QRST is a rectangle. Find the value of x and the length of each diagonal. QS = 5x + 12 and RT = 6x – 2
Answers
We can draw the rectangle QRST as:
The two diagonals of a rectangle will have the same length, so we can write:
[tex]\begin{gathered} QS=RT \\ 5x+12=6x-2 \\ 5x-6x=-2-12 \\ -x=-14 \\ x=14 \end{gathered}[/tex]With the value of x, we can calculate the length of the diagonal:
[tex]QS=5x+12=5\cdot14+12=70+12=82[/tex]Answer: the lengths of the diagonals QS and RT is 82.
The value of x is 14 and the length of each diagonal would be 82 units.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that QRST is a rectangle.
We have to determine the value of x and the length of each diagonal.
QS = 5x + 12 and RT = 6x – 2
Because a rectangle's two diagonals will be the same length, we may write:
QS = RT
5x + 12 = 6x – 2
Rearrange the terms in the above equation,
6x - 5x = 12 + 2
x = 14
The value of x is 14.
So, QS = 5(14) + 12 and RT = 6(14) – 2
So, QS = RT = 82
Therefore, the length of each diagonal would be 82 units.
Learn more about the Area of the rectangle here:
brainly.com/question/20693059
#SPJ2
Related Questions
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
Answers
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
hello I don't you can help me with this please
Answers
Approximately 10 hours
1) Gathering the data
Initial temperature: 79º F
0.8 each hour
84º
2) We can write an exponential function to find that out. So let's do it this way:
[tex]\begin{gathered} T_f=T_0(1+0.8)^h \\ 84=79(1.8)^h \\ \frac{84}{79}=\frac{79(1.8)^h}{79} \\ 1.06=1.8^h \\ \log _{10}1.06=\log _{10}1.8^h \\ h\log _{10}1.8=\log _{10}1.06 \\ h=10.087 \end{gathered}[/tex]Notice that since the temperature is rising, we have to add one to the factor, otherwise, it will decrease it.
Now let's convert that decimal number so that we may have a better approximation:
10 hours and 4 minutes
f (x) = 2x -1find f (-4)
Answers
f(x)=2x-1
we repleace the x with the number -4
f(-4)=2(-4)-1=-8-1=-9
f(-4)=-9
How do I graph y = -4x + 6 thanks!
Answers
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.
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.
Answers
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
60 inches =___ feet please and thank you for your help
Answers
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]What is 6/24 in lowest terms(I’m reporting wrong answers)
Answers
The greatest common factor of 6 and 24 is 6.
Divide the numerator and denominator by 6.
6/24 = (6/6) / (24/6) = 1/4
What value for x makes the following statement true?
Answers
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.
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
Answers
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
which would it be? …….
Answers
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.
A town’s population increases at a constant rate. In 2010 the population was 56,000 . By 2012 the population had increased to 81,000 . If this trend continues, predict the population in 2016. The population will be Number in 2016.
Answers
Given: A town's population increases at a constant rate. In 2010 the population was 56,000. By 2012 the population had increased to 81,000.
Required: To predict the population in 2016.
Explanation: The population is increasing at a constant rate. In 2 years, the increase in population is-
[tex]81000-56000=25000[/tex]Thus the slope (or rate of change of population per year) is-
[tex]\frac{25000}{2}=12500[/tex]Thus, in 2016 after 6 years, the increase in population will be-
[tex]12500\times6=75000[/tex]Hence, the population in 2016 will be-
[tex]56000+75000=131000[/tex]Final Answer: The population will be 131,000 in 2016.
divide decimals by decimals 033 divided by 688
Answers
The given numbers are 0.33 divided by 6.88
[tex]\frac{0.33}{6.88}=0.0479[/tex]Answer : 0.0479
QUESTION IS IN IMAGE!! DONT SHOW WORK JUST THE ANSWER UNLESS YOU NEED TO
Answers
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°
What is the inverse equation for h(x) = 2log(x-3) ?
Answers
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]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.)
Answers
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
6. Analyze Marc has one dollar, one quarter, one dime, one nickel, and
one penny. He spends 35 cents. How much money does he have left?
A $0.76
B $0.96
$1.06
D $1.16
Answers
$1.41 - .35= $1.06
A student plays the following game. He tossed three coins. If he gets exactly two heads he wins $5. If he gets exactly one head he wins $3. Otherwise, he loses $2. On the average, how much should he win or lose per play of the game?
Answers
A student plays the following game. He tossed three coins. If he gets exactly two heads he wins $5. If he gets exactly one head he wins $3. Otherwise, he loses $2. On the average, how much should he win or lose per play of the game?
we have that
If he gets exactly two heads he wins $5.
the probability is
P=2/8
If he gets exactly one head he wins $3
the probability is
P=1/8
we have that
2/8+1/8=3/8
that means, that the probaility of any other result is 1-3/8=5/8
therefore
he win or lose per play
(2/8)*$5+(1/8)*$3-(5/8)*$2=(10/8)+(3/8)-(10/8)=3/8=$0.375
the answer is
He win $0.375 per game6. Examine the two-way frequency table below.Gold Medals Silver Medals Bronze MedalsUSA 201842Spain 2511France 192726Based on the data in the two-way frequency table, what is the probability that a randomly selected player won a bronze medal given that the player represented Spain?22.4%24.4%13.995.5%PREVIOURPREVIOUS6 ofNEXTREVIEWSALSion outINTL
Answers
From the table, we can get the total number of players that took part in the games.
See the new table below;
From the table, we got the sum of players from each country, and also the sum of medals won by each player. This gave us a total of 201 when we calculate the total medals collected or the total from all the countries. Hence, the name two-way.
From the table, the number of Spain players that won bronze is 11, hence, the probability is;
[tex]\begin{gathered} \text{Probability = }\frac{n\text{umber of required outcome}}{n\text{ umber of total possible outcomes}} \\ P(\text{Spain player with bronze)= }\frac{n\text{ umber of Spain player that won bronze}}{\text{total n umber of players}} \\ =\text{ }\frac{11}{201} \\ =0.0547 \\ \text{Taking this to percentage, we have it to be 0.0547 x 100} \\ =5.47 \\ =5.5 \end{gathered}[/tex]Therefore, the probability of selecting a Spain player that won a bronze medal at random is 5.5%
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”?
Answers
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
Two more than the cube root of a number
Answers
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?
Answers
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.
Jessica states -79 will make the inequality true.-80 > ? _> -89O FactO Fib
Answers
-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
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
Answers
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]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?
Answers
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
Which system of inequalities is shown? O Ayx у 2 в ух y2 с. у.х y2 р. уки
Answers
First, we need to find the equations of the two dotted lines.
One of the lines is parallel to the x-axis and passes through the point (0, 2), then its equation is:
y = 2
The other line has a slope of 1 and intercepts the y-axis at the point (0,0). Using the slope-intercept form with m = 1 and b = 0, its equation is:
y = mx + b
y = 1*x + 0
y = x
Given that the shaded region is below both lines and the lines are not included in the solution, then we need to use a "<" sign in the inequalities. Finally, the system of inequalities is:
y < x
y < 2
I need help to find an surface area! I will include a full photo.
Answers
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]1 Decide whether the graph shown below is a function or not.
Answers
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.
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
Answers
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:
find an equation for the line that passes through the points (-1,5) and (-5,1)
Answers
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]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
Answers
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