft)\text{.}[/tex]Simplifying the above result we get:
[tex]60\cdot(\frac{1}{12}ft)=\frac{60}{12}ft=5ft\text{.}[/tex]Answer:
[tex]60\text{ inches=5 feet.}[/tex]The accompanying box-and-whisker plots can be used to compare the annual incomes of three professions. Based on the box-and-whisker plots, which statement is true?a - the median income for nuclear engineers is greater than the income of all musiciansb - the median income for police officers and musicians is the samec - all nuclear engineers earn more than all police officersd - a musician will eventually earn more than a police officer
a - Median income for nuclear engineers: $70,000. Some musicians earn more than $120,000. FALSE
b - Median income for police officers: $30,000
Median income for musicians: $30,000
TRUE
c - Some nuclear engineers earn between $50,0000 and $60,0000
Also, some police officers earn between $50,0000 and $60,0000
FALSE
d - box-and-whisker plots don't allow us to predict future events. Then, maybe or maybe not a musician will eventually earn more than a police officer
Using the formula for the area of the triangle area equals 1/2 times base times height write an expression for the area of triangle ABC. The line BD bisects the line AC perpendicularity hence this has made triangle ABD and BCD right triangles
Using the formula:
[tex]A=\frac{b\cdot h}{2}[/tex]Where:
b = base
h = height
From the diagram:
b = AC
h = BD
So:
[tex]A=\frac{AC\cdot BD}{2}[/tex]