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In the $xy$-plane, line $k$ is defined by $x+y=0$. Line $j$ is perpendicular to line $k$, and the $y$-intercept of line $j$ is (0,3). Which of the following is an equation of line $j$ ?
MathAlgebra
$$2x+3y=7$$ $$10x+15y=35$$<br/><br/>For each real number $r$, which of the following points lies on the graph of each equation in the $xy$-plane for the given system?
MathAlgebra
A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?
MathAlgebra
A proposal for a new library was included on an election ballot. A radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?
MathAlgebra
For the function $f_{i}$ if $f(3x)=x-6$ for all values of $x$, what is the value of $f(6)$?
MathAlgebra
$F=2.50x+7.00y$<br/><br/>In the equation above, $F$ represents the total amount of money, in dollars, a food truck charges for $x$ drinks and $y$ salads. The price, in dollars, of each drink is the same, and the price, in dollars, of each salad is the same. Which of the following is the best interpretation for the number 7.00 in this context?
MathAlgebra
The equation $\(9x+5=a(x+b)\)$, where \(a\) and \(b\) are constants, has no solutions. Which of the following must be true?<br/><br/>I. \(a=9\)<br/><br/>III. \(b=5\)<br/><br/>III. \(b\neq\frac{5}{9}\)
MathAlgebra
An object hangs from a spring. The formula $\mathcal{E}=30+2w$ relates the length $\mathcal{E}$, in centimeters, of the spring to the weight $w$, in newtons, of the object. Which of the following describes the meaning of the 2 in this context?
MathAlgebra
A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of 500 pounds if each box weighs 120 pounds?
MathAlgebra
$\begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|c|}{Energy per Gram of Typical Macronutrients} \\ \hline Macronutrient & Food calories & Kiljoules \\ \hline Protein & 4.0 & 16.7 \\ \hline Fat & 9.0 & 37.7 \\ \hline Carbohydrate & 4.0 & 16.7 \\ \hline \end{tabular}$ The table above gives the typical amounts of energy per gram, expressed in both food calories and kiljoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from $p$ grams of protein, $f$ grams of fat, and $c$ grams of carbohydrate, which of the following expresses $f$ in terms of $p$ and $c$ ?<br/><br/>\[\begin{array}{l}{\mbox{\small A}.}\ f=20+\frac{4}{9}(p+c)\\ \\ {\mbox{\small B}.}\ f=20-\frac{4}{9}(p+c)\\ \\ {\mbox{\small C}.}\ f=20-\frac{4}{9}(p-c)\\ \\ {\mbox{\small D}.}\ f=20+\frac{9}{4}(p+c)\\ \end{array}\]
MathAlgebra
$66a=66a$<br/><br/>How many solutions does the given equation have?
MathAlgebra
One of the two equations in a linear system is $2x+6y=10$. The system has no solution. Which of the following could be the other equation in the system?
MathAlgebra
The function $h$ is defined by $h(x)=x+200$. What is the value of $h(50)$?
MathAlgebra
$k+12=336\$$<br/><br/>What is the solution to the given equation?
MathAlgebra
A model estimates that whales from the genus _Eschrichtius_ travel 72 to 77 miles in the ocean each day during their migration. Based on this model, which inequality represents the estimated total number of miles, $x$, a whale from the genus _Eschrichtius_ could travel in 16 days of its migration?
MathAlgebra
The function $f$ is defined by $f(x)=5x+8$. For what value of $x$ does $f(x)=58$?
MathAlgebra
$\(y=70x+8\)$<br/><br/>Which table gives three values of $\(x\)$ and their corresponding values of $\(y\)$ for the given equation?<br/><br/>$\begin{tabular}{c c|c} \hline \(A\). & \(x\) & \(y\) \\ \hline<br/>0 & 8 \\ \hline<br/>2 & 148 \\ \hline<br/>4 & 288 \\ \hline B. & \(x\) & \(y\) \\ \hline<br/>0 & 70 \\ \hline<br/>2 & 78 \\ \hline<br/>4 & 86 \\ \hline C. & \(x\) & \(y\) \\ \hline<br/>0 & 70 \\ \hline<br/>2 & 140 \\ \hline<br/>4 & 280 \\ \hline D. & \(x\) & \
MathAlgebra
Hana deposited a fixed amount into her bank account each month. The function $f(t)=100+25t$ gives the amount, in dollars, in Hana's bank account after $t$ monthly deposits. What is the best interpretation of 25 in this context?
MathAlgebra
$$2.5b+5r=80$$<br/><br/>The given equation describes the relationship between the number of birds, $b$, and the number of reptiles, $r$, that can be cared for at a pet care business on a given day. If the business cares for $16$ reptiles on a given day, how many birds can it care for on this day?
MathAlgebra
In the linear function $h$, $h(0)=41$ and $h(1)=40$. Which equation defines $h)$?
MathAlgebra
$4x-9y=9y+5$<br/><br/>$hy=2+4x$<br/><br/>In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?
MathAlgebra
A shipment consists of 5-pound boxes and 10-pound boxes with a total weight of 220 pounds. There are 13 10-pound boxes in the shipment. How many 5-pound boxes are in the shipment?
MathAlgebra
An elementary school teacher is ordering $x$ workbooks and $y$ sets of flash cards for a math class. The teacher must order at least 20 items, but the total cost of the order must not be over $80. If the workbooks cost $3 each and the flash cards cost $4 per set, which of the following systems of inequalities models this situation?<br/><br/>$$\begin{array}{c}x+y\geq 20\\ \mbox{
MathAlgebra
$y=2x-3$<br/><br/>$3y=5x$<br/><br/>In the solution to the system of equations above, what is the value of $y$ ?
MathAlgebra
Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is 63 inches. The equation $3x+6y=63$ represents this situation, where $x$ is the number of sides of figure A and $y$ is the number of sides of figure B. Which statement is the best interpretation of 6 in this context?
MathAlgebra